Coherence theory

Christopher C. Davis

doi:10.1017/CBO9781139016629.023

22 - Coherence theory

Published online by Cambridge University Press: 05 June 2014

Christopher C. Davis

Show author details

Christopher C. Davis: Affiliation:
University of Maryland, College Park

Book contents

Get access

Summary

Introduction

In this chapter we will put the concept of coherence on a more mathematical basis. This will involve the formal definition of a number of functions that are used to describe the coherence properties of optical fields. These include the analytic signal, various correlation functions, and the degree of coherence for describing both temporal and spatial coherence. We shall see that the degree of temporal coherence is quantitatively related to the lineshape function and that the degree of spatial coherence between two points is determined by the size, intensity distribution, and location of an illuminating source. We will use the wave equation, and special solutions to the wave equation called Green's functions, to show how spatial coherence varies from point to point.

The chapter will conclude with a discussion of how the intensity fluctuations of a source depend on its coherence properties, and we will examine a specific scheme, namely the Hanbury Brown–Twiss experiment, by means of which this relationship is studied. This discussion will involve a discussion of “photon statistics,” namely the time variation of the “detection” of photons from a source. In a quantum-mechanical context, square-law detectors respond to these quantized excitations of the optical field, which we call photons.

In classical coherence theory it is advantageous to represent the real electromagnetic field by a complex quantity, both for its mathematical simplicity and because it serves to emphasize that coherence theory deals with phenomena that are sensitive to the “envelope” or average intensity of the field.

Type: Chapter
Information: Lasers and Electro-optics
Fundamentals and Engineering
, pp. 736 - 782

DOI: https://doi.org/10.1017/CBO9781139016629.023 [Opens in a new window]

Publisher: Cambridge University Press

Print publication year: 2014

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1] L., Mandel and E., Wolf, Optical Coherence and Quantum Optics, Cambridge: Cambridge University Press, 1995.Google Scholar

[2] P. M., Morse and H., Feohbach, Methods of Theoretical Physics, New York: McGraw-Hill, 1953.Google Scholar

[3] W. R., LePage, Complex Variables and the Laplace Transform for Engineers, New York: Dover, 1961.Google Scholar

[4] J., Perina, Coherence of Light, London: Van Nostrand Reinhold, 1972.Google Scholar

[5] M., Françon, Optical Interferometry, New York: Academic Press, 1966.Google Scholar

[6] B. P., Lathi, Linear Systems and Signals, 2nd edn., Oxford: Oxford University Press, 2004.Google Scholar

[7] J. G., Proakis and M., Salehi, Communication Systems Engineering, Englewood Cliffs, NJ: Prentice-Hall, 1994.Google Scholar

[8] H., Margenau and G. M., Murphy, The Mathematics of Physics and Chemistry, 2nd edn., Princeton, MA: Van Nostrand, 1956.Google Scholar

[9] L. D., Landau and E. M., Lifshitz, Statistical Physics, 2nd revised edn., Oxford: Pergamon, 1969.Google Scholar

[10] M., Born and E., Wolf, Principles of Optics, 7th edn., Cambridge: Cambridge University Press, 1999.Google Scholar

[11] J. W., Goodman, Introduction to Fourier Optics, New York: McGraw-Hill, 1968.Google Scholar

[12] R. Hanbury, Brown and R. Q., Twiss, “A new type of interferometer for use in radio astronomy,” Phil. Mag. 45, 663–682, 1954.Google Scholar

[13] R. Hanbury, Brown and R. Q., Twiss, “A test of a new type of stellar interferometer on Sirius,” Nature 178, 1046–1048, 1956.Google Scholar

[14] R. Hanbury, Brown and R. Q., Twiss, “Interferometry of the intensity fluctuations in light III. Applications to astronomy,” Proc. Roy. Soc. A248, 199–221, 1958.Google Scholar

[15] R. Hanbury, Brown and R. Q., Twiss, “Interferometry of the intensity fluctuations in light IV. A test of an intensity interferometer on Sirius A,” Proc. Roy. Soc. A248, 222–237, 1958.Google Scholar

[16] D. T., Gillespie, Markov Processes: An Introduction for Physical Scientists, San Diego, CA: Academic Press, 1992.Google Scholar

[17] F., Reif, Fundamentals of Statistical and Thermal Physics, New York: McGraw-Hill, 1965.Google Scholar

[18] R., London, The Quantum Theory of Light, 3rdedn., Oxford: Oxford University Press, 2000.Google Scholar

[19] D. F., Walls, “Squeezed states of light,” Nature 305, 141–146, 1983.Google Scholar

[20] H. P., Yuen, “Two-photon coherent states of the radiation field,” Phys. Rev. 13, 2226–2243, 1976.Google Scholar

[21] H. P., Yuen and J. H., Shapiro, “Generation and detection of two-photon coherent states in degenerate four-wave mixing,” Opt. Lett. 3, 334–336, 1979.Google Scholar

[22] R. J., Glauber, “Coherent and incoherent states of radiation field,” Phys. Rev. 131, 2766–2767, 1963.Google Scholar

Book contents

22 - Coherence theory

Summary

Access options

References

Save book to Kindle

Save book to Dropbox

Save book to Google Drive