ObjectiveIn a space-integrated ground information network, high-speed laser communication is a key technology for high-speed intersatellite data transmission. Owing to its high sensitivity and strong anti-interference capabilities, coherent laser communication has become an ideal choice for long-distance inter-satellite communication. However, traditional analog coherent demodulation technology requires a complex optical analog lock-in loop (OPLL) control system and places high demands on the performance of the local oscillator laser, which increases the complexity and cost of the system. To address these issues, a new carrier recovery method is explored in this study and combined with digital coherent demodulation technology to reduce the system complexity.MethodsA carrier recovery method for a coherent receiver based on semiconductor laser injection locking technology is investigated, and digital demodulation technology is used to realize signal reception. Manchester-coded binary phase-shift keying (BPSK) modulation technology is used at the transmitter to effectively retain the carrier component in the transmitted optical signal. The carrier component in the modulated light is filtered and amplified via semiconductor laser injection locking technology at the receiver, which is frequency-shifted by 160 MHz using an acousto-optic modulator before entering the 90° optical hybrid. The frequency shift reduces the effect of low-frequency beat noise on the system. A balanced photodetector with alternating current coupling is used to detect the mixed signal, and an oscilloscope is employed to collect the signal. The collected signal is processed offline to obtain a demodulated encoded signal.Results and DiscussionsExperiments are conducted on carrier recovery based on injection-locking technology at the receiver end. The impacts of different modulation depths, signal rates, and injection ratios on the performance of the local oscillator light after injection locking are analyzed. A decrease in the modulation rate and increases in the modulation depth and injection power can increase the proportion of the signal components contained in the recovered carrier spectrum, thereby reducing the quality of carrier recovery. In practical applications, selecting an appropriate modulation depth and injection power is beneficial for improving the carrier recovery quality. The demodulation of BPSK coherent communication signals at 5 Gbit/s is achieved, and the impact of various parameters is compared using the error vector magnitude (EVM). For signals with the baud rate of 5 GHz, the baseband signal is successfully demodulated at modulation depths of 0.33, 0.42, and 0.49. In these cases, increasing the modulation depth results in a gradual decrease in the EVM, indicating that a higher modulation depth is beneficial for reducing the EVM. However, for signals with the baud rate of 4 GHz, the EVM at the modulation depth of 0.42 is lower than that at 0.49. This is because in previous experiments, for signals with the modulation depth of 0.49 at 4 GHz, the depression near the carrier component is reduced, and the local oscillator light mixed with the signal components can not successfully demodulate the baseband signal. Therefore, the EVM can be used to measure the combined quality of the local oscillator light recovered by injection locking and the signal light. For signals at 3 GHz, owing to the small depression near the carrier component, the signal can not be demodulated even at the modulation depth of 0.33, and the change in the EVM is not significant at this time.ConclusionsThe proposed coherent communication system based on the semiconductor laser injection-locking carrier recovery technology combines the advantages of high-bandwidth optical locking and digital coherent tuning. A homodyne carrier signal can be recovered from the signal light using an optical method and effective mixed signals can be obtained using a distributed feedback (DFB) laser with a linewidth in the MHz range. Complex electronic feedback loops are not required, significantly reducing the system complexity. As a result, the demodulation of BPSK coherent communication signals at 5 Gbit/s without BER is achieved. This research can provide a simple and effective technical method for the carrier recovery of local oscillator light and is expected to be applied to high-precision coherent demodulation scenarios, including space coherent laser communication, lidar, and optical computing.

ObjectiveIn recent years, wireless optical communication (WOC) has received increasing attention. WOC is applicable to diverse applications, including those pertaining to terrestrial and underwater communications. Terrestrial WOC is similarly known as free-space optical (FSO) communication. Compared with the existing radio frequency (RF) communication system, FSO systems offer the advantages of large bandwidth, high data rate, reusable equipment and wavelength, high security, and anti-electromagnetic interference. WOC applied in an underwater environment is known as underwater wireless optical communication (UWOC). Compared with underwater acoustic and underwater RF communications, UWOC offers a higher transmission rate, lower link delay, and lower implementation cost. Whether on land or underwater, turbulence fading significantly affects the performance of WOC systems. Transmit-laser selection (TLS) has been proposed as an effective technique for mitigating fading. For the typical TLS under ideal assumptions, the laser source with the highest instantaneous received signal-to-noise ratio (SNR), i.e., the best laser source, is selected for signal transmission. However, a suboptimal or worse source may be selected owing to channel-estimation and/or feedback errors. Additionally, to accommodate deep-ocean explorations, land platforms may be required to transmit information to underwater platforms through reliable wireless links, which are typically vertical links. Therefore, in this study, we propose a mixed communication system (FSO-VUWOC) comprising FSO communication and vertical UWOC (VUWOC) with generalized transmit-laser selection (GTLS) to realize land and ocean integrated communication. The GTLS considers the selection of non-optimal light sources due to various errors in the actual scene.MethodsFirst, considering the atmospheric turbulence channel and the multilayer cascade vertical underwater turbulence channel based on a gamma-gamma distribution, as well as applying the Meijer G function and Gauss hypergeometric function, we derive the closed-form outage-probability expression for the FSO-VUWOC system with GTLS. Subsequently, by performing an asymptotic analysis of the outage probability under a high SNR, we obtain the diversity order of the system. Finally, the derivation results above are verified via numerical simulation.Results and DiscussionsThe outage-probability and diversity-order performances of the system were simulated and verified, and the performances of the FSO-VUWOC system with GTLS (where the number of light sources was set to five) and without GTLS (where the number of laser sources was one) were compared. First, we analyzed the outage probability of the FSO-VUWOC system under different VUWOC and FSO link distances (Figs. 3 and 4). As the link distance increases, the outage probability increases rapidly. Moreover, the outage-probability performance of the GTLS system under different VUWOC and FSO link distances is significantly better than that of the system without GTLS. Second, we investigated the effect of the selected laser-source index on the outage-probability performance (Fig. 5). Compared with the system without GTLS, the system with GTLS yields better outage-probability performance. For the system with GTLS, its outage-probability performance deteriorates as the selected laser-source index increases. For example, the system without GTLS requires an average SNR of 55.5 dB to achieve a target outage probability of 10-3. Meanwhile, the system with GTLS requires an average SNR of 22.5 dB to achieve a target outage probability of 10-3 under the ideal condition where the best laser source is selected. If the second-, third-, and fourth-best laser sources are selected owing to channel-estimation and/or feedback errors, then the required average SNR increases to 28.5 dB, 35.0 dB, and 44.0 dB, respectively. Third, we investigated the effect of the number of laser sources on the outage probability (Fig. 6). The outage probability decreases significantly as the number of laser sources increases. For example, when the number of laser sources is three and the second-best laser source is selected, to achieve a target outage probability of 10-3, the system with GTLS requires an average SNR of 40.0 dB. If the number of laser sources increases to four and five, then the required average SNR decreases to 33.5 dB and 28.5 dB, respectively. Therefore, increasing the number of laser sources within the scope of hardware cost effectively improves the performance of the FSO-VUWOC system. Finally, the effects of the VUWOC and FSO link distances, the laser-source index selected, and the number of laser sources on the diversity order were analyzed (Figs. 7, 8, and 9). The results show that the diversity order of the FSO-VUWOC system with GTLS depends on the number of laser sources in the two links, the laser-source index selected, and the minimum turbulence parameter.ConclusionsIn this study, a mixed communication system (FSO-VUWOC) comprising FSO communication and VUWOC with GTLS is proposed to realize integrated land and ocean communication. Under a multilayer cascaded gamma-gamma ocean turbulence channel and a gamma-gamma atmospheric turbulence channel, we derived the exact closed-form outage-probability expression based on the Meijer G function and the Gauss hypergeometric function. Subsequently, we analyzed the diversity-order expression under a high SNR based on the outage-probability results. Finally, the simulation results are presented to verify the accuracy of our derivation, and the effects of the link distances of the VUWOC and FSO communication, the laser-source index selected, and the number of laser sources on the outage probability and diversity order were analyzed. The analysis and simulation results show that the FSO-VUWOC system with GTLS outperforms the FSO-VUWOC system without GTLS in terms of outage probability. Additionally, increasing the link distance and utilizing non-optimal laser sources deteriorates the outage probability and diversity order. By contrast, increasing the number of laser sources significantly improves the system performance.

ObjectiveFiber-optic grating hydrophones have a wide range of marine applications, such as underwater target detection, marine resource exploration, and ocean background noise measurements. As fiber grating hydrophones usually use weak reflectivity gratings with a reflectance below 5%, they can reach an order of magnitude comparable to that of Rayleigh scattering after multiple grating reflections and are therefore more sensitive to Rayleigh parasitic interference of the leading fiber. In this study, a leading fiber Rayleigh parasitic interference model is developed for fiber-grating hydrophone arrays, and the concept of highly sensitive Rayleigh scattering segments is proposed. Theoretical analyses show that the number and spatial distribution of high-sensitivity Rayleigh scattering segments in the leading fiber are related to the length of the leading fiber and the interrogation frequency and that the length of each high-sensitivity Rayleigh scattering segment is the same as the length of the fiber between the two gratings. The high-sensitivity Rayleigh scattering segments introduce interference in the leading fiber between them and the fiber grating hydrophone units. The parasitic interference introduced into the hydrophone phase demodulation results in an increase in the system background noise. The experiments reveal that Rayleigh parasitic interference in the leading fiber can cause a step change in the background noise level of the fiber grating hydrophone array, with a maximum difference in the response amplitude of approximately 10 dB before and after the jump. After the jump, the amplitude of the noise signal increases more slowly as the number of highly sensitive Rayleigh scattering segments increases, with the amplitude of the noise signal increasing by approximately 5 dB for each additional highly sensitive Rayleigh scattering segment without causing nonlinear effects, subject to the constraint that the distribution probability is no less than 90%.MethodsIn this study, a model of leading fiber Rayleigh parasitic interference is developed for fiber grating hydrophone arrays, and the precise spatial distribution of highly sensitive Rayleigh scattering segments is calculated. The various states of the leading fiber noise at different locations caused by parasitic interference are observed experimentally, and the stepwise growth patterns of the leading fiber background noise level caused by Rayleigh parasitic interference are summarized.Results and DiscussionsTheoretical derivations show that parasitic interference necessitates the demodulation of the superposition results of the main interference and multiple parasitic interferences at the dry end. When there is leading-fiber interference between the highly sensitive Rayleigh scattering segment and the primitive sensing grating, the parasitic interference increases the impact of the leading-fiber noise. In experiments, the presence of a highly sensitive Rayleigh scattering segment is the root cause of the step change. The same leading fiber interference before and after the first highly sensitive Rayleigh scattering point results in a step change in the background noise amplitude, and a large fluctuation is obtained in the background noise amplitude when demodulating after the jump. After the jump point, the noise signal amplitude of the fiber-grating hydrophone array increases slowly as the number of highly sensitive Rayleigh scattering segments increase.ConclusionsParasitic interference in leading fiber Rayleigh scattering, causes a step change in the background noise level of the fiber grating hydrophone array, with a maximum difference of approximately 10 dB in the response amplitude of the noise signal at the jump. After the jump point, the noise signal amplitude increases more slowly as the number of highly sensitive Rayleigh scattering segments increases. The noise signal amplitude increases by approximately 3 dB for each additional highly sensitive Rayleigh scattering segment without causing nonlinear effects, subject to a distribution probability of no less than 90%.

ObjectiveDue to the dependence of the dynamic interference phenomenon on the AC-Stark energy shift and atomic stabilization mechanism under extreme ultraviolet (XUV) fields, a higher XUV light intensity is necessary to observe the dynamic interference phenomenon of hydrogen atoms. This poses a challenge for experimental verification. Accordingly, in this work, infrared (IR) auxiliary pulses were introduced to modulate the ionized electrons, providing a solid theoretical basis for the experimental verification of dynamic interference phenomena.MethodsNumerical solutions of the three-dimensional time-dependent Schr?dinger equation (TDSE) were employed to compute the photoelectron energy spectrum of ground-state hydrogen atoms exposed to IR + XUV two-color laser pulses. The radial part of the wave function was discretized using the finite element discrete variable method (FEDVR), while the split-Lanczos method was utilized for the wave function propagation. By varying the pulse delay, IR pulse intensity, and full width at half maximum (FWHM) of the XUV pulse, we comprehensively analyzed their impact on the multi-peak structure observed in the photoelectron energy spectrum. Utilizing the strong field approximation (SFA) and saddle point approximation (SPA), we successfully replicated the multi-peak structure observed in the TDSE calculations and examined the underlying physical mechanisms responsible for this intricate phenomenon.Results and DiscussionsInitially, for a short period of the infrared pulse, the dynamic interference phenomenon was most pronounced when the peak position of the XUV pulse coincided with the extreme position of the infrared pulse. This caused a shift in the peak position and variation in the number of peaks in the photoelectron energy spectrum (Fig. 2). Furthermore, an increase in the intensity of the infrared laser light led to a transition from a single peak to a multi-peak structure in the photoelectron energy spectrum, with simultaneous shifts in the peak positions and troughs. Consequently, a higher intensity of the infrared pulse accentuates the dynamic interference phenomenon (Fig. 3). Additionally, as the FWHM of the XUV pulse increased, the amplitude and number of peaks expanded, while the positions of the peaks and troughs remained constant, highlighting the close relationship between the dynamic interference phenomenon and the duration of the XUV pulse (Fig. 4). Our calculations using SPA reveal that in scenarios where both the infrared laser pulse and XUV pulse comprise a few periods, dynamic interference arose from the interference between the emitted electron wave packets at the rising and falling edges (Fig. 5). The subsequent analysis focused on the variation in the photoelectron energy spectrum with the FWHM of the XUV pulse in multicycle infrared pulse settings. We discovered that as the FWHM of the XUV pulse increased, the photoelectron energy spectrum transformed from broad bands to finer stripes, indicating that the spectral structure is a result of the mutual interference of all the emitted electron wave packets, rather than just the interference in the few-cycle scenario (Fig. 6). Moreover, our calculations demonstrate that with a small FWHM of the XUV pulse, the peak spacing on the photoelectron spectrum exceeds the infrared photon energy. However, as the FWHM of the XUV pulse increased, additional small peaks emerged on the photoelectron spectrum, with their peak components aligning with the energy of a single infrared photon (Fig. 7).ConclusionsThe time multi-slit interference of ground-state hydrogen atoms exposed to linearly polarized IR and XUV two-color fields was investigated and our calculations reveal that the most pronounced dynamic interference occurs when the peak position of the XUV pulse coincides with the extreme position of the infrared pulse. In the XUV laser field, the AC-Stark energy shift induced by a strong laser causes a significant phase difference in the emitted electron wave packet, giving rise to the observed dynamic interference phenomenon. Furthermore, we found that the dynamic interference phenomenon in the XUV laser field is intricately linked to the atomic stabilization mechanism, necessitating sufficient laser light intensity in a single XUV laser. Regarding infrared-assisted dynamic interference, our model calculations demonstrate a close relationship between the dynamic interference in the two-color field and the infrared pulse vector potential, which modulates the ionized electrons to generate the required phase difference between the interfering electron wave packets. Comparing our theoretical findings with the experimental conditions of XUV pulse ground-state hydrogen atom ionization, the required XUV laser peak intensity is significantly reduced under a two-color field. This reduction has the potential to streamline the experimental laser requirements. Furthermore, our analysis of the temporal multi-slit interference structure, which emerges as the lengths of the infrared and XUV pulses increase, provides valuable insights beyond the temporal double-slit interference of the rising and falling edges of the pulse. In conclusion, our calculations offer substantial theoretical guidance for experimentally verifying the existence of dynamic interference phenomena, paving the way for the further exploration and validation of these intriguing quantum dynamics.

ObjectiveO-band lasers find widespread use in fiber optic communication, medical treatments, measurements, and sensing. For example, in fiber optic communication, they serve as light sources for short-distance communications, such as those between data centers, and for detecting optical signals in fiber optic communication links. In medical applications, the main components of biological tissues—such as water, oxygenated hemoglobin, and melanin—exhibit minimal transmission losses at a wavelength of 1.3 μm, making O-band lasers suitable for laser surgeries and imaging. The specific wavelength range renders O-band lasers indispensable tools in these applications. However, achieving a narrow linewidth output in semiconductor lasers can result in high costs. Additionally, the challenge of fusion splicing fluoride-based fibers with conventional silica fibers significantly restricts the widespread adoption of praseodymium-doped fiber lasers.Benefiting from its broadband emission characteristics in the near-infrared spectral region, bismuth (Bi) is considered a highly promising gain medium for manufacturing optical devices. A series of lasers based on bismuth-doped fibers has rapidly developed. Although some O-band bismuth-doped fiber lasers have been reported internationally, these lasers typically require pump powers in the range of several watts to achieve high slope efficiencies, while also exhibiting relatively low signal-to-noise ratios. Therefore, further optimization of O-band bismuth-doped fiber laser performance is necessary.MethodWe initially examine the emission characteristics of the bismuth-doped fiber. Our measurements reveal that the emission spans the entire O-band, ranging from 1260 nm to 1360 nm, with notable amplified spontaneous emission (ASE) power levels between 1300 nm and 1350 nm. Taking into account losses from optical devices and fibers, we designate 1310 nm as the operational wavelength for the bismuth-doped fiber laser. Constructed with a ring cavity structure, the bismuth-doped fiber laser comprises a total cavity length of approximately 125 m. This length includes 120- m-long bismuth-doped fiber (BDF) and a 5-m-long fiber connecting other optical components inside the cavity through all-fiber fusion splicing. A semiconductor laser, boasting a maximum output power of 550 mW at a wavelength of 1240 nm, acts as the pump source. This laser is linked to the pump end of wavelength division multiplexers (WDM1 and WDM2) for 1240 nm and 1310 nm. To safeguard the pump, isolators (isolator 1 and isolator 2) are strategically positioned between the pump source and WDM. For wavelength selection, a circulator and a fiber Bragg grating (FBG) are employed. To ensure unidirectional transmission within the cavity, the isolator 3 and the circulator are employed, with the isolators mitigating optical component reflection effects. Laser output is facilitated through a coupler. Upon constructing the bismuth-doped fiber laser (BDFL), we examine the impact of varying coupling ratios on laser output and determine the optimal ratio. Additionally, we compare the effects of different pumping methods on laser output.Results and DiscussionsWe explore the impact of varying output coupling ratios on laser output power by employing couplers set at 10∶90, 20∶80, and 50∶50, with results depicted in Fig. 3. Across different output coupling ratios, once the input pump power surpasses the laser threshold power, the laser output demonstrates a linear increase with pump power. For a given pump input power, the laser output power steadily rises with the output coupling ratio escalating from 10∶90, through 20∶80, reaching 50∶50 and 80∶20, and marginally decreases as the coupling ratio peaks at 90∶10. At a pump output power of 1000 mW, the maximum output power registers at 127.3 mW (80∶20 coupling ratio), boasting a maximum slope efficiency of 14.44% (80∶20 coupling ratio). Figure 4 illustrates the fluctuation of output power concerning output coupling ratio across various pump input powers. At lower input powers, the optimal output coupling ratio falls between 70∶30 and 80∶20, progressively increasing to approximately 80∶20 as the input power escalates. Figure 5 showcases the output spectrum of the BDFL, revealing a peak wavelength of 1310.22 nm, an OSNR exceeding 60 dB, a 3 dB linewidth of around 0.036 nm, output power stability within ±0.06 dB, and wavelength stability below 0.01 nm.After identifying the optimal coupling ratio as 80∶20, we proceed to compare the effects of different pumping methods on laser output. Figure 8 displays the laser output spectra under forward and backward pumping configurations, both showcasing a central wavelength of 1310.22 nm and consistently maintained OSNRs around 60 dB. The 3 dB linewidths under forward and backward pumping configurations measure approximately 0.032 nm and 0.04 nm, respectively. In Fig. 9, we depict the variation of output power with input power under three pumping configurations. The laser thresholds for all three pumping configurations hover around 240 mW. Once the input power surpasses the threshold, the output power linearly increases with input power. Considering the pump coupling efficiency, backward pumping maximizes both output power and slope efficiency, peaking at 136.4 mW and 18.92%, respectively, at an input power of 1000 mW.ConclusionsIn summary, we have constructed a bismuth-doped fiber laser utilizing a ring cavity structure and explored its output under varying coupling ratios. Our findings reveal that at the optimal coupling ratio of 80∶20, the laser outputs a central wavelength of 1310.22 nm, an OSNR exceeding 60 dB, a slope efficiency of 14.44%, and achieves a maximum output power of 127.3 mW at an input power of 1000 mW. Furthermore, we conducte a comparison of different pumping methods on laser output. Among the three methods, forward pumping yields the lowest laser output power and slope efficiency, while backward pumping produces the highest, reaching 136.4 mW and 18.92%, respectively. In conclusion, we have realized a bismuth-doped fiber laser with high OSNR and relatively high efficiency, boasting a simple structure. This laser offers valuable insights for the advancement of O-band fiber lasers.

ObjectiveThe Hermite-Gauss eigensolution of confocal or spherical cavities significantly affects lasers, and the transmission laws of these cavities have been extensively investigated. When multiple transverse-mode oscillations are present, lasers are partially spatially coherent. In 1969, Arnuaud proposed a range of degenerate cavities that can yield a low-coherence laser output. In 2013, Nixon et al. experimentally demonstrated that a 4F degenerate cavity can generate low-coherence lasers, which can effectively reduce the scattering contrast while simultaneously controlling the diaphragm size in the intracavity spectrum to achieve a spatially coherent optical-field output of the 4F degenerate cavity. In 2015, Chriki et al. demonstrated that altering the geometry of the diaphragm in the spectral plane of the cavity can alter the shape of the spatial-coherence function of the optical field output. These studies showed that a 4F degenerate cavity can generate low-spatial-coherence lasers with adjustable spatial coherence to achieve scatter suppression during imaging. Most studies analyzed the 4F degenerate cavity’s output field using a multitransverse mode laser. This approximation explains the spatial properties of the 4F degenerate cavity’s output field. However, some conflicts exist, such as the shape of the beam output from the 4F degenerate cavity changing during transmission, whereas the shape of the Hermite-Gauss beam remains constant during linear transmission. Therefore, the transverse light-field distribution in a 4F degenerate cavity must be re-analyzed.MethodsA 4F degenerate cavity laser is constructed with circular diaphragms of varying sizes on its spectral plane. The near and far fields are measured in different cases using a charge-coupled device (CCD) and spatial coherence distributions are measured at various locations within the optical field. This study analyze the transverse and longitudinal modes in a 4F degenerate cavity using the Fresnel-Kirchhoff diffraction equation. Finally, the light intensity and coherence distribution of the 4F degenerate cavity’s light field are compared with those of the Schell model.Results and DiscussionsThe near- and far-field light intensity distributions of the output light field of the 4F degenerate laser cavity in the three cases are shown in Figs. 2(a)?(f). Near-field distributions were compared when diaphragms of different sizes were inserted into the spectral plane. The edges of the near field become clearer as the small hole in the spectral plane enlarges, thus resulting in a more homogeneous overall light intensity. However, a strong spot appears at the center of the light spot owing to residual reflection. When a diaphragm with a small diameter is present in the spectrum, the shape of the far-field light matches that of the diaphragm. When no diaphragm is present in the spectral plane of the cavity, the near-field light intensity of the 4F degenerate cavity’s light field shows an approximately flat-top distribution [Fig. 2(g)], whereas the far-field light intensity shows a conical distribution, as shown in Fig. 2(h). The shape of the optical field changes significantly, thus demonstrating that the Hermite-Gauss mode is not an inherent mode of the 4F degenerate cavity. In the ideal case, when no diaphragm is present in the cavity, the resonance of the 4F degenerate cavity (Fig. 3) is formed between point A on M1 and point A' on M2. No correlation is indicated among the different points. When a diaphragm is inserted into the spectral plane of the cavity, the electric field at point A' is altered. Meanwhile, the shape and width of the electric field change with the diaphragm shape. This results in a certain shape and width of the electric field at point A', which is noncoherently superimposed on the light field of the surrounding points. Consequently, spatial coherence is created in the light field. The spatial-coherence function of the partially coherent light in the Schell model is shown in Fig. 5. This is consistent with the experimental results, where the spatial coherence initially decreases to zero, followed by a discernible difference between the two.ConclusionsIn this study, the transverse and longitudinal modes of a 4F degenerate cavity were investigated using the Fresnel-Kirchhoff diffraction formula and the formation of laser coherence. The results indicate that the intrinsic mode of the 4F degenerate cavity is not the Hermite-Gauss mode. Additionally, the intracavity spectral plane diaphragm affects not only the spatial coherence of the 4F degenerate cavity’s output light field but also the width of its longitudinal mode. The near- and far-field shapes of the output optical field differ significantly in the absence of an intracavity spectral-plane diaphragm. This inconsistency with the transmission law of the Hermite-Gauss mode confirms the theoretical analysis of the transverse mode of the 4F degenerate cavity. The spatial-coherence distribution was measured after circular diaphragms of varying sizes were inserted into the spectral plane of the cavity. The results show that the spatial coherence of the output optical field decreases as the size of the spectral-plane diaphragm increases. The spatial coherence of the output light field of the 4F degenerate cavity was compared with the partially coherent light of the Schell model. The results show that the output light field of the 4F degenerate cavity with a circular diaphragm inserted in the spectral plane differs slightly from that of the Schell model but can be approximated using the Schell model.

ObjectivePrecise pulse-time shaping is a key technology for operation control and precise physics experiments in high-power laser facilities. Inertial confinement fusion (ICF) laser drivers require that the front-end system generates arbitrary shaping optical pulses to satisfy the time waveform requirements of target physics experiments. To reduce the number of arbitrary waveform generators (AWGs) in a system, multiple shaping pulses are typically generated in the form of pulse trains. However, in the process of time shaping, the earlier pulses affect later pulses. This effect is amplified during the subsequent transmission of the pulse, and this reduces pulse quality. In the pulse generation systems of ICF laser drivers, this effect is detrimental to the precise pulse time shaping of the injected laser, reducing the energy utilization rate of the laser pulse. This significantly affects aspects such as the energy transmission and focusing of the laser, target ablation, plasma formation, and fusion reaction efficiency. The front-end systems of high-power laser facilities generate multiple pulses by utilizing time division multiplexing technology. Therefore, the objective of this study is to solve the crosstalk problem between multiple pulses and further improve the time shaping characteristics of laser pulses.MethodsFigure 2 shows the front-end system structure of a multi-output high-power laser facilities based on time division multiplexing. First, the continuous-wave laser required by the system was generated and then modulated using an acousto-optic modulator (AOM) into a microsecond pulsed laser. The output is amplified using a fiber amplifier to increase the energy of the pulsed laser. Subsequently, a four-way fiber beam splitter was used to divide the pulsed laser into four outputs, which then entered their respective electro-optical modulators. Simultaneously, a sequence pulse containing four sub-pulses was generated by a high-precision AWG; this pulse can be independently and arbitrarily shaped. Subsequently, after being selected as a single pulse by the radio frequency (RF) switch, it was divided into four channels, enters their respective RF amplifiers, and acts on each electro-optical modulator. Finally, an arbitrary shaping output of the four optical pulses was realized.Results and DiscussionsThe signal-to-noise ratio (SNR) of the output pulse of the proposed system is larger, indicating that the output optical pulse has enhanced anti-interference properties (Table 1). In addition, the rising time and shortest pulse of the optical pulse were within 100 ps; this indicates that the response speed of the RF switch is within a reasonable range, and its high-frequency characteristics barely affect the output pulse quality. An AWG is then used to output a wide pulse trains of 25 ns. The SNR of the output optical pulse in the comparison scheme is 36.86 dB, whereas that of the output optical pulse under the system design scheme is 42.76 dB. Furthermore, an AWG is utilized to output a large contrast shaping pulse, which is selected as a single pulse by the RF switch; the contrast ratio of the output optical pulse is 601∶1.ConclusionsA multi-output system with independent shaping capability, based on time division multiplexing technology, is proposed to meet the requirements of multi-channel signal generation in the front-end system of high-power laser facilities and address the problem of crosstalk between pulses. Notably, the system entails the use of RF switches. It can select the electrical pulse train directly from the output of the AWG; then, each channel passes through the RF amplifier and electro-optical modulator separately. Thus, the arbitrary shaping output of multiple optical pulses can be realized. Based on the single channel of the AWG, the scheme can realize four optical pulse outputs with an independent arbitrary time shaping ability. It can achieve an output with a rising edge of 55 ps, a continuously adjustable pulse width ranging from 67 ps to 25 ns, and a pulse contrast higher than 500∶1. The system can effectively improve the SNR of the output optical pulse and avoid interference between signals; this is conducive to the improvement of the time shaping ability of the laser pulse. Thus, this study provides a technical scheme for the output of several arbitrary time shaping pulses in high-power laser facilities.

ObjectiveOwing to the rapid development of new energy technologies such as lithium batteries, photovoltaics, and display semiconductors, higher requirements have been imposed for the average power, pulse energy, and pulse duration of lasers. Pulsed lasers, with average power levels in kilowatts and pulse energies in millijoules, have been researched and developed extensively. Currently, pulsed lasers are implemented via two different implementations: direct oscillator power amplification and main oscillator power amplification (MOPA). The former directly increases the power and energy of the laser oscillator, and as the power and energy increase continuously, an increase in the risk of intracavity damage limits the further power scaling of the laser. The latter rod- or slab-amplification technology affects the beam quality of the laser as the power increases. In this study, a laser system combining disk regeneration pre-amplification technology and disk multipass amplification technology is proposed, with the laser pulse output exhibiting a pulse duration of less than 6.8 ps, an average output power of 1102 W, an optical efficiency of 50.1%, a beam quality factor M2 of less than 1.4, and a power stability of 1.29% obtained at a repetition rate of 1 MHz. Additionally, under a repetition rate of 100 kHz, the maximum output pulse energy is 8.23 mJ and the M2 is less than 1.5.MethodsIn this study, MOPA technology based on the domestic 30 MHz fiber seed is adopted. The seed repetition rate is decreased to 1 MHz and the fiber seed is injected into the disk-regeneration gain module, which results in a laser output of 151 W. Subsequently, the fiber seed is injected into the disk multipass gain module for main amplification, and an average power output of 1102 W is realized. The output pulse duration is less than 6.8 ps, the optical efficiency is 50.1%, the M2 is less than 1.4, and the power stability is 1.29%. The output power is 823 W and the maximum pulse energy is 8.23 mJ under a repetition rate of 100 kHz.Results and DiscussionsThe kilowatt laser system obtains a picosecond pulsed laser with a power level of 151 W and a repetition rate of 1 MHz through regenerative pre-amplification. Additionally, it injects the fiber seed into the main amplifier for amplification. The disk crystal diameter used in the main amplifier is 19 mm, the radius of curvature is 50 m, the thickness is 100 μm, and the doped mass fraction is 10%; additionally, the disk crystal is water cooled at 25 °C. The pump source is a fiber-coupled semiconductor laser with a center wavelength of 969 nm and a maximum output power of 3000 W. The distance between the disk and mirror is approximately 0.5 m. The reflective mirrors of the amplifier are plane mirrors, and the laser is self-imaged through the disk crystal thermal lens to form a self-reproduction mode.ConclusionsIn this study, using a domestically produced disk gain module, a seed source, and a pump gain module, a picosecond pulse laser output with a M2 better than 1.4, a maximum power of 1102 W, a pulse duration of 6.8 ps, and an optical-to-optical conversion efficiency of 50.1% is obtained at a repetition rate of 1 MHz. Meanwhile, a laser pulse output with M2 better than 1.5, an average power of 823 W, and a maximum pulse energy of 8.23 mJ is obtained at a repetition rate of 100 kHz.

ObjectiveMagnetic-responsive robots can achieve remote, rapid, and flexible motion under magnetic field actuation. However, existing magnetic robots are limited by fixed magnetic domains and soft matrices, which restricts their deformability and load-bearing capacity, thus limiting their widespread application in complex environments. In this study, a shape memory composite material is designed with reprogrammable magnetic domains. Through the synergistic action of laser and magnetic fields, the shape memory polymer film is patterned and re-encoded, resulting in various shape-reconfigurable and stiffness-variable opto-magnetic responsive robots. As a result, the limitations of traditional magnetic robots are overcome in terms of limited deformability and weak load-bearing capacity. Moreover, this work provides a new approach for developing adaptive robots capable of performing complex tasks.MethodsThe robot is constructed from reprogrammable shape memory composite (RM-SMC), integrating shape memory polymer (SMP) and embedded magnetic microcapsules. These microcapsules, composed of phase-change polymer ethyl vinyl acetate (EVA) encapsulating NdFeB magnetic particles, enable internal magnetic domain reprogramming within the RM-SMC film. Initially, the two-dimensional RM-SMC structure is magnetized in a 1.2 T magnetic field, aligning the magnetic domains along the film thickness direction. Upon near-infrared laser irradiation, the encapsulated NdFeB@EVA microcapsules rapidly absorb heat, causing the EVA to melt at its phase change temperature (90 ℃). This allows the magnetic particles to reorient along the external programming magnetic field (Bp), enabling internal magnetic particle re-encoding. Via subsequent global heating with low-power near-infrared laser, the RM-SMC temperature is increased to its glass transition temperature (Tg), transitioning it to an elastomer. Due to opposite magnetic domains in adjacent areas, the material deforms into a three-dimensional shape under a vertical actuation magnetic field (Ba), with folding deformation occurring along the boundary of these areas. Upon cooling below Tg, the material locks into this three-dimensional shape, maintaining stiffness even after magnetic field removal.Results and DiscussionsWe prepare NdFeB@EVA magnetic microcapsules using a phase separation method and incorporate them into SMP to form the RM-SMC film (Fig. 1). Additionally, we obtain two-dimensional patterns under different designs via laser cutting (Fig. 2). Testing shows that the glass transition temperature of RM-SMC is 77 ℃. Under the combined action of near-infrared laser and external magnetic field, we can encode the anisotropy of magnetic domains within the film. Moreover, the film demonstrates excellent reprogramming and stable deformation capabilities over 100 repeated tests (Figs. 3 and 4). Based on the reprogrammability of RM-SMC films, different torque and torsion directions can be generated by encoding the magnetic domain direction at different positions of the films in response to the driving magnetic field, enabling rapid and reversible transitions between planar and three-dimensional complex structures (Fig. 5). Additionally, this study utilizes the reconstructive deformation and shape-maintenance capabilities of RM-SMC films to prepare magnetic-responsive micro-robots capable of switching among different configurations. The rolling robot can move on flat ground and slopes under the driving of an 80 mT rotating magnetic field, recover its two-dimensional shape as a bridge through heating, as well as withstand a 5 g object (Fig. 6). Further, the cargo robot can transport a 1 g object directionally, while the helical robot can spiral drive in water under the driving of a rotating magnetic field (Figs. 7 and 8).ConclusionsIn this work, reprogramming technology and shape memory polymers are altered to develop a new reprogrammable magnetic shape memory composite material, consisting of NdFeB@EVA magnetic microcapsules and SMP. Through synergistic control of a near-infrared laser and an external magnetic field, insitu encoding of magnetic domains is achieved in a two-dimensional structure. This allows the structure to exhibit various complex three-dimensional shapes, maintaining form without energy consumption, and demonstrating high load-bearing capacity and variable stiffness. This method enables the cost-effective preparation of magnetic-responsive robots capable of freely switching among different configurations and motion modes. Moreover, this advancement not only offers increased flexibility in robot control, but also promises a more convenient and efficient robot operation experience in practical applications. Thus, the developed novel reprogrammable magnetic shape memory robot injects new vitality into the field of robotics and provides strong technical support for achieving higher-level robot control and applications.

ObjectiveThe detection of the surface morphology of glow discharge sputtering craters is of great significance in scientific research, engineering applications, and product quality control. The depth, size, and shape of the sputtering crater reflect the conditions of the glow discharge and sputtering rate. The surface morphology of the glow discharge sputter craters is also crucial for the layer-by-layer analysis of the plated samples. High-precision instruments, such as white light interferometers, are available in the market to detect the surface morphology of glow discharge sputtering craters and reconstruct the crater profile. However, such instruments are expensive, which increases the economic burden on small- and medium-sized research institutes and enterprises. Compared with white light interferometers and other high-precision detection instruments, optical coherence chromatography (OCT) instruments are cheaper, and their detection accuracy can meet the application requirements of glow discharge sputtering crater topography measurement. Thus, the cost performance is higher. Moreover, the application of the SD-OCT technology in the field of glow discharge analysis has not yet been reported. Therefore, this study adopts OCT technology combined with glow discharge analysis technology and proposes a surface topography detection method based on spectral domain optical coherence chromatography (SD-OCT) for large sputtering craters of glow discharges.MethodsGlow-discharge, large-sized sputtering crater surface topography is detected via SD-OCT. An SD-OCT system is used to scan the large sputtering crater produced by glow discharge to obtain complete images of sputtering craters. By extracting the original spectral signal data from the image, filtering, denoising, and peaking processing are performed to eliminate the noise interference and accurately locate the spectral peak. The original data are stitched together to recover the complete sputter crater depth information. After the peak position data are obtained, the transverse and longitudinal coordinates of the crater depth profile are determined to reconstruct and correct the glow-discharge large-size sputtering crater profile to obtain more accurate and reliable surface topography characteristics of the sputtering crater. The method is designed to accurately measure the surface topography of large-sized sputtering craters and to provide strong technical support for scientific research and industrial applications in related fields.Results and DiscussionsFigure 9 shows the comparison of 2D contour maps measured by two methods for different sputtering craters with an average depth of 10?50 μm. Figures 9(a1)?(d1) show the sputtering crater profiles reconstructed using the SD-OCT detection method, and Figs. 9 (a2)?(d2) show the sputtering crater profiles measured using the white light interferometer. Figure 9 shows that at the same sampling location, the crater depth profiles obtained using the two methods are consistent. The SD-OCT detection method proposed in this study can accurately reflect the cut surface topography of the glow-discharge sputtering crater of a sample and reconstruct the sputtering crater depth profile. As shown in Fig. 10, the crater depth and sputtering rate measured by the glow-discharge sputtering rate detection method based on SD-OCT are consistent with the measured results of the white light interferometer, and the sputtering rate curve has a good correlation. The relative errors of the two measurement methods are within 3.97%. Moreover, the depth of a large-size glow-discharge sputtering crater is usually tens of microns to hundreds of microns. Hence, this method can meet the measurement requirements of the depth of glow-discharge sputtering craters above 1.88 μm, and it can realize the reliable detection of the glow-discharge sputtering rate. The use of SD-OCT for the standard sample sputtering rate correction and quantitative conversion of the elemental mass fraction can provide accurate qualitative judgments as well as important quantitative information. Figure 12 shows that zinc is the main element on the surface of a galvanized sheet, and the mass fraction of zinc gradually decreases with sputtering time, whereas the mass fraction of iron gradually increases with time. When the sputtering time is 200?300 s, an interface layer of zinc and iron forms in the galvanized sheet.ConclusionsThrough the combination of glow-discharge spectroscopy and SD-OCT, the main work of this study is as follows. A detection method for glow-discharge large-size sputtering crater surface topography based on SD-OCT is studied. The contour reconstruction of a large-size glow-discharge sputtering crater (diameter of 15?40 mm) and the accurate detection of the glow-discharge sputtering rate are realized through peak searching, denoising, and stitching the original data of an SD-OCT-scanned sputtering crater image. The glow-discharge sputtering rate data obtained using this method are compared with those obtained using a white light interferometer. The maximum relative error is 3.97%, thereby verifying the reliability of this method. In addition, the SD-OCT low-discharge large-sized sputtering crater surface topography detection method is used to complete the layer-by-layer analysis of galvanized plates along the depth direction, thereby realizing the application of this method in the analysis of galvanized plates and providing a new and effective solution for the detection of glow-discharge sputtering crater topography and sputtering rates.

ObjectiveLong focal lenses, which are a crucial optical element, are utilized extensively in high-power laser devices, including National Inertial Fusion and Shenguang (SG) laser devices in China. Thousands of large-aperture spherical and aspherical lenses have been employed in these expansive laser systems. These lenses have apertures larger than 400 mm×400 mm and focal lengths exceeding 10 m. They are primarily utilized in spatial filters to filter high-frequency components within the Fourier spectrum. This process facilitates image transmission and enhances the beam quality of the system, thereby augmenting its output power. The accurate measurement of the focal lengths of these lenses and the precise positioning of the focus directly affect the installation of the laser system and its spatial filtering effect. As the quality of high-power laser device beams improves and their load-capacity requirements increase, the demand for transmission using long-focal-length lenses increases. Consequently, the focal length and transmission wavefront distribution of long-focus lenses must be regulated strictly. These two parameters are pivotal indicators and indispensable for achieving optimal performance. Currently, the focal length and the two transmission wavefront indices of long-focus lenses are measured independently. This process presents challenges such as difficulty in accurately determining the focal length and high demands on the measurement system during parameter evaluation.MethodsThis study introduces a comprehensive measurement method for large-aperture, long-focal-length lenses based on phase recovery. The proposed method integrates a combined lens-measurement technique, thus significantly reducing the length of the optical path required for measurement, as compared with the ptychographic iterative engine (PIE) phase-measurement technology. This integration enhances the resistance of the system to environmental interference. The proposed method enhances the focusing precision of lenses with extended focal lengths by reconstructing the wavefront distribution of the examined lens. Subsequently, it infers the light-intensity distribution at various distances to determine the focus position. Using a digital benchmark, the wavefront error is derived from the deviation of the lens wavefront under measurement. Subsequently, this error is compared with respect to the standard spherical wavefront. By incorporating background cursor calibration, the optical component requirements of the system are reduced significantly.Results and DiscussionsIn this study, we develop a reversible measurement device for lenses with long focal lengths, as illustrated in Fig. 2. Subsequently, the feasibility of this method is validated using a lens with a focal length of 16 m. Two sets of diffraction spots are obtained meticulously in a double-exposure format. Subsequently, an intricate amplitude reconstruction is performed using the ePIE algorithm. The morphology of the light-spot distribution on any plane proximal to the focal plane is successfully determined. As shown in Fig. 5, the relative error of the PV value between the measured wavefront error of the reference lens and the interferometer measurement is 2.6%. This indicates the favorable precision of the PIE wavefront measurement. We comprehensively analyze the effects of individual positional and phase-measurement errors associated with the PIE on both focal-length and wavefront measurements. The findings indicate that the positional error predominantly affects the focal length, with the error transfer coefficient of the moving distance exhibiting the greatest magnitude. The most significant effect of the PIE measurement error is reflected in the wavefront measurement, as shown in Table 1. In the future, we plan to enhance the precision of our measurements based on the findings from our error analysis.ConclusionsThis study introduces a comprehensive measurement method for large-aperture, long-focal-length lenses based on phase recovery. This method allows for the simultaneous measurement of multiple parameters, including the focal length and wavefront, thereby eliminating the requirement for multiple measuring devices. The viability of the proposed method is substantiated by its application using a lens with a focal length of 16 m. This approach effectively addresses the challenges associated with focus determination and the stringent requirements for measurement systems involving long-focal-length lenses. Additionally, it offers several advantages, including a straightforward and flexible measurement process, minimal space requirements, and robust resistance to environmental interference.

ObjectiveExtreme ultraviolet (EUV) lithography is the most advanced lithographic technology. However, during exposure processes, even small defects in masks can cause significant changes in the critical dimensions (CD) of wafers. Therefore, detecting and repairing defects of a certain size in masks is crucial. As the chip technology nodes decreases, detecting and repairing mask defects become increasingly challenging. EUV mask defects are classified into amplitude and phase defects, based on their positions and effects on reflection fields. Amplitude defects are typically located at the top or absorption layers of multilayer films. They significantly reduced the overall reflectivity of the multilayer films to EUV light at the defect sites, directly affecting the amplitude of the reflected field. However, most phase defects are found in the substrate or multilayer film, deforming of the multilayer film and affecting the phase of the reflected light. Although the total reflectivity of the multilayer film for EUV light remains high, the phase shift of the reflected field has a small impact on the amplitude. Compared with amplitude defects, phase defects are more challenging to detect and almost impossible to repair. Owing to the difficulty in detecting phase defects through optical and electron beam inspections, a photochemical inspection is necessary for EUV masks. Samsung developed an extreme ultraviolet lithography mask defect inspection system (EMDRS) that uses higher harmonics to generate EUV light sources capable of detecting both amplitude and phase defects. However, imaging processes resulted in blurred scanned images and reduced resolution of the defect detection system, owing to the sizes and shapes of light spots. Hence, a binary image deblurring algorithm is proposed in this study to improve the resolution of EUV mask defect detection systems.MethodsThe EMDRS employs a zone plate to focus coherent EUV light onto the mask surface, creating an illumination spot of 82 nm. The reflection intensity within the receiving angle of the detector is measured. The focused EUV light irradiates the mask surface at an incident angle of 6°, and factors like 3D shadowing help narrow line widths after scanning. However, for simulation purposes, this study assumes the EUV mask as a two-dimensional surface. The sample image primarily consists of space/line images. A transfer function f(x,y) is established to represent the reflection field of the sample. Currently, EUV mask patterns can be simplified into two cases: reflection or non-reflection of EUV light. Hence, the function f(x,y) is a binary distribution under ideal conditions. For calculation convenience, amplitude defects are assumed to completely block the reflection of the EUV light by the multilayer film, thereby reducing the amplitude of the reflected field to zero. In the case of phase defects, the effect of the multilayer film on EUV light reflectivity is assumed to be negligible, affecting only the phase while maintaining a constant amplitude at the defect site. The sample image is scanned point by point using a Gaussian spot with a beam waist diameter of 81 nm and scanning step of 1 nm. Then, the scanned image of the sample is subjected to deblurring. Broken line, pinhole, and phase defects were used as examples, and it was observed that employing a deblurring algorithm to process the scanned images considerably enhanced the resolution of the EUV mask defect detection system.Results and DiscussionsIn the simulation of the broken-line defects (Fig. 3), a line with a 4 nm segment missing in the middle was introduced into the space/line image with a period of 120 nm to emulate a real broken-line defect in the mask. Deblurring of the scanned image caused the defects to become clearer, making them easier to identify, and the contrast of the defect signal was improved by 52.03%. Pinhole defects showed the most significant enhancement (Fig. 4). A square pinhole defect measuring 10 nm×10 nm was added to each sample pattern. After deblurring, the defect signal in the image was enhanced significantly, resulting in a 64.89% improvement. Broken-line and pinhole defects are amplitude defects, whereas phase defects are more challenging to detect. In the simulation of a phase defect (Fig. 5), a phase defect with dimensions of 50 nm×50 nm was designed with an amplitude of 1 and Gaussian-shaped phase changes. The phase at the center was π/2. Deblurring of the scanned image amplified the intensity of the defect signal, improving the contrast of the defect signal by 44.96%. We analyzed the defect signals under different system noises (Fig. 6) and found that the signal contrast of the three defects increased by 58.75%, 62.17%, and 44.48% by the addition of Gaussian noise with an average amplitude of 1%. The enhancement effect of the deblurring algorithm on the defect signals became weak when the system noise amplitude increased to 4%.ConclusionsThis study applied a text image deblurring method based on L0 regularization intensity and gradient prior to the resolution improving of a EUV mask defect detection system. A blind deblurring method that leverages prior knowledge and iterative optimization was used to obtain a clear image. The deblurring process could be completed solely by inputting a blurred image, without requiring additional information, such as faculae. Simulation research on broken line, pinhole, and phase defects demonstrated that deblurring scanned images result in clearer defect images, with improvements of 52.03%, 64.89%, and 44.96% in signal contrast, respectively. This enhancement significantly improves the detection capabilities of mask defect detection systems, thereby satisfying the demand of smaller lithography process nodes.

ObjectiveLaser-induced periodic surface structure (LIPSS) is a type of periodic micro-nanostructure formed on solid surfaces irradiated by laser light. The generation of periodic micro-nano-structures can improve material surface properties such as optical properties, surface hydrophilicity/hydrophobicity, biomedical properties, and friction properties. Furthermore, this can lead to a wide range of applications in the field of material surface functionalization. Prefabricated structures on material surfaces have been shown to modulate the electromagnetic field energy distribution on material surfaces, which in turn affects the formation of LIPSS on material surfaces. In extant studies, only the influence of prefabricated structures on the electromagnetic field distribution has been discussed. However, there is a significant difference between the thermal effects produced by laser pulses with pulse widths in the order of nanoseconds and picoseconds on the surface of the material. Hence, the aim of this study is to investigate the mechanism of nanosecond- and picosecond laser-induced periodic structure formation assisted by the prefabricated structure on the surface of single-crystalline germanium.MethodsFirst, the difference in surface temperature changes between picosecond and nanosecond laser irradiation of prefabricated structures is investigated using a two-temperature model. During laser irradiation of the target, the maximum temperature in the center of the groove surface will be higher than the melting point of the single-crystal germanium. This suggests the presence of a molten layer on the surface of the target in the process of laser irradiation. The semiconductor material is instantaneously transformed into a metallic state, which permits the excitation of surface plasma excitations. An interference model of surface plasmon excitations (SPP) is then used to explain the formation mechanism of LIPSS in semiconductor materials. By numerically solving Maxwell equations, the electromagnetic field energy distribution, i.e., the distribution of surface plasmonic excitons, is obtained when the laser irradiates the prefabricated grating.Results and DiscussionsAt energy densities in the range of 0.12?0.14 J/cm2, the bottom of the grating groove under nanosecond laser irradiation changes from none to the melting region as the laser energy density increases, while the picosecond laser melting region does not change significantly (Fig. 3). As the period of the prefabricated grating increases, the electric field intensity distribution changes with the groove width. The enhancement is larger when the groove width is equal to or close to an odd multiple of the SPP half-wavelength, whereas the enhancement is significantly weaker when the groove width is equal to or close to an even multiple of the SPP half-wavelength (Fig. 7). As the laser energy density increases, the fusion region on the surface of the prefabricated grating expands, resulting in a stronger electric field at the bottom of the prefabricated grating groove (Fig. 10). Different prefabricated grating heights result in varying electric field distributions at the bottom of the groove. For grating heights less than 100 nm, the periodic electric field distribution at the groove bottom is affected. Conversely, for heights exceeding 200 nm, the energy entering the bottom of the groove reduces, leading to a narrower range of periodic electric field distribution (Fig. 13). Additionally, the electric field intensity at the bottom of the groove decreases as the grating duty cycle increases beyond 0.5. When the duty cycle is less than 0.5, the electric field intensity decreases with an increase in duty cycle if the groove width is small. However, it increases if the groove width is large (Fig. 14). Incident laser wavelengths of 355 nm and 1030 nm create periodic electric field distributions on the grating ridges with periods of approximately 348 nm and 976 nm, respectively (Fig. 16). Furthermore, thermal effect analysis of different pulse widths shows that the parameter space where nanosecond lasers can produce LIPSS is narrower than that for picosecond lasers (Fig. 17).ConclusionsIn this study, the effects of different prefabricated structure parameters, laser thermal effects, and varying wavelengths of incident laser are examined on the electromagnetic field energy distribution on the surface of single-crystal germanium. The larger the fusion region on the prefabricated grating, the stronger the electric field intensity at the bottom of the groove, facilitating the formation of periodic structures on the material surface. At lower heights of the prefabricated grating, the electric field intensity at the bottom of the grating groove is influenced by scattering at the junctions of the grating sidewalls with the bottom and ridge. This interference disrupts the distribution of the periodic electric field at the bottom of the grating groove, reducing the probability of forming periodic structures there. Conversely, at higher grating heights, less energy reaches the bottom of the groove, making it difficult to generate periodic structures. A grating duty cycle in the range of 0.4 to 0.6 is typically more effective. For both ultraviolet and infrared incident lasers, the prefabricated surface produces a near-wavelength periodic electric field distribution, which can result in the formation of near-wavelength periodic structures on the surface of the material. The findings of this study may provide useful references for generating laser-induced periodic structures on semiconductor surfaces using prefabricated structures.

ObjectiveMost optical sensors obtain a large number of observations in a short time. Image data obtained by image sensors have many feature points, and point cloud data obtained by laser scanners contain a large number of three-dimensional coordinates. In image matching and point cloud fitting, weighted total least squares (WTLS) consider the errors in the observation vector and coefficient matrix, displaying higher accuracy and better statistical properties than least squares (LS). However, WTLS has not been widely used in image registration and point cloud fitting because the computational efficiency is too low to satisfy real-time requirements when the adjustment model contains a large number of observations.MethodsOne of the main reasons for the decreased efficiency in WTLS is the inversion of matrices with large dimensions. The complexity of a matrix inversion operation is proportional to the cube of its dimension. For example, if the matrix dimension increases 10 times, its time complexity increases 1000 times. To reduce the calculation time, we propose a solution based on the grouping strategy, named sequential total least squares (STLS), which is inspired by the sequential solution of the Gauss-Helmert model that has a calculation time less than that of the batch solution. The proposed algorithm groups all observations into many independent parts, recursively updating parameters, as new observations are added to existing estimated results. STLS consists of an outer iteration and inner recursion. The matrix dimension involved in the operation process is much smaller than that of the existing WTLS algorithm, thereby overcoming the efficiency issues of the existing WTLS method.Results and DiscussionsSimulated and measured data were used to test the efficiency of the proposed algorithm, comparing it to several existing WTLS algorithms, including traditional WTLS, structured total least squares (TLS), and the alternative method in partial errors-in-variables models. In the following three experiments, STLS divided all observations into 20 groups on average. First, in the simulated image registration experiment involving 1000 identical points, the root mean-squared error (RMSE) of LS was larger than that of WTLS (Table 1), which illustrated the necessity of considering the errors in the source image. STLS obtained the same RMSE as the existing WTLS methods because there was no difference between their mathematical models and objective functions. The average running time of STLS was only 0.176 s, whereas the existing WTLS method required at least 10.078 s (Table 2), which corresponded to a time ratio of 1.75%. With an increase in the number of identical points in the registration, the running time of STLS was still much smaller than that of the structured TLS (Fig. 2). Second, STLS was more accurate than LS with less bias when using wall images for affine transformation (Fig. 3), and the running time was less than 2% of the existing WLTS schemes (Table 3). Third, when fitting the plane containing 3120 wall point clouds in the WHU-TLS database (Fig. 4), STLS only took 0.381 s, whereas the existing WTLS algorithm required at least 22.317 s (Table 4), which corresponded to an increase in efficiency by more than 50 times.ConclusionsIn this era of big data, the computational efficiency of an algorithm is as important as its numerical performance. The observation values obtained by optical sensors are very large, imposing a heavy computational burden on the existing WTLS algorithm. By grouping observations, the dimension of the matrix is reduced significantly during the operation, as proven in the three experiments demonstrating the obvious efficiency improvement provided by STLS. Further research can still be done on the proposed algorithm. In the presence of outliers, the estimation results of this algorithm are seriously distorted, necessitating an increase in robustness. Numerous observation values are obtained by optical sensors. Therefore, the next step is to extend this algorithm to other models that contain a large number of observations, such as point cloud registration.

ObjectiveLaser-induced breakdown spectroscopy (LIBS) has the advantages of in situ, real-time, rapid detection, no sample pretreatment, and great potential for elemental analysis. However, when LIBS is used to detect liquid samples, water splashing, surface ripples, and plasma quenching reduce the detection sensitivity and accuracy, which limits the performance and development of LIBS in liquid detection. Conventional enhancement techniques for LIBS liquid detection require complicated experimental setups or sample preparation processes, which negates the advantages of LIBS. Previous studies have shown that the dispersed phase of wheat starch mixed with liquid samples can form a high-viscosity colloidal state, which effectively reduces the effects of water splashing and surface ripples and significantly improves detection sensitivity. The sample preparation process with this method is simple and only requires 30 s, which meets the requirements of LIBS liquid detection. To improve the detection performance of the dispersed-phase enhancement technique, the research problems related to enhancement characteristics, enhancement mechanism, and quantitative analysis techniques are analyzed and discussed in this study.MethodsWe first test the LIBS enhancement of various dispersed phases and investigate the enhancement characteristics of the dispersed phases through experiments to investigate the effects of dispersed phase mass fractions and atmospheric drying on the LIBS intensity. The enhancement mechanism of the dispersed phase is analyzed by diagnosing the plasma electron temperature and electron density of the liquid sample and by considering two samples with different dispersed phase mass fractions using the Saha?Boltzmann and Stark broadening methods. The local thermodynamic equilibrium state of the plasma is evaluated according to the McWhirter criterion to ensure the validity of the calculations of the plasma electron temperature. Then, an Al I 396.15 nm calibration curve is constructed to evaluate the detection performance of the dispersed-phase LIBS. The effect of drying time on the detection performance of dispersed-phase LIBS is also analyzed. Finally, a partial least squares regression model is constructed for the quantitative analysis of the dispersed-phase LIBS, and the effect of the generalized spectral method on the quantitative analysis of the partial least squares regression is investigated.Results and DiscussionsThe results show that the spectral enhancement of the dispersed phase is more effective as the mass fraction of the dispersed phase increases under the premise of uniform mixing (Fig. 5). In addition, under atmospheric drying, moisture volatilization can enhance the spectral intensity. The structure of the high mass fraction dispersed-phase sample is more conducive to moisture volatilization, which leads to a rapid improvement in the spectral intensity of the detected element (Fig. 6). The time evolutions of the plasma electron temperature and electron density for the liquid sample and dispersed-phase samples with high and low mass fractions are consistent, which indicates that the electron temperature and electron density cannot explain the spectral enhancement of the dispersed phase, and the enhancement mechanism of the dispersed phase is related to the increase in the ablation of the detected elements. Compared to that of direct liquid detection, the detection sensitivity is improved by 6.03 times after the liquid is prepared as a high mass fraction dispersed-phase sample using wheat starch, and it increases to 17.26 times after 1 h atmospheric drying (Table 2). Unlike when constructing the partial least squares regression model with only spectral data, this study reduces the prediction error of the partial least squares regression model by utilizing the generalized spectral method with drying time as an additional feature dimension, with the average relative error and predicted root-mean-square error of the model reduced by 23.95% and 14.10%, respectively.ConclusionsA simple and fast method for detecting metals in liquids using the dispersed-phase LIBS technique is presented in this study. The enhancement effect of dispersed-phase LIBS is investigated and determined to be related to the mass fraction of the dispersed phase. On the premise of uniform mixing, the structure of a mixed sample with a high dispersed-phase mass fraction is more stable, and the enhancement effect is better. In addition, the LIBS enhancement effect of the high mass fraction dispersed-phase sample can be further improved by atmospheric drying. The enhancement mechanism of dispersed-phase LIBS is analyzed by calculating the plasma electron temperature and electron density, and the results show that the enhancement mechanism is not related to the electron temperature and electron density but rather to the increase in the ablation of the detected element. Al as the target element in the liquid and wheat starch as the dispersed phase are used to evaluate the detection performance of dispersed-phase LIBS. Compared to that of direct liquid detection, the detection sensitivity is improved by 6.03 times using dispersed-phase LIBS and increases to 17.26 times after 1 h drying. A partial least squares regression model is constructed for the quantitative analysis of the dispersed-phase LIBS. Using the generalized spectral method, the drying time is introduced for partial least squares regression modeling as an additional feature dimension, and the average relative error and predicted root-mean-square error of the model are reduced by 23.95% and 14.10%, respectively.

ObjectiveTunable diode laser absorption spectroscopy (TDLAS) tomography is an important optical non-invasive combustion-detection technique that enables the imaging of critical flow-field parameters in the combustion field. The existing network-based TDLAS temperature tomographic algorithms are typically constructed with a fixed spatial resolution. If the target resolution is changed, then the network structure should be adjusted and the network retrained accordingly. Images reconstructed by these separate networks do not present a clear spatial correspondence, which renders it inconvenient to combine features in images with different spatial resolutions for combustion diagnosis. Hence, multiresolution spatial discretization modeling and multiresolution temperature-distribution reconstruction were introduced into TDLAS tomography. Based on reconstruction at two spatial resolutions as an example, a dual-domain multiscale feature-based multiresolution temperature tomographic network (DMFMMnet) was constructed.MethodsThe proposed DMFMMnet extracts and adaptively merges multiscale spatial features in the TDLAS measurement and image domains to reconstruct low-resolution and high-resolution temperature images with spatial correspondence. First, it extracts multiscale spatial correlation features from TDLAS measurements and reconstructs the overall profile of the temperature distribution rapidly at a low resolution using a low-resolution reconstruction block (LBlock). Second, it performs multiscale feature extraction and adaptive feature merging on the reconstructed low-resolution temperature image using an image-domain multiscale feature extraction and merging block (IMBlock). Third, it combines multiscale spatial features extracted in the TDLAS measurement and image domains to reconstruct a high-resolution temperature image, which presents detailed features of the temperature distribution via feature enhancement and a high-resolution reconstruction block (HBlock).Results and DiscussionsTo examine the performance of the proposed DMFMMnet, it was compared with two existing network-based temperature tomographic algorithms. One is based on a convolutional neural network (H-CNN) and the other is based on a hierarchical vision Transformer and multiscale feature merging (HVTMFnet). These two networks were adjusted and trained for low-resolution reconstruction (with suffix -LR) and high-resolution reconstruction (with suffix -HR), separately. Furthermore, to examine the super-resolution reconstruction performance of IMBlock and HBlock in DMFMMnet, they were compared with the classical bicubic linear interpolation (bicubic) and two super-resolution networks, i.e., super-resolution using deep convolutional networks (SRCNNs) and Transformer for single-image super-resolution (ESRT). The resulting high-resolution reconstruction networks combined with LBlock are referred to as LBlock+Bicubic, LBlock+SRCNN, and LBlock+ESRT. In the simulations, the dataset was generated using a fire dynamics simulator (FDS). Tests were performed in the signal-to-noise ratio (SNR) range of 25 dB‒45 dB. The peak signal-to-noise ratio (PSNR) and structural similarity (SSIM) were used to measure the reconstruction quality. The simulation results show that, for low-resolution reconstruction, the average PSNR values obtained by DMFMMnet are higher than those obtained by H-CNN-LR and HVTMFnet-LR at any SNR (Table 2). For high-resolution reconstruction, the average PSNR values obtained by DMFMMnet are higher than those obtained by H-CNN-HR, HVTMFnet-HR, LBlock+Bicubic, LBlock+SRCNN, and LBlock+ESRT in the SNR range of 30 dB‒45 dB (Table 3). In terms of subjective quality, the low-resolution temperature image reconstructed by DMFMMnet reflects the overall contour of the temperature distribution more clearly than those reconstructed by H-CNN-LR and HVTMFnet-LR (Fig. 7), whereas the high-resolution temperature image reconstructed by DMFMMnet shows more accurate and detailed information than those reconstructed by H-CNN-HR, HVTMFnet-HR, LBlock+Bicubic, LBlock+SRCNN, and LBlock+ESRT (Fig. 8). In the multiresolution temperature reconstruction experiments based on actual TDLAS measurements, the flame contour in the low-resolution temperature image reconstructed by DMFMMnet is more consistent with that of an annular burner, as compared with those reconstructed by H-CNN-LR and HVTMFnet-LR. The high-resolution temperature image reconstructed by DMFMMnet shows more explicit thermal-diffusion characteristics in the combustion field than those reconstructed by H-CNN-HR, HVTMFnet-HR, LBlock+Bicubic, LBlock+SRCNN, and LBlock+ESRT (Fig. 9). Additionally, compared with the peak temperature values retrieved by the other algorithms, the peak temperature values retrieved by DMFMMnet are more similar to the highest temperature values measured by the thermocouples.ConclusionsMultiresolution spatial discretization modeling and multiresolution temperature reconstruction were introduced into TDLAS tomography. A multiresolution temperature tomography network (DMFMMnet) based on dual-domain multiscale feature merging was constructed. This network reconstructs temperature images at two spatial resolutions with different computing costs, which can balance between imaging time and resolution. The simulation results show that the average PSNR values of the low-resolution temperature images reconstructed by DMFMMnet are 24.95%‒32.79% and 0.66%‒3.28% higher than those reconstructed by H-CNN-LR and HVTMFnet-LR, respectively, in the SNR range of 25 dB‒40 dB. The average PSNR values of the high-resolution temperature images reconstructed by DMFMMnet are 32.63%‒38.67%, 2.34%‒6.18%, 3.18%‒9.24%, 3.22%‒6.48%, and 0.29%‒1.18% higher than those reconstructed by H-CNN-HR, HVTMFnet-HR, LBlock+Bicubic, LBlock+SRCNN, and LBlock+ESRT, respectively, in the SNR range of 30 dB‒45 dB. The flame contours in the low-resolution temperature images and the detailed features in the high-resolution temperature images reconstructed by DMFMMnet are more similar to the ground-truth phantoms, as compared with the algorithms investigated. Experiments based on actual measurements obtained from the TDLAS sensor show that the temperature images reconstructed by DMFMMnet can more accurately reflect the actual heat conduction in the combustion field, as compared with the algorithms investigated.

ObjectiveWith the rapid development of traditional Chinese medicine (TCM) and increasing attention paid to dietary therapy and health preservation, the market for Chinese patent medicines, medicinal materials, and medicated diets is expanding rapidly. Consequently, there is a growing demand for TCM raw materials, with concerns about the quality and heavy metal contamination of TCM materials attracting widespread attention. Although China has intensified its supervision of heavy metal content in commonly sold TCM raw materials and TCM decoction pieces, issues related to excessive heavy metal content remain, especially in rhizome and root TCM materials, which are more prone to adsorbing heavy metal elements from the environment. Therefore, real-time accurate monitoring of heavy metal concentration, to abide by TCM material market regulations, is of great significance in mitigating pollution risk and enhancing the safety of TCM materials.Laser-induced breakdown spectroscopy (LIBS), which is capable of real-time, rapid, and simultaneous detection of multiple components, has emerged as a promising metal detection technology and is considered one of the most promising analytical methods in the field of TCM material quality monitoring. However, in practice, regional differences and inherent genetic characteristics of TCM material matrix samples make it difficult to obtain comparable or similar matrix samples for calibration, complicating the accurate quantification of the elements to be tested in TCM materials and placing higher demands on the processing of LIBS spectral data. In recent years, deep learning methods, with an ability for powerful representation learning and discovering intrinsic patterns in high-dimensional data, have become a hotspot in LIBS quantitative analysis research. The premise of successful deep-learning methods is model training based on a large amount of labeled data. However, in LIBS spectral detection and quantitative analysis of TCM materials, the complexity of the TCM material matrix complicates the collection and accurate calibration of a large amount of labeled data. Consequently, the amount of data required for quantitative analysis model training is insufficient. In contrast, obtaining unlabeled LIBS spectral data from TCM materials is relatively easy. Thus, methods to improve the performance of deep learning using unlabeled data are urgently required.In TCM, white peony root (WPR) is a common medicinal and dietary rhizome that can be contaminated with heavy metals during its growth, processing, storage, and sale. This study proposes a semi-supervised deep learning framework for predicting the content of two heavy metal elements, Pb and Cd, based on WPR LIBS data. The framework includes a sequence modeling module based on multilayer multichannel causal convolution, which transforms one-dimensional discrete LIBS data into a two-dimensional dense embedding matrix. Additionally, a feature extraction module based on multiresolution one-dimensional sequential convolution is designed to extract semantic features for Pb and Cd content prediction. An autoencoder module that guides the network to learn the topological information from the original data is used for reconstructing the LIBS data, thereby enabling the full utilization of the unlabeled data. This framework addresses the problem of poor prediction performance of heavy metals content in white peony caused by the high cost of obtaining labeled data in practical applications.MethodsThis study proposes a semi-supervised sequential learning framework for predicting the Pb and Cd contents in WPR based on LIBS data. A parameter-shared dual-branch network is employed to model labeled and unlabeled white peony LIBS data in a unified network using end-to-end training. First, discrete LIBS data were transformed into dense embedding matrices through multilayer multichannel causal convolutions for sequential modeling. Then, a multiresolution one-dimensional temporal convolution module was utilized to extract semantic feature representations for labeled and unlabeled WPR LIBS data from the dense embedding matrices. The parameters of both the multilayer multichannel causal convolutions and the multiresolution one-dimensional temporal convolution module were shared among the branches of the labeled and unlabeled data. Subsequently, the semantic feature representations of the labeled white peony LIBS data were fed into a prediction module composed of a deep neural network (DNN) for regression prediction of Pb and Cd contents. To fully utilize the unlabeled data in guiding the training of the feature extraction module, both labeled and unlabeled features were reconstructed using an autoencoder module to capture the original discrete LIBS spectral data features.Results and DiscussionsThis study compares and studies the impact of different optimizers. The proposed multiresolution one-dimensional sequential convolution was combined with the Adam optimizer, and the quantitative analysis results of four commonly used deep learning sequence data feature extraction models, including DNN, long short-term memory (LSTM), bidirectional LSTM (BiLSTM), and Transformer, were studied regarding their effectiveness as semi-supervised learning strategies. The results indicate that compared with other commonly used sequence data feature extraction methods, the proposed one-dimensional multiresolution sequential convolution combined with the Adam optimizer converges faster, achieves a loss convergence value closer to 0, and exhibits smaller prediction errors on the test set (Fig.6, Table 2). After incorporating semi-supervised learning with unlabeled data, the average relative errors in predicting the Pb and Cd contents decreased to 4.12% and 3.32% (Table 3), respectively, on the test set, demonstrating good spectral reproducibility with an average relative error of 0.22% between the original and reconstructed spectral data (Fig.11). In comparative studies, the integration of LIBS technology with semi-supervised learning, effectively alleviated the dependency of deep learning models on labeled data during training, reducing the cost and challenges in heavy metal detection applications of white peony LIBS, thereby providing a more effective method for the quantitative analysis of complex elemental compositions in traditional Chinese medicinal materials.ConclusionsIn response to the challenge of high acquisition costs in practical applications for labeled LIBS data in predicting heavy metal content in WPR, a semi-supervised sequential learning method was proposed to predict the Pb and Cd contents of WPR using a complex matrix based on LIBS data. The algorithm consists of a parameter-shared dual-branch deep-learning network that models both labeled and unlabeled LIBS data in a unified framework for end-to-end training. Discrete LIBS data were transformed into dense embedding vector matrices using multilayer, multichannel causal convolutions. By combining the local features of LIBS spectral characteristic lines with sample element content-related features, multiresolution one-dimensional sequential convolutions were employed to extract local contextual semantic features from LIBS spectral dense embedding vector matrices. The regression module for Pb and Cd contents was trained using only the labeled data. To fully utilize the knowledge embedded in the unlabeled data and enhance the feature extraction capability of the model, an autoencoder was utilized to reconstruct the discrete LIBS data of all WPR samples. In experimental comparisons, the impact of different optimizers on model training was investigated using only labeled data, providing quantitative analysis results using multiresolution one-dimensional temporal convolution which was compared with four other sequence data feature extraction structures: DNN, LSTM, BiLSTM, and Transformer. The results indicate that the proposed multiresolution one-dimensional temporal convolution model combined with the Adam optimizer converges faster and achieves smaller prediction errors on the test set (Pb: 5.54%, Cd: 5.16%). After incorporating unlabeled data for semi-supervised learning, the average relative errors for the Pb and Cd predictions in the test set decreased to 4.12% and 3.32%, respectively.

ObjectiveTerahertz (THz) waveguides are essential functional devices for the long-distance propagation and interconnection of THz waves; thus, they play an increasingly important role in THz applications, i.e., in wireless communications, medical imaging, and security inspections. To achieve high transmission efficiency and integration, various THz waveguides using different guiding mechanisms have been developed, including dielectric, photonic crystal, anti-resonance, and surface plasmonic waveguides. Recently, graphene-based hybrid plasmonic THz waveguides have attracted significant attention because of their tunable and flexible transmission. However, the inherent optical properties of two-dimensional graphene, such as the low absorption of incident waves and weak electromagnetic response, pose challenges in the design of high-performance waveguides. Emerging three-dimensional Dirac semimetals (3D DSMs) have high carrier mobilities and tunable energy band characteristics comparable to those of graphene, while overcoming the above-mentioned inherent shortcomings of graphene. In this study, we propose a tunable broadband hybrid plasmonic THz waveguide based on a 3D DSM dielectric ridge structure. The transmission characteristics are systematically simulated using the finite element method, and the effects of the structural parameters and Fermi energy of the DSM are analyzed.MethodsA THz waveguide structure is designed in this study based on a 3D DSM hybrid plasmonic mechanism, which comprises a DSM layer, SiO2 layer, and Si layer from top to bottom (Fig. 1). The corresponding thicknesses are optimized to be 4, 2, and 10 μm, respectively. First, the complex permittivity of the 3D DSM at different Fermi levels in the THz regime is calculated based on the Kubo formula and two-band model (Fig. 2). Finite element method-based simulations are performed to reveal the quantitative influences of the structural geometric parameters and DSM Fermi energy on the THz transmission characteristics, including the real part of the effective mode index, normalized mode area, propagation length, figure of merit, and propagation mode.Results and DiscussionsThe simulated results show that the effective mode refractive index decreases and the normalized mode area increases with increasing dielectric gap height. Owing to the enhanced low-loss dielectric mode characteristics, the propagation length and figure of merit (FOM) increase with the gap height, and the 3D DSM plasmonic properties weaken as the frequency increases (Fig. 3). It can be observed from the mode-field diagram that the loss of the waveguide gradually decreases as the gap height increases, and most of the modes in the waveguide can be restricted from propagating at the tip of the rhombic Si region (Fig. 4). As the size of the rhombic Si medium increases, more modes propagate into the high-refractive-index Si medium, and the role of the dielectric mode increases. As the mixed mode confined by the 3D DSM layer is weakened, the effective mode refractive index and mode area increase, and the dielectric mode gradually becomes dominant in the mixed mode, causing an increase in the propagation length (Fig. 5). Finally, the influence of the Fermi level on the propagation characteristics is analyzed. As the Fermi level changes from 0.01 eV to 0.1 eV, the propagation length of the waveguide can be greatly tuned from 3.33×102 μm to 1.72×104 μm with the maximum modulation depth of the propagation length up to 98.06%, and a modulation depth of more than 90% in the broad frequency range of 0.5?2.0 THz can be achieved (Fig. 7).ConclusionsA tunable broadband THz waveguide based on a 3D DSM is demonstrated through numerical simulations. The transmission characteristics in response to the dielectric gap height, medium size, and Fermi level of 3D DSM are investigated. The simulated results show that as the gap height increases, the real parts of the effective mode refractive index, normalized mode area, and propagation length increase. The side length of the rhombus medium also has a certain impact on the propagation characteristics. Specifically, the real parts of the effective mode refractive index, mode area, and propagation length increase with the side length of the rhombus medium. The Fermi level has a significant effect on the propagation characteristics. As the Fermi level of the 3D DSM increases, the real part of the effective mode refractive index decreases, whereas the mode area and propagation length increase. As the Fermi level increases from 0.01 eV to 0.10 eV, the propagation length of the waveguide increases from 3.33×102 μm to 1.72×104 μm, and the modulation depth of the propagation length exceeds 90% in the broadband working frequency of 0.5?2.0 THz. These findings provide an important reference for understanding the propagation mechanism of 3D DSM hybrid plasmonic waveguides, hence they are good candidates for various applications in tunable and broadband THz waveguides and modulators.

ObjectiveTerahertz waves are underdeveloped waves between microwaves and infrared waves that exhibit abundant spectral resources and have received wide attention in many fields, including medical detection, security imaging, and communication. Polarization is an important characteristic of electromagnetic waves, and a metasurface can flexibly control the propagation of light waves using its subwavelength structural unit, thus rendering it suitable for the design of lightweight and compact polarization converters. Research on terahertz polarization converters based on metasurfaces is expected to promote the development of terahertz wave bands. However, to realize practical applications of terahertz systems in the future, improving metasurface-based terahertz polarization converters is necessary. First, a simple structure can be designed to enable polarization conversion, thereby enhancing its advantages in the design process and practical applications. Second, the operating bandwidth of the polarization-conversion device can be expanded, and a wide bandwidth operating range can improve the spectrum utilization of terahertz systems. Furthermore, the polarization-conversion effect must be enhanced to ensure stable optical performance. In this study, the proposed terahertz-line polarization-conversion metasurface based on a double split-ring resonator features a simple design process, few structural parameters, high optimization efficiency, and a wide operating bandwidth. Moreover, through the structural optimization and design of notches on a double-split-ring resonator, the structure can achieve efficient polarization conversion over the entire operating frequency band. The metasurface structure designed in this study may promote the application of terahertz technology in fields such as wireless communication, liquid-crystal displays, and medical detection.MethodsThe structure proposed in this study comprises a long, metal, rectangular bar connected to a double split-ring resonator, with two symmetrical notches on the double split-ring resonator, which improves the overall performance of the polarization converter. Numerical simulations were performed to evaluate the effectiveness of the metasurface. The simulations were conducted using CST Microwave Studio, where a frequency-domain solver was used to calculate the metasurface reflection coefficients. Subsequently, these coefficients were processed to extract the evaluation parameters for the cross-polarization converter. The resonance modes at each resonant point were identified based on the distribution of surface currents, and the underlying physical mechanism facilitating cross-polarization conversion was analyzed based on the interactions of electric and magnetic dipoles corresponding to their respective dipole moments.Results and DiscussionsThe metasurface structure proposed in this study can achieve excellent polarization conversion over a wide bandwidth operating range. In the range of 2.55?7.61 THz, Ryy is lower than 0.3 and Rxy exceeds 0.9. Based on these two parameters, the polarization conversion ratio (PCR), which reflects the polarization-conversion performance, exceeds 0.9, thus indicating the excellent polarization-conversion capability of the metasurface over the entire operating band. The polarization-converting metasurface has an operating bandwidth of 5.06 THz, with a relative bandwidth of 99.4%, thus demonstrating its excellent broadband performance (Fig. 2). The ability to realize polarization conversion in such a wide operating band is endowed by the two notches on the double-split-ring resonator. A comparison between notched and non-notched metasurface structures shows that the former exhibits a prominent resonance-enhancement effect at 6.31 THz and 7.49 THz, which is endowed by the notched structure on the entire polarization-converting metasurface, whose PCR exceeds 0.9 in the entire operating band (Fig. 3). The physical mechanisms facilitating polarization conversion were elucidated by analyzing the distribution of surface currents at various resonance points. The enhancement effect of the notched structure on cross-polarization conversion was analyzed via comparative analysis, where the dimensional parameter x1 is shown to significantly affect polarization conversion. This effect was further clarified by decomposing the electric-field components (Figs. 4, 5, and 7). The effect of the metasurface structural parameters on polarization conversion was analyzed via parameter scanning. This paper clarifies the effects of structural parameters t2, w1, x1, and y1 on the PCR and reveals the geometric factors affecting the polarization-conversion capability of the metasurface (Fig. 6).ConclusionsIn this study, a terahertz polarization-converting metasurface with a simple structure and a wide bandwidth operating range is proposed based on a double split-ring resonator. Results of CST simulation show that the polarization converter encompasses the frequency band of 2.55?7.61 THz, has a PCR exceeding 0.9 in an entire frequency band with a bandwidth of 5.06 THz, and exhibits a relative bandwidth of 99.4%. The mechanism by which the notched structure affects the cross-polarization conversion effect was derived by decomposing the electric-field components. Additionally, the physical mechanism of the broadband cross-polarization conversion effect was derived by analyzing the surface current. The proposed structure is applicable to terahertz wireless communications, liquid-crystal displays, and security imaging.