Positive-branch Unstable Resonator Research Articles

Investigation of the Beam Quality of a Compact Non-Chain Pulsed DF Laser with a Confocal Positive Branch Unstable Resonator

The results of detailed studies on the beam quality of a non-chain pulsed electric discharged DF laser based on a compact inner cavity confocal positive branch unstable resonator were presented herein. The theoretical and experimental divergence angles for magnification M = 1.65, 1.85, 2.05, and 2.25 were calculated according to Fraunhofer diffraction and measured by the method of calibrated apertures. The smallest divergence of θ = 0.66 mrad was obtained with M = 2.25 in our experiment, which is 1.95 times the theoretical value. The corresponding far-field energy density at 10 km distance from the laser exit was 82.8 mJ/m2. The beam quality and energy density were increased by 11 and 91 times, respectively, compared with a similar stable resonator in our lab.

Wavefront aberration analysis in misalignment passive positive-branch unstable laser resonators

Eigenmode of resonators with asymmetric circular mirrors based on misalignment passive positive-branch unstable resonator is investigated in the paper. To do so, we use iterative algorithm to simulate the effect of intracavity phase perturbation on eigenmode structure properties of the passive confocal unstable resonator. On this basis, further experiment of output beam properties on a misaligned passive unstable laser resonator has been performed by adopting Hartmann–Shack (H–S) method and Zernike modal wavefront reconstruction. Wavefront distribution and the first 35-order Zernike coefficient included in the wavefront are obtained. The results show that intracavity tilt perturbation notablely affects outcoupled beam intensity distribution, and will also increase some high-order aberrations of beam phase properties. However, low-order Zernike tilt aberration is the main component with phase-tilted perturbation is introduced into resonator cavity. Defocus, low-order astigmatism and coma aberration will all be brought with the augument of phase tilt aberration, which will obviously degrade output beam quality. When intracavity compensating elements are adopted for optical aberration correction, the correction of tilt aberration should be considered first.

Improvement of beam quality in unstable resonators by a conical output coupler

A novel conical output coupler for positive-branch unstable resonators has been proposed to improve the output beam quality. With the application of an inner cone annular scraper and an outer cone reflector, a realization of the output beam from unstable resonator with solid core is introduced. The feasibility of this conical output coupler with solid beam is examined numerically and experimentally with the help of a commercial fast transverse flow (FTF) CO2 laser. The characteristics of the output coupling beam in near field and far field are discussed. Under the definition of 86.5 % power content, the M pc 2 factors of original annular beam and improved solid beam are 5.22 and 1.16 in simulation. In experiment, the M pc 2 factor of the original annular beam from the commercial FTF CO2 laser is more than 10, while the M pc 2 factor of the improved solid beam is 3.82. Both simulation and experimental results show that the beam quality can be improved a lot by introducing this output coupling configuration.

Numerical investigation of unstable resonator for generating radially or azimuthally polarized beams

We present the calculations of intracavity radiation for a confocal positive-branch unstable resonator with a radially or azimuthally selective mirror. We carried out beam propagation in the resonator by the fox-li iterative method using jones vector calculus for the polarization state. The optimization of the resonator for generating a high-power radially or azimuthally polarized beam is discussed.

Analysis of lasing in chemical oxygen-iodine lasers with unstable resonators using a geometric-optics model

A simple geometric-optics model is developed that describes the power extraction in chemical oxygen-iodine lasers (COILs) with unstable resonators. The positive and negative branch unstable resonators with cylindrical mirrors that were recently used in COILs are studied theoretically. The optical extraction efficiency, spatial distributions of the intracavity radiation intensity in the flow direction, and the intensity in the far field are calculated for both kinds of resonator as a function of both the resonator and the COIL parameters. The optimal resonator magnifications that correspond to the maximum intensity in the far field are found.

Mode Competition During the Pulse Formation in Passively $Q$-switched Nd:YAG Lasers

We present a detailed theoretical and experimental study of the development of the EM field in pulsed, passively Q-switched solid-state lasers. We solve the rate equations separately for the gain medium and a passive Q-switch, thus accounting for the beam propagation and profile variations between them. Our model enables us to follow the pulse formation from a randomly generated seed EM field, thus monitoring the instantaneous beam pattern. The rate equations used include excited-state absorption in saturable absorber as well as the pumping term. The latter proves to be important when analyzing the beam profiles when passive Q-switching is used. In the case of stronger pumping, the formation of the second laser pulse is observed and shows mode structure characteristic of higher order Laguerre-Gaussian beams. Theoretical results are compared with experiment for three different types of laser resonators. Positive-branch unstable resonators with an ordinary and a super-Gaussian output mirror were studied in order to obtain top-hat beam profile. A plano-concave stable resonator was used as a reference. The calculated beam profiles and temporal developments are in good agreement with the experimental results which proves that the presented computational method can be used to predict the performance of other resonator designs.

Numerical investigation of beam quality in unstable optical resonators and the effects of practical imperfections

Field characteristics and beam quality of confocal positive branch unstable resonator under some practical imperfections has been investigated. Based on Fresnel–Kirchhoff integral, the near and far field intensity of the resonator was calculated numerically. Using the second order moment method, the beam quality factor, M2 of the resonator was also calculated. Variety of practical distorting affects, mainly misalignment, off-axis, and thermal deflection of the mirrors, as well as gain non-uniformity were considered in these calculations. The results show that the beam quality factor is more sensitive to the off-axis and misalignment distortions while the non-uniform gain has significant effect only for unusual conditions. The effects of geometrical parameters, i.e. Fresnel number as well as magnification factor on the beam quality were also investigated.

Numerical characterizations of unstable optical resonators and evaluation of the geometry effects

Unstable resonators have been widely used in high-power gas lasers as well as solid-state lasers. The phase and the spatial distribution of intensity of these lasers are very important in some applications such as material processing. In this paper, unstable resonators with three different geometries have been characterized numerically and the results have been compared and evaluated. Based on the Fresnel–Kirchhoff integral, the two-dimensional phase and intensity have been calculated for three different positive branch unstable resonators. The results show that the resonators with rectangular geometry have the best performance for near-field as well as far-field intensity, which is more suitable for material processing. The calculations also show that the maximum output power can be extracted from the rectangular resonator with spherical surface, while the circular resonator with spherical surface has minimum output power. The results also show that the laser has a higher divergence for the cylindrical resonator in compare with those for the circular and rectangular resonators.

Experimental investigation and numerical simulation of the spatio-temporal dynamics of nanosecond pulses in Q-switched Nd:YAG lasers

This paper reports on an experimental investigation and numerical simulation of the spatio-temporal dynamics of the pulse formation in flashlamp-pumped Q-switched Nd:YAG lasers. The temporal evolution of the spatial intensity distribution is measured with a fast two-dimensional CCD camera. The measurements are performed for two lasers with different cavity configurations. A laser with an optically stable resonator and an internal mode aperture generated pulses with a spatial intensity distribution which is Gaussian at all times during the 10-ns-long pulse. During the pulse evolution the value of the beam-quality factor M2 remains below 1.3. In a laser with a positive-branch unstable resonator the laser pulse also starts with a Gaussian intensity distribution, but becomes rapidly non-Gaussian. The corresponding M2 values increase from about 1 at the beginning of the formation of the pulse to more than 12 in the tail of the pulse. The measurements are compared with the results of a numerical simulation which takes the laser amplification, the properties of the laser cavity, and the diffraction of the beam in the laser cavity into account. The spatio-temporal dynamics of the pulse formation predicted by the numerical model are in good agreement with the experimental results.

Advantages of negative-branch compared with positive-branch one-dimensional unstable resonators

Effects of small misalignments in positive- and negative-branch strip confocal unstable resonators have been compared at the same absolute values of collimated Fresnel numbers and at the same Fresnel numbers. We show that positions of beam modes in negative-branch unstable resonators are far less sensitive to misalignment because of both geometric features and diffraction effects of beam flipping in the resonators.

High spatial intensity 10 W-CuBr laser with hydrogen additives

High beam quality output has been demonstrated from a single medium-scale (2 cm dia. × 50 cm) CuBr laser with hydrogen additives. The addition of hydrogen leads to beam divergence reduction and laser power lift-up finally yielding 5-fold increase in laser power spatial intensity compared with the case of no hydrogen added. With a simple positive-branch unstable resonator practical (pulse-average) divergence of ∼80 μrad is achieved. The easy-feasible sealed-off version of CuBr laser makes it an attractive source for many high-quality laser beam applications.

Performance of Nd:YAG lasers in coupled generalized self-filtering and positive-branch unstable resonators

A new optical resonator based on the combination of a generalized self-filtering unstable resonator (GSFUR) and a positive-branch unstable resonator (PBUR) in a three-mirror scheme is reported. It is shown both theoretically and experimentally that a nearly diffraction-limited Gaussian-output laser beam with a large mode volume can be obtained with this cavity design. The laser cavity is particularly interesting for use in high-threshold pumped gain media and eliminates some disadvantages of the SFUR and GSFUR designs. This resonator, with an effective magnification of -6.16, was applied to a pulsed Nd:YAG laser in free-running and in Q-switched modes of operation. The output energy was approximately 70 mJ, 5.5 times greater than when a single GSFUR design was used. The output beam had a pulse duration of approximately 30 ns in the Q-switched mode of operation and a beam divergence of 0.26 mrad. The required relations for the GSFUR-PBUR optical design and the output energy were derived and verified experimentally.

On the beam pointing variation of a long pulse XeCl [formula omitted] excimer laser fitted with unstable resonators

A theory for the beam pointing variation of the optical beam from a pulsed XeCl ∗ excimer laser equipped with a positive branch unstable resonator is introduced. The measurements are in good agreement with the calculations.

Variable reflectivity unstable resonators for a long pulse XeCl excimer laser

The divergence of a long pulse, low gain XeCl excimer laser has been improved using confocal positive branch unstable resonators with variable reflectivity mirrors as outcouplers. With variable reflectivity unstable resonators, nearly diffraction limited beams are obtained. Variable reflectivity resonators lead to high brightness beams (9.1×10 14 W/(cm 2 sr)). Different reflection profiles were studied with respect to their influence on the beam quality and the energy extraction.

Beam divergence studies on hard edge unstable resonators for a long pulse XeCl excimer laser

The focusability of a long pulse XeCl excimer laser has been improved using confocal positive branch unstable resonators where the outcoupling is done through the convex mirror. A nearly diffraction limited output beam is obtained from hard edge unstable resonators. An improvement of the far field energy distribution is achieved with partial reflecting hard edge outcoupling mirrors. The phase delay between the central part of the beam and the beam edge caused by these partial reflecting mirrors can be reduced by using phase unifying mirrors. Using unstable resonators a brightness of 1.4 × 10 15 W/cm 2 sr has been obtained from a long pulse XeCl excimer laser

Time-resolved divergence measurement of an excimer laser beam by the knife-edge technique

We present a simple method to measure the time-evolution of the divergence of pulsed laser beams, joining the time-resolution capability of photodetectors and the space-resolved information of the knife-edge technique. We measured the time-integrated and the time-resolved divergence of a long pulsewidth, high output energy XeCl laser ( λ = 308 nm), equipped with positive branch unstable resonators having either magnification factor M = 5 or M = 9. In both cases, the time-resolved beam divergence was smaller than the time-integrated one for most of the 100 ns full-width-at-half-maximum laser pulse duration. A minimum divergence of (40 × 23) μrad 2 at 86.5% energy content and a peak radiance of 9 × 10 14 W/cm 2/ster were achieved a few ns before the peak of the laser pulse, for the case of M = 9. The corresponding time-integrated values were (56 × 38) μrad 2 and 5 × 10 14 W/cm 2/ster, respectively.

Transverse-mode selection in apertured super-Gaussian resonators: an experimental and numerical investigation for a pulsed CO_2 Doppler lidar transmitter

A representative prototype of a high-energy, long-pulse, and narrow-bandwidth pulsed CO(2) laser suitable for a spaceborne Doppler wind lidar application has been developed. We obtained 10 J of output energy at greater than 8% efficiency in long, narrow-bandwidth, single-longitudinal, and transverse-mode pulses. We used a positive branch unstable resonator with a fourth-order super-Gaussian mirror as the output coupler. Experiments were carried out to assess the effect of intracavity hard apertures of different diameters that induce diffractive perturbation of the theoretical field and reduce the transverse-mode selectivity of the cavity. An upper limit to the choice of the mirror soft radius has been found, which allows optimization of the trade-off between laser efficiency and beam quality. We determined experimentally that a value of 0.75-0.8 for the ratio between the exp(-1) diameter of the beam intensity and the laser clear aperture gave a single-transverse-mode operation without significant loss of efficiency.

Development and characterisation of an XeCl excimer laser-generated soft-X-ray plasma source and its applications

A large-aperture, long-pulse XeCl excimer laser has been used to generate a soft-X-ray plasma source. Several laser optical configurations have been employed to optimise X-ray emission, including positive-branch unstable resonators and injection by seeding the gain region of the laser with a small commercial excimer laser, resulting in power densities in the range 1012–1014 W cm−2. The characteristics of the plasma source for each different laser configuration and for different target materials are investigated. The most suitable source conditions (spectral energy distribution, time duration, etc.) for specific applications are discussed.

Positive-branch unstable resonators with thermal lens compensation

In order to compensate for thermal lensing in Nd : YAG rod active media, placed in unstable resonators with a super-Gaussian reflectivity profile of the output mirror, a deformable thin glass plate was used as the rear mirror. Unstable resonators with a magnification of M = 1.8 and with one and two Nd : YAG rods inside were investigated. By a proper variation of the radius of the thin glass plate, the magnification of the resonator was maintained constant by varying the refractive powers of the rods. For compensated resonators, the output energy of the laser working at 10 Hz repetition rate and pump energies up to 50 J per pulse was close to those obtained for a 1 Hz repetition rate.

Variable reflectivity mirror unstable resonator with deformable mirror thermal compensation

For thermal lensing compensation of a Nd:YAG rod, placed in different positive-branch unstable resonators with super-Gaussian reflectivity profile of the output mirror, a deformable thin glass plate was used as the rear mirror. Unstable resonators with magnifications of M = 1.5 and M = 1.8 were designed for 0.8 mm·mrad value of the beam quality. For unloaded resonators the output energies of a laser working at 10 Hz repetition rate and pump energies up to 50 J per pulse were close to those obtained for 1 Hz repetition rate.