Design of retrodiffraction gratings for polarization-insensitive and polarization-sensitive characteristics by using the Taguchi method

We present the design of retrodiffraction gratings that utilize total internal reflection (TIR) in a lamellar configuration to achieve high performance for both TE and TM polarized light and polarization-sensitive performance for gratings behaving as polarizer filters; the design was based on rigorous coupled wave analysis (RCWA) and the Taguchi method. The components can thus be fabricated from a single dielectric material and do not have to be coated with a metallic or dielectric film layer to enhance the reflectance. The effects of the structural and optical parameters of lamellar gratings were investigated, and the TIR gratings in a lamellar configuration were structurally and optically optimized in terms of the signal-to-noise ratio (S/N) and a statistical analysis of variance (ANOVA) of the refractive index, grating period, filling factor, and grating depth as control factors and the estimated efficiency by RCWA as a noise factor. For more accurate robustness, a two-step optimization process was used for each purpose. For TIR gratings designed to perform similarly for TE and TM incident polarization, the -1st-order efficiencies were estimated to be up to 92.0% and 88.5% for TE and TM polarization, respectively. Also, for the TIR gratings designed to achieve polarization-sensitive performance when behaving as a polarizer filters, the -1st-order diffraction efficiencies for TE and TM polarization were estimated to be up to 95.5% and 2.7%, respectively. From these analysis results, it was confirmed that the Taguchi method shows feasibility for an optimization approach to a technique for designing optical devices.     

Analysis and design of a concave diffraction grating with total-internal-reflection facets by a hybrid diffraction method

A novel hybrid diffraction method is introduced to simulate the diffraction and imaging of a planar-integrated concave grating that has total internal reflection (TIR) facets. The Kirchhoff-Huygens diffraction formula is adopted to simulate the propagation of the lightwave field in the free-propagation region, and a rigorous coupled-wave analysis is used to calculate the polarization-dependent diffraction by the grating. The hybrid diffraction method can be used to analyze accurately the imaging properties as well as the polarization-dependent diffraction characteristics of a concave grating. The dependence of several merit parameters of a concave grating with TIR facets on its basic geometric parameters is studied. Compared with one with metallic echelle facets, a concave grating with TIR facets shows a much lower polarization-dependent loss. Since more performance specifications can be considered in the design of a concave grating than with the conventional scalar method, design error can be reduced greatly with the present hybrid diffraction method.     

Polarization-insensitive high-dispersion total internal reflection diffraction gratings

We report the first experimental realization of total internal reflection (TIR) diffraction gratings. Performance of less than 0.7-dB insertion loss (IL) for both TE and TM polarizations and 0.5-dB polarization-dependent loss (PDL) are predicted over a 50-nm spectral bandwidth with simultaneous fabrication tolerances on the depth and the duty cycle of binary gratings of +/-5% and +/-14%, respectively. Nineteen gratings were fabricated that met these specifications, yielding IL and PDL values less than 0.6 and 0.2 dB, respectively, across the entire 50-nm bandwidth. Measurements made under the Littrow configuration resulted in high efficiency and low PDL across a 100-nm bandwidth, with up to 100% diffraction efficiency within the experimental measurement error.     

Diffraction efficiency of 200-nm-period critical-angle transmission gratings in the soft x-ray and extreme ultraviolet wavelength bands

We report on measurements of the diffraction efficiency of 200-nm-period freestanding blazed transmission gratings for wavelengths in the 0.96 to 19.4 nm range. These critical-angle transmission (CAT) gratings achieve highly efficient blazing over a broad band via total external reflection off the sidewalls of smooth, tens of nanometer thin ultrahigh aspect-ratio silicon grating bars and thus combine the advantages of blazed x-ray reflection gratings with those of more conventional x-ray transmission gratings. Prototype gratings with maximum depths of 3.2 and 6 μm were investigated at two different blaze angles. In these initial CAT gratings the grating bars are monolithically connected to a cross support mesh that only leaves less than half of the grating area unobstructed. Because of our initial fabrication approach, the support mesh bars feature a strongly trapezoidal cross section that leads to varying CAT grating depths and partial absorption of diffracted orders. While theory predicts broadband absolute diffraction efficiencies as high as 60% for ideal CAT gratings without a support mesh, experimental results show efficiencies in the range of ～50-100% of theoretical predictions when taking the effects of the support mesh into account. Future minimization of the support mesh therefore promises broadband CAT grating absolute diffraction efficiencies of 50% or higher.     

High-efficiency metallic diffraction gratings for laser applications

The design and fabrication of large-area, high-efficiency metallic gratings for use in high-power laser systems is described. The gratings exhibit a diffraction efficiency in excess of 95% in the m = -1 order (Littrow mount) and have a high threshold for laser damage. Computations and experimental measurements are presented that illustrate the effect of grating shape and polarization on efficiency. A simple theory for optical damage to metallic diffraction gratings is developed and compared with experimental measurements of the laser-damage threshold over the pulse range from 400 fs to >1 ns.     

Effect of Slab Interfaces on Diffraction of Visible Light by a Thick Volume Grating

Abstract

A theory of visible light diffraction by a volume grating is given for the case when reflection at slab interfaces cannot be neglected. A method of approximate solution of the second-order coupled-wave equations, applicable over a wide range of the grating vector orientation, is proposed. An appropriate boundary-value problem is discussed and solved in the two-wave approximation. The results are analytical and expressed in matrix notation suitable for both transmission and reflection diffraction gratings. Particular attention is given to the diffraction regime that arises in a slanted grating under the total internal reflection of the diffracted wave (TIRDW). Strong transmission anomalies occurring in the vicinity of the TIRDW threshold are established and analysed.     

High-efficiency reflective diffraction gratings in fused silica as (de)multiplexers at 1.55microm for dense wavelength division multiplexing application

We describe high-efficiency, high-dispersion reflection gratings fabricated in bulk fused silica illuminated by incident lights in the C + L bands as (de)multiplexers for dense wavelength division multiplexing (DWDM) application. Based on the phenomenon of total internal reflection, gratings with optimized profile parameters exhibit diffraction efficiencies of more than 90% under TM- and TE-polarized incident lights for 101-nm spectral bandwidths (1520-1620 nm) and can reach an efficiency of greater than 97% for both polarizations at a wavelength of 1550 nm. Without loss of metal absorption, without coating of dielectric film layers, and independent of tooth shape, this new kind of grating should be of great interest for DWDM application.     

Finite-number-of-periods holographic gratings with finite-width incident beams: analysis using the finite-difference frequency-domain method

The effects of finite number of periods (FNP) and finite incident beams on the diffraction efficiencies of holographic gratings are investigated by the finite-difference frequency-domain (FDFD) method. Gratings comprising 20, 15, 10, 5, and 3 periods illuminated by TE and TM incident light with various beam sizes are analyzed with the FDFD method and compared with the rigorous coupled-wave analysis (RCWA). Both unslanted and slanted gratings are treated in transmission as well as in reflection configurations. In general, the effect of the FNP is a decrease in the diffraction efficiency with a decrease in the number of periods of the grating. Similarly, a decrease in incident-beam width causes a decrease in the diffraction efficiency. Exceptions appear in off-Bragg incidence in which a smaller beam width could result in higher diffraction efficiency. For beam widths greater than 10 grating periods and for gratings with more than 20 periods in width, the diffraction efficiencies slowly converge to the values predicted by the RCWA (infinite incident beam and infinite-number-of-periods grating) for both TE and TM polarizations. Furthermore, the effects of FNP holographic gratings on their diffraction performance are found to be comparable to their counterparts of FNP surface-relief gratings.     

Two-fold mechanism of the interaction of incident light with a phase diffraction grating

It is suggested to use antireflection diffraction gratings for introducing light into the active regions of optoelectronic devices. The dependence of the diffraction efficiency on the grating groove depth, which controls the reflection from the optical surface and forms the diffraction order in the material, has been numerically modeled.     

All-dielectric reflection gratings: a study of the physical mechanism for achieving high efficiency

The physical mechanism for the all-dielectric reflection gratings to achieve high efficiency in the -1st-order Littrow mounting is studied. The all-dielectric gratings consist of two parts, a surface-relief grating and a highly reflecting dielectric stack. The surface-relief grating sits on top of the reflecting stack. A simple analytical expression for diffraction efficiency is obtained in terms of the S-matrix elements of the two parts. By analyzing the expression we show that the diffraction can be interpreted as the interference of a symmetric wave and an antisymmetric wave. The conditions for achieving high diffraction efficiency are also identified. The analytical results are illustrated by numerical computations.     

Extreme-ultraviolet efficiency measurements of freestanding transmission gratings

We report new, near-normal-incidence, transmission grating efficiency results at selected extreme-ultraviolet wavelengths between 4.5 and 30.5 nm for two transmission gratings, one with a period of 200 nm and the other with a period of 400 nm. These gratings consist of opaque gold bars separated by open spaces that have been produced by photolithography techniques commonly used to produce electronic components. The gold bars and the open spaces are nominally of the same width. Both gratings have a thickness of 470 nm. The transmission efficiency at the central, first, and, when possible, second order of diffraction was measured. In addition, guided-wave phenomena at nonnormal angles of incidence, as well as transmission differences depending on which side of the grating was illuminated, were investigated. The observed guided-wave effects allow one to selectively enhance the transmission of the grating at desired wavelengths, as is realized with a blazed reflection grating.     

Action from tunable periodic structures. II. Experimental observation of electric field-induced diffraction peaks

As previously predicted [Appl. Opt. 40, 5583 (2001)], we have now observed electric field-induced diffraction peaks in transmission and reflection experiments by use of a LiNbO3 sample with interdigital planar electrodes that serve as a diffraction grating. The magnitudes of the new peaks in the reflection experiments are ten times larger than those in the transmission experiments. We interpret these effects in terms of a field-induced refractive-index change produced by the linear electro-optic effect. The positive and negative changes in the refractive index produce two diffraction gratings that are period doubled with respect to the original grating and that have a phase difference between them. The superposition of the diffracted light from these gratings is shown to account for the new peaks. From the relative magnitude of the new peak to that of the central peak, we estimate the refractive-index change to be 0.004.     

改善MEMS闪耀光栅衍射效率的研究

研究了在硅材料上利用MEMS (Micro-Electro-Mechanical System)的各向异性腐蚀技术制备 闪耀光栅。采用氧化削尖工艺去除光栅制备过程中掩膜在闪耀面上留下的平台,得到一个连续的闪耀面;同时对闪耀面进行表面抛光,改善闪耀面的粗糙度,减小对入射光的散射。理论分析和实验测试证明,该工艺方法能够将MEMS闪耀光栅的衍射效率提高10%左右。     

Diffraction properties of volume holographic gratings for an ultrashort pulsed beam with different polarization states readout

The diffraction properties of volume holographic gratings are studied when the gratings are illuminated by an ultrashort pulsed beam with different polarization states. The developed coupled wave theory of Kogelnik is used. Considering the dispersion effect of the grating media, solutions for the diffracted and transmitted intensities, diffraction efficiencies and the bandwidths of the gratings are given in transmission volume holographic gratings and reflection volume holographic gratings. The bandwidths of the gratings are reduced by the dispersion effect of the grating media. They also have different influences on the diffraction of an ultrashort pulsed beam with different polarization states. For different values of the ratio of the spectral bandwidth of the input pulse to that of the grating, the changes of the spectral and temporal distributions of the diffracted intensities, as well as the diffraction efficiencies of the gratings are shown.     

Development of multilayer laminar-type diffraction gratings to achieve high diffraction efficiencies in the 1-8 keV energy region

W/C and Co/SiO(2) multilayer gratings have been fabricated by depositing a multilayer coating on the surface of laminar-type holographic master gratings. The diffraction efficiency was measured by reflectometers in the energy region of 0.6-8.0 keV at synchrotron radiation facilities as well as with an x-ray diffractometer at 8.05 keV. The Co/SiO(2) and W/C multilayer gratings showed peak diffraction efficiencies of 0.47 and 0.38 at 6.0 and 8.0 keV, respectively. To our knowledge, the peak efficiency of the W/C multilayer grating is the highest measured with hard x rays. The diffraction efficiency of the Co/SiO(2) multilayer gratings was higher than that of the W/C multilayer grating in the energy range of 2.5-6.0 keV. However, it decreased significantly in the energy above the K absorption edge of Co (7.71 keV). For the Co/SiO(2) multilayer grating, the measured diffraction efficiencies agreed with the calculated curves assuming a rms roughness of approximately 1 nm.     

Submicrometer gratings for solar energy applications

Diffractive optical structures for increasing the efficiency of crystalline silicon solar cells are discussed. As a consequence of the indirect band gap, light absorption becomes very ineffective near the band edge. This can be remedied by use of optimized diffraction gratings that lead to light trapping. We present blazed gratings that increase the optically effective cell thickness by approximately a factor of 5. In addition we present a wideband antireflection structure for glass that consists of a diffraction grating with a dielectric overcoat, which leads to an average reflection of less than 0.6% in the wavelength range between 300 and 2100 nm.     

Optimization of a rhomb-type quarter-wave phase retarder

Apreviously reported two-reflection, undeviating-beam total internal reflection (TIR) quarter-wave phase retarder is optimized. The specifications and characteristics of the device are sensitive to the refractive index n of the rhomb material. In particular, the size of the rhomb can be reduced by a factor of 11 for the same aperture size if a glass with n = 1.70 is used instead of one with n = 1.53. Optimal conditions are in the refractive-index interval n = 1.68-1.71. Coated rhombs of this type are mentioned.     

Polarization-dependent diffraction efficiency of a photorefractive volume grating and suppression of this efficiency

In terms of refractive-index ellipsoid of a uniaxial crystal, the relationship between the diffraction efficiency of a volume grating and the polarization state of a readout beam is theoretically analyzed. The direction of a refractive light beam and the corresponding refractive-index modulation will both be changed by a variation of the polarization state. In the polarization state of the readout beam, which may lead to a strong variation in the diffraction efficiency of the volume grating. This kind of polarization-dependent diffraction efficiency of a volume grating in an anisotropic crystal is extremely disadvantageous for some applications. A method to suppress the polarization-dependent diffraction efficiency by use of double volume gratings is presented, and experiments with LiNbO3:Fe crystal are also demonstrated. The experimental results indicate that this method can well suppress the polarization-dependent diffraction efficiency of a volume grating. Furthermore, the diffraction properties of the double volume gratings are almost independent of the polarization state of the readout beam. The relative values of the diffraction peaks are calculated on the basis of the relationship between index modulation and the state of polarization. The experimental values are in good agreement with the theoretical analyses.     

Crossed phase gratings with diffractive optical elements

Orienting two identical or complementary diffractive gratings with a small angle between the grating grooves allows a new crossed-grating device to be constructed. This device has an effective profile that varies locally. For understanding the effects of this variation and the diffraction efficiency of the gratings, the local profiles were correlated with the moiré period of the crossed-grating system by use of various techniques. Asymmetric intensity behavior in the first order of the crossed gratings was seen. Effectively, the diffraction efficiency of the crossed gratings yielded a response equivalent to that of a grating with variable blaze that could be useful in optical computing as a passive optical switching device. One of several models is described that creates greater asymmetric behavior.     

Holographic patterning of luminescent photopolymer nanocomposites

Volume phase gratings in the photopolymerisable composites, containing luminescent nanoparticles have been fabricated for the first time. Nanoparticles of LaPO₄, doped by Ce³⁺ and Tb³⁺ ions (the trade name is REN-X-green) with high luminescence quantum yield were used as a luminescent inorganic additive. The holographic gratings in such materials are formed as a result of the diffusion distribution of the nanoparticles during exposure of photopolymerisable composites to interference pattern. The influence of the pre-polymer formulation and the holographic patterning parameters on the grating formation is comprehensively investigated. The use of the optimised pre-polymer syrup containing two monomers with sufficiently different polymerisation rates allows fabrication of gratings with diffraction efficiency up to 80% at low optical losses (< 5%) (20 μm film thickness). To obtain maximum diffraction efficiency the intensity and the period of the interference pattern were optimised for each formulation. In addition maximum diffraction efficiency was achieved with the nanocomposites containing 30–32 wt.% of nanoparticles. On the other hand the highest possible modulation of the nanoparticles' concentration was obtained for the concentration of about 20 wt.%. In this case maximum ordering of the nanoparticles in the polymer matrix is achieved. The photoluminescence of the nanoparticles within the homogeneous polymer film and within the grating has been measured. The example application of the photopolymerisable composite containing luminescence inorganic nanoparticles in holographic security technology has been demonstrated.