Intracavity Aberration Research Articles

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.

Generation of higher-order Laguerre–Gaussian modes from a diode-pumped Pr3+:LiYF4 laser with an intra-cavity spherical aberration

We demonstrate, for the first time to the best of our knowledge, the direct generation of higher-order Laguerre–Gaussian (LG) petal modes, formed of the coherent superposition of positive and negative LG modes with the topological charge of ± ℓ as an eigen mode, from a compact diode end-pumped P r 3 + : L i Y F 4 (YLF) laser with an intra-cavity lens configuration. The on-axis displacement of the intra-cavity lens with spherical aberration allows the selective operation of the desired higher-order LG modes with | ℓ | ≤ 31 from the laser cavity at 640 nm and 607 nm. Such visible higher-order LG modes will offer new applications in optical manipulation, quantum/optical underwater telecommunication, and microfabrication.

Intra-Cavity Adaptive Correction of a Unidirectional Nd:YAG Slab Unstable Travelling-Wave Resonator

The required surface shape of the intra-cavity deformable mirror (DM) is not conjugate with the aberration in an unstable standing-wave resonator, which makes the adaptive correction inside the resonator complicated. In this letter, an unstable travelling-wave resonator structure with an intra-cavity adaptive optics (AO) system is proposed to solve this problem. More specifically, the Shark-Hartmann wavefront sensor (SHWFS) and a 980 nm probe beam are employed to measure the aberration of the Nd:YAG slab during lasing operation. A tip/tilt mirror (TTM) is used to correct the intra-cavity tilt, and a DM is employed to compensate for all the remaining intra-cavity aberration. By placing both the wavefront correctors (DM and TTM) and the Nd:YAG slab in the collimated part of the travelling-wave resonator, the required surface shape of the DM is well conjugate with the measured aberration. Experimental results show the proposed method can effectively improve the performance of solid-state slab lasers. After correction, the output power increased from 1312 W to 1587 W, and the corresponding optical-to-optical efficiency increased from 19.5% to 23.6%. Meanwhile, the beam quality <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\beta $ </tex-math></inline-formula> was improved from 9.7 to 1.8.

Adaptive optics compensation inside an Nd: YAG unstable ring laser: Tilt correction performance

The unstable ring resonator is a promising architecture for high power solid-state oscillators with intra-cavity adaptive optics. In this paper, we present adaptive compensation of intra-cavity tilt in an Nd: YAG unstable ring laser using a probe beam and a far-field camera to detect the tilt. A numerical model of the ring resonator is established based on the Fox–Li method, through which the influence of intra-cavity tilt is studied, and the optimal strategy of tilt correction is proposed and evaluated. An experiment with an unstable Nd: YAG slab ring laser is developed. With 40μrad tilt on the zigzag direction and 130μrad tilt on the non-zigzag direction compensated during lasing, the output power increased from 77.2W to 87.0W. The above results lay the foundation for adaptive optics techniques to compensate for the intra-cavity aberrations in high power solid-state unstable ring lasers.

Mode characteristics investigations on a side pumped electro-optic Q-switched Nd:YAG laser

The influence of representative aberration on the performance of a side pumped electro-optic Q-switched Nd:YAG lasers was demonstrated. The spatial and temporal behavior of the laser with intracavity disturbation was modeled using a numerical calculation of the diffraction integral equations and then experimentally characterized. The eigenmode properties, including the coaxial state with thermal effect of the active medium and geometric misalignment of the cavity OC mirror have been analyzed. Zernike polynomials are further adopted to describe beam distortions by combining the model wavefront reconstruction. Experiment illustrates that the lower-order Zernike aberration such as Z3, Z4 Z5 and Z10, etc. caused by the typical phase disturbation will significantly affect the mode characteristics and the uniform symmetry of wavefront. Other related beam properties e.g. PSF can also be acquired by further calculation. In addition, the proposed method has the merit of working stability and high efficiency. Corresponding strategies are suggested to consider active compensation of intracavity aberration in such lasers.

Analysis of mode wavefront characteristics for passively Q-switched slab Nd:YAG laser

The eigenmode of resonators with symmetric circular mirrors used in solid-state lasers is investigated. Further experiments on output beam quality on a passive Q-switched zigzag slab Nd:YAG laser have been performed by adopting Hartmann–Shack and Zernike–mode reconstruction methods. By the means of peak-valley and root mean square errors of the wavefront distribution, each order of Zernike aberrations are achieved accurately. Moreover, the distribution of circle energy in the far-field and corresponding beam evaluation factors can also be obtained by further calculation. Experimental results indicate that the wavefront aberration is mainly concentrated in the first 10 Zernike aberrations, which mainly includes the defocus Z 3 , the low-order astigmatism Z 5 , the coma aberration Z 6 , and the spherical aberration Z 10 , because of the crystal thermal effect and the intracavity phase perturbation. The method can be used to further analyze the compensation of intracavity aberration and optimal design for such lasers.

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.

Analysis of laser modes in high power unstable resonators with intra-cavity wavefront aberrations

A semi-analytical calculation framework is proposed to calculate the eigenmodes of a general laser resonator with arbitrary intra-cavity wavefront aberrations. By solving a linear eigenvalue equation in the complex space, the mode intensity distributions of the eigenmodes in high power unstable resonators are obtained, indicating that due to the aberrations the area of fundamental mode significantly shrinks to form the localized mode with extremely high power intensity. The beam quality, mode area, threshold gain, and operation reliability are compared between the traditional unstable resonator and the one with a graded reflectivity mirror. The simulation results disclose that with a graded reflectivity mirror more high-order modes participate in mode competition and the localized mode effect of fundamental mode is weakened.

Analyzing Output Phase Properties of Confocal Positive-Branch Laser Resonators by Use of Hartmann-Shack Sensor

The effect of intracavity aberrated perturbation on output mode structure properties of passive confocal unstable resonator is been experimentally researched by adopting H-S wavefront sensor and Zernike modal wavefront reconstruction on the basis of numerical simulation. Results show that intracavity tilted perturbation notablely affects outcoupled intensity distribution, and will also increase some high-order aberrations of beam phase properties. However, low-order Zernike tilt aberration is the main component when phase-tilted perturbation is introduced into the resonator. Defocus, astigmatism and coma aberration will all be brought, and also such high-order aberration included in wavefront will directly degrade output beam quality. When correction device of adaptive optics adopted for intracavity aberration correction, correction of tilted aberration should be considered firstly.

Analysis of Maladjustment Sensitivity and Calibration Method for a Positive-Branch Confocal Unstable Resonator

The effect of intracavity aberration perturbation on output mode structure properties of unstable laser resonator is been experimentally researched using Hartmann-Shack wavefront sensor on the basis of numerical analysis. Results show that intracavity tilt aberration notablely affects outcoupled intensity distribution, but only a small intracavity tilt perturbation will not obviously augment the high-order aberrations of beam phase properties. The tilt aberration, coma aberration and astigmatism will all be brought, and also tilt aberration is the main component when intracavity mirrors have a vertical movement along the direction of optic axis. When adaptive optical elements such as deformable mirrors are adopted for intracavity aberration correction, the correction for tilt aberration should be considered firstly.

Non-linear corrections to aberration sensitivity of unstable-cavity geometries

The aberration sensitivity of unstable-cavity geometries is studied by incorporating the change of the ray path by the intra-cavity aberrations in geometric-optic approximation. The first order non-linear correction in a positive branch, confocal unstable cavity is obtained analytically. In particular, as the optic field passes through an aberration plane in which the higher order aberrations are presented, more higher order aberrations are induced on the wavefront of optic field, and the original transverse modes are mixed. This mode mixing is studied by introducing non-constant propagation matrices. Similar to the linear results, we find that the non-linear corrections to aberration sensitivity decreases when geometric magnification or aberration orders increase.

Theoretical analysis of intracavity tilt perturbation and aberration correction for unstable laser resonators

The influence on an outcoupled mode by introducing intracavity tilt perturbation in an unstable resonator is developed. The intra-cavity mode properties and Zernike aberration with the intracavity mirror's misadjustment are calculated theoretically. The experimental results about the relations of intracavity perturbation and the properties of mode aberration are presented by adopting a Shack-Hartmann (H-S) wavefront sensor. The results show that the intracavity perturbation of the concave mirror has a more remarkable effect on outcoupled beam quality than that of the convex mirror. For a large Fresnel-number resonator, the tilt angle of the intracavity mirror has a near-linear relationship with the extracavity Zernike tilt coefficient. The ratio of the tilt aberration coefficient approaches the magnification of the unstable resonator if equivalent perturbation is applied to the concave and convex mirrors, respectively. Furthermore, astigmatism and defocus also increase with tilt aberration of the mode. So an intracavity phase-corrected element used in an unstable resonator will be most effective when placed as near as possible to the concave mirror plane. Based on these results, a control system for correcting intracavity tilt aberrations is established, and the aberration-corrected results are presented.

Unstable resonators of high-power chemical oxygen—iodine lasers

Configurations of unstable resonators are considered depending on the basic parameters of a high-power chemical oxygen—iodine laser and the design of an unstable resonator is proposed which provides the compensation of the inhomogeneity of the small-signal gain downstream of the active medium, a high energy efficiency, and stability to intracavity aberrations. The optical scheme of this resonator is presented and its properties are analysed by simulating numerically the kinetics of the active medium and resonator itself in the diffraction approximation.

Phase correction of radiation emitted by a powerful industrial laser with higher mode selection

Special features of operation of a high-power industrial CO2 laser with selection and correction of the phases of higher transverse modes are investigated theoretically and experimentally. An effective conversion of the higher-mode oscillation field into a narrow beam with inphase optical oscillations with an output power up to 1 kW with the help of a phase corrector is reported for the first time. The angular divergence is reduced to one-third of the value typical of a multimode beam. The physical origin of intracavity aberrations, which deteriorate the beam quality, is analysed. It is shown that the most significant effect is produced by an optical wedge-type aberration emerging due to transverse circulation of the active medium and transverse discharge. The prospects of application of this method for obtaining more powerful narrow laser beams are discussed.

Self-pumped phase-conjugate diode-pumped Nd:YAG loop resonator

We demonstrate a self-pumped phase-conjugate diode-pumped Nd:YAG loop resonator. In the injected configuration a maximum phase-conjugate reflectivity of 32 is obtained. The output beam has a pulse shape of ~30 ns , which shows the self- Q -switching ability of the resonator. By use of a low-refractive-output coupler, a self-starting version was produced. The resonator operated in a stable diffraction-limited TEM(00) mode, even with severe intracavity phase aberrations. A maximum energy of 5.5 mJ (2.4% of the energy of the high-brightness stacks that was incident upon the Nd:YAG crystals) in a 20-ns single-longitudinal-mode pulse was measured.

Gain-grating analysis of a self-starting self-pumped phase-conjugate Nd:YAG loop resonator

We investigate both experimentally and theoretically the contribution of the different gain gratings in a self-starting self-pumped phase-conjugate Nd:YAG loop resonator. Thanks to a transient model, we show that the transmission-grating configuration is more efficient than the reflection-grating configuration, and that their temporal dynamics are different, in agreement with the experiment. Maximum extraction is obtained for the four-grating configuration. The output beam is a high-quality diffraction-limited TEM/sub 00/ mode, even with severe intracavity phase aberrations, and has a single-longitudinal-mode pulse shape of /spl sim/13 ns, with maximum energy of /spl sim/130 mJ up to 30 Hz. We also investigate the role of the output coupler reflectivity on the output pulse energy and formation. Finally, the influence of the different gratings on the ability of such a self-starting loop resonator to correct for polarization distorsions is studied.

Second-order theory of the aberration sensitivity of a positive-branch, confocal unstable cavity

A second-order theory of the aberration sensitivity that is characteristic of a positive-branch, confocal unstable cavity is presented within the framework of the Fresnel–Kirchhoff diffraction integral formulation of the transverse-mode structure. The analysis includes the effects of the ray-trajectory deviation due to the intracavity aberration source and also takes into account diffraction at the cavity feedback aperture. The dependence of the aberration sensitivity on the applied aberration source strength as well as its dependence on the cavity Fresnel number is described. This new analysis shows that the zeroth-order geometric approximation that is due to Anan’ev [ Sov. J. Quantum Electron., Vol. 1, 565 ( 1972)] is obtained in the limit as the applied intracavity aberration strength goes to zero. In addition, the diffractive behavior of the aberration sensitivity is shown to increase to its geometric value as the Fresnel number of the unstable cavity is increased, this increase being more rapid for larger transverse aberration order k.

Unstable-cavity sensitivity to spatially localized intracavity phase aberrations

The geometric theory of the aberration sensitivity of an unstable cavity to a spatially localized intracavity phase distortion is provided. Such a localized perturbation source could be caused by a small imperfection in some intracavity mirror (such as a deformable mirror) or by a turbulence zone in the flow field of a gas-laser gain medium. This geometric theory, first developed by Anan’ev [ Sov. J. Quantum Electron.1, 565 ( 1972)] for a uniformly extended intracavity aberration source completely filling the cavity, yields the cavity phase-weighting coefficients that determine the resultant phase-aberration structure outcoupled from the unstable resonator. The analysis presented here provides the dependence of these coefficients on the cavity magnification, the axial position (with respect to the feedback mirror), the transverse location (with respect to the unperturbed optic axis) of the aberration source, the transverse dimension of the source, and the aberration structure characterizing the source.

Aberration sensitivity of unstable-cavity geometries

This paper presents a tutorial review of the aberration-sensitivity characteristic of unstable-cavity geometries. The general formulation of the set of aberration-sensitivity coefficients for an unstable cavity is provided, and the geometric approximation of their behavior is fully developed. The influence of the diffractive formation of the transverse-mode field distribution on the aberration sensitivity is considered in detail, and the interrelationship between this sensitivity measure and the diffractive transverse-mode discrimination of the cavity is described. The theory is developed for both standing-wave and traveling-wave (ring) cavities. Methods of modifying the aberration-sensitivity behavior for a given unstable-cavity geometry are also considered; these include aperture apodization, intracavity spatial filtering, and intracavity beam rotation. Finally, the application of an intracavity adaptive-optic system for the purpose of transverse-mode control in the presence of uncontrollable intracavity aberration sources is considered from both the geometric and the diffractive theories.

Propriétés spatiales et temporelles des résonateurs lasers munis de miroirs à conjugaison de phase

The properties of laser resonators with one phase-conjugate mirror are reviewed. All these resonators are geometrically stable; their resonant frequencies are determined by the frequencies of the pump waves, while the spacing between the satellite resonant frequencies is fixed by the cavity length. Their diffraction losses are higher on the phase-conjugate mirror than on the conventional mirror. Phase-conjugate resonators are less sensitive to intracavity aberrations than conventional resonators. They can be used for short-pulse compression when the phase-conjugate mirror is produced by degenerate four-wave mixing in a nonlinear medium with pump waves consisting of mode-locked pulse trains. [Translated by the journal]