Waveguide Diffraction Gratings Research Articles

Interference pattern generation in evanescent electromagnetic waves for nanoscale lithography using waveguide diffraction gratings

The generation of interference patterns of evanescent electromagnetic waves with an essentially subwavelength period using dielectric waveguide diffraction gratings is considered. Using simulations within the framework of the electromagnetic theory, the possibility of obtaining high-quality interference patterns due to enhancement of evanescent diffraction orders under resonance conditions is demonstrated. The contrast of the interference patterns in the case of TE polarisation of the incident wave is close to unity. The field intensity in the near-field interference maxima exceeds the intensity of the incident wave by 25–100 times. The possibility of generation of the interference patterns of evanescent waves corresponding to higher diffraction orders is shown. The use of higher orders reduces the requirements to the fabrication technology and allows generation of interference patterns with a high spatial frequency, using diffraction gratings with a low spatial frequency. Examples of generating interference patters with periods six times smaller than those of the used diffraction gratings are presented.

Recording and Analysis of the Radiation Spectrum in the Infrared Band by Means of Bragg Waveguide Gratings

A method of spatial separation of the spectral components of electromagnetic radiation based on the use of waveguide diffraction gratings is proposed. Optimization of the parameters of the detecting part of a spectrum recorder that employs the proposed method is realized by means of numerical simulation.

Four-wave coupled-mode theory of obliquely incident plane waves on waveguide diffraction gratings

Diffraction of plane waves, obliquely incident on a (waveguide) grating with infinitely long grooves, is analyzed with the four-wave coupled-mode theory (CMT). Unlike the ordinary analysis that considers only coupling between pairs (i.e., TE+↔TE-,TE+↔TM-,TM+↔TE-, or TM+↔TM-), the simultaneous interaction among these waves is properly accounted for. The field variation along the grating and the impulse response representation of the grating (reflectivity and transmission as functions of the plane-wave incidence angle) are calculated. Significant differences between the ordinary (two-wave) CMT and the four-wave CMT are observed over a wide range of incident angles.

High-efficiency diffractive waveguide lenses by parametric optimization

The first-order diffraction efficiency of a waveguide diffraction grating is maximized, for a wide range of grating periods, by optimization of the effective-index modulation profile. Three different values of effective-index modulation in the range of 0.02-0.11 are considered. The analysis is performed with the thin-grating-decomposition method. The results are verified by electromagnetic grating theory and applied to the construction of diffractive waveguide lenses with an improved overall efficiency. In the neighborhood of the optical axis, the optimized lens structure is a close approximation of a gradient-thickness Fresnel lens. Significant deviations from this shape appear when the local grating period reduces below ~ 15-25λ, where ~ is the wavelength of the guided mode. Near the edges of a high-numerical-aperture lens, where the local period is ~ 3-6λ, an approximate Bragg grating structure is obtained.

Curved grating fabrication techniques for surface-emitting distributed feedback lasers

We report on techniques for the fabrication of curved waveguide diffraction gratings for use in novel semiconductor laser structures. In particular, we consider the development of concentric-circle gratings to be employed in circularly symmetric, surface-emitting semiconductor lasers. The gratings are defined using electron-beam lithography and subsequently etched into the semiconductor surface by chemically assisted ion-beam etching. Issues to be addressed include grating design requirements, pattern representation, and scan method. We provide examples of how these techniques can be implemented and their impact on the resulting laser performance.

Circularly symmetric distributed feedback laser: coupled mode treatment of TE vector fields

The vector orientation of transverse electric (TE) fields in deriving coupled mode equations for radially outward- and inward-going modes in a circular waveguide diffraction grating is treated. The equations are derived for cylindrical waves in a system that is translationally invariant along the cylinder axis; the derivation is then extended to the waveguide geometry. The coupled mode equations are used to describe the operation of the circularly symmetric distributed feedback (DFB) laser. While predicting a similar dependence of the laser threshold gain on an azimuthal mode order to that found by a simpler, scalar-field treatment, the vector-field treatment predicts a fundamental difference in the location of the cavity resonances. The circular DFB laser is expected to lase in multiple azimuthal modes but maintain a relatively narrow overall spectral width. >

Ideal mode expansion for planar optical waveguides: application to the TM–TM coupling coefficient for grating structures

We derive the coupled equations for the ideal modes of an optical waveguide, using a Green function technique, and use these to determine the TM–TM coupling coefficient for a periodic waveguide diffraction grating. The results are consistent with experimental observations, in marked contrast to the results of more conventional versions of the ideal mode expansion. Further, our approach can deal with more general corrugated structures than can easily be done with other methods.

Analysis of waveguide gratings: a comparison of the results of Rouard’s method and coupled-mode theory

Recently we introduced a new computational tool for the analysis of waveguide diffraction gratings based on Rouard’s method, a recursive technique used in thin-film coating design. In this paper we compare the reflectivities predicted by Rouard’s method with those found by using the ideal mode expansion of coupled-mode theory for both periodic and aperiodic gratings. We find empirically that the two methods are in excellent agreement, with typical differences in reflectivity of less than 1%.

Analysis of waveguide gratings: application of Rouard’s method

This paper describes the adaptation of Rouard’s method, a familiar computational technique used in thin-film coating design, to the analysis of waveguide diffraction gratings. The approach can be used to generate the spectral and the angular characteristics of arbitrary straight-line gratings (periodic or nonperiodic), is easy to implement on a computer, and provides an intuitively appealing picture of the operation of such gratings. The application of the thin-film method is extended to periodic gratings as well as to gratings having either a linear or a quadratic chirp in period. Specific examples are used to compare the results of the thin-film computational method with those predicted by previous authors.

Comparison of two approaches to the waveguide scattering problem: TM polarization

Two theoretical formalisms, the most widely used version of coupled-mode theory and a first-order boundary-perturbation theory, are used to analyze the interaction between optical guided waves and surface roughness on an asymmetric planar waveguide. Each formalism is applied to two distinct problems for both TE and TM guided waves: (1) the determination of the far-field radiation patterns from randomly rough surfaces (with explicit results for the case of a sinusoidal roughness); and (2) the determination of guided-wave reflectivities from waveguide diffraction gratings. In all cases, the theoretical predictions agree for the TE polarization but disagree significantly for the TM polarization.

Optical properties of specially shaped waveguide diffraction gratings

Bragg diffraction in a planar optical waveguide by a grating in the form of a characteristic parallellogram results in a Hankel spatial spectral transformation of a one-dimensional input image. It is found that all the main optical transformations given by planar or cylindrical lens optics can be obtained by this means.

Diffraction efficiency of waveguide gratings: Brewster's law

The coupled-mode equations are solved for the case of a TEO guided wave obliquely incident upon a waveguide diffraction grating. The solution involves an approximation in which the coupling coefficient is replaced by its spatial average over one period of the grating. The angular dependence of the TE0-TE0 reflectivity of the grating exhibits a null for an angle of incidence that satisfies a relation that is reminiscent of Brewster's law.