By J. A. Arnaud
Beam And Fiber Optics
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Additional info for Beam and Fiber Optics
In a wave theory, the latter follows from the proportionality of the canonical momentum to the wave vector. Thus the law of refraction follows quite generally from isotropy and translational invariance of the medium. A generalized form of the law of refraction is needed if we omit the assumption of isotropy. The essential concepts of ray propagation appear, in fact, most clearly when the medium lacks isotropy. Let us consider a charged particle traversing two closely spaced grids carrying equal and opposite current densities, as shown in Fig.
Vz also increases with the transverse mode number m. This is a consequence of the transverse dimension of the beam being limited. Because the wave vector has a transverse component, its axial component kz = ω/ν2 is reduced. The resonance frequency of any trans verse mode, m = 0, 1, 2, . . is therefore higher than one would expect on the basis of the simple violin string model discussed earlier, and it further increases as m increases. A typical response of optical resonator is shown in Fig. l-23c.
K. Tien, J. P. Gordon, and J. R. Whinnery, Proc. IEEE 53, 129 (1965). E. " Wiley, New York, 1970. N. S. Kapany and J. J. " Academic Press, New York, 1972. R. Ulrich and R. J. Martin, Appl Opt. 10, 2077 (1971). J. Nishizawa and A. Otsuka, Appl. Phys. Lett. 21, 48 (1972). R. K. " Univ. of California Press, Berkeley, California, 1964. G. Toraldo Di Francia, Opt. Ada 1, 157 (1955). E. A. J. Marcatili and R. A. Schmeltzer, Bell Syst. Tech. J. 43, 1783 (1964). H. G. Booker and W. Walkinshaw, in "Meteorological Factors in Radio-Wave Propaga tion," p.
Beam and Fiber Optics by J. A. Arnaud