An Introduction to Modern Solid State Physics - download pdf or read online

By Yuri M. Galperin

ISBN-10: 7301121628

ISBN-13: 9787301121627

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Extra info for An Introduction to Modern Solid State Physics

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E-r Oz' If - 7'[ - 1 / ? f~cei[t'~(x-x')+k 27r ~ _ ~ . 65) Comparison with Eq. 66) Finally we insert this result into Eq. 62) to yield R a y l e i g h ' s s e c o n d i n t e g r a l formula: p(x,y,z) - 1 / ? 67) with z > z'. This formula relates the spatial pressure in one plane to the spatial pressure in another plane. It gives a forward propagation formula by convolving the pressure in the plane z' =constant with a propagator gp projecting the field to a more distant plane (z > z'). Later we will look at the inverse of this equation so that we can backpropagate the spatial acoustic pressure field.

6: Evanescent wave traveling parallel to x axis, decaying exponentially in the vertical direction. In k-space this wave falls outside the radiation circle, as shown. All plane waves outside the radiation circle are subsonic. From Eq. 38) so t h a t the intensity is f IAl2e -21'': ~ - 2wpo (k~i + kyj). 39) F r o m this it is clear t h a t the power flows parallel to the (x, y) plane in the direction kx~ + ku), decaying exponentially in the z direction. T h e direction of the evanescent 26 CHAPTER 2.

The sinusoidal variation of pressure along the two axes is shown gray scale C H A P T E R 2. P L A N E I I'AVES 22 Figure 2 . 3 : Plane wave illustration showing trace matching. Snapshot at t - 0. The insert on the right shouts the equivalent k-space representation. The trace wave is supersonic, and lies within the radiation circle of radius k. coded, with white-gray representing positive pressure and black-gray negative pressure. Since pressure must be continuous throughout space (no sources), adjacent regions along the two axes must have the same pressure.

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An Introduction to Modern Solid State Physics by Yuri M. Galperin


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