Edward D. Farnum

Master mode-locking theory for few-femtosecond pulses.

We propose a model that is valid for ultrafast pulse propagation in a mode-locked laser cavity in the few-femtosecond pulse regime, thus deriving the equivalent of the master mode-locking equation for ultrashort pulses that has dominated mode-locking theory for two decades. The short-pulse equation with dissipative gain and loss terms allows for the generation of stable ultrashort optical pulses from initial white noise, thus providing the first theoretical framework for quantifying the pulse dynamics and stability as pulses widths approach the attosecond regime.

Short-pulse perturbation theory

A perturbation theory for the short-pulse equation is developed to investigate the effects of various perturbations on optical solitons propagating in nonlinear media in the few femtosecond to subfemtosecond regime. The theory is formulated using a variational approach since linearization of the exact solution is not tractable. A variety of physically realizable perturbations are considered, culminating in perturbations that result from considering short-pulse mode locking. In each case, the analytic results presented are in agreement with full numerical simulations of the short-pulse theory. Given the tremendous success of soliton perturbation theory in the theoretical realm of optical solitons, the short-pulse perturbation theory attempts to provide the same theoretical framework for understanding physically realizable mechanisms that affect pulse evolution and stability when nearing the attosecond regime.

Variational dynamics of spatial solitons in quasi-phase-matched quadratic media

We consider the stability and dynamics of quasi-phase-matched (QPM) solitons which are generated in materials with cascaded quadratic nonlinearity. The use of a variational reduction in conjunction with a Poincare (periodic orbit) analysis gives a reduced differential equation model which captures the leading-order fast and slow behaviours of the pulse dynamics. This strengthens previous results pertaining to the existence of QPM solitons, and further suggests that they are robust under even large perturbations. However, the perturbed QPM solitons are shown to manifest a slow scale behaviour which persists even for large propagation distances. This slow scale behaviour is qualitatively described with our averaging methods and is to be expected in physically realizable systems.

Mode-locking theory for ultra-short few-femtosecond laser pulses

We propose a new model which is valid for ultra-fast pulse propagation in a mode-locked laser cavity in the few femtosecond to hundreds of attoseconds pulse regime, thus deriving the equivalent of the master mode-locking equation for ultra-short pulses that has dominated mode-locking theory for two decades. The short pulse equation with dissipative gain and loss terms allows for the generation of stable ultra-short optical pulses from initial white-noise,thus providing the first theoretical framework for quantifying the pulse dynamics and stability as pulseswidths approach the attosecond regime.

Mode-locked laser pulse sources for wavelength division multiplexing

Recent theoretical investigations have demonstrated that the stability of mode-locked solution of multiple frequency channels depends on the degree of inhomogeneity in gain saturation. In this paper, these results are generalized to determine conditions on each of the system parameters necessary for both the stability and existence of mode-locked pulse solutions for an arbitrary number of frequency channels. In particular, we find that the parameters governing saturable intensity discrimination and gain inhomogeneity in the laser cavity also determine the position of bifurcations of solution types. These bifurcations are completely characterized in terms of these parameters. In addition to influencing the stability of mode-locked solutions, we determine a balance between cubic gain and quintic loss, which is necessary for existence of solutions as well. Furthermore, we determine the critical degree of inhomogeneous gain broadening required to support pulses in multiple frequency channels.

Bifurcation and stability in a low-dimensional model for multiple-frequency mode-locked lasers

Recent theoretical investigations have demonstrated that the stability of mode-locked solutions of multiple frequency channels depends on the degree of inhomogeneity in gain saturation. In this article, these results are generalized to determine conditions on each of the system parameters necessary for both the stability and the existence of mode-locked pulse solutions for an arbitrary number of frequency channels. In particular, we find that the parameters governing saturable intensity discrimination and gain inhomogeneity in the laser cavity also determine the position of bifurcations of solution types. These bifurcations are completely characterized in terms of these parameters. In addition to influencing the stability of mode-locked solutions, we determine a balance between cubic gain and quintic loss, which is necessary for the existence of solutions as well. Furthermore, we determine the critical degree of inhomogeneous gain broadening required to support pulses in multiple-frequency channels.

Waveguide arrays and spectral filtering for multi-frequency mode-locked pulse sources

Current optical fiber-communication networks increasingly rely on wavelength-division multiplexing (WDM) technologies in conjunction with optical time-division multiplexing (OTDM) of individual WDM channels. The combination of high-repetition-rate data streams with a large number of WDM channels has pushed transmission rates to nearly 1 TB/s, creating a demand for all-optical transmission sources that can generate pico-second modelocked pulses at various wavelengths. Through nonlinear mode-coupling in a wave-guide array and a periodically applied multi-notch frequency filter, robust multi-frequency mode-locking can be achieved in a laser cavity in both the normal and anomalous dispersion regimes. We develop a theoretical description of this multiplewavelength mode-locking, and characterize the mode-locked solutions and their stability for an arbitrary number of frequency channels. The theoretical investigations demonstrate that the stability of the mode-locked pulse solutions of multiple frequency channels depends on the degree of inhomogenity in gain saturation. Specifically, only a small amount of inhomogeneous gain-broadening is needed for multi-frequency operation in the laser. In this presentation, the conditions on the system parameters necessary for generating stable mode-locking is explored for arbitrary number of frequency channels. The model suggests a promising source for multi-frequency photonic applications.

Application of waveguide arrays and spectral filtering for a multi-frequency picosecond mode-locked pulse source

Current optical fiber-communication networks increasingly rely on wavelength-division multiplexing (WDM) technologies in conjunction with optical time-division multiplexing (OTDM) of individual WDM channels. The combination of high-repetition-rate data streams with a large number of WDM channels has pushed transmission rates to nearly 1 TB/s, creating a demand for all-optical transmission sources that can generate pico-second modelocked pulses at various wavelengths. Through nonlinear mode-coupling in a wave-guide array and a periodically applied multi-notch frequency filter, robust multi-frequency mode-locking can be achieved in a laser cavity in both the normal and anomalous dispersion regimes. We develop a theoretical description of this multiplewavelength mode-locking, and characterize the mode-locked solutions and their stability for an arbitrary number of frequency channels. The theoretical investigations demonstrate that the stability of the mode-locked pulse solutions of multiple frequency channels depends on the degree of inhomogenity in gain saturation. Specifically, only a small amount of inhomogeneous gain-broadening is needed for multi-frequency operation in the laser. In this presentation, the conditions on the system parameters necessary for generating stable mode-locking is explored for arbitrary number of frequency channels. The model suggests a promising source for multi-frequency photonic applications.

Multi-Frequency Mode-Locking with Waveguide Arrays

A new mode-locking model is presented in which nonlinear mode-coupling along with a periodically applied frequency filter is used to achieve stable and robust multi-frequency passive mode-locking.