We present a theory of the Fano resonance for optical resonators, based on a temporal coupled-mode formalism. This theory is applicable to the general scheme of a single optical resonance coupled with multiple input and output ports. We show that the coupling constants in such a theory are strongly constrained by energy-conservation and time-reversal symmetry considerations. In particular, for a two-port symmetric structure, Fano-resonant line shape can be derived by using only these symmetry considerations. We validate the analysis by comparing the theoretical predictions with three-dimensional finite-difference time-domain simulations of guided resonance in photonic crystal slabs. Such a theory may prove to be useful for response-function synthesis in filter and sensor applications.

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Temporal coupled-mode theory for the Fano resonance in optical resonators

Under certain conditions, a resonance phenomenon can occur in waveguide grating structures. Such structures have multilayer configuration, the most basic of which is comprised of a substrate, a thin dielectric layer or semiconductor waveguide layer, and an additional transparent layer in which a grating is etched. When such a structure is illuminated with an incident light beam, part of the beam is directly transmitted and part is diffracted and subsequently trapped in the waveguide layer. Some of the trapped light is then rediffracted outwards, so that it interferes destructively with the transmitted part of the light beam. At a specific wavelength and angular orientation of the incident beam, the structure "resonates"; namely, complete interference occurs and no light is transmitted. This paper reviews previous investigations on the resonance phenomena and presents analytic and numerical models for evaluating the resonance as a function of the geometric and optical parameters of the structures and incident radiation.

Resonant grating waveguide structures

A high-efficiency guided-mode resonance reflection filter is reported. The device consists of a surface-relief photoresist grating and an underlying HfO (2) waveguide layer deposited on a fused-silica substrate. The spectral response measured with a dye-laser beam at normal incidence exhibited a peak reflectance of 98% at a wavelength of 860 nm with sideband reflectance below approximately 5% extending over the wavelength range provided by the dye (800-900 nm). At normal incidence the filter linewidth was 2.2 nm. High-efficiency double-peak resonances occurred at nonnormal incidence, with the spectral locations of the maxima vayring with the incidence angle. The filter response at various angles of incidence agreed well with the theoretically calculated reflectance curves.

High-efficiency guided-mode resonance filter

Resonant waveguide gratings (RWGs), also known as guided mode resonant (GMR) gratings or waveguide-mode resonant gratings, are dielectric structures where these resonant diffractive elements benefit from lateral leaky guided modes from UV to microwave frequencies in many different configurations. A broad range of optical effects are obtained using RWGs such as waveguide coupling, filtering, focusing, field enhancement and nonlinear effects, magneto-optical Kerr effect, or electromagnetically induced transparency. Thanks to their high degree of optical tunability (wavelength, phase, polarization, intensity) and the variety of fabrication processes and materials available, RWGs have been implemented in a broad scope of applications in research and industry: refractive index and fluorescence biosensors, solar cells and photodetectors, signal processing, polarizers and wave plates, spectrometers, active tunable filters, mirrors for lasers and optical security features. The aim of this review is to discuss the latest developments in the field including numerical modeling, manufacturing, the physics, and applications of RWGs. Scientists and engineers interested in using RWGs for their application will also find links to the standard tools and references in modeling and fabrication according to their needs.

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Recent Advances in Resonant Waveguide Gratings

A new ray picture model based on the multiple interference of light waves in dielectric resonant grating–waveguide structures is presented. The model clearly elucidates the phase relationship between the incident plane wave and the waves diffracted from the resonant grating structure that is responsible for the interference of these waves. As a result of this interference process the incident wave can be totally reflected at a certain wavelength and orientation angle. The model is used to describe and analyze this resonance behavior of the grating–waveguide structures as a function of wavelength and incidence angle. The analysis is verified experimentally with semiconductor (InGaAsP/InP) structures at wavelengths of 1.55 μm and also with dielectric (silicon nitride/SiO2) structures at wavelengths of 0.6 μm. All of the structures were formed by electron beam lithography and chemical vapor deposition. The measured results reveal that subnanometer resonance bandwidths and finesses as large as 6000 can be achieved at contrast ratios of 50 with relatively compact structures.

Resonant grating–waveguide structures for visible and near-infrared radiation

Resonant grating–waveguide structures formed with InP/InGaAsP semiconductor materials were tested to show light modulation at a wavelength of 1.55 μm. Narrow, subnanometer resonant spectral bandwidths and a ratio of reflected intensities between resonance and away from resonance of greater than 50 were measured. For a resonant structure with an area of 3 mm × 3 mm, the modulation frequency reached 5 MHz.

Light modulation with resonant grating–waveguide structures

The application of an optical grating structure on a substrate, by electron beam lithography comprises: (a) forming initially a basic screen on the electron-sensitive varnish coating to inscribe the superimposed grating structure, the screen of equidistant points or lines, with an interval and frequency matching the periods of the grating structure and the number of grating periods; (b) inscribing the basic screen in the start position in the varnish coating by an electron beam; (c) computing displacement for a further deflection of the electron beam from the grating periods and the max. and min. Bragg periods; (d) deflecting the electron beam; and (e) inscribing the screen in the varnish coating in the deflected exposed position, by the electron beam; and (f) repeating the processes until the overlaid grating is complete.

Optical grating structure inscription by electron beam lithography

Electron-beam lithography is the technique of choice to generate in a flexible and accurate way structures and components in the micrometer region and below Due to its particular exposure strategy, ie matching equidistant subfields to a complete pattern, electron-beam systems show typical displacement effects known as stitching errors These errors can be of dramatic disturbance if they occur in high resolution patterns This paper presents an exposure scheme which essentially reduces stitching errors by using a multiple exposure technique The influence of this technique on the value of stitching errors and its interference with the process window as well as total processing time is reported

Essential reduction of stitching errors in electron-beam lithography using a multiple-exposure technique

Complex relief-type resist surfaces are of increasing interest for applications in optical and photonic devices. They can be fabricated by using direct write electron beam lithography. The crucial point in the fabrication of such reliefs is the inexact approach to the desired resist profile and the increased roughness of the resist surface. This work focusses on three important steps towards a better realization of smooth profiles, i.e. an improvement in beam position accuracy, a reduction of exposure errors caused by the insufficiency of the conversion software and a smoothing technique applied after development. The introduced techniques are expected to considerably improve the functionality of relief type devices.

Application of smoothing techniques to relief-type resist surfaces generated by direct write electron-beam lithography

Semiconductor lasers with a wide tuning range can be fabricated with the use of super structure gratings (SSG). In this paper we give a short introduction to SSGs, the technical problem of their realization and the existing techniques to generate SSGs. A method is presented to generate 'true' continuously chirped gratings overcoming the technical restrictions. Furthermore we make a proposal how to characterize SSGs in resist profiles.

Ralf Steingrueber

Papers

Light modulation with resonant grating–waveguide structures

Optical grating structure inscription by electron beam lithography

Essential reduction of stitching errors in electron-beam lithography using a multiple-exposure technique

Application of smoothing techniques to relief-type resist surfaces generated by direct write electron-beam lithography

Exposure and characterization of superstructure gratings for DBR lasers generated by direct write electron-beam lithography