Unstable Laser Resonators Research Articles

Design of a real-time automatic resonator alignment method for unstable resonators

The auto-alignment method for unstable resonators proposed in this paper innovatively replaces the secondary mirror of traditional unstable resonators with a double-convex lens coated with a high reflective film on one side, and installs the primary mirror on a designed electrically adjustable bracket. During the laser emission process, the computer calculates the relative displacement of the centroid of the far-field spot on the camera detection surface to determine the magnitude of the resonator misalignment, and simultaneously controls the electrically adjustable bracket to complete the compensation for the resonator misalignment. Finally, the experimental results show that when using the real-time automatic resonator alignment method, the output power of the laser remains very stable with a relative standard deviation of the normalized power less than 1.1% (if the auto-alignment method is not adopted, the output power will decay to 89.8% of the peak value). Therefore, this method can effectively solve the resonator misalignment problem of unstable resonator lasers. In addition, this method has the advantages of simple optical path structure and high detection speed while ensuring high accuracy.

4 J unstable cavity direct-liquid-cooled disk laser

A quasi-continuous unstable laser resonator with a direct-liquid-cooled method is developed. The refractive index matching liquid and 10 pieces of 45 m m × 18 m m × 2 m m Nd:YLF crystals with different doping levels are used as coolant and gain media, respectively. The stepped transmittance convex and concave mirrors are used as the cavity mirror to construct the unstable resonator. Experimentally, the flow rate of the coolant is 5 m/s and the effective amplification rate of the unstable cavity is 1.3. A quasi-continuous output single-pulse energy of 4 J is obtained with the optical-optical efficiency of 20%, the repetition frequency of 250 Hz, the wavelength of 1047 nm, and the beam quality factor β of 10 approximately. By introducing an adaptive optical (AO) system into the cavity, a higher power and higher beam quality laser is expected to be achieved.

Fractal light from lasers

Fractals, complex shapes with structure at multiple scales, have long been observed in Nature: as symmetric fractals in plants and sea shells, and as statistical fractals in clouds, mountains and coastlines. With their highly polished spherical mirrors, laser resonators are almost the precise opposite of Nature, and so it came as a surprise when, in 1998, transverse intensity cross-sections of the eigenmodes of unstable canonical resonators were predicted to be fractals [Karman et al., Nature 402, 138 (1999)]. Experimental verification has so far remained elusive. Here we observe a variety of fractal shapes in transverse intensity cross-sections through the lowest-loss eigenmodes of unstable canonical laser resonators, thereby demonstrating the controlled generation of fractal light inside a laser cavity. We also advance the existing theory of fractal laser modes, first by predicting 3D self-similar fractal structure around the centre of the magnified self-conjugate plane, second by showing, quantitatively, that intensity cross-sections are most self-similar in the magnified self-conjugate plane. Our work offers a significant advance in the understanding of a fundamental symmetry of Nature as found in lasers.

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.

Experimental and theoretical study of finite-aperture tapered unstable resonator lasers

We present experimental and theoretical results of a novel finite-aperture tapered unstable resonator laser under pulsed and CW operations. At a current of 16 A an output power of about 10 W is reached. The beam parameter increases from M2 ≈ 10 at P = 1 W to M2 ≈ 20 at P = 10 W. Spatial–temporal simulations were performed to elucidate this experimental finding.

Unstable resonator with reduced output coupling

The properties of a laser beam coupled out of a standard unstable laser resonator are heavily dependent on the chosen resonator magnification. A higher magnification results in a higher output coupling and a better beam quality. But in some configurations, an unstable resonator with a low output coupling in combination with a good beam quality is desirable. In order to reduce the output coupling for a particular resonator, magnification fractions of the outcoupled radiation are reflected back into the cavity. In the confocal case, the output mirror consists of a spherical inner section with a high reflectivity and a flat outer section with a partial reflectivity coating. With the application of the unstable resonator with reduced output coupling (URROC), magnification and output coupling can be adjusted independently from each other and it is possible to get a good beam quality and a high power extraction for lasers with a large low gain medium. The feasibility of this resonator design is examined numerically and experimentally with the help of a chemical oxygen iodine laser.

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.

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.

非稳腔输出环状激光束的聚集分析

非稳腔输出环状激光束的聚集分析

Novel Approach to Finite-Aperture Tapered Unstable Resonator Lasers

We present a novel concept of a finite-aperture tapered unstable resonator laser based on two distributed Bragg reflectors at the rear and front facets with different lateral widths. An analysis of the passive resonator, as well as a spatiotemporal simulation of the active device, is presented. A variation of the ratio between the widths of both Bragg reflectors changes the losses of the lateral modes differently, leading to certain geometries with good modal discrimination and beam quality. The principle of operation is demonstrated by fabrication and experimental characterization of a first-generation of device.

High brightness from unstable resonator mid-IR semiconductor lasers

We compare the performance of several optically pumped unstable resonator semiconductor lasers with cavity lengths of 4, 5, and 6 mm and operating in the mid-IR at 4.7 μm. The unstable resonator lasers (URLs) were fabricated by polishing a diverging cylindrical mirror on one of the facets. In general, the URL beam quality (BQ) was 1–2 times diffraction limited when operated at pump powers below 30 W (URL power ≤6 W) As the pump power is increased, the BQ is observed to degrade; at 60 W the URL’s were ∼3.5 times diffraction limited (URL power ≈11 W). The highest brightness URL, a 4-mm long device, was compared with an equivalent 4-mm long Fabry–Perot (FP) laser operated at different cavity widths. The performance of the broad area URL (500 μm width), as assessed by power-in-the-bucket measurements, was superior to both wide stripe (500 μm) and narrow pump stripe (100 μm) FP lasers.

Nanosecond non-diffracting Bessel green beam generated directly from an unstable resonator by active method

An intracavity frequency-doubled Nd∶YAG nanosecond Bessel green laser is designed in an axicon-based Bessel and Bessel-Gaussian resonator. The unstable laser resonator is composed of a refraction axicon and a convex mirror. The gain medium Nd∶YAG rod is pumped by a single flash-lamp which is working in a pulsed mode and a KTP crystal is used for intracavity second-harmonic generation. Nanosecond Bessel green beam is generated directly from the laser by active method when pumping voltage is 350 V. The pulse with width of 55.1 ns, central wavelength at 532 nm, spectral line width of 0.8 nm and diameter of central spot of 192 μm is obtained. Fresnel-Kirchhoff diffraction integral and the Fox-Li algorithm is used to extract the dominant mode of the cavity and the experimental results are consistent with those of the numerical simulation.

Design of optical coupling systems between two-dimensional quasi-stadium laser diodes and single-mode optical fibers

Optical coupling systems between a two-dimensional quasi-stadium laser diode and single-mode optical fibers using gradient-index rod lenses are designed for both stable and unstable laser resonators for the first time. A novel numerical approach using a combination of the extended Fox-Li calculation method and Gaussian beam transformations is proposed. In the case of a stable laser resonator, two kinds of beam propagation modes appear, namely the axis mode, in which an optical beam propagates along the cavity axis, and the ring mode, in which optical beams propagate along the diamond-shaped trajectory. The coupling efficiencies are found to be 54% for the axis mode and 52% for the ring mode. In contrast, an unstable laser resonator exhibits complicated modes, in which several highly directional beams are emitted from the end mirrors. The total coupling efficiency for these output beams is calculated to be 9.6%. The 3-dB tolerances for the lens pitch and alignment angles of the gradient-index rod lenses are also discussed.

High-Power Tapered Unstable-Resonator Laser Diode With a Fiber-Bragg-Grating Reflector

We designed a tapered unstable-resonator laser diode consisting of a 3-mm-long tapered amplifier and a fiber-Bragg-grating reflector, both of which were coupled with a biconical microlens at the fiber end. The amplifier was composed of an InGaAs single quantum well inside a waveguide, which had an optical confinement factor of 1.2%, a tapered current constriction of 6deg in full angle, and an input width of 10 mum. The grating reflector was fabricated in a polarization-maintaining fiber with a reflectivity of 99% and a reflection bandwidth of 0.19 nm. A biconical microlens with vertical and horizontal radii of 3.5 and 11 mum, respectively, was fabricated at the fiber end to increase the coupling efficiency between the tapered amplifier and the grating reflector. An output power of 3.2 W was obtained at a wavelength of 1064 nm in multimode operation for the grating reflection bandwidth.

Investigation of the convex mirror cooling of a transversely excited atmospheric (TEA) CO2coaxial output unstable resonator laser

A coaxial unstable resonator using a vortex tube to cool a convex mirror has been developed for a transversely excited atmospheric (TEA) CO2 laser. The time dependent thermal deformation of the convex mirror was analyzed by using the finite element method. The simulated results indicate that the vortex-tube-cooling system can remarkably reduce the thermal deformation of the convex mirror, especially at long working times. Also, an experimental verification was carried out, and the results show that the developed vortex-tube-cooling coaxial unstable resonator system is an effective and applicable cooling method for a convex mirror. The divergence angle drops from 3.19 to 1.78 mrad, and the times-diffraction-limit factor β decreases from 6.94 to 1.78 if using the vortex-tube-cooling system when the repetition rate is 3 Hz and the continuous working time is 300 s.

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.

Self-oscillation perturbations in a fast-flow unstable resonator laser

It is shown with the help of numerical simulation that various mechanisms of self-oscillation instability exist and self-oscillation perturbations of various types may appear in an unstable resonator with a transverse flow of the active medium and a nonuniform internal pumping. The interaction of different self-oscillation perturbations, manifested in pulling and locking of oscillation frequencies and a variation of their increments, is studied. Analytic relations describing the spatial structure of perturbation modes and used for evaluating their frequencies and increments from steady-state generation parameters are presented.

Calculating higher-order modes of one-dimensional unstable laser resonators

Methods for calculating the mode profiles of unstable optical resonators are reviewed. Southwell's virtual source method (especially its inherent approximations and range of validity) is examined in depth, and ways of extending the celebrated Fox-Li method to handle higher-order modes are discussed.

Calculating higher-order modes of one-dimensional unstable laser resonators

Abstract Methods for calculating the mode profiles of unstable optical resonators are reviewed. Southwell's virtual source method (especially its inherent approximations and range of validity) is examined in depth, and ways of extending the celebrated Fox-Li method to handle higher-order modes are discussed.

Multifunctional gratings for surface-emitting lasers: design and implementation.

We experimentally demonstrate the use of two different multifunctional grating couplers in surface-emitting lasers for improved beam quality and advanced beam profiles. The lasers used for the demonstration are grating-based unstable resonator lasers, each with a grating coupler for surface emission and beam shaping. The new design method, described in detail, allows for simultaneous optimization of arbitrary feedback and outcoupling characteristics of the grating coupler. The first coupler is designed to reduce feedback to the resonator that would otherwise disturb the operation of the laser and lower the beam quality and to produce an output beam focused to four spots. The second coupler is designed to provide the feedback needed to support the unstable resonator, eliminating one feedback grating, and simultaneously focus the output beam to a single spot. As far as we know, this is the first time such multifunctional couplers are used in grating-coupled surface-emitting lasers. The couplers provide near-diffraction-limited spots that are a considerable improvement compared with previous lasers with no feedback control in the couplers.