Topics
Contents Diffraction and Gratings, 48 Article(s)
A broadband polarization-independent two-port beam splitter under normal incidence based on encapsulated metal-dielectric reflective grating
Zhengkun Yin, Yunkai Lu, Junjie Yu, and Changhe Zhou

An encapsulated metal-dielectric reflective grating is presented for broadband polarization-independent two-port beam splitting under normal incidence at the central wavelength of 800 nm. Different from traditional two-port grating splitters in the resonant region, this grating splitter is capable of separating light energy into ±1st orders with high efficiency in a broad waveband for both TE and TM polarizations. A unified method is proposed here for designing this grating splitter, which enables one to choose a grating structure quickly to realize an ultrabroad working waveband. The simulation results indicate that a bandwidth of 46.4 nm could be achieved for diffraction efficiency (defined as the ratio of the light energy diffracted only at the first order to the incident light energy) over 46% at the central wavelength of 800 nm. Moreover, the parameters of the grating structure can be flexibly adjusted with wavelengths using the unified method for various other applications, such as augmented reality, optical interconnections for computing, coherent beam combination, and complex vector beam shaping.

Chinese Optics Letters
Jul. 10, 2020, Vol. 18 Issue 7 070501 (2020)
Scalable Talbot effect of periodic array objects
Rui Yang, Zhenfa Xue, Zhiyong Shi, Liqiang Zhou, and Linwei Zhu

A type of scalable self-imaging capable of variable magnification or minification of periodic objects is demonstrated in the focal plane of a lens illuminated by a point source. The theory and the experimental results show that the self-imaging phenomenon can also be realized in the focal plane of a lens regardless of whether the distances satisfy the lens formula or not. The particular property of this scalable self-imaging effect is that the images in the focal plane can be controlled with different scaling factors only when the distances between the point source and the periodic object satisfy a certain condition. This discovery should open a new field of diffraction imaging and new application opportunities in precision measurement.

Chinese Optics Letters
Mar. 10, 2020, Vol. 18 Issue 3 030501 (2020)
Chirped pulse amplification: review and prospective from diffractive optics [Invited]
Changhe Zhou

It is well-known that the chirped pulse amplification (CPA) technique won the award for the 2018 Nobel Prize in Physics to Mourou and Strickland. The compression and stretching using gratings is the essence of the CPA technique for amplifying femtosecond laser pulses. It seems the public is less aware that there are also other structures for compression and stretching of femtosecond laser pulses using other diffractive gratings, such as doubled-density gratings and deep-etched gratings. Therefore, from the view of diffractive optics, the CPA technique is reviewed with different approaches and experimental implementations that are not only useful for a more comprehensive retrospective overview of CPA, but also for the prospective of the CPA technique, which might lead us to new areas of picometer and femtometer optics in the future.

Chinese Optics Letters
Editors' PickNov. 10, 2020, Vol. 18 Issue 11 110502 (2020)
New kind of Hermite–Gaussian-like optical vortex generated by cross phase
Chen Wang, Yuan Ren, Tong Liu, Linlin Chen, and Song Qiu

We propose a new kind of optical vortex called the Hermite–Gaussian-like optical vortex (HGOV) inspired by the cross phase (CP). Theoretically, we investigate how the CP is decoupled from the phase of a cylindrical lens. We also investigate the propagation characteristics of an HGOV, which has a Hermite–Gaussian-like intensity distribution but still retains the orbital angular momentum. Furthermore, we derive the Fresnel diffraction integral of an HGOV and study the purity at infinity. Besides, we show a novel function of the self-measurement of the HGOV. Finally, we show that we can change the relative positions of singularities and the direction of an HGOV precisely, which facilitates applications in optical micro-manipulation.

Chinese Optics Letters
Oct. 10, 2020, Vol. 18 Issue 10 100501 (2020)
Multi-band imaging and focusing of photonic crystal flat lens with scatterer-size gradient
Yuan Cen, Jianlan Xie, and Jianjun Liu

In this Letter, a photonic crystal (PC) flat lens with a scatterer-size gradient is proposed, which simultaneously achieves imaging of the point source and sub-wavelength focusing of the plane wave in the first, second, and fifth bands. The imaging of the point source breaks through the diffraction limit in the second and fifth bands. The PC flat lens with the scatterer-size gradient is expected to be used in a new multifunctional optical imaging and focusing device, which improves the application potential of a PC flat lens.

Chinese Optics Letters
Aug. 10, 2019, Vol. 17 Issue 8 080501 (2019)
Detour phase Talbot array illuminator
Zhigang Li, Rui Yang, Meiyu Sun, Jing Han, Dengying Zhang, Jiannong Chen, Dawei Zhang, and Linwei Zhu

In this Letter, we propose a simple and effective approach for transforming a conventional Talbot array illuminator (TAI) with multilevel phase steps into a binary-phase TAI (BP-TAI) through detour phase encoding. The BP-TAI is a binary (0 π) phase-only diffractive optical element, which can be utilized to generate a large-scale focal spots array with a high compression ratio. As an example, we design a square BP-TAI with the fraction parameter β = 15 for achieving a square multifocal lattice with a high compression ratio β2. Theoretical analysis and experimental results demonstrate that the detour phase encoding is efficient for designing the BP-TAI, especially with the high compression ratio. Such results may be exploited in practical large-scale optical trapping and X-ray imaging.

Chinese Optics Letters
Jul. 10, 2019, Vol. 17 Issue 7 070501 (2019)
Diffraction of relativistic vortex harmonics with fractional average orbital angular momentum
Shasha Li, Baifei Shen, Wenpeng Wang, Zhigang Bu, Hao Zhang, Hui Zhang, and Shuhua Zhai

Vortex harmonics with fractional average orbital angular momentum are generated when a relativistic fractional vortex beam is incident on and reflected from an over-dense plane plasma target. A two-step model is presented to explain the far-field patterns of the harmonics. In the first step, a fundamental spot-shaped hole is produced during the hole-boring stage, and harmonics are generated simultaneously. In the second step, different order harmonics are diffracted by the hole and propagate to the far field. This process can be accurately described by the Fraunhofer diffraction theory. This work facilitates a basic recognition of fractional vortex beams.

Chinese Optics Letters
May. 10, 2019, Vol. 17 Issue 5 050501 (2019)
Angular filtering by volume Bragg grating in photothermorefractive glass for nanosecond laser pulse
Baoxing Xiong, Fan Gao, Xiang Zhang, and Xiao Yuan

The two-dimensional angular filter based on volume Bragg gratings in photothermorefractive glass for a nanosecond (ns) laser pulse is demonstrated. The experimental results show that the near-field beam quality of the laser pulse was effectively improved. The near-field modulation and contrast ratio were improved by 1.75 and 4.48 times, respectively. The power spectral density curves showed that the spatial frequencies more than 0.9 mm 1 in the x direction and 1.2 mm 1 in the y direction were effectively suppressed.

Chinese Optics Letters
Apr. 10, 2019, Vol. 17 Issue 4 040501 (2019)
Grating coupler efficiency enhancement by double layer interference
Huashan Yang, Fuling Zhang, Lemeng Leng, Zhaobang Zeng, Yue Shao, Hui Zhang, Nan Yang, and Xiangning Chen

A simple method for improving grating couplers’ coupling efficiency without any extra microfabrication processes is proposed. This method can improve the coupling efficiency with 1.69 dB by utilizing the combined interference in the cladding layer and air gap between the cladding surface and the paralleled angle polished fiber facet. The proposed method can be applied to various kinds of on-chip grating couplers. Back reflection, 1 dB bandwidth, and fiber alignment tolerance have also been improved at the same time.

Chinese Optics Letters
Mar. 10, 2019, Vol. 17 Issue 3 030501 (2019)
Perfect absorption in a monolayer graphene at the near-infrared using a compound waveguide grating by robust critical coupling
Jinhua Hu, Jia Fu, Xiuhong Liu, Danping Ren, Jijun Zhao, and Yongqing Huang

We present a perfect graphene absorber with a compound waveguide grating at the near-infrared. The analytical approach is mainly based on the coupled leaky mode theory, which turns the design of the absorber to finding out the required leaky modes supported by the grating structure. Perfect absorption occurs only when the radiative loss of the leaky mode matches the intrinsic absorption loss, which is also named the critical coupling condition. Furthermore, we also demonstrate that the critical coupling of the system can be robustly controlled, and the perfect absorption wavelength can be easily tuned by adjusting the parameters of the compound waveguide grating.

Chinese Optics Letters
Jan. 10, 2019, Vol. 17 Issue 1 010501 (2019)
Effects of mask-alignment error on point spread function for multi-level Fresnel diffractive lenses
Dun Liu, Shibin Wu, Wei Yang, Lihua Wang, Bin Fan, and Fan Wu

The full aperture complex amplitude transmittance function of a multi-level diffraction lens with mask-alignment errors was derived based on scalar diffraction theory. The point spread function (PSF) was calculated by the Kirchhoff diffraction integral. It is found that the radius of the Airy disk increases with the increase of the error in the direction of misalignment, and the image center shifts along the direction of misalignment. A four-level diffractive lens with a diameter of 80 mm was fabricated, and its PSF and diffraction efficiency of +1st order were calculated and measured. The distribution of PSF is consistent with the calculated results, and the tested diffraction efficiency is slightly smaller than the calculated value; the relative error is 5.71%.

Chinese Optics Letters
Sep. 10, 2018, Vol. 16 Issue 9 090501 (2018)
Beam combination at any angles with a multilayer grating
Ci Yin, Shiyao Fu, Yahui Zhang, Yanwang Zhai, Heng Zhou, and Chunqing Gao

A scheme for beam combination at any angles employing a specially designed multilayer grating is proposed. Such a grating is able to convert noncoaxial laser beams to coaxial ones, and the combined beams are able to output along the normal line of the grating. The intensity and the phase structure of combined beams can also be controlled. The experiments are carried out by loading an encoded grating on a liquid-crystal spatial light modulator. The results agree well with the simulations. This method of beam combination with a multilayer grating serves to simplify the complexity of beam combination.

Chinese Optics Letters
Aug. 10, 2018, Vol. 16 Issue 8 080502 (2018)
Generation of X-ray vortex with ultra-long depth of focus using axial line-focused spiral zone plates
Huaping Zang, Chenglong Zheng, Quanping Fan, Chuanke Wang, Lai Wei, Leifeng Cao, Xiangru Wang, and Erjun Liang

We propose axial line-focused spiral zone plates (ALFSZPs) for generating tightly focused X-ray vortex beams with ultra-long depth of focus (DOF) along the propagation direction. In this typical design, compared with the conventional spiral zone plates (SZPs) under the same numerical aperture (NA), the DOF of ALFSZPs has been extended to an ultra-length by optimizing the corresponding parameters. Besides, it also exhibits lower side lobes and smaller dark cores in the whole focus volume. The diameters of dark cores increase as the topological charge value increases.

Chinese Optics Letters
Aug. 10, 2018, Vol. 16 Issue 8 080501 (2018)
High-harmonic-generation-inspired preparation of optical vortex arrays with arbitrary-order topological charges
Wuhong Zhang, and Lixiang Chen

In the process of high-harmonic generation with a Laguerre-Gaussian (LG) mode, it was well established that the topological charge could be of an N-fold increase due to angular momentum conservation. Here, by mimicking the effect of high-harmonic generation, we devise a simple algorithm to generate optical vortex arrays carrying arbitrary topological charges with a single phase-only spatial light modulator. By initially preparing a coaxial superposition of suitable low-order LG modes, we demonstrate experimentally that the topological charges of the embedded vortices can be multiplied and transformed into arbitrarily high orders on demand, while the array structure remains unchanged. Our algorithm offers a concise way to efficiently manipulate the structured light beams and holds promise in optical micromanipulation and remote sensing.

Chinese Optics Letters
Mar. 10, 2018, Vol. 16 Issue 3 030501 (2018)
Propagation dynamics of ring Airy Gaussian beams with cosine modulated optical vortices
Feili Wang, Cibo Lou, and Yi Liang

We numerically investigate the propagation properties of ring Airy Gaussian beams (RAGBs) with cosine modulated optical vortices (CMOV). In comparison to the common RAGBs without any modulation, the dynamic propagation of RAGBs with CMOV exhibits a unique feature: the rings of RAGBs with CMOV will gradually shrink into several main lobes with the increase of the propagation distance. The number of lobes and the peak intensity of each lobe are determined by the factors of cosine modulated function. By designing the initial phase, we can easily change the transversal location of the peak intensity. Our results may find potential applications in optical manipulations.

Chinese Optics Letters
Nov. 10, 2018, Vol. 16 Issue 11 110502 (2018)
Generation of all-fiber femtosecond vortex laser based on NPR mode-locking and mechanical LPG
Zhiming Zhang, Wei Wei, Liqin Tang, Jie Yang, Jiewei Guo, Lei Ding, and Yigang Li

An all-fiber femtosecond vortex laser based on common fiber components is constructed. It can produce femtosecond orbital angular momentum modes whose time pulse width is 398 fs. The topological charge of output orbital angular momentum (OAM) modes from this laser can be adjusted among 0, +1, and 1 easily while it is also easy to convert between continuous OAM modes and pulse OAM modes.

Chinese Optics Letters
Nov. 10, 2018, Vol. 16 Issue 11 110501 (2018)
Manipulation of the overall polarization orientation in the focal volume of high numerical objectives
Jiannong Chen, Linwei Zhu, and Zhigang Li

We propose an approach for tuning the three-dimensional polarization of a focusing subwavelength spot by a high numerical aperture objective. The incident beams are composed of a radially polarized beam, an azimuthally polarized beam, and a linearly polarized beam with three different weighting factors, respectively. A specially designed adjustable amplitude angular selector is also inserted at the back aperture of the objective for tuning the polarization azimuthally. It is shown that any desired overall polarization orientation can be obtained. We calculated the overall polarization orientation in the focal volume. It is found that the polar angle of the overall polarization orientation can be arbitrarily tuned by the combination of a radially polarized beam and a linearly polarized beam with different weighting factors, and the azimuthal angle can be tuned by rotating the orientation of the linearly polarized beam azimuthally.

Chinese Optics Letters
Jan. 10, 2018, Vol. 16 Issue 1 010501 (2018)
Investigation of Fano resonance in compound resonant waveguide gratings for optical sensing
Jinhua Hu, Xiuhong Liu, Jijun Zhao, and Jun Zou

An optical sensor is designed to support the Fano effect based on a compound resonant waveguide grating (CRWG). The transmission spectra of the CRWG are investigated by utilizing a theoretical method that combines the temporal coupled mode theory with the eigenmode information of the grating structure. The theoretical results, which are observed to agree closely with those acquired by rigorous coupled-wave analysis, show that the linewidth of the transmission spectrum decreases upon increasing the distance between the grating strips, and the central resonance frequency decreases as the refractive index of the analyte increases. Here, the proposed CRWG structures will find potential uses in optical sensing.

Chinese Optics Letters
Mar. 10, 2017, Vol. 15 Issue 3 030502 (2017)
Deformation of orbital angular momentum modes in bending ring-core fiber
Haozhe Yan, Shangyuan Li, Zhengyang Xie, Xiaoping Zheng, Cheng Du, Hanyi Zhang, and Bingkun Zhou

We present the investigation on deformation of orbital angular momentum (OAM) modes in bending ring-core fibers (RCFs) with different structure sizes through numerical and experimental studies. The effective refractive index differences of even and odd fiber eigenmodes, which constitute OAM±1,1 modes, induced by RCF bending and their impacts on the OAM±1,1 mode intensity distributions are analyzed. Bending experiments are also carried out on three different RCFs, and the results match well with simulation values. It is found that RCFs with smaller inner and outer radii show preferable tolerance to the fiber bending.

Chinese Optics Letters
Mar. 10, 2017, Vol. 15 Issue 3 030501 (2017)
High efficiency positive and negative phase zone plates
Renfang Hu, Jian Chen, Faiz Wali, Shengxiang Wang, Kun Gao, and Gang Liu

We design a new kind of phase zone plates (PZPs) to improve the diffraction efficiency of soft x ray zone plates (ZPs). The design replaces blank parts of PZPs with metals of negative phase shift at the working energy, which is called as the positive and negative PZPs (PNPZPs). According to the calculation, PNPZPs have a higher maximum efficiency than conventional ZPs with the same zone width. With the help of a negative phase coefficient, it is much easier to achieve a π phase shift in one period, resulting in a smaller zone height. This design can help fabricate finer PZPs to achieve a better image resolution.

Chinese Optics Letters
Feb. 10, 2017, Vol. 15 Issue 2 020501 (2017)
Application of metal nanoparticles/porous silicon diffraction grating in rhodamine 6 G fluorescence signal enhancement
Jiajia Wang, Zhenhong Jia, Changwu Lv, and Yanyu Li

We present a technique for fabricating a fluorescence enhancement device composed of metal nanoparticles (NPs) and porous silicon (PSi) diffraction grating. The fluorescence emission enhancement properties of the PSi and the fluorescence enhancement of the probe molecules are studied on PSi gratings. The fluorescence enhancement of the probe molecules on a fluorescence enhancement device is further improved through the deposition of metal NPs onto the PSi grating. In comparison to metal NP/PSi devices, metal NP periodic distributions can produce a stronger fluorescence enhancement that couples with the PSi grating fluorescence enhancement to achieve an overall three-fold enhancement of the fluorescence intensity.

Chinese Optics Letters
Nov. 10, 2017, Vol. 15 Issue 11 110501 (2017)
Near-field holography enhanced with antireflection coatings—an improved method for fabricating diffraction gratings
Yuanfang Li, Huoyao Chen, Stefanie Kroker, Thomas Käsebier, Zhengkun Liu, Keqiang Qiu, Ying Liu, Ernst-Bernhard Kley, Xiangdong Xu, Yilin Hong, and Shaojun Fu

Near-field holography (NFH), with its virtues of precise critical dimensions and high throughput, has a great potential for the realization of soft x-ray diffraction gratings. We show that NFH with reflections reduced by the integration of antireflective coatings (ARCs) simplifies the NFH process relative to that of setups using refractive index liquids. Based on the proposed NFH with ARCs, gold-coated laminar gratings were fabricated using NFH and subsequent ion beam etching. The efficiency angular spectrum shows that the stray light of the gratings is reduced one level of magnitude by the suppression of interface reflections during NFH.

Chinese Optics Letters
Sep. 10, 2016, Vol. 14 Issue 9 090501 (2016)
Diagnostics of the topological charge of optical vortex by a phase-diffractive element
Shiyao Fu, Tonglu Wang, Yan Gao, and Chunqing Gao

A phase-diffractive optical element is designed to measure the topological charge of optical vortices. We use the scalar diffraction theory to calculate the far-field diffraction patterns. The simulation results show that almost all of the power of the incident beams is diffracted to the same diffraction order, and this approach is also effective for multi-ring optical vortices. We upload this phase-diffractive optical element on the liquid crystal spatial light modulator to do the experiment. The observed far-field diffraction patterns fit well with the simulation results.

Chinese Optics Letters
Aug. 10, 2016, Vol. 14 Issue 8 080501 (2016)
Generation of polarization vortex beams by segmented quarter-wave plates
Jingtao Xin, Xiaoping Lou, Zhehai Zhou, Mingli Dong, and Lianqing Zhu

A spatially variable retardation device, an SQWP, is designed to generate polarization vortex beams. The transformation of Laguerre–Gaussian beams by the SQWP is further studied, and it is found that the SQWPs can also be used to generate helical beams and measure the topological charges of helical beams.

Chinese Optics Letters
Jul. 10, 2016, Vol. 14 Issue 7 070501 (2016)
Sidelobes suppression in angular filtering with volume Bragg gratings combination
Fan Gao, Xiao Yuan, and Xiang Zhang

A method for beam diffraction sidelobe suppression based on the combination of volume Bragg gratings (VBGs) with different thicknesses or periods for angular filtering is proposed and performed. Simulated and experimental results show that the beam diffraction sidelobe is reduced from 12% to less than 1% with the non-sidelobe angular filter. The non-sidelobe angular filtering based on VBGs with thicknesses of 2.5 and 2.9 mm is simulated and demonstrated. The near-field distribution of filtered beams through the non-sidelobe angular filter is obviously smoother than that of the single VBG. The near-field modulation and contrast ratio (C) of filtered beams are found to be improved 1.17 and 1.66 times that of the single VBG. The far-field C of the filtered beam is improved to about 100∶1 and the power spectral density analysis shows that the cutoff frequency of the angular filter is greatly optimized with the VBG combination.

Chinese Optics Letters
Jun. 10, 2016, Vol. 14 Issue 6 060502 (2016)
Optimization of a guided-mode resonance filter by varying the thickness of the buffer layer
Hsiang I. Hsu, Po-Tsung Wu, and Cheng-Sheng Huang

In this Letter, we demonstrate that by adjusting the thickness of the buffer layer, the optical responses of a guided-mode resonance filter (GMRF) can be improved for sensor applications. The GMRF is fabricated using a replica molding with a plastic substrate and a UV-curable polymer. SiO2 buffer layers of different thicknesses are deposited before the waveguide-layer deposition. The sensitivity of the GMRFs decreases slightly with increasing SiO2 layer thickness. By contrast, the full width at half-maximum reduces substantially with increasing SiO2 layer thickness, resulting in the improvement of the overall figure of merit.

Chinese Optics Letters
Mar. 10, 2016, Vol. 14 Issue 3 030501 (2016)
Effects of fabrication errors on diffraction efficiency for a diffractive membrane
Ruoqiu Wang, Zhiyu Zhang, Chengli Guo, Donglin Xue, and Xuejun Zhang

The demand for space-borne telescopes with an aperture of 20 m is forcing the development of large diameter diffractive Fresnel zone lenses (FZLs) on membranes. However, due to the fabrication errors of multi-level microstructures, the real diffraction efficiency is always significantly smaller than the theoretical value. In this Letter, the effects of a set of fabrication errors on the diffraction efficiency for a diffractive membrane are studied. In order to verify the proposed models, a 4-level membrane FZL with a diameter of 320 mm is fabricated. The fabrication errors of the membrane FZL are measured, and its diffraction efficiency in the +1 order is also tested. The results show that the tested diffraction efficiency is very close to the calculated value based on the proposed models. It is expected that the present work could play a theoretical guiding role in the future development of space-borne diffractive telescopes.

Chinese Optics Letters
Dec. 10, 2016, Vol. 14 Issue 12 120501 (2016)
Experimental demonstration of twisted light’s diffraction theory based on digital spiral imaging
Wuhong Zhang, Ziwen Wu, Jikang Wang, and Lixiang Chen

We present both numerical and experimental results to study the diffraction of twisted light beams based on orbital angular momentum (OAM) eigenmode decomposition, where the total initial field, including light and aperture, is represented by a two-dimensional spectrum of Laguerre–Gaussian modes. We use a phase-only spatial light modulator to display a holographic grating for both generating the twisted light and mimicking the finite aperture. We take a triangular aperture as an example to describe the diffraction behavior of a twisted light beam carrying an OAM number of =3 from the near-field to far-field regions, where the interesting gradual formation of triangular bright lattices are observed. An excellent agreement between the numerical simulations and experimental observations is clearly seen. It is noted that this method is particularly useful for the study of the diffraction of twisted light fields incident on any apertures of rotational symmetry.

Chinese Optics Letters
Nov. 10, 2016, Vol. 14 Issue 11 110501 (2016)
Low-cost method of fabricating large-aperture, high efficiency, Fresnel diffractive membrane optic using a modified moiré technique
Jian Zhang, Mengjuan Li, Ganghua Yin, Jianchao Jiao, Zhengkun Liu, Xiangdong Xu, and Shaojun Fu

To reduce the cost and achieve high diffraction efficiency, a modified moiré technique for fabricating a large-aperture multi-level Fresnel membrane optic by a novel design of alignment marks is proposed. The modified moiré fringes vary more sensitively with the actual misalignment. Hence, the alignment accuracy is significantly improved. Using the proposed method, a 20 μm thick, four-level Fresnel diffractive polyimide membrane optic with a 200 mm diameter is made, which exhibits over 62% diffraction efficiency into the +1 order, and an efficiency root mean square of 0.051.

Chinese Optics Letters
Oct. 10, 2016, Vol. 14 Issue 10 100501 (2016)
Characterization of external refractive index sensitivity of a photonic crystal fiber long-period grating
Fei Tian, Jiri Kanka, and Henry Du

Long-period gratings (LPGs) are fabricated in a photonic crystal fiber (PCF) using the symmetric point-by-point CO2 laser irradiation method to explore the sensitivity characterization of PCF–LPG. Numerical simulation is used to guide the investigation. It is found that the refractive index (RI) sensitivity of PCF–LPG depends on the coupled cladding modes as well as the coupled resonance wavelength (RW) of the LPG. Experimental studies show that the longer the RW, the higher the RI sensitivity for the same cladding mode. At similar RWs, the lower the cladding mode, the higher the RI sensitivity of PCF–LPG.

Chinese Optics Letters
Jul. 10, 2015, Vol. 13 Issue 7 070501 (2015)
Design of two-dimensional apodized grating couplers with Gaussian diffractive mode
Hua Wu, Chong Li, Qiaoli Liu, Bai Liu, Jian Dong, Lei Shi, and Xia Guo

Two-dimensional apodized grating couplers are proposed with grating grooves realized by a series of nano-rectangles, with the feasibility of digital tailoring the equivalent refractive index of each groove in order to obtain the Gaussian output diffractive mode in order to enhance the coupling efficiency to the optical fiber. According to the requirement of leakage factor distribution for a Gaussian output profile, the corresponding effective refractive index of the grating groove, duty cycle, and period are designed according to the equivalent medium theory. The peak coupling efficiency of 93.1% at 1550 nm and 3 dB bandwidth of 82 nm are achieved.

Chinese Optics Letters
May. 10, 2015, Vol. 13 Issue 5 050501 (2015)
Solving characteristic equation of orbital angular momentum modes in a ring fiber
Yixiao Zhu, and Fan Zhang

The characteristic equation of orbital angular momentum modes in a ring fiber is derived. By solving the equation with the graphical method, mode distribution in a ring fiber can be precisely determined for arbitrary fiber parameters without relying on simulation of the vector field. This will provide a useful method to determine the separation between quasi-degenerate modes in a ring fiber.

Chinese Optics Letters
Mar. 10, 2015, Vol. 13 Issue 3 030501 (2015)
Diffractive self-imaging based on selective etching of a ferroelectric domain inversion grating
Yunlin Chen, Tianwei Fan, and Man Tong

A hexagonal array grating based on selective etching of a 2D ferroelectric domain inversion in a periodically poled MgO-doped LiNbO3 crystal is fabricated. The effects to the diffractive self-imaging as a function of diffraction distance for a fixed phase difference and array duty cycle of the grating is theoretically analyzed. The Talbot diffractive self-imaging properties after selective etching of a 2D ferroelectric domain inversion grating under a fixed phase difference are experimentally demonstrated. A good agreement between theoretical and experimental results is observed.

Chinese Optics Letters
Feb. 10, 2015, Vol. 13 Issue 2 020502 (2015)
Free space optical beam coupled to surface plasmonic polariton waves via designed grooves in metal film
Yuegang Chen, and Zhiyuan Li

Surface plasmonic polariton (SPP) waves with complicated wavefronts have important implications in nanophotonic sciences and applications. The surface electromagnetic wave holography method is applied to designed grooves on a metal surface for coupling a plane wave in free space to complicated wavefront SPP waves. The grooves illuminated by the plane wave incident from free space serve as secondary SPP waves sources, that radiate cylindrical SPP waves. New controllable wavefronts originate from these secondary SPP waves interfering with each other, based on the Huygens–Fresnel principle. Several applications of the method are demonstrated, such as converting coupling waves in free space into focusing SPP waves on a metal surface.

Chinese Optics Letters
Feb. 10, 2015, Vol. 13 Issue 2 020501 (2015)
Filament diameter measurement system based on dual diffraction
Songtao Yang, Bo Chen, Bin Lin, and Xiangqun Cao

This Letter proposes a brand-new filament diameter measurement method based on what is called “dual diffraction,” in that a grating is added behind the filament to make full use of its subdivision and amplification characteristics. Higher measurement accuracy is achieved by this method compared with the traditional diffraction method. To verify its accuracy, three standard filaments with nominal values of 100.2, 120.1, and 140.8 μm are measured by the dual diffraction method and traditional diffraction method under the same experimental conditions. The relative measurement errors of the new method are less than 0.75%, and its average relative error is reduced by 56% compared with the traditional diffraction method.

Chinese Optics Letters
Dec. 10, 2015, Vol. 13 Issue 12 120501 (2015)
Free-space optical data links based on coaxial sidelobe-modified optical vortices
Meng Zhang, Ping Jia, Yuru Li, Ting Lei, Zhaohui Li, and Xiaocong Yuan

We propose and demonstrate free-space optical data links based on coaxial sidelobe-modified optical vortices (CSMOVs). In contrast to the optical communication systems based on amplitude, frequency, or phase detection, the proposed scheme uses the radii ratio between the principle ring and the first sidelobe of the CSMOV. Therefore, the demand of stringent alignment and/or accurate phase matching is released. We design and optimize a composite computer-generated hologram to generate a CSMOV with four topological charges (TCs). Extracted from the images captured by a CCD camera, the radii ratio between the principle ring and the first sidelobe of different TCs are consistent with the theoretical values.

Chinese Optics Letters
Oct. 10, 2015, Vol. 13 Issue 10 100502 (2015)
Symmetrical short-period and high signal-to-noise ratio heterodyne grating interferometer
Cunbao Lin, Shuhua Yan, Zhiguang Du, Guochao Wang, and Chunhua Wei

A symmetrical heterodyne grating interferometer with both a short period and high signal-to-noise ratio is proposed. It possesses good immunity to environmental disturbances and can simultaneously achieve high resolution and stability. The experimental results show that the standard deviation of 24.67 nm can be realized for the long range of 10 mm. The measurement resolution of better than 2 nm is achieved with the theoretical resolution of 12 pm. Additionally, system stability at less than ±1.5 nm is obtained in just over 10 min. The measurement errors, including cosine error, nonlinear error and non-common path error, are discussed as well.

Chinese Optics Letters
Oct. 10, 2015, Vol. 13 Issue 10 100501 (2015)
Design and fabrication of thin-film spatial filter
Ying Zhang, Hongji Qi, Kui Yi, Yanzhi Wang, Hongbo He, and Jianda Shao

The combination of lens and pinhole limits the enhancement of the laser output power in the high-power laser system. Low-pass spatial filter without focusing can surmount the drawbacks of the pinhole filters. The low-pass spatial filters based on multilayer dielectric film are analyzed and their filtering performances are validated. The non-focusing low-pass spatial filter is successfully explored to substitute for the focusing one. The design method is based on phase-shifted Rugate thin-film spatial filter, narrow bandpass filter and the combined device of long-wave-pass and short-wave-pass cutoff filters, and the angular spectrum bandwidth of bandpass filter are up to submillimeter radians. We mainly discuss three design methods and point out their advantages and disadvantages to find out the best one. The experimental results show that the effects of random and system error during depositing the filter is mainly responsible for the deviation of the designed and measured values.

Chinese Optics Letters
Sep. 10, 2014, Vol. 12 Issue s2 S20501 (2014)
High Performance and Compact 1×3 Beam Splitter Based on Parallel Silicon Waveguide
Junbo Yang, Suzhi Xu, Kuo Zhou, and Jia Xu

We propose a novel and compact broadband 1×3 beam splitter (BS), which is based on optical tunneling between neighbor and parallel waveguides; thus, it is used to couple energy from one waveguide to another. This device consists of three parallel planar waveguides, in which the energy is transferred in a coherent fashion, so that the direction of propagation is maintained. For complete energy transfer to occur between the neighbor waveguides, they must have identical propagation constants. Thus, indices and height of the waveguide layers are controlled very carefully to provide matching propagation constants. The total length of BS is only about 7 μm. The simulation and analysis show that the BS for transverse magnetic (TM) light at a wavelength of 1.55 μm is designed to split incident light into three beams, whose power is 20, 34, and 18%, respectively. The wavelength bandwidth reaches up to 52 nm with an increase in wavelength from 1.49 to 1.542 μm, in which the maximum power difference of three output ports is less than 10%; moreover, the minimum is nearly 0. BS designed here particularly suits for optical communication and optical information processing.

Chinese Optics Letters
Mar. 20, 2014, Vol. 12 Issue s1 S10501 (2014)
Generation of concentric multi-ring laser beam pattern with dif ferent intensity distribution
Shuzhen Nie, Jin Yu, Gang Yu, Qiaofeng Tan, and Zhongwei Fan

A method to shape the incident laser beam into a concentric multi-ring pattern with different intensity distribution is presented based on geometrical transform method and energy conservation. The output two and three rings are designed as examples to verify the validity of the method. The real shaped rings are produced by the spatial light modulation (SLM) and the experimental results show that the shaped laser beam can satisfy the design requirements.

Chinese Optics Letters
Jul. 17, 2013, Vol. 11 Issue s2 S20501 (2013)
Simplified mode analysis of guided mode resonance gratings with asymmetric coatings
Jun Wu, Changhe Zhou, Hongchao Cao, Anduo Hu, Wenting Sun, and Wei Jia

A simplified modal method to explain the resonance phenomenon in guided mode resonance (GMR) gratings with asymmetric coatings is presented. The resonance observed is due to the interaction of two propagation modes inside the grating. The reflectivity spectra and electric field distributions calculated from the simplified modal method are compared using rigorous coupled-wave analysis (RCWA). The influences of high-order evanescent modes on the resonance peak are analyzed. A matrix Fabry-Perot (FP) resonance condition is developed to evaluate the resonance wavelength. An explanation for the resonance phenomenon observed based on the FP resonance phase condition is also proposed and demonstrated. The simplified method provides clear physical insights into GMR gratings that are useful for the analysis of a variety of other resonance gratings.

Chinese Optics Letters
Apr. 29, 2013, Vol. 11 Issue 6 060501 (2013)
Dual beam deflection of liquid crystal optical phased array
Fei Pan, Lingjiang Kong, Xiaobo Yang, Yue Ai, and Yan Zhou

Dual beam deflection models based on one dimensional liquid crystal optical phased array (LCOPA) are discussed and compared in this letter. The far-field diffraction performance of the models is influenced by various impact factors, such as fill factor and fringing electric fields. For optimizing far-field diffraction performance, the combined influence of different impact factors is analyzed and a phase iterative algorithm which use the root-mean-square (RMS) phase deviation as a performance index is presented. The proposed algorithm is able to reduce phase deviation and improve the performance of far-field diffraction pattern at the same time. The simulation and experiments used in the letter effectively verify the proposed algorithm.

Chinese Optics Letters
Dec. 20, 2012, Vol. 10 Issue s2 S20502 (2012)
Modeling and analysis of liquid crystal optical phased array
Lingjiang Kong, Zhenhua Lin, Feng Xiao, and Yue Ai

A comprehensive physical model describing the dependence of the steering performances on the various physical parameters of a liquid crystal optical phased array (LCOPA) is proposed. Then several typical factors affecting the steering performances of the LCOPA are investigated. The quantificational computation and simulation of the influence factors are discussed in details, the relationship between key performances of LCOPA with the influence factors are analyzed numerically, and the optimization methods are conducted based on analysis results. Finally, the experimental results of laser are compared with the simulation results based on the comprehensive model, the simulation far-field diffraction patterns are basically accord with experimental photographs.

Chinese Optics Letters
Nov. 09, 2012, Vol. 10 Issue s2 S20501 (2012)
Pure-phase apodizer for generating double ring-shaped focuses
Jiannong Chen, Qinfeng Xu, and Gang Wang

We propose two design methods of concentric multi-belt pure phase apodizer and phase modulation functions for generating two ring-shaped focuses by focusing the linearly polarized doughnut-shaped beam with a high numerical aperture objective. The phase modulation functions for odd and even belt are verified effectively by numerical simulation. The distance of the two focuses and the position of each focus can be controlled or separately adjusted by the use of liquid crystal spatial phase modulation. It could be useful in optical trapping, particle stacking, alignment and transportation.

Chinese Optics Letters
May. 16, 2012, Vol. 10 Issue s1 S10501 (2012)
Ef fect of shape, height, and interparticle spacing of Au nanoparticles on the sensing performance of Au nanoparticle array
Junhua Li, Qiang Kan, Chunxia Wang, and Hongda Chen

The effect of shape, height, and interparticle spacing of Au nanoparticles (NPs) on the sensing performance of Au NP array is systematically investigated. Lengthening the major axis of elliptical NPs with the minor axis kept constant will cause the redshift of the local surface plasmon (LSP) resonance mode, enhance the sensitivity, and widen the resonance peaks. Larger height corresponds to smaller LSP resonance wavelength and narrower resonance peak. With each NP size unchanged, larger interparticle spacing corresponds to larger resonance wavelength and smaller full-width at half-maximum (FWHM). Moreover, duty cycle is important for sensitivity, which is largest when the duty cycle is 0.4.

Chinese Optics Letters
Jun. 16, 2011, Vol. 9 Issue 9 090501 (2011)
Multimode resonance bandpass filter with twin wideband channels
Zhenhua Wang, Yonggang Wu, Zihuan Xia, Renchen Liu, Gang Lv, Heyun Wu, and Pinglin Tang

A bandpass filter with twin wideband channels in a single-layer guided-mode resonance grating is presented. Strong refractive-index modulation is used to support the excitation of multimode resonances TE1,0, TE1,1, TE2,0, TE1,2, and TE2,1, which are excited by the first and second diffraction orders, relate asymmetrical line shapes and broad low-transmission bands, where TE is the transverse electric. Taking advantage of narrow linewidth and sharp edge line shape in the spectra of TE2, (v is the mode), a bandpass filter with form factors of 0.61 and 0.7 for long- and short-wave channels is presented to demonstrate this concept.

Chinese Optics Letters
Jun. 16, 2011, Vol. 9 Issue 8 080501 (2011)
Reflex optical sensor based on dual metal gratings with high angular sensitivity
Ji Xu, Chen Cheng, Qiang Bai, Jing Chen, and Jianping Ding

An interesting reflection phenomenon in a dual metal grating (DMG) structure is studied, which is related to the competition between Fabry-Perot (F-P) resonance effect and evanescent-field coupling effect inside the gap between the two composing single metal gratings. This competition leads to high angular sensitivity in response to the refractive index variation of the sample solution in the gap. A reflex optical sensor with high sensitivity based on DMG for detecting the change in refractive index is proposed and its performance theoretically is discussed.

Chinese Optics Letters
Jul. 09, 2021, Vol. 9 Issue 6 060501 (2011)
Wave breaking in tapered holey fibers
Shuguang Li, Lei Zhang, Bo Fu, Yi Zheng, Ying Han, and Xingtao Zhao

We numerically study the propagation of 1-ps laser pulse in three tapered holey fibers (THFs). The curvature indices of the concave, linear, and convex tapers are 2.0, 1.0, and 0.5, respectively. The central wavelength, located in the normal dispersion regime, is 800 nm. The nonlinear coefficient of the THFs increases from the initial 0.095 m

Chinese Optics Letters
Jul. 09, 2021, Vol. 9 Issue 3 030601 (2011)
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