Abstract
We perform a first-principles calculation of the quantum-limited laser linewidth, testing the predictions of recently developed theories of the laser linewidth based on fluctuations about the known steady-state laser solutions against traditional forms of the Schawlow-Townes linewidth. The numerical study is based on finite-difference time-domain simulations of the semiclassical Maxwell-Bloch lasing equations, augmented with Langevin force terms, and includes the effects of dispersion, losses due to the open boundary of the laser cavity, and non-linear coupling between the amplitude and phase fluctuations (α factor). We find quantitative agreement between the numerical results and the predictions of the noisy steady-state ab initio laser theory (N-SALT), both in the variation of the linewidth with output power, as well as the emergence of side-peaks due to relaxation oscillations.
Highlights
The most important property of lasers not captured by semiclassical theories, which treat the fields via Maxwell’s equations, is the intrinsic laser linewidth due to quantum fluctuations.Above the laser threshold these fluctuations cause a diffusion in the phase of the emitted laser signal, leading to a broadening of the observed line, which would have zero width within semiclassical theory
The rates and frequency are given in units of c/L, the number of atoms in the cavity is given in terms of the state ab initio laser theory (SALT) units of 4πθ 2/(hγ⊥), and the output power is given in the SALT units of 4θ 2/(h 2γ⊥γ )
We found excellent quantitative agreement between the noisy steady-state ab initio laser theory (N-SALT) linewidth predictions and the Finite Difference Time Domain (FDTD) simulations, while finding substantial deviations from the ‘fully corrected’ Schawlow-Townes theory, demonstrating that the intertwining of the cavity decay rate, Petermann factor, incomplete inversion factor, bad-cavity correction and Henry α factor in the N-SALT linewidth formula is necessary and correct
Summary
The laser threshold these fluctuations cause a diffusion in the phase of the emitted laser signal, leading to a broadening of the observed line, which would have zero width within semiclassical theory. The magnitude of this linewidth depends upon the geometry of the laser cavity as well as upon the output power of the laser, and was first calculated by Schawlow and Townes [1], and the standard formula arising from their work, the “Schawlow-Townes” (ST). The α factor arises from the coupling between intensity and phase fluctuations, and takes different forms depending on the nature of the gain medium For atomic media it was first recognized by
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