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THEORY OF THE OPTICAL FREQUENCY TRANSLATOR
1.M. A. Duguay, L. E. Hargrove, and K. B. Jefferts, Appl. Phys. Letters 9, 287 (1966).
2.H. S. Black, Modulation Theory (D. Van Nostrand and Co., Toronto, New York, London), p. 188.
3.We are indebted to J. A. Morrison for suggesting the use of this integral representation.
4.J. A. Morrison has shown that it is unnecessary to replace the sum by an integral, since it is possible to make use instead of a theta‐function identity. When this is done, the integrand of Eq. (8) comes out as the first term of an infinite series. The next term, however, is smaller by a factor of the order of and may safely be neglected.
5.G. N. Watson, Bessel Functions, 2nd Ed. (Cambridge, 1941), p. 188.
6.G. N. Watson, op. cit., p. 248.
7.Equation (11), of course, is the result that would have been obtained if the input had consisted of just a single frequency In that case, however, Eq. (11) would have held for any n′ The output signal then has appreciable amplitude at all frequencies from to
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