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 variations depending on the position. Both results imply substantial changes of spontaneous emission rates and patterns for a local emitter embedded in the structure and make this system attractive for the fabrication of a 3D photonic crystal with controlled radiative properties.
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.
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, …
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…
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…
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 p…
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…
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.
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 …
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 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…
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…
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…
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…
There is immense scientific interest in the properties of resonant thin films embroidered with periodic nanoscale features. This device class possesses considerable innovation potential. Accordingly, we report unpolarized broadband reflectors enabled by a serial arrangement of a pair of polarized subwavelength gratings. Optimized with numerical methods, our elemental gratings consist of a partially-etched crystalline-silicon film on a quartz substrate. The resulting reflectors exhibit extremely wide spectral reflection bands in one polarization. By arranging two such reflectors sequentially wi…
We report the realization of a two--dimensional optical microscope for surface plasmons polaritons (SPPs) based on parabolic Bragg mirrors. These mirrors are built from lithographically fabricated gold nanostructures on gold thin films. We show by direct imaging by leakage radiation microscopy that the magnification power of the SPP microscope follows basic predictions of geometrical optics. Spatial resolution down to the value set by the diffraction limit is demonstrated.
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.
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…
Effects of surface roughness and top layer thickness on the performance of Fabry-Perot cavities and responsive open resonators based on distributed Bragg reflectors
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…
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…
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…
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…
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 …
Ultrafast programmable Bragg reflection in photonic integrated circuits
John A. Paulson School of Engineering and Applied Sciences, Harvard University（哈佛大学约翰·A·保尔森工程与应用科学学院）；Quantum Science and Engineering, Harvard University（哈佛大学量子科学与工程）
Since thin-film silicon solar cells have limited optical absorption, we explore the effect of a nanostructured back reflector to recycle the unabsorbed light. As a back reflector we investigate a 3D photonic band gap crystal made from silicon that is readily integrated with the thin films. We numerically obtain the optical properties by solving the 3D time-harmonic Maxwell equations using the finite-element method, and model silicon with experimentally determined optical constants. The absorption enhancement relevant for photovoltaics is obtained by weighting the absorption spectra with the AM…
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…
The development of efficient sources of single photons and entangled photon pairs emitting in the low-loss wavelength region around 1550 nm is crucial for long-distance quantum communication. Moreover, direct fiber coupling and electrical carrier injection are highly desirable for deployment in compact and user-friendly systems integrated with the existing fiber infrastructure. Here we present a detailed design study of circular Bragg gratings etched in InP slabs and operating in the telecom C-band. These devices enable the simultaneous enhancement of the X and XX spectral lines, with collecti…
We report the experimental realization of an elliptical Bragg reflector acting as an interferometer for propagating surface plasmon sSPd waves. We investigate SP interferometry in this device using a leakage radiation microscope and we compare our observations with a theoretical model for SP propagation. Strong SP focalization as a function of laser polarization orientation is observed and justified.
We describe a semi-analytical approach for three-dimensional analysis of photonic crystal fibre devices. The approach relies on modal transmission-line theory. We offer two examples illustrating the utilization of this approach in photonic crystal fibres: the verification of the coupling action in a photonic crystal fibre coupler and the modal reflectivity in a photonic crystal fibre distributed Bragg reflector.
The employment of magneto-optical materials to fabricate photonic crystals gives the unique opportunity to achieve optical tuning by applying a magnetic field. In this study we have simulated the transmission spectrum of a microcavity in which the Bragg reflectors are made with silica (SiO2) and yttria (Y2O3) and the defect layer is made with TGG (Tb3Ga5O12). We show that the application of an external magnetic field results in a tuning of the defect mode of the microcavity. In the simulations we have considered the wavelength dependence of the refractive indexes and the Verdet constants of th…
We present hitherto unknown forms of soliton dynamics in the forbidden frequency gap of a Bragg reflector, modified by periodic layers of near-resonant two-level systems (TLS). Remarkably, even extremely low TLS densities create an allowed band within the forbidden gap. This spectrum gives rise, for any Bragg reflectivity, to a vast family of stable gap solitons, both standing and moving, having a unique analytic form, an arbitrary pulse area, and inelastic collision properties. These findings suggest new possibilities of transmission control, noise filtering or ``dynamical cavities'' (self-tr…
We propose and analyze a novel regenerative amplifier free electron laser (FEL) to produce fully coherent x-ray pulses. The method makes use of narrow-bandwidth Bragg crystals to form an x-ray feedback loop around a relatively short undulator. Self-amplified spontaneous emission (SASE) from the leading electron bunch in a bunch train is spectrally filtered by the Bragg reflectors and is brought back to the beginning of the undulator to interact repeatedly with subsequent bunches in the bunch train. The FEL interaction with these short bunches not only amplifies the radiation intensity but also…
Light scattering by a two-dimensional photonic crystal slab (PCS) can result in dramatic interference effects associated with Fano resonances. Such devices offer appealing alternatives to distributed Bragg reflectors or filters for various applications such as optical wavelength and polarization filters, reflectors, semiconductor lasers, photodetectors, bio-sensors, or non-linear optical components. Suspended PCSs also find natural applications in the field of optomechanics, where the mechanical modes of a suspended slab interact via radiation pressure with the optical field of a high finesse …
The combination of grating-based frequency-selective optical feedback mechanisms, such as distributed feedback (DFB) or distributed Bragg reflector (DBR) structures, with quantum dot (QD) gain materials is a main approach towards ultra-high-performance semiconductor lasers for many key novel applications, either as stand-alone sources or as on-chip sources in photonic integrated circuits. However, the fabrication of conventional buried Bragg grating structures on GaAs, GaAs/Si, GaSb and other material platforms have been met with major material regrowth difficulties. We report a novel and univ…
