Recently the limitations of single-mode fiber (SMF) in terms of transmission capacity cannot be ignored. With the increasing demand for data volume, mode-division-multiplexing (MDM) technology has attracted increasing attention due to the tremendous data-carrying capacity [1,2]. High-order modes (HOMs) with unique spatial intensity and polarization distribution properties, such as cylindrical vector beams (CVBs) and optical vortex beams (OVBs), show rich prospects in many important applications including material processing [3], super-resolution microscopes [4], optical tweezers [5], optical sensing [6], and nanoparticle manipulation [7].

Different methods to generate CVBs both in free space and optical fibers have been suggested, such as Q-plates [8], spiral phase plates [9], spatial light modulators [10], subwavelength gratings [11], mode-selective couplers (MSCs) [12], acoustically induced fiber gratings (AIFGs) [13], and long-period fiber gratings (LPFGs) [14]. Generally, all-fiber devices have the advantages of low insertion loss and better compatibility with optical fiber communication links. Compared with other all-fiber mode conversion components, AIFGs have unique properties of polarization-dependent coupling, dynamic switching, and wavelength tunability. Therefore, many studies of implementing dynamically switchable CVBs and OVBs based on AIFGs have been constantly proposed. For example, Kim et al. demonstrated an acousto-optic mode converter based on a tapered optical fiber to efficiently generate orbital angular momentum (OAM) states in 2018, where the fiber diameter is tapered to 20 μm, which can greatly increase the effective refractive index difference between the HE21 mode and other cylindrical vector (CV) modes [15]. In 2020, Zhang et al. presented that the generation of CVBs can be achieved in a solid-core ring fiber by using an AIFG, and the 3-dB bandwidth of three resonance peaks is 0.16 nm [16]. In 2021, Ramachandran et al. proposed an all-fiber acousto-optic generator with wide spectral tunability based on a special vortex fiber, achieving the generation of OAM modes over 230 nm in the visible and near-IR wavelength ranges [17]. So far, AIFGs capable of mode conversion of CVBs can be successfully manufactured by different fibers and methods; the remaining important issue is to improve the conversion bandwidth of AIFGs.

Meanwhile, the AIFGs are also commonly used in mode-locked (ML) fiber lasers. In 2020, Huang et al. built an acoustically tunable ultrafast laser with single-wall carbon nanotubes as a saturable absorber, and the broadband tunability was provided by an acousto-optic structure fabricated with an etched SMF [18]. In 2024, Xu et al. constructed a frequency shift feedback ML fiber laser based on the frequency shift characteristics of the AIFG, and dynamic mode switching between LP11a and LP11b modes was achieved [19]. Although many all-fiber ML lasers can provide stable pulse trains, it poses a challenge to achieve femtosecond pulses due to the narrow conversion bandwidth of the mode converters. Recently, a number of studies on LPFGs based on the dispersion turning point (DTP) which can realize broadband mode conversion have been presented [20–23]. For example, Zhou et al. demonstrated a waveband-tunable broadband OAM mode converter based on a helical long-period fiber grating (HLPFG) and a DTP tuning technique achieved by thinning the optical fiber [20]. However, an AIFG based on the DTP has not yet been presented.

In this paper, we first propose and demonstrate, to our best knowledge, the broadband AIFG (BAIFG) based on the DTP of fiber high-order dispersion. The wavelength of the DTP can be tuned between 1500 nm and 1650 nm according to the fiber diameter, and the 3-dB bandwidth is more than 125 nm with mode conversion efficiency of 95%. More importantly, the generation of HE21odd, HE21even, and HE21mixed (HE21odd+evenorHE21odd-even) modes can be realized separately by controlling the polarization state of the incident light, which is also the first discovery of broadband CVBs in AIFGs. In addition, it is demonstrated that ultrashort pulses generated by an ML fiber laser can be converted to HOMs without walk-off effect during the acousto-optic region. Considering the unique characteristics of the BAIFG components, such as dynamic switching, broadband generation of a single CV mode, and the tunability of DTP wavelength, these features will be beneficial for their applications in ultrafast laser systems.

The acousto-optic mode converter is one kind of active radio frequency (RF)-driving fiber component based on electro-acoustic conversion and acousto-optic interaction effects in silica fiber media. An AIFG is composed of a piezoelectric transducer (PZT) driven by an RF signal and an aluminum horn utilized for amplifying the signal, which is capable of generating flexural acoustic waves propagating along the few-mode fiber (FMF) and forming a dynamic LPFG. It is recently reported that spin angular momentum (SAM) of phonons can be transformed into OAM of photons and the inversion of the topological charge of the optical vortex is achieved based on the fiber acousto-optic interaction in the AIFGs [24,25]. Core-mode conversion between the fundamental mode (LP01) and HOMs can be achieved when the phase-matching condition LB=Λ is satisfied [26,27], where LB=λ/(n01−n11) is the beat length and Λ=(πRC/f)1/2 is the period of the LPFG caused by the AIFG. λ represents the resonant wavelength, while n01 and n11 correspond to the effective refractive indices of the LP01 mode and HOMs, respectively. R means the cladding radius of the FMF, f is the frequency of the RF signal, and C=5760m/s represents the speed of the acoustic wave in optical fiber.

Initially, the phase-matching curves (PMCs) for the CV modes (TE01, HE21odd/even, TM01) of the LP11 mode are calculated by finite element analysis (COMSOL) for the home-fabricated FMF with a double-clad structure and the ring-core fiber (RCF). The radius of the core (r1)/inner cladding (r2)/outer cladding (r3) of the FMF is 6.25/18/62.5 μm, and the relative refractive index difference (Δ) of the core and inner cladding is 0.0031. As shown in Fig. 1(a), the simulated PMCs of the FMF are found to be parabolic and their tangent points are the DTP wavelengths of degenerated CV modes, which means broadband conversion between CV modes and the LP01 mode occurs around 1500 nm, meeting the phase-matching condition. This phenomenon is consistent with the results observed in broadband LPFGs [28,29], in which two resonant responses emerged into a broadband conversion at the DTP wavelength, which is inherently determined by the fiber dimension and refractive index (RI) parameters. Since the index-modulation LPFG period by CO2 radiation is sensitive to temperature and bending perturbance, as an alternative and flexible solution, the accuracy of the LPFG structure formed in the AIFG can be achieved by tuning the RF frequency with fine resolution.

Actually, the spectral dependence of the resonant wavelength λ and Λ can be expressed as dΛ/dλ=Δng/Δn2, where Δng=ng0−ng1 represents the difference of group effective refractive indices between LP01 and LP11 modes [30]. The principle of broadband mode conversion at the DTP wavelength is referring to group velocity (GV) matching Δng=0. As shown by the orange line in Fig. 1(a), the GV matching between degenerated CV modes of LP11 and LP01 modes is satisfied at the wavelength of 1500 nm, thus resulting in broadband mode conversion, which is of significance to be implemented for the ultrashort pulses with a wide spectrum. It is worth noting that the period of the AIFG can be equal to the minimum value of beat length (corresponding to the HE21 mode) by precisely controlling the RF frequency, in which case the HE21 mode can be efficiently selected from other CV modes.

A setup consisting of a super-continuum light source (YSL, SC-5) and an optical spectrum analyzer (Yokogawa, AQ6375) is used to monitor the transmission spectra of the BAIFG. The conversion efficiency of HOMs from the LP01 mode is represented by the depth of sinking dip on the spectrum propagating through a piece of SMF, due to the attenuation of HOMs. The transmission spectrum of the AIFG fabricated with the FMF is depicted in Fig. 1(b), indicating that the mode conversion with the efficiency of 9.5 dB (89%) occurs at the central wavelength of 1500 nm with the 3-dB bandwidth of 80 nm when applying RF frequency (f=2.291MHz) on the PZT. To our knowledge, this is the first report on broadband acousto-optic mode converter working at the DTP wavelength. As known that the HOMs are degenerated and transmitted stably in the RCF due to Δneff>10−4 [31,32], the AIFG made with an RCF is commonly employed to achieve selective output of CV modes. Similarly, the PMCs are simulated for an RCF with an inner core radius (r1)/outer core radius (r2)/cladding radius (r3) of 3.5/7.5/62.5 μm and the Δ of 0.0189, as shown in Fig. 1(c). Different from that at the DTP, the beat lengths decrease and intersect with the AIFG period, leading to a relatively narrower bandwidth. It can be observed that the LP01 mode can be coupled as TM01, HE21odd/even, and TE01 modes at three resonant wavelengths (λ1=1455nm, λ2=1550nm, λ3=1631nm) under the condition of LB=Λ=1950μm. The measured transmission spectrum of the AIFG is displayed in Fig. 1(d), which reveals that three CV modes are found at the wavelengths of 1454 nm, 1550 nm, and 1626 nm when f=303kHz.

The experimental results closely correspond with the simulation. The large differences of the beat length for CV modes lead to their mode resonance at a large wavelength separation. However, it can only be used with narrow linewidth picosecond lasers because the 3-dB bandwidth of HE21 resonance is around 10 nm and its nonnegligible GV matching also shortens the effective length of the LPFG, limiting its application in the femtosecond lasers.

In order to control the DTP located at the desired wavelength, the FMFs are etched to change the PMCs. The cladding diameter of the FMF is decreased to lower the RF frequency and enhance the mode conversion efficiency [33]. When the diameter is etched to only one cladding layer, the influence of air with an RI of 1 is indispensable. As the cladding diameter diminishes, the relative RI difference between the core and cladding increases. Figure 2(a) presents the PMCs for the FMF with a diameter of 34 μm; compared with the results in Fig. 1(a), it is noted that the wavelength of the DTP increases from 1500 nm to 1550 nm. This is the first discovery of the DTP tunability in the AIFGs, allowing for the selection of the desired DTP wavelengths. In particular, it is found that only the HE21 mode can satisfy the phase-matching condition when LB=699μm, i.e., broadband mode conversion from the LP01 to HE21 mode can be achieved at the wavelength of 1550 nm at this time. The large beat length difference (ΔLB) between TM01 and HE21 modes is conducive to the individual output of the HE21 mode. Dependence of ΔLB between three CV modes on the different cladding diameters is plotted in Fig. 2(b), which reveals that the relationship of LBTE01>LBTM01>LBHE21 is maintained across different diameters, while LBTM01<LBHE21 is satisfied in the RCF as shown in Fig. 1(c). It is worth noting that ΔLBTM01−HE21 gradually increases when the diameter is less than 38 μm, suggesting that a smaller diameter of the FMF is more conducive to the exclusive generation of the HE21 mode. Additionally, the relationship between the central wavelength and the diameter is displayed by the red curve in Fig. 2(b), showing that the DTP wavelength increases from 1500 nm only when the diameter is less than 45 μm, and at the diameter of 34 μm, the DTP corresponds to a central wavelength of 1550 nm.

In the experiment, the FMF is first immersed in the BOE solution of mixed HF and NH4F [34]. After about 6 h, the diameter of the FMF is reduced to 34 μm, and then it is prepared for an AIFG with the acousto-optic interaction length of 50 mm. The transmission spectra with different applied RF signals (f) are shown in Fig. 2(c). Two resonant dips are separated at the wavelength when RF frequencies are smaller than the exact one applied to generate the DTP. As the frequency increases, these two dips gradually merge into a single broadband resonance. Mode conversion with a 3-dB bandwidth of 125 nm is obtained when f=730kHz indicating that this AIFG can convert the LP01 mode to the HE21 mode across the wavelength range from 1475 nm to 1600 nm, with the efficiency of 95%. Thus, the BAIFG is demonstrated to provide the feasibility for mode conversion of femtosecond pulses.

The correlation between the wavelengths of two resonance dips and RF frequencies for various etched cladding diameters is illustrated in Fig. 2(d). The relationship between the resonance wavelengths and frequencies is parabolic. When the fiber diameter is etched to 34 μm, the central wavelength experiences a red shift due to the influence of external air, which is consistent with the simulation results. Consequently, it is crucial to meticulously regulate the fiber diameter to 34 μm to ensure that the mode conversion of the AIFG occurs at the central wavelength of 1550 nm, which requires that the etched method needs to be sufficiently precise, as the diameter error of 1 μm can result in a wavelength shift of approximately 25 nm. It is experimentally observed that the coupling efficiency and conversion bandwidth of the BAIFGs are increased by etching the FMF.

Theoretically, it has been verified by the transmission spectra of an AIFG that the broadband mode conversion can be achieved at the wavelength of 1550 nm. The pattern detection of polarized projection is needed to further confirm that a broadband HE21 mode can be generated. The experimental setups for generating and detecting CVBs and OAMs based on the BAIFG are shown in Fig. 3. A narrow linewidth light from the tunable semiconductor laser (TSL) operating in the wavelength range from 1480 nm to 1600 nm is coupled into the FMF. By adjusting the voltage and frequency of the RF applied to the PZT and changing the polarization state of incident light through a polarization controller (PC), the LP01 mode is converted into degenerate CVBs of the LP11 mode, which are detected for its polarization distributions by rotating a polarizer (P) placed in front of the charge-coupled device (CCD), as shown in Fig. 3(a). The first-order CV modes in an FMF can be considered as a linear combination of left- and right-handed circularly polarized OAM (CP-OAM) modes carrying opposite topological charges [35,36]. Therefore, in the case of a single CV mode, two CP-OAM modes can be excited by the combination of a quarter-wave plate (QWP) and a polarizer with the angle of ±π/4. The OAM detection diagram is depicted in Fig. 3(b), where the OAM modes converted from CVBs enter into the self-interference system composed of two mirrors (M1, M2) and a beam splitter (BS). By fine-tuning the position and angle of the mirrors on both sides, the separated beams are made to overlap at the intersection point and interfere with each other spatially. The formation of OAMs can be tested by observing whether the interference patterns have fork stripes.

The doughnut-intensity beam of the HE21 mode generated by the BAIFG and its polarization distributions at different wavelengths are measured when f=730kHz, as shown in Fig. 4(a). It can be confirmed that a hybrid CV mode (HE21mixed) can be produced steadily in the wavelength range of 1490 nm to 1590 nm. Moreover, the tunability of the RF frequency applied to the BAIFG is approximately 5 kHz (compared to 3 kHz for ordinary AIFGs), meaning that the mode conversion efficiency at 1550 nm reaches 90% in the frequency range of 729 kHz to 734 kHz. The mode patterns measured at different frequencies are displayed in Fig. 4(b), which further validates the stable generation of the HE21mixed mode.

Based on polarization-dependent and vector-mode coupling characteristic of the AIFG, the CV modes are determined by the polarization state of the fundamental mode [37]. The direction of the acoustic vibration is defined as x; the HE11x mode will couple into TM01 and HE21even, while the HE11y mode can be converted to TE01 and HE21odd. The arbitrarily linearly polarized states of incident light are easily controlled by a PC, so that the HE21mixed mode can be generated conveniently. And precise adjustment of the input polarization state can also separately achieve the conversion of HE21even and HE21odd modes, as shown in Fig. 4(c). Furthermore, the interference patterns in Fig. 4(d) confirm that the HE21mixed mode can be resoundingly converted into OAM+1 and OAM−1 passing through a QWP with the polarizer set at angles of π/4 and −π/4, respectively [38]. Therefore, fast vortex mode switching can be achieved from the inputs of CV modes passing through the wave plates with fixed angles.

The stochastic parallel gradient descent (SPGD) algorithm based on deep learning (DL) composed of a well-trained CNN model and an SPGD algorithm, can be employed to further verify the purity of mode patterns measured in the experiment with high accuracy [39,40]. The CNN algorithm has global search ability and excellent real-time performance, meanwhile the SPGD has fast convergence ability [41]. The predicted parameters from the CNN are used as the initial values of the SPGD, so the accuracy and efficiency of mode decomposition based on the DL-SPGD algorithm can be greatly improved. In order to retrieve the mode coefficients of four degenerated CV modes of the LP11 mode, the original and reconstructed near-field light intensity distributions should be compared according to their spatially variant polarized intensities. The modal field distributions in the FMF can be expressed as Ein=∑k=14ρkeiθkEk,(1)where ρk, θk, and Ek correspond to the modal amplitude, phase, and electric field of four CV modes. And the modal weights ρk2 need to satisfy the condition of ∑14ρk2=1. The rough global optimization values (ρi and θi) of the CV mode coefficients obtained by the CNN model are directly set to the initial values of the variables in the SPGD algorithm. Then random perturbations (δρi and δθi) are generated to acquire a temporary reconstructed intensity distribution (Ire), and the average beam correlation (J) between the measured one (Ime) and Ire can be calculated, which is described as J=|∬(Ire−Ire¯)(Ime−Ime¯)rdrdφ∬(Ire−Ire¯)2rdrdφ∬(Ime−Ime¯)2rdrdφ|,(2)where Ire(me)¯ represents the mean value of the reconstructed or measured fields. When the condition |Ji+1−Ji|<10−5 is satisfied after certain iterations, the weight (ρ0) and phase (θ0) are considered to be converged. The specific flow of the algorithm is explained in detail in Ref. [40].

As demonstrated in Fig. 5(a), the measured and reconstructed intensity patterns of the HE21mixed mode have great consistency. Then polarization distributions from Figs. 4(a)–4(c) are used for mode decomposition. It is found that the average ratio of HE21odd and HE21even modes is about 0.45:0.55 according to the decomposed results at different wavelengths, as depicted in Fig. 5(b). Similarly, the mean mode proportion at different frequencies is about 0.4:0.6, as shown in Fig. 5(c), and the phase differences between HE21odd and HE21even modes are all found nearly to be π. The above results indicate that the CV modes generated by a BAIFG have high stability over a wide range of wavelengths and RF frequencies. A slight difference in the polarization state of the incident light during the experiment led to a different ratio in these two cases. Additionally, the predicted modal weights of HE21odd and HE21even modes are over 97%, as described in Fig. 5(d), indicating the generation of a single CV mode with high purity by adjusting the polarization state of the LP01 mode.

The BAIFG, with a 3-dB conversion bandwidth of 125 nm and a conversion efficiency of over 95%, provides the potential for generating femtosecond pulses in HOMs [42]. As shown in Fig. 6(a), the BAIFG is integrated with a figure-9 femtosecond ML fiber laser to deliver the femtosecond pulse carrying the CV modes outside the cavity, and in combination with the reverse pumping scheme to achieve power amplification of the CV modes. The nonlinear amplifying loop mirror (NALM) as a saturable absorber is based on a 2×2 optical coupler (OC) made from polarization-maintaining (PM) SMF with a coupling ratio of 30:70. The nonlinear phase shift related to light intensity is accumulated by clockwise and anticlockwise propagated light through the NALM, capable of generating ML pulses within the cavity. A piece of 1.8 m PM dispersion compensating fiber (DCF) is used for cavity dispersion compensation, and the gain medium is the PM erbium-doped fiber (EDF) with the length of 0.4 m. The ML fiber laser has an overall cavity length of 6.25 m and the net cavity dispersion is about −0.017ps2. A nonreciprocal phase shifter (NPS) can optimize the self-starting characteristics of the ML fiber laser by increasing the nonlinear phase difference [43].

The transversal-mode intensities of LP01 and OAM modes and their spectrum performances of the ML fiber laser with the BAIFG are characterized in Fig. 6(b). The spectrum indicates that the central wavelength of the LP01 mode is 1560 nm with a 3-dB bandwidth of 35 nm, which can be encompassed by the 3-dB bandwidth of the BAIFG (125 nm), suggesting that the mode conversion does not alter the broadband spectral characteristics. Importantly, the group velocities of LP01 and HE21 modes are equal within the wavelength spectrum of the broadband AIFG, so there is almost no walk-off effect during the acousto-optic region, ensuring efficient mode conversion for femtosecond pulses. As the dependence of output power on pump power is displayed in Fig. 6(c), it is noticed that the fiber laser is working at the CW state when the pump power is below the ML threshold (80 mW). Increasing the pump power continuously, it is able to operate self-starting and stable mode-locking. The ML pulse with an RF signal with a fundamental frequency of 38.011 MHz and a signal-to-noise ratio (SNR) of 73 dB is shown in Fig. 6(d), which reveals that the pulse has high inter-pulse stability. And the inset exhibits the pulse trains measured by an oscilloscope at the pump power of 80 mW. The autocorrelation trace with a pulse duration of 120 fs is plotted in Fig. 6(e), and the calculated time–bandwidth product of the pulse is about 0.8. The pulse can be further narrowed by optimizing the intracavity dispersion and the length of DCF outside the cavity.

The mode patterns of femtosecond pulses measured from port 1 are shown in Fig. 7(a), revealing that corresponding HE21even, HE21odd, and HE21mixed modes can also be obtained under different polarizations. Their mode weights are calculated in Fig. 7(b). It is noticed that HE21odd and HE21even proportions of the HE21mixed modes respectively are 54% and 46%, and high purities of the single HE21odd and HE21even modes reach 93.6% and 98%, respectively. The results suggest that the high-purity mode conversion of ultrashort pulses can be realized efficiently with the BAIFG.

The output power of the ML laser is around 1 mW due to the low pump threshold of 80 mW, and a few-mode reverse pumping amplification method is employed to increase the power of femtosecond pulses in HOMs for further power scaling [44,45]. The FM-EDF with the core/cladding diameter of 20.6/125 μm is home-made [46]. As the pump power increases, the spectral evolutions of output laser measured at port 2 are depicted in Fig. 8(a), presenting that femtosecond pulses can be efficiently amplified by this method. However, pulse duration will be broadened in the process of pump amplification due to the nonuniform gain spectrum of the FM-EDF. And the output powers of the LP01, LP11, and OAM modes are measured, as shown in Fig. 8(b). Since the EDF has higher losses for low-power signal light, the growth slope of LP11 and OAM modes is slightly lower than that of LP01, but it is still capable of amplifying the original output (1 mW) to over 40 mW. Mode patterns of LP11 and OAM at different pump powers are displayed in Fig. 8(c), indicating that the high purity can be maintained after the amplification. Additionally, a self-interference experiment of the annular beam with the pump power of 200 mW is conducted. The interference patterns in Fig. 8(d) demonstrate that the amplified femtosecond pulses can still generate OAM±1 by adjusting the phase between the modes by a PC.

In addition to obtaining the broadband AIFG at the 1.5 μm waveband, we also achieve the broadband mode conversion at the wavelength of 1.0 μm waveband with the TMF (Corning 28e, r1/r2=4/62.5μm, Δ=0.004). The PMCs with fiber diameters etched from 125 μm to 30 μm are shown in Fig. 9(a), indicating that broadband mode conversion centered at the wavelengths of 1105 nm and 1113 nm also can be achieved when both phase and group-velocity matching conditions are satisfied. It is calculated that the required RF frequency for the cladding diameter of 125 μm should be 7.34 MHz, much higher than that (1.48 MHz) when the cladding diameter is etched to 30 μm. The method of reducing the RF frequency by etching the cladding thickness of the fiber is more feasible experimentally because the center frequency of the PZT is 1.7 MHz. The DTP wavelength drift of only 8 nm is due to the smaller core radius (4 μm) of this TMF, which generally requires a thinner cladding diameter to significantly affect the wavelength of the DTP. The transmission spectra of the BAIFG with a fiber diameter of 30 μm are seen in Fig. 9(b), showing that the central wavelength is 1113 nm and the 3-dB bandwidth is about 105 nm. This also proves that BAIFGs capable of broadband mode conversion at 1.0 and 1.5 μm wavebands have been successfully fabricated.

It is difficult to produce the large beat length difference between CV modes in ordinary step-index TMFs due to their small relative RI difference. Therefore, it is desirable to design an RCF with the DTP wavelength at 1550 nm to further realize the broadband conversion of a single CV beam. First, it is found through the simulation that the wavelength of the DTP can be reduced by decreasing the RI difference. A typical RCF with inner radius (r1) and outer core radius (r2) of 3.5 and 7.5 μm and Δ of 0.0034 is found that the DTP wavelength is 2025 nm, as shown in the red dotted box in Fig. 10(a). The DTP wavelength can also be shifted by changing the fiber parameters, r1 and r2. Figure 10(b) shows the simulation results of an RCF (r1/r2=3.5/6μm, Δ=0.0034), showing that the DTP wavelength is decreased to 1550 nm. It is worth mentioning that the generation of broadband TM01 mode is more convenient in this fiber structure, because the beat length difference between the TM01 and HE21 modes (ΔLBHE21−TM01) is 3.93 μm, compared to that (−0.7μm) of the FMF. The challenge that remains is efficient coupling or generation of LP01 mode of the RCF, and such ring-core fibers need to be redesigned and reconsidered for fiber dispersion engineering.

Meanwhile, when the DTP wavelength is located at 1550 nm, the relationship between r1 and r2 is studied, as shown in Fig. 10(c). Δr=r2−r1 is the thickness of the ring core, which will decrease as r1 increases while Δ is fixed to be 0.0034. These RCFs with specific fiber structures (r1, r2, Δn) will have the DTP wavelength at 1550 nm, represented by the red dots in Fig. 10(c), and ΔLBHE21−TM01 under different structures gradually minish with the decreases of r1 represented by the blue dots. It can be seen that ΔLBHE21−TM01 is zero when r1=1.28μm, meaning that when r1 is less than 1.28 μm, the beat length of HE21 and TM01 modes will be exchanged. Furthermore, the beat length of the HE21 mode is the smallest and the ΔLBHE21−TM01 is about −0.46μm when r1=0.5μm, as shown in Fig. 10(d). Therefore, it is feasible to change the CV mode (TM01 or HE21 mode) which can implement the broadband mode conversion and the DTP wavelength by designing different fiber structures.

In conclusion, we propose a novel broadband AIFG component based on the DTP of fiber dispersion with a 3-dB bandwidth of 125 nm and a conversion efficiency of 95%, which can be used as a wideband LPFG alternative to address its sensitivity to temperature and bending perturbation. The bandwidth of the proposed BAIFG is more than 10 times that of the traditional AIFG, which also provides the feasibility for implementation of mode conversion of femtosecond pulses. It is proved both experimentally and theoretically that the wavelength tunability of the DTP can be achieved by etching the fiber cladding diameter to change the phase and group-velocity matching conditions, which is the first discovery of the DTP tunability in the AIFGs. Based on polarization-dependent and vector-mode coupling characteristics of the BAIFG, a single CV mode can be converted individually by adjusting the polarization of incident light and has high stability over a wide range of wavelengths and RF frequencies, according to the results of pattern decomposition with the DL-SPGD algorithm. In addition, fast vortex mode switching can be achieved from the inputs of CV modes passing through the mode control system composed of a QWP and a polarizer with the angle of ±π/4. Based on a figure-9 femtosecond ML laser, ultrashort pulses are converted to HOMs without walk-off effect during the acousto-optic region due to the conversion bandwidth of hundreds of nanometers of the BAIFG. Furthermore, the power of femtosecond pulses in HOMs can be efficiently improved by a power-scaling method of few-mode reverse pumping amplification. Finally, another fiber is used to realize the broadband mode conversion at the wavelength band of 1.0 μm, and the DTP wavelength of the RCF with different structures is discussed, showing that the beat length difference between TM01 and HE21 modes is larger with the increase of r1 when the DTP wavelength is 1550 nm, which is conducive to realizing the broadband generation of a single CV mode. The proposed BAIFG components based on the DTP tunability may enable important applications in the area of material processing, super-resolution microscopes, and optical communications.

Acknowledgment. X. Zeng acknowledges the support of the Program for Professor of Special Appointment (Eastern Scholar) at Shanghai Institutions of Higher Learning.