Abstract
In this chapter we discuss interaction of radiation and atoms and obtain the relationship between absorption and emission processes. We show that for light amplification a state of population inversion should be created in the atomic system. We also obtain an expression for the gain coefficient of the system. This is followed by a discussion of two-level, three-level, and four-level systems using the rate equation approach. Finally a discussion of various mechanisms leading to broadening of spectral lines is discussed.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsNotes
- 1.
We will show in Section 4.5 that \(g(\omega_0)\Delta \omega \) equals \((2/\pi)\) and \((4\ln 2/\pi)^{1/2}\) for Lorentzian and Gaussian lineshape functions, respectively.
- 2.
Ruby laser active medium consists of Cr+3-doped ion Al2O3 and is an example of a three level laser. More details regarding the ruby laser are given in Section 10.2.
- 3.
We are considering here a single electron atom with r representing the position of the electron with respect to the nucleus. Thus the electric dipole moment of the atom is given by p = e r because the direction of the dipole moment is from negative to the positive charge. The interaction energy of a dipole placed in an electric field \({E}\ {\textrm{is}} \ -\vec{p}.{E} \) is which leads to Eq. (4.62).
- 4.
- 5.
It can be shown that \(\left|\int\psi_{1}^{\ast}{\textbf{r}}\psi_2{\textrm d}\tau\right|^2\) has the same value for transition from anyone of the states (n = 2, l = 1, m = 0) or (n = 2, l = 1, m = -1) or (n = 2, l = 1, m = -1) to ( n = 2, l = 0, m = 0) state. However, the matrix element for the transition from (n = 2, l = 0, m = 0) state to the (n = 1, l = 0, m = 0) state is zero. This implies that the corresponding dipole transition is forbidden.
References
Ghatak, A. K., and Lokanathan, S. (2004), Quantum Mechanics, Macmillan, New Delhi.
Gopal, E. S. R. (1974), Statistical Mechanics and Properties of Matter, Wiley, New York.
McFarlane, R. A., Bennet, W. R., and Lamb, W. E. (1963), Single mode tuning dip in the power output of an He–Ne Optical maser, Appl. Phys. Lett. 2, 189.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2011 Springer Science+Business Media, LLC
About this chapter
Cite this chapter
Thyagarajan, K., Ghatak, A. (2011). Einstein Coefficients and Light Amplification. In: Lasers. Graduate Texts in Physics. Springer, Boston, MA. https://doi.org/10.1007/978-1-4419-6442-7_4
Download citation
DOI: https://doi.org/10.1007/978-1-4419-6442-7_4
Published:
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4419-6441-0
Online ISBN: 978-1-4419-6442-7
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)