L. Solymar

Magnetoinductive waves in one, two, and three dimensions

The propagation of waves supported by capacitively loaded loops is investigated using a circuit model in which each loop is coupled magnetically to a number of other loops. Since the coupling is due to induced voltages the waves are referred to as magnetoinductive (MI) waves. The mathematical formulations are mostly analytical thanks to long standing previous work on the magnetic and electric fields generated by currents flowing in loops. Retardation is neglected, i.e., dimensions of the structure are assumed to be small relative to the free space wavelength. The dispersion relations, derived in the most general case for a tetragonal three-dimensional structure, exhibit both forward and backward waves within a pass band. It is shown that for reproducing the salient features of the waves it is sufficient to take nearest neighbor coupling into account but coupling between loops further away must also be considered if higher accuracy is required. The investigations include that of resonances, conditions for ...

Space-charge field in photorefractive materials at large modulation

The nonlinear differential equations for degenerate two-wave mixing in a photorefractive material that permits large modulation are solved by a numerical technique under steady-state conditions.

A general two‐dimensional theory for volume holograms

Coupled partial differential equations are derived for the amplitude of the electric field in a general two‐dimensional volume hologram. Nonuniform amplitude distributions, nonplanar wave fronts, losses, and non‐Bragg incidence are considered both for dielectric and absorption gratings. The formulation is in holographic terminology but the equations are valid for weakly modulated Bragg devices in general.

Transient energy transfer during hologram formation in photorefractive crystals

The temporal and spatial variation of the beam intensities and space charge electric field during hologram formation in a photorefractive crystal are determined by solving the relevant partial differential equations. Starting with the equations of Kukhtarev, Markov and Odulov [1], analytic and numerical solutions are presented for a range of parameters for the time evolution of the energy transfer between the optical beams, the appearance of the space charge electric field, the phase angle between the interference pattern and the space charge field, and the bending of the grating.

Observations of Spatial Subharmonics arising during Two-Wave Mixing in BSO

During two-wave mixing experiments in BSO, output beams have been observed which result from diffraction of the pump beams from subharmonics of the grating vector recorded within the crystal. The subharmonic beams are characterised as a function of pump beam detuning and electric field, and our observations are contrasted with those reported earlier.

Experimental and theoretical study of magneto-inductive waves supported by one-dimensional arrays of ''swiss rolls''

The propagation of magneto-inductive waves in a one-dimensional array of “swiss roll” metamaterial has been studied. It was found that long-range interactions over the whole of the array must be included to describe the excitations accurately. Using the dispersion relations deduced from experimental data on pairs of elements, the coupling coefficients between all the elements in the array have been determined by matching the experimental and theoretical curves. The relative amplitudes and phases of the excitations on each element in a 31-member array have been measured and compared with the theoretical prediction based on the previously derived coupling coefficients. Excellent agreement between the predicted and measured behavior is found, provided that a full set of coupling coefficients is used.

Transient energy transfer in photorefractive materials; An analytic solution

Abstract The partial differential equations of Kukhtarev et al. (1977) which describe the time dependence of hologram formation in photorefractive materials are solved analytically in the strong beam approximation using the Riemann method. The output power of the weak beam is plotted in several examples for both diffusion and drift dominated electron transport mechanisms.

Planar volume phase holograms formed in bleached photographic emulsions.

Volume phase holograms are formed by a standard process in commercially available photographic emulsion. The material is characterized before recording, and initial experimental results are presented for reconstruction under index-matched conditions. An initial comparison is made using two-wave coupled-wave theory and a technique of curve fitting with experimental measurements of transmission and diffraction efficiency. The model works well close to the Bragg condition, but several differences are noted between theory and experiment away from the Bragg condition. An anomalous absorptive effect is noted in transmission. An improved model is then formulated, again using coupled-wave theory, and capable of analytic solution, taking into account phase and absorption modulation, a second harmonic in the grating profile and the appearance of some higher diffraction orders. Using this model, all the initial experimental results are satisfactorily explained, and the effect of spurious gratings in the hologram response is noted. The model is then used with an extensive set of experimental results to deduce the major characteristics of the material, including saturation of the modulation with exposure. The formulation of a mixed grating and possible dispersion of the modulation are also investigated. Suggestions are made for the design of more complicated components using this material and for material improvement.

Diffraction Efficiency and Angular Selectivity of Volume Phase Holograms Recorded in Photorefractive Materials

The recording and replay of volume phase gratings in photorefractive crystals is investigated for both transmission and reflection geometries. Differential equations are derived and solved for a range of parameters including the length of the crystal, the magnitude, spatial distribution and phase angle of the refractive index modulation, the beam ratio at recording, and the angular range at replay. The recording process is assumed to reach a steady-state limit before replay with a weak probe beam. Solution of the repaly equations is mainly by numerical integration, although analytic solutions are derived for special cases. It is found that in certain cases the diffraction efficiency can be greatly increased by replaying the hologram at an angle different from the recording angle.

Onset of subharmonics generated by forward wave interactions in Bi12SiO20

The threshold conditions, under which a spatial subharmonic beam may arise when a Bi12SiO20 crystal is illuminated by two pump beams, are investigated. It is shown that a nonlinear theory based on the material equations leads to good qualitative agreement with experiments