Proceedings Volume 4270

Laser Resonators IV

cover
Proceedings Volume 4270

Laser Resonators IV

View the digital version of this volume at SPIE Digital Libarary.

Volume Details

Date Published: 24 April 2001
Contents: 10 Sessions, 31 Papers, 0 Presentations
Conference: Photonics West 2001 - LASE 2001
Volume Number: 4270

Table of Contents

icon_mobile_dropdown

Table of Contents

All links to SPIE Proceedings will open in the SPIE Digital Library. external link icon
View Session icon_mobile_dropdown
  • Opening Session
  • Active Laser Resonators
  • Laser Resonator Design
  • Laser Beam Monitoring and Diagnostics
  • Poster Session
  • Lasers with Fibers and Fiber Lasers
  • Microresonators
  • Novel Laser Considerations
  • Intracavity Laser Beam Correction and Formation
  • Laser Beam Control and Formation
  • Poster Session
  • Laser Beam Monitoring and Diagnostics
Opening Session
icon_mobile_dropdown
Most efficient beams for frequency mixing in second-order nonlinear crystals
Vittorio C. Magni
It is not established, in principle, that gaussian beams are the most efficient ones for optical sum and difference frequency generation in second order nonlinear crystals; in fact, other profiles, such as Bessel and supergaussian shaped beams have been proposed to enhance the efficiency. Here, we analyze this problem and show what beams give the absolute maximum power conversion efficiency. The analysis, which neglects the pump power depletion, is based on the beam expansion in series of Laguerre-Gauss modes and on the numerical determination of the expansion coefficients that maximize the conversion efficiency. The optimal profiles have a flat wave front at the center of the crystal and a transverse profile similar to a gaussian curve, except for a weak ring of intensity surrounding the central peak. The absolute maximum of the efficiency is not much greater than the value obtainable with optimally focused gaussian beams. For second harmonic generation a detailed comparison of the optimal beam to supergaussian beams and to Bessel-like beams is also presented.
Exploiting thermal effects in high-power lasers
Thomas Graf, Eduard Wyss, Marc Schmid, et al.
An adaptive negative thermal lens that compensates for the power-dependent positive thermal lens in a transversally diodepumped Nd:YAG laser rod is presented. We demonstrate that the proposed technique leads to a reduction of the total thermal lens by more than an order of magnitude. In addition we propose a novel method to obtain a linearly polarised output beam from a Nd:YAG laser without a compensation for the thermally induced birefringence.
Nonlinear optics with liquid hydrogen droplet
Satoshi Uetake, Kohzo Hakuta
Nonlinear optics in a liquid hydrogen droplet is discussed. We carry out the stimulated Raman scattering (SRS) experiments using high-Q whispering gallery modes. We show that the liquid hydrogen droplet readily leads to high cavity Q-values exceeding 109 from ultraviolet to visible wavelength region. Using the high-Q liquid-hydrogen droplet, we demonstrate that, by pumping with an ultraviolet laser radiation, the SRS generates multiorder SRS sideband series through vibrational and rotational coherences covering whole ultraviolet-visible region from 200 nm to 900 nm, which may turn out as a super wideband optical comb generator. We also show that the SRS in the liquid hydrogen droplet proceeds for continuous operation with multiorder sidebands.
Active Laser Resonators
icon_mobile_dropdown
Fiber optic beam homogenizer and resonator design for 5-kW class supersonic chemical oxygen-iodine laser (COIL)
Shiv C. Dass, Kip R. Kendrick, Charles A. Helms, et al.
The Chemical Oxygen- Iodine Laser (COIL) beam of 5.3 kW average power was homogenized by transmitting through a low-loss fiber optic with a rectangular core. The fiber optic integrator transformed the beam into a beam with a uniform illumination. The exit aperture ofthe fiber was then imaged by projection optics and the beam uniformity was analyzed in the image plane. These experiments demonstrated a simple technique ofproviding a highly uniform beam over a large target area by using the low loss fiber. The desired rectangular beam footprints were achieved without the use of an external aperture The beam profiles and power were recorded and analyzed before and after the fiber. The COIL used for this puipose was specially configured for a stable resonator to produce a near-square cross section, low divergence, and multimode beam.
Closed-loop adaptive system for laser beam control
This paper discusses the novel adaptive optical closed ioop system with bimorph mirror as a wavefront corrector and Shack- Hartmann wavefront sensor to compensate for the aberrations of the laser beam occurred during the distribution of the beam from laser to processed material. Adaptive system can correct for the low-order aberrations in the real-time —the frequency of corrected aberrations is less then 25 (30) Hz. The amplitude of such aberrations — about 7 microns. These parameters are mostly determined by utilized Shack-Hartmann wavefront sensor. Number of corrected aberrations —up to 15th Zernike polynomial (excluding tip-tilt).
Active-mirror amplifier for high average power
This work presents a concept and scaling considerations for a diode-pumped solid-state laser operating in the active mirror mode. The laser uses relatively thin gain medium with large aperture that is pressured-clamped onto a transparent substrate with an internal microchannel type heat exchanger. Pump radiation is injected through the transparent substrate into the back face of the gain medium. Effective reduction of transverse temperature gradients makes this laser suitable for operation at high-average power while delivering good beam quality.
Bessel-Gauss laser resonators
J. Rogel-Salazar, G. H. C. New, Peter F. Muys, et al.
We present a geometrical optics analysis of a novel laser cavity with conical mirrors (reflective axicons). A further two dimensional study of the cavity is carried out through formal diffraction theory. We will show that the profile of the modes of such resonator are approximately Bessel-Gauss beams. The design also supports higher order modes, however these turn out to be unstable when perubations are present, they eventually decay to the lowest order mode. An explanation for the Bessel structure is due to the conical nature of the wave-front induced by the axicons, while the bell-shaped profile arises from the finite extent of the cavity.
Laser Resonator Design
icon_mobile_dropdown
Off-axis one-sided negative-branch unstable resonators compared with positive-branch unstable resonators in wave-optics characteristics
Koji Yasui, Yushi Takenaka
Wave optics calculations for power losses and mode profiles of off-axis positive branch and negative branch unstable resonators have been investigated. The beam modes become fully one-sided with moderate power losses by shaving one side of the front mirror by 70% to 90% for a positive branch unstable resonator, and by 33% (=(|M|-1)/|M|) to 80% for a negative branch unstable. At the conference, we also discuss the advantage of negative branch unstable resonators for the applications to high-power lasers.
Laser Beam Monitoring and Diagnostics
icon_mobile_dropdown
Intelligent beam monitoring and diagnostics for CO2 lasers
Stefan Kaierle, Stefan Mann, Juergen Ortmann, et al.
Changes in the laser beam quality caused by pollution, wasting or defects of the optical components and the laser beam source usually only can be detected by time-consumptive methods. Therefore a system is developed to automate and simplify the diagnosis of the laser beam radiation. As a solution a laser beam analyzer is permanently integrated into the laser system, an ergonomic user software is developed and the analyzer, the tooling-machine, and the laser are controlled by one computer. The user of a laser machine is enabled with this system to detect changes in the beam quality in an early state by daily measurements which are easy and fast to be carried out. Failures can be retraced to defects of the laser source, the beam guiding system, and the focussing optics by the use of image processing methods and fuzzy algorithms. Furthermore it is possible to detect stealing changes in the beam mode structure. Within the scope of quality assurance the data can be archived according to EN ISO 900x to be able to assign processing parameters to work-pieces.
Poster Session
icon_mobile_dropdown
Optimization of tunable CO2 laser outputs by automated setting of intracavity emission polarization for each line
Yuri N. Bulkin, Anatoliy A. Adamenkov, Evgeniy A. Kudryashov, et al.
The present paper is concerned with automatic optimization of tunable CO2 laser emission power that has been realized by changing the in-resonator polarization direction. We have begun with the investigation into the experimental reflection efficiency of the grating in use for first and zero diffraction orders as a function of the incident polarization plane orientation relative to the grating line length obtained from the first-order Littrow system. The dependencies measured were then used to determined the angle ?(J) between the grating line length and the polarization vector such that the zero-order reflection factor was equal to its optimal value that is a function ofthe active medium gain for the J-th line, active length, and useless loss inside the laser cavity. After this, the monitoring and control software of the laser has been enhanced with the ?(J)-values found out in accordance with the above procedure for each laser line associated with its intrinsic gain. Hence, the laser tuning in J-th line is accompanied with automatic orientation ofthe Brewster window at the angle ?(J). Due to the given optimization we were able to acquire for each particular line the highest power at the maximum line amount in the output spectrum.
In-situ monitoring of the optical cavity of diffraction-grating line-selection CO2 laser by Wang's method
Yuzhi Wang
When adjusting the resonator of a half-infracavity or an extracavity of gas lasers, a He—Ne laser beam was usually used. When the He—Ne laser beam is tuned-in the light-axis ofthe gas laser, a reflecting light from the Brewster window can be seen clearly. While if another visible laser light ( He—Ne light also good) is sent inversely along the path ofthe above reflecting lights this light can be sent into the resonator via the Brewster window. Thus, a light-probe is created for in situ monitoring the optical cavity. Practice showed that this method is especially useful for monitoring the cavity of diffraction-grating line-selection CO2 lasers.
Fundamental investigation on the plane IR (total internal reflection) prism resonator
Xiaoyan Chen, Yuzhi Wang, Li Wang, et al.
Based upon the matrix optics, a fundamental investigation on the plane-rectangular prism cavity and the p1anedirectional reflecting prism cavity has been performed. The result showed that: (1) The characters ofthe cavity as well as the laser beam do not change when adopting prism as a reflector; (2)the rectangular prism cavity is insensitive to the angle misalignment in the xoz plane; while the directional reflecting prism is insensitive to all angle misalignment.
Compensation of quasi-optical-wedge effect by plane-prism cavity
Yuzhi Wang, Xiaoyan Chen, Gang Zhao
Experimental and theoretical studies on the thermal stability of optical cavity have been performed. The focal length of the thermal lens measured was 4~6cm for our laser system. By applying disalignrnent transfer matrix method, analyses ofthe thermal stability for parallel plane cavity, plane-rectangular prism cavity and the plane-TIR (total internal reflection) prisni one were performed. The results showed that: ( 1 ) The plane-rectangular prism cavity can compensate the thermal effect in one direction; ( 2) The plane-TIR prism cavity can compensate the thermal effect in all direction.
Low-ignition-voltage helium neon laser: I. Breakdown characteristics of capillary discharges
Yuzhi Wang, Zonglin Huang
In 1980s, Quan-sheng Gao [1], a Chinese engineers had invented a new type of helium neon laser which possesses lower ignition voltage. This new laser has the advantage that only needs a power supply with 2 / 3 voltage of that of the traditional type. Its physical mechanism had encouraged several Chinese scholars to try to make interpretations. However, up to now, a satisfactory interpretation has not been obtained. From the viewpoint ofthe authors, this is because of lack ofexperimental details. Therefore, the authors have performed several experiments for this laser, mainly, from capillary discharges to the performances of the laser. In this paper, some experimental results of the capillary dischareges are reported. The results concerning the laser performances and related interpretations will be presented in the second paper [2] For performing experiments on capillary discharges a vacuum system called 630 1 type low vacuum calibrating system, was rearranged so that it can supply several kinds of gases with high accuracy pressure readings , see Fig. 1 . The breakdown characteristics of capillaries with various diameters have been investigated for six kinds of gases, i.e. H2, N2, He, Ne, Ar, and Kr, within a pressure range of 10~2000pa (10 -1~ 20 Torr approx.). For comparison, the characteristics of the parallel-electrode systems and of the minielectrode systems free from wall-effects were also performed. The following conclusions have been abtained: ( 1 ) The breakdown voltage of capillary tube is always higher than that of the ideal parallel electrode systems provided that the distances between electrodes are equal. (2) Paschen's law is no longer valid for the case of capillary discharges. A theoretical analysis is also presented. These results are useful in the interpretation of the mechanism of Gao's lasers.
Low-ignition-voltage helium neon laser: II. Mechanism of lowering ignition voltage
Yuzhi Wang, Zonglin Huang
For the purpose of studying the mechanism of lowering ignition voltage in the Gao-type He-Ne laser, three kinds of laser tubes (the traditional type , the Gao-type I and Gao-type II , see Fig. 1 .) have been made and ignition voltage measurements were performed in several gases (He, Ne, He-Ne, Ar, Kr, H2 and N2). The experimental results showed that the ignition voltages for Gao-types are fairly lower than that of the traditioni one, but this effect persists only within a certain range of gas pressure. As the gas pressure inereases to a certain value P0, which depends on the gas kind, the lowering effects vanish. Figure 1 shows schematically the three kinds oflaser tubes, while Figure 2 shows the dependences ofbreakdown voltages on gas pressures. It is seen that the lowering effect tends to zero as gas pressure increases. A theoretical explanation for the experimental results is also given.
Dielectric resonators based on amorphous silicon
In this paper, we report on the design, modeling, fabrication, and characterization of dielectric microresonators based on hydrogenated amorphous silicon nitride and hydrogenated amorphous silicon oxide. The microresonators were modelled using the transfer matrix method (TMM). Quarter wavelength thick stacks of hydrogenated amorphous silicon nitride and hydrogenated amorphous silicon oxide were consecutively deposited using low temperature plasma enhanced chemical vapor deposition (PECVD). For the characterization of the dielectric microresonators the intrinsic photoluminescence of the amorphous silicon nitride is used. The photoluminescence is enhanced by at least an order of magnitude at the resonance wavelength of 710 nm. The minimum resonance linewidth is 6 nm, corresponding to a quality factor of 118. The maximum rejection bandwidth of the distributed Bragg reflector (DBR) is 150 nm. The enhancement and inhibition of the photoluminescence is understood by the modified photon density of states of the dielectric microresonator. The linewidth of the photoluminescence is also narrowed with respect to the linewidth of the bulk amorphous silicon nitride, again due to the presence of the electromagnetic modes of the microresonator.
Lasers with Fibers and Fiber Lasers
icon_mobile_dropdown
Efficient diode-pumped double-clad Tm-doped silica fiber laser with a ring cavity
Jianqiu Xu, Jianren Lu, Mahendra Prabhu, et al.
We demonstrate a novel ring cavity for diode-pumped double-clad Tm-doped ber laser, which is constructed by placing the 45o angle-polished output end before the input end and the pump and laser power can re-launched into the ber. This design can reduce the reabsorption by using short length of bers without loss of pump efficiency. Furthermore, by adjusting the distance between the ber end and the objective lens, uni-directional output can be obtained. With a 80 cm long ber, 2.7 W single-mode continuous-wave output is generated for 11.5 W launched pump power.
Spectral beam combining model for fiber lasers
Spectrally multiplexed, high brightness, beam combining for power scaling and WDM communications applications has advantages over coherent combining, and is suitable for use with high gain bandwidth lasers. A diffraction grating forces oscillation at distinct wavelengths in a laser array in the external resonator configuration proposed by T.Y. Fan, et al [Opt. Lett.25 , 405-407 (2000)], producing a multi-wavelength output of overlapping beams. A unified diffraction integral-based treatment is used to formulate a design principle by which to jointly optimize most significant measures of performance, such as efficiency, bandwidth, and beam quality. The sensitivity to errors in alignment and positioning is also characterized. The transform lens aberrations are shown to ultimately determine the maximum array size, and the design criterion is applied to test and propose improvements in the lens. Initial comparisons show agreement within estimated experimental uncertainty margins with MIT/LL proof-of-principle measurements on an Yb-doped fiber laser array. To illustrate, we foresee a feasible rectilinear 100 - emitter array system using a multi-element aspheric lens, with <5%array-center-to-end efficiency drop, yielding beam quality M2 ? 1.2 in the transverse (array) direction, and close to unity in the lateral direction. Application to the efficient coupling of a laser array to a multimode fiber core is discussed as fmal example.
Novel circular-beam equalizing techniques using graded-index (GI) fiber optics for high-power laser diode
Yushi Takenaka, Lalit B. Sharma, Keisuke Furuta, et al.
We demonstrate a novel method of equalizing laser diode beam into circular beam. The method uses the twist effect of graded index(GI) fiber optics. An asymmetric laser diode beam with the beam qualities of M2=500 in the slow axis and M2=4 in the fist axis is successfully converted into a symmetric circular beam with the beam quality of M2=175. The circular output beam with 92% coupling efficiency is obtained by using a 5m long GI1200 fiber for 2W laser diode array. We have Ibund that the required minimum length of G11200 fiber is 550mm for circular beam equalizing. We extend the experiments to higher power source with higher asymmetric beam qualities of M2=3000/M2=4. By using a large core diameter ofGI10000 fiber, the higher asymmetric beam is not converted into a perct symmetric beam. We consider that the length is too short Ibr this large core fiber. Since the GI1200 fiber required 550mm, the GI10000 fiber should require at least 4583mm, however, the fiber length is limited to 500mm because ofthe production matter. By slightly bending the fiber, however, we have succeeded in generating symmetric beam with improved beam quality of M2=2000. The average beam quality is preserved when the asymmetric ratio is not high and the beam quality degradation ratio is investigated up to asymmetric ratios of 750.
Microresonators
icon_mobile_dropdown
Locking and laser-frequency tracking of a microsphere whispering-gallery mode
We report advances in compression tuning of fused-silica microsphere whispering-gallery resonances and a practical use of the improved compression tuner. The advances include extending the tuning range and enhancing the tuner’s response speed; these lead to the new application of using the tuner to lock to a laser, keeping a single whispering-gallery mode on resonance as the laser frequency is scanned. The resonance frequency of the mode to be locked is weakly modulated by axial compression of the microsphere, and phase-sensitive detection of the fiber-coupled optical throughput is used for locking. Using a laser wavelength of either 1570 nm or 830 nm, we demonstrate a locked tracking range exceeding 30 GHz for a microsphere of 120 GHz free spectral range. The improved tuner design that makes this application possible allows coarse tuning over 1 THz and piezoelectric tuning over 80 GHz. Compression modulation rates of up to 13 kHz have also been achieved with this tuner, producing a tuning speed of at least 16 GHz/ms.
Novel whispering-gallery resonators for lasers, modulators, and sensors
Vladimir S. Ilchenko, Lute Maleki
This report describes novel whispering-gallery resonators with added physical properties, including a micro-toroidal cavity with large free spectral range ~4OOGHz and finesse >104, a lithium niobatespherical cavity in a high-efficiency X-band electro-optic modulator, and an immersed silica microsphere as high-resolution chemical sensor.
Evanescent and refractive side-coupled high-Q resonances of noncircular 2D micropillars
Side-coupling between 2-D micropillars and waveguides that allows a gap spacing larger than the sub-micron range would open opportunities for integrated photonic devices. Two microcavity designs, square and oval, were investigated. The square allows longer interaction length and the oval allows refractive coupling thus larger gap spacing. In the elastic scattering of ? 210-micron square microcavity in fused silica, multi-mode cavity resonances were imaged from the square sidewall. Based on a two-dimensional k-space representation, we accounted for the multi modes by different normal modes with trajectories confined by total internal reflection. The cavity-mode trajectories need not be closed after each round trip. In oval microcavities, the ray trajectories are typically irregular. Light rays that are initially confined by total internal reflection could subsequently escape by refraction (according to Snell’s law) in the vicinity of the higher-curvature region. Periodic filter spectrum in the elastic scattering of oval microcavity was observed in specific input and output coupling directions in the far-field. We interpreted the filter spectrum as the multiple-ray interference of the refractively outputcoupled cavity modes at the detector.
Coupling of a guided mode with a microresonator: effect of the size of the resonator
Kenjiro Miyano, Hiroshi Ishikawa
Optical coupling between a spherical microresonator and a plane dielectric substrate is investigated for small spheres whose diameter is only a few ten times as large as the optical wavelength. The coupling is monitored in real space by observing the interference pattern of the propagating wave in the substrate and the scattered wave from the sphere in the coupling region. A series of numerical model calculations successfully reproduced the interference pattern, by which significant insight into the coupling phenomena has been gained. Especially, it is found that the smallness of the resonator size relaxes the phase matching requirement considerably while maintaining the overall coupling strength. Therefore, its utility is much enhanced in the application as a part of an optical waveguide. The different roles played by the frequency (temporal matching) and the propagation constant (spatial matching) in the resonant coupling is clarified.
Thermorefractive noise in microspheres
Thermodynamical fluctuations of temperature in microspheres transform to fluctuations of its resonance frequencies due to coefficient of thermal refraction. These fluctuations produce additional phase and amplitude noise in the output of the cavity. The implications of this noise for laser stabilization and other applications are discussed. Experimental conditions for the direct observation of this new effect are given.
Novel Laser Considerations
icon_mobile_dropdown
Performance and design considerations of angled-grating semiconductor lasers
John R. Marciante, Andrew M. Sarangan, David J. Bossert
In this paper, we examine the performance of the angled-grating laser. The spatial characteristics of the device and design considerations for diffraction-limited performance are explored. The optical spectrum is studied in terms of the device geometry, and suitability to different applications is examined. Finally, the limits of high-power operation are investigated, and scalability to higher diffraction-limited performance is discussed.
Diffractive focusing of wide-aperture beams: theory and experiment
It is shown theoretically and experimentally that when a Gaussian beam illuminates a bicomponent diffraction system with small Fresnel numbers, consisting of two plane screens with circular apertures on given optical axes, in a near zone of the second screen the effect of diffractive multifocal focusing of radiation is observed. In this case, the diffraction picture from the second screen in the focal planes represents the circular nonlocal bands of the Fresnel zones with a bright narrow peak at the center, whose intensity can exceed by six times the value of the incident wave intensity. The proposed diffractive method allows the focusing of the wide-aperture beams without using classical refraction elements such as lenses and prisms, and it is applicable to both low-intensive and high-power radiation. The energy efficiency of diffractive focusing of Gaussian beams is as high as 70%. Such a method can improve the energy efficiency of the fiber coupling of diode lasers and can increase the intensity of radiation on a fiber exit up to a factor of ten.
Intracavity Laser Beam Correction and Formation
icon_mobile_dropdown
Aberration correction in double-pass amplifiers through the use of phase-conjugate mirrors and/or adaptive optics
Corrrection of birefringence induced effects (depolarization and bipolar focusing) was achieved in double-pass amplifiers using a Faraday rotator placed between the laser rod and the retroreflecting optic. A necessary condition was that each ray in the beam retraced its path through the amplifying medium. Retrace was limited by imperfect conjugate-beam fidelity and by nonreciprocal double-pass indices of refraction.We compare various retroreflectors: stimulated Brillouin scatter phase-conjugate-mirrors (PCMs), PCMs with relay lenses to image the rod principal plane onto the PCM entrance aperture (IPCMs), IPCMs with external, adaptively-adjusted, astigmatism-correcting cylindrical doublets, and all adaptive optics imaging variable-radius-mirrors (IVRMs). Results with flashlamp pumped, Nd:Cr:GSGG double-pass amplifiers show that average output power increased fivefold with a Faraday rotator plus complete nonlinear optics retroreflector package (IPCM+cylindrical zoom), and that this represents an 80% increase over the power achieved using just a PCM. Far better results are, however, achieved with an IVRM.
Application of static phase control elements to high-power solid state lasers
Thomas H. Bett, Andrew R. Barnes, N. W. Hopps, et al.
We describe development of passive phase correction elements to compensate for static phase errors and prompt thermally induced aberrations in the reconfigured HELEN laser. Partial compensation of cooling effects is also included in the design. Phase elements have been fabricated through lithographic processes using amplitude masks. The masks were generated from measured laser wavefronts. The phase profiles have been measured experimentally and the effect on the HELEN laser wavefront and far field intensity distribution have been calculated by combining these phase profiles with the measured laser wavefronts. The calculations show improvements in Strehl ratio from a factor of 2 up to a factor of 7 depending on the configuration.
Laser Beam Control and Formation
icon_mobile_dropdown
Comparison of adaptive resonators and multipass amplifiers for efficient power extraction with good beam quality
Andrew M. Scott, A. P. G. Davies
Considerable work is being undertaken to develop laser sources with increasingly high power and good beam quality. In all solid state lasers, especially cw ones, optical pumping causes heat to be generated in the gain volume which is conducted away via a surface. The associated temperature gradient produces refractive index variations which degrade the beam quality.
Poster Session
icon_mobile_dropdown
Analysis of laser cavities with self-starting Kerr-lens mode locking
Jinan Xia, Minhee Lee
The ABCD matrix and the general formulae of cavity g parameters are used to analyze and ca!culate the characteristic parameters of a Kerr-lens mode-locking laser. The result shows that KLM strength in the laser is very sensitive to the defocusing distance of the te!escope formed by the two mirrors locating at the two sides of Kerr medium. The mechanism for self-starting operation of Kerr-lens mode-locking laser is studied. Several types of cavity structures with which selfstarting operation of Kerr-lens mode-locking lasers may be achieved are presented. In addition the position of a hard or soft aperture similar as a fast saturable absorber in a KLM laser is discussed.
Laser Beam Monitoring and Diagnostics
icon_mobile_dropdown
Definition, meaning, and measurement of coherence parameters
It is a well-known rule of thumb that the intensity profiles of a beam are smoother andless structured the less the transverse coherence of the beam is. In this paper it will be shown that the global degree of coherence as well as the lateral coherence length is related to the width of the Fourier power spectra ofthe profiles the beam takes on under propagation and hencecan be considered as a quantitative measure of the smoothness of the beam. A spin-off of these considerations is a simple non-interferometric measurement procedure for both, the global degree of coherence of a beam and the lateral coherence length.