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Journal of the Optical Society of America

Journal of the Optical Society of America

  • Vol. 59, Iss. 11 — Nov. 1, 1969
  • pp: 1446–1452

Photoelectric Detection with Two-Photon Absorption

A. K. JAISWAL and G. S. AGARWAL  »View Author Affiliations


JOSA, Vol. 59, Issue 11, pp. 1446-1452 (1969)
http://dx.doi.org/10.1364/JOSA.59.001446


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Abstract

A formula for the photoelectron-counting distribution for a two-photon detector is derived quantum mechanically assuming that the ionising transitions in the atoms of the detector take place through the simultaneous absorption of two photons. It is assumed that the incident light is quasimonochromatic. It is shown that the distribution of the photoelectrons is given by the average of a Poisson distribution, the parameter of the distribution being proportional to the time integral of the square of the instantaneous light intensity. Counting distributions for the thermal (gaussian) light and for some models of laser light are obtained for the limiting case when the counting-time interval <i>T</i> is short compared to the coherence time <i>T<sub>c</sub></i> of the light. An approximate formula for arbitrary time intervals for the counting distribution of thermal light is also proposed.

Citation
A. K. JAISWAL and G. S. AGARWAL, "Photoelectric Detection with Two-Photon Absorption," J. Opt. Soc. Am. 59, 1446-1452 (1969)
http://www.opticsinfobase.org/josa/abstract.cfm?URI=josa-59-11-1446


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References

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  13. The original derivation of Mandel was based on semiclassical arguments. The corresponding quantum-mechanical derivation of the formula was given by R. J. Glauber, in Quantum Optics and Electronics, Les Houches 1964, C. Dewitt, A. Blandin, and C. Cohen-Tannoudji, Eds. (Gordon and Breach, New York, 1965), p. 65. See also P. L. Kelley and W. H. Kleiner, Phys. Rev. 136, A316 (1964).
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  16. The contribution of the A2 term is also easily taken into account. It may be shown that the final result is still given by Eq. (30) except that the quantum-efficiency parameter a changes slightly. The new value of α is [equation] Here 〈f|0〉 represents the scalar product between the ground-state wavefunction and the final-state (free-electron) wave-function.
  17. E. C. G. Sudarshan, Phys. Rev. Letters 10, 277 (1963). A detailed discussion of the diagonal representation is given in Ref. 11. See also R. J. Glauber, Phys. Rev. 131, 2766 (1963).
  18. M. Born and E. Wolf, Principles of Optics (Pergamon Press, Ltd., Oxford, England, 1965), 3rd ed., Ch. X.
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  20. The representation of V in the form Eq. (24) assumes that the incident light is plane polarized. However, the results are easily generalized to the case of partially polarized light. If the incident light is of thermal origin, then as well known we may consider it as the superposition of two linearly polarized, statistically independent components with average intensities equal to ½(1+P)〈I〉 and ½(1−P)〈I〉, respectively, where P is the degree of polarization. It is also assumed that the condition of cross-spectral purity is satisfied. In this case, the final result (30) remains unchanged. (See also Sec. IIIA.) For the partially polarized light of nonthermal origin, the expression for the photoelectron counting distribution may be shown to be [equation] where [equation] and [equation]
  21. See Ref. 9, Appendix B. Similar arguments are summarized in L. Mandel, Phys. Rev. 152, 438 (1966).
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  27. G. Bédard, J. C. Chang, and L. Mandel, Phys. Rev. 160, 1496 (1967).
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