Model of the nonlinear operation of a laser with a gaussian mirror

Abstract

In this paper a semi-classical model of the nonlinear operation of a laser is extended to describe a laser with a Gaussian mirror. Modified nonlinear self-consistent equations including transverse and longitudinal field dependence, gain saturation, spatial hole burning and nonlinear dispersion effects are derived. With the help of an energy theorem an approximate solution for steady-state single mode operation is presented, which relates the small signal gain to the output power and the laser system characteristic parameters. The laser output power characteristics are presented for various cavity configurations, especially, revealing an influence of the Gaussian mirror parameter on the power efficiency of the laser.     

Self-pulsing in a Laser Model with Discrete Gain and Loss

Abstract

A new model of a multimode homogeneously broadened unidirectional ring cavity laser is presented. Gain and loss are modelled as discrete elements taking the form of a thin laser medium of negligible extent and a partially reflecting mirror forming a cavity with a finite round-trip time. In this way, an exact analytic solution to the stability problem of the c.w. state can be obtained. It is shown that a second threshold exists for any mirror transmissivity and, when using a semitransparent mirror, that it can be reached by pumping seven times above laser threshold. Numerical solutions are presented, including periodic, quasi-periodic and chaotic oscillations. Well known mean-field limit self-pulsations are here predicted for any mirror transmissivity and suitable pump parameter, and are shown to be particular cases of a more general class of instabilities involving excitation of one or more cavity modes by Rabi frequency modulation; the resulting dynamics reflect a complex interaction among the excited modes and the Rabi frequency modulation. The present model predicts, in particular, transition to chaos from a frequency locked limit cycle or from a two-dimensional torus.     

Pulse Shaping in a Laser with an Irradiance-dependent Cavity Mirror

Abstract

The effect of an irradiance-dependent cavity mirror on the shape of a laser pulse is considered in the context of the CO₂ laser, using an InSb etalon as the mirror, with special reference to the production of square pulses. A dynamical instability is found experimentally, in numerical solutions of a rate equation model, and in a simplified stability analysis. This instability leads to a transient ringing, or even a train of short pulses rather than the more desirable long square pulse, unless the response time of the nonlinear mirror is very short.     

Design of polarization-selective diffractive phase elements in a laser cavity

We report a new design for a polarization-selective laser cavity with birefringent diffractive phase elements. This laser cavity can create two modes with different polarizations and profiles launched separately from two end mirrors. The numerical simulation results show that the constructed laser cavity can successfully generate two orthogonal polarization modes with a uniform circular shaped pattern output from one end mirror and a uniform square-shaped pattern output from another end mirror.     

Simplified intracavity phase plates for increasing laser-mode discrimination

Recently, a new class of laser resonators was introduced that utilizes diffractive mirrors and an additional intracavity diffractive phase element. High modal discrimination and low fundamental-mode loss were achieved simultaneously by use of sinusoidal and pseudorandom diffractive phase elements. An intracavity phase element consisting of a simple single-step phase modulation is approximated by a Gaussian with a small radius. Explicit expressions are obtained for the modal-discrimination factor as a function of resonator parameters with a Gaussian output mirror. Numerical simulations are performed for a phase element with a step singularity in the phase function, the fundamental mode of this cavity being super-Gaussian. The modal discrimination of the cavity is studied for different radii of the single-step phase modulation, the position of the phase plate, and the cavity Fresnel number. Optimum solutions are found for a plane output mirror with either a striped or a circular shape.     

A phase-conjugate Twyman-Green interferometer with increased sensitivity for laser beam collimation

Abstract

A Twyman-Green interferometer having a phase-conjugate mirror in one arm and double mirror in another arm is described to measure divergence and to check the collimation of a laser beam. It uses an internally self-pumped phase conjugation in BaTiO₃ crystal as phase-conjugate mirror. The use of double mirror gives a dual interference field which results in improved sensitivity in collimation testing. The dual-field interferogram is also useful in easily distinguishing between the divergent and convergent nature of the test beam. Measurement results are presented.     

Self-seeded Ti: Sapphire laser with an active feedback mirror

Abstract

A single-longitudinal mode (SLM) dual-cavity pulsed Ti:sapphire laser is presented. It is self-seeded by means of an active feedback mirror (AFM) consisting of a partially reflecting mirror and additional active medium. The use of AFM results in an increase of both the laser output energy and overall conversion efficiency by a factor of about 1.4 compared to results achieved with a passive feedback mirror, under equivalent conditions. A reliable, temporally stable SLM regime of operation is achieved in the 740–820 nm spectral range.     

Diffractive optical element used in an external feedback configuration to tune the wavelength of uncoated Fabry-Pérot diode lasers

Abstract

A diffractive optical element (DOE) has been designed, fabricated and used in an external feedback configuration to set the wavelength of operation of uncoated Fabry-Pérot diode lasers. The DOE was designed to replace the conventional elements of an external feedback system, which are a collimating lens and grating in the Littrow configuration. The goal was to simplify use of the external cavity laser by replacing the lens and grating with a single optical element while maintaining the performance that is achieved with a grating and lens. Four DOEs were fabricated with two different focal lengths and two different reflectivities. DOE external cavity lasers were tested for maximum tunable range and stability of the wavelength of operation and compared with an external cavity laser based on a lens and grating in the Littrow configuration. A 40 nm tuning range was achieved with the DOE external cavity laser and this is comparable with the tuning range of the external cavity lasers based on a grating and collimating lens in the Littrow configuration.     

Experimental Evaluation of a Fibre Raman Oscillator Having Fibre Grating Reflectors

Abstract

We report on the construction and characterization of a novel fibre Raman oscillator which used fibre grating reflectors rather than discrete mirrors to form the Raman resonator. This was synchronously pumped by a c.w. mode-locked Nd : YAG laser operating at 1·06 µm. Spectral and temporal characteristics of such oscillators formed by two gratings and by one grating and a conventional mirror are presented.     

Optomechanical effect on the Dicke quantum phase transition and quasi-particle damping in a Bose–Einstein condensate: a new tool to measure weak force

Abstract

We make a semi-classical steady state analysis of the influence of mirror motion on the quantum phase transition for an optomechanical Dicke model in the thermodynamic limit. An additional external mechanical pump is shown to modify the critical value of atom–photon coupling needed to observe the quantum phase transition. We further show how to choose the mechanical pump frequency and cavity–laser detuning to produce extremely cold condensates. The present system can be used as a quantum device to measure weak forces.     

The Laser Amplifier with a Stimulated Scattering Mirror

Abstract

A laser scheme with scattered volume employed as a cavity mirror is considered. The laser threshold and the output pulse characteristics are calculated.     

Ti:Al2O3 laser pumped by radiation from a copper-vapor laser

A scheme enabling spatial matching of copper-vapor laser radiation, which pumps a mode of an Al₂O₃:Ti laser cavity, has been developed and implemented. It is shown that copper vapor lasers as pump sources for titanium-sapphire lasers are fully capable of competing with conventional pump sources. Pis’ma Zh. Tekh. Fiz. 25, 6–11 (September 26, 1999)     

Oscillation characteristics analysis of transversely and coaxially pumped Ti-diffused Nd:MgO:LiNbO3 waveguide lasers

Abstract

A theoretical analysis of oscillation characteristics is developed for Ti-diffused Nd:MgO:LiNbO₃ waveguide lasers by using the formalism of mode overlap. Simple and explicit expressions in terms of mode sizes are derived for effective mode volume and coupling efficiency between pump mode and laser mode, which are directly proportional to the threshold pump power and slope efficiency, respectively, both for transverse and coaxial pumping considering the spatial distribution of the pump beam and the laser beam. A comparison for the two pumping configuration has shown that the transverse pumping requires much higher input pump power and has much lower slope efficiency than the coaxial pumping. The fundamental transverse mode (TM ₀) oscillation conditions relative to the cavity loss are also discussed for the two pumping configurations.

Indexing terms: Ti-diffused Nd:MgO:LiNbO ₃ waveguide laser, effective mode volume and coupling efficiency, threshold pump power and slope efficiency, transverse and coaxial pumping, single mode oscillation condition.     

Numerical simulation of a high-average-power diode-pumped ytterbium-doped YAG laser with an unstable cavity and a super-Gaussian mirror

A numerical technique with which to compute the output characteristics of a solid-state laser with an unstable cavity and a super-Gaussian coupling mirror is proposed. This technique is applied to an Yb:YAG actively Q-switched laser. With this formalism, the mode formation for the fundamental mode is analyzed and the performance achievable by such a laser for various cavity parameters is determined. Then the results obtained with such a cavity are compared with those given for a stable cavity with graded phase output mirror that is also used for obtaining super-Gaussian mode.     

The standard model in cavity quantum electrodynamics. II. Coupling constants and atom field interaction

Abstract

Specific forms of the travelling and trapped vector mode functions for a three-dimensional Fabry-Perot cavity are developed from the general results of the preceding paper, with parameters describing the output cavity mirror chosen for a typical high Q cavity case. Cavity and external quasi-mode functions associated with the quasi-mode theory of macroscopic canonical quantization are then obtained via an idealized choice of output mirror parameters. The coupling constants describing photon exchange processes between the single cavity quasi-mode associated with each Fabry-Perot resonance and various external quasi-modes are calculated, and their slow dependence on the external quasi-mode frequency shows that the conditions for irreversible Markovian damping of the cavity quasi-mode are satisfied. For radiative atoms placed in the cavity the coupling constants for energy exchange processes with sideways travelling external quasi-modes also vary slowely, so that Markovian spontaneous emission damping occurs for the radiative atoms. However, their coupling with the isolated cavity quasi-modes is associated with reversible photon exchanges as represented via one photon Rabi frequencies. The standard model in cavity quantum electrodynamics, in which the basic processes are described by a cavity damping rate, a radiative atom spontaneous decay rate and an atom-cavity mode coupling constant has now been justified in terms of the quasi-mode theory of macroscopic canonical quantization.     

Estimating stress intensity factors with singular components of the total finite element solution

Displacement formulated singular elements are compared to isoparametric quarter-node elements. The total stress and displacement solution for each element is decomposed into singular and regular components for evaluating stress intensity factors. Specific relationships between nodal displacements and the singular component of stress are presented for the isoparametric element at selected locations within the element. Numerical results for K_I and K_II in the slant crack problem are presented. The singular components are shown to produce superior results when considering crack opening displacements.     

Spherically symmetric GRIN amplitude formers

Abstract

A new type of spherically symmetric gradient index element is presented. These elements are able to transform an optical field from a point source with a predetermined radiation pattern into an arbitrary amplitude distribution in the target plane. The design method is illustrated with four examples of amplitude formers that produce irradiance distributions that are constant, Gaussian, triangular and ring-shaped.     

Shortening of Free-running XeCl Laser Pulses by Stimulated Brillouin Scattering

Abstract

A stimulated Brillouin scattering mirror has been used to ‘temporally tune’ from nanoseconds to subnanoseconds the width of laser pulses generated by a free running XeCl oscillator, equipped with a super-Gaussian reflectivity unstable resonator. Pulse shortening techniques by stimulated Brillouin scattering (SBS) and by truncated SBS have been investigated. A maximum pulse shortening of about fifty has been achieved by truncated SBS.     

A Diode-laser-bar Pumped Stable CW Nd: YAG Slab Laser and its Frequency Doubling

Abstract

A high power Nd: YAG mini-slab laser transversely pumped by two diode laser arrays has been investigated. The simplicity and compactness of this pumping scheme provides intrinsic stability in both the output power and the beam pointing. A linearly polarized TEM₀₀ mode output power of 3·6 W at 1064 nm was achieved with a linear cavity, and 1 W of single frequency green light at 532 nm was generated by intracavity doubling in a ring cavity.     

Design and performance of diffractive optics for custom laser resonators

Diffractive optical elements are used as end mirrors and internal phase plates in an optical resonator. A single diffractive end mirror is used to produce an arbitrary real-mode profile, and two diffractive mirrors are used to produce complex profiles. Diffractive mirror feature size and phase quantization are shown to affect the shape of the fundamental mode, the fundamental-mode loss, and the discrimination against higher-order modes. Additional transparent phase plates are shown to enhance the modal discrimination of the resonator at the cost of reduced fabrication tolerances of the diffractive optics. A 10-cm-long diffractive resonator design is shown that supports an 8.5-mm-wide fundamental mode with a theoretical second-order mode discrimination of 25% and a negligible loss to the fundamental mode.