A Bragg resonator uses dielectric plates within a metallic cavity to confine the energy within a central free space region. The importance of the permittivity is shown with a better Q-factor possible using higher permittivity materials of larger intrinsic dielectric losses. This is because the electric energy in the reflectors decreases proportionally to the square root of permittivity and the coupling to the metallic losses decrease linearly. In a sapphire resonator with a single reflector pair a Q-factor of 2.34x10^5 is obtained, which may be improved on by up to a factor of 2 using higher permittivity materials.
The reflectivity of various Bragg reflectors in connection to waveguide structures, including nanowires, has been investigated using modal reflection and transmission matrices. A semi-analytical model was applied yielding increased understanding of the diffraction effects present in such gratings. Planar waveguides and nanowire lasers are considered in particular. Two geometries are compared; Bragg reflectors within the waveguides are shown to have significant advantages compared to Bragg reflectors in the substrate, when diffraction effects are significant.
We present plasmonic Bragg reflectors for increasing the extraordinary optical transmission through periodic arrays of subwavelength apertures in a metal film. The increase in transmission arises by preventing loss at the edges of the array. The plasmonic Bragg reflectors have periodicity of half the usual array's periodicity. Nano-hole arrays flanked thus by reflectors exchibited double the transmission as compared to the arrays without reflectors. These structures may also be used to isolate devices in plasmonic integrated circuits.
We show how the recently found quasi-bound state in the continuum optical states in dielectric antennae can be utilized to engineer pillar microcavities design with the substantially optimized quality factor to mode volume ratio.
This paper reports on design, measurement and optimisation of a Tamm plasmon metal-DBR cavity for use in the green part of the visible spectrum. It uses an optimised silver layer thickness and a porous DBR created using a novel electro-chemical etching technique. This device has applications in low cost lasers, photodetectors and photoconductive switches for the visible wavelength range.
We propose a composite multilayer structure consist of graphene Tamm plasmon and Bragg reflector with defect layer to realize the low threshold and tunable optical bistability (OB) at the terahertz frequencies. This low-threshold OB originates from the couple of the Tamm plasmon (TP) and the defect mode (DM). We discuss the influence of graphene and the DM on the hysteretic response of the TM-polarized reflected light. It is found that the switch-up and switch-down threshold required to observe the optical bistable behavior are lowered markedly due to the excitation of the TP and DM. Besides, …
A series of thin layers of alternating refractive index is known to make a good optical mirror over certain bands of frequency. Such a device - often termed the Bragg reflector - is usually introduced to students within the first years of an undergraduate degree, often in isolation from other parts of the course. Here we show that the basic physics of wave propagation through a stratified medium can be used to illustrate some more modern developments in optics as well as quantum physics; from transfer matrix techniques, to the optical properties of cold trapped atoms, optomechanical cooling, a…
We report on the efficacy of a novel design for dielectric laser accelerators by adding a distributed Bragg reflector (DBR) to a dual pillar grating accelerating structure. This mimics a double-sided laser illumination, resulting in an enhanced longitudinal electric field while reducing the deflecting transverse effects, when compared to single-sided illumination. We improve the coupling efficiency of the incident electric field into the accelerating mode by 57 percent. The 12 $μ$m long structures accelerate sub-relativistic 28 keV electrons with gradients of up to 200 MeV/m in theory and 133 …
The photonic band dispersion and density of states (DOS) are calculated for the three-dimensional (3D) hexagonal structure corresponding to a distributed Bragg reflector patterned with a 2D triangular lattice of circular holes. Results for the Si/SiO$_2$ and GaAs/AlGaAs systems determine the optimal parameters for which a gap in the 2D plane occurs and overlaps the 1D gap of the multilayer. The DOS is considerably reduced in correspondence with the overlap of 2D and 1D gaps. Also, the local density of states (i.e., the DOS weighted with the squared electric field at a given point) has strong v…
Distributed bragg reflectors (DBRs) consisting of ZnO and amorphous silicon (a-Si) were prepared by magnetron sputtering method for selective light trapping. The quarter-wavelength ZnO/a-Si DBRs with only 6 periods exhibit a peak reflectance of above 99% and have a full width at half maximum that is greater than 347 nm in the range of visible to infrared. The 6-pair reversed quarter-wavelength ZnO/a-Si DBRs also have a peak reflectance of 98%. Combination of the two ZnO/a-Si DBRs leads to a broader stopband from 686 nm to 1354 nm. Using the ZnO/a-Si DBRs as the rear reflector of a-Si thin film…
We demonstrate a combination of optical and electronic feedback that significantly narrows the linewidth of distributed Bragg reflector lasers (DBRs). We use optical feedback from a long external fiber path to reduce the high-frequency noise of the laser. An electro-optic modulator placed inside the optical feedback path allows us to apply electronic feedback to the laser frequency with very large bandwidth, enabling robust and stable locking to a reference cavity that suppresses low-frequency components of laser noise. The combination of optical and electronic feedback allows us to significan…
There are two main physical properties needed to fabricate 1D photonic structures and form perfect photonic bandgaps: the quality of the thickness periodicity and the refractive index of their components. Porous silicon (PS) is a nano-structured material widely used to prepare 1D photonic crystals due to the ease of tuning its porosity and its refractive index by changing the fabrication conditions. Since the morphology of PS changes with porosity, the determination of PS's refractive index is no easy task. To find the optical properties of PS we can use different effective medium approximatio…
A hybrid computational method of plane-wave and cylindrical-wave expansions for distributed Bragg-reflector (DBR) pillars is proposed. The plane-wave expansion is employed to represent the one-dimensional periodic structure of the DBR. The cylindrical-wave expansion is employed to describe the scattering by circular pillars with the DBR structure inside. This formalism enables us to calculate the radiation fields, $t$-matrices, scattering cross sections, photonic band structures, and quality factors of the DBR pillars. Furthermore, optical properties of arrayed DBR pillars are also investigate…
We discuss a phase-sensitive technique for remote interrogation of passive Bragg grating Fabry-Perot resonators. It is based on Pound-Drever-Hall laser frequency locking, using radio-frequency phase modulation sidebands to derive an error signal from the complex optical response, near resonance, of a Fabry-Perot interferometer. We examine how modulation frequency and resonance bandwidth affect this error signal. Experimental results are presented that demonstrate when the laser is locked, this method detects differential phase shifts in the optical carrier relative to its sidebands, due to min…
Experimental Demonstration of Plasmon-Enabled Monolithic Bragg Reflectors for Infrared Light via Inverse Design
Wrocław University of Science and Technology（弗罗茨瓦夫科技大学）；Lodz University of Technology（罗兹理工大学）；Łukasiewicz Research Network — Institute of Microelectronics and Photonics（卢卡谢维奇研究网络微电子与光子学研究所）
We propose and analyze a new type of a resonator in an annular geometry which is based on a single defect surrounded by radial Bragg reflectors on both sides. We show that the conditions for efficient mode confinement are different from those of the conventional Bragg waveguiding in a rectangular geometry. A simple and intuitive approach to the design of optimal radial Bragg reflectors is proposed and employed, yielding chirped gratings. Small bending radii and strong control over the resonator dispersion are possible by the Bragg confinement. A design compromise between large Free Spectral Ra…
With transfer matrix theory, we study the transmission of a distributed Bragg reflector (DBR) with two dielectric gratings on top and on the bottom. Owing to the diffraction of the two gratings, the transmission shows a comb-like spectrum which red shifts with increasing the grating period during the forbidden band of the DBR. The number density of the comb peaks increases with increasing the number of the DBR cells, while the ratio of the average full width at half maximum (FWHM) of the transmission peaks in the transmission comb to the corresponding average free spectral range, being about 0…
We investigate Tamm plasmon (TP) modes in a metal/semiconductor distributed Bragg reflector (DBR) interface. A thin Ag (silver) layer with an optimized thickness (~ 55 nm from simulation) was deposited on nanoporous GaN DBRs fabricated using electrochemical etching on freestanding semipolar GaN substrates. The reflectivity spectra of the DBRs are compared before and after the Ag deposition and with that of a blanket Ag layer deposited on GaN. The results indicate presence of a TP mode at ~ 455 nm on the structure after the Ag deposition. An active medium can also be accommodated within the mod…
The authors report on observation of Bragg confined mode in a hollow cylindrical dielectric cavity. A resonance was observed at 13.4 $GHz$ with an unloaded Q-factor of order $2\times10^5$, which is more than a factor of 6 above the dielectric loss limit. Previously such modes have only been realized from pure Transverse Electric modes with no azimuthal variations and only the $E_ϕ$ component. From rigorous numeric simulations it is shown that the mode is a hybrid mode with non-zero azimuthal variations and with dominant $E_r$ and $E_ϕ$ electric field components and $H_z$ magnetic field compone…
Adiabatic following has been an widely-employed technique for achieving near-complete population transfer in a two-level quantum mechanical system. The theoretical basis, however, could be generalized to a broad class of systems exhibiting SU(2) symmetry. In the present work, we present an analogy of population transfer dynamics of two level system with that of light propagation in a classical one-dimensional photonic crystal, commonly known as distributed-Bragg-reflector (DBR).This formalism facilitates in adapting the idea of adiabatic following, more precisely the rapid adiabatic passage (R…
We demonstrate an amplitude-based micro-displacement sensor that uses a plastic photonic bandgap Bragg fiber with one end coated with a silver layer. The reflection intensity of the Bragg fiber is characterized in response to different displacements (or bending curvatures). We note that the Bragg reflector of the fiber acts as an efficient mode stripper for the wavelengths near the edge of the fiber bandgap, which makes the sensor extremely sensitive to bending or displacements at these wavelengths. Besides, by comparison of the Bragg fiber sensor to a sensor based on a regular multimode fiber…
Adiabatic following has been an widely-employed technique for achieving near-complete population transfer in a `two-level' quantum mechanical system. The theoretical basis, however, could be generalized to a broad class of systems exhibiting SU(2) symmetry. In the present work, we present an analogy of population transfer dynamics of two level atomic system with that of light propagation in a classical `one-dimensional' photonic crystal, commonly known as distributed-Bragg-reflector (DBR). This formalism facilitates in adapting the idea of adiabatic following, more precisely the rapid adiabati…
We demonstrate Kerr-frequency-comb generation with nanofabricated Fabry-Perot resonators with photonic-crystal-reflector (PCR) end mirrors. The PCR group-velocity-dispersion (GVD) is engineered to counteract the strong normal GVD of a rectangular waveguide fabricated on a thin, 450 nm silicon nitride device layer. The reflectors provide the resonators with both the high optical quality factor and anomalous GVD required for Kerr-comb generation. We report design, fabrication, and characterization of devices in the 1550 nm wavelengths bands, including the GVD spectrum and quality factor. Kerr-co…
We report intracavity Bragg scattering induced by photorefractive (PR) effect in high-Q lithium niobate (LN) ring resonators at cryogenic temperatures. We show that, when a cavity mode is strongly excited, the PR effect imprints a long-lived periodic space-charge field. This residual field in turn creates a refractive index modulation pattern that dramatically enhances the back scattering of an incoming probe light, and results in selective and reconfigurable mode splittings. This PR-induced Bragg scattering effect, despite being undesired for many applications, could be utilized to enable opt…
In this paper we propose a new optical ring resonator with a very high Q-factor, to be used as a basic element in a wide range of physics and engineering applications. We theoretically demonstrate that in large size conventional ring resonators, a value of the Q-factor higher than 109 is achievable by exploiting the band-edge resonances in a waveguiding long period Bragg grating closed loop, excited through a bus waveguide. The dispersion introduced by the Bragg grating is responsible for a reduction in the band edge resonance linewidth, which is inversely proportional to the square of the num…
Effects of surface roughness and top layer thickness on the performance of Fabry-Perot cavities and responsive open resonators based on distributed Bragg reflectors
Distributed Bragg Reflectors (DBR) are well-established photonic structures that are used in many photonic applications. However, most of the DBRs are based on different materials or require post-process etching which can hinder integration with other components in the final photonic structure. Here, we demonstrate the fabrication of DBR structures consisting only of undoped boron nitride (BN) layers with high refractive index contrast by using Metal-Organic Chemical Vapor Deposition (MOCVD). This has been achieved in a single process, without the need for any post-process etching. The differe…
We report a versatile and cost-effective way of controlling the unsaturated loss, modulation depth and saturation fluence of graphene-based saturable absorbers (GSAs), by changing the thickness of a spacer between SLG and a high-reflection mirror. This allows us to modulate the electric field intensity enhancement at the GSA from 0 up to 400%, due to the interference of incident and reflected light at the mirror. The unsaturated loss of the SLG-mirror-assembly can be reduced to$\sim$0. We use this to mode-lock a VECSEL from 935 to 981nm. This approach can be applied to integrate SLG into vario…
We theoretically investigate integrated photonic resonators formed by two mutually coupled Sagnac loop reflectors (MC-SLRs). Mode interference in the MC-SLR resonators is tailored to achieve versatile filter shapes with high performance, which enable flexible spectral engineering for diverse applications. By adjusting the reflectivity of the Sagnac loop reflectors (SLRs) as well as the coupling strength between different SLRs, we achieve optical analogues of Fano resonance with ultrahigh spectral slope rates, wavelength interleaving / non-blocking switching functions with significantly enhance…
The scattering of weak dispersive waves (DW) on several equally spaced temporal solitons is studied. It is shown by systematic numerical simulations that the reflection of the DWs from the soliton trains strongly depends on the distance between the solitons. The dependence of the reflection and transmission coefficients on the inter-soliton distance and the frequency of the incident waves is studied in detail, revealing fascinating quasi-periodic behavior. The analogy between the observed nonlinear phenomena in temporal domain and usual Fabry-Perot and Bragg resonators is discussed.
Micro-domes based on a combination of metallic and dielectric multilayer mirrors are studied using a fully vectorial numerical basis-expansion method that accurately accounts for the effects of an arbitrary Bragg stack and can efficiently cover a large range of dome shapes and sizes. Results are examined from three different viewpoints: (i) the ray-optics limit, (ii) the (semi-) confocal limit for which exact wave solutions are known, and (iii) the paraxial approximation using vectorial Gaussian beams.
We study nonlinear wave phenomena in coupled ring resonator optical waveguides in the tight coupling regime. A discrete model for the system dynamics is put forward and its steady state nonlinear Bloch modes are derived. The switching behavior of the transmission system is addressed numerically and the results are explained in the light of this analytical result. We also present a numerical study on the spontaneous generation of Bragg solitons from a continuous-wave input.
Lasing at telecommunication wavelengths from annular resonators employing radial Bragg reflectors is demonstrated at room temperature under pulsed optical pumping. Sub milliwatt pump threshold levels are observed for resonators with 0.5-1.5 wavelengths wide defects of radii 7-8 mm. The quality factors of the resonator modal fields are estimated to be on the order of a few thousands. The electromagnetic field is shown to be guided by the defect. Good agreement is found between the measured and calculated spectrum.
A novel class of circular resonators, based on a radial defect surrounded by Bragg reflectors, is studied in detail. Simple rules for the design and analysis of such structures are derived using a transfer matrix formalism. Unlike conventional ring resonators, annular Bragg resonators (ABR) are not limited by the total internal reflection condition, and can exhibit both large free spectral ranges and low bend losses. The Bragg reflection mechanism enables the confinement of light within a defect consisting of a low refractive index medium (such as air). Strong atom-photon interaction can be ac…
We introduce a monolithic Brillouin generator based on a semiconductor micropillar cavity embedding a high frequency nanoacoustic resonator operating in the hundreds of GHz range. The concept of two nested resonators allows an independent design of the ultrahigh frequency Brillouin spectrum and of the optical device. We develop an optical free-space technique to characterize spontaneous Brillouin scattering in this monolithic device and propose a measurement protocol that maximizes the Brillouin generation efficiency in the presence of optically induced thermal effects. The compact and versati…
Deep and fast electro-optic modulation is critical for high-speed near infrared signal processing. We combine the electro-absorption tunability of graphene with the high-Q resonance of a Bragg-based Fabry-Perot resonator at λ=1550 nm and show that ~100% free-space signal modulation (>50 dB extinction ratio, <1 dB insertion loss) at high speed (>1 GHz) can always be achieved independently of graphene quality (mobility), provided the device is operating in reflection mode and tuned in critical coupling with graphene. Remarkably, the critical coupling mechanism produces a higher extinction ratio …
Polymer compounds from titania-doped polyethylene are fabricated and their linear optical properties characterized by THz-TDS. We show that high concentration of dopants not only enhances the refractive index of the composite material, but also can dramatically raise its absorption coefficient. We demonstrate that the design of Bragg reflectors based on lossy composite polymers depends on finding a compromise between index contrast and corresponding losses. A small absorption value is also shown to be favorable, compared to an ideal lossless reflector, as it enables to smooth the transmission …
We study the optical properties associated to both the polariton gap and the Bragg gap in periodic resonator-waveguide coupled system, based on the temporal coupled mode theory and the transfer matrix method. By the complex band and the transmission spectrum, it is feasible to tune the interaction between multiple Bragg scattering and the local resonance, which may give rise to analogous phenomena of electromagnetically induced transparency (EIT). We further design a plasmonic slot waveguide side-coupled with local plasmonic resonator to demonstrate the EIT-like effects in the near-infared ban…
It is shown that cavities formed between a multilayer quarter-wave Bragg reflector and a metal mirror which support Tamm plasmons can be modelled by using a hard-mirror approximation including appropriate penetration depths into the mirrors. Results from this model are in excellent agreement with those found by numerical methods. In addition Tamm modes that are laterally confined by the presence of a metallic disc deposited on the Bragg reflector can be described by the effective index model that is commonly used for vertical-cavity surface-emitting lasers (VCSELs). This enables the lateral mo…
We theoretically investigate advanced multi-functional integrated photonic filters formed by three waveguide coupled Sagnac loop reflectors (3WC-SLRs). By tailoring the coherent mode interference, the spectral response of the 3WC-SLR resonators is engineered to achieve diverse filtering functions with high performance. These include optical analogues of Fano resonances that yield ultrahigh spectral extinction ratios (ERs) and slope rates, resonance mode splitting with high ERs and low free spectral ranges, and classical Butterworth, Bessel, Chebyshev, and elliptic filters. A detailed analysis …
We report that $> 80%$ of the photons generated inside a photonic crystal slab resonator can be funneled within a small divergence angle of $\pm 30^\circ$. The far-field radiation properties of a photonic crystal slab resonant mode are modified by tuning the cavity geometry and by placing a reflector below the cavity. The former method directly shapes the near-field distribution so as to achieve directional and linearly-polarized far-field patterns. The latter modification takes advantage of the interference effect between the original waves and the reflected waves to enhance the energy-direct…
Nanowires (NWs) with a unique one-dimensional structure can monolithically integrate high-quality III-V semiconductors onto Si platform, which is highly promising to build lasers for Si photonics. However, the lasing from vertically-standing NWs on silicon is much more difficult to achieve compared with NWs broken off from substrates, causing significant challenges in the integration. Here, the challenge of achieving vertically-standing NW lasers is systematically analyzed. The poor optical reflectivity at the NW/Si interface results severe optical field leakage to the substrate, and the commo…
We present high-performance megahertz micromechanical oscillators based on freestanding epitaxial AlGaAs distributed Bragg reflectors. Compared with dielectric reflectors, the low mechanical loss of the monocrystalline heterostructure gives rise to significant improvements in the achievable mechanical quality factor Q while simultaneously exhibiting near unity reflectivity. Experimental characterization yields an optical reflectivity exceeding 99.98% and mechanical quality factors up to 20 000 at 4 K. This materials system is not only an interesting candidate for optical coatings with ultralow…
A new platform for fabricating polariton lasers operating at room temperature is introduced: nitride-based distributed Bragg reflectors epitaxially grown on patterned silicon substrates. The patterning allows for an enhanced strain relaxation thereby enabling to stack a large number of crack-free AlN/AlGaN pairs and achieve cavity quality factors of several thousands with a large spatial homogeneity. GaN and ZnO active regions are epitaxially grown thereon and the cavities are completed with top dielectric Bragg reflectors. The two structures display strong-coupling and polariton lasing at roo…
Sub-wavelength dielectric gratings (SWG) have emerged recently as a promising alternative to distributed-Bragg-reflection (DBR) dielectric stacks for broadband, high-reflectivity filtering applications. A SWG structure composed of a single dielectric layer with the appropriate patterning can sometimes perform as well as thirty or forty dielectric DBR layers, while providing new functionalities such as polarization control and near-field amplification. In this paper, we introduce a remarkable property of grating mirrors that cannot be realized by their DBR counterpart: we show that a non-period…
We use a phenomenological Hamiltonian approach to derive a set of coupled mode equations that describe light propagation in waveguides that are periodically side-coupled to microcavities. The structure exhibits both Bragg gap and (polariton like) resonator gap in the dispersion relation. The origin and physical significance of the two types of gaps are discussed. The coupled-mode equations derived from the effective field formalism are valid deep within the Bragg gaps and resonator gaps.
In this paper, forward and backward propagating waves and reflectivity in an optical waveguide structure namely the fiber Bragg reflector also considered as a one dimensional photonic crystal, are analytically computed using coupled mode theory for different grating lengths and coupling conditions. AlxGa1-xN/GaN material composition is considered as unit block of the periodic organization, and refractive index of AlxGa1-xN is taken to be dependent on material composition, bandgap and operating wavelength following Adachis' model. The structure being considered is the Bragg grating where increa…
