Spatial solitons in a semiconductor microresonator

We show experimentally the existence of bright and dark spatial solitons in a passive quantum-well-semi-conductor resonator of large Fresnel number with mixed absorptive defocusing nonlinearity. Several of the solitons can exist simultaneously as required for applications. Received: 17 November 2000 / Published online: 13 December 2000     

Optical target and spiral patterns in a single-mirror feedback scheme

Spatio-temporal structures with a regular time dependence are observed in a nonlinear optical system consisting of a sodium-vapour cell and a single feedback mirror. Target and spiral patterns appear spontaneously in the intensity of the transmitted light field as a result of a self-organisation process. In contrast to the results obtained in most other pattern-forming systems, the radial motion of the waves is directed towards the centre. The emergence of oscillatory structures is traced back to a Hopf bifurcation at a finite wave number. The preference for a radial drift motion is due to a nonlinear guiding effect which results from phase gradients created by the inhomogeneous pump profile. The direction of the drift can be reversed by externally applied phase gradients. The system is a striking example of a case in which the radial variation of the pump profile has a decisive influence on pattern formation. Received: 31 July 2002 / Revised version: 30 October 2002 / Published online: 26 February 2003 RID="*" ID="*"Corresponding author. Fax: +49-251/83-33513, E-mail: huneus@uni-muenster.de     

Multiple-pattern stability in a photorefractive feedback system

We report on the observation of a multiple-pattern stability region in a photorefractive single-feedback system. Whereas hexagonal patterns are predominant for feedback with positive diffraction length we show that a variety of stable non-hexagonal patterns are generated for certain negative diffraction lengths. For the same values of the control parameters square, rectangular, or squeezed hexagonal patterns are found alternating in time. Besides these pure states, we found a number of different mixed-pattern states. We review the linear stability analysis for this system and show that the special shape of the threshold curves in the investigated parameter region gives a first explanation for the occurrence of a multiple-pattern region. Received: 22 June 1999 / Revised version: 30 August 1999 / Published online: 3 November 1999     

Incoherent optical switching of semiconductor resonator solitons

We demonstrate experimentally the bistable nature of the bright resonator solitons in a semiconductor microresonator with mixed absorptive/defocusing nonlinearity and show that they can be written and erased by incoherent local optical injection. Received: 22 February 2001 / Published online: 27 April 2001     

Optical pattern formation in alkali metal vapors: Mechanisms, phenomena and use

The phenomena in optical pattern formation are reviewed using a single mirror feedback experiment as an example. The nonlinear medium is sodium metal vapor. We discuss the mechanism responsible for the spontaneous formation of spatial structures and the selection between simple periodic patterns as hexagons and squares. Introducing a polarization changing element in the feedback loop, quasiperiodic patterns with a twelve-fold rotational symmetry are obtained and their properties are studied by filtering methods in Fourier space. Finally, we discuss the formation of localized states as spatial solitons due to a self-induced lensing effect. Their interaction is studied and the formation of clusters provides a link between localized states and extended patterns. Genuine optical features, such as the polarization degrees of freedom, the experimental accessibility of the Fourier space, and the possibility to control the optical susceptibility of atomic vapors by means of an external magnetic field, provide very powerful tools for investigating the principles of pattern formation. Received: 15 July 2000 / Revised version: 7 November 2000 / Published online: 6 December 2000     

Coherent switching of semiconductor resonator solitons

We demonstrate the switching on and off of spatial solitons in a semiconductor microresonator by injection of light coherent with the background illumination. The results give evidence that the formation of the solitons and their switching are not limited by thermal processes. Received: 11 February 2002 / Revised version: 25 April 2002 / Published online: 8 August 2002     

Counterpropagating pattern dynamics: From narrow to broad beams

The development of patterns in counterpropagating (CP) beams in saturable Kerr-like media is investigated in a numerical study, by varying the width of beams. A model of interacting mutually incoherent beams is adopted, with slow local changes in the index of refraction, and a numerical simulation of propagating beams is performed for different values of the driving parameters. Linear stability analysis (LSA) of CP beams is carried out, and a modulational instability threshold for the appearance of side beams is determined. The results of LSA, concerning the instability of plane waves, are compared with the numerical results concerning broad hyper-Gaussian beams whose width is varied. Qualitative agreement is found, due to the similarity between plane waves and flat-top hyper-Gaussian beam profiles. Owing to very slow quasi-steady-state changes in the system during time evolution, the transverse characteristics of beam distributions, determined by LSA, are found to persist for long in the transient evolution of CP beams.     

Transverse effects and mode couplings in OPOS

00 pump field. The corresponding differential equations for the time evolution of the self-consistent mode amplitudes are derived for typical cavity geometries including the propagation integrals within the crystal. We discuss the new physical effects introduced by these couplings in some typical cases. This includes a change of the OPO threshold and stable simultaneous oscillation of several mode pairs with fixed relative phases as well as oscillating self-pulsing type solutions. Received: 12 January 1998/Accepted: 11 February 1998     

Numerical analysis of the spatial behaviour of nanosecond optical parametric oscillators of beta-barium borate

We report on a numerical analysis of the temporal and spatial beam properties of nanosecond optical parametric oscillators (OPOs). The analysis is performed for a 355-nm-pumped critically phase-matched OPO of beta-barium borate. The calculations provide detailed information on the dependence of the OPO beam quality (measured by the quality factor M ²) on pump energy. An important result is the strong increase of the M ² value for pump energies exceeding 1–2 times the energy at threshold. Furthermore, a temporal analysis of single OPO pulses indicates that the M ² value strongly increases during the first few nanoseconds of the OPO oscillation. This increase is understood by considering the temporal dynamics of the spatial profiles of the OPO signal beam and the depleted pump radiation. Received: 1 April 1999 / Revised version: 26 July 1999 / Published online: 20 October 1999     

Reduction of the specular reflectivity from Feinberg’s Cat conjugator operating in auto-oscillation mode

An incomplete correlation is discovered between the phase conjugate reflectivity in Feinberg’s Cat conjugator generating a train of regular pulses with the cw incident pump wave and inhibited specular reflectivity from the sample. The frequency chirp within every spike of conjugate wave is shown to affect the efficiency of the secondary phase conjugator generating auxiliary waves in the direction of Fresnel reflection of the incident wave. Received: 25 November 1998 / Revised version: 11 January 1999 / Published online: 31 March 1999     

Multiline coherent oscillation in photorefractive crystals with two species of movable carriers

The coherent oscillation, because of nearly degenerate four-wave mixing in photorefractive crystals with two types of movable charge carriers, occurs at two spectral lines symmetrically shifted with respect to the pump frequency. Consequently the output oscillation exhibits the high contrast intensity modulation. The frequency separation of two oscillation modes (and modulation frequency of the output intensity) depend on the incident light intensity and spatial frequency of the developing grating. A model is presented explaining this type of oscillation by the two-maxima shape of the gain spectrum in crystals with sufficiently different relaxation times of two space-charge gratings, one formed by movable electrons and the other one by movable holes. The experimental data for coherent oscillator with tin hypothiodiphosphate (Sn₂P₂S₆) are in reasonable quantitative agreement with the calculations. Received: 12 November 1998 / Revised version: 11 January 1999 / Published online: 7 April 1999     

Intensity noise of pump-enhanced continuous-wave optical parametric oscillators

4 (RTA), which provides a threshold pump power of 16 mW. The maximum signal wave power is 23 mW at a wavelength of 1243 nm. The spectral bandwidth of the signal wave is less than 750 kHz. Received: 3 February 1998     

Coherent anti-Stokes Raman scattering velocimetry with nearly degenerate pumps

The time evolution of the anti-Stokes signal produced from the non-linear interaction of a short Stokes pulse and two long pump pulses that are nearly degenerate in frequency has been investigated. It is shown that this approach allows us to specify the accuracy of CARS (coherent anti-Stokes Raman scattering) velocimetry and to extend the range of operation of the method. In addition, an original optical scheme capable of delivering short visible pulses with good spatial and spectral properties is reported. The optical bench has been used for the characterisation of a low-pressure laminar Mach-10 flow. Received: 24 October 2001 / Revised version: 8 January 2002 / Published online: 14 March 2002     

Intracavity frequency mixing in pulsed optical parametric oscillators for the efficient generation of continuously tunable ultraviolet radiation

Received: 4 May 1998/Revised version: 8 July 1998     

Femtosecond nonresonant degenerate four-wave mixing at atmospheric pressure and in a free jet

2 , N₂, and CO₂. For CO₂ additional experiments have been performed at reduced pressure and in a molecular beam. By delaying the probe pulse a periodic recovery of the DFWM signal is observed. The period of these transients can be assigned unambiguously to rotational Raman transitions of the ground state within the laser bandwidth. The decay of the transients yields the collisional dephasing of the Raman-induced polarization. At zero delay also optical-field-induced birefringence of electronic nature contributes to the signal. The different time scales of the Raman and electronic effects allow us to estimate their relative strength. Received: 3 August 1998 / Revised version: 21 October 1998 / Published online: 24 February 1999     

Broadband degenerate four-wave mixing of OH for flame thermometry

Received: 7 July 1997/Revised version: 23 December 1997     

Exact solutions of discrete complex cubic-quintic Ginzburg-Landau equation with non-local quintic term

In this paper, via the extended tanh-function approach, the abundant exact solutions for discrete complex cubic-quintic Ginzburg-Landau equation, including chirpless bright soliton, chirpless dark soliton, constant magnitude solution (plane wave solution), triangular function solutions and some solutions with alternating phases, etc. are obtained. Meanwhile, the range of parameters where some exact solution exist are given. Among these solutions, solutions with alternating phases do not have continuous analogs. Moreover, in the lattice, the points of singularity of tan-type and sec-type solutions can be ‘between sites’ and thus the singularities can be avoided.     

Investigation of the spatial beam quality of pulsed ns-OPOs

This paper reports on an experimental investigation of the spatial beam quality of a pulsed nanosecond optical parametric oscillator (OPO). The OPO is a 355 nm pumped type-I BBO-OPO. The spatial quality of the OPO output is characterized by the M²-parameter in dependence of other experimental parameters such as resonator length, pump-beam diameter, pump-pulse duration and pump energy. The results obtained indicate, that an appropriate choice of these parameters substantially improves the spatial beam quality of the OPO output. Received: 19 November 2002 / Revised version: 3 February 2003 / Published online: 5 May 2003 RID="*" ID="*"Corresponding author. Fax: +49-631/205-3906, E-mail: anstett@rhrk.uni-kl.de     

Optical parametric oscillators for high pulse energy and high average power operation based on large aperture periodically poled KTP and RTA

We report on optical parametric oscillators (OPOs) based on large aperture periodically poled KTiOPO₄ (PPKTP) and RbTiOAsO₄ (PPRTA) pumped with high pulse energy and high average power Q-switched solid-state lasers. The OPOs were pumped with 1064-nm pulses of a diode-pumped Nd:YVO₄ laser at 20 kHz repetition rate. The emitted signal wavelengths were 1.72 μm and 1.58 μm and the idler wavelengths were 2.79 μm and 3.26 μm, respectively. Pumping the PPKTP OPO with 7.2 W and the PPRTA OPO with 8 W average power, 2 W and 1.3 W total OPO output powers were generated. Two-dimensional measurements of the total OPO output power, the signal wavelength and the signal bandwidth in dependence on the crystal location indicated a good uniformity of the quasiphasematching structure over the entire 3-mm-thick crystals. This allowed pumping with larger pump beams and therefore with pulse energies of tens of millijoules. Pumping with different flash-lamp-pumped lasers, good OPO performance and high output pulse energies could be achieved for all pump lasers. Maximum input pulse energies of 56 mJ gave output pulse energies of as much as 18 mJ. The temperature tuning behaviors of both OPOs were measured, showing excellent agreement with calculated temperature tuning curves. New equations for temperature dispersion in RTA are presented. These results show that large-aperture PPKTP and PPRTA crystals are well suited for tunable nanosecond OPO operation with multi-watt average pump power and several tens of millijoules pump pulse energies. Received: 7 September 2001 / Published online: 7 November 2001     

Solitons and vortices in lasers

We give in this article the mathematical background for pattern formation in nonlinear active resonators, elucidating the relation of optics with other fields of physics, and demonstrate experimentally the existence, properties, and dynamics of: (i) vortices in lasers, (ii) bright spatial solitons in lasers with saturable absorber, and (iii) spatial solitons in degenerate parametric mixing. All these structures are by definition bistable so that they are potentially useful for parallel optical information processing. Received: 8 June 1998