Born approximation for the nonparaxial scalar treatment of thick phase gratings

The conventional design of phase gratings or kinoforms with a paraxial transmission function is restricted to the paraxial domain and thin elements. Therefore, the design and analysis of thick phase-relief structures require a nonparaxial theory, as given by the Born approximation. The Born approximation is derived as an extension of the scalar thin-element theory, which is applicable for thick elements with large propagation angles. As an example, general prism gratings on curved surfaces are treated.     

On the zero-thickness model of diffractive optical elements

In a recent paper [J. Opt. Soc. Am. A 16, 113 (1999)] a thin-element approximation of diffractive optical elements was used to describe diffraction of oblique incident wave fronts. This expression motivated by a ray optical analysis is shown to be incorrect. I discuss how the thin-element approximation can be generalized to arbitrary diffraction geometries. This includes an intuitive interpretation of the results.     

Analysis of optical elements with the local plane-interface approximation

The local plane-interface approximation (LPIA) is a method for propagating electromagnetic fields through the inhomogeneous regions (e.g., elements) of an optical system. The LPIA is the superclass of all approximations that replace the usually curved optical interfaces with local tangential planes. Therefore the LPIA is restricted to smooth optical surfaces. A maximum radius of curvature of the optical interface of the order of a few wavelengths is a rough estimate for the validity of the LPIA. Two important approximation levels of the LPIA are the thin-element approximation (TEA) and a geometric-optical version of the LPIA (LPIA(ray)). The latter combines the wave-optical propagation of an electromagnetic field in the homogeneous region of an optical system with a ray-tracing step in the inhomogeneous region. We discuss the regions of validity of the LPIA in general and the approximation levels LPIA(ray) and TEA in detail.     

Effects of abrupt surface-profile transitions in nonparaxial diffractive optics

It is shown that the failure of the thin-element approximation of diffractive optics may, in the first approximation, be attributed to local diffraction effects caused by the abrupt vertical transitions in binary surface-relief profiles. We determine the field disturbance caused by a single-step transition (of given height) by rigorous diffraction theory. Associating such a disturbance with each individual transition point in the profile, we obtain a computationally efficient refinement of the thin-element approximation for the analysis and design of diffractive elements in the nonparaxial domain. The results agree well with those obtained by global application of rigorous diffraction theory, provided that the smallest features in the binary profile are larger than approximately one optical wavelength.     

Electromagnetic approach to the thin element approximation

Abstract

We show that the rigorous Fourier modal method yields the thin element approximation when the feature sizes and the period tend to infinity. The transversal eigenmodes of the structure can be divided into sets whose effective refractive index corresponds to the refractive indices of the grating. Each set can be treated as the thin element approximation with constant amplitude and piecewise continuous phase transmission. We also demonstrate that the primary reason for the rapid failure of the thin element approximation with thick binary structures is attributable to destructive interference of the waveguide modes.     

Diffractive optical elements for intra-cavity beam-shaping of laser modes

Abstract

Diffractive optical elements (DOE) are applied as intra-cavity mode selection devices for customizing the fundamental mode of laser resonators for high power laser systems. Using a phase-conjugating mode selecting element (MSE) in a laser oscillator, we are able to produce a good approximation to a super-Gaussian mode with a near flat intensity profile. This offers higher energy extraction from any following laser amplifiers compared to an unmodified Gaussian TEM₀₀ mode. Two different designs for operation in a 1 m cavity length Nd:YAG master oscillator are presented. Both designs are surface relief phase elements fabricated in fused silica using photolithography with reactive-ion etching to produce 16 level elements for use in transmission. One element is designed to replace the cavity end mirror, while the other stands off an arbitrary distance from the end mirror. A novel iterated design for these transmissive elements is introduced. Numerical results and experimental measurements are presented and discussed.     

Rigorous and approximate analysis of metallic gratings in soft X-ray and EUV regions

Abstract

In deep ultraviolet and soft X-ray regions the complex refractive indices of metals differ substantially from their values in the visible region of the spectrum. The implications of this fact are analysed for metallic gratings illuminated by electromagnetic fields with wavelengths ranging from soft X‐rays to near infrared, concentrating on short wavelengths. In particular, we study metal-stripe gratings (linear polarizers for visible light) by rigorous diffraction theory to determine the short-wavelength region in which a combination of the geometrical thin-element approximation and the theory of single-layer films can be applied. Then we study inductive grid filters for protection of X-ray detectors from infrared radiation in space applications.     

Multi-channel terahertz wavelength division demultiplexer with defects-coupled photonic crystal waveguide

Abstract

Terahertz (THz) wavelength division demultiplexer based on a compact defects-coupled photonic crystal waveguide is proposed and demonstrated numerically. This device consists of an input waveguide that perpendicularly coupled with a series of defects cavities, each of which captures the resonance frequency from the input waveguide. Coupled-mode theory and finite element method are used to analyze the transmission properties of the structure. It is found that the transmission wavelength centered around 1 THz can be adjusted by changing the geometrical parameters of defects cavities, which equals to THz waves generated by optical methods such as difference frequency generation and optical rectification. Applications in this frequency range are urgently needed. Furthermore, the highest transmission efficiency of 0.94 can be achieved when a perfect wavelength-selective mirror is set in the output waveguide.     

Simulation of light propagation by local spherical interface approximation

A new local elementary interface approximation is introduced for the modeling of wave propagation through interfaces between homogeneous media. The incident wave and the surface profile are approximated locally by a spherical wave and a spherical surface, respectively. The wave field travels through the modulated structure according to the laws of geometrical optics, being refracted by the surface and propagating to the output plane locally as a geometric spherical wave. Diffraction theory is applied to propagate the field from the output plane onwards. We provide comparisons of the method with the thin-element approximation, the local plane-wave and interface approach, and rigorous diffraction theory using a sinusoidal surface-relief grating as an example. We illustrate the power of the new method by applying it to the analysis of a diffractive beam splitter.     

Temporal superresolution: An application of frequency filtering by a grating in the resonance domain

Abstract

A diffraction grating in the resonance domain is known to exhibit significant change in diffraction efficiencies with a small change of the grating parameters. It is proposed that this property can be utilized for frequency filtering, when polychromatic light illuminates the grating. As an example, compression of a femtosecond optical pulse is numerically demonstrated with the concept of superresolution. Suppression of zeroth diffraction order by suitably optimized grating structure induces the pulse width to narrow. This scheme considerably simplifies existing optical pulse shaping systems.     

Nonlinear Interference Devices for All-optical Self-routeing

Abstract

Conceptual devices for all-optical self-routeing are discussed, based on particular interference phenomena associated with modified, nonlinear Fabry-Perot cavities. The transmitted amplitude and phase are calculated for cavities composed of III-V semiconductor materials. Within the physical optics approximation the transmission of Gaussian beam profiles and their associated diffraction patterns are obtained. By engineering an asymmetry in the transmitted phase which depends upon the input intensity, an angular deflection of the beam profile can be produced under optical control. The simplest examples indicate that deflections of a beam through several degrees are theoretically feasible. Practical implementations of this effect are discussed.     

Role of Bose enhancement in photoassociation

Abstract

We discuss the role of Bose enhancement of the dipole matrix element in photoassociation, using stimulated Raman adiabatic passage as an example. In a non-degenerate gas the time scale for coherent optical transients tends to infinity in the thermodynamic limit, whereas Bose enhancement keeps this time scale finite in a condensate. Coherent transients are therefore absent in photoassociation of a thermal non-degenerate gas, but are feasible if the gas is a condensate.     

Efficiency analysis of diffractive lenses

Multilevel diffractive optical elements are necessary for achieving high-efficiency performance. Here the diffraction efficiency of a multilevel phase-only diffractive lens is analyzed. Approximate, as well as more accurate, approaches are presented. Both plane-wave and Gaussian illumination are discussed. It is shown that for many practical cases the diffraction efficiency can be determined by only a single parameter that takes into account the spatial bandwidth product as well as the focal length of the lens and the illumination wavelength. The analysis is based on the scalar theory and the thin-element approximation. Justification for doing this is presented. The results are valid for lenses with at least F/5.     

Optimization of an optical filter with a square-shaped passband based on coupled microcavities

Abstract

An approach using simple analytical theory has been developed for the design of multilayered spectral optical filters based on coupled microcavities. The method has been applied to find the parameters of the optimal structure, providing a near square-shaped transmission band. The case of normal and oblique incident light has been considered. It is shown that the situation corresponding to the weak coupling-strong coupling threshold for coupled cavity modes is optimal for achieving a square-shaped transmission band.     

The use of optical fibres in radio astronomy

Abstract

The low loss and ease of use of optical fibres for data transmission offers a number of advantages over traditional methods of bringing signals from radio telescopes together. Aperture synthesis techniques involve the correlation of signals from each pair of telescopes in the array. The requirements of radio astronomy systems, where the broad-band noise-like signals from each telescope have to be brought together coherently over distances as large as hundreds of km or greater in some cases, are discussed in this paper. A number of arrays around the world currently use fibres for data transmission and also for the coherent transfer of local oscillator signals. Further developments in the use of optical fibres in radio astronomy are described as well as new instruments planned for the next millennium, where fibre interconnections will be an essential part of their design.     

Aberrated Optical Systems with Optimum Apodizers for the Strehl Ratio: Axial and Extra-axial Point-spread Function and Modulation-transfer Function

Abstract

The amplitude distribution at the aperture of an optical system for off-axis object points due to the introduction of a non-uniform transmission filter depends on the transmission function and on the longitudinal filter position. The effects of several filters on the axial and extra-axial point-spread function (PSF) and modulation-transfer function (MTF) of an optical system for different filter positions are studied. The filter transmission function and the filter position are obtained by the optimization of the axial and extra-axial Strehl ratios. The axial and extra-axial effects of the filters on the PSF and on the MTF are analogous. There are some positions of the filter for which the overall performance is significantly improved. The optimum longitudinal positioning of the apodizing filter is achieved in a process which is analogous to the stop shift effect in conventional optical design. The lack of radial symmetry in the off-axis wavefront aberration function at any particular field angle is convolved with the apodizing function and this leads to the anticipated improvement.     

Pulsed-mode analysis of soft-X-ray radiation passing through capillary waveguides

Abstract

Soft-X-ray radiation passing through capillary waveguides is theoretically analysed by the pulsed-mode method. We consider the optical guiding by straight and tapered waveguides in the spectral range 100–2000 eV. As an example, we calculate the intensity distribution, transmission coefficient and gain factor for the radiation passing through SiO₂ waveguides.     

Spectral noise analysis of single- and double-pass Er3+ - doped LiNbO3 waveguide amplifiers

Abstract

In this paper we report the derivation and evaluation of the spectral optical gain, spectral noise figure, amplified spontaneous emission photon number and signal-to-noise ratio in single- and double-pass configurations for an Er³⁺-doped LiNbO₃ waveguide amplifier pumped near 1484nm. The theoretical analysis was made using the small-gain approximation in the unsaturated regime. The simulations show the evolution of the above-mentioned parameters under various pumping regimes and waveguide lengths. The results obtained show how the model can be used for the design of Er³⁺-doped LiNbO₃ waveguide amplifiers.     

On chip optical isolator based on non-linear silicon photonic crystal by using asymmetric engineering waveguide

We propose an optical isolator formed in a nanoscale structure based on non-linear silicon photonic crystal that can be easily realized on an optical integrated chip. The structure comprises an engineered waveguide that is coupled to a L₂ cavity. By using a passive ultra-compact cavity-based isolator, without changing incident characteristics such as mode or frequency in outputs, an admirable transmission contrast of 20.5 dB with a small insertion loss (in the forward direction) of ?14.8 dB is achieved. The isolator attains a broad isolating linewidth operation of 0.9 nm without bistability response that is outstanding in comparison with the currently proposed cavity-based isolators. The non-linear Fano resonances that are created by the interplay between the non-linearity and spatial asymmetry notion in the structure play a critical role in the isolator efficiency. In this study, the finite-difference time-domain and finite element methods are used for simulations.     

Uniform luminance design of the direct‐type backlight unit of liquid crystal displays using neural networks

Abstract

Light efficiency optimization of a direct‐type backlight unit (BLU) of the liquid crystal display (LCD) is considered in this paper. The purpose of this research is to obtain the greatest uniformity in a direct‐type BLU, while the brightness is maintained in a satisfactory level.

It is difficult to find a numerical optimization algorithm that is readily applicable to this problem because of the existence of discrete variables, implicit objective functions and constraints, or even binary constraints. The sequential neural‐network approximation (SNA) method is designed specifically for this type of engineering design optimization problem. In this paper, a two variable LCD BLU design example is presented first to illustrate the design process using the SNA method. Then a four variable LCD BLU design optimization problem is solved.