Design, Fabrication and Test of a Soft X-Ray Even-Order Transmission Grating

Most transmission gratings in the x-ray region work with their first orders and dispersion is limited by the line density achievable with current fabrication technology. We present a novel design of a two-dimensional x-ray transmission grating. The grating works with higher dispersion using its second orders, and the influence from first and third orders can be suppressed. A grating according to the novel design is fabricated and its diffraction performance is tested in comparison with a traditional x-ray transmission grating with the same line density. The novel grating could be especially useful when high dispersion is desired while the fabrication of high-density gratings becomes more difficult.     

Analysis of restriction factors of widening diffraction bandwidth of multilayer dielectric grating

In order to design a multilayer dielectric grating with wide-bandwidth diffraction spectrum, the restriction factors of both the reflection bandwidth of multilayer dielectric high-reflectivity mirror and the guided-mode resonance phenomenon are studied in detail. The reflection characteristics of high-reflectivity mirror in zeroth and 1st transmitted diffraction orders are quantitatively evaluated. It is found that the reflection bandwidth of high-reflectivity mirror in 1st transmitted diffraction order, which determines the final diffraction bandwidth of multilayer dielectric grating, is evidently compressed. Furthermore, it is demonstrated that the reducing of grating period is an effective approach to the elimination of guided mode resonance over a required broad band range both spectrally and angularly. In addition, the expressions for calculating the maximum period ensuring no guided mode resonance in the required bandwidth are derived. Finally, two high-efficiency pulse-compression gratings with broad-band are presented.     

Broadband Terahertz Polarization Converter and Asymmetric Transmission Based on Coupled Dielectric‐Metal Grating

Coupled dielectric‐metal gratings are investigated for broadband terahertz (THz) wave polarization conversion and asymmetric transmission by the experiments and numerical simulations, which are composed of the subwavelength Si grating and metallic wire grating layers. The dielectric grating layer with a large artificial birefringence and low dispersion is employed as a phase engineered waveplate, and the metal wire grating arranged with a 45° angle to the dielectric grating is utilized as a high‐efficiency polarizer. Due to the subwavelength integration, this coupled grating presents a local resonance coupling mechanism between dielectric and metal gratings, which greatly enhances the polarization rotation and expands the bandwidth, not a simple combination with dielectric and metallic gratings. The results demonstrate that a broadband asymmetric transmission with an extinction ratio of 30dB from 0.2 to 1.2 THz is achieved and the highest transmission of 90% can be obtained. It provides a simple way towards practical applications for THz artificial dispersion materials, polarization control and asymmetric transmission.     

Polarizing beam splitter of deep-etched triangular-groove fused-silica gratings

We investigated the use of a deep-etched fused-silica grating with triangular-shaped grooves as a highly efficient polarizing beam splitter (PBS). A triangular-groove PBS grating is designed at a wavelength of 1550 nm to be used in optical communication. When it is illuminated in Littrow mounting, the transmitted TE- and TM-polarized waves are mainly diffracted in the minus-first and zeroth orders, respectively. The design condition is based on the average differences of the grating mode indices, which is verified by using rigorous coupled-wave analysis. The designed PBS grating is highly efficient over the C+L band range for both TE and TM polarizations (>97.68%). It is shown that such a triangular-groove PBS grating can exhibit a higher diffraction efficiency, a larger extinction ratio, and less reflection loss than the binary-phase fused-silica PBS grating.     

Theoretical reflective performance of a sandwiched two-layer grating polarizer

The reflective polarizer is described by a sandwiched two-layer grating with a metal slab. Such a new polarizer is aimed to improve the performance of a reflective grating-based polarizer. The grating is optimized with the usual duty cycle of 0.5, where TE and TM polarizations are reflected in the –1st and the 0th diffraction orders, respectively. With optimized grating parameters, the extinction ratio can reach 45.5 dB and 41.9 dB in two diffraction orders, which are greatly improved compared with the conventional reported surface grating polarizer with the simple structure. Attractive merits of the new design are high efficiency, high extinction ratio, wide incident wavelength bandwidth for TE polarization, and wide angular range for TM polarization. Numerical results are expected to open new opportunities for the design of a grating-based polarizer with the enhanced performance by the complicated grating configuration.     

Peculiarities of spontaneous grating generation in light-sensitive waveguide layers during holographic grating formation

The generation of spontaneous (noise) gratings during the simultaneous formation of a holographic grating in thin (on the order of the cutoff thickness of the TE₀ waveguide mode) AgCl-Ag films by two laser beams with λ = 532 nm and polarization vectors that make an angle of 45° with the plane of incidence have been studied. The electron microscopy images and diffraction patterns have revealed a significant difference of the spontaneous-grating structure from the structure obtained under irradiation by one laser beam. The spontaneous gratings have a significant spread in the directions of their wave vector, and the diffraction pattern (recorded using a probe beam with λ = 337 nm) has the form of a bundle of diverging arcs that intersect at one point. This difference is caused by self-diffraction from the holographic grating, which is responsible for the main diffraction peaks with odd orders, the growth of spontaneous gratings because of the interference of the beams diffracted by the holographic grating with the waveguide TE₀ modes scattered in the film, and silver transport to the interference minima. The diffraction patterns are quantitatively analyzed and the period of the new (formed under two-beam irradiation) spontaneous gratings is calculated. The calculation results are in good agreement with the experimental data.     

Surface plasmon resonance transmission filters at 1053nm based on metallic grating with narrow slit

Metallic gratings with narrow slits can lead to special optical properties such as strongly enhancing the transmission and considerably strengthening the polarized effect. A narrow-band filter suitable for application in optical communication is designed by sandwiching a metallic grating between two identical dielectric films. The maximum transmission can reach 96% after optimizing the parameters of films and grating at a central wavelength of 1053 nm. It is the first time, to our knowledge, that such high transmission has been reported since the discovery of the extraordinarily high transmission through periodic holes or slits; moreover, the extremely polarized effect is also found in P mode of this symmetric grating.     

Optimal design of sub-wavelength metal rectangular gratings for polarizing beam splitter based on effective medium theory

A novel optimal design of sub-wavelength metal rectangular gratings for the polarizing beam splitter (PBS) is proposed. The method is based on effective medium theory and the method of designing single layer antireflection coating. The polarization performance of PBS is discussed by rigorous couple-wave analysis (RCWA) method at a wavelength of 1550~nm. The result shows that sub-wavelength metal rectangular grating is characterized by a high reflectivity, like metal films for TE polarization, and high transmissivity, like dielectric films for TM polarization. The optimal design accords well with the results simulated by RCWA method.     

The Effect of Radiation on Transmission of Quasi-Periodic Multi-Layer Planar Dielectric Gratings

The transmission characteristics of quasi-periodic multi-layer planar dielectric gratings are systematically investigated by a method that combines the multimode network theory with rigorous mode matching method. The effect of radiation on the transmission characteristics of the multi-layer dielectric gratings is discussed in details, and some guidelines are given for accurate design of the gratings.     

Unified design of wavelength-independent deep-etched fused-silica gratings

We present a unified design of wavelength-independent deep-etched fused-silica gratings as polarizing beam splitters and polarization-independent two-port beam splitters by using the simplified modal method. By defining unified grating parameters as the ratio of incident wavelength to grating period and the ratio of groove depth to grating period, unified grating structures are found to be approximately wavelength-independent, which is based on the modal view of the accumulated phase difference of two excited propagating grating modes. Diffraction efficiencies given by the rigorous coupled-wave analysis (RCWA) verified this unified design at the wavelength of 1064 nm. It should be noted that this unified design of wavelength-independent gratings is an analytic result, which is impossible to be derived with the well-known numerical RCWA. Modal method is powerful and presents a clear physical picture for us to obtain this unified design. Therefore, this unified design can be used as a general guideline for designing deep-etched fused-silica gratings as beam splitters for practical applications from ultraviolet to near infrared.     

Electromagnetic response of a compound plasmonic–dielectric system with coupled-grating-induced transparency

We propose a compound plasmonic–dielectric system consisting of one-dimension metallic gratings made of core–shell membranes and a Si grating waveguide with periodic grooves on one side, to investigate the coupled-grating-induced transparency (CGIT) effect. Both elements of the system can support certain resonant modes respectively, which have almost identical resonant frequencies but highly different quality factors, which are demonstrated by a theory model and the coupled mode theory. The electromagnetic response of the compound plasmonic–dielectric system induces coupling between these two types of gratings resonators and causes a transparency phenomenon due to the destructive interference of the resonant modes. The results show that the CGIT effect is associated with remarkable improvement of the group index corresponding to high transmission efficiency.     

Complete Polarization Conversion Characteristics of Dielectric Grating Composed of Left-Handed Materials

The TE/TM polarization conversion characteristics of dielectric grating composed of left-handed materials for the case of plane wave oblique incidence are carefully investigated by a method which combines the multimode network theory with the rigorous mode matching method. It is indicated that complete polarization conversion between TE and TM modes can be realized using left-handed gratings. This can hardly achieve in the conventional right-handed gratings. Comparisons of polarization conversion properties between right-handed gratings and left-handed gratings are given with physical explanations. This unique merit of left-handed periodic structure is of important significance for accurate design of new millimeter wave TE/TM polarization converters.     

Polarization-independent triangular-groove fused-silica gratings with high efficiency at a wavelength of 1550 nm

We describe polarization-independent triangular-groove fused-silica gratings illuminated by incident lights in the C + L bands as (de)multiplexers for dense wavelength division multiplexing (DWDM) application. The physical mechanisms of the grating can be shown clearly by using the simplified modal method with consideration of the corresponding accumulated average phase difference of two excited propagating grating modes, which illustrates that the grating structure depends mainly on the ratio of the average effective indices difference to the incident wavelength. Exact grating profile is optimized by using the rigorous coupled-wave analysis (RCWA). With the optimized grating parameters, the grating exhibits diffraction efficiencies of greater than 90% under TE- and TM-polarized incident lights for 101 nm spectral bandwidths (1500-1601 nm) and it can reach an efficiency of more than 99% for both polarizations at a wavelength of 1550 nm. Without loss of metal absorption, coating of dielectric film layers, the designed triangular-groove fused-silica grating should be of great interest for DWDM application.     

共振域矩形介质光栅的逆向设计

采用模态法研究了共振域光栅分束器及闪耀光栅等光学器件的设计原理及逆向设计方法,给出了-1级非偏振闪耀光栅的典型设计示例。研究表明,自准直角入射时,光束在光栅内传输将激发产生离散模,通过调节离散模透过光栅传输时的累积相位差,可对衍射光进行调控,实现偏振(非偏振)分束、偏振(非偏振)闪耀等功能。采用严格耦合波法对基于模态法逆向设计的-1级非偏振石英闪耀光栅的几何参数进行验证,计算结果显示两者非常吻合,证明了该方法的正确性。     

Polarization-selective subwavelength grating used with 193 nm light

Hyper-NA ArF (193 nm) immersion lithography is one of the most potential technologies to achieve 32 nm critical dimension node. At the corresponding large angles in the photoresist, control of polarization becomes necessary. A polarization beam splitter (PBS) based on a subwavelength dielectric grating has been designed for use with 193 nm light. The polarization-selective property of such grating is explained by the mechanism of mode interference. The designed grating working as a 1 × 2 beam splitter can transmit TM wave (∼ 90%) to the zeroth order with extinction ratio of 753, and it diffracts TE wave (∼ 80%) to the −1st order with extinction ratio of 300.     

亚波长光栅的偏振闪耀特性

 使用琼斯矩阵的方法推导了连续结构亚波长光栅的衍射方程,给出了光栅衍射效率表达式,对偏振特性与衍射特性进行了研究。发现连续结构亚波长光栅仅存在３个衍射级,总衍射效率为100%,且衍射效率可在衍射级间任意分配,0级的偏振态与入射光的偏振态相同,±1级衍射光偏振态与入射光无关,－1级为左旋圆偏振光,＋1级为右旋圆偏振光。通过设置入射光偏振态与光栅相位延迟等参数,可使光栅具有闪耀特性,据此可用于设计高效偏振光分束器和偏振光开关。     

Thin and thick diffraction gratings: Thin matrix decomposition method

A brief review of the properties of transmission diffraction gratings is presented. Two types of gratings will be analyzed: thin and volume gratings explaining how the efficiency of the different orders that propagate inside the gratings can be calculated in both cases. For thin diffraction gratings the so-called amplitude transmittance method is applied in order to get the amplitude of the different orders, whereas in the case of volume gratings more complex methods are needed, such as Coupled Wave or modal theories. We will comment on the thin matrix decomposition method (TMDM), firstly proposed by Alferness, which gives a very intuitive approach and connects the properties of thin gratings to the properties of volume ones. The thin matrix decomposition method consists in dividing the volume grating in a number of thin gratings and applying the amplitude transmittance method to each thin grating. In this way the output of a grating will be considered as the input of the next and any individual grating can be treated by the amplitude transmittance method. The novelty of this work is that a comparison is made between the analytical expressions obtained by Alferness using the TMDM with the numerical results obtained using the coupled wave (CW) and rigorous coupled wave (RCW) theories for the efficiencies of the zero, first and second order when a plane wave incides onto a sinusoidal diffracion grating at the second on-Bragg replay angular condition.     

长周期光纤光栅(LPFGs)的谱结构研究

利用相位匹配条件,从理论和实验上研究了均匀LPFGs的谱结构特点.结果表明,导模和不同包层模耦合产生的光谱特性有很大差别.在模序较小时,谱宽较小;模序增加,谱宽也增加;在某一模序附近,谱宽达到最大;以后随模序增加,谱宽迅速减小.给出了LPFGs中透射谱的最大损耗率及3 dB带宽与包层模序、光栅周期、耦合系数和栅长的关系.这些关系对设计满足特定最大损耗率和带宽的带阻滤波器或增益均衡器提供一种理论参考.选用不同的包层模、耦合系数和栅长,可以设计出谱宽很大或很小的LPFGs.     

Analysis and design of grating couplers

Based on an accurate perturbation analysis of the guiding properties of dielectric gratings, simple design criteria are developed for grating couplers which transfer the energy of a beam into or out of an optical waveguide. Gratings having arbitrary groove shapes are considered and explicit formulae are given for the leakage parameters of gratings with symmetric profiles. The results cover TE_v and TM_v modes and they apply to both shallow and deep grating grooves. The variation of the leakage parameter α in rectangular gratings is examined in detail; these rectangular gratings are then used as basic configurations for predicting the characteristics of other grating profiles. Particular attention is given to trapezoidal and triangular profiles and gratings with asymmetric profiles are also discussed.     

A reflective surface-relief two-layer grating for splitting beams with the polarization-selective property

A polarization-selective beam splitter is presented based on a reflective surface-relief two-layer grating with a metal slab. The grating is composed of two dielectric layers and a metal slab on the substrate. For TE polarization, efficiencies of 97.58% can be diffracted into the reflective −1st order. For TM polarization, two-port output of 47.55% and 47.11% can be split into the 0th order and the −1st order, respectively. Such a polarization-selective beam splitter can be fulfilled by one grating in reflection. The grating depths of two layers are optimized by using rigorous coupled-wave analysis with the given duty cycle of 0.6 and period of 1100 nm. The performance for different incident conditions is investigated when the incident wavelength and angle deviate from the central wavelength and the Bragg angle, respectively. For TM polarization, good uniformity can still be achieved within the given incident wavelength and angle regions. For TE polarization, the reflective polarization-selective beam splitter can have merits of wideband for different incident wavelengths.