Plane-parallel Cavity Research Articles

Analysis of millimeter-wave Fabry-Perot cavities using the FDTD technique

The finite-difference time-domain (FDTD) technique combined with periodic boundary conditions (PBC's) is applied to the study of infinite periodic three-dimensional structures excited by normally incident plane waves. Berenger's PML (perfectly matched layers) are employed as absorbing boundary conditions to simulate free space. The method takes into account dielectric and metallic losses. It has been developed to study plane parallel Fabry-Perot cavities with two-dimensional metal mesh mirrors. Experimental results in the 60 GHz band show good agreement with simulation.

Coherence temporal evolution in Gaussian cavities of different lengths

The temporal evolution of the beam-quality factor M2 is investigated in plane-parallel cavities of different Fresnel numbers with a Gaussian reflectivity mirror and applied to a Xe–Cl excimer laser. The Fresnel number is changed by varying resonator length. Laser radiation of higher spatial coherence is provided by the cavity of greater length (2.5 m) and then of lower Fresnel number after the first transit. Indeed, the beam spatial coherence decreases with cavity length. It is also shown that the Gaussian mirror affects the properties of the oscillating laser radiation only at the very first cavity round trips. The near- and far-field spatial characteristics of the laser radiation do not vary after a few transits inside the cavity. Experimental results are supported by a theory formerly developed for the evolution of the parameters of Gaussian Schell-model beams propagating in Gaussian cavities.

Beam-divergence control of excimers with plane-parallel Gaussian cavities

Plane-parallel cavities with Gaussian-reflectivity-profile mirrors as full reflectors were applied to a XeCl laser, and the near- and the far-field characteristics of the laser radiation were analyzed. It is shown that excimer lasers fitted with plane-parallel Gaussian cavities deliver laser radiation with a beam-quality factor M(2) that is more than 50% smaller than that of laser beams delivered by conventional plane-parallel cavities. The effect of the Gaussian mirror spot size on M(2) was also investigated, and it is shown that the narrowing of the Gaussian mirror spot size reduces the beam-quality-factor value.

Coherence evolution of laser beams in cavities with variable-reflectivity mirrors

A theoretical analysis of the time evolution of spatial coherence in a large Fresnel-number laser cavity with use of the second-moment-analysis method and assuming quadratic (Gaussian) variable-reflectivity mirrors was found also to provide a satisfactory description of coherence growth inside a pulsed high-gain laser with use of either super-Gaussian or phase-unifying mirrors. The theoretical results are found to be in good agreement with the detailed experimental results from a high-gain, short-pulse Xe–Cl laser having a plane-parallel cavity equipped with both types of mirror.

Simulation de la propagation d'un faisceau laser à travers un interféromètre Fabry-Perot

In order to define specifications for the Virgo gravitational wave interferometric detector optical components, a method for evaluating the transfer function of an arbitrary Fabry-Perot interferometer is presented. The calculation, which is based on an expansion method on Hermite - Gauss functions, takes into account defects of the cavity geometry, of the mirror surfaces, and of the incident field shape. In order to test the method three simple cases are investigated. First, a plane-parallel cavity with a very high finesse is illuminated by a Gaussian beam. The results show that the transfer function peaks are not symmetrical. Then a half confocal cavity is illuminated by a matched Gaussian beam, but the beam is off-axis and interference patterns are generated on the centre of the flat input mirror. Finally, the effects of roughness on the finesses of a stable cavity are shown.

Parameters evolution of laser beams with quite general transverse intensity profile

A plane-parallel cavity with a Gaussian reflectivity mirror has been applied to a XeCl laser medium having a spatially variable gain distribution. The evolution of the beam parameters has been experimentally analyzed as a function of the number of round trips. It is shown that in this case of intensity profiles affected by the spatial and temporal properties of the active medium gain, a theory formerly developed for the beam-parameter evolution of Gaussian Schell-model beams provides a satisfactory description of experimental measurements for the first few round trips.

Experimental investigation of eigenmodes of empty optical resonators with apertures

The spectra of an eigenmodal set of optical resonators with apertures are measured experimentally. Frequency shifts predicted by theory are confirmed for plane-parallel cavities. It is also shown that the local shape of the wave front at the aperture is significant for manifestation of these phenomena.

Transient states analysis of a partially coherent laser beam propagating through a Gaussian cavity

The transient states of a laser beam propagating through a plane-parallel cavity with a Gaussian graded reflectivity mirror are numerically and experimentally investigated in the far-field, i.e., in the region around the focal plane of a positive lens, where variations in the beam are enhanced. The evolution of significant parameters (quality factor M/sup 2/, spot-size and focusing distance), from which all the others can be deduced, is studied from transit to transit. It is found that the type of evolution in the first cavity round-trips depends strongly on the initial values of beam parameters at the first emission from the active medium. It is also found that the laser system used in the experiment does not reach equilibrium during the pulse time. A satisfactory accordance between experimental and numerical data has been found. >

Theory of transverse modes in end-pumped microchip lasers

I analyze the formation of transverse modes in a microchip solid-state laser with plane-parallel cavity mirrors, generalizing the traditional mean-field limit of laser theory. Owing to the balance between mode diffraction and focusing effects induced by the pump beam, the transverse dimension of the laser modes is shown to depend on the cavity Q factor. To provide further insight, a one-dimensional model for an end-pumped microchip laser is also presented. The model gives analytical solutions for the threshold and for the intensity profile of different transverse modes and allows us to study the effects of narrow pump beams. In particular, it is predicted that decreasing the dimensions of the pump beam will lead to longitudinal mode hopping with a corresponding discontinuity in the transverse-mode profile.

Hybrid Wavefront-Resonance Representation for Transient Scattering by an Open Cavity Part II: Numerical Results and Interpretation

In this second part in a three part sequence, the hybrid wavefront-resonance scheme developed in Part I is applied and explored numerically for the transient field scattered by a plane parallel waveguide cavity configuration. Emphasis is on validating the effectiveness of this representation and on explaining the observed features in the scattered signal at early, intermediate, and at late observation times. Utilizing results reported earlier for the complex resonances [3], it is shown that the late-time observables carry the signature of a cluster of high-Q internal resonances that occurs near modal cutoff frequency, in the form of a slowly decaying typical waveform which is independent of the incident angle or the excitation pulse but is related to the cavity dimensions. The early-time field is expressed as a rapidly decaying series of external wavefront interactions, while at intermediate times the internal resonances synthesize the dispersive guided mode return. The convergence of the resonance series...

Hybrid Wavefront-Resonance Representation for Transient Scattering by an Open Cavity Part III: Analytical Models for the Late Time Oscillations

The numerical results of the second portion of this three part sequence dealing with transient scattering by an open ended plane-parallel waveguide cavity, clearly reveal the existence of a distinct late-time observable in the form of a slowly decaying, aspect-independent typical waveform that carries the signature of a cluster of high-Q resonances that occur near the cavity's mode cutoff frequencies. In this paper, we derive analytic approximations for the resonance frequencies, for the late-time waveform, and for the low-frequency beats that appear in this late-time waveform. These observables are related to the cavity dimensions. It is shown that the late-time waveform is essentially independent of the incidence angle and of the excitation pulse.

Transverse Modes of Microchip Solid State Lasers

Abstract We present a model for an end pumped microchip solid state laser with plane-parallel cavity mirrors. Our model has a transversely varying gain and gives the laser threshold, output intensity, frequency and the transverse mode profiles in terms of the cavity detuning, cavity losses and other relevant parameters. We have also adapted the model to derive the pump threshold for simultaneous operation of two transverse models. We find that these lasers almost always operate on the fundamental mode and only for broad pump beams and high pump powers can higher order modes be excited.

Laser-diode-pumped phase-locked Nd:YAG laser arrays

Scaling of an efficient and compact diode-end-pumped Nd:YAG laser was demonstrated by two-dimensional phase-locked arrays. The arrays of stable resonators were formed by multiple thermal lenses induced by the simultaneous end-pumping of laser-diode-coupled fibers. Because of partial overlap of each transverse mode, the output was phase locked. Various configurations of pumping fibers were tested to study phase locking. It was found that minimization of the coherently coupled intensity between adjacent array elements have good prediction for phase difference between modes. When the plane parallel cavity as long as 30 mm was pumped by 2*2 laser diode coupled fibers, phase-locked 1.8-W continuous wave 1.06- mu m output was obtained with 55% slope efficiency. 1.2-W single longitudinal mode output with single-lobe beam profile was obtained by using a spatial phase filter and the twisted mode method. >

Numerical investigation of modes of a planeparallel cavity with periodic mirrors

Numerical investigation of modes of a planeparallel cavity with periodic mirrors

Observation of optical bistability due to resonator configuration transition

In this Letter, a new kind of active optical bistability is discussed. The basic principle underlying the operation of the optically bistable laser is based on stable-unstable cavity configuration transitions of an active optical resonator. Generally speaking, a laser system showing both pump- and laser-induced lensing (focusing or defocusing) effects may display such a hysteresis loop in its input-output characteristics. This bistability is experimentally demonstrated using a flashlamp-pumped, Nd-doped gadolinium gallium garnet rod placed in a plane-parallel optical cavity.

A new general cavity theory

A new general cavity theory for photons is derived that takes into account secondary electron scattering at the cavity boundaries. The proposed model is used to calculate both the effective stopping power ratio as well as the dose distribution inside plane parallel cavities of lithium fluoride surrounded by aluminium, copper or lead. A comparison is made between the proposed model, the well known Burlin model, and experimental data.

Closed-cavity solutions with partially coherent fields in the space-frequency domain

Closed or stable optical cavities, used frequently to determine the efficiency of high performance chemical laser nozzles, are designed primarily for maximum multimode power extraction from the medium. The very large (>500) Fresnel numbers associated with such cavities have in the past necessitated their analytical modeling by representing them as plane-parallel Fabry-Perot or rooftop cavities. In this paper, a rigorous 2-D scalar diffraction formalism of the closed cavity is presented in which quasi-monochromatic partially coherent fields in the space-frequency domain are used to obtain quasi-steady state but stable solutions using a simplified gain model. Small power fluctuations in the numerical iterative solution history that displays no monotonic increasing or decreasing trends are interpreted as the redistribution of energy from one degenerate set of high-order transverse modes into another. The degree of coherence in the second-order spatial correlation function (or the mutual coherence function) required of the input fields which permit such solutions is presented. Further, it is shown that the upstream/downstream coupling in this closed cavity occurs as a natural consequence of the physical model itself rather than through some artificial geometrical means, such as that introduced in the rooftop model. The axial variation in the resulting mode width is in excellent agreement with the Hermite-Gaussian distribution predicted for the particular geometry of interest. The computed closed-cavity power variation with mode width using a simplified gain model shows qualitative agreement with experimentally observed trends; quantitative agreement is poor and is ascribed to the rudimentary nature of the gain model. In the limiting case of small Fresnel numbers (NF ∼ 1) this procedure yields, in the bare cavity, the well-known fundamental mode of the cavity when appropriate symmetry constraints are applied.

Photochemical xenon-oxide laser

Theoretical and experimental investigations are described, aimed at the develo pment, construction, and study of the features of a photochemical xenon-oxide laser whose action is based on the photodecomposition of nitrous oxide by vacuum ultraviolet radiation of an open hlgh-current discharge with formation of oxygen atoms followed by oxidation of the xenon. The theoretical problems connected with the determination of the mechanism and the calculation of the kinetics of the physicochemical processes in an XeO laser are considered. A numerical computation of the pumping is carried out, and the inversion and gain on the laser transition are calculated. The construction of the laser is described, as well as an experimental procedure for obtaining the optimal temperatures, composition, and pressure of the working-mixture components. The spectral composition of the laser radiation and the energy characteristics of the laser are investigated. The heat released in the course of the photolysis, the constants of the quenching rates of the upper laser state of XeO (21Σ+), and the vibrational relaxation of the lower state of XeO (11Σ+) are estimated. The internal losses in the active medium of the photochemical XeO laser are theoretically investigated. The possibility of increasing the volume of the active medium using a plane-parallel cavity is estimated.

Influence of superradiance in active media with large gains on the energy characteristics of giant-pulse lasers

We carried out experiments which made it possible to substantiate the approximate calculation. An active element of cylindrical shape made from YAG with neodymium (with a 5 • mm diameter) was used to measure the dependence of the value of the population inversion A = Nm/No (where N m is the population of the metastable level in the four-level lasing scheme and No is the concentration of active ions) on the pumping energy, which we shall characterize in the following by the dimensionless parameter K =W:4r32 (where W14 is the probability of a transition from level 1 to level 4 under the action of the pumping radiation, and i/r32 is the probability of a spontaneous transition between the laser levels). For this purpose, the pumping energy corresponding to the threshold for the appearance of stimulated emission was determined in a plane-parallel cavity with various values of the losses ~, and the quantity A =B/o32No (where os2 is the cross section of the lasing transition) was determined. The dependence obtained is presented in Fig. la. From the figure it is seen that the value of the population inversion A has a tendency to reach saturation as K is increased. The restriction of A with increasing pumping energy owing to the influence of superradiance is also supported by the investigation of plots of the dependence of the time-integrated luminescence intensity I in the direction of the longitudinal axis of the sample on the pumping energy obtained by integrating the signal from the light detector. Figure 1 presents plots of the dependence of I on K for crystals of YAG with neodymium having a diameter of 5 x 50 mm for luminescence at the output wavelength Iz and at a wavelength of ~0.9 ~m I2 (the 4F3/2-+4/9/2 transition). As we see from Fig. I, with the same values of K at which the restriction of A (see Fig. la) and the value of I2, which reflect the population of the metastable level, is observed, the value of II increases sharply owing to the significant enhancement of the luminescence at the output wavelength along the sample. (Similar investigations for crystals of YAL with neodymium were carried out in [2].) Thus, the restriction of A with increasing pumping energy is due to the influence of the superradiance.

Some effects of spatially nonuniform pumping in pulsed optical parametric oscillators

Previous analyses of the large signal operation of optical parametric oscillators have considered uniform plane-wave pump beams. These analyses are not adequate to describe the behavior of efficient pulsed oscillators pumped by beams having nonuniform intensity profiles and pulse durations that are short enough that the steady-state transverse modes of the oscillator cavity do not become established. This situation is typical of oscillators with plane-parallel cavities pumped by Q -switched lasers. This paper theoretically and experimentally investigates the behavior of such oscillators when pumped with beams having Gaussian intensity profiles. Each of the three basic external optical parametric oscillators are considered. For simplified cases it is shown that the response to a Gaussian pump beam is quantitatively and qualitatively much different than that predicted by the uniform plane-wave calculations. Experimental results in fair agreement with these calculations are presented. More importantly, uniform plane-wave behavior was observed by using an aperture to probe a small section of the pump beam transmitted through the oscillator. This useful technique gives a sensitive indication of the oscillator operation and, at present, it is the most accurate means of measuring thresholds in pulsed oscillators. As a result of our calculations and experiments, previous experimental observations that were puzzling are now well understood.