Bragg Interaction Research Articles

Bragg resonances in a two-layer fluid

AbstractEquations are derived to approximately describe the propagation of small amplitude surface and interfacial waves across small irregularities in depth in a two-layer fluid. When the irregularities are sinusoidal, Bragg interaction effects between an incident surface wave and the bottom corrugations can lead to a large-amplitude reflected interfacial wave or a large-amplitude transmitted interfacial wave if the incident surface wave is relatively long and the lower layer shallow in comparison with the upper layer.

Second-order bragg interaction in double grating couplers: TM mode

An analytical treatment of the second-order Bragg interaction is presented for the transverse magnetic mode of a dielectric film waveguide having gratings on both the film-cover and the film-substrate interfaces. Four canonical equations that describe the interactions of two guided waves propagating in the opposite directions in the film and the normally incident and radiated free waves in the cover and the substrate are deduced.

Double-grating thin-film devices based on second-order Bragg interaction

Four coupled-mode equations describing the characteristics of the second-order Bragg interaction are derived for the transverse electric mode of a dielectric film waveguide with periodic corrugations on both the film-cover and the film-substrate interfaces. The characteristics of the frequency-selective filter, output coupler, input coupler, and distributed feedback laser are obtained. Proper choice of the design parameters leads to a frequency-selective filter radiating neither in the cover nor in the substrate, a highly efficient output coupler radiating only in the cover, and an efficient input coupler exciting a guided wave only in one direction. Similarly, in the distributed feedback laser, a suitable choice of the parameters of the two gratings provides a mechanism for controlling the oscillation characteristics of the laser. The attractive feature of the double-grating design is that the characteristics of the thin-film devices are not very sensitive to small deviations of the grating parameters from their designed values.

Two-dimensional strong, acousto-optic interaction between arbitrary light and sound profiles: a Fourier transform approach

A spatial Fourier transform approach is employed to investigate the acoustooptic interaction with cw, profiled sound and an incident light beam. Two coupled differential equations which describe the near Bragg interaction are derived in the spatial frequency domain. Since there is no analytic solution for these coupled equations, a well-known numerical technique, viz., the Range-Kutta method is used to solve the equations. Detailed numerical simulation, involving Fourier transforming the input light beam profile to calculate the spectra of the scattered light beams and, hence, their profiles in space using the inverse transform, are presented.

Series solution for two-frequency Bragg interaction using the orpel–Poon multiple-scattering model

The two-frequency acousto-optic interaction is analytically solved in the Bragg regime by use of a multiple-scattering model that was previously described by Korpel and Poon [ J. Opt. Soc. Am.70, 817– 820 ( 1980)]. The method uses Feynman diagrams to conceptualize the problem and demonstrates the applicability of such a method to model a relatively complex system. The solution presented is compared with that derived by Hecht [ IEEE Trans. Sonics Ultrason.SU-24, 7– 18 ( 1977)], who used a coupled-mode approach. The derivation of our solution is relatively simple and leads to a formulation that appears to be more compact. Numerical evaluations have demonstrated their equivalence. We present results that illustrate the dependence of the diffracted beam intensities on the amplitude of the two acoustic waves.

Thin film devices based on second order Bragg interaction

For an active dielectric film waveguide with different passive dielectrics for the cover and the substrate and with periodic corrugations on the upper surface, the characteristics of the second order Bragg interaction are investigated for the transverse electric mode with reference to such applications as frequency-selective reflector, couplers, and distributed feedback laser. Four canonical equations that are valid for a distributed coupler with two guided waves and two free waves, incident and radiated, one each in the cover and the substrate, are deduced systematically. The coupling coefficients are shown to satisfy all the requirements imposed by symmetry, reciprocity, and power conservation. From the solution of the canonical equations with the appropriate terminal conditions, the characteristics of the devices are obtained. The design parameters leading to the optimum performance of these devices are determined. For the distributed feedback laser, the frequencies of oscillation, the corresponding gain thresholds, and the relative power distributions in the two guided and the two radiated waves are obtained for the first few modes in the neighborhood of the second order Bragg frequency. The modifications of the characteristics introduced by the presence of a phase shifting section on the grating structure are analyzed for symmetrical and asymmetrical grating configurations. The effects of radiation and the phase shifting section on the separation of the gain thresholds of the neighboring lower order laser modes are investigated with a view to increasing the possibility of a single mode oscillation. Selected numerical results are presented to illustrate the important characteristics of the various thin film devices based on the second-order Bragg interaction.

Observation of higher-order Floquet modes in magneto-acoustic interactions

The higher-order space-time Floquet harmonics resulting from the scattering of magnetostatic waves by surface acoustic waves have been investigated. Experimental results are reported on the observation of these higher-order modes in magneto-acoustic Bragg interactions in magnetic films. The results are compared to the theoretical predictions based on the coupled-mode analysis.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Acoustooptic bragg interaction of waves having a complex space-time spectrum in an anisotropic medium. II

Acoustooptic bragg interaction of waves having a complex space-time spectrum in an anisotropic medium. II

Acoustooptic bragg interaction of waves having a complex space-time spectrum in an anisotropic medium. I

Acoustooptic bragg interaction of waves having a complex space-time spectrum in an anisotropic medium. I

A rigorous analysis of a thin‐film dielectric waveguide with a sinusoidal surface corrugation

The problem of wave guidance in thin‐film dielectric waveguides is formulated using the modematching method in the sense of least squares. The result is applied to analysis of the first‐order Bragg interactions in a three‐layered dielectric waveguide having a sinusoidal surface corrugation. The precise numerical results of the dispersion relation near the first‐order stopband are presented for both of the lowest TE and TM modes and compared with those obtained by a conventional perturbation approximation.

Switchable fiber-optic tap using acoustic transducers deposited upon the fiber surface

A new electronically switchable fiber-optic tap is demonstrated. The tap consists of an array of acoustic transducers fabricated directly upon the side of a cylindrical single-mode fiber. The transducer array generates an acoustic field that is focused on the fiber core and that satisfies the Bragg condition, allowing light to be deflected out of the fiber by the acousto-optic Bragg interaction. The amount of light tapped is linearly proportional to the rf power driving the transducer array. The bandwidth of the tap is 920 MHz centered at 3.3 GHz, with a maximum tap efficiency of 0.4% per watt of rf input.

Strong acoustooptic interaction in the field of a focused acoustic wave

The acoustooptic interaction of complex optical and acoustic radiation fields in a crystal is investigated. Differential equations are obtained for the diffracted light field in an anisotropic medium. A general solution of this equation is found for weak Bragg interaction. The problem of strong acoustooptic interaction in the field of a focused acoustic wave is solved. The solutions describe the diffracted field near the acoustic lens and also in the vicinity of its focus. The asymptotic behavior of the solutions at small and large acoustic powers is determined.

The impact of higher-order bragg terms on radar sea return

The possibility that radar sea return observed using aKu band fan beam Doppler airborne scatterometer flown over crude oil artificial spills might have been back-scattered via the second-order Bragg interaction is surmised. An attempt is made to justify the absence of the first-order Bragg term.

Three-mode coupling in a dielectric slab waveguide with doubly periodic surface corrugations

The characteristics of a three-mode coupling in a dielectric slab waveguide attached doubly periodic surface corrugations are investigated. The coupled-mode equations governing the first-order Bragg interactions of three TE modes are systematically derived with the help of perturbation procedure. For the case where the waveguide is symmetric and the three TE modes are lowest even modes, the coupled-mode equations are solved to obtain the reflection and transmission characteristics of the periodic waveguide of finite length. The results are compared with those of the two related two-mode couplings in a dielectric slab waveguide with a singly periodic surface corrugation.

Bragg Interaction of Electromagnetic Waves in a Ferrite Slab Periodically Loaded with Metal Strips

The waveguiding characteristics of electromagnetic TE waves in a ferrite slab periodically loaded with metal strips are investigated. Theoretical formulation by means of the spectral domain approach is employed to obtain the Brillouin diagrams of two types of volume modes and a surface mode. It is found that the nonreciprocal properties of waves depend on the metal strip profile and bias magnetic field strength. Experiments on the magnetic-field dependence of the Bragg frequency and the stop bandwidth are carried out in the millimeter-wave frequencies. Typical results obtained from a polycrystalline YIG slab with periodic gold strips deposited on one surface are stop bandwidth about 2.14 GHz, with return loss about 2 dB at the Bragg frequency of 47.5 GHz, for the bias magnetic-field strength of 5.7 kG. The Bragg frequency can be tuned over the range of 1.39 GHz by varying the bias magnetic field from 0 to 8.2 kG. Experimental results show good agreement with theoretical predictions.

Analysis of magnetostatic surface wave in a periodically corrugated YIG layered films by perturbation method

The symmetric first-order Bragg interaction of the magnetostatic surface wave (MSSW) in a periodically corrugated YIG film layered structure is investigated analytically by perturbation method. The first-order dispersion relation of the MSSW in this system is derived systematically by a singular perturbation method using multiple space scales. The obtained analytical results are not only possible to evaluate the characteristics of the system, but also its numerical computation give a designing basis at composing the microwave filter.

Guided-Wave Experiments with Dielectric Waveguides Having Finite Periodic Corrugation

A planar dielectric waveguide having finite periodic rectangular corrugation is investigated analytically and experimentally, in case of surface waves propagating at an angle to the corrugation. In analytical considerations, a finitely corrugated guide is regarded as consisting of many step discontinuities connected by a length of uniform slab waveguide, and its propagation characteristics in the Bragg interaction region are derived from a cascaded connection of the transmission matrix expressing a step discontinuity. Although the present method takes only surface wave modes into account and neglects the wave with continuous spectrum, the calculated results show an excellent agreement with experimental ones which are performed for art H-guide in the microwave region.

First-Order Bragg Interactions in a Gyromagnetic-Dielectric Waveguide

First-order Bragg interactions in a gyromagnetic-dielectric waveguide are investigated theoretically. With the aid of a singular perturbation procedure the coupled mode equations governing the nature of transverse electric wave interactions are derived. Bragg reflection characteristics are shown numerically as a function of the magnetic field.

Stopbands of the first-order Bragg interaction in a parallel-plate wave guide having multiperiodic wall corrugations

The stopbands of the first-order Bragg interaction in a parallel-plate waveguide having multiperiodic wall undulations are investigated via the perturbation method of multiple scales. For a structure having two periods, the first-order Bragg interaction Involves two as well as three coupled modes. Transition curves separating passbands from stopbands are found for all possible interactions. The effect of the multiple periodicity in the structure is found to be an increased band-width for the attenuation band as well as considerable attenuation throughout the band owing to the Increased number of Interactions. This is useful for the design of multichannel narrow-band microwave filters. The analysis is carried out for the first three dominant modes of the structure.

Three-mode coupling in a passive dielectric waveguide with index modulation

The characteristics of a three-mode coupling in a passive dielectric waveguide are investigated for the case of even TE modes. The index is assumed to have a doubly periodic harmonic variation in the propagation direction. By a singular perturbation procedure using multiple space scales, the coupled-mode equations governing the Bragg interactions are systematically deduced. The three-mode coupling causes a stop band in frequency and the characteristics of the resulting evanescent mode are analyzed. For a periodic dielectric waveguide of finite length, the three coupled-mode equations are solved subject to suitable boundary conditions to obtain the reflection and the transmission coefficients. The frequency response of the reflection and the transmission coefficients are investigated and compared with the results of the pair of corresponding two-mode couplings. Representative numerical results are presented to illustrate the characteristics of the interaction of the three modes.