This chapter uses the density matrix methods of Chap. 4 to find the polarization induced by one or two cw plane waves in two-level media. The density matrix is extended in a form known as the population matrix, which treats collections of atomic responses simply. Section 5-1 deals with homogeneously-broadened media, while Sec. 5-2 includes inhomogeneous broadening. The induced polarization is used as a source in the slowly-varying Maxwell equations to yield a nonlinear Beer’s law for propagation. The population matrix equations of motion are solved in the important rate equation approximation, which assumes that the dipole lifetime T 2 is short compared to times for which the field envelope or population difference vary appreciably. The concepts of power-broadening and spectral hole burning are developed.
KeywordsDensity Matrix Population Difference Optical Bistability Dimensionless Intensity Spectral Hole Burning
Unable to display preview. Download preview PDF.
- Bennett, W. R., Jr. (1962), Appl. Opt. Suppl. 1, 24.Google Scholar
- Bloembergen, N,E. M. Purcell, and R. V. Pound (1948), Phys. Rev. 73, 679.Google Scholar
- Gardiner, C. W. (1986), Phys. Rev. Lett. 56 (1917). This paper discusses the squeezed vacuum leading to Eqs. (129).Google Scholar
- Levenson, Marc D., Introduction to Nonlinear Laser Spectroscopy (1982), Academic Press, New York.Google Scholar
- Stenholm, S. (1984), Foundations of Laser Spectroscopy, John-Wiley & Sons, New York. This is an excellent textbook on nonlinear laser spectroscopy.Google Scholar
- The two-photon two-level model (Sec. 5–4) has been discussed in many papers starting with: M. Takatsuji (1971), Phys. Rev. A4, 808; B. R. Mollow (1971), Phys. Rev. A4, 1666.Google Scholar
- Discussions of semiconductor media and lasers are given inGoogle Scholar
- Agrawal, G. P., and N. K. Dutta (1986), Long-Wavelength Semiconductor Lasers Van Nostrand Reinhold Co., New York.Google Scholar
- Chow, W. W., G. C. Dente, and D. Depatie (1987), IEEE J. Quant. Electron. E-23 1314.Google Scholar
- A derivation of “generalized Bloch equations” for semiconductor media is given by Lindberg, M. and S. W. Koch (1988), Phys. Rev. B38,3342.Google Scholar
- The specialization of these generalized Bloch equations to the simple model of Sec. 5–5 is given by Sargent, M. III, F. Zhou, S. W. Koch (1988), Phys. Rev. A38, 4673.Google Scholar