Lanthanide series ions are considered in the context of acquiring spectroscopic parameters and their application to modelling of quasifour-level lasers. Tm:Ho codoped crystals of YLiF4 (YLF) and the isomorphs LuLiF4 (LuLF) and GdLiF4 (GdLF) as 2.0 μm lasers are used for illustration of the experimental and theoretical techniques presented here. While these materials have similar physical properties, they differ in the strength of the crystal field at the site of optically active lanthanide dopant ions such as Tm3+ and Ho3+. This is due in part to the size of the Lu3+, Y3+, and Gd3+ ions, which comprise part of the host lattice, but ionicity plays a role as well. This selection of lanthanide: host materials provides a useful basis on which to assess laser materials with regards to changes in the strength of the crystal field at the dopant ion site. It is demonstrated that Tm:Ho:LuLF has a larger crystal field splitting than Tm:Ho:YLF and Tm:Ho:GdLF, leading to smaller thermal populations in the Ho lower laser level. To assess this effect quantitatively, the energy levels of the first ten manifolds in Ho:LuLF have been determined. Measurement of Ho:XLiF4 (X=Y,Lu,Gd) emission cross sections at 2.0 μm, Tm:XLiF4 pump absorption cross sections around 0.78 μm, manifold to manifold decay times and energy transfer parameters in Tm:Ho:XLiF4 systems are also determined to provide a consistent set of parameters to use in laser modeling. The techniques presented here are applicable to any lanthanide series ion in a crystalline host. A theoretical laser model has been developed that is easily adapted to any lanthanide ion in a crystal host. The model is used to predict diode side-pumped laser performance of Tm:Ho:LuLF and Tm:Ho:YLF using input parameters determined from the spectroscopy presented here. An explanation is presented for the improved performance of Tm:Ho:LuLF over Tm:Ho:YLF by modeling the laser. A demonstration that small changes in lower laser thermal population can substantially alter laser performance is noted, an effect that has not been fully appreciated previously.

Spectroscopy and modeling of solid state lanthanide lasers: Application to trivalent Tm3+ and Ho3+ in YLiF4 and LuLiF4

Optical fibers in which gain-guiding effects are significant or even dominant compared with conventional index guiding may become of practical interest for future high-power single-mode fiber lasers. I derive the propagation characteristics of symmetrical slab waveguides and cylindrical optical fibers having arbitrary amounts of mixed gain and index guiding, assuming a single uniform transverse profile for both the gain and the refractive-index steps. Optical fibers of this type are best characterized by using a complex-valued v-squared parameter in place of the real-valued v parameter commonly used to describe conventional index-guided optical fibers.

Propagating modes in gain-guided optical fibers.

Transversely pumped dye-laser systems are investigated theoretically and experimentally. A set of coupled rate equations for the excited-state population densities and for the photon fluxes in both directions, at all wavelengths, is presented. Both the temporal and spatial dependence of these quantities are accounted for. The equations are solved numerically for a variety of practical situations, and analytical approximations for some limiting cases are discussed. The results describe the dependence of the amplified-spontaneous-emission (ASE) output flux on pumping rate, the spectral narrowing process, and the effects of gain saturation. It is found that under practical laboratory conditions the gain of such dye systems saturates rapidly. Consequently, at high pumping rates the output varies linearly with pump intensity, and the conversion efficiency from pump to ASE photons approaches unity. The performance of dyedaser amplifiers is described by the same set of equations, and the gain characteristics of such systems are analyzed as a function of input signal intensity and pumping rate. The theoretical calculations are compared with the results of a set of experiments, and good agreement is found. The operation characteristics of a dye-laser amplifier are evaluated and utilized in the design of a narrow-band oscillator-amplifier system.

Amplified spontaneous emission and signal amplification in dye-laser systems

Beams of light interacting with nonlinear-optical materials naturally form complex transverse profiles. Self-focusing, filamentation, modulational instabilities, spontaneous pattern formation and symmetry breaking, nonlinear waveguiding, and transverse mode excitation are but some of the many phenomena that are observed in lasers, in optical bistability, and in the free interaction of beams. As an introduction to a special issue of the Journal of the Optical Society of America B on transverse effects in nonlinear-optical systems, we provide this overview of history and current work.

Overview of transverse effects in nonlinear-optical systems

Design considerations and performance of a prism beam expander are presented. Using a prism beam expander and holographic grating, a dye laser pumped by a nitrogen laser has given 15 kW of diffraction limited power in 0.1–0.2 cm−1 linewidth. Addition of a single etalon gave a single frequency output of 10 kW in a linewidth of less than 0.01 cm−1.

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A simple beam expander for frequency narrowing of dye lasers

A pulsed dye laser system with a narrow-band signal injected into the cavity is considered. The injection starts prior to the excitation pulse. It is shown that during a transient period, injection locking can be achieved for a much wider range of parameters than under conventional CW conditions. The analysis is based on a set of coupled rate equations for the population densities and photon fluxes at all wavelengths. These are solved numerically with appropriate initial and boundary conditions. Analytical approximations, which are helpful for understanding the behavior of such systems, are presented. Both straight, two-mirror cavities, and ring laser cavities are discussed. The temporal evolution of the spectral components at all wavelengths is described. The range of tunability in this mode of operation and its dependence on various parameters, such as pulse length, cavity dimensions, and injection intensity are discussed.

Analysis of injection locking in pulsed dye laser systems

A tunable, very narrow bandwidth, flashpumped dye laser is described. Publse energies up to 50 mJ at a bandwidth of less than 30 MHz, and with a divergence of 0.4 mrad, are obtained. Spectral narrowing and tuning is achieved by injection locking of the pulsed laser to the radiation, of a tunable cw dye laser. The cavity is designed for single longitudinal and transverse mode operation, with a mode diameter large enough to fill the active medium.

A tunable, single mode, injection-locked flashlamp pumped dye laser

A general procedure for calculating all the eigenmodes of optical resonators with mirrors having Gaussian reflectivity profiles is described. The eigenmodes are expanded in terms of the freely propagating Hermite-Gaussian beams. The expansion enables one to apply well known matrix techniques to this kind of systems. The eigenvalues found determine the eigenfrequencies and the mode discrimination properties of such resonators.

Eigenmodes of optical resonators with mirrors having Gaussian reflectivity profiles.

A new technique for simultaneous operation of a dye laser at a number of independently tunable wavelengths is described. The system utilizes holographic wavelength selectors in succession, each aligned to choose one particular wavelength, and the output beam contains these wavelengths collinearly. Strong competition effects due to the homogeneous broadening of the amplifying medium reduce the multiple‐wavelength tuning range. By proper adjustment of the components in the device, this range can be increased to cover most of the single‐wavelength tuning region. The operational characteristics and the experimental results obtained at two‐wavelength operation are presented and discussed.

U. Ganiel

Papers

Amplified spontaneous emission and signal amplification in dye-laser systems

Analysis of injection locking in pulsed dye laser systems

A tunable, single mode, injection-locked flashlamp pumped dye laser

Eigenmodes of optical resonators with mirrors having Gaussian reflectivity profiles.

Simultaneous multiple-wavelength operation of a tunable dye laser