Investigation of the effect of finite grating size on the performance of guided-mode resonance filters

Compact coherent perfect absorbers using topological guided-mode resonances

We propose a topological coherent perfect absorber that enables almost ideal performance with remarkably compact device footprint and tight incident beams. The proposed structure is based on a topological junction of two guided-mode-resonance gratings. The structure provides robust systematic ways of remarkably tight lateral confinement of the absorbing resonance mode and near-perfect mode-match to arbitrary incident beams, which are unavailable with the conventional approaches. We demonstrate an exemplary amorphous Si thin-film structure that enables near-perfect absorptance modulation between 1.7 and 99% with device footprint width of 30-μm and 10-μm-wide incident Gaussian beams. Therefore, our proposed approach greatly improves practicality of guided-mode-resonance coherent perfect absorbers.

Performance of finite-size metal-dielectric nanoslits metasurface optical filters

In this work, we analyze the performance of finite-size metal-dielectric nanoslits guided mode resonance metasurface optical filters by using finite-difference time-domain simulations and spatial Fourier transform analysis. It is shown that in the direction of the nanoslits period, the critical size required to maintain the performance of the corresponding infinite size filter is the product of the nanoslits period and the quality factor of the infinite size filter. Size reduction in this dimension below the critical dimension reduces the peak transmittance and broadens the spectral linewidth of the filter. In the dimension orthogonal to the nanoslits period direction, the critical dimension size required is not related to the quality factor of the corresponding infinite size filter. Our analysis shows that the critical size is 12 times the filter peak wavelength in the orthogonal dimension for maintaining the filter performance. The 12 times filter wavelength requirement corresponds to the second zero of the Fourier transform of the aperture function.

Suppressing the mechanochromism of flexible photonic crystals

Photonic crystal slabs (PCS) are a promising platform for optical biosensing. Yet, flexible applications based on PCS for biosensing have been limited, as the mechanical properties influence the optical ones. Here, we show the suppression of the mechanochromism effect for flexible PCS. We obtained flexible photonic crystal slabs by sputtering of a dielectric 100 nm Nb₂O₅ high refractive index layer onto a flexible nanostructured polydimethylsiloxane (PDMS) substrate with 370 nm grating period. The PCS exhibit a guided mode resonance at around 650 nm. We demonstrate that these flexible photonic crystal slabs show less than 0.5 nm resonance shift for 4% strain and call them stabilized PCS (sPCS). We compare this to a resonance shift of ∼21 nm for ∼4% strain of a flexible photonic crystal with a flexible nanoparticle high index layer (mechanochromatic PCS, mPCS). This high resonance shift is expected from the Bragg equations, where 4% grating period change correspond to approximately 4% change of the resonance wavelength (i.e., ∼26 nm at a resonance wavelength of 650 nm), if changes in the mode effective refractive index are neglected. In a stretch series we obtain color-to-strain dependencies of 4.79 nm/% strain for mPCS and 0.11 nm/% strain for our stabilized sPCS. We analyze the suppression of the mechanochromism with detailed microscopy results. We observe that fissures and fractures form in the rigid waveguiding layer of the sPCS upon mechanical stress. An algorithm based on Holistically-Nested Edge Detection (HED) is used for automated counting of cracks. Rigid photonic crystal cells with sizes on the order of 10 µm to 100 µm are formed that explain the stable optical properties. Even more stable optical properties with less than 0.03 nm wavelength shift per 1% strain are demonstrated for sPCS with an additional dielectric 100 nm SiO₂ low index layer beneath the Nb₂O₅ waveguide layer decoupling the waveguide further from the flexible PDMS substrate.

Spatially entangled photon pairs from lithium niobate nonlocal metasurfaces

Metasurfaces consisting of nanoscale structures are underpinning new physical principles for the creation and shaping of quantum states of light. Multiphoton states that are entangled in spatial or angular domains are an essential resource for many quantum applications; however, their production traditionally relies on bulky nonlinear crystals. We predict and demonstrate experimentally the generation of spatially entangled photon pairs through spontaneous parametric down-conversion from a metasurface incorporating a nonlinear thin film of lithium niobate covered by a silica meta-grating. We measure the correlations of photon pairs and identify their spatial antibunching through violation of the classical Cauchy-Schwarz inequality, witnessing the presence of multimode entanglement. Simultaneously, the photon-pair rate is strongly enhanced by 450 times as compared to unpatterned films because of high-quality-factor resonances. These results pave the way to miniaturization of various quantum devices by incorporating ultrathin metasurfaces functioning as room temperature sources of quantum-entangled photons.

Collimation and finite-size effects in suspended resonant guided-mode gratings

The optical transmission of resonant guided-mode gratings patterned on suspended silicon nitride thin films and illuminated at normal incidence with a Gaussian beam is investigated both experimentally and theoretically. Effects due to the beam focusing and its finite size are accounted for by a phenomenological coupled-mode model whose predictions are found to be in very good agreement with the experimentally measured spectra for various grating structures and beam sizes, and which allow for a detailed analysis of the respective magnitude of these effects. These results are highly relevant for the design and optimization of such suspended structured films that are widely used for photonics, sensing, and optomechanics applications.

Bi-layered composite gratings with high diffraction efficiency enabled by near-field coupling

In this paper, we present a design method for bi-layered composite gratings to achieve high diffraction efficiency. These composite gratings feature strong near-field coupling between their constituent dielectric subwavelength gratings, thus enabling high-efficiency first-order diffraction in the far-field. An intuitive explanation based on a wavevector matching condition for such high diffraction efficiency composite gratings is provided. According to theoretical analysis, a design strategy for the proposed composite gratings is developed and verified by numerical simulations with gratings working in both TE and TM modes. The proposed strategy could open door to develop bi-layered composite gratings for manipulating diffracted waves with high efficiency, thus may potentially enable new applications in photonic systems.

Creation of Fano resonances and bound states in the continuum in metallic metasurface superlattices

A perfect metal film with a periodic arrangement of cut-through slits, an anisotropic metallic metamaterial film, mimics a dielectric slab and supports guided electromagnetic waves in the direction perpendicular to the slits. Since the guided Bloch modes exist only below the light line, conventional metallic metamaterial films do not exhibit interesting leaky-wave effects, such as bound states in the continuum and Fano resonances. Here, we introduce metallic metasurface superlattices that include multiple slits in a period and demonstrate that the superlattices support the Fano resonances and bound states in the continuum. We show that the number of Fano resonances and bound states depend on the number of slits in a period of superlattices through rigorous finite element method simulations. Experimental results in microwave region also support the creation of Fano resonance and bound states in the continuum by the increment of the number of slits in a period of superlattices.

Artificial Structural Colors and Applications

Structural colors are colors generated by the interaction between incident light and nanostructures. Structural colors have been studied for decades due to their promising advantages of long-term stability and environmentally friendly properties compared with conventional pigments and dyes. Previous studies have demonstrated many artificial structural colors inspired by naturally generated colors from plants and animals. Moreover, many strategies consisting of different principles have been reported to achieve dynamically tunable structural colors. Furthermore, the artificial structural colors can have multiple functions besides decoration, such as absorbing solar energy, anti-counterfeiting, and information encryption. In the present work, we reviewed the typical artificial structural colors generated by multilayer films, photonic crystals, and metasurfaces according to the type of structures, and discussed the approaches to achieve dynamically tunable structural colors.

Ultra Stable Molecular Sensors by Submicron Referencing and Why They Should Be Interrogated by Optical Diffraction-Part II. Experimental Demonstration

Label-free optical biosensors are an invaluable tool for molecular interaction analysis. Over the past 30 years, refractometric biosensors and, in particular, surface plasmon resonance have matured to the de facto standard of this field despite a significant cross reactivity to environmental and experimental noise sources. In this paper, we demonstrate that sensors that apply the spatial affinity lock-in principle (part I) and perform readout by diffraction overcome the drawbacks of established refractometric biosensors. We show this with a direct comparison of the cover refractive index jump sensitivity as well as the surface mass resolution of an unstabilized diffractometric biosensor with a state-of-the-art Biacore 8k. A combined refractometric diffractometric biosensor demonstrates that a refractometric sensor requires a much higher measurement precision than the diffractometric to achieve the same resolution. In a conceptual and quantitative discussion, we elucidate the physical reasons behind and define the figure of merit of diffractometric biosensors. Because low-precision unstabilized diffractometric devices achieve the same resolution as bulky stabilized refractometric sensors, we believe that label-free optical sensors might soon move beyond the drug discovery lab as miniaturized, mass-produced environmental/medical sensors. In fact, combined with the right surface chemistry and recognition element, they might even bring the senses of smell/taste to our smart devices.

Polarization independent enhancement of zeroth order diffracted second harmonic from multilayer gallium selenide on a silicon resonant metasurface

We demonstrate polarization-independent resonant-enhancement of second harmonic generation (SHG) from multilayer Gallium Selenide (GaSe) on a silicon-based resonant metasurface. Two-dimensional hexagonal photonic lattice with circularly symmetric silicon meta-atoms are designed to achieve resonant field enhancement at the fundamental wavelength independent of the incident polarization direction. Such structures are however found to exhibit strong resonant field depolarization effects at the fundamental excitation fields resulting in modified nonlinear polarization components when compared to the native GaSe layer. Furthermore, the sub-wavelength metasurface designed to have resonances at the fundamental wavelengths act as a higher order diffraction grating at the second harmonic wavelength. Nonlinear wave propagation simulations show that the higher order diffracted SHG exhibit strong polarization dependent enhancement with characteristics very different from the native GaSe layer. In this context, polarization independent enhancement of the second harmonic signal is achieved only for the zeroth order diffracted component. Experimental study of second harmonic generation from the GaSe layer integrated with the silicon metasurface shows maximum nonlinear signal enhancement on-resonance with polarization dependence identical to the native GaSe layer by selectively detecting the zeroth-order diffracted component. This work shows that it is not sufficient to use symmetric meta-atoms in such 2D material integrated resonant metasurfaces for achieving polarization independent nonlinear optical enhancement. Depolarization of the resonant fields and higher-order diffraction at the nonlinear signal wavelength need to be considered as well.

Design of a narrowband retroreflector based on guided-mode resonance

A narrowband retroreflector consisting of a grating coupler and a waveguide cavity integrated on a highly reflective substrate is proposed. A theoretical model based on coupled-mode theories is discussed to provide analytical expression of the reflection and transmission coefficients under oblique incidence. The retroreflector was designed with a 20-µm aperture for 1540-nm-wavelength operation and 8-deg-angle incidence. Finite-difference time-domain simulation showed a retroreflection spectrum with a bandwidth of 2 nm and a maximum retroreflectance of 85% and a minimum specular reflectance of 5%.

Tunable terahertz guided-mode resonance filter with a variable grating period

A variable grating period made of quartz has been applied to fabricate a tunable guided mode resonance (TGMR) filter with transverse-electric (TE) and -magnetic (TM) modes in the terahertz (THz) region. We prepared three TGMR filters with grating periods of 5.0, 3.3, and 1.7 μm/mm over the length of the filter. For the 5.0 μm/mm, the resolution of resonance frequency shift of the TE_0,1, TE_1.1, and TM_0,1 was 3.6, 4.0, and 3.4 GHz/mm, respectively. With a metal slit spacing of 2 mm located in front of the TGMR filter, the movable range of the TGMR was 24 mm, and the resonance frequency could be shifted up to 87, 96, and 82 GHz, where the center frequencies of each resonance were 0.402, 0.579, and 0.460 THz, for the TE_0,1, TE_1.1, and TM_0,1, respectively. Furthermore, because the TGMR and guided mode resonance (GMR) filters are placed independently in the THz beam path, both tunable and fixed resonances can be obtained at the same time in the spectrum.

Transmission characteristics of all-dielectric guided-mode resonance filter in the THz region

In this study we report the first on the terahertz (THz) transmission characteristics of a guided-mode resonance (GMR) filter made of all-dielectric material. Two strong transverse electric (TE) resonance modes, TE0,1 and TE1,1, and one strong transverse magnetic (TM) resonance mode, TM0,1, were detected. The measured resonances can be explained by diffraction from the grating surface of the GMR filter, and by guiding along the inside of the filter (slab waveguide). Because two identical GMR filters were employed to overcome limited grating numbers, the measured Q-factors of the TM0,1, TE1,1, and TM0,1 modes were as high as 62.9, 71.0, and 74.4 respectively. Also, we obtained polarization efficiencies of up to 96.9, 96.3, and 92.9% for the TM0,1, TM1,1, and TM0,1 modes, respectively, when the GMR filter was rotated to 90°. By increasing the incident THz beam angle, one TE resonance can be divided into two TE resonances, and the resonant frequency can be adjusted like a THz tunable resonance filter. Furthermore, when the GMR filters were inserted between Teflon plates, only the TM1,1 mode was perfectly removed. The designed GMR filter has a high Q-factor, tunable filter, good polarizer, and good modulator characteristics. These experimental results were in good agreement with simulation results.

Performance analysis of waveguide-mode resonant optical filters with stochastic design parameters

The performance of optical filters with resonant waveguide gratings is investigated numerically in a stochastic context, assuming random fluctuations of various design variables. Specifically, we derive stochastic models based on polynomial chaos expansions, whose involved coefficients are obtained by computing spectral projections via sparse-grid quadrature. The latter exploits purely deterministic results from a rigorous coupled-wave analysis solver and requires less simulation data than standard Monte Carlo (MC) techniques. The statistical moments of the filter's spectral response are calculated reliably, as the comparison against reference results from MC analysis verifies, and the extraction of the Sobol indices reveals the structure's sensitivity with respect to specific design parameters. Moreover, the present analysis clearly points out that neglecting even small geometric variations in the filter design may produce misleading conclusions regarding the corresponding performance, with undesirable consequences in real-life applications.

Tunable guided-mode resonance filter with a gradient grating period fabricated by casting a stretched PDMS grating wedge

A compact, tunable guided-mode resonant filter (GMRF) is experimentally demonstrated whose spectral reflectance wavelength varies as a function of the illumination position on the device. The GMRF consists of a grating of gradient-varying period ranging from 402.5 to 466.6 nm, which is obtained by casting a stretched polydimethylsiloxane (PDMS) grating wedge. By spatially changing the illumination position on the GMRF over 11 mm, a spectral reflectance peak with low sidelobes varies from 596.8 to 684.1 nm. The influence on the resonance efficiency and the limitation of the wavelength tuning range are discussed in depth. The GMRF is a good candidate as a functional filtering component in wavelength selection and sensing applications.

Broadband on-chip near-infrared spectroscopy based on a plasmonic grating filter array

We demonstrate an ultra-compact, broadband on-chip near-infrared (NIR) spectroscopy system based on a narrow-band plasmonic filter array. The entire filter array, consisting of 28 individual subwavelength metallic gratings, was monolithically integrated in a thin gold film on a quartz substrate, covering a 270 nm spectra from 1510 nm to 1780 nm. In order to achieve a high spectral resolution, extremely narrow slits are created for the gratings with a polymer waveguide layer on top, generating narrow-band guided-mode resonances through coupling with the surface-plasmon resonances of the metallic gratings. Experimental results show that the transmission bands of the filter array have full width at half-maximum of only 7 nm-13 nm, which is sufficient for NIR spectroscopy. The NIR absorption spectroscopy of xylene using the on-chip plasmonic filter array matches very well with the results from conventional Fourier transform infrared spectroscopy, which proves the great potential for NIR sensing applications.

Guided-mode resonance, resonant grating thickness, and finite-size effects in dielectric laser acceleration structures

The possibility of exciting guided-mode resonances in dielectric grating laser accelerator structures is discussed. Finite-element method calculations of the accelerating electromagnetic field are presented both for periodic boundary conditions (infinite periodicity) and for finite gratings.

Effect of finite metallic grating size on Rayleigh anomaly-surface plasmon polariton resonances

Rayleigh anomalies (RAs) and surface plasmon polaritons (SPPs) on subwavelength metallic gratings play pivotal roles in many interesting phenomena such as extraordinary optical transmission. In this work, we present a theoretical analysis of the effect of finite metallic grating size on RA-SPP resonances based on the combination of rigorous coupled wave analysis and finite aperture diffraction. One-dimensional arrays of gold subwavelength gratings with different device sizes were fabricated and the optical transmission spectra were measured. As the grating size shrinks, the broadening of the RA-SPP resonances is predicted by the theoretical model. For the first order RA-SPP resonances, the results from this model are in good agreement with the spectra measured from the fabricated plasmonic gratings.

Determination of cavity length of cavity-resonator-integrated guided-mode resonance filter

A cavity-resonator-integrated guided-mode resonance filter is a kind of narrowband filters, which uses a resonance effect of a waveguide cavity. Two experimental methods for determining the cavity length were investigated in order to estimate the response time of the filter. SiO(2)-based filters for operation at 1540-nm wavelength were fabricated and their cavity lengths were determined from measured resonance wavelengths. In the both of methods, the cavity length determined to be 65 μm and the response time was estimated to be 4 psec.

Two dimensional analysis of finite size high-contrast gratings for applications in VCSELs

2-dimensional simulations of high-contrast gratings (HCGs) of finite size are carried out, targeting at their applications in vertical-cavity surface-emitting lasers (VCSELs). Finite HCGs show a very different behavior from infinite grating ones. The reflectivity of a finite HCG strongly depends on the HCG size and the source size. Our simulation results predict finite reflectivity and transmission values, well consistent with reported experimental results. The band of high reflectivity (>99.5%) of finite HCGs is less broad as compared to the infinite case. Losses into a guided mode excited in the HCG plane are identified as being at the root. This guided mode is excited due to the nonzero angular components in the finite source size, and greatly enhances the transmission and the light leakage from the slab. In addition, the simulation results show that the details of the finite HCG can shape the output beam, whilst a Gaussian-like reflected wave is typically achieved. Our simulations can explain the current discrepancies between numerical predictions of reflectivities approaching 100% and working HCG-VCSELs showing finite reflectivities and nearly Gaussian-like output. Consequently, our analysis of finite HCGs is indispensable for HCG-VCSEL design.

Finite-size limitations on Quality factor of guided resonance modes in 2D photonic crystals

High-Q guided resonance modes in two-dimensional photonic crystals, enable high field intensity in small volumes that can be exploited to realize high performance sensors. We show through simulations and experiments how the Q-factor of guided resonance modes varies with the size of the photonic crystal, and that this variation is due to loss caused by scattering of in-plane propagating modes at the lattice boundary and coupling of incident light to fully guided modes that exist in the homogeneous slab outside the lattice boundary. A photonic crystal with reflecting boundaries, realized by Bragg mirrors with a band gap for in-plane propagating modes, has been designed to suppress these edge effects. The new design represents a way around the fundamental limitation on Q-factors for guided resonances in finite photonic crystals. Results are presented for both simulated and fabricated structures.

Polarization-independent guided-mode resonance filter with cross-integrated waveguide resonators

A cavity-resonator-integrated guided-mode resonance filter (CRIGF) has been proposed and investigated in order to realize high-efficiency narrowband reflection with a small aperture. The CRIGF consists of a grating coupler integrated in a cavity resonator constructed by a pair of distributed Bragg reflectors on a thin-film waveguide. This time, orthogonally crossed integration of two CRIGFs was demonstrated in order to obtain polarization-independent reflection spectrum. An SiO2-based device with 10 μm aperture was designed and fabricated for around 850 nm wavelength operation, and narrowband polarization-independent reflection was confirmed experimentally.

Cavity-resonator-integrated guided-mode resonance filter for aperture miniaturization

A guided-mode resonance filter integrated in a waveguide cavity resonator constructed by two distributed Bragg reflectors is designed and fabricated for miniaturization of aperture size. Reflection efficiency of >90% and wavelength selectivity of 0.4 nm are predicted in the designed SiO(2)-based filter with 50-μm aperture by a numerical calculation using the finite-difference time-domain method. A maximum reflectance of 67% with 0.5-nm bandwidth is experimentally demonstrated by the fabricated device at around 850-nm wavelength.

Performance of conformal guided mode resonance filters

Guided mode resonance (GMR) filters are highly functional micro-optics capable of narrowband spectral filtering. GMR devices have previously been demonstrated on flat substrates using a wide range of materials and configurations. In this Letter, we apply a soft lithographic technique followed by the deposition of dielectric layers to generate GMR filters on a concave lens surface. Resonances of the resulting conformal GMR filters are experimentally measured and characterized, and the results are compared to the performance of similar GMR filters fabricated on flat surfaces.

Depolarization of quasi-monochromatic light by thin resonant gratings

Using rigorous diffraction theory, we show that it is possible to depolarize quasi-monochromatic light using a fully deterministic, thin optical element. The principle is based on polarization-sensitive resonant gratings in total-internal-reflection configuration, and careful numerical design by the Fourier modal method. We present numerical examples for 0.1 nm and 10 nm bandwidths.

Dynamic guided-mode resonant grating filter with quadratic electro-optic effect

We propose a novel and simple concept of dynamic switching of guided-mode resonant grating filters with quadratic electro-optic effect within a waveguide layer modulated by external fields due to comb-shaped electrodes that also behave as a grating. As the device has subwavelength structure, the performance must be analyzed electromagnetically. We describe numerical simulation with the finite-difference time-domain method specially modified so that it can treat inhomogeneous anisotropic media such as lead lanthanum zirconate titanate.

Implementation of a graded-index medium by use of subwavelength structures with graded fill factor

We present a novel configuration for the implementation of subwavelength-based graded-index devices. The proposed concept is based on the etching of one-dimensional subwavelength gratings into a high-index slab waveguide to achieve the desired effective index distribution. A graded-index profile can be achieved by gradually modifying the duty ratio of the grating along the horizontal axis, while the beam is confined in the vertical direction by the slab waveguide. On the basis of this concept, novel graded-index lenses and waveguides are both proposed and characterized numerically by use of finite-difference time-domain and finite-element analysis. The proposed devices can be used for guiding, imaging, optical signal processing, mode matching, coupling, and other applications while offering the intrinsic advantages of on-chip integration such as miniaturization, eliminating the need to align each component separately, and compatibility with standard microfabrication techniques for manufacturability.

Numerical study on an asymmetric guided-mode resonant grating with a Kerr medium for optical switching

Optical switching effects of a guided-mode resonant grating (GMRG) with a Kerr medium have been simulated with the nonlinear finite differential time domain (FDTD) method. An asymmetric waveguide grating with a large second spatial harmonic component has been proposed for the optical switch. Resonant reflection occurs at both of the band-edge wavelengths. These wavelengths are used for the pump light and the probe light. The enhanced electric field of the pump light changes the resonant wavelength for the probe light as a result of the Kerr effect. We designed the GMRG with resonant wavelengths of 1489.6 and 1630 nm, which were used for the pump light and the probe light, respectively. When the grating material has a third-order susceptibility chi(3) of 8.5 x 10(-10) esu, the transmittance of the probe light changes from 0 to 80% by increasing the intensity of the pump light from 0 to 60 kW/mm2.

Effect of finite grating, waveguide width, and end-facet geometry on resonant subwavelength grating reflectivity

Resonant subwavelength gratings (RSGs) offer narrowband high reflectivity with low-reflectivity sidebands. Analysis with the commonly used rigorous coupled-wave analysis assumes an RSG with infinite lateral extent and illumination by plane waves. This analysis is performed with a finite-difference semivectorial high-order accurate two-dimensional Helmholtz code that is able to simulate the entire finite RSG structure in the dimension of the grating vector. We study the effect of finite beam size on RSG reflectivity, resonant wavelength, and spectral response width. Independently, we study the effect of a finite RSG by varying the waveguide length and number of grating periods while fixing the beam size. We show that the placement of the waveguide end facets relative to the termination of the grating has a significant effect on the reflectivity and response width.

Tunable, oblique incidence resonant grating filter for telecommunications

We have designed a tunable, oblique-incidence resonant grating filter that covers the C band as an add-drop device for incident TE-polarized light. We tune the filter by tilting a microelectromechanical systems platform onto which the filter is attached. The fabrication tolerances as well as the role of finite incident-beam size and limited device size were addressed. The maximum achievable efficiency of a finite-area device as well as a scaling law that relates the resonance peak width and the minimum device size is derived. In good agreement with simulations, measurements indicate a negligible change in shape of the resonance peak from 1526 nm at a 45 degrees angle of incidence to 1573 nm at a 53 degrees angle with a full width at half-maximum of 0.4 nm. In this range the shift of the peak wavelength is linear with respect to changes in the angle of incidence.

Controlling the spectral response in guided-mode resonance filter design

Techniques for controlling spectral width are used in conjunction with thin-film techniques in the design of guided-mode resonance (GMR) filters to provide simultaneous control over line-shape symmetry, sideband levels, and spectral width. Several factors that could limit the minimum spectral width are discussed. We used interference effects for passband shaping by stacking multiple GMR filters on top of one another. A design is presented for a 200-GHz telecommunications filter along with a tolerance analysis. Compared with a conventional thin-film filter, the GMR filter has fewer layers and looser thickness tolerances. Grating fabrication tolerances are also discussed.

Dispersion relation of guided-mode resonances and Bragg peaks in dielectric diffraction gratings

We present the dispersion relation of guided-mode resonances in non-dissipative dielectric diffraction gratings, both for s-polarized (TE mode) and p-polarized (TM mode) incident waves. We present a simple approximate theory as well as a rigorous calculation within the so-called coupled-wave theory. We discuss the dependence of the positions and the lifetimes of the resonances on the thickness of the gratings and on the strength of its modulation. We find that the diffraction efficiency of the different orders show peaks at different Bragg orders.

Guided-mode resonant subwavelength gratings: effects of finite beams and finite gratings

The effects of finite beams and finite gratings on the performance of guided-mode resonant subwavelength gratings are characterized by using the rigorous boundary element method. The gratings are strongly modulated, have a finite number of periods, and are illuminated by normally incident Gaussian beams. Quantitative results are presented for silicon-on-sapphire resonant gratings and gallium arsenide-aluminum arsenide resonant gratings.