Nonlinear Interaction of Microwave Electric Fields and Sound in LiNbO3

Abstract

The parametric interaction between two oppositely traveling sound waves and a nonspatially varying (k=O) rf electric field in lithium niobate is illustrated in this paper. A pump frequency near 3 GHz is used to parametrically amplify the sound wave at one-half the pump frequency. In addition with a pump field that is sufficiently strong parametric oscillations occur within the crystal and this process forms a method of generating sound waves throughout the crystal volume. Finally, we have found that this type of parametric mixing of two sound waves can be used to obtain convolution signals in real time by monitoring the electric polarization generated within the crystal at twice the signal frequency.

Wave phase conjugation of ultrasonic beams

“…, ÒÑÒÇÓÇÚÐÞÇ ×ÖÓßÇ-ÍÑÏÒÑÐÇÐÕÞ ÂÍÖÔÕËÚÇ-ÔÍÑÅÑ ÒÑÎâ A q Ë B q ÔÄâÊÂÐÞ ÕÑÌ ÉÇ ÔËÔÕÇÏÑÌ ÑAEÐÑÏÇÓÐÞØ ÒÂÓÂÏÇÕÓËÚÇÔÍËØ ÖÓÂÄÐÇÐËÌ, ÚÕÑ Ë ÂÏÒÎËÕÖAEÞ ÍÑÎÎË-ÐÇÂÓÐÞØ ÒÎÑÔÍËØ ÄÑÎÐ [34,80]: ´ÂÍÑÇ ÓÂÊÄËÕËÇ ÒÓÑÙÇÔÔ ÖÔËÎÇÐËâ ÑÃÓÂÕÐÑÌ ÄÑÎÐÞ Ð ÐÂÚÂÎßÐÑÌ ÔÕÂAEËË ÍÂÚÇÔÕÄÇÐÐÑ ÂÐÂÎÑÅËÚÐÑ ÐÂÃÎáAEÂÄÛÇ-ÏÖÔâ ÓÂÐÇÇ ÊÂÒÑÓÑÅÑÄÑÏÖ ÖÔËÎÇÐËá РÅËÒÇÓÊÄÖÍÑÄÞØ ÚÂÔÕÑÕÂØ Ä ÐËÑÃÂÕÇ ÎËÕËâ [34].°ÐÑ ÄÒÑÎÐÇ ÖÍÎÂAEÞÄÂÇÕÔâ Ä ÓÂÏÍË ÐÇÔÕÂÙËÑÐÂÓÐÑÌ ÎËÐÇÌÐÑÌ ÕÇÑÓËË [78,80], ÔÑÅÎÂÔÐÑ ÍÑÕÑÓÑÌ AEÎâ d-ÑÃÓÂÊÐÑÅÑ ÄØÑAEÐÑÅÑ ÔËÅÐÂÎÂ Ë ÄÓÇÏÇÐ, ÐÇ ÒÓÇÄÑÔØÑAEâÜËØ ÄÓÇÏÇÐË AEÄÑÌÐÑÅÑ ÒÓÑÃÇÅ ÄÑÎÐÞ ÒÑ ÂÍÕËÄÐÑÌ ÊÑÐÇ (t`T 2Lav), ÓÇÛÇÐËÇ ÔËÔÕÇÏÞ (4.3) ËÏÇÇÕ ÄËAE ³ÒËÔÑÍ ÎËÕÇÓÂÕÖÓÞ…”

Nonlinear surface acoustic waves on an elastic solid of general anisotropy

“…We use (x~, x2, x3) as Cartesian coordinates in the reference configuration of the body and ui(x ~, x 2, x 3, t) as the components of the particle displacements at time t. The equations of motion are then piii = %.j (1) where p is the density in the reference state (assumed to be constant) and o~j is the (first) Piola-Kirchhoff stress tensor. We use dots to denote time derivatives, the comma notation for derivatives with respect to xj, and the summation convention for repeated suffixes.…”

“…The solution of equations of the type (40) is discussed in the final section of reference [1]. We shall not pursue the solution here since our aim is to determine simply the boundary function ~,.…”

“…As a result, there is interest in using surface waves in the design of certain non-linear acoustic devices, such as parametric amplifiers [1].…”

Stimulated Brillouin Scattering of High‐Power Helicon Waves in Longitudinally Magnetized Cubic Piezoelectric Semiconducting Plasmas

“…may be scattered a t various angles but the scattering maximizes in a backward direction with a characteristic frequency downshift of the acoustic frequency [l]. Accounts of the theory of SBS was given initially by Kroll [2] and Tang [3] and was reviewed by Starunov Nonetheless, the present investigation has been made under the following assumptions: (i) the electric field amplitude of the pump employed in the present investigation has been taken to be less than the damage threshold of the crystal considered ; (ii) we have neglected the effects of nonlinear material parameters which play significant roles in strongly pizoelectric semiconductors like LiNbO, [17] by restricting our analysis to moderately piezoelectric semicondcutors [18], viz., 111-V binary compounds ; (iii) the semiconductor has a n isotropic and nondegenerate conduction band; (iv) the band non-parabolicity which contributes about 3% over the parabolic band structure has been neglected [18, 191; (v) we have assumed electron concentrations such that the electron plasma frequencies are large enough and nearly equal to the pump frequency; (vi) we have assumed that the pump wave vector k, is pearly equal to twice the wave vector of the acoustic wave k (k,, = 2k).…”