Confocal Unstable Resonator Research Articles

Analytical study of the beam quality of a diode-pumped alkali laser with unstable resonator

Analytical model of Cs diode-pumped alkali laser with unstable confocal resonator is reported. Two of the parameters characterizing the quality of the output beam were studied: the axial luminous intensity in the far field and the power in the bucket (PIB). The far-field axial light intensity and PIB were compared with their values for a truncated Gaussian reference beam whose aperture was limited by the aperture of the large resonator mirror and 99% of the Gaussian beam energy passed through the aperture of this mirror. For large values of the unstable resonator magnification factor m > 5, the far-field axial light intensity is approximately 40% larger than that of the Gaussian reference beam. Analysis of the PIB curves showed that for large m > 5, the values of the integrated fractional encircled power within a sufficiently large diffraction angles for the unstable resonator exceed its values for the reference Gaussian beam.

Unstable confocal resonator with external flat semi-transparent mirror for additional feedback

Main characteristics (mode structure of power loss, divergence of resonant radiation) of a three-mirror laser cavity with additional feedback are theoretically studied in the Fresnel approximation on the basis of the Fox-Lee integral equation. The resonator consists of two spherical mirrors, which form an unstable confocal resonator, and a flat semi-transparent mirror, which is installed outside the reference unstable resonator perpendicular to its optical axis. The flat coupling mirror returns part of the radiation back inside the resonator. The level of additional feedback is determined by the reflection coefficient of the flat mirror and the position of the mirror along the optical axis of the resonator. Variation of these parameters makes it possible to control the transparency of the three-mirror resonator over a wide range, up to values close to zero. Results of this paper can be used in the development of high-power lasers with wide aperture (Fresnel numbers of ∼100) on the basis of low-gain active media.

Intracavity adaptive correction of an unstable standing-wave resonator based on reconstruction matrix optimization.

Due to the existence of the expanding beam portion in the positive branch confocal unstable resonator, the laser passes through the intracavity deformable mirror (DM) twice with different apertures, which makes it complicated to calculate the required compensation surface of the DM. In this paper, an adaptive compensation method for intracavity aberrations based on reconstruction matrix optimization is proposed to solve this problem. A collimated probe laser of 976 nm and a Shack-Hartmann wavefront sensor (SHWFS) are introduced from the outside of the resonator to detect intracavity aberrations. The feasibility and effectiveness of this method are verified by numerical simulations and the passive resonator testbed system. By adopting the optimized reconstruction matrix, the control voltages of the intracavity DM can be directly calculated from the SHWFS slopes. After compensation by the intracavity DM, the beam quality β of the annular beam coupled out from the scraper is improved from 6.2 times diffraction limit to 1.6 times diffraction limit.

Adjusting and Determining the Direction of the Axis of a Telescopic Resonator

Abstract—A method for adjusting an unstable confocal resonator and determining its axis direction using an angular reflector is proposed. A semiconductor laser was used as an auxiliary laser, which set the direction of the cavity axis. A collimator was used as the device that controls tuning. A corner reflector mounted inside the resonator from the side of the concave mirror made it possible to create the “direct” and “reverse” passages of the beam of the collimator through the resonator. This makes it possible to observe images of the collimator scale in the eyepiece from the “direct” and “return” passages. Fine tuning of the resonator is carried out by combining the centers of the scales, while the axis of the resonator coincides with the axis of the collimator.

Analysis of defocus aberration characteristics on a typical passively confocal unstable resonator

The analytical treatment of typical defocus aberration and its impact on the mode wavefront properties of a confocal structural laser resonator is discussed. Numerical modeling of the system is deduced to predict the influence of defocus disturbation on mode intensity and phase distribution. In addition, an experimental method by combining Zernike aberration function and wavefront reconstruction to measure the dynamic wavefront aberration for such lasers has been developed. Beam mode characteristics, including the alignment state and defocus aberration perturbation have been presented. It is shown that the typical Zernike aberration such as A3, A5 and A10 caused by intracavity perturbation significantly affected the beam properties, PSF profiles and circle energy distribution in the far field. The experimental results show that defocus aberration characteristics can be used as an effective basis for dynamic compensation of typical aberration in such lasers. Furthermore, corresponding strategies are proposed to implement the active correction of typical optical aberration in such resonators.

Excess noise of the misaligned off-axis confocal unstable resonators

The misalignment of the output mirror will cause serious decline of the output power of the positive branch off-axial confocal unstable resonators. In this paper, we try to explain this phenomenon by investigating the excess noise factor K for the misaligned resonator. Numerical result shows that the jump of the value of K due to the well-known mode crossing also occurs periodically against the degree of the misalignment (ε), the locations and the period of the jump are related the equivalent Fresnel number Neq. In addition, it shows the value of K, the loss, and the far-field divergence angle are small even for large downward misalignment, it implies that it may be able to gain laser output under the condition.

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.

160 W laser-diode end-pumped Nd:YVO4 slab laser with positive branch hybrid resonator

In this paper, we present an experiment on a continuous-wave Nd:YVO4 Innoslab laser diode-pumped at 808 nm. The LD stack is composed of six bars, with the central wavelength fixed at 808 nm by adjusting the cooling water temperature. The emission from each diode laser bar is individually collimated by micro lens, which is coupled into a coupling system. The coupling system includes a planar waveguide, four cylindrical lenses and a spherical lens. The planar waveguide is used to shape the emitting beams of LD to obtain uniform distribution. The coupling system leads to a pump power loss of ~12%. By the coupling system, we obtain a homogeneous pumping line of ~0.4 mm22 mm coupled into the 0.3 at. % Nd:YVO4 (22 mm10 mm1 mm) crystal. The Nd:YVO4 crystal is a-cut with c axis along 22 mm direction. Indium foil is used for uniform thermal contact and cooling. The laser crystal is mounted between two water-cooled copper heat sinks with two large faces 22 mm10 mm. The heat conduction inside the laser crystal is quasionedimensional. The two 22 mm1 mm surfaces are polished and antireflectioncoated for the pump light and the laser light. Temperature of LD stack and laser crystal are controlled by cooling circulating water. The resonator consists of the input mirror (M1) and the output mirror (M2). M1 is a concave mirror with a radius of R1=500 mm, which is coated for high refection (HR) at 1064 nm and high transmission (HT) at 808 nm. The output mirror (M2) is a cylindrical mirror with a radius of R2=-350 mm, which is coated for HR at 1064 nm. M2 is cut and polished at one edge where the large beam exits. M1 and M2 constitute a stable resonator in vertical direction and off-axis unstable positive confocal resonator in the horizontal direction. In theory, the length of the resonator is L=(R1+R2)/2=75 mm. In fact, the length of the resonator is the same as the theoretical value. The equivalent transmission of the resonator is T=1-|R2/R1|=30%. At a pumping power of 462 W, a maximum power of 160 W continuous wave laser output is obtained, with the stability being 2.6%. Considering 88% of the coupling efficiency and 95% of absorbed efficiency, the optical-to-optical efficiency and slope efficiency are 41.5% and 47.7%, respectively. When the output power is 145 W, the beam quality M2 factors in the stable direction and unstable direction are 2.21 and 1.37, respectively. With the help of the ANSYS software, the temperature distribution in the crystal at the pumped power of 462 W is demonstrated. The temperature distributions are analogous to exponential decays in the Z-direction and parabola decay in the Y-direction, respectively. The maximum temperature difference is 71.6 K in our experiment. The thermal lens is negligible in the unstable direction because the temperature distribution is uniform. That is why the Innoslab laser is beneficial to the power scaling, as it keeps the power density constant, and enlarges the size of gain medium in the unstable direction to inject bigger power to obtain a higher power output, and maintain the constant beam quality.

Intracavity CH 4 Raman laser using negative-branch unstable resonator

An intracavity Q-switched Nd:YAG/CH4 Raman laser is realized based on the configuration of a negative-branch confocal unstable resonator. A numerical model of the bare resonator was introduced to simulate the fundamental transverse mode and calculate the loss of the fundamental resonator. With different magnifications of the fundamental resonator, the first Stokes output energy was presented as a function of the discharge voltage. The influence of the Stokes resonator on Raman conversion was analyzed. With a fundamental resonator magnification of 1.1, a maximum output energy of 58 mJ was obtained, and the corresponding photon conversion efficiency was 48%.

Array of unstable resonators for a laser with an annular gain geometry

The application of an array of confocal unstable resonators, formed by spherical mirrors, to a laser with an annular active medium, is considered. The results of numerical simulations show that the proposed design generates high quality output beams in gas and solid-state lasers with low to moderate amplitude of intracavity aberrations.

Numerical study of unstable resonator in thin disk laser

In this paper a disk laser with unstable resonator is investigated numerically. Using Collins integral and diffraction theory, a positive branch confocal unstable resonator with a thin disk shape active medium is simulated. Thermal lensing of the disk is considered in our research. Laser beam profile and output power are calculated for unstable resonator with variable internal lens. The calculations show instability of output laser beam during pump power increasing due to changes of disk dioptric power. Also calculations show that power extraction is only possible for lasers with not too thin disks.

非链式脉冲DF激光器非稳腔设计与实验研究

By employing positive branch confocal unstable resonator, design of cavity parameters and experimental research on non-chain pulsed DF laser are carried out. The advantages of suppressing divergence angle and improving beam quality are shown by comparing plano-concave stable resonator with unstable resonator. To estimate the beam quality, diffraction limit magnification is chosen as evaluating criterion, which can incarnate both the energy focusing degree and divergence angle excursion. 86.5% enveloping energy is used to define spot size, and 90-10 knife edge method is adopted to measure it. Nine sets of mirrors with different magnifications and mode volumes are tested and compared, and optimization method of unstable cavity parameters is concluded. Taking energy, divergence and diffraction limit magnification into account, the optimal parameters are M=1.89, D=40 mm. Laser beam with divergence angle of 0.74 mrad, =1.35, laser energy of 1.86 J, and peak power of 16.4 MW is obtained at these parameters.

550 mJ Q-switched cryogenic Ho:YLF oscillator pumped with a 100 W Tm:fiber laser

We report 550 mJ pulses with 14 ns FWHM duration at 1 Hz repetition rate from a Q-switched cryogenic Ho:YLF oscillator pumped with 100 W in 35 ms by a Tm:fiber laser. The laser has a confocal unstable resonator with a graded-reflectance output coupler, resulting in a beam quality of M(2) = 1.5. Pulse energies of 416 and 343 mJ were obtained at 10 and 20 Hz repetition rate, respectively.

Production of extended plasma channels in atmospheric air by amplitude-modulated UV radiation of GARPUN-MTW Ti : sapphire—KrF laser. Part 1. Regenerative amplification of subpicosecond pulses in a wide-aperture electron beam pumped KrF amplifier

Regenerative amplification of single and multiple ultrashort subpicosecond UV pulses in a wide-aperture KrF amplifier with an unstable confocal resonator was investigated on the GARPUN-MTW hybrid laser system. Amplitude-modulated 100-ns long UV radiation pulses with an energy of several tens of joules were obtained at the output of the system. The pulses were a combination of a quasi-stationary oscillation pulse and a train of amplified ultrashort pulses (USPs) with a peak power of 0.2–0.3 TW, which exceeded the power of free-running lasing pulse by three orders of magnitude. The population inversion recovery time in the active KrF laser medium was estimated: τc ≤ 2.0 ns. Trains of USPs spaced at an interval Δt ≈ τc were shown to exhibit the highest amplification efficiency. The production of amplitude-modulated UV pulses opens up the way to the production and maintenance of extended plasma channels in atmospheric air.

Production of extended plasma channels in atmospheric air by amplitude-modulated UV radiation of GARPUN-MTW Ti : sapphire – KrF laser. Part 1. Regenerative amplification of subpicosecond pulses in a wide-aperture electron beam pumped KrF amplifier

Regenerative amplification of single and multiple ultrashort subpicosecond UV pulses in a wide-aperture KrF amplifier with an unstable confocal resonator was investigated on the GARPUN-MTW hybrid laser system. Amplitude-modulated long UV radiation pulses with an energy of several tens of joules were obtained at the output of the system. The pulses were a combination of a quasi-stationary oscillation pulse and a train of amplified ultrashort pulses (USPs) with a peak power of , which exceeded the power of free-running lasing pulse by three orders of magnitude. The population inversion recovery time in the active KrF laser medium was estimated: . Trains of USPs spaced at an interval were shown to exhibit the highest amplification efficiency. The production of amplitude-modulated UV pulses opens up the way to the production and maintenance of extended plasma channels in atmospheric air.

Production of extended plasma channels in atmospheric air by amplitude-modulated UV radiation of GARPUN-MTW Ti : sapphire – KrF laser. Part 2. Accumulation of plasma electrons and electric discharge control

The problem of the production of extended () plasma channels is studied in atmospheric air by amplitude-modulated laser pulses of UV radiation, which are a superposition of a subpicosecond USP train amplified in a regenerative KrF amplifier with an unstable confocal resonator and a quasi-stationary lasing pulse. The USPs possess a high () peak power and efficiently ionise oxygen molecules due to multiphoton ionisation, and the quasi-stationary lasing pulse, which has a relatively long duration (), maintains the electron density at a level by suppressing electron attachment to oxygen. Experiments in laser triggering of high-voltage electric discharges suggest that the use of combined pulses results in a significant lowering of the breakdown threshold and enables controlling the discharge trajectory with a higher efficiency in comparison with smooth pulses. It was shown that controlled breakdowns may develop with a delay of tens of microseconds relative to the laser pulse, which is many orders of magnitude greater than the lifetime of free electrons in the laser-induced plasma. We propose a mechanism for this breakdown, which involves speeding-up of the avalanche ionisation of the air by negative molecular oxygen ions with a low electron binding energy () and a long lifetime (), which are produced upon cessation of the laser pulse.

Study of the structure and parameters of a KrF excimer laser beam

For a KrF excimer laser with a confocal unstable resonator, energy distribution over the beam cross-section was measured with the aid of luminescence in the glass induced by the UV laser radiation. A complex fine structure of the beam has been found. In an area close to the focus, measurements were carried out by means of two different methods—via thermal paper blackening and via ablation craters on a glass surface. The complex beam structure above has been shown to persist also in the immediate vicinity of the beam waist. Measured cross-sectional waist dimensions varied significantly within a range from 0.3 to 0.6–1.3 mrad depending on the measuring procedure applied. Using a short-focus nonaberrational lens one could obtain a focal spot with linear dimensions of several tens of micrometers.

Influence of thermal deformations of resonators on propagation properties of laser annular beams through turbulent atmosphere

Based on the laser field from a positive confocal unstable resonator, considering the influence of thermal distortion of the internal resonator mirror on the annular beam, the propagation characteristics of the annular beam through turbulent atmosphere are investigated by means of the fast Fourier transform algorithm (FFT). The intensity distributions of the output laser far-field are obtained to analyze the propagation characteristics of laser annular beam through the turbulent atmosphere, which is a function about different propagation distances. The results show that the peak intensity of the laser pattern becomes depressed and the spread of the far field diagram patterns is broadened under the increasing of the transmission distance and the thermal distortion of the laser resonator. β-parameter and strehl ratio are introduced to estimate the annular beam quality characteristics. It is found that the annular beam through strong turbulence influences much less obviously than the annular beam through weak turbulence on the quality characteristics with thermal distortion. In the same atmospheric conditions with a certain distance, the greater the mirror thermal distortion is, the worse the annular beam quality characteristics is.

Excess noise in strip off-axis confocal unstable resonators

The lowest-loss mode and higher-order modes in strip off-axis confocal unstable resonators are calculated by the eigenvector method. The moduli of all pairs of the adjacent order eigenvalues exhibit crossing behavior. For the lowest- and next-lowest-loss modes, crossings occur when the equivalent Fresnel number N eq is close to s + 0.08 (s positive integer), and the lowest-loss mode profile calculated by the Fox–Li iteration is no longer self-reproducing, but the superposition of both eigenmodes with unfixed complex weights varies as the number of iterations. Numerical calculations of excess noise factors K in strip off-axis confocal unstable resonators are described in detail. The value of K shows an irregular resonance switching against N eq. The hybrid model presented by van Eijkelenborg et al. is modified in this paper, and shows a good quantitative agreement with nonorthogonality theory.

Mode calculations in asymmetrically aberrated laser resonators using the Huygens–Fresnel kernel formulation

A theoretical framework is presented for calculating three-dimensional resonator modes of both stable and unstable laser resonators. The resonant modes of an optical resonator are computed using a kernel formulation of the resonator round-trip Huygens-Fresnel diffraction integral. To substantiate the validity of this method, both stable and unstable resonator mode results are presented. The predicted lowest loss and higher order modes of a semi-confocal stable resonator are in agreement with the analytic formulation. Higher order modes are determined for an asymmetrically aberrated confocal unstable resonator, whose lowest loss unaberrated mode is consistent with published results. The three-dimensional kernel method provides a means to evaluate multi-mode configurations with two-dimensional aberrations that cannot be decomposed into one-dimensional representations.