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

Bloch-surface-wave resonance in a cavity resonator for focusing retroreflection

A wavelength-selective retroreflector for a diverging wave will be an attractive external mirror for compact wavelength-stabilized semiconductor lasers and consists of a focusing grating coupler and a cavity resonator. In this Letter, the retroreflector utilizing a Bloch surface wave (BSW) resonance was theoretically investigated for improving the retro-reflectance in comparison to a previously reported structure utilizing guided-mode resonance (GMR). A retroreflector with an aperture size of 31 µm and focal length of 67 µm was designed for an operation wavelength of 1550 nm. The maximum retro-reflectance is predicted by numerical simulation to be higher by 11% than that of the GMR-based retroreflector.

Selective excitation of high-order modes in two-dimensional cavity resonator integrated grating filters

The selective spatial mode excitation of a bi-dimensional grating-coupled micro-cavity called a cavity resonator integrated grating filter (CRIGF) is reported using an incident beam shaped to reproduce the theoretical emission profiles of the device in one and subsequently two dimensions. In both cases, the selective excitation of modes up to order 10 (per direction) is confirmed by responses exhibiting one (respectively two) spectrally narrowband resonance(s) with a good extinction of the other modes, the latter being shown to depend on the parity and order(s) of the involved modes. These results pave the way toward the demonstration of multi-wavelength spatially selective reflectors or fiber-to-waveguide couplers. Also, subject to an appropriate choice of the materials constituting the CRIGF, this work can be extended to obtain mode-selectable laser emission or nonlinear frequency conversion.

Reflection characteristics of a cavity-resonator-integrated guided-mode resonance mirror for a microdiameter Gaussian beam

A guided-mode resonance mirror was designed for reflecting a vertically incident Gaussian beam of 3.6-µm beam waist to a backpropagating Gaussian beam. A grating coupler (GC) is integrated in a waveguide resonance cavity consisting of a pair of distributed Bragg reflectors (DBRs) on a reflection substrate. An incident free-space wave is coupled by the GC into the waveguide, and the guided wave is resonated in the waveguide cavity and coupled out by the same GC to a free-space wave simultaneously in resonance condition. The reflection phase can vary by 2π rad, according to wavelength in a wavelength band of resonance. The grating fill factors of the GC were apodized to have a Gaussian profile in its coupling strength and resultantly maximize a Gaussian reflectance defined by the power ratio of backpropagating Gaussian beam to the incident Gaussian beam. The fill factors of the DBR were also apodized in the boundary zone to the GC in order to avoid discontinuity in equivalent refractive index distribution and resultant scattering loss. Guided-mode resonance mirrors were fabricated and characterized. The Gaussian reflectance of the mirror with the grating apodization was measured to be 90%, higher by 10% than that of the mirror without apodization. It is also demonstrated that the reflection phase changes more than π rad within wavelength band of 1 nm. The fill factor apodization narrows the resonance band.

Inverse-cavity structure for low-threshold miniature lasers

Creating micro and nano lasers, high threshold gain is an inherent problem that have critically restricted their great technological potentials. Here, we propose an inverse-cavity laser structure where its threshold gain in the shortest-cavity regime is order-of-magnitude lower than the conventional cavity configurations. In the proposed structure, a resonant feedback mechanism efficiently transfers external optical gain to the cavity mode at a higher rate for a shorter cavity, hence resulting in the threshold gain reducing with decreasing cavity length in stark contrast to the conventional cavity structures. We provide a fundamental theory and rigorous numerical analyses confirming the feasibility of the proposed structure. Remarkably, the threshold gain reduces down by a factor ~ 10⁻³ for a vertical-cavity surface-emitting laser structure and ~ 0.17 for a lattice-plasmonic nanocavity structure. Therefore, the proposed approach may produce extremely efficient miniature lasers desirable for variety of applications potentially beyond the present limitations.

Cavity resonator-integrated guided-mode resonance filters with on-chip electro- and thermo-optic tuning

Cavity resonator grating filters (CRIGFs) integrated on lithium niobate on insulator (LNOI) with electrical tuning elements are reported. The resonance wavelength of the filters is in the 780 nm range. Integrated thermo-optical tuning range of 2.5 nm is measured using integrated resistors, whilst a 0.7 nm electro-optical tuning range using capacitive metallic pads is achieved with ±400V drive voltage.

Strongly Enhanced Second Harmonic Generation in a Thin Film Lithium Niobate Heterostructure Cavity

Boosting second-order optical nonlinear frequency conversion over subwavelength thickness has long been pursued through optical resonance in micro- and nanophotonics. However, the availability of thin film materials with high second-order nonlinearity is limited to III-V semiconductors, which have low transparency in the visible. Here, we experimentally demonstrated strongly enhanced second harmonic generation in one-dimensional heterostructure cavities on thin film lithium niobate. A guided-mode resonance resonator and distributed Bragg reflectors are combined for both efficient coupling and electromagnetic field localization. Over 1200 times second harmonic generation enhancement is experimentally realized compared with flat thin film lithium niobate through optimizing the trade-off between quality factor and mode volume, leading to a record high normalized conversion efficiency of 2.03×10^{-5}  cm^{2}/GW under 1.92  MW/cm^{2} pump intensity. Our approach could inspire the miniaturization and integration of compact resonant nonlinear photonic devices on thin film lithium niobate.

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.

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%.

Extended cavity quantum cascade laser with cavity resonator integrated grating filter

We report on an extended cavity quantum cascade laser based on a cavity resonator integrated grating filter (CRIGF) that acts as both cavity end-reflector and spectral selector. Stable, mode-hop free, single-mode emission around 2150 cm^-1 is obtained over large injection current ranges (more than 50 mA) with a typical threshold around 290 mA. A digital frequency tuning over more than 65 cm^-1 is obtained by changing the periodicity of the CRIGF ending the extended cavity.

Angle- and polarization-independent mid-infrared narrowband optical filters using dense arrays of resonant cavities

We report design and experimental verification of narrowband mid-infrared optical filters with transmission characteristics that are practically constant over a wide range of incident angles. The filter employs a dense array of dielectric resonant cavities in a metal film, where the transmission of each cavity depends upon localized rather than travelling fields, making the filter fundamentally angle-independent. We show experimentally a transmission around 90% from normal incidence up to 60°. Simulations show that the filter becomes polarization-independent when geometry of the cavities is azimuthally symmetric.

Second-harmonic-generation enhancement in cavity resonator integrated grating filters

We demonstrate numerically and experimentally second-harmonic generation (SHG) in a cavity resonator integrated grating filter (CRIGF, a planar cavity resonator made of Bragg grating reflectors) around 1550 nm. SHG is modeled numerically for several different systems, including a thin plane layer of LiNbO₃ without and with a grating coupler to excite a waveguide mode. We demonstrate that when the waveguide mode is confined to a CRIGF, designed to work with focused incident beams, the SHG power is increased more than 30 times, compared to the case of a single grating coupler used with an almost collimated pump beam.

Mid-infrared cavity resonator integrated grating filters

Cavity Resonator Grating Filters (CRIGFs) working in the Mid-Infrared are reported, with narrow-band resonant reflectivity peaks around 2200 cm^-1 (4.6 µm). They are fabricated in the GaAs/AlGaAs material system that can potentially cover the whole [1-12] µm spectral range. TE-polarized peak reflectivity is 30% with a 4 cm^-1 full width at half maximum.

Wavelength division multiplexer based on cavity-resonator-integrated guided-mode resonance filters for a compact multi-wavelength light source

Cavity-resonator-integrated guided-mode resonance filters (CRIGF) consisting of a grating coupler in a waveguide resonator formed by two distributed Bragg reflectors of different reflectances can act as a wavelength-selective reflector and an input waveguide coupler for an incident free-space wave. Integration of CRIGFs in a waveguide is proposed to give an array of external mirrors and a wavelength division multiplexer for constructing a compact multi-wavelength light source. Four CRIGFs of 10-μm-size aperture with a wavelength spacing of 15 nm were designed and fabricated. The reflectance of 62% and output efficiency of higher than 18% were theoretically predicted. Multiplexing of four wavelengths was confirmed experimentally.

Tunable graded cavity resonator integrated grating filters

We demonstrated Graded Cavity Resonator Integrated Grating Filters (G-CRIGFs) that are narrowband spectral reflectors, spectrally tunable over more than 40 nm around 850 nm using a spatial gradient. A simple analytical model is introduced and validated experimentally to determine spectral performance of G-CRIGFs from the spectral properties of a standard Cavity Resonator Integrated Grating Filter (CRIGF).

Divergence-tolerant resonant bandpass filters

Bandpass filters based on subwavelength dielectric gratings are grounded in physical principles that are totally distinct from their thin-film counterparts. Ease in fabrication, design scalability, material sparsity, and on-chip integration compatibility makes them a promising alternative especially for long-wavelength applications. Here we demonstrate the interesting attribute of resonant bandpass filters of high angular stability for fully conical light incidence. Fashioning an experimental bandpass filter with a subwavelength silicon grating on a quartz substrate, we show that fully conical incidence provides an angular full width at half-maximum linewidth of ∼9.5° compared to a linewidth of ∼0.1° for classical incidence. Slow angular variation of the central wavelength with full conical incidence arises via a corresponding slow angular variation of the resonant second diffraction orders driving the pertinent leaky modes. Moreover, full conical incidence maintains a profile with a single passband as opposed to the formation of two passbands characteristic of resonant subwavelength gratings under classical incidence. Our experimental results demonstrate excellent stability in angle, spectral profile, linewidth, and efficiency.

Cavity-resonator-integrated guided-mode resonance band-stop reflector

A cavity-resonator-integrated guided-mode resonance filter (CRIGF) consists of a grating coupler inside a pair of distributed Bragg reflectors. A combination of a CRIGF with a high-reflection substrate can provide a new type of a band-stop reflector with a small aperture for a vertically incident wave from air. A narrow stopband was theoretically predicted and experimentally demonstrated. It was quantitatively shown that reflection spectra depended on optical-buffer-layer thickness. The reflector of 10-μm aperture was fabricated and characterized. The extinction ratio in reflectance was measured to be lower than -20 dB at a resonance wavelength. The bandwidth at -3 dB was 0.15 nm.

Two-dimensional grating for narrow-band filtering with large angular tolerances

A two-dimensional periodic sub-wavelength array of vertical dielectric cylinders on a glass substrate is studied numerically using three different electromagnetic approaches. It is shown that such structure can present a narrow-band spectral resonance characterized by large angular tolerances and 100% maximum in reflection. In particular, in a two-nanometer spectral bandwidth the reflectivity stays above 90% within angles of incidence exceeding 10 degrees for unpolarized light. Bloch modal analysis shows that these properties are due to the excitation of a hybrid mode that is created in the structure by a guided-like mode and a localized cavity mode. The first one is due to the collective effect of the array, while the second one comes from the mode(s) of a single step-index fiber.

Electromagnetic modeling of large subwavelength-patterned highly resonant structures

The rigorous modeling of large (hundreds of wavelengths) optical resonant components patterned at a subwavelength scale remains a major issue, especially when long range interactions cannot be neglected. In this Letter, we compare the performances of the discrete dipole approximation approach to that of the Fourier modal, the finite element and the finite difference time domain methods, for simulating the spectral behavior of a cavity resonator integrated grating filter (CRIGF). When the component is invariant along one axis (two-dimensional configuration), the four techniques yield similar results, despite the modeling difficulty of such a structure. We also demonstrate, for the first time to the best of our knowledge, the rigorous modeling of a three-dimensional CRIGF.

High-order modes in cavity-resonator-integrated guided-mode resonance filters (CRIGFs)

Cavity-resonator-integrated guided-mode resonance filters (CRIGFs) are optical filters based on weak coupling by a grating between a free-space propagating optical mode and a guided mode, like guided-mode resonance filters (GMRFs). As compared to GMRFs they offer narrowband reflection with small aperture and high angular acceptance. We report experimental characterization and theoretical modeling of unexpected high-order reflected modes in such devices. Using coupled-mode modeling and moiré analysis we provide physical insight on key mechanisms ruling CRIGF properties. This model could serve as a simple and efficient framework to design new reflectors with tailored spatial and spectral modal reflectivities.

Design of guided-mode resonance mirrors for short laser cavities

A guided-mode resonance mirror (GMRM) consists of a waveguide grating integrated on an optical buffer layer on a high-reflection substrate. An incident free-space wave at the resonance wavelength is once coupled by the grating to a guided mode and coupled again by the same grating back to free space. The reflection characteristics of a GMRM are numerically calculated and theoretically analyzed. It is predicted that notch filtering or flat reflection spectra are obtained depending on the optical buffer layer thickness. Design of short cavities using a GMRM is discussed for potential application in surface-mount packaging of diode lasers onto a photonic circuit board.

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.

Reflection characteristics of guided-mode resonance filter combined with bottom mirror

A new type of mirror, based on guided-mode resonance, was proposed and discussed to provide a mirror having high reflectance and large wavelength dependence of reflection phase variation. The proposed mirror consists of a surface grating integrated in a channel waveguide on a high-reflection layer. A SiO2-based device was fabricated for 0.85-μm wavelength operation, and reflection phase variation of almost π, with wavelength change of sub-nanometers, was confirmed experimentally.

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.

High angular tolerance and reflectivity with narrow bandwidth cavity-resonator-integrated guided-mode resonance filter

Guided mode resonance filters (GMRFs) are a promising new generation of reflective narrow band filters, that combine structural simplicity with high efficiency. However their intrinsic poor angular tolerance and huge area limit their use in real life applications. Cavity-resonator-integrated guided-mode resonance filters (CRIGFs) are a new class of reflective narrow band filters. They offer in theory narrow-band high-reflectivity with a much smaller footprint than GMRF. Here we demonstrate that for tightly focused incident beams adapted to the CRIGF size, we can obtain simultaneously high spectral selecitivity, high reflectivity, high angular acceptance with large alignment tolerances. We demonstrate experimentally reflectivity above 74%, angular acceptance greater than ±4.2° for a narrow-band (1.4 nm wide at 847 nm) CRIGF.