Robert Magnusson

Theory and applications of guided-mode resonance filters

The guided-mode resonance properties of planar dielectric waveguide gratings are presented and explained. It is shown that these structures function as filters that produce complete exchange of energy between forward- and backward-propagating diffracted waves with smooth line shapes and arbitrarily narrow filter linewidths. Simple expressions based on rigorous coupled-wave theory and on classical slab waveguide theory give a clear view and quantification of the inherent TE/TM polarization separation and the free spectral ranges of the filters. Furthermore, the resonance regimes, defining the parametric regions of the guided-mode resonances, can be directly visualized. It is shown that the linewidths of the resonances can be controlled by the grating modulation amplitude and by the degree of mode confinement (refractive-index difference at the boundaries). Examples presented of potential uses for these elements include a narrow-line polarized laser, a tunable polarized laser, a photorefractive tunable filter, and an electro-optic switch. The guided-mode resonance filter represents a basic new optical element with significant potential for practical applications.

Guided-mode resonances in planar dielectric-layer diffraction gratings

The guided-mode resonance behavior of the evanescent and propagating fields associated with an unslanted, planar diffraction grating is studied by means of the rigorous coupled-wave theory. For weakly modulated gratings, the condition on the guided-mode wave number of the corresponding unmodulated dielectric-layer waveguide may be used to predict the range of the incident angle or wavelength within which the resonances can be excited. Furthermore, the locations of the resonances are predicted approximately by the eigenvalue equation of the waveguide. As the modulation amplitude increases, the location and shape of the resonances are described in detail by the rigorous coupled-wave theory. The results presented demonstrate that the resonances can cause rapid variations in the intensity of the external propagating diffracted waves.

Resonant leaky-mode spectral-band engineering and device applications.

Single-layer subwavelength periodic waveguide films with binary profiles are applied to design numerous passive guided-mode resonance elements. It is shown that the grating profile critically influences the spectral characteristics of such devices. In particular, the symmetry of the profile controls the resonance spectral density. Symmetric profiles generate a single resonance on either side of the second stopband whereas two resonances arise, one on each side of the band, for asymmetric structures. Moreover, the profiles Fourier harmonic content, along with the absolute value of the grating modulation strength, affects the resonance linewidths and their relative locations. Computed Brillouin diagrams are presented to illustrate many key properties of the resonant leaky-mode spectra in relation to modulation strength and profile symmetry at the second stopband. Associated mode plots elucidate the spatial distribution of the leaky-mode field amplitude at resonance and show that, for small modulation, the mode shape may be simple whereas at higher modulation, the shape appears as a complex mixture of modes. By computing device spectra as function of the modulation strength, the buildup of the final spectral properties is illustrated and the contributions of the various leaky modes clarified. The results presented include wavelength and angular spectra for several example devices including narrow linewidth bandpass filters with extended low sidebands for TE and TM polarization, wideband reflectors for TE and TM polarization, polarizer, polarization-independent element, and a wideband antireflector, all with only a single binary layer with one-dimensional periodicity. These results demonstrate new dimensions in optical device design and may provide complementary capability with the field of thin-film optics.

High-efficiency guided-mode resonance filter

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.

Reflection and transmission guided-mode resonance filters

New reflection and transmission optical filters based on guided-mode resonances in multilayer waveguide gratings are characterized and compared with homogeneous thin-film filters. These guided-mode resonance filters are implemented by integration of diffraction gratings into classical thin-film multilayers to produce high-efficiency filter response and arbitrarily low sidebands extended over a large spectral range. Compared with homogeneous thin-film reflection filters, guided-mode resonance reflection filters require significantly fewer layers for a narrow linewidth and a high peak response to be obtained. The single-grating transmission filters presented have a narrower linewidth than Fabry–Perot filters with an equal number of layers and similar materials while maintaining high peak transmittance and low sidebands.

Multilayer waveguide-grating filters

The properties of guided-mode resonance reflection filters constructed with multiple thin-film layers are addressed. Greatly improved filter characteristics are shown to follow by the incorporation of multiple homogeneous layers with the spatially modulated layer. Calculated results for single-layer, double-layer, and triple-layer filter structures are presented. Whereas good filter characteristics are obtainable with single layers that are half-resonance-wavelength thick, there remains a residual reflection in the sidebands unless the cover and the substrate permittivities are equal. With double-layer and triple-layer designs, extensive wavelength ranges with low sideband-reflectance values are shown to be possible without requiring equal cover and substrate permittivities. The antireflection properties of the layer stack can be understood if the modulated layer is modeled as a homogeneous layer characterized by its average relative permittivity. However, as the grating-modulation index increases, this approximation deteriorates. In particular it is found that, for a given high modulation index, the double-layer antireflection thin-film approximation fails, whereas for the same modulation in a triple-layer system it holds firmly. Multilayer designs can thus have significantly large filter passbands, as they may contain heavily modulated resonant gratings without corruption of the ideal filter characteristics.

Design of waveguide-grating filters with symmetrical line shapes and low sidebands

We show that ideal reflection filters can be designed by combining guided-mode resonance effects in waveguide gratings with antireflection effects of thin-film structures. Since the guided-mode resonance effect overrides the antireflection effect this filter provides a symmetrical line shape with near-zero reflectivity over appreciable wavelength bands adjacent to the resonance wavelength. In the single-layer filter the same layer functions as the waveguide grating supporting the resonance and as the antireflection layer suppressing reflection around the resonance. A multilayer design allows the filter resonance peak to have a wide surrounding region of low reflectance. The central resonance wavelength, the filter linewidth, the range of the low sidebands, and the resonance line shape are all under the control of the designer.

Physical basis for wideband resonant reflectors

In this paper, we address resonant leaky-mode reflectors made with a periodic silicon layer on an insulating substrate. Our objective is to explain the physical basis for their operation and to quantify the bandwidth provided by a single resonant layer by illustrative examples for both TE and TM polarized incident light. We find that the number of participating leaky modes and their excitation conditions affect the bandwidth. We show that recently reported experimental [1, 2] wideband reflectors operate under leaky-mode resonance. These compact reflectors are new elements with many potential applications in photonic systems. The results presented explaining their physical basis will aid in their continued development.

Transmission bandpass guided-mode resonance filters.

It is shown that the guided-mode resonance effects associated with waveguide gratings can be used to realize transmission bandpass filters. The key idea is the integration of the resonant waveguide gratings into a dielectric multilayer structure that efficiently reflects the off-resonance spectral components while passing the resonant part. This concept is applied to design multilayer transmission bandpass filters with high efficiency, narrow linewidth, symmetrical response, and low sidebands.

Use of nondegenerate resonant leaky modes to fashion diverse optical spectra.

In this paper, we show that bandstop and bandpass filters with versatile spectral attributes can be implemented with modulated films possessing asymmetric grating profiles. The profile asymmetry breaks the resonant leaky mode degeneracy at normal incidence thereby permitting precise spectral spacing of interacting leaky modes with interesting implications in optical filter design. Several example filters, containing only a single grating layer, are designed with this methodology to demonstrate the concept.