2D Bragg Resonator Research Articles

2D Bragg Resonators Based on Planar Dielectric Waveguides (from Theory to Model-Based Testing)

Using analytical approaches and CST Microwave Studio 3D simulation, the electrodynamic characteristics of 2D Bragg resonators based on planar dielectric waveguides with doubly periodic corrugation are theoretically analyzed. Such resonators are of great interest to obtain directed narrow-band radiation in heterolasers with large active regions. Model electrodynamic experiments on the “cold” testing of such structures in the millimeter range are performed. Good agreement between the experimental and simulation results is shown, including the existence of the highest-Q mode within the Bragg reflection band in the absence of defects in the periodicity.

Dynamics of semiconductor lasers with two-dimensional distributed feedback

We develop a nonlinear model of a laser exploiting two-dimensional (2D) distributed feedback (2D DFL). This feedback mechanism can be realized in a 2D Bragg resonator formed by a dielectric structure with the thickness having double-periodical sinusoidal or chessboard modulation. A 2D Bragg resonator is shown to possess high selectivity over both the longitudinal and the transverse coordinates and to have fundamental modes in the center of the forbidden band gap. Within the semiclassical approach, we study the nonlinear dynamics of 2D DFL and demonstrate spatial synchronization of radiation from an extended active medium. Specific features of 2D DFL operation with active medium amplifying modes of TM and TE (quantum-well lasers) polarization are also discussed.

Generation of a spatially coherent field structure in free-electron masers with 2D distributed feedback

Nonlinear dynamics of free-electron masers (FEMs) is studied in the planar geometry with 2D distributed feedback (DFB). As is distinct from previous works, the field structure is not fixed with respect to the three spatial coordinates including the coordinate that is orthogonal to surfaces of the plates of the 2D Bragg resonator. Conditions on the allowed oversize parameter (ratio of the gap between the resonator plates to wavelength) under which the steady-state generation remains stable upon variation in electron-beam parameters are derived. It is demonstrated that, at a relatively large gap, variations in the mismatch lead to the jumps of oscillation frequency that correspond to the excitation of bunches of modes with different transverse indices of partial waves. The results of simulation using a particle-in-cell method are presented for a FEM prototype with 2D DFB that is created using an ELMI accelerator at the Institute of Nuclear Physics, Siberian Branch, Russian Academy of Sciences. The simulated results show that narrow-band spatially coherent radiation can be generated at experimental parameters of the electron beam and electrodynamic system. The advantages of 2D Bragg structures in comparison with conventional 1D structures are demonstrated for FEMs.

Structures with two‐dimensional distributed feedback for a laser realization on Si:Er basis

AbstractUsing 2D distributed feedback (DFB) exploiting 2D Bragg resonators for a Si:Er lasers is suggested. Self excitation conditions are defined analytically. Numerical simulation of the nonlinear dynamics demonstrates that 2D DFB can provide synchronization of radiation for wide active media. A test laser‐like Si/SOI structure is fabricated and described. (© 2014 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

High selective two-dimensional Bragg resonators of planar geometry: Theoretical, computational, and experimental study

Electrodynamic properties of two-dimensional (2D) planar Bragg resonators realising 2D distributed feedback were studied. It is shown that high selectivity of a 2D Bragg resonator originates from the specificity of the dispersion diagrams of normal waves in a double-periodic corrugated unbounded planar waveguide resulting in formation of high-Q eigenmodes in the vicinity of the Bragg resonance frequency. Results of theoretical analysis in the frame of geometric-optical approach of coupled-wave theory coincide well with 3D simulations using the code CST “Microwave Studio” and are corroborated by data obtained in “cold” microwave tests. Frequency dependences of scattering coefficients were measured for incident wave-beams of different structures and excitation of the high-Q eigenmodes has been demonstrated.

Azimuthal selection of modes in free-electron masers with coaxial Bragg resonators

A comparative analysis of the selective characteristics of Bragg resonators with various types of periodic corrugation is performed. In the simplest case of the azimuthal symmetric corrugation in a highly overmoded resonator (a large ratio of the perimeter to the wavelength), the Q factors of modes with different numbers of azimuthal variations are almost equal and the mode frequencies are close on the scale of the gain band of electron flow. A certain rarefaction of the mode spectrum can be attained using the helical corrugation when the traveling wave is coupled with the whispering-gallery modes and the frequency interval between the high-Q modes of the resonator with different azimuthal indices is determined by the interval between the critical frequencies of the whispering-gallery modes. The doubly periodic corrugation employed in the 2D Bragg resonators at the same (as in the case of the helical corrugation) intermode distance allows the Q-factor selection of a single azimuthal symmetric mode. The analysis is based on the method of coupled waves and the direct numerical simulation using standard codes.

Mechanism of azimuthal mode selection in two-dimensional coaxial Bragg resonators

The analysis of electrodynamic properties of two-dimensional (2D) Bragg resonators of coaxial geometry realizing 2D distributed feedback was carried out using a quasioptical approach of coupled-wave theory and three-dimensional (3D) simulations. It is shown that the high selectivity of a 2D Bragg resonator over the azimuthal index originates from the topological difference in the dispersion diagrams of the normal symmetrical and nonsymmetrical waves near the Bragg resonance frequency in a double-periodic corrugated unbounded waveguide. For a symmetrical mode near the Bragg frequency it was found that the group velocity tends to zero as well as its first derivative. This peculiarity of the dispersion characteristic provides the conditions for the formation of an eigenmode with a Q-factor essentially exceeding the Q-factors of other modes. The results of the theoretical analysis coincide well with results of 3D simulations using the CST code “MICROWAVE STUDIO” and confirm the high azimuthal selectivity of the system.

Dynamics of lasers with two-dimensional distributed feedback

A model of a laser exploiting two-dimensional (2D) distributed feedback is developed. A new feedback mechanism can be realized using a dielectric structure with the width having double-periodical sinusoidal or chessboard modulation. It is shown that 2D Bragg resonator possesses high selectivity over both the longitudinal and the transverse indices. Within semi-classical approach nonlinear dynamics of 2D distributed feedback laser (DFL) is studied and spatial synchronization of radiation from extended active medium is demonstrated.

Using two-dimensional distributed feedback for the synchronization of emission from laser active media

It is shown that two-dimensional (2D) Bragg resonance structures can be used for the synchronization of emission from a spatially developed laser active medium. Analysis of the dynamics of a laser with 2D distributed feedback shows that stationary lasing with a frequency and a spatial structure of the field close to the fundamental mode of a 2D Bragg resonator is possible in the structures with large values of the Fresnel parameter.

On the mechanism of high selectivity of two-dimensional coaxial Bragg resonators

The analysis of electrodynamic properties of two-dimensional (2D) Bragg resonators of coaxial-geometry realizing 2D distributed feedback was carried out with diffraction effects taken into account. Such resonators represent coaxial waveguide sections with a shallow double-periodic corrugation, which provides mutual coupling of four partial waves. It is shown that the high selectivity of 2D Bragg resonators over the azimuthal mode index can be explained by different behavior of the normal symmetrical and non-symmetrical waves near the Bragg resonance in an unbound double-periodic corrugated waveguide.

Experimental and theoretical study of 2D Bragg structures for a coaxial free electron maser

Experimental results are presented of the first observation of two-dimensional distributed feedback in a coaxial 2D-Bragg structure. The use of two-dimensional distributed feedback has been proposed as a method of producing spatially coherent radiation from extremely powerful large sized relativistic electron beams. To obtain coherent high-power (GW) microwave and millimetre wave radiation, 2D Bragg resonators are needed to overcome the problems of mode selection and synchronisation of radiation from different parts of an oversized beam. The design and cold microwave measurements of a 2D Bragg coaxial structure for use in a Free Electron Maser (FEM) driven by an annular electron beam of circumference 25 times larger than the radiation wavelength is presented. The cavity for the 2D Bragg FEM consists of two 2D Bragg coaxial reflectors separated by a regular coaxial waveguide. The formation of pure two-dimensional distributed feedback without a mixture of one-dimensional parasitic feedback was demonstrated for the first time in this series of experiments. The first experimental comparison of 2D and 1D Bragg structures was also conducted and good agreement between experimental results and theoretical predictions was observed. The eigenmodes of the two-mirror cavity were calculated and it was shown that a single-mode steady-state operation regime could be obtained in a FEM based on such a novel cavity.

Progress of the Strathclyde Free Electron Maser experiment using a 2D Bragg structure

The use of two-dimensional (2D) Bragg resonators of coaxial geometry, realising two-dimensional distributed feedback, is considered as a method of providing additional mode selection and producing spatially coherent radiation from oversized annular electron beams. The main goals of the project are to prove operability of a FEM using 2D Bragg structures and compare the performance of the FEM using the novel 2D Bragg resonators with conventional 1D Bragg resonators.

Theory and design of a free-electron maser with two-dimensional feedback driven by a sheet electron beam.

The use of two-dimensional Bragg resonators of planar geometry, realizing two-dimensional (2D) distributed feedback, is considered as a method of producing spatially coherent radiation from a large sheet electron beam. The spectrum of eigenmodes is found for a 2D Bragg resonator when the sides of the resonator are open and also when they are closed. The higher selectivity of the open resonator in comparison with the closed one is shown. A time-domain analysis of the excitation of an open 2D Bragg resonator by a sheet electron beam demonstrates that a single-mode steady-state oscillation regime may be obtained for a sheet electron beam of width 100-1000 wavelengths. Nevertheless, for a free-electron maser (FEM) with a closed 2D Bragg resonator, a steady-state regime can also be realized if the beam width does not exceed 50-100 wavelengths. The parameters for a FEM with a 2D planar Bragg resonator driven by a sheet electron beam based on the U-2 accelerator (INP RAS, Novosibirsk) are estimated and the project is described.

Two-dimensional double-periodic Bragg resonators for free electron lasers

To realize spatial coherent radiation of ribbon relativistic electron beams with the transverse dimension essentially exceeding the wavelength, we propose the use of a two-dimensional distributed feedback. This feedback can be provided in a Bragg resonator formed by two double-periodic corrugating metal plates, when additional transverse electromagnetic energy fluxes, that synchronize the radiation of individual parts of the electron beam, take place. Eigenmodes of the 2D Bragg resonator are found and its high selectivity is proved.