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 Range (FSR) requirements and fabrication tolerances is suggested.
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 propose a new class of compact integrated optical circulators providing a large isolation level while maintaining a straightforward technological feasibility. Their layout is based on a nonreciprocal radial Bragg cavity composed of concentric magneto-optical rings. The circulator ports are standard rib waveguides, butt-coupled to the cavity by cutting through its outer rings. The device is specifically designed for operation in a uniform external magnetic field. Using a coupled-mode description of the complete cavity/waveguide-port system, we explore the rich behaviour of cavity circulators…
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 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 theoretical study, the author firstly discusses the wave interference of Bragg diffraction inside 3D crystal, followed by quantum mechanical interpretation on the diffraction process, and proves that the interference fringe between Bragg diffraction and the incident beam is identical to the lattice plane. By introducing the beam expander concept, we may explain the image projection mechanism of Bragg diffractions propagating through TEM: Transmission Electron Microscope. In practice, we will take projection images at zone axes, because of its symmetric high-density diffractions associa…
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…
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.
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.
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…
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.
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…
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…
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…
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…
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 …
We demonstrate single-mode lasing at telecommunication wavelengths from a circular nanocavity employing a radial Bragg reflector. Ultra-small modal volume and Sub milliwatt pump threshold level are observed for lasers with InGaAsP quantum well active membrane. The electromagnetic field is shown to be tightly confined within the 300nm central pillar of the cavity. The quality factors of the resonator modal fields are estimated to be on the order of a few thousands.
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.
We report on miniature GaAs disk optomechanical resonators vibrating in air in the radiofrequency range. The flexural modes of the disks are studied by scanning electron microscopy and optical interferometry, and correctly modeled with the elasticity theory for annular plates. The mechanical damping is systematically measured, and confronted with original analytical models for air damping. Formulas are derived that correctly reproduce both the mechanical modes and the damping behavior, and can serve as design tools for optomechanical applications in fluidic environment.
Effects of surface roughness and top layer thickness on the performance of Fabry-Perot cavities and responsive open resonators based on distributed Bragg reflectors
A radial transverse resonance model for two cylindrical concentric layers with different complex dielectric constants is presented. An inverse problem with four unknowns - 3 physical material parameters and one dimensional dielectric layer thickness parameter- is solved by employing TE110 and TE210 modes with different radial field distribution. First a Newton-Raphson algorithm is used to solve a least square problem with a Lorentzian function (as resonance model and "measured" data generator). Then found resonance frequencies and quality factors are used in a second inverse Newton-Raphson alg…
In this paper, we report the model and the experimental demonstration of a new optical resonator formed by inserting a Fiber Bragg Grating (FBG) in a closed fiber loop. The spectral characteristics of the ring depend on the reflectivity of the FBG. When the FBG reflectivity tends to zero, the overall resonant system exhibits the usual degenerate mode conditions. On the other hand, when the reflection coefficient FBG is not vanishing, the spectral features of the resonator display split resonant modes associated to the degeneracy removal of two counterpropagating modes that resonate within the …
We present an analytic perturbation theory which extends the paraxial approximation for a common cylindrically symmetric stable optical resonator and incorporates the differential, polarization-dependent reflectivity of a Bragg mirror. The degeneracy of Laguerre-Gauss modes with distinct orbital angular momentum (OAM) and polarization, but identical transverse order N, will become observably lifted at sufficiently small size and high finesse. The resulting paraxial eigenmodes possess two distinct OAM components, the fractional composition subtly depending on mirror structure.
Electromagnetic resonators, which are based on optical cavities or electronic circuits, are key elements to enhance and control light-matter interaction. In the THz range, current optical cavities exhibit very high-quality factors with $(λ/2)^3$ mode volumes limited by diffraction, whereas resonant electronic circuits show low quality factor but provide strong subwavelength effective volume ($10^{-6} λ^3$). To overcome the limitations of each type of resonator, great efforts are being devoted to improving the performances of current methods or to the emergence of original approaches. Here, we …
Numerical calculation of vector electromagnetic modes of plano-concave microcavities reveals that the polarization-dependent reflectivity of a flat Bragg mirror can lead to unexpected cavity field distributions for nominally paraxial modes. Even in a rotationally symmetric resonator, certain pairs of orbital angular momenta are necessarily mixed in an excitation-independent way to form doublets. A characteristic mixing angle is identified, which even in the paraxial limit can be designed to have large values. This correction to Gaussian theory is zeroth-order in deviations from paraxiality. We…
In this paper, the transfer matrix method is used to investigate the reflectance properties in a symmetric defective annular photonic crystal (APC) containing semiconductor, high-$T_c$ superconductor and a radial defect layer. Numerical results offer many noteworthy features that can be very useful in designing optical devices. In this regard, the geometric effects of alternate layers on the optical reflectance of our defective APC structure by changing the thickness of different layers would be investigated. Then, the possibility of controlling the spectral position of existed photonic band g…
Two major challenges in the development of optomechanical devices are achieving a low mechanical and optical loss rate and vibration isolation from the environment. We address both issues by fabricating trampoline resonators made from low pressure chemical vapor deposition (LPCVD) Si$_3$N$_4$ with a distributed bragg reflector (DBR) mirror. We design a nested double resonator structure with 80 dB of mechanical isolation from the mounting surface at the inner resonator frequency, and we demonstrate up to 45 dB of isolation at lower frequencies in agreement with the design. We reliably fabricate…
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…
Extending the cavity length of diode lasers with feedback from Bragg structures and ring resonators is highly effective for obtaining ultra-narrow laser linewidths. However, cavity length extension also decreases the free-spectral range of the cavity. This reduces the wavelength range of continuous laser tuning that can be achieved with a given phase shift of an intracavity phase tuning element. We present a method that increases the range of continuous tuning to that of a short equivalent laser cavity, while maintaining the ultra-narrow linewidth of a long cavity. Using a single-frequency hyb…
The device applications of plasmonic systems such as graphene and two dimensional electron gases (2DEGs) in III-V heterostructures include terahertz detectors, mixers, oscillators and modulators. These two dimensional (2D) plasmonic systems are not only well-suited for device integration, but also enable the broad tunability of underdamped plasma excitations via an applied electric field. We present demonstrations of the coherent coupling of multiple voltage tuned GaAs/AlGaAs 2D plasmonic resonators under terahertz irradiation. By utilizing a plasmonic homodyne mixing mechanism to downconvert …
