Phase Locking of CO(2) Lasers

A method of phase locking two CO(2) lasers by radiation exchange is presented. This phase-locking was achieved by use of a copper prism as a beam folding device in the resonators and extraction of the output radiation by a common output coupler. Energy exchange led to a phase-locked state if several locking conditions were fulfilled. The amount of radiation injected from one resonator to the second cavity could be adjusted by movement of the prism. The influence of the strength of coupling on the locking range was studied. The beat signal between the two unlocked lasers could be measured, whereas in the case of phase-locked operation twice the intensity was detected. Despite the inclusion of several assumptions, a simplified mathematical model delivered good agreement between calculated and experimental results.     

Stable injection locking of diode lasers through a phase-modulated double phase-conjugate mirror

The stable injection locking of 0.8-mum diode lasers with a double phase-conjugate mirror (DPCM) was achieved. Phase modulation by piezoelectric transducers allowed us to keep two input beams of the DPCM mutually incoherent during locking. We preserved the high performance of the DPCM and retained stable locking for more than an hour.     

Ring resonator for lasers with annular gain media

A ring resonator for lasers with annular gain media is presented. The resonator consists of two annular mirrors. While the radiation is reflected back and forth between the two annular mirrors, diffraction effects induce an additional azimuthal radiation flux. Output coupling is obtained through a decentered coupling aperture on the circumference of one of the two mirrors. The azimuthal radiation flux permits the extraction of optical power from the whole gain volume through the coupling aperture. The azimuthal radiation flux can revolve in two directions. The associated modes are degenerate, and random jumping between unidirectional and bidirectional operation is observed. Unidirectional operation has been stabilized but remains very sensitive to mirror alignment. High extraction efficiencies have been demonstrated experimentally with this resonator with a diffusion-cooled CO(2) laser and 2 times diffraction-limited beams have been obtained. An empty resonator model that shows the effect of edge diffraction at the coupling aperture on the resonator modes is also given.     

Manifestation of active medium astigmatism at transverse mode locking in a diode end-pumped stable resonator laser

Transverse mode locking in a diode end-pumped Nd:YAG laser with up to approximately 140 cm resonator length was investigated. It was found that for each resonator degeneracy, there are two degenerate lengths where the fundamental mode is very different from the Gaussian mode. Fundamental mode intensity patterns for these lengths expand in directions perpendicular to each other. Experimental results are in a good agreement with numerical calculations, taking into account active medium (AM) astigmatism and inhomogeneous gain. Optical powers of astigmatic AM can be found directly from measurements of degenerate lengths without using numerical modeling.     

Electromechanical coupling constant extraction of thin-film piezoelectric materials using a bulk acoustic wave resonator

Thin-film piezoelectric materials such as ZnO and AlN have great potential for on-chip devices such as filters, actuators and sensors. The electromechanical coupling constant is an important material parameter which determines the piezoelectric response of these films. This paper presents a technique based on the Butterworth Van-Dyke (BVD) model which, together with a simple one-mask over-moded resonator, can be used to extract the bulk, one-dimensional electromechanical coupling constant K(2) of any piezoelectrically active thin-film. The BVD model is used to explicitly define the series resonance, parallel resonance, and quality factor Q of any given resonating mode. Common methods of defining the series resonance, parallel resonance, and Q are shown to be inaccurate for low coupling, lossy resonators such as the over-moded resonator. Specifically, an electromechanical coupling constant K(2) of (2.6+/-0.1)% was measured for an (002) c-axis textured AlN film with an X-ray diffraction rocking curve of 7.5 degrees using the BVD based extraction technique.     

Two-faceted mirror for active integration of coherent high-power laser beams

A new integration method suited for spatially coherent high-power laser beams is demonstrated. The integrator system is based on a mirror with two facets, one of which can vibrate under the action of a piezoelectric translator. After reflection in the faceted mirror, the beam intensity distribution is modified to obtain greater uniformity. However, because of the coherence of the reflected beamlets, this distribution is affected by an interference pattern. The active integration consists of a periodic displacement of the moving facet that causes the interference pattern to vibrate, and its contribution to the intensity profile therefore averages out (fringe visibility within a 5% range). The combination of a faceted mirror and a simple imaging system results in an intensity profile with good uniformity over large spot sizes. Both simulated and experimental results are presented, the latter showing that a final uniformity within a 10% range can be achieved and it is limited mainly by diffraction at the edges of the facets.     

COIL emission of a modified negative branch confocal unstable resonator

A modified negative branch confocal unstable resonator (MNBUR) was coupled to the chemical oxygen-iodine laser (COIL) device of the German Aerospace Center. It consists of two spherical mirrors and a rectangular scraper for power extraction. Experimentally measured distributions of the near- and far-field intensities and the near-field phase were found in close agreement to numerical calculations. The extracted power came up to approximately 90% of the power as expected for a stable resonator coupled to the same volume of the active medium. The output power revealed a considerable insensitivity towards tilts of the resonator mirrors and the ideal arrangement of the scraper was found to be straightforward by monitoring the near-field distributions of intensity and phase. The beam quality achieved with the MNBUR of an extremely low magnification of only 1.04 was rather poor but nevertheless in accordance with theory. The demonstrated consistency between theory and experiment makes the MNBUR an attractive candidate for lasers that allow for higher magnification. In particular, it promises high brilliance in application to 100 kW class COIL devices, superior to the conventional negative branch confocal unstable resonator.     

L-shaped piezoelectric motor--part I: design and experimental analysis

This paper proposes an L-shaped piezoelectric motor consisting of two piezoelectric bimorphs of different lengths arranged perpendicularly to each other. The coupling of the bending vibration mode of the bimorphs results in an elliptical motion at the tip. A detailed finite element model was developed to optimize the dimensions of bimorph to achieve an effective coupling at the resonance frequency of 246 Hz. The motor was characterized by developing rotational and linear stages. The linear stage was tested with different friction contact surfaces and the maximum velocity was measured to be 12 mm/s. The rotational stage was used to obtain additional performance characteristics from the motor: maximum velocity of 120 rad/s, mechanical torque of 4.7 × 10-(5) N·m, and efficiency of 8.55%.     

Coherent coupling of vertical-cavity surface-emitting laser arrays and efficient beam combining by diffractive optical elements: concept and experimental verification

A phase-locked diode-laser system based on master-slave coupling of two-dimensional vertical-cavity surface-emitting laser (VCSEL) arrays by injection locking is presented. Frequencies and phases are adjusted by laser-trimmed microresistors. Additional beam-transformation optics consisting of two diffractive optical elements (DOEs) and a Fourier lens concentrates most of the far-field power in a nearly diffraction-limited beam. Both the VCSEL array and the microlens array are monolithically integrated and mounted in a compact module. With an array of 21 slave lasers a system coherence of 95% (for several hours) and of nearly 90% (for several months) has been demonstrated without any active phase control. The scalability of the output power has been verified by locking of an array of 77 slave lasers with a system coherence of 78%. The optical system efficiency is 20-23%; with beam-transformation optics this efficiency could be improved to 44%.     

Far field intensity of a partially locked optical phased array

The effects of imperfect frequency locking on the performance of an optical phased array were investigated. An analytic expression was obtained for the far field intensity pattern in terms of the degree of mutual coherence between lasers. The results of the analytical study were applied to determine the Strehl ratio of an injection coupled optical phased array for different degrees of slave resonator length control, ratios of injected to slave laser intensities, and pulse durations.     

Analysis of lasing in gas-flow lasers with stable resonators

A model is developed that describes the power extraction in chemical oxygen-iodine lasers (COIL's) and CO(2) gasdynamic lasers with stable resonators when a large number of transverse Hermite-Gaussian eigenmodes oscillate. The extraction efficiency, mode intensities, and intensity distribution along the flow depend only on two parameters. The first is the ratio gamma(0) of the residence time of the gas in the resonator to the O(2)((1)D) or N(2)(v) energy extraction time and the second is the ratio of the threshold to the small-signal gain. The efficiency is maximum for gamma(0) ? infinity and decreases rapidly as gamma(0) decreases. It is found that for a range of parameters corresponding to the highest efficiencies the intensity distribution along the flow is nonuniform and has two peaks near the upstream and downstream sections of the resonator. In this case only the highest-order modes that totally fill the resonator cross section oscillate (the so-called, experimentally observed sugar scooping bimodal intensity distribution). For the range of parameters corresponding to smaller efficiencies the intensity is uniform. In this case all the modes participate in lasing; however, the intensities of the high-order modes are larger than those of the low order. The current model is compared with the plane-mirror Fabry-Perot resonator model and with the constant intraresonator intensity and rooftop models of COIL's with stable resonators. The extraction efficiency calculated with the last two models is close to that estimated from our model. However, the intensity distribution cannot be calculated correctly using the Fabry-Perot, the constant intraresonator intensity, or the rooftop model.     

Extracting the electromechanical coupling constant of piezoelectric thin film by the high-tone bulk acoustic resonator technique

In this paper, a new approach is proposed to rapidly and accurately measure the electromechanical coupling constant K(t)(2) of thin film piezoelectric material, which is critically important for real-time quality control of the piezoelectric film growth in mass production. An ideal lossy bulk acoustic resonator (LBAR) model is introduced and the theory behind the method is presented. A high-tone bulk acoustic resonator (HBAR) was fabricated on a silicon wafer. The impedance response of the resonator was measured, from which the K(t)(2) of the piezoelectric material was extracted. To illustrate the potential of the proposed technique to extract material properties, two HBAR devices employing AlN as the piezoelectric material were fabricated using an RF sputter system with known good and bad deposition conditions; the extracted K(t)(2) values of the piezoelectric material are compared.     

Picosecond Phase Conjugation and Two-wave Coupling in Strontium Barium Niobate

Abstract

Picosecond phase conjugation and two-wave coupling in cerium-doped strontium barium niobate at 778 nm were studied. The phase conjugation reflectivity at 778 nm was measured to be R _pc = 58%. It is close to that pumped by a continuous-wave pump source. The temporal width t _pc and spectral width δγ_pc of the phase conjugate pulse were measured to be the same as that of the pump pulse. The intensity coupling gain of two-wave coupling as a function of time delay τ_D between two beams was also studied.     

Electric field control of a Bragg diffraction optical beam splitter based on a cubic K(0.99)Li(0.01)Ta(0.63)Nb(0.37)O3 single crystal

We have realized an electric field controlled Bragg diffraction optical beam splitter based on a photorefractive Bragg diffraction grating. In our experiments, the splitter was produced by wave coupling (532.0 nm) with a potassium lithium tantalate niobate single crystal. In the process of splitting, the incident beam could be split into multioutput beams by the splitter. The influence of an externally applied electric field was studied, and the results show that the intensity of the Bragg diffraction could be controlled by the electric field. The polarization properties of the splitter are discussed.     

Characterization of electromechanical coupling coefficients of piezoelectric films using composite resonators

By analyzing the resonance frequency spectrum of a composite resonator consisting of a piezoelectric ceramic film deposited on a substrate plate, the thickness extensional mode electromechanical coupling coefficient of the film, k(t)(2), can be directly calculated from the effective coupling factor values, k(eff )(2), for two special modes of the resonator. The effects of the mechanical loss in the piezoelectric films on the measurement are investigated by numerical simulation, and some guidelines for improving the accuracy of the k(t)(2) measurement are reported.     

Optical-fiber double-loop resonator with a nonplanar 3 × 3 fiber coupler

We present for the first time to our knowledge a new and simple single-mode optical-fiber double-loop resonator. The double-loop resonator consists of two fiber loops constructed from a nonplanar 3 × 3 directional fiber coupler and two fiber delay lines. When the lengths of the fiber loops are different, additional periodic-resonance notches appear. The depths and the positions of these notches depend on the difference between the phase changes, and the coupling of the two fiber loops. This double-loop resonator can be used as a spectral filter and a sensor.     

Finite element modelling of nanostructured piezoelectric resonators (NAPIERs)

A new modification to the traditional piezoelectric thin film bulk acoustic wave resonator (FBAR) and solidly mounted acoustic wave resonator (SMR) is proven to significantly improve their performances. The proposed design involves the surface micro/nano structuring of planar piezoelectric thin films to realize an array of a large number of rod-like structures. In contrast to the plate-like thickness extensional resonance in traditional FBAR and SMR devices, the rod-like structures can be excited in their length extensional resonance, yielding a higher electromechanical coupling factor and effectively eliminating the spurious resonances from lateral modes of vibration. The designs have been investigated by two and three-dimensional finite element analyses and one-dimensional transmissionline modelling. The results show that significant increases in the electromechanical coupling factor of ca. 40% can be achieved by using the rod-like length extensional resonances as compared with the plate-like thickness extensional resonances in traditional devices. Simulations show that rod width-to-thickness aspect ratios of less than 0.5 could result in an electromechanical coupling factor (k2eff) of over 10% for a zinc oxide device, compared with approximately 7% for a conventional design.     

Beam Splitter Model of Two-beam Coupling in Photorefractive Materials

Abstract

The phenomenon of two-beam coupling in photorefractive crystals results from the interaction of two beams with the index grating written by those two beams. In this paper we show that the process can be understood by considering the photorefractive crystal to be a nonlinear beam splitter, with reflectivity and transmission coefficients dependent upon the relative intensities of the two beams. The relative phase relationships upon reflection, determined by the Fresnel equations, as well as the phase shift between the intensity and index grating, are the sources of the asymmetric coupling. A simple derivation of coupled mode equations describing two-beam coupling based upon the beam splitter model is proffered.     

Analysis of nonlinear transient responses of piezoelectric resonators

The electric transient response method is an effective technique to evaluate material constants of piezoelectric ceramics under high-power driving. In this study, we tried to incorporate nonlinear piezoelectric behaviors in the analysis of transient responses. As a base for handling the nonlinear piezoelectric responses, we proposed an assumption that the electric displacement is proportional to the strain without phase lag, which could be described by a real and constant piezoelectric e-coefficient. Piezoelectric constitutive equations including nonlinear responses were proposed to calculate transient responses of a piezoelectric resonator. The envelopes and waveforms of current and vibration velocity in transient responses observed in some piezoelectric ceramics could be fitted with the calculation including nonlinear responses. The procedure for calculation of mechanical quality factor Q(m) for piezoelectric resonators with nonlinear behaviors was also proposed.