The search for robust, low-noise modelocked comb sources has attracted significant attention during the last two decades. Passively modelocked fiber lasers are among the most attractive comb sources. The most important design problems for a passively modelocked laser include: (1) finding a region in the laser’s adjustable parameter space where it operates stably, (2) optimizing the pulse profile within that region, and (3) lowering the noise level. Adjustable parameters will typically include the cavity length, the pump power, and the amplifier gain, which may be a function of the pump power, the pump wavelength, and both the material and geometry of the gain medium.
There are two basic computational approaches for modeling passively modelocked laser systems: the evolutionary approach and the dynamical approach. In the evolutionary approach, which replicates the physical behavior of the laser, one launches light into the simulated laser and follows it for many round trips in the laser. If one obtains a stationary or periodically-stationary modelocked pulse, the laser is deemed stable and, if no such pulse is found, the laser is deemed unstable. The effect of noise can be studied by using a random number generator to add computational noise. In the dynamical approach, one first obtains a single modelocked pulse solution either analytically or by using the evolutionary approach. Next, one finds the pulse parameters as the laser parameters vary by solving a root-finding algorithm. One then linearizes the evolution equations about the steady-state solution and determines the eigenvalues of the linearized equation, which we refer to as the equation’s dynamical spectrum. If any eigenvalue has a positive real part, then the modelocked pulse is unstable. The effect of noise can be determined by calculating the noise that enters each of the modes in the dynamical spectrum, whose amplitudes are described by either a Langevin process or a random walk process.
The evolutionary approach is intuitive and straightforward to program, and it is widely used. However, it is computationally time-consuming to determine the stable operating regions and can give ambiguous results near a stability boundary. When evaluating the noise levels, Monte Carlo simulations, which are based upon the evolutionary approach, are often prohibitively expensive computationally. By comparison, the dynamical approach is more difficult to program, but it is computationally rapid, yields unambiguous results for the stability, and avoids computationally expensive Monte Carlo simulations. The two approaches are complementary to each other. However, the dynamical approach can be a powerful tool for system design and optimization and has historically been undertilized.
In this dissertation, we discuss the dynamical approach that we have developed for design and optimization of passively modelocked laser systems. This approach provides deep insights into the instability mechanisms of the laser that impact or limit modelocking, and makes it possible to rapidly and unambiguously map out the regions of stable operation in a large parameter space. For a given system setup, we can calculate the noise level in the laser cavity within minutes on a desktop computer.
Compared to Monte Carlo simulations, we will show that the dynamical approach improves the computational efficiency by more than three orders of magnitude. We will apply the dynamical approach to a laser with a fast saturable absorber and to a laser with a slow saturable absorber. We apply our model of a laser with a slow saturable absorber to a fiber comb laser with a semiconductor absorbing mirror (SESAM) that was developed at National Institute of Standards and Technology (NIST), Boulder, CO. We optimize its parameters and show that it is possible to increase its output power and bandwidth while lowering the pump power that is needed.
|Advisor:||Menyuk, Curtis R.|
|Commitee:||Carruthers, Thomas F., Draganescu, Andrei, Johnson, Anthony M., Shih, Yanhua, Yan, Li|
|School:||University of Maryland, Baltimore County|
|School Location:||United States -- Maryland|
|Source:||DAI-B 80/01(E), Dissertation Abstracts International|
|Subjects:||Computational physics, Electrical engineering, Optics|
|Keywords:||Comb lasers, Mode-locked lasers, Nonlinear dynamics, Numerical methods, Sidebands, Stability|
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