Small‐Signal Analysis of Internal (Coupling‐Type) Modulation of Lasers (original) (raw)
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Research Article| October 01 1964
Bell Telephone Laboratories, Incorporated, Murray Hill, New Jersey
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J. Appl. Phys. 35, 2870–2876 (1964)
The internal modulation of lasers by a variation of cavity losses is analyzed in terms of the normal modes of the system. Time‐dependent perturbation theory is used to describe the results of resistive mode coupling when the losses are modulated with small signals. For the single‐mode oscillator, an expression is obtained for the amplitude distortion in the modulation index of the light produced by a coupling‐type internal modulator when the losses are modulated at a frequency commensurate with the separation between longitudinal modes of the laser cavity. Low distortion is obtained when the modulating frequency is noncommensurate with the longitudinal‐mode frequency separation. The internal coupling‐type modulator in its present form can provide small amounts of modulation over bandwidths limited to the separation between adjacent interferometer cavity normal modes.
For a multimode oscillator, modulation of the internal losses at a frequency equal to the separation between adjacent longitudinal modes produces a pulse‐modulated output wave. The average intensity is unchanged and the peak intensity is increased over the intensity of the unmodulated laser by a factor equal to the number of oscillating modes.
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By a single‐mode oscillator, we mean an arrangement where the frequency separation between adjacent cavity modes exceeds the inhomogeneous linewidth of the active medium. Such oscillators have been constructed recently using the 6328‐Å transition of the He‐Ne system. For details see,
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It should be mentioned in this connection that by introducing dispersion or mode suppression in the interferometer cavity it should be possible to reduce the deleterious effects of mode coupling on the modulator performance. The problem of mode suppression in interferometers has been treated by
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The series of cosine terms in Eq. (32) is a sum of harmonic terms whose phases are in arithmetic progression. This type of function is very similar to those obtained in the analysis of diffraction gratings. Accordingly, it is expected that Eq. (32) will give rise to interference phenomena with the result that Et will peak periodically with time. By summing the series given in Eq. (32), one can show that the intensity I given by EtEt* becomes
I/Ip = {[sin(N+1)φm−(−1)m sinNφm]/sinφm}2
, in which Ip = EpEp* is the intensity of any one mode and φm = ωmt+θm.
Recent independent experimental work performed by
L. E.
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,
R. L.
Fork
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M. A.
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We point out in this regard that the two principal indices of refraction in a crystal of symmetry D2d such as KDP have identical induced electro‐optic effects but of different sign. Hence the phase retardation φ is directly proportional to the electro‐optic effect, whereas the phase factor ψ is independent of this effect. We conclude therefore that no first‐order phase changes occur as the light propagates through the KDP crystal.
K. Gürs and R. Müller, in Proceedings of the Symposium on Optical Masers (Polytechnic Press, New York, 1963).
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© 1964 The American Institute of Physics.
1964
The American Institute of Physics
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