By Ting-Chung Poon
This worthwhile textbook serves reasons. the 1st is to introduce a few conventional themes akin to matrix formalism of geometrical optics, wave propagation and diffraction, and a few basic history on fourier optics. the second one is to offer the necessities of acousto-optics and electro-optics, and supply the scholars with adventure in modeling the speculation and purposes utilizing a primary software program software MATLAB®. The booklet relies at the authors' personal in-class lectures in addition to researches within the area.
Readership: First-year/senior graudate scholars in engineering and physics; scientists and engineers prepared within the fundamentals of acousto-optics and electro-optics
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Extra resources for Engineering optics with Matlab
Finally, we present solutions of the wave equation in a spherical coordinate system. For spherical symmetry ( Dllxp = 0 = o/o6>), the wave equation, Eq. 2-13), with Eq. 2 v2 dt2 ' K ] Now, the above equation is of the same form as Eq. 2-18). Hence, using Eq. 2-19), we can write down the solution of Eq. 2-23) with u>o/ko = v. )], Eq. 2-23) takes the form of i> (R, t) = ~cxp[j(u;0t - koR)], which is called a spherical wave. 2 Maxwell's equations in phasor domain: Intrinsic impedance, the Poynting vector, and polarization The electromagnetic fields and the current and charge densities considered so far are real functions of space and time.
However, we remark that Eq. 1-1) is not independent of Eq. 1-4) and, similarly, Eq. 1-2) is a consequence of Eq. 1-3). By taking the divergence on both sides of Eqs. 1-11) dt which is the principle of conservation of charge, we can show that V • T> = pv. Similarly, Eq. 1-2) is a consequence of Eq. 1-3). Hence, from Eqs. 1-4), we really have six independent scalar equations (three scalar equations for each curl equation) and twelve unknowns. The unknowns are the x, y, and z components of £, T>, "H, and B.
Since the ratio oV^o is a constant, the medium of propagation is said to be nondispersive. We can then re-express Eq. 2-17b) + k0zaz. fcois called the propagation vector and |fco| = ^o; &x, &y, and az denote the unit vectors in the x, y, and z directions, respectively. ,i/j(z,t), the wave equation [Eq. 2-18) v ' and its general solution is i>(z, t) = cif(co0t - k0z) + c2 g(co0t + k0z), v = coQ/k0. 2-19) Note that Eq. 2-16) comprises the superposition of two waves, traveling in opposite directions.