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Output coupling in optical cavities and lasers : a quantum theoretical approach

紀公雄 氏原

Published Jan 1, 2010• 2 citations
OpenAlex

Abstract

1 A one-dimensional optical cavity with output coupling-classical analysis- 2 A one-dimensional optical cavity with output coupling-quantum analysis- 3 A one-dimensional quasimode laser: General formulation 4 A one-dimensional quasimode laser-Semiclassical and quantum analysis- 5 A one-dimensional laser with output coupling -Derivation of the laser equation of motion- 6 A one-dimensional laser with output coupling-Contour integral method- 7 A one-dimensional laser with output coupling-Semiclassical linear gain analysis 8 A one-dimensional laser with output coupling-Semiclassical nonlinear gain analysis 9 A one-dimensional laser with output coupling-Quantum linear gain analysis- 10 A one-dimensional laser with output coupling -Quantum nonlinear gain analysis- 11 Analysis of a one-dimensional laser with two-side output coupling -The propagation method- 12 A one-dimensional laser with output coupling -Summary and interpretation of the results- 13 Spontaneous emission in a one-dimensional optical cavity with output coupling 14 Theory of excess noise 15 Quantum theory of the output coupling of an optical cavity Appendices

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Physical Review A•Sep 1, 1979•9 citations
1 A one-dimensional optical cavity with output coupling-classical analysis- 2 A one-dimensional optical cavity with output coupling-quantum analysis- 3 A one-dimensional quasimode laser: General formulation 4 A one-dimensional quasimode laser-Semiclassical and quantum analysis- 5 A one-dimensional laser with output coupling -Derivation of the laser equation of motion- 6 A one-dimensional laser with output coupling-Contour integral method- 7 A one-dimensional laser with output coupling-Semiclassical linear gain analysis 8 A one-dimensional laser with output coupling-Semiclassical nonlinear gain analysis 9 A one-dimensional laser with output coupling-Quantum linear gain analysis- 10 A one-dimensional laser with output coupling -Quantum nonlinear gain analysis- 11 Analysis of a one-dimensional laser with two-side output coupling -The propagation method- 12 A one-dimensional laser with output coupling -Summary and interpretation of the results- 13 Spontaneous emission in a one-dimensional optical cavity with output coupling 14 Theory of excess noise 15 Quantum theory of the output coupling of an optical cavity Appendices
In this chapter, a one-dimensional optical cavity with output coupling is con-sidered. The optical cavity has transmission loss at one or both of the end surfaces. The classical, natural cavity mode is defined, and decaying or growing mode functions are derived using the cavity boundary conditions. A series of resonant modes appears. But these modes are not orthogonal to each other and are not suitable for quantum-mechanical analysis of the optical field inside or outside of the cavity. Hypothetical boundaries are added at infinity in order to obtain orthogonal wave mode functions that satisfy the cavity and infinity boundary conditions. These new mode functions are suitable for field quantization, where each mode is quantized separately and the electric field of an optical wave is made up of contributions from each mode. Some results of quantization are described in the next chapter. Chapter 3 deals with the usual quasimode model: a perfect cavity with distributed internal loss or with a fictitious loss reservoir.
Subthreshold operation of a one-dimensional laser having output coupling is analyzed quantum mechanically under the assumption of constant population inversion. The conventional quantum Langevin theory of the laser is improved in that the spatial behavior of the field is treated exactly by use of a multimode formulation of the field of the universe. This formulation allows the thermal noise to be derived automatically without introducing any artificial damping mechanism for the field; this noise comes from the statistical nature of the initial state of the field. The analysis shows that the cavity quasimodes are excited, that the linewidth formula differs from that of a conventional theory by a factor determined by the field distribution excited in the cavity, and that, outside the cavity, the quantum-mechanical coherence function is propagated with the velocity of light.
A quantum theory of spontaneous emission from an initially excited two-level atom in a one-dimensional optical cavity with output coupling from both sides is developed. Orthonormal mode functions with a continuous spectrum are employed, which are derived by imposing a periodic boundary condition on the whole space with a period much larger than the cavity length. The delay differential equation of the atomic state of Cook and Milonni [Phys. Rev. A 35, 5081 (1987)] is re-derived in a strict manner, where the reflectivity of the cavity mirrors is included naturally in the mode functions. An approximate solution at a single-resonant-mode limit shows the results of ``vacuum'' Rabi oscillation in an underdamped cavity and enhanced spontaneous emission rate in an overdamped cavity. For the latter case, it is found that in the optical range the spontaneous emission rate is enhanced by a factor F (finesse of the cavity).
For pt.IV see J. Phys. Soc. Japan, vol.47, p.217-224 (1982). Spontaneous emission in a lossy one-dimensional cavity is analyzed under the perturbation approximation and the Wigner-Weisskopf approximation. The cavity loss due to output coupling is treated quantum mechanically by the use of a set of continuously distributed radiation modes. The enhancement and reduction factors in the spontaneous emission probability due to the presence of the cavity structure are derived. Interesting transients in spontaneous emission during a time of the order of the cavity decay time are predicted, which leads to an interpretation of the enhancement or the reduction in spontaneous emission in terms of feedback and self-interference effects. The detection of the emitted photon by a detector atom outside the cavity is also discussed.>
Phase noise of a one-dimensional laser with output coupling that is oscillating well above threshold is analyzed on the basis of a multimode formulation of the field. The phase diffusion, both in time and space, is calculated for the output beam taking into account the lowest-order moments of the thermal and the quantum noise forces. Thermal noise is introduced automatically without assuming any absorbing atoms or heatbaths, and is interpreted as the amplified, ambient thermal radiation that penetrates the laser cavity. Quantum noise is treated by the quantum Langevin method. The resulting linewidth formula differs from that of a conventional theory by factors that are determined by the degree of output coupling and by the nonuniform distribution of the saturated gain in the cavity.
The quantum theory is developed for an arbitrarily stratified one-dimensional optical cavity which transmits light at one of its end The field is expanded in terms of the modes of the universe and each universal mode is quantized separately by means of the usual method. A class of coherent states which yields oscillation wave shapes of the cavity quasimodes as the field eigenvalue is studied. A state of this class gives an eigenvalue for the annihilation operator of a universal mode which is an analytic function of the mode frequency except for a mode-dependent phase factor. The mathematical meaning of the phase factor is studied. A new scheme of field quantization is developed which absorbs the above phase factor and yields simpler forms of the eigenvalue equations for the above class of states. For a state of the class, the local intensity, its fluctuation, and the various correlations of the field decay with time. For the local field inside or outside of an optical structure which is coupled to the free space, the almost definite phase relationship among the universal modes plays a decisive role.