Confocal Resonator Research Articles

Investigation in the far field characteristics of TM polarized Gaussian beam from the vectorial structure

Based on the vectorial structure of electromagnetic beam and the method of stationary phase, the analytical TE and TM terms of TM polarized Gaussian beam, the rigorous solution of Maxwell's equations for a confocal resonator, have been presented in the far field. Then in terms of the vectorial structure, TM polarized Gaussian beam is compared with Gaussian TEM 00 mode. The TE term is located at the y-axis, and the TM term the x-axis. At the non-paraxial case, the whole beam spot is elliptical, and the long axis is located at the y-axis. Moreover, the whole beam spot of TM polarized Gaussian beam is smaller than that of Gaussian TEM 00 mode. At the paraxial case, the whole beam spot is circular, and TM polarized Gaussian beam reduces to be Gaussian TEM 00 mode.

Waveguide submillimetre laser with a uniform output beam

A method for producing non-Gaussian light beams with a uniform intensity profile is described. The method is based on the use of a combined waveguide quasi-optical resonator containing a generalised confocal resonator with an inhomogeneous mirror with absorbing inhomogeneities discretely located on its surface and a hollow dielectric waveguide whose size satisfies the conditions of self-imaging of a uniform field in it. The existence of quasi-homogeneous beams at the output of an optically pumped 0.1188-mm waveguide CH3OH laser with a amplitude-stepped mirror is confirmed theoretically and experimentally.

Modified negative-branch confocal unstable resonator

A new type of unstable resonator, suitable for a laser with a large medium cross section and a small or median output coupling, is presented. The resonator configuration, a modification of a negative-branch confocal unstable resonator, is numerically investigated. The basis of the theory is the Fresnel-Kirchhoff integral equation, and the calculations describe a passive resonator. With respect to output mirror tilting, the calculations confirm that the modified negative-branch confocal unstable resonator is less sensitive to mirror misalignments than the conventional negative-branch confocal unstable resonator. Furthermore, the modified resonator improves the beam quality in comparison with the conventional unstable resonator.

Filamentary coagulation of particles from water-heterogeneous systems in the field of an acoustic resonator

The coagulation of particles from water-heterogeneous systems in the field of a confocal ultrasonic resonator is studied. It is found that, at frequencies of several megahertz, when acoustic power of about 1 W is applied to the resonator, long stable filaments consisting of the material of the heterogeneous system are formed in the vicinity of the resonator axis. The filaments consist of thin disks formed by coalescent particles spaced at intervals strictly equal to half of the sound wavelength. The features of this coagulation are determined for suspensions of various nature (metal and dielectric particles, colloidal solutions, and oil emulsions). It is established that the coagulation in a standing acoustic wave occurs faster than under natural conditions (under the influence of gravity). The possibility of using this effect for cleaning liquids from impurities and separating hyperfine particles without employing filter materials is discussed.

불안정형 레이저 공진기 정렬을 위한 null 렌즈 설계

공초점 불안정형 공진기의 광학 정렬을 정밀하게 수행할 수 있는 새로운 개념의 null 렌즈 광학 정렬 방법을 제안하였다. 제안된 정렬 방법은 3.5 m 공진기에 적용하여 민감도 분석을 통해 실용성 여부를 판단하였으며, 공진기의 길이 변화가 1.0 mm 발생하였을 때와 반사경이 광축에 대하여 1.0 mrad 기울었을 때에 대한 pupil map 분석 데이터를 제시하였다. The use of null optics is proposed as a new concept for the precise alignment of a confocal unstable resonator. The characteristics of the proposed null optics are investigated and analysed with the designed null lens for a real confocal unstable resonator of which the length is 3.5 m. As a result of the analysis, the pupil map data are shown about the despace error of 1.0 mm and tilt error of 1.0 mrad.

Integral plug-in RF module in a CO 2 hybrid-waveguide laser: Its performance and overall evaluation

This work describes the performance of a compact “in-house built” radio–frequency (RF)-excited CO 2 slab waveguide laser which has the innovation of having a plugged-in RF generator–amplifier module directly connected into the positive electrode of the laser head. The design circuit parameters include a matching circuit and a feed-through element as a whole. The overall laser performance takes into account the waveguide dimension ( y-axis) as approximately one-tenth of the free space transverse dimension ( x-axis). The optical resonator is calculated to be in the regime of the negative branch for unstable confocal resonators, having focal lengths of f 1 = 21.49 cm and f 2 = 19.39 cm with geometrical amplification of 1.108. Optical output coupling mirror was set to ∼9.7%. The calculated waveguide length is 37.73 cm whilst the total resonator length was adjusted to 42 cm to allow coupling losses less than 1%. The laser operational efficiency was about 12% and the output beam quality of 1.13 which is close to the ideal Gaussian beam. The optical output power was accomplished by playing with different gas compositions to have a final optimized gas proportion of 1:1:2.7:0.3 correspondingly to CO 2, N 2, He and Xe as admixture.

Off-Axis Confocal Unstable Resonator for Large-Bore High-Power Laser Chemical Pumped Oxygen–Iodine Energy Transfer Laser

An exotic resonator called the off-axis confocal unstable resonator is analyzed for large-bore low-gain high-saturation-intensity high-power lasers such as chemical pumped oxygen–iodine energy transfer laser (COIL), for which suitable resonators with high beam quality have not existed until now. The result of the calculations clearly showed that the off-axis confocal unstable resonator could produce multi-kW output with excellent beam quality for COIL.

Simulation of optical field in laser resonators cavity by eigenvector method

In this paper, an Eigenvector method (EM) for the calculation of optical resonator modes and beam propagation is introduced, in which the transit matrix of an optical resonator is obtained by dividing the mirror into finite grids based on the Fresnel–Kirchoff diffractive integral equation. Then, the eigenvectors, representing the multimode characteristics of the resonator, can be calculated by solving the integral matrix eigenequation. The merits of EM include that the considerably simpler procedure of solution of eigenvectors of the matrix eigenequation replaces the complicated iteration in traditional methods, and there is no dependence on the initial field distribution, and a number of modes can be derived once and the discrimination capability of the resonator can be evaluated easily. The examples using EM to simulate con-focal resonators with small or large Fresnel numbers are given, and the calculated results, well matched with Fox–Li method or Lagueree–Gaussian approximation analytical solution, prove that EM is highly feasible and reasonable.

Speed modulation technique to achieve simultaneous deposition of 3-in. double-sided Y–Ba–Cu–O thin films

We present a sputtering system which allows simultaneous deposition of high- T c superconducting films on both sides of the substrates up to 3-in. diameter. In order to enhance the homogeneity of 3-in. thin films, a speed-modulated bi-axial rotation method has been introduced, by which the thickness deviation of 3-in. thin films is reduced to less than 5%. The crystalline structure and superconducting properties are measured. The full width at half maximum values of X-ray diffraction ω-scan on YBa 2Cu 3O 7− δ (0 0 5) reflection are 0.15° and 0.21° for the center and the edge, respectively. The measured superconducting transition temperatures T c range from 89.8 K to 90.2 K and the critical current densities j c mapped by j c-scan Leipzig system at 77 K, 0 T are about 2.1–2.5 MA/cm 2. The majority of the wafer area has microwave surface resistances R s (75 K, 145 GHz, 0 T) measured by confocal resonator in the range of 45–80 mΩ. The breakdown field demonstrating the high-frequency power handling capability is higher than 5 mT at 8.5 GHz and 77 K.

Surface High-Energy Laser

We describe a design strategy for high-power solid-state laser oscillators using local correction of thermally induced optical distortion. This offers a potential for scaling lowest order Gaussian mode solid-state laser oscillators directly to high average power, e.g. >100 kW, while using a relatively simple near confocal ring resonator. The waste heat is necessarily produced in the gain region; however, the design strategy facilitates scaling by allowing the laser oscillator to function as though the waste heat was produced in a surface region external to the gain medium.

Output Beam Quality of Edge Pumped Planar Waveguide Lasers with Confocal Unstable Resonators

Output beam quality of edge pumped planar waveguide lasers with confocal unstable resonators is investigated by diffraction methods, taking into account gain saturation, asymmetric pumping, and beam interaction. The influences of pumping uniformity, doping concentration, cavity length and effective Fresnel number are analyzed with respect to output beam quality and pumping efficiency. It is found that good beam quality and high efficiency can be obtained with asymmetric pumping and optimized negative branch confocal unstable resonators.

Coupled mode competition in unstable resonators using the exact cavity equations of motion with dynamic gain

The dynamic coupled mode (DCM) method has been applied to study the transverse mode competition in optical resonators. In this work a differential equation for the homogeneously saturating dynamic gain is included in the original dynamic coupled mode method, thus increasing its physical resemblance and allowing the retrieval of gain temporal evolution at every point within the lasing medium. This new model provides a realistic temporal evolution of the mode competition and gain saturation within the resonator, which can give further information on spatial coherence properties. The new general formulation does not assume that lasing medium fills the optical cavity and is suitable for modelling the dependence of small-signal gain and power gain on the transverse and longitudinal coordinates. The application of the method to a typical CO2 unstable confocal resonator is fully described; results and their connection to relevant physical properties of gas lasers, such as spiking and relaxation oscillations, are discussed. Results of the numerical implementation of the DCM method with dynamic gain are in very good agreement with experimental measurements reported previously.

An investigation of a solid–liquid phase-change-cooled mirror

This article details a new design for a laser-reflecting mirror utilizing phase-change-cooling technology, which is innovative in using spiral cooling ducts filled with solid-liquid phase-change material to maintain a constant temperature inside the reflecting mirror in a positive-branch telescopic, virtually confocal unstable resonator. The structure no longer needs the 45° scraper plate that is always utilized in a positive-branch telescopic, virtually confocal unstable resonator for coupling the output and provides a high-quality coaxial laser output. The numerical calculation results show, that when phase-change cooling is utilized, the localized maximum temperature dropped from 44 to 33°C. Experiments show that the total surface deformation of a copper mirror dropped from 1.4 µm to 0.27 µm when using phase-change cooling, after continued laser exposure for 10 s and, under the same conditions, that of a silicon mirror dropped from 1.1 µm to 0.4 µm.

Efficient, high power, Q-switched Nd:YLF slab laser end-pumped by diode stack

A high power diode stack end-pumped electro-optically Q-switched Nd:YLF slab laser with a stable and off-axis negative-branch confocal unstable hybrid resonator was demonstrated. By using a cylindrical lens in the stable direction the thermal lens effect was compensated. Pulse energy of 25mJ was obtained with a pulse width of 22.4ns at repetition rates of 500Hz and a conversion efficiency of 22%. The stability was better than 0.8% and the beam propagation M2 factor was about 1.2.

Propagation characteristics of TM Gaussian beam

The propagation characteristics of TM polarized Gaussian beam, which is the rigorous solution of an eigenfunction problem for a confocal resonator, have been investigated using the nonparaxial vectorial moment theory of light beam propagation. The analytical expressions of the beam propagation factors are given by means of Fourier transform. Both the transversal second-order moment beam widths follow a simple hyperbolic variational law. For nonparaxial case, however, beam has different propagating features in the two transversal directions. As to paraxial case, its propagation approximately reduces to that of scalar Gaussian beam TEM 00 mode.

A novel eigenvector method for calculation of optical resonator modes and beam propagation

In this paper,a novel eigenvector method (EM) for calculation of optical resonator modes and beam propagation is introduced,in which the new transit matrix of an optical resonator is obtained by dividing the mirror into finite grids based on Fresnel-Kirchhoff diffracted integral equation. Then,the eigenvectors of the transit matrix,representing the multi-mode characteristics of the resonator,can be calculated by solving the matrix eigen-equation. The field distributions inside or outside the resonator,resulting from the known eigenvectors on the resonator mirror,can be derived by EM. The merits of EM include that the consider ably simpler procedure for solution of eigenvectors of the matrix eigen-equation replaces the complicated iteration in traditional methods,and there is no depen dence on the initial field distribution,and a number of modes can be derived on ce and the discrimination capability of the resonator can be evaluated easily. T he example of using EM to simulate the confocal resonator is given,and the calculated results,well matched with the Fox-Li method and Laguerre-Gaussian approx imatie analytical solution,prove that EM is highly effective and reasonable.

Stable range enhancement in a symmetric confocal two-rod resonator with 90° optical rotator

We propose a method to eliminate the narrow unstable region of a symmetric two-rod resonator with a 90/spl deg/ optical rotator which is used to compensate for thermal birefringence of the laser rod. The narrow unstable region is caused by the difference between the thermal focal lengths of the radial and tangential directions of a laser rod. Using the g-diagram analysis, we find that the narrow unstable region can be removed in the resonator configuration of a symmetric confocal type. We investigate the effect of the distance between two rods of the proposed resonator on the stability and the beam quality.

Two-dimensional time-resolved modelling of copper HyBrID laser beam quality

A numerical model is used to describe the spatio-temporal evolution of the beam delivered by a pulsed copper HyBrID laser. The model takes diffraction, transient gain saturation and the cavity geometry into account. The time evolution of experimentally accessible beam parameters, like M 2, power-in-the-bucket or brightness, is deduced. The model is applied to the description of a copper HyBrID flat–flat cavity and to the optimization of an unstable confocal positive branch copper HyBrID resonator.

Observation of collective-emission-induced cooling of atoms in an optical cavity.

We report the observation of collective-emission-induced, velocity-dependent light forces. One-third of a falling sample containing 3 x 10(6) cesium atoms illuminated by a horizontal standing wave is stopped by cooperatively emitting light into a vertically oriented, confocal resonator. We observe decelerations up to 1500 m/s(2) and cooling to temperatures as low as 7 microK, well below the free-space Doppler limit. The measured forces substantially exceed those predicted for a single two-level atom.

Numerical methods for solving the eigenvalue problem for a positive branch confocal unstable resonator

The resonator problem for a positive branch confocal unstable resonator reduces to a Fredholm homogeneous integral equation of the second kind, whose numerical solution here is based on a sequence of algebraic eigenvalue problems. We compare two algorithms for the solution of an optical resonator problem. These are obtained by (i) successive degenerate kernel approximation by Taylor polynomials of the Fredholm kernel and (ii) Nyström’s method with Simpson’s rule as the subordinate numerical integration method. The numerical results arising from these routines compare well with other published results, and have the added advantage of simplicity and easy adaptability to other resonator problems.