Curvature Of Mirror Research Articles

Macroscopic parameters and line shapes of a gas laser

The theory of line shapes in monomode weak-gain gas lasers which we have developed recently shows that asymmetries of Lamb dips are governed by opposite lens effects which arise from population and saturation inhomogeneities. The competition between these effects depends on the geometrical characteristics of the laser. It is our aim in this paper to illustrate experimentally this fact with the 3.39-\ensuremath{\mu}m line of a He-Ne laser. To get a strongly diverging beam we have chosen a quasihemispheric resonator whose length (57 cm) almost equals the radius of curvature of the concave mirror ($R=60$ cm). The amplifying tube is about 20 cm long and is placed on the side of either the plane or the concave mirror, thus allowing us to vary the saturation inhomogeneity. In the first case the inhomogeneity is stronger and causes the maximum of intensity to be on the low-frequency side of the line, while in the second case population and saturation inhomogeneities are of the same order. We have repeated the experiment with two tubes having different internal diameters (8 and 4 mm) in order to vary the population effects. In the case of the narrower tube one observes a gradual passage from a low- to a high-frequency type of asymmetry when the discharge current is increased. This observation is explained by an increase of the lens effect due to saturation which overcomes the one due to population. Applying our previously developed theoretical methods, we find the results in qualitative agreement with these experiments.

Line shapes of a « sensitive » laser

Inhomogeneities of population and saturation are responsible for lens effects in gas lasers. They give rise to an asymmetric Lamb dip. Generally, one of these inhomogeneities is predominant and thus determines the sense of the asymmetry. However, since the two kinds of inhomogeneities are modified by the geometric parameters, it may happen that they give lens effects of the same magnitude, but of opposite sign. In such a case of competing effects which cancel each other, the line shape may vary strongly when a parameter is changed. A laser of this kind will be called «sensitive». In this paper we use as an example a quasi-hemispheric He-Ne laser whose length (57 cm) is almost equal to the radius of curvature (60 cm) of the concave mirror. We show experimentally that the sense of the asymmetry may be changed by the discharge current and that the line shape also depends on the diameter of the diaphragm. This behaviour reveals the competition between the two effects. We numerically calculate the line shapes by using methods which we have developed recently. Qualitatively, we find these results in excellent agreement with the experiments Laser «sensible»: un laser a gaz ou les inhomogeneites de saturation et de population entrent en competition en fonction des parametres geometriques du laser: la forme de raie peut varier beaucoup pour un faible changement de parametres. Exemple d'un laser quasi hemispherique a Me-Ne dont la longueur est presque egale au rayon de courbure du miroir concave

Resonator optimization for passively mode-locked lasers

The role of the resonator parameters, in stabilizing the output of passively mode-locked lasers is analyzed. Analytic expressions are derived for the range of optimal values for the radii of curvature of the resonator mirrors, and the position of the major elements, for the most commonly used configurations. The predictions are verified by experiment, for a specific case.

Measurement Of Long Radius Of Curvature

Several methods for the measurement of very long radius of curvature of a convex or concave spherical mirror are reviewed in this paper. These methods have relevance in the measurement of the radii of curvature of laser mirrors. The accuracies achievable with the various methods are compared and summarized.

Selective properties of a linear resonator with an asymmetric dispersive component

Theoretical and experimental investigations were made of the selective properties of a linear resonator with an asymmetrically located dispersive component in the case when the dimensions of the end reflectors are limited by stops. When the equivalent Fresnel number is less than unity, the resonator band depends strongly on the dimensions of the stops, position of the dispersive component in the resonator, telescopic coefficient, and mirror curvature. A good agreement between the theory and experiment shows that the proposed calculation method can be used in the optimization of the parameters of small-aperture dispersive resonators frequently employed in dye lasers.

Mirror fields for tower-type solar power plants

To obtain, in a receiver C, a point image of parallel rays tilted at an angle ψ with respect to the normal at the mirror centre S, the mirror surface must be a portion of a paraboloid having its focus in C, and its axis directed towards the sun and passing through S. Since this paraboloid will change with the sun's position, such a mirror is impossible. In this paper, it is suggested that the various paraboloid sectors should be replaced by double-curvature mirrors, driven in such a way as to maintain the minimum mirror curvature in the sun-mirror-receiver plane. The results thus obtained are compared with those obtained using a spherical mirror. Finally, the procedure used to determine the actual mirror field for a receiver, when the diameter of the aperture, the height, and the inclination of the axis are given, is reported.

A Method for Measuring High Reflectivity

Reflectivity measurement of highly reflective mirrors was made easily and efficiently, using a He–Ne laser, ordinary lenses and mirrors, and a silicon solar cell. The power of the incident and the reflected light beams are precisely compared by use of light beam switching by a rotating mirror and electronic sampling and integration. As the method utilized a single reflection at a point on the test mirror, it enables point-by-point measurement and is not influenced by the mirror curvature. The accuracy of the measurement was ±0.03%, and the nonlinearity of the photo-sensor and the electronics used in the measurement was assumed small enough compared to 2%.

Construction and performance of a 20-pps unstable Nd:YAG oscillator

A positive branch Nd:YAG unstable oscillator has been constructed using a small reflecting spot centered on an antireflection coated substrate as the output mirror. The confocal condition is achieved by taking account of the lens effect of the rod as well as the back mirror curvature. Q-switched output energies of 180 mJ in 10 ns have been obtained in a diffraction limited beam with a divergence of less than 0.25 mrad, at an overall efficiency of 1.3%.

Coupling losses in laser resonators containing a hollow rectangular dielectric waveguide

This paper discusses the losses in coupling radiation from the guide into free space and back into the guide for a hollow rectangular dielectric waveguide laser resonator with external spherical mirrors. Computations of the coupling loss for the EH11 lowest-order mode of a square guide, as a function of mirror curvature and position, are presented in the limit of large mirror aperture. It is shown that some mirror positions and radii provide low coupling losses.

Transverse mode control in high gain, millimeter bore, waveguide lasers

A technique is presented for assuring TEM <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">00</inf> transverse mode operation in visible wavelength lasers with bore diameters of 0.1- 1.0 mm. This then is a solution to the problem of obtaining TEM <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">00</inf> mode output from pulse pumped dye lasers which have high and non-uniform gain. The desired mode control is achieved by confining the lasing medium in a waveguide and placing each resonator mirror so that its focal plane, rather than its center of curvature, lies at the nearest waveguide opening. Thus, the far-field pattern of the field distribution emerging from the waveguide opening is focused by the mirror back into the waveguide. For the proper choice of mirror curvature, the width of the central lobe of the far-field pattern is such that over 99 percent of the energy couples into the two lowest order modes of the waveguide. The waveguide transmits this bell-shaped field distribution to the opposite end where the process of propagating to the mirror and being reimaged is repeated. The end result is that a pulsed, laser pumped, waveguide dye laser has been made to produce a mode of the same quality as a TEM <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">00</inf> mode, CW, HeNe laser. This technique has also improved the output mode distribution of flashlamp pumped dye lasers. Analysis of the resonator shows that a TEM <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">00</inf> mode having a curved wavefront at the waveguide opening couples primarily to both the EH <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">11</inf> and EH <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">12</inf> waveguide modes. The amplitudes of the EH <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">11</inf> and EH <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">12</inf> modes, however, have a complex phase difference which results in a refocusing of the field distribution when both propagate in a hollow waveguide. The refocusing is shown to be a periodic function of the length of the waveguide. In addition, it is shown that as a result of gain or propagation loss differences for the two waveguide modes, the phase radius of curvature of the TEM <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">00</inf> mode of a waveguide resonator does not in general match the mirror curvatures. This model of TEM <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">00</inf> mode coupling to the EH <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">11</inf> plus EH <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">12</inf> modes results in a clearer physical insight into the interaction between the waveguide and free space portions of the resonator.

Paraxial ray analysis of a cat's-eye retroreflector

The cat's-eye retroreflector is a passive optical system consisting of a secondary mirror placed at the focal point of a primary lens. We analyze the cat's eye using the paraxial ray matrix approach. The position of the equivalent reflecting surface and the angular field of view of a realizable cat's eye are functions of the radius of curvature of the secondary mirror. The field of view is maximum for a secondary mirror with a concave radius of curvature equal to the focal length of the primary lens. We further derive the general dependence of retroreflection errors on misadjustment of the secondary mirror.

Large-mode-volume stable resonators

An extension of previous work on mode competition is used to show that transverse modes can be suppressed at high power levels, provided that the ratio of the fundamental-mode-irradiance spatial minimum to maximum exceeds a minimum value. Fox–Li-type calculations are used to establish that spatial uniformity of irradiance may be achieved by using convex central mirrors, to spread out the mode volume, surrounded by annular concave mirrors, to produce stability and low diffraction loss. Amplitude and phase distributions have been obtained for Fresnel numbers up to eight and for a variety of mirror curvatures. An optimum choice of parameters is shown to be available for all Fresnel numbers investigated.

Resonator Theory for Hollow Waveguide Lasers

A numerical technique has been developed for analyzing the transverse modes of waveguide lasers with external mirrors. Propagation outside the guide is computed with the Fresnel-Kirchhoff diffraction integral and within the guide by decomposing the fields into the characteristic modes of the guide structure. The transverse modes of the entire waveguide-mirror system fall into a number of distinct classes: TE(0m), TM(0m), EH(1m), EH(2m), etc. For each class of modes, the, corresponding guide modes form a complete and orthogonal set and may be used as basis vectors to describe those modes. This reduces the mode analysis of the waveguide resonator to the diagonalization of a small (5 x 5 or 10 x 10) complex matrix. Guide losses, coupling losses, and mode shapes will be discussed for a number of interesting cases, with the Fresnel number of the waveguide ranging from 0.1 to 1.0 and with various values of mirror curvature and position. It will be shown that some vales of resonator parameters are particularly advantageous for achieving single mode operation.

Skylab Multispectral Scanner (5-192)â€

In this paper we describe the design and performance of a Multispectral Scanner. The optical system of Skylab Multispectral Scanner (S-192) consists of an image plane scanner (telescope), a spectrometer for separation of the radiation into 13 spectral bands, and a 13-element (Hg,Cd)Te detector array. The image plane scanner is a new system based on three interrelated main features: (1) a reflective adaptation of the Schmidt principle; (2) a conical line scan in which all field elements are brought to and corrected on axis; and (3) a scanning arrangement in which the aperture stop of the system, located in a relay unit, is imaged at the center of curvature of the spherical primary mirror. Replacing the physical stop used in the classical Schmidt configuration with a virtual one makes the system much more compact. As a consequence of the image plane scanning and the Schmidt symmetry, the system scans at a large radial angle (11-degree diameter) and at an extremely high rate (6000 rpm) with relatively small scanning mirrors and a large entrance pupil diameter (43 cm). The spectrometer divides the radiation into 13 spectral bands, 12 of which are located between 0.4 and 2.35 micrometers and the other, 10.2-12.5 micrometers. A dichroic beamsplitter separates the far IR band from the 12 lower wavelength bands, which are dispersed by prisms. Photographic reproductions of the actual flight recordings show 80-meter resolution at an altitude of 440 km.

Kinetics of the stimulated emission of a CaF2:Dy2+laser with a hemispherical resonator

Experimental investigation was made of the kinetics of the stimulated emission of a CaF2:Dy2+ laser with a resonator formed by a plane mirror evaporated directly on the end of the fluoride crystal and an external spherical mirror. When the resonator geometry was sufficiently far from the stability limit, the pulsed emission of the laser was in the form of a transient spiking, decaying to a quasisteady-state level. The rate of decay depended strongly only on the aperture parameter of the resonator, which governed the number of the transverse modes which were excited, but was independent of the ratio of the resonator length to the radius of curvature of the spherical mirror in a fairly wide range of both these parameters. When the resonator geometry was close to the stability limit, the laser emitted random spikes. A large number of transverse modes were emitted in the continuous regime, which was characterized by a constant emission level with a slight spiking. A strong selection of the transverse modes under continuous pumping conditions resulted in the generation of regular undamped spikes.

Mode structure of active resonators

An analysis is made of the mode structure of lasers when the interaction with the active medium is taken into account. We consider the combined effect of gain and refractive-index variations for arbitrary mirror configurations. Using a dimensionless round-trip matrix for a medium with a quadratic variation of the propagation constant with distance from the optic axis, dimensionless beam parameters are derived in terms of cavity and medium parameters. Beam waist and radius of curvature are obtained explicitly as a function of a dimensionless parameter containing the variation of propagation constant, wavelength, and cavity length. The spot size depends only on the absolute value of the gain variation, whereas the deviation of the radius of curvature of the beam from the mirror curvature changes sign when the sign of the gain variation is reversed. As long as radial gain variations are present stable oscillations can always be obtained for any set of curved and/or flat mirrors. For large gain variations the spot size and radius of curvature of the outcoming beam become independent of mirror curvatures.

Finite-aperture waveguide-laser resonators

A general theory of finite-aperture waveguide-laser resonators is developed which represents the external reflectors by matrices which couple linearly polarized waveguide modes having the same azimuthal symmetry. The theory allows the determination of resonator efficiency, resonator frequencies, and laser near- and far-field patterns. Computations of the coupling loss for the fundamental waveguide mode as a function of mirror curvature, separation, and aperture are in good agreement with recent infinite-aperture calculations in the limit of apertures and indicate three low-loss configurations: 1) radius of curvature mirrors close to the guide; 2) large radius of curvature mirrors centered at the guide entrance: and 3) generally smaller curvature mirrors separated by half their curvature from the guide entrance. The importance of higher order waveguide modes in determining laser output power and far-field patterns is demonstrated experimentally and compared to theoretical predictions. Design guidelines for the construction of high-efficiency CO 2 , CO, and He-Ne waveguide-laser resonators are summarized in tabular form.

Parametric studies on CO2 TEA lasers with extracavity and intracavity electrodes

Measurements were made of power output from a 1-m resistance-limited CO2 TEA laser with changing electrode configuration and spacing, mirror curvature, gas composition and pressure, and applied voltage. A maximum power of 20 MW was emitted from an extracavity plane-parallel pin-plate oscillator with a 4-cm electrode separation. An intracavity concentric electrode system with equal diameter yielded 1.4 MW.

Error Analysis to: Method for Approximating the Radius of Curvature of Small Concave Spherical Mirrors Using a He–Ne Laser

Get PDF Email Share Share with Facebook Tweet This Post on reddit Share with LinkedIn Add to CiteULike Add to Mendeley Add to BibSonomy Get Citation Copy Citation Text J. D. Evans, "Error Analysis to: Method for Approximating the Radius of Curvature of Small Concave Spherical Mirrors Using a He–Ne Laser," Appl. Opt. 11, 945-946 (1972) Export Citation BibTex Endnote (RIS) HTML Plain Text Citation alert Save article

Method for Approximating the Radius of Curvature of Small Concave Spherical Mirrors Using a He–Ne Laser

Get PDF Email Share Share with Facebook Tweet This Post on reddit Share with LinkedIn Add to CiteULike Add to Mendeley Add to BibSonomy Get Citation Copy Citation Text J. D. Evans and Frank Cooke, "Method for Approximating the Radius of Curvature of Small Concave Spherical Mirrors Using a He–Ne Laser," Appl. Opt. 10, 995-996 (1971) Export Citation BibTex Endnote (RIS) HTML Plain Text Citation alert Save article