Phase locking of CO(2) lasers by the use of diffraction effects

A technique to phase lock CO(2) lasers with spatially separated active media was investigated. Only reflective optics (except for the output coupler) were used, in view of applications of this method in the field of high-power lasers. Phase locking was established when the beams of two resonator branches were made to propagate very close to each other along the so-called coupling path. As a result of diffraction effects both resonators were exchanging energy, establishing a phase-locked operation mode when several locking conditions were fulfilled. A maximum coupling coefficient (the ratio between the diffracted intensity in the second cavity and the intercavity intensity in the first resonator) of 2.6% could be achieved. Because phase locking was highly dependent on the difference between the two resonator lengths, a length control that uses a piezoelectric translator connected to one of the resonator mirrors was used. To detect phase locking, the intensity maximum of the interference pattern of the two laser beams was monitored with a fast detector. By application of a ramp signal to the piezoelectric translator and detection of the peak intensity, the locking range could be measured. Up to a mismatch of the resonator lengths of λ/130, locking could be maintained. The measurements were compared with results of a computer simulation with Huygens-Fresnel integrals to describe diffraction and the one-dimensional Maxwellian equations to calculate supermodes and to analyze their stability. The numerical results showed an excellent agreement with the measured values.     

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%.     

Active synchronization and carrier phase locking of two separate mode-locked femtosecond lasers

Two independent mode-locked femtosecond lasers are synchronized to an unprecedented precision. The rms timing jitter between the lasers is 4.3 fs observed within a 160 Hz bandwidth over tens of seconds, or 26 fs within a 50 kHz bandwidth. Novel multi-stage phase-locked loops help to preserve this ultrahigh timing resolution while setting on arbitrary delay between the two pulse trains (0–5 ns). Under such synchronization, phase locking between the carrier frequencies of the two femtosecond lasers has been achieved. It is also demonstrated that the same level of synchronization can be achieved with two lasers at different repetition frequencies.     

Experiments with active phase matching of parallel-amplified Multiline HF laser beams by a phase-locked Mach-Zehnder interferometer

Active phase matching of multiline HF laser beams by means of a phase-locked Mach-Zehnder interferometer was demonstrated by locking the interferometer to the central interference fringe at zero optical path length difference. The central fringe could be found by varying the spectral content of the input beam. Laser amplification in one leg of the interferometer decreased fringe visibility without adversely affecting locking. Single-line fringe patterns produced by an array spectrometer (while the interferometer was operated in its scanning mode) were analyzed to show that no significant dispersion occurred in the amplifier. The techniques developed have potential for measuring dispersion mismatch between larger parallel amplifiers. These experiments demonstrated in principle that a number of multiline HF amplified beams can be recombined and phase-matched to produce a high beam quality output beam.     

On the Determination of Spectral Properties of Non-stationary Radiation

The measurement of the time-dependent spectrum of non-stationary radiation is of interest, for instance, in the field of ultrashort-time spectroscopy using picosecond lasers. The incident non-stationary radiation is characterized by the time-dependent input spectrum. The electric field strength of the radiation in the exit plane of a grating spectrometer and of a prism spectrometer is analysed in terms of its dependence on time and on the spectral coordinate. The action of the grating spectrometer is regarded as a special case of diffraction at an arbitrary diaphragm. The intensity registered by a square-law detector as a function of time and the spectral coordinate (output spectrum) is calculated as a function of the input spectrum. The input spectrum can be determined from the output spectrum by mathematical operations for cases important in practise (very short light-pulses, intrinsically stationary radiation). Moreover, the conditions are investigated under which the output spectrum resembles the input spectrum, taking into account the influence of noise. Two examples of intrinsically stationary radiation (bandwidth-limited pulse, fluorescence of a two-level system) are studied in more detail. For experimental verification the ouput spectrum of a single ultrashort light pulse has been measured under the condition of different spectrometer time constants.     

Experimental demonstration of an optical phased array antenna for laser space communications

The feasibility of an optical phased array antenna applicable for spaceborne laser communications was experimentally demonstrated. Heterodyne optical phase-locked loops provide for a defined phase relationship between the collimated output beams of three single-mode fibers. In the far field the beams interfere with a measured efficiency of 99%. The main lobe of the interference pattern can be moved by phase shifting the subaperture output beams. The setup permitted agile beam steering within an angular range of 1 mr and a response time of 0.7 ms. We propose an operational optical phased array antenna fed by seven lasers, featuring high transmit power and redundance.     

A Stabilized HCN Laser for Infrared Frequency Synthesis

Infrared frequencies have recently been synthesized in suitable diodes up to 88 THz with accuracies of parts in 109. Stabilized lasers are necessary in order to make frequency measurements of higher accuracy. The hydrogen-cyanide laser is the lowest frequency basis laser used in these synthesis schemes, and its stabilization has been the subject of recent interest. The laser is stabilized by locking it to a phase-locked microwave reference chain. Two servo loops are utilized. The first loop is a relatively slow frequency-lock loop with the correction applied to a piezoelectric-translator driver. This loop not only accommodates thermal expansion of the laser, but also serves as an acquisition aiding loop for the second servo. The latter is a phase-locked system with the correction applied to the laser discharge current controller. Data regarding the system stability are presented.     

Beam propagation constants for a radial laser array

The beam quality of a radial laser array, quantified in terms of the M(2) propagation constant, is determined as a function of array element configuration. A lower bound on array M(2) is estimated for both phase-locked and nonphase-locked conditions. It is shown that, to achieve near-unity M(2) array, either aperture filling or spatial filtering is required in addition to phase locking. An aperture-filling method suitable for radial arrays of CO(2) slab lasers is presented.     

Instrumentation for multistep excitation of lithium atoms to Rydberg states

We have developed a diode laser apparatus to excite Li from its ground 2S state, through 2P and 3S, to its Rydberg states with three cw diode lasers operating at λ = 671 nm, 813 nm, and 630-635 nm. A He-Ne laser at λ = 633 is sometimes used in place of the 635-nm diode laser for the last step. The output power of each of these lasers was ~1 mW. We describe our technique of locking the first two lasers on Li resonance lines by obtaining a fluorescent signal from the second decay (3S ? 2P) that is normally overpowered by a strong background of fluorescent light from the first decay (2P ? 2S). We used two balanced photodiodes to reject the strong fluorescent light without loss of collection efficiency. A rejection ratio as high as 100 has been obtained.     

The Threshold of Phase Locking in the System of Two Multi-Junction Superconducting Loops

Coherent behavior (phase locking) in the system of two superconducting loops containing arrays of Josephson junctions and influencing each other by means of mutual inductance was numerically investigated. It is shown that under certain conditions the mutual interaction between loops can result in total phase-locking of the system. The threshold of the locking state depends on the strength of the interaction (mutual inductance). It is found that the basic behavior of the system in the phase-locked state can be explained by means of simple model of single multi-junction loop with an effective inductance which depends on mutual inductance. It is shown that synchronization in this system is possible and the mutual interaction increases the stability of phase locking in arrays.     

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.     

Measurement of the Sensitivity Function in a Time-Domain Atomic Interferometer

We present here an analysis of the sensitivity of a time-domain atomic interferometer to the phase noise of the lasers used to manipulate the atomic wave packets. The sensitivity function is calculated in the case of a three-pulse Mach-Zehnder interferometer, which is the configuration of the two inertial sensors we are building at the Laboratoire National de Metrologie et d'Essais-Systeme de References Temps-Espace. We successfully compare this calculation to experimental measurements. The sensitivity of the interferometer is limited by the phase noise of the lasers as well as by residual vibrations. We evaluate the performance that could be obtained with state-of-the-art quartz oscillators, as well as the impact of the residual phase noise of the phase-locked loop. Requirements on the level of vibrations are derived from the same formalism.     

Study of dispersion compensation in femtosecond lasers

Abstract

We present a formal analysis of dispersion compensation in femtosecond lasers and provide a detailed examination of the relevant features in Ti: sapphire and Cr: LiSAF lasers. It is shown that the essential of dispersion compensation up to the fourth order consists of searching for the solutions of a group of three linear equations. With the use of a prism pair, complete compensation of both the second- and the third-order dispersion corresponds to solving two of the three equations with the prism separation and the intraprism beam path length as variables. Owing to the limitations on the practically achievable prism separation and the intraprism path length in a laser set-up, only some of these solutions are physically meaningful; hence both zero second- and third-order cavity dispersion may be realized merely within a certain specific spectral range. The fourth-order dispersion, however, cannot be completely compensated for in this case unless a third control variable is introduced. It is also shown that the dominant parameter in determining the spectral region where dispersion is minimized is the difference between the ratio of the third-order dispersion to the second-order dispersion of the laser rod and that of the selected prism pair material. This also explains the major differences between Ti: sapphire and Cr: LiSAF lasers in terms of dispersion compensation.     

基于光学锁相环的高稳定度激光稳频方法研究

报道了一种基于光学锁相环的高稳定度激光稳频方法,用于提高可调谐外腔半导体激光器(TECDL)的频率稳定度和准确度。自行研制的光学锁相环电路采用数字鉴相与差分运算相结合的方式获得高灵敏度的鉴频鉴相误差信号,并通过高速模拟PID实现整个系统的闭环锁定。利用该光学锁相环系统进行了TECDL偏频锁定至光学频率梳(OFC)的实验,实验结果表明环路锁定后拍频频率波动在±0.3Hz范围内,偏置频率为50MHz时,光学锁相环系统在1s和1000s积分时间的相对阿伦方差分别为1.5×10^-9和8.5×10^-13。系统锁定后,拍频线宽由500kHz压缩至2kHz。该研究表明采用基于光学锁相环的激光稳频方法可以实现亚Hz级的激光频差控制,通过将TECDL偏频锁定至高稳定度的参考激光源可显著提高其频率稳定度,使其能够满足超精密测量、冷原子/离子干涉测量等领域对激光频率稳定度和准确度的要求。     

Characteristics of the injection-locked master-slave lasers

The system of injection-locked master-slave lasers (MSLs) has been studied. The solutions to the rate equations describing the phase-locked state of MSLs have been given. The equation to test the stability of the phase-locked state of slave lasers has been deduced, and the stabilities of the phase-locked state have been studied under the conditions in which the system operates in the in-phase and out-phase modes, respectively. Finally, other properties of phase-locked MSLs have been investigated.     

Toward a 3:1 frequency divider based on parametric oscillation using AgGaS(2) and PPLN crystals

Frequency divide-by-two (2:1) and divide-by-three (3:1) optical parametric oscillators (OPOs) are basic devices for the implementation of future accurate optical frequency division chains. We report our latest development toward a phase-locked 3:1 frequency division of a radiation at lambda(p) approximately 843 nm (355.9 THz), using doubly resonant oscillators (DROs) based on silver gallium sulfide (AgGaS(2 ) or AGS) and multigrating periodically poled lithium niobate (PPLN). Although stable single-mode pair operation is achievable without any active cavity length servo with the AGS-DRO, because of a strong passive thermal feedback servo, the PPLN-DRO requires an active intensity side-of-fringe locking servo to maintain long-term, single-mode pair operation. To overcome the limited idler output power (<1 mW) due to the weak mirror transmissivity at 2.53 mum, a CaF (2) Brewster-oriented plate was inserted in a longer-cavity PPLN-DRO as a variable output coupler. About 3 mW of idler wave is thus coupled outside the cavity, yielding 15 nW of doubled-idler. We obtained a 30 dB signal-to-noise ratio beatnote in a 100 kHz resolution bandwidth of a spectrum analyser. This beat signal will be used to phase-lock the divider.     

Dynamics, bifurcations and chaos in coupled lasers

Experiments and numerical modelling on two different class B lasers that are subjected to external optical light injection are presented. This presentation includes ways of measuring the changes in the laser output, how to numerically describe the systems and how to construct diagrams of the dynamical states in the plane frequency detuning between lasers and injection strength. The scenarios for the semiconductor laser include an area of frequency locking and islands of chaotic behaviour embedded in and mixed with periodic doubling regimes. Using a rate equation model, the largest Lyapunov exponent is calculated as a measure of the stability of equilibriums and the amount of chaos in chaotic regimes. In the solid-state laser case, different dynamical regions were clearly observed. The found boundaries were identified experimentally, using an identification method, and numerically, from bifurcation analysis, as Hopf, saddle-node, period-doubling and torus bifurcations.     

High Transmission LiF Prism Monochromator for Separation of VUV Wavelengths in Frequency Mixing Experiments

Abstract

We describe a simple, high throughput, LiF prism monochromator for the vacuum ultraviolet (VUV). The instrument throughput is 30% at 145 nm and the output can be tuned within the range 120–185 nm. The very high dispersion of LiF in the VUV means that neither narrow slits nor high precision are required. The suitability of this instrument for separation of coherent VUV radiation, generated by four-wave mixing, from the intense fundamental laser radiation (at 212 nm and the visible) is demonstrated. General advantages in throughput, polarization and resistance to radiation damage of such a prism instrument compared to a diffraction grating monochromator are discussed.     

Phase effects in broad-stripe curved-grating distributed feedback heterolasers

Phase effects in AlGaAs/GaAs quantum-well curved-grating distributed feedback (c-DFB) lasers with focused output radiation has been theoretically studied. The results of analysis are compared to experimental data available for the analogous curved-grating distributed Bragg reflector (c-DBR) lasers. It is shown that allowance for the indicated phase effects in the design of a c-DFB laser resonator is of key importance in ensuring the perfect spectral and spatial characteristics of the output radiation of such lasers.     

Long-term frequency stabilization of a continuous-wave tunable laser with the help of a precision wavelengthmeter

For the first time to our knowledge we experimentally demonstrate an efficient method for the reduction of long-term radiation line drift in single-frequency cw Ti:sapphire and dye lasers that relies on a fast and precise wavelengthmeter together with a digital-analog feedback system. Generation line drift of lasers is reduced approximately by an order of magnitude down to 40 MHz/h, which corresponds to the residual drift in readings of the wavelengthmeter itself. The implemented automatic frequency control system allows us to lock the laser generation frequency to a specified absolute value. This approach may be used in single-frequency lasers of different types (solid-state, fiber, diode, dye lasers, etc.) and allows reduction by an order of magnitude or more of the long-term generation line drift in lasers that are not equipped with other systems for long-term stabilization of output radiation frequency.