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.

/pdf/temporal-coupled-mode-theory-for-the-fano-resonance-in-2okwo9a7sx.pdf

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

We present a three-dimensional analysis of guided resonances in photonic crystal slab structures that leads to a new understanding of the complex spectral properties of such systems. Specifically, we calculate the dispersion diagrams, the modal patterns, and transmission and reflection spectra of these resonances. From these calculations, a key observation emerges involving the presence of two temporal pathways for transmission and reflection processes. Using this insight, we introduce a general physical model that explains the essential features of complex spectral properties. Finally, we show that the quality factors of these resonances are strongly influenced by the symmetry of the modes and the strength of the index modulation.

/pdf/analysis-of-guided-resonances-in-photonic-crystal-slabs-3pdthsk0hb.pdf

Analysis of guided resonances in photonic crystal slabs

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

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.

/pdf/recent-advances-in-resonant-waveguide-gratings-17dyntevmn.pdf

Recent Advances in Resonant Waveguide Gratings

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 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

Under certain conditions, a high-finesse resonance phenomenon can occur in a grating waveguide structure (GWS). By varying these conditions, a shift in the resonance wavelength can be achieved. Specifically, utilizing the high finesse property of the GWS, small changes in the refractive index can result in a tuning range larger than the resonance bandwidth. Here, we consider different electric-field and charge carrier mechanisms that can affect the refractive index in semiconductor materials, and exploit them in order to control the refractive index change and, therefore, the resonance wavelength in the GWS. The predicted results are verified experimentally with an active GWS formed with semiconductor materials and operated in a reverse voltage configuration.

/pdf/active-semiconductor-based-grating-waveguide-structures-3u79q2r8rg.pdf

Active semiconductor-based grating waveguide structures

Hybrid semiconductor polymer resonant grating waveguide structures

When a grating-waveguide structure is illuminated with an incident light beam at a specific wavelength and angular orientation, a resonant phenomenon occurs. The resonance spectral bandwidth can be very narrow, so the structure can serve either as a spectral filter or an optical modulator. The basic principles, analytic and numerical models, design and fabrication procedures, and calculated and experimental results are presented. The results reveal that passive resonant structures can have spectral bandwidths as low as 0.085 nm, and active structures can be modulated at 10 MHz.

Resonant Structures for Optical Processing and Communication

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Light modulation with resonant grating–waveguide structures

Active semiconductor-based grating waveguide structures

Hybrid semiconductor polymer resonant grating waveguide structures

Resonant Structures for Optical Processing and Communication