Slanted Gratings Research Articles

Reflection characteristics of obliquely incident surface acoustic waves from groove and aluminum gratings on {100}-cut gallium arsenide

In this article we present an experimental study of the surface acoustic wave behavior of a slanted reflector array on {100}-cut, 〈110〉-propagating GaAs. The thorough examination of both Al stripes and grooves on GaAs unveiled previously unknown information about the behavior of slanted gratings on {100}-cut GaAs. We discovered that etched grooves provide a strong reflection coefficient (C=0.29) while Al stripes do not (C=0.014). These data were obtained from measurements of the reflection characteristics for slanted gratings on GaAs. Potential device applications include an ultralow power acoustic charge transport device which does not require an interdigital transducer.

Compact broadband 5-bit photonic true-time-delay module for phased-array antennas

Photonic true-time-delay (TTD) lines offer many advantages over their electronic counterparts and are attracting more and more research effort. We demonstrate a device with 32 TTD lines (5-bit) based on substrate guided-wave propagation combined with slanted photopolymer volume phase gratings on a quartz substrate. System design, device fabrication, optimization of fan-out intensity uniformity, and device performance evaluation are addressed as well. The device has a measured bandwidth of up to 2.4 THz and a measured fan-out delay step of 50 ps. The fan-out beam intensity uniformity is within +/-10% . The packing density is 2.5 delay lines/cm(2), which is to our knowledge the highest demonstrated thus far.

Substrate mode hologram for optical interconnects

A novel method of substrate mode hologram (SMH) design and fabrication is presented. The coupling between a homogeneous plane wave and an arbitrary free propagating wave is achieved via a total internally reflected (TIR) wave. The input slanted plane grating, recorded in an orthochromatic holographic medium, accomplishes the homogeneous plane wave to TIR wave coupling. The TIR wave is transformed to the free propagating wave by the output aperiodic aplanar inhomogeneous grating recorded in a panchromatic holographic medium. Aberration-free conversion between the incident plane wave and the Gaussian wave is reported for coupling efficiency of 57%.

Design and fabrication of binary slanted surface-relief gratings for a planar optical interconnection

We propose the use of binary slanted surface-relief gratings with parallel-groove walls as input and output couplers in a planar optical interconnect. Parametric optimization of cascaded output couplers is employed to design an interconnect consisting of N output couplers producing a uniform intensity distribution with a high efficiency that may be realized in one lithographic etching step. The sensitivity of a N = 4 interconnect to various fabrication errors is analyzed. We demonstrate the operation of a slanted surface-relief grating manufactured with electron-beam lithography and reactive-ion etching for an operating wavelength of lambda = 0.633 mum.

Holographic recording characteristics of an acrylamide-based photopolymer

Recent research on an acrylamide-based photopolymerizable holographic recording material is presented. The recording characteristics of the material are discussed in detail in terms of sensitivity, diffraction efficiency, recording linearity, resolution limit, and sources of noise. Although the resolution is not sufficient for reflection holography, the recording characteristics are excellent for transmission gratings. The material was found to suffer no shrinkage during recording, and high-diffraction-efficiency slanted gratings were made. Finally, the suitability of this self-developing material to both double-exposure and real-time holographic interferometry is demonstrated.

Simple measuring technique for the diffraction efficiency of slanted volume gratings at various wavelengths

To measure diffraction efficiencies of gratings as a function of wavelength, it is necessary to have quasi-monochromatic light sources of various wavelengths. We propose a method to measure the wavelength dependence of the grating diffraction efficiency by using a quasi-monochromatic light source. This method of estimating the real diffraction characteristics of the gratings for various wavelengths is very useful and simple. First the diffraction efficiency of the grating as a function of various incident-beam angles of monochromatic light is measured, then, using these data, we can obtain the diffraction efficiencies for various wavelengths of the same incident angle of light by virtue of a mathematical-conversion method. The mathematical-conversion results for two laminated differently slanted angle gratings of the same volume grating period are in good agreement with the experimental ones.

Measurement of the spatial phase shift in high-gain photorefractive materials

The correct determination of the spatial phase shift ø(p) in photorefractive materials is crucial to the proper characterization of novel materials. It is shown that the grating translation techniques commonly used for the measurement of ø(p) need to be reevaluated for high-gain materials. Strong energy and phase coupling leads to nonuniform slanted gratings, which result in an apparent dependence of the phase shift of the beam ratio and the optical polarization. A revised theory is presented, and analytical solutions are obtained for the special case of ø(p)?pi/2 . Numerical solutions for arbitrary ø(p) are in good agreement with measurements in a photorefractive polymer.

Scattering analysis of slanted fiber gratings

The diffraction efficiency of a tilted in-core fiber grating is analyzed with the scattering formalism and the first Born approximation. Without any prior physical assumptions about the shape or direction of the scattered wave, it is shown that diffraction occurs when the so-called Bragg conditions are nearly satisfied and the interaction process can be described by a pair of coupled first-order differential equations that are exactly the same as those obtained through the coupled-mode analysis.

High packing density 2.5 THz true-time-delay lines using spatially multiplexed substrate guided waves in conjunction with volume holograms on a single substrate

A 3-bit true-time-delay lines device having a packing density of 5 lincs/cm/sup 2/ with a minimum delay step of /spl sim/100 ps is designed, fabricated and demonstrated. This device is based on substrate guided wave propagation combined with slanted photopolymer volume phase gratings. In this paper, we report the delay and bandwidth measurements for the 3-bit delay lines fabricated on BK-7 glass substrates with a substrate bouncing angle of 45/spl deg/. The power fluctuation among the outputs due to the cascading fanout effect (a serious drawback for real system applications) is experimentally investigated as well. A power fluctuation controlled to within /spl plusmn/10% is achieved. A femtosecond laser pulse is sent through the device and a bandwidth measurement of up to 2.5 THz is obtained. The delay step is measured by employing an ultrafast photodetector together with a sampling scope. The true-time-delay device presented herein has the potential to be integrated with photodetector arrays due to its planar structure on a single substrate together with the surface normal fan-in and fan-out features.

Large fanout optical interconnects using thick holographic gratings and substrate wave propagation

Substrate wave propagation and Bragg diffraction by multiplexed holographic gratings have been used to demonstrate a new 1-to-30 fanout optical interconnect having an overall diffraction efficiency of 87.8% at 514.5 nm and an individual channel efficiency of approximately 3.0 +/- 0.8%. The device configuration utilizes the large multiplexing capability of dichromated gelatin polymer films and substrate total internal reflection to realize large channel fanouts within the plane of a soda-lime glass substrate. A simplified theoretical formulation is presented to treat the corresponding three-dimensional holographic diffraction problem in the Bragg regime for slanted phase gratings. Results are compared with experimentally measured quantities for singly exposed phase gratings in different polarization conditions and incident angle orientations. The limitations of using multiplexed holograms in multiplanar substrate interconnection applications are also discussed.

Bragg diffraction in the vicinity of Wood anomalies

Bragg diffraction of electromagnetic waves from slanted volume holographic gratings with the diffracted beam approaching grazing incidence has been studied. In particular, interesting nonanalytic perturbation behavior was obtained by using a coupled-wave analysis. Additionally, a perturbation approach is presented for completeness.

Rigorous 3-D coupled wave diffraction analysis of multiple superposed gratings in anisotropic media

The diffraction by two planar slanted fringe gratings superposed in the same volume of an anisotropic medium is treated using rigorous 3-D vector coupled wave analysis. Arbitrary angle of incidence and polarization are included. Both phase and/or amplitude slanted gratings in anisotropic media are treated in the analysis. The external boundary regions can be either isotropic (for bulk applications) or uniaxial anisotropic (for integrated applications). Both forward- and backward-diffracted orders are characterized by a number pair (i(l),i(2)), where i(l) and i(2) are integers. The Floquet condition is discussed for the case of two superposed gratings. When the external regions are anisotropic, each diffracted order has an ordinary (O), and an extraordinary (E) component. The analysis is also generalized for an arbitrary number of superposed gratings. The numerical complexity is discussed. In the case of equal grating periodicities along the boundaries, the diffracted orders become degenerate in the external regions. In this case, an alternative analysis that utilizes a cascaded stack of unslanted gratings can be used. Limiting cases are also presented. The various Bragg conditions are identified and quantified. Sample calculations presented include the quantification of the crosstalk between two superposed gratings, the evaluation of the effects of coupled Bragg conditions in beam combining applications, design and analysis of a beam splitter and a beam combiner, demonstration of the use of a cascaded stack of unslanted gratings of constant modulation to represent two superposed gratings that have the same periodicity along the boundaries, and finally evaluation of the effect of the phase difference between two gratings. The same analysis applies in the limiting cases of isotropic materials, single slanted gratings, etc. Applications of this analysis include optical storage, optical digital truth table look-up processing, neural nets, optical interconnects, beam splitting, and beam combining.

Analysis of acoustic-wave detection sensitivity using Bragg-regime diffraction gratings

The application of slanted Bragg-regime diffraction gratings as wave mixers to detect weak acoustic waves is analyzed. The expression for the amplitude-modulated output intensity is given, and the signal-to-noise ratio in the shot-noise limit is obtained. The minimum detectable acoustic grating strength is shown to be of the order of 10−7 rad/Hz1/2.

Rigorous three-dimensional coupled-wave diffraction analysis of single and cascaded anisotropic gratings

The diffraction by one or an arbitrary number of cascaded anisotropic planar gratings with slanted fringes is analyzed by using rigorous three-dimensional vector coupled-wave theory. Arbitrary angle of incidence and polarization are treated. The existence of uniaxial external regions and the treatment of both phase and amplitude anisotropic slanted gratings are included in the analysis. The anisotropy and the three-dimensionality of the problem cause coupling between orthogonally polarized waves. The Bragg conditions for various combinations of ordinary (O) and extraordinary (E) polarized waves are quantified. Sample calculations are presented for single anisotropic gratings (a lithium niobate hologram in air and an interdigitated-electrode-induced electro-optic grating in an optical waveguide), for two cascaded anisotropic gratings (a pair of interdigitated-electrode-induced gratings satisfying the OOO forward Bragg condition, the EEE forward Bragg condition, and the OOO backward Bragg condition), and for multiple cascaded gratings (a lithium niobate hologram with depth modulation). The same analysis applies in the limiting cases of isotropic materials, a grating vector lying in the plane of incidence, etc. Applications for this analysis include optical storage, switching, modulation, deflection, and data processing.

Theoretical diffraction efficiency for slanted uncoupled absorption multiplex holograms

Analytical solutions describing the reconstruction obtained from a multiplex hologram that has been made with two incoherent holographic exposures are presented. Angular separation between the two object waves is greater than the angular selectivity bandwidth of each of the two elementary uncoupled gratings. The analysis gives results characterizing the diffraction efficiency of these gratings. Incoherent superposition of N uncoupled and slanted gratings is easily described by a simple generalization.

Analysis of anisotropic dielectric gratings

A method for analyzing slanted anisotropic gratings is presented. The propagation of electromagnetic waves in the periodic anisotropic media is described by coupled-wave equations in a unified matrix form expressing the coupling of the space harmonics in the grating region. The solution of the equations is reduced to an eigenvalue problem of this coupling matrix. Through introduction of the concepts of transmission and boundary matrices, the diffraction properties of general slanted gratings are obtained rigorously by systematic matrix calculations that are easily implemented on a computer. The calculated results indicate that not only TE–TE or TM–TM but also TE–TM diffractions take place in general slanted gratings.

Rigorous coupled-wave analysis of planar-grating diffraction

A rigorous coupled-wave approach is used to analyze diffraction by general planar gratings bounded by two different media. The grating fringes may have any orientation (slanted or unslanted) with respect to the grating surfaces. The analysis is based on a state-variables representation and results in a unifying, easily computer-implementable matrix formulation of the general planar-grating diffraction problem. Accurate diffraction characteristics are presented for the first time to the authors’ knowledge for general slanted gratings. This present rigorous formulation is compared with rigorous modal theory, approximate two-wave modal theory, approximate multiwave coupled-wave theory, and approximate two-wave coupled-wave theory. Typical errors in the diffraction characteristics introduced by these various approximate theories are evaluated for transmission, slanted, and reflection gratings. Inclusion of higher-order waves in a theory is important for obtaining accurate predictions when forward-diffracted orders are dominant (transmission-grating behavior). Conversely, when backward-diffracted orders dominate (reflection-grating behavior), second derivatives of the field amplitudes and boundary diffraction need to be included to produce accurate results.

A comparison of the optical path and differential equation methods for optically thin phase gratings

It is shown that the optical path method may lead to an approximate solution of the wave equation valid under a wide range of conditions for slanted phase gratings of arbitrary profile. Analytic solutions are given for sinusoidal and sawtooth gratings, and the accuracy of the approximations is checked by comparison with numerical solutions. The conditions under which sawtooth gratings may yield 100% efficiency are clarified.

Momentum Consideration for Diffraction of Light by Phase Gratings

The theoretical form of the diffracted light amplitude for the case of a light beam incident on phase gratings having refractive-index variation and surface corrugations simultaneously is derived on the basis of momentum conservation law. The theory remains valid for various gratings such as thin and thick gratings, unslanted and slanted fringe gratings and transmission and reflection gratings as long as the incident light is not strongly attenuated.