What is SALT?

My work with Prof. Douglas Stone at Yale University focused on developing new semiclassical and fully quantum theories of laser systems, along with numerical methods to validate these theories. Much of this work centered on a recently developed semiclassical theory of lasers, called the steady-state ab initio laser theory (SALT), that treats exactly both the loss of light through the cavity boundary and the non-linear spatial hole-burning of the gain medium due to its interaction with the light in the cavity in continuous wave operation of the laser. SALT predicts the thresholds and frequencies of the lasing modes, as well as yielding the output power and spatial profile of these modes as a function of the pump strength [1]. Comparison of SALT to finite difference, time domain (FDTD) simulations of the same lasers shows quantitative agreement [2], and a direct experimental test of SALT is yielding promising preliminary results.

Developing the most general semiclassical laser theory

Many laser theories, including SALT, are developed using a two-level gain medium, but in reality, most gain media exhibit many atomic levels, multiple lasing transitions, and possibly diffusion of the gain carriers, which counteracts the effects of spatial hole-burning and partial pumping of the gain medium (if present). Most previous treatments of such complex gain media focus on one-dimensional systems leading to approximations for both the spatial structure of the lasing modes and the effects of diffusion. In addition the effects of diffusion on a partially pumped gain medium have not been considered previously. However, using a SALT-like approach, I have showed that multiple atomic levels, lasing transitions, and gain diffusion can all be treated exactly under steady-state conditions in structures of any dimensionality, leading to the most general semiclassical laser theory of which we are aware [3]. This complex-SALT theory agrees quantitatively with FDTD simulations and demonstrates qualitative agreement with previous experimental results in quantum cascade lasers. Finally, this work also demonstrates initial results from a model which treats a semiconductor gain media with a continuum of available lasing transitions within SALT. This work follows up on earlier work I performed, detailing how an arbitrary number of atomic levels with a single lasing transition can be renormalized to an effective two-level system in the steady-state regime, as well as showing the numerical efficiency of SALT when compared against FDTD [2].

Treatment of injected signals in SALT

Another important topic in modern laser physics is the use of an injected signal into a "slave" laser, which amplifies the incident signal from the "master" laser, producing greater gain in the slave laser, while retaining many of the noise properties of the master laser. There has also been great interest in the study of injected lasers theoretically since in certain parameter regimes they can exhibit chaotic dynamics. However, in the steady-state regime these more exotic theories are not applicable, and the only previously known theory is one based on synchronization, the frequency of the self-oscillating signal in the slave laser is pulled in to the frequency of the injected signal as the pump on the slave laser is increased. I have demonstrated that injected signals can also be treated by a generalized version of SALT, termed injection-SALT (I-SALT), enabling an exact treatment of the mode competition between an injected signal and any self-oscillating signals within the slave laser cavity [4]. Unlike the previously developed theory, I-SALT predicts repulsion of the self-oscillating frequency from the injected frequency, and this behavior has been confirmed quantitatively with FDTD simulations. Furthermore, I-SALT naturally treats multiple self- oscillating signals and injected signals in multiple dimensions, which no previous theory couldaccommodate.

Designing an incoherent light source

A prominent challenge in many optical imaging techniques, such as optical coherence tomography, is finding a light source that is both bright and spatially incoherent to minimize speckle. Traditionally, continuous wave lasers have been unable to fill this role due to speckle, yielding intractable artifacts in the resulting signal. My most recent work with SALT has been designing a laser cavity that is optimized for multi-mode, speckle-free, continuous wave emission for use in optical imaging experiments. We accomplished this by choosing a cavity in which the ray dynamics of the lasing modes are chaotic, thus delocalizing the modes and yielding reduced mode competition from spatial hole-burning, while simultaneously producing many passive cavity modes with similar Q-values. Devices built based on this prediction have been fabricated and tested by Prof. Hui Cao's group at Yale, and the experimental results were found to match the theoretical predictions for the optimal cavity [5].

Developing and testing a theory of the quantum laser linewidth

Since the development of the quantum limited laser linewidth due to phase fluctuations from spontaneous emission events by Schawlow and Townes, many subsequent corrections have been discovered. These corrections have all been considered to be mutually independent, and include the Petermann factor, due to the non-orthogonality of the cavity modes, the incomplete inversion factor, and the bad-cavity correction, a linewidth reduction due to dispersion effects. Recently, a new method of calculating the intrinsic laser linewidth in terms of quantum fluctuations around the SALT steady- state was developed [6], which demonstrated that the Petermann factor and bad-cavity corrections to the Schawlow-Townes linewidth are intertwined, and can only be separated in certain limits. We are pursuing this work with Prof. Steven Johnson's group at MIT, developing a coupled mode theory that encompasses all known contributions to the laser linewidth, including not only the Petermann, bad-cavity, and incomplete inversion corrections, but also the very important Henry alpha-factor [7], again demonstrating that in general these effects are not simply multiplicative. I have helped to develop this theory and I am verifying this theory quantitatively by using an FDTD algorithm coupled to the Langevin equations of the gain medium. Such verification has never before been achieved due to the long simulation times required. However, we are able to circumvent this difficulty by simulating microcavities, for which these recent theories are optimized, and demonstrate that the noisy-FDTD does indeed quantitatively reproduce the predictions of the coupled mode theory, in contrast to that of the corrected Schawlow-Townes linewidth.


[1] H. E. Türeci, A. D. Stone, and B. Collier, "Self-consistent multimode lasing theory for complex or random lasing media," Phys. Rev. A 74, 043822 (2006).

[2] A. Cerjan, Y. D. Chong, L. Ge, and A. D. Stone, "Steady-state ab-initio laser theory for N-level lasers," Opt. Express 20 474-488 (2012).

[3] A. Cerjan, Y. D. Chong, and A. D. Stone, "Steady-state ab initio laser theory for complex gain media," Opt. Express 23, 6455-6477 (2015).

[4] A. Cerjan and A. D. Stone, "Steady-state \textit{ab initio} theory of lasers with injected signals," Phys. Rev. A 90, 013840 (2014).

[5] B. Redding, A. Cerjan, X. Huang, M. L. Lee, A. D. Stone, M. A. Choma, and H. Cao, "Low-Spatial Coherence Electrically-Pumped Semiconductor Laser for Speckle-Free Full-Field Imaging," Proc. Natl. Acad. Sci. USA 112, 1304-1309 (2015).

[6] Y. D. Chong and A. D. Stone, "General linewidth formula for steady-state multimode lasing in arbitrary cavities," Phys. Rev. Lett. 109 063902 (2012).

[7] A. Pick, A. Cerjan, D. Liu, A. W. Rodriguez, A. D. Stone, Y. D. Chong, and S. G. Johnson, "Ab-initio multimode linewidth theory for arbitrary inhomogeneous laser cavities," arXiv: 1502.07268.