Pitch-modulated phase grating and its application to displacement encoder

Abstract

A binary phase grating with modulated pitch is investigated for a simple displacement encoder. The grating consists of a binary phase grating to eliminate the zeroth-order diffraction, and the pitch of the grating is modulated to compensate the higher harmonics of the encoder displacement signal. Therefore, an undistorted sinusoidal signal as a function of displacement is obtained by simply superimposing a conventional binary grating on the pitch-modulated phase gratings for any air gap between the gratings. The characteristics of the proposed gratings and the encoder signal are investigated by the Fresnel diffraction theory. The proposed grating has been fabricated lithographically, and the signal was examined experimentally. Considering these results, the proposed technique can suppress interpolation error and will be useful for an encoder in precision machining.     

Characterization of 1D diffractive optical elements by phase inversion

Abstract

We consider the feature dimensions of selected 1D diffractive optical elements (DOE) such that the Fourier transform based Gerchberg-Saxton (GS) iterative scalar phase retrieval algorithm, as calibrated by the results of vector coupled-wave theory, may be used for phase reconstruction. We consider examples only of continuous surface relief and binary (two level, not multi-level) phase-only DOE. Experimental phase distribution for rectangular and blazed gratings with ～ 5λ period agree within experimental limits with scalar theory, and, for the rectangular grating, were shown to agree also with the vector theory. Phase distributions are considered for a continuously varying linear blazed grating with 10λ periodicity, its sampled binary equivalent with minimum feature sizes of 0.1λ and for continuous linear blazed gratings with period varied from ～ 16λ to ～ 2λ. The vector calculations show an average linear dependence of the phase on grating period, but the vector curves are displaced to lower values from the scalar results by an increasing amount as the grating period is reduced. Grating performance is more influenced by the size of the grating period than the subwavelength size of the features in a binary representation. Reasonable equivalence is found in the prediction of correct phase distributions between scalar and vector theory for grating periods > ～ 5λ.     

Coherent control of symmetric and asymmetric diffraction grating via relative phase

ABSTRACT

We present a theoretical model to realize the symmetric and asymmetric diffraction grating in a four-level atomic medium. The proposed atomic medium follows a double lambda configuration where four fields interact with it. We get control over symmetric and asymmetric behavior of the diffraction grating by manipulating the relative phase of the fields. Interestingly, the symmetric and asymmetric diffraction grating become prominent when the vortex beam is used instead of the plane wave. Enhanced first, second, and third-order diffraction gratings are achieved via the vortex beam. Further, we find control over asymmetric diffraction gratings by the relative phase of the fields. Coherent control of asymmetric diffraction grating in negative and positive diffracted angles is also achieved via the relative phase.     

High transmissivity optical filter with phase gratings: Architecture and analysis

Abstract

A type of optical filter, the phase grating filter (PGF), which uses cascaded rectangular phase gratings or a single echelon grating as a wavelength selector, is proposed and analysed. The PGF has similar properties to conventional the Lyot birefringent filter but higher light transmittance thanks to elimination of the use of any polarizer.     

Dichromated Gelatin Reflection Gratings

Abstract

Reflection gratings were recorded in dichromated gelatin by using a non-symmetrical recording geometry. In addition to the primary grating, secondary gratings were also formed, as is generally known. It is found that the secondary gratings assist the structure stability during development in the exposure energy range (50–100) mJ cm^?2. The structure containing these secondary gratings is more rigid than those without and the reflection grating period is more stable during the development process in this exposure energy range, which is most suitable for the transmission grating formation. Secondary gratings also cause unwanted noise, but the noise level is low and the improved stability outweighs the extra noise.     

Lamellar Gratings as Polarization Components for Specularly Reflected Beams

Abstract

High spatial frequency lamellar gratings are shown to function as phase compensators, quarter-wave and half-wave retarders, and polarization rotators that operate on specularly reflected (zeroth-order) beams. These gratings are designed using rigorous coupled-wave and modal grating diffraction theories. Controlling the geometrical parameters of these gratings allows for engineering the phase retardation and polarization conversion introduced to a reflected beam. Fabrication and operational tolerances for these elements are discussed. Wavelength and polar angle of incidence variation affect the performance of these elements more strongly than variations in other geometrical and operational parameters.     

The Finite-conjugate Self-imaging and the Generalized Lau Effect Due to Complex Gratings

Abstract

Laser induced gratings in nonlinear optical media, which are complex or phase gratings, are the key structures in many applications involving laser beam-nonlinear material interactions. The concept of coded imaging of self-imaging structures, developed elsewhere, has been utilized to make a comprehensive study of the self-imaging properties, at finite conjugates, of model complex or phase gratings. The same approach has been used to extend our previous work on the generalized Lau effect. An interesting application of the self-imaging process has been made to visualize, at a certain primary magnification, laser induced thin photorefractive grating in a BSO crystal. Possible applications of this technique include visualization of dynamic or developed laser induced gratings in thin nonlinear optical materials.     

A Blazed Holographic Concave Grating for Monochromators

Abstract

The theory of blazed holographic gratings given in a previous paper is applied to the design of a blazed holographic aberration-corrected spherical concave grating. Two solution types are found which cover different ranges of blaze wavelength and aberration. The use of the refractive indices of the substrate, and the medium in front of the photoresist, as optimising parameters is demonstrated. Four ray-traced solution examples are given which include the distributions of blaze angle and wavelength across the grating surface.     

Non-uniformities in Thick Dichromated Gelatin Transmission Gratings

Abstract

The angular characteristics of transmission gratings are studied for the case when three parameters, namely the dielectric-constant modulation, the average dielectric constant and the grating vector vary with distance in the grating. The diffraction efficiency is worked out with the aid of a coupled-wave theory for linear and quadratic variation of the parameters. Gratings recorded in thick (≈ 60 µm) dichromated gelatin plates are measured. The spatial variations of the parameters are deduced by comparing the experimental and theoretical results.     

T-matrix Approach for Calculating the Electromagnetic Fields Diffracted by a Corrugated,Anisotropic Grating

Abstract

The diffraction of electromagnetic plane waves incident on a corrugated grating made of a uniaxial dielectric material is studied using a fully vectorial treatment based on a T-matrix approach and the Rayleigh hypothesis. The optic axis is considered parallel to the mean surface of the periodic interface. The theory is exemplified numerically for the case of sinusoidal gratings made of sodium nitrate.     

Non-uniformities in Dichromated Gelatin Reflection Gratings

Abstract

A theoretical model for non-uniform volume gratings is described in which the refractive index modulation and grating vector are allowed to vary with depth. The predictions of the model are compared with the measured angular response of reflection gratings recorded in dichromated gelatin and the variations of the grating parameters with depth are deduced. Gratings produced by different processing techniques are analysed and the effects of processing on grating non-uniformities are discussed.     

Statistical Model for Noise Gratings Recorded in Volume Holograms

Abstract

A statistical model is used to study the formation of noise gratings in holograms and the mechanism that causes radiation scattering in them. The theoretical model presented describes noise scattering in terms of diffraction due to the high number of spurious gratings formed during the recording stage by the interference of a single reference beam with its own scattered radiation. Numerical results calculated from the theory showing the dependence of noise grating efficiency on exposure are compared with experimental results obtained with bleached emulsions, and good agreement is found.     

Pulsed Laser Written Diffraction Gratings in Liquid Crystal Polymers

Abstract

In this work the writing of diffraction gratings in liquid crystal polymer films is studied, where the exposure mechanism is thermal and takes the material from an opaque to a transparent state. A pulsed ruby laser is used to write gratings and the evolution of diffraction is monitored using a continuous wave laser. The resulting diffraction efficiency is compared with an analytic theory for a range of laser pulse energies and grating spacings. Results from the comparison are very good, and final efficiencies of around 5% are obtained, which is near the theoretical maximum for the material used.     

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.     

Integral equation method with parametrization of grating profile theory and experiments

Abstract

Theories and their numerical implementations to rigorously solve Maxwell's equations are fundamental in diffractive optics. Various rigorous methods have been developed in the past which allow the analysis and synthesis of diffraction gratings. The basis of the great majority of rigorous methods is the Fourier series expansion of the permittivity function. Unfortunately the Fourier expansion can easily give poor results for the TM mode. By using an integral method with parametrization of the grating profile this problem can be overcome for surface modulated gratings. The theory and a comparison of theoretical and experimental results are presented.     

Computation of the near-field pattern with the coupled-wave method for transverse magnetic polarization

Abstract

In this paper, an accurate method for computing the elecromagnetic field distribution in lamellar gratings is proposed. The method that relies on the rigorous coupled-wave analysis provides accurate numerical results and avoids possible sources of artefacts due to permittivity discontinuities. Its performance is analysed through various lamellar grating cases, including dielectric and metallic materials, the visible and near-infrared (1–10 μm) regions of the spectrum. Special attention is placed on field singularities which are in general present at the grating wedges for transverse magnetic polarization.     

Lau Effect in Reflection

Abstract

The interference phenomenon known as the Lau effect is usually produced when two transmission gratings are located in tandem and are illuminated incoherently. This paper extends the study on this effect by analysing the optical arrangement in which the second transmission grating is replaced by a reflection grating. The interference fringes produced under incoherent illumination in this new reflection Lau geometry are, in certain respect, similar to those in the usual transmission geometry. The new set of fringes, however, become changeable in their profile when one of the gratings is subjected to an in-plane translatory motion in the direction perpendicular to the grating lines. The characteristics of the fringe formation phenomenon are examined quantitatively from the viewpoint of the incoherent superposition of multi-diffraction patterns of the gratings. We present a theoretical analysis and a supporting experimental verification of this phenomenon.     

Waveguide confinement of cerenkov second-harmonic generation through a graded-index grating coupler: Electromagnetic optimization

Abstract

The feasibility of making a frequency doubler for integrated optics is studied with the electromagnetic theory of gratings and graded-index waveguides as a tool. The device consists of a first waveguide filled with a sol-gel nonlinear material doped or grafted with a nonlinear chromophore whose thickness is chosen to generate a second-harmonic Cerenkov radiation in a dispersive glass substrate. The Cerenkov radiation is coupled into a second waveguide through a graded-index layer produced by ion exchange into glass, lying on top of an ion-etched grating coupler. The aim of the study is to optimize the optogeometrical parameters of the device in order to obtain a resonance line of the second waveguide modes that has an angular width large enough to match the experimental constraints, and which leads to a good enough coupling coefficient. The electromagnetic theory of grating couplers is developed into an S-matrix propagation algorithm form in order to be combined with the electromagnetic analysis of the thick graded-index waveguide with a view to analysing the device.     

Non-uniform Transient Gratings Induced by Laser Pulses in Nonlinear Media

The excitation of transient gratings induced by the interference of two equal parts of a short laser pulse in nonlinear media with one- or two-photon absorption is considered. The pulse-induced grating displays completely the pulse self-interference pattern; it is not periodic but has the form of a spatially non-uniform permittivity stratification. The grating amplitudes are described by pulse correlation functions. They contain information on the pulse shape and are sensitive to its phase modulation. The diffraction efficiency of the induced grating is calculated using electrodynamic perturbation theory. It is shown that the measurement of the spectral or angular distribution of the diffracted probe light enables the grating amplitude to be computed. The correlation functions of individual pulses can be determined in this way. Some applications of the pulse-induced gratings are proposed, as is a simplified technique for measuring the pulse width. The practicability of the grating in real nonlinear media is estimated.     

Relaxation of the Talbot condition in generalized grating imaging

We can form a grating image with two gratings having different pitches with an extended light source. It is called generalized grating imaging or the Talbot-Lau effect. When we want to obtain high contrast image with pure absorption gratings or pure phase gratings, the separation between the two gratings is restricted. This corresponds to the Talbot condition. In this paper, we propose to use a combination of absorption grating and phase grating to relax the separation restriction. The theory of generalized grating imaging is applied to the system with this kind of grating. Simulations are performed for calculating contrast variation and show that the proposed system practically relaxes the Talbot condition. An experiment verifies the result of the simulation.