Higher-order Laguerre-Gauss mode generation and interferometry for gravitational wave detectors

We report on the first experimental demonstration of higher-order Laguerre-Gauss (LG(p)(?)) mode generation and interferometry using a method scalable to the requirements of gravitational wave (GW) detection. GW detectors which use higher-order LG(p)(?) modes will be less susceptible to mirror thermal noise, which is expected to limit the sensitivity of all currently planned terrestrial detectors. We used a diffractive optic and a mode-cleaner cavity to convert a fundamental LG(0)(0) Gaussian beam into an LG(3)(3) mode with a purity of 98%. The ratio between the power of the LG(0)(0) mode of our laser and the power of the LG(3)(3) transmitted by the cavity was 36%. By measuring the transmission of our setup using the LG(0)(0), we inferred that the conversion efficiency specific to the LG(3)(3) mode was 49%. We illuminated a Michelson interferometer with the LG(3)(3) beam and achieved a visibility of 97%.     

Influence of spatial mode matching in end-pumped solid state lasers

We present investigations on the influence of mode matching on the efficiency of longitudinally pumped solid state lasers. In a theoretical part we enhance an existing model for four level lasers from idealized cylindrical modes to arbitary pump and laser modes in a random relative position thereby neglecting beam deformation due to thermal effects. The theoretical predictions were confirmed experimentally with an end-pumped Nd:YAG rod operated at 1064 nm. To investigate the effect of misalignment on the efficiency we used a Ti-Sapphire pump laser which was displaced relative to the laser beam. To establish the influence of arbitary pump modes on laser performance a diode laser equipped with coupling optics served as pump source for the same resonator. The resulting decrease in slope efficiency compared to the Ti-Sapphire pumped system could be explained in terms of limited mode overlap due to the characteristic pump field distribution produced by the diode coupling optics.     

A continuous-mode model of the mode locking in a pump-modulated laser

The active mode-locking process of the multimode laser with an external pump modulation is theoretically investigated in the frequency domain within the framework of the continuous-mode approximation. Intermode interaction and mode-coupling effects, including both AM and FM modulations, are naturally considered in a hierarchical equation of the mode components derived from the multimode Maxwell-Bloch equations. It is reduced to a continuous-mode equation that can be solved analytically in a stationary case, and used to discuss the spectral line shape and the phase dynamics of mode-components as a function of modulation amplitude and detuning of the modulation frequency. We predict a novel oscillation existing below the threshold of the ordinary complete mode-locking: The intensity of the total electric field yields a stable pulse train but its phase varies irregularly in time. This semi-locked state is characterized by a nonlinear chirping, an asymmetric spectrum, and drifting phases of the field mode-components.     

Laguerre-Gaussian modes selection in diode-pumped solid-state lasers

Over the last twenty years, diode pumping of solid-state lasers has opened new prospects for the mode control and formation of Laguerre-Gaussian (LG) beams, enabling a large variety of applications. Experiments on scalar and vector LG modes selection in Nd³⁺- and Yb³⁺-doped ceramics and crystal lasers carried out at the Institute for Laser Science, Tokyo are reviewed. Selection of LG modes from low to high orders using intra-cavity elements, polarization-selective mirrors, or shaping the pump beam profile, is considered. Illustrations of record-high-order LG hollow modes, multiring modes with highly directional propagation properties, characteristics of cw and pulsed lasers with radially or azimuthally polarized beams of high polarization purity are presented. General solutions of the wave equation for the axi-symmetric electric field, which describe LG beams of various profiles, are proposed for data analysis. In parallel, a short review on LG modes selection studies carried out at other laboratories is given.     

Effect of the spiral phase element on the radial-polarization (0, 1) LG beam

Radially-polarized beams can be strongly amplified without significant birefringent-induced aberrations. However, radially-polarized beam is a high-order beam, and therefore has to be transformed into a fundamental Gaussian beam for reduction the beam-propagation factor M². In effort to transform the radially-polarized beam to a nearly-Gaussian beam, we consider effect of a spiral phase element (SPE) on the Laguerre-Gaussian (LG) (0, 1)^∗ beam with radial polarization, and compare this with the case when the input beam is a LG (0, 1)^∗ beam with spiral phase and uniform or random polarization. The LG (0, 1)^∗ beam with radial polarization, despite its identity in intensity profile to the beam with spiral phase, has distinctly different properties when interacting with the SPE. With the SPE and spatial filter, we transformed the radially-polarized (0, 1)^∗ mode with M² = 2.8 to a nearly-Gaussian beam with M² = 1.7. Measured transformation efficiency was 50%, and the beam brightness P/(M²)² was practically unchanged. The SPE affects polarization state of the radially-polarized beam, leading to appearance of spin angular momentum in the beam center at the far-field.     

Temporal synchronization of independently tunable single longitudinal mode hybrid CO2 lasers

We report a quantitative study of temporal synchronization of two independently tunable, single longitudinal mode, hybrid CO₂ lasers, sharing a common high pressure section. The theoretical estimates for the dependence of the laser pulse build up time on the cw section pressure are in satisfactory agreement with the experimental results. Further, we show that temporal synchronization over a larger frequency range with no significant degradation of peak power or longitudinal mode selection is possible, by utilising the cw section gain length and cavity Q as additional control parameters.     

LD end pumped, actively mode locked and passively Q-switched Nd:YAP laser at 1341 nm

An end pumped Nd:YAP laser at 1341 nm is actively mode locked and passively Q-switched. Pumping was done with a pulsed high power laser diode with maximum power 425 W. V³⁺:YAG with 61% initial transmission served as saturable absorber, and an acousto-optic modulator is used for active mode locking. The output pulse train with 69 ns duration has a total energy of 3.2 mJ with ±4% shot-to-shot fluctuation. The peak output energy of a single mode locked pulse is 0.25 mJ. The pulse duration of a single mode locked pulse is less than 800 ps. The output laser beam is nearly diffraction limited with 1.6 mm diameter, and beam propagation factor M² about 1.3.     

Calculation of optimal fiber radius and whispering-gallery mode spectra for a fiber-coupled microsphere

Coupled-mode theory is used to numerically calculate the coupling coefficients between the modes of a tapered fiber and those of a fused-silica microsphere. In the visible and near-infrared wavelength ranges, typical tapered fibers are multimode. To maximize the photon tunneling from the fundamental fiber mode to the microsphere whispering-gallery mode and to minimize the tunneling from the sphere to higher-order fiber modes, the optimal fiber radius is found to be somewhat smaller than that for phase matching. Also calculated are whispering-gallery mode spectra that take into account the eccentricity of the microsphere and the fact that in an experiment the tapered fiber is not necessarily perfectly aligned with the equatorial plane of the microsphere.     

High efficiency TEM00 mode, diode-pumped, conduction-cooled, Nd:YAG zig-zag slab laser

We report a compact, conduction-cooled, highly efficient, continuous wave (CW) Nd:YAG slab laser in diode-side-pumped geometry. To achieve high efficiency, a novel laser head for Nd:YAG slab has been developed. For an absorbed pump power of 27.6 W, maximum output power of 10.4 W in multimode and 8.2 W in near-diffraction-limited beam quality has been obtained. Slope and optical-to-optical conversion efficiencies are 45.3% and 37.7% in multimode with beam quality factors (M²) in x and y directions equal to 32 and 8, respectively. TEM₀₀ mode operation was achieved in a hybrid resonator with slope and optical-to-optical conversion efficiencies of 43.2% and 29.7%, respectively. Beam quality factors in x and y directions are ?1.5 and ?1.6 for the whole output power range. The laser radiation was linearly polarized and polarization contrast ratios are >1200:1 in the multimode and 1800:1 in the TEM₀₀ mode operation. In passive Q-switching with Cr⁴⁺:YAG crystal of 68% initial transmission, 18 ns pulsewidth has been achieved with an average power of 2 W at a repetition rate of 16 kHz.     

Generation of thin and hollow beams by the axicon with a large open angle

We propose a method to produce diffraction-free thin and hollow beams. The method is based on Laguerre-Gaussian (LG) beams incident on a large open-angle axicon. We use the vector diffraction integrals and stationary phase method to deduce a simple and analytical formula of the propagating field of the linearly polarized LG beams through an axicon. The numerical results show that the hollow beams of whose diameter is in the order of the wavelength can be obtained by using the axicon with the refractive index n = 2 and the open angle α = 25°. These diffraction-free thin and hollow beams may be very useful to accurately trap and manipulate atoms. However, when the open angle is over large, the conversion efficiency from the LG beam to the diffraction-free hollow beam will decrease obviously.     

Controlled two-pulse generation in Q-switch mode from a single laser using Q-modulator with frustrated total internal reflection

In this work a cavity design for double-pulse generation in Q-switched mode from a single laser is proposed, based on the construction of a second laser channel using a FTIR (frustrated total internal reflection) Q-modulator. A time interval between the two pulses from 500 ns to 120 μs is obtained in a Nd:YAG laser. A comparison with other methods and cavity designs for double-pulse generation is presented. The case when this technique is applied on a tunable laser with metastable upper laser level (Cr:LiCAF, Cr:LiSAF, Alexandrite, Co:MgF₂ or other) is also considered. Even though the method presented in the paper does not rely only on the cavity configuration proposed, some advantages can be obtained – both polarization and wavelength-independent tuning without polarization and wavelength restrictions in combination with the possibility of different wavelengths and polarizations in each pulse. Moreover, by using an active medium generating wavelengths around and up to 3 μm, the Pockels-cell-Q-switch optical transmission problems can be avoided. Received: 9 May 2001 / Revised version: 2 August 2001 / Published online: 15 October 2001     

Passive mode locking of thin-disk lasers: effects of spatial hole burning

We recently demonstrated that passive mode locking of a thin-disk Yb:YAG laser is possible and that this concept leads to sources of femtosecond pulses with very high average power. Here we discuss in detail the effect of spatial hole burning on the mode-locking behavior of such lasers. We have developed an efficient numerical model and arrive at quantitative stability criteria which agree well with experimental data. The main result is that stable soliton mode locking can in general be obtained only in a certain range of pulse durations. We use our model to investigate the influence of various cavity parameters and the situation for different gain media. We also consider several methods to reduce the effect of spatial hole burning in order to expand the range of possible pulse durations. Received: 4 September 2000 / Published online: 10 January 2001     

Numerical study of active mode locking in pulsed solid-state lasers

Transient mode locking of spiking solid-state lasers is studied with the help of two theoretical approaches. The first of them is an extension of the previous transient theory with single-mode rate equations to find the limited spike build-up time depending on the modulation index. The second is based on semiclassical multimode equations describing both spiking behaviour and formation of the picosecond pulse from the initial noise. The derivation of the equations as well as a comparison of results from both approaches are given. The obtained numerical results agree with experimental data. It is shown that the pulsewidth in a spiking laser can approach the small value predicted by the steady-state theory. This minimal pulsewidth can be reached at a smaller modulation index than predicted by the standard transient mode locking theory. The minimal modulation index for generation of good picosecond pulses free of noise is found to be 0.6 in our case. Losses connected with amplitude modulation have a negligible effect on spike build-up time and pulse duration.     

Laser mode manipulation by intracavity dynamic holography: Application to mode selection

Intra-cavity dynamic holography is proposed as a self-adaptive, easy to set up technique for efficient laser mode manipulation. A first implementation is presented here as a longitudinal mode selector providing a spectacular spectral narrowing in linear laser cavities operating both in the pulsed and the cw regimes. Received: 12 April 1999 / Published online: 24 June 1999     

Additive-pulse mode locking of a diode-pumped Nd3+:YVO4 laser

We demonstrate self-starting additive-pulse mode locking of a diode-pumped Nd³⁺:YVO₄ laser. Pulse durations of 2.7 ps are measured at a repetition frequency of 90.7 MHz and at an average output power of 1.1 W. This corresponds to a peak power of 4.5 kW. Received: 27 June 2001 / Revised version: 10 October 2001 / Published online: 29 November 2001     

Photonic crystal fiber for fundamental mode operation of multicore fiber lasers and amplifiers

A mode-selection method based on a single-mode photonic crystal fiber (PCF) in the multicore fiber (MCF) lasers is presented. The designed PCF has a central core region formed by a missing air-hole, and three air-hole rings. With an appropriate choice of the design parameters of the PCF, the power coupling between the fundamental mode (FM) of the PCF and the fundamental MCF mode can be much higher than those between the FM and the other supermodes. As a result, the fundamental MCF mode has the maximum power reflection coefficient on the right-hand side of the MCF laser cavity, and dominates the output laser power. Since the maximum power of the fundamental MCF mode will lead to the desired laser beam profile, higher the fraction of the fundamental MCF mode power contained in the total output power contributes to higher beam quality. The numerical simulations show that the effectiveness of the fundamental MCF mode-selection is higher in the MCF lasers with the PCF as a mode-selection component than in the MCF lasers based on the free-space Talbot cavity method. Additionally, for the MCF amplifiers, an approach is presented to decrease the sensitivity of the amplifier performance to the variation of Gaussian beam waist utilizing the coupling between the Gaussian beam and the FM of the PCF. The numerical results show that this method can effectively increase the design flexibility for a broad range of the Gaussian beam waist.     

Theory of passive mode locking of colour-center lasers by a fast saturable absorber

A theoretical model of passive mode locking of colour-center lasers by an effective fast saturable absorber is presented where a hybrid saturation scheme is applied to consider the interaction of the mode-locked pulse with the gain medium. Intracavity group-velocity dispersion and Kerr-type nonlinearity are taken into account and their combined action can result in solition-like pulse shaping and shortening. Chirped steady-state solutions whose carrier frequency can be shifted with respect to the central frequency of the gain are found in a limited range of the parameters specifying the problem.     

Generation of a radially polarized doughnut mode of high quality

We present an experimental set-up to generate laser beams with locally varying polarization distribution. In a linear set-up, a radially polarized beam of high quality regarding intensity distribution, polarization and phase-front distortion is generated. This beam can be used for tight focusing. Further applications are discussed.     

Single longitudinal mode interaction between a uranium atomic beam and a modified Hänsch-type pulsed dye laser

Laser-induced fluorescence is used as a diagnostic tool for testing the tuning between a longitudinal mode of a nitrogen-pumped dye laser and a uranium spectroscopic level in an atomic beam. According to a simple resonator model, the tuning instabilities can be ascribed to thermal drifts in the dye-laser system. Problems encountered in attempting a single mode scanning are also described.The work described in this paper was carried out at the ENEA Laboratory while P. Benetti was assigned to this Laboratory (1981)     

Frequency stabilization and transverse mode discrimination in injection-seeded unstable resonator TEA CO2 lasers

Longitudinal mode selection by injection has been demonstrated as a viable technique for TEA-CO₂ lasers with pulse energies of a Joule or greater. Once reliable generation of single-longitudinal-mode (SLM) pulses is obtained, one can study the characteristics and the causes of intrapulse frequency variation. These include the effect of the decaying plasma, the thermal gradient due to the energy dissipation associated with the laser mechanism itself, and the pressure shift of the center frequency of the laser transition. The use of the positive-branch unstable resonator as an efficient means of coupling a discharge with large spatial dimensions to an optical cavity mode introduces another concern: namely, what can be done to emphasize transverse mode discrimination in an unstable resonator cavity while maintaining high coupling efficiency. These issues are discussed in this paper, and relevant experimental results are included.