John J. Degnan

Optimization of passively Q-switched lasers

In optimizing passively Q-switched lasers, there is a unique choice of output coupler and unsaturated absorber transmission which maximizes the laser output energy and efficiency for each three-way combination of laser gain medium, absorber medium, and pump intensity (i.e, inversion density). In the present paper, we generalize and solve the three coupled differential equations which describe the passively Q-switched laser to obtain closed form solutions for key laser parameters such as the output energy and pulsewidth. We then apply the Lagrange multiplier technique to determine the optimum mirror reflectivities and unsaturated absorber transmissions as a function of two dimensionless variables. The first variable, z, corresponds to the ratio of the logarithmic round-trip small signal gain to the round-trip dissipative (nonuseful) optical loss and is identical to that which was used in previous treatments to optimize the rapidly Q-switched laser. The second variable, /spl alpha/, is unique to the passively Q-switched laser and is equal to the saturation energy density of the amplifying medium divided by the saturation energy density of the absorber. It is largely determined by the ration of the absorber to stimulated emission cross sections, but also depends on the speed of relaxation mechanisms in the amplifying and absorbing media relative to the resonator photon decay time. Several design curves, valid for all four level amplifying and absorbing media, are then generated. These permit the design of an optimum passively Q-switched laser and an estimate of its key performance parameters to be obtained quickly with the aid of a simple hand calculator. In the limit of large /spl alpha/ (>10), the design curves are virtually indistinguishable from the rapidly Q-switched case. The curves can also be used to perform rapid tradeoff studies of different absorbing materials. The theory can also be applied to CW-pumped, repetitively Q-switched systems through a simple multiplicative factor for the laser gain. The theory is applied to the analysis of a passively Q-switched Nd:YAG laser previously reported in the literature and shown to give excellent agreement with the experimental results. >

Theory of the optimally coupled Q-switched laser

The general equations describing Q-switched laser operation are transcendental in nature and require numerical solutions, which greatly complicates the optimization of real devices. Here, it is shown that, using the mathematical technique of Lagrange multipliers, one can derive simple analytic expressions for all of the key parameters of the optimally coupled laser, i.e. one which uses an optimum reflector to obtain maximum laser efficiency for a given pump level. These parameters can all be expressed as functions of a single dimensionless variable z, defined as the ratio of the unsaturated small-signal gain to the dissipative (nonuseful) optical loss, multiplied by a few simple constants. Laser design tradeoff studies and performance projections can be accomplished quickly with the help of several graphs and a simple hand calculator. Sample calculations for a high-grain Nd:YAG and a low-gain alexandrite laser are presented as illustrations of the technique. >

The waveguide laser: A review

The present article reviews the fundamental physical principles essential to an understanding of waveguide gas and liquid lasers, and the current technological state of these devices. At the present time, waveguide laser transitions span the visible through submillimeter regions of the wavelength spectrum. The introduction discusses the many applications of waveguide lasers and the wide variety of laser configurations that are possible. Section 1 summarizes the properties of modes in hollow dielectric waveguides of circular, rectangular, and planar cross section. Section 2 considers various approaches to optical feedback including internal and external mirror Fabry-Perot type resonators, hollow waveguide distributed feedback structures, and ring-resonant configurations. Section 3 discusses those aspects of molecular kinetic and laser theory pertinent to the design and optimization of waveguide gas lasers such as the scaling laws for discharge-excited gas lasers, molecular models useful in maximizing the oscillation bandwidth, the effects of gas flow rate, and the physics of optically-pumped far-infrared lasers. Finally, a review of the waveguide gas and liquid lasers reported to date is given in Section 4.

Satellite Laser Ranging: Current Status and Future Prospects

This paper is intended to be a nonmathematical tutorial on the subject of satellite laser ranging (SLR) with an emphasis on the characteristics and capabilities of present and future field-hardware and operational methods. Following a brief introduction to the basic concept of SLR and the many science applications of both satellite and lunar laser ranging, we discuss the developmental history of each of the major components which make up the ranging machine, i.e., the laser transmitter, photomultiplier, discriminator, and time interval unit. At the same time, we attempt to identify the sources of range error in each of the devices and present, whenever possible, experimental data which quantifies the magnitude of these errors. We also describe some of the subtleties associated with the operation of these devices in the field. Following the discussions on hardware and system calibration techniques, we briefly describe some error sources external to the basic ranging machine, but highly relevant to SLR, which are introduced by the target, atmospheric channel, ground surveys, epoch timekeeping, geopotential models, and numerical propagation errors. We summarize the description of modern day hardware with samples of actual satellite data, obtained as early as 1981, which show orbital fits with a 1.5 cm single shot rms and normal point rms of less than 3 mm with only 1-6 percent data editing. We conclude the paper with a discussion of ongoing research to develop systems potentially capable of millimeter absolute accuracies over satellite distances.

Optical antenna gain. 1: transmitting antennas.

The gain of centrally obscured optical transmitting antennas is analyzed in detail. The calculations, resulting in near- and far-field antenna gain patterns, assume a circular antenna illuminated by a laser operating in the TEM(00) mode. A simple polynomial equation is derived for matching the incident source distribution to a general antenna configuration for maximum on-axis gain. An interpretation of the resultant gain curves allows a number of auxiliary design curves to be drawn that display the losses in antenna gain due to pointing errors and the cone angle of the beam in the far field as a function of antenna aperture size and its central obscuration. The results are presented in a series of graphs that allow the rapid and accurate evaluation of the antenna gain which may then be substituted into the conventional range equation.

Waveguide Laser Mode Patterns in the Near and Far Field

The difference in notations used by researchers in the dielectric waveguide field and those primarily interested in waveguide lasers is discussed, and the equations for the field components of the various modes in large radius hollow dielectric waveguides are rederived in terms of the more widely used notation. Certain linear combinations of these modes that give linearly polarized field distributions are then considered to be launched into free-space at a waveguide termination. The resultant Fresnel and Fraunhofer field distributions are useful in identifying the modes of oscillation and in choosing mirror apertures that will restrict oscillation on the fundamental waveguide mode.

Optical Antenna Gain. 2: Receiving Antennas

Expressions are derived for the gain of a centrally obscured, circular optical antenna when used as the collecting and focusing optics in a laser receiver which include losses due to (1) blockage of the incoming light by the central obscuration, (2) the spillover of energy at the detector, and (3) the effect of local oscillator distribution in the case of heterodyne or homodyne detection. Numerical results are presented for direct detection and for three types of local oscillator distributions (uniform, Gaussian, and matched) in the case of heterodyne or homodyne detection. The results are presented in several graphs that allow the rapid evaluation of receiver gain for an arbitrary set of telescope and detector parameters. It is found that, for uniform illumination by the LO, the optimum SNR is obtained when the detector radius is approximately 0.74 times the Airy disk radius. The use of an optimized Gaussian (spot size = 0.46 times the Airy disk radius) improves the receiver gain by less than 1 dB. Theuse results are insensitive to the size of the central obscuration.

Effects of thermalization on Q-switched laser properties

The conventional rate equations for a Q-switched laser are augmented to explicitly include the effects of time- and level-dependent pumping, thermalization among the sublevels in the upper and lower multiplets, and multiplet relaxation in a homogeneously broadened four-level laser medium. To make the numerical computations more generally valid, we introduce a number of dimensionless variables. We show that the initial set of five coupled differential equations can be reduced to a simple set of two coupled equations for the inversion density and photon flux. Via numerical modeling, we have investigated the manner in which both thermalization and lower multiplet relaxation affect Nd:YAG laser characteristics such as output energy and temporal waveform. Our numerical results confirm earlier predictions that the Q-switched Nd:YAG laser output energy increases monotonically by a factor of 3.33 as one progresses from the assumption of slow to rapid thermalization and by an additional factor of 1.46 if one further assumes a terminal multiplet relaxation which is fast relative to the resonator photon decay time. We also find that the laser pulsewidth is substantially broadened when the resonator photon decay time is comparable to the thermalization, and to a lesser extent, the terminal multiplet relaxation times.

The Geoscience Laser Altimetry/Ranging System

The Geoscience Laser Altimetry/Ranging System (GLARS) is a planned highly precise laser distance-measuring system to be used for geoscience measurements requiring extremely accurate geodetic observations from a space platform. The system combines the attributes of a pointable laser ranging system making observations to retroreflectors placed on the ground with those of a nadir-looking laser altimeter making height observations to ground, ice sheet, and oceanic surfaces. In the ranging mode, centimeter-level precise baseline and station coordinate determinations will be made on grids consisting of 100 to 200 targets separated by distances from a few tens of kilometers to about 1000 km. These measurements will be used for studies of seismic zone crustal deformations and tectonic plate motions. Ranging measurements will also be made to a coarser, but globally distributed, array of retroreflectors for both precise geodetic and orbit determination applications. In the altimetric mode, relative height determinations will be obtained with approximately decimeter vertical precision and 70-100-m horizontal resolution. Altimetric profiles consisting of nearly contiguous spots will be available when the system is operated at 40 pulses per second. The height data will be used to study surface topography and roughness, ice sheet and lava flow thickness, and ocean dynamics. Waveform digitization will provide a measure of the vertical extent of topography within each footprint.

A Ray Analysis of Optical Resonators Formed by Two Spherical Mirrors

A paraxial resonance equation is derived. This gives the mirror separation as a function of the radii of curvature of the mirrors and an integer N which is the number of return transits necessary to form a closed path of rays. Differentiating the paraxial resonance equation gives a formula for the relative mode density as a function of mirror separation. It is shown that the output power from a laser incorporating solid mirrors is inversely proportional to the mode density. In the case of hole coupling, the output power follows the same general profile but dips in power occur at the mirror separations corresponding to the resonance configurations of modes characterized by low values of N. Further confirmation of the paraxial resonance equation is obtained from passive resonators in which conic interference fringes and sudden increases in transmitted intensity are found to occur at the predicted mirror separations for low values of N corresponding to mode-degenerate configurations. The positions of the vertices of the ray traces are found to correspond to the patterns of discrete spots which are obtained in the output of a CO(2) laser incorporating Brewster angle windows and a solid germanium mirror. The laser configurations which give maximum output power are plotted as a cliff of constant height above the g(1)g(2) plane of the stability diagram, where g(1) and g(2) are the configuration coordinates. The relative merits of all possible cavity configurations having one mirror in common are shown as a set of equipower contours, and the hyperbolic curves of constant N are also superimposed on the stability diagram. The advantages of simplicity and directness in using the ray model are made clear.