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Criteria for x‐ray superradiance
1.See, for example, (a) M. A. Duguay and P. M. Rentzepis, Appl. Phys. Lett. 10, 350 (1967);
1.(b) B. Lax and A. H. Guenther, Appl. Phys. Lett. 21, 361 (1972);
1.(c) R. A. McCorkle, Phys. Rev. Lett. 29, 982 (1972);
1.(d) R. C. Elton, R. W. Waynant, R. A. Andrews, and M. H. Reilly, Naval Research Laboratory Report No. 7412, 1972 (unpublished), and references therein;
1.(e) P. J. Mallozzi, H. M. Epstein, R. G. Jung, D. C. Applebaum, B. P. Fairand, W. J. Gallagher, R. L. Uecker, and M. C. Muckerheide, J. Appl. Phys. 45, 1891 (1974).
2.F. A. Hopf, P. Meystre, M. O. Scully, and J. F. Seely, Phys. Rev. Lett. 35, 511 (1975).
3.N. Skribanowitz, I. P. Herman, J. C. MacGillivray, and M. S. Feld, Phys. Rev. Lett. 30, 309 (1973).
4.I. P. Herman, J. C. MacGillivray, N. Skribanowitz, and M. S. Feld, in Laser Spectroscopy, edited by R. G. Brewer and A. Moordian (Plenum, New York, 1974).
5.M. Gross, C. Fabre, P. Pillet, and S. Haroche, Phys. Rev. Lett. 36, 1035 (1976).
6.J. C. MacGillivray and M. S. Feld, Phys. Rev. A 14, 1169 (1976).
7.R. Friedberg and S. R. Hartmann, Phys. Rev. Lett. A 37, 285 (1971).
8.When the upper‐ and lower‐level populations decay at different rates, Eq. (11c) of Ref. 6 must be replaced by separate equations for and
9.Curves of are easily obtained from rate‐equation analyses, such as those of Ref. 1 (d). As in Ref. 1 (d), degenerate levels must be taken into account.
10.In general, Usually, f is essentially independent of T.
11.Equation (7c) can be solved graphically using curves such as those of Ref. 1(d). The exact shape of has little effect on the observed output, for reasons discussed in Ref. 6.
12.This condition for no loss of efficiency is more stringent than the condition of Ref. 1 (d), since always [see text above Eq. (9)].
13.The effective dephasing time should also be but this does not introduce a new condition, as is shown in Ref. 14.
14.J. C. MacGillivray and M. S. Feld, Phys. Rev. (to be published).
15.The pulse is steady state in retarded time, i.e., its waveform does not change as it propagates.
16.A. Icsevgi and W. E. Lamb, Jr., Phys. Rev. 185, 517 (1969).
17.R. Bonifacio, F. A. Hopf, P. Meystre, and M. O. Scully, Phys. Rev. A 12, 2568 (1975).
18.F. T. Arecchi and E. Courtens, Phys. Rev. A 2, 1730 (1970).
19.The rate equations used are Eqs: (58) and (63) of Ref. 6, with modified as indicated in Ref. 8.
20.The equation relating and R for the rate‐equation case [Fig. 1 (b)] is In where (Ref. 6) with α obtained from R. The threshold occurs at
21.In the rate‐equation picture this buildup of P is instantaneous. Note that the rate equations can be obtained from the Maxwell‐Schrödinger equations of Ref. 6 by setting
22.Reference 2 describes the smaller output (compared to rate equations) as a spatial delay in the growth of the gain (laser lethargy).
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