Laser Model in the High-Q Limit

Z. Ficek, Mohamed Ridza Wahiddin

Published Apr 19, 2016• 0 citations

Abstract

In this chapter, we turn our considerations to the simplest model of a laser that includes all the essential features of any practical laser. The one-photon losses (due to coupling to the environment), linear gain (due to inverted atoms) and saturation (due to nonlinear loss), that are experienced by a single-mode (laser) cavity are all included in the calculations and their role in the laser properties is fully explored.We point out that all lasersmust have these three elements to operate as a laser. If there is only a linear gain, then of course there can be no output, since an output causes a loss. With both gain and loss, but not saturation, the laser intensity is either near zero (well below threshold), or else it rises inﬁnitely (well above threshold). Neither case is very useful as a model of a real laser, which has a ﬁnite output above threshold. This is why a saturation mechanism is needed, such as an intensity dependent nonlinear loss. This simple model used here is then obtainable in the limit of a high-Q laser operating not too far above threshold.

DOI: 10.1201/b16875-24

Related papers

Quantum theory of a one-dimensional laser with output coupling: Linear approximation

J.C. Penaforte, B. Baseia

A simple model of a one-dimensional optical cavity having output coupling is used to develop a fully quantized linear laser theory. The present model and procedure, which work directly within the continuous spectrum, allow us to find a simple treatment that leads to explicit solutions for the field inside and outside the laser cavity. The threshold condition for laser light onset is obtained by assuming the field operating in a single collective mode and the usual adiabatic hypothesis. A development that removes this later restriction is also discussed and outlined.

Physical Review ASep 1, 198439 citations

Intensity characteristics of inversionless lasers from induced atomic coherence

Yifu Zhu, Min Xiao, Yang Zhao

We analyze a laser system consisting of N closed three-level atoms confined in a single-mode cavity and derive the conditions for the onset of lasing without inversion or with inversion. We calculate the steady-state gain and lasing in the system and show that far above the lasing threshold, depending on the pumping and decay rates, the inversionless laser may operate in three different regimes, where the intensity of the laser depends linearly on N, is proportional to \ensuremath{\surd}N , or independent of N.

Physical Review AMay 1, 19948 citations

Non-linear properties of strongly pumped lasers

Gennady A. Koganov, R. Shuker

Bloch equations for the atomic population and the polarization/coherence and the equation of motion for the photon number in a laser are solved in steady state as a function of the pump rate. Two level atom and two modes of three levels atom are investigated. Close to threshold the usual linear dependence of the intensity on the pump rate in found for all cases. However, far above threshold strongly nonlinear dependence is encountered. In the cases for which the pump connects the lower lasing state to one of the excited states the character of the non-linearity differs crucially from the cases when the pump in not related directly to the lower lasing state. Non-monotonic dependence of laser intensity upon the pump rate is predicted. Detailed discussion of the nonlinear behavior is presented, including saturation and depletion effects.

arXiv:quant-ph/9801045Jan 22, 19980 citations

Q-function approach to a two-photon laser

Ning Lu

A quantum theory of a two-photon laser is developed by making use of the antinormal-ordering Q function. Starting from the microscopic atom-field interaction Hamiltonian for cascade three-level atoms and including saturable absorbers, we first present a master equation for the field-density operator, and then transform the master equation into a Fokker-Planck equation for the Q function. The Q-function approach enables us to study the two-photon laser analytically, obtaining simple expressions for nonlinear gain, mean photon number, frequency pulling, natural linewidth, and photon-number variance in a unified method. We find that the field in a two-photon laser will build up from a vacuum without triggering if its linear gain is larger than the cavity loss. Also hysteresis can occur in the two-photon laser even without triggering. With an overall two-photon resonance, the normalized photon-number variance approaches a common value 11/8 well above ``threshold,'' independent of the one-photon detuning. We compare these results with previous results obtained from an effective interaction Hamiltonian. We find that the domain of validity of the effective Hamiltonian for the photon-number variance is much smaller than that for the mean photon number. Well above ``threshold'' the effective Hamiltonian overestimates both the natural linewidth and the photon-number variance.

Physical Review ADec 1, 199012 citations

QUANTUM THEORY OF THE LASER

Murray, Iii Sargent

In this chapter we treat single-mode laser operation in which both the atoms and the field obey the laws of quantum mechanics. For simplicity, we suppose for most of the discussion that the field is tuned to atomic line center and that the active atoms are two-level systems which pass through the cavity in a time r, as in Sec. 16-1. To simulate a homogeneously broadened medium, we suppose that the transit times are distributed with the probability y exp(— yr). The more realistic (and complicated) calculation underlying the theory of Chap. 8 is given in Appendix I. We also suppose that excitation occurs only to the upper level; Probs. 17-13 and 17-14 consider excitation to the lower level as well. We describe cavity losses by an ensemble of nonresonant atoms injected into the lower level, as discussed in Sec. 16-1. The response of these “loss” atoms does not saturate (i.e., small coupling constant), as does that of the active atoms. The loss atoms here play the same role as the fictitious con ductivity in the semiclassical laser theory of Chap. 8. As shown in Sec. 16-5, an equivalent description is obtained by a reservoir of simple harmonic os cillators with a spread of frequencies. Our discussion depends on the reservoir theory of Sec. 16-1, in which the reduced density operator represents the ra diation field. In Chap. 20 we give a related development in which the Langevin (Heisenberg picture) approach is used.

CRC Press eBooksMar 5, 20180 citations

Population Inversion, Saturation, and Laser Systems

Surendra Singh

This chapter begins with a heuristic derivation of atomic population rate equations which include changes to level populations due to stimulated transitions as well as level relaxations and pump. These equations are used to study the saturation of population inversion with increasing light intensity and its dependence on the type of gain medium (three-level gain media vs. four-level gain media), lineshape and nature of line broadening (homogeneous vs inhomogeneous broadening). How saturation affects lineshape and thus gain and absorption giving rise to phenomena like power broadening and spectral hole burning is also discussed. The chapter summarizes the equations of motion for atomic polarization, inversion and the cavity field describing their nonlinear dynamical coupling. These equations, known as the Maxwell-Bloch equations, provide a complete description of atom-field interaction in a laser. Approximations of these equations, including the rate equation approximation, to deal with different laser classes are briefly described. These will be used in the next few chapters to explore and understand the rich and varied behavior of lasers. The chapter ends with a summary of select gain media for different types of commonly used lasers.

CRC Press eBooksSep 23, 20260 citations