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

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

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

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

Dynamics of a Low-Dimensional Model for Short Pulse Mode Locking

Emerging ultra-fast mode-locked lasers are now capable of generating pulses in the few to sub-femtosecond regime. Using recent theoretical innovations around the short pulse equation, we characterize the mode locking dynamics using a low-dimensional representation of the pulse parameters. The theory is formulated using a variational approach, since linearization of the exact solution is not tractable. The dominant dynamics can be characterized in a geometrical way using phase-plane analysis. Of note is our ability to determine the underlying bifurcations that occur due to changes in the fiber laser cavity parameters, including the onset of the multi-pulsing instability. The theory can aid in design principles for generating robust and highly-stable mode-locked pulses

Solitons and ultra-short optical waves: The short-pulse equation versus the nonlinear schrödinger equation

Summary: This chapter presents a comparison between the standard center-frequency expansion commonly used today for modeling optical transmission systems and mode-locked lasers, and a new, short-pulse theory that attempts to directly account for the broadband nature of ultra-short pulses. The radically different asymptotic regimes used in both theories are highlighted and contrasted, suggesting that serious consideration should be taken in developing further short-pulse theory. The chapter first introduces governing Maxwell\u27s equations. It then considers the reduction of the governing equations under linear propagation effects and the asymptotic scalings of the nonlinear Schrodinger equation (NLS) and short-pulse equation (SPE). The chapter augments the linear propagation by considering an instantaneous nonlinear response. It also considers a more realistic nonlinear time-response, and the application of the SPE theory to mode-locked lasers and contrasts it to standard NLS approaches. Controlled Vocabulary Terms: electromagnetic pulse; Maxwell equations; Schrodinger equatio

Mode locking in the few-femtosecond regime using waveguide arrays and the coupled short-pulse equations

A new theoretical model is proposed for characterizing the ultrashort (few femtoseconds and below) propagation dynamics in a laser cavity that is mode locked with a waveguide array. The theory circumvents the standard and problematic center-frequency expansion methods that typically result in the nonlinear Schrdinger-based master mode-locking equation. The resulting short-pulse-equation framework, which is the equivalent of the nonlinear Schrdinger equation for ultrafast pulses, provides an asymptotically valid description of the electric-field amplitude, even if pulses are shortened below a single cycle of the electric field. Given the lack of theory in the ultrafast regime, the model provides the beginning theoretical framework for quantifying the pulse dynamics and stability, as pulsewidths approach the attosecond regime. © 2006 IEEE

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. © 2011 SPIE

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 fewfemtosecond 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. © 2010 Optical Society of America

Multifrequency mode-locked lasers

A theoretical model is constructed that describes the operation of a pulsed mode-locked laser simultaneously operating at N frequency channels. The model, which is a combination of standard WDM interactions in the canonical master mode-locking model subject to both self- and cavity-saturating gain effects, results in mode-locking dynamics that qualitatively describe the N-frequency channel operation. It is further in agreement with the observed experimental dual-frequency (N=2) laser operation. In the model, it is the combination of self- and cavity-gain saturation that simultaneously allows for mode-locking at N frequencies, which can be of significantly different energies and pulse widths. The model provides a framework for understanding the operation and stability of identically mode-locked pulses at multiple frequencies, thus contributing to the characterization of the increasingly important and timely technology of dual- and multifrequency mode-locked laser cavities. © 2008 Optical Society of America