Detection of small phase modulation using two-wave mixing in photorefractive crystals

Two-wave mixing of phase-modulated beams in photorefractive crystals under a dc electric field is studied both theoretically and experimentally. Based on the vectorial theory of light diffraction in crystals of cubic symmetry, we derived an analytical expression that describes the phase demodulation in crystals with an arbitrarily oriented electric field. The phase-demodulation technique was used for estimation of the space-charge field created in photorefractive crystals. It is shown that the space-charge-field grating created in GaP and Bi₁₂TiO₂₀ crystals is much smaller than that predicted from the one-level band-transport model of the photorefractive effect. Received: 12 December 2000 / Revised version: 8 February 2001 / Published online: 27 April 2001     

Two-wave mixing of phase-modulated beams in GaP under a dc electric field

Two-wave mixing of phase-modulated light beams in crystals of cubic symmetry is analyzed on the basis of the vectorial theory of light diffraction. We derive an analytical expression for phase-to-intensity transformation in crystals of the 43m point group of symmetry, which differs from the previously obtained solution based on the scalar approach. The most effective transformation is achieved when the amplitude of the space-charge-field grating is equal to the quarter-wave field. It is shown that the space-charge-field grating created in GaP semi-insulating crystal at the wavelength of 632 nm is much smaller than can be predicted from the one-level band-transport model.     

Near-field optics with photonic crystals

Finite-difference time-domain (FDTD) analysis of light propagation in a defect mode of a two-dimensional photonic band-gap (PBG) structure demonstrates that the light field is localized in such a structure within areas with subwavelength (λ/10) sizes. FDTD simulations reveal efficient formation of an evanescent wave at the output of such a PBG structure, permitting the subwavelength resolution to be achieved in the near field. A probe object with a size less than the wavelength of incident light is shown to perturb the near-field distribution behind the PBG structure and to change the signal detected in the far-field zone. The field intensity distribution inside a PBG structure is also sensitive to the presence of a probe object, offering a way to control the light field localized in defect modes of PBG structures. Received: 9 August 1999 / Accepted: 18 October 1999 / Published online: 10 November 1999     

Dynamic light beam deflection caused by space charge waves in photorefractive crystals

During holographic recording in photorefractive crystals (BSO, BGO, and BTO) by an oscillating interference pattern we observe a strong dynamic deflection of the laser beams reflected from the crystal’s surface. The theoretical treatment shows that this new effect is associated with a nonlinear interaction of space charge gratings resulting in a quasi-homogeneous oscillating space charge field which provides deformations of the crystal via the piezoelectric effect. Received: 3 August 1999 / Accepted 5 August 1999 / Published online: 8 September 1999     

Performance improvement of a holographic double-exposure interferometer by heating of the photorefractive recording crystal

A holographic double-exposure interferometer for quasi real-time analysis is realized, utilizing a photorefractive BTO:Cd crystal for hologram recording. Heating of the crystal reduces the time required to reach the steady-state working situation. Light-induced absorption losses are reduced by heating as well. Additionally, the diffraction efficiency is increased by this method. A sixfold increase in the light intensity of the reconstructed interferogram is achieved. Received: 2 December 1998 / Revised version: 28 January 1999 / Published online: 7 April 1999     

Reflection of cold atoms by a cobalt single crystal

We have demonstrated that a cobalt single crystal can be used to make a remarkably smooth retro-reflector for cold paramagnetic atoms. The crystal is cut so that its surface lies in the (0001) plane and the atoms are reflected by the magnetic field above the surface due to the self-organized pattern of magnetic domains in the material. We find that the reflectivity for suitably polarized atoms exceeds 90% and may well be unity. We use the angular spread of a reflected atom cloud to measure the roughness of the mirror. We find that the angular variation of the equivalent hard reflecting surface is (3.1±0.3°)rms for atoms dropped onto the mirror from a height of 2 cm. Received: 29 November 1999 / Revised version: 24 February 2000 / Published online: 5 April 2000     

Holographic recording by excitation of metastable electronic states in Na2[Fe(CN)5NO]·2H2O: a new photorefractive effect

Elementary holographic phase gratings can be written in single crystals of Na₂[Fe(CN)₅NO]·2H₂O, sodiumnitroprusside, by excitation of metastable electronic states in the blue–green spectral range. For light polarized parallel to the crystallographic a and b axes of the orthorhombic crystal the light-induced modulation of the refractive index reaches Δn≈2×10^-3 at λ=514.5 nm. Although the largest population of the metastable states is reached for light polarized parallel to the crystallographic c axis, a photorefractive response is not observed. In contrast to electro-optic photorefractive materials the photorefractive effect depends mono-exponentially on the exposure and on the modulation of the incident light interference pattern. Beam-coupling experiments demonstrate that written gratings are in phase with the interference pattern in correspondence with the fact that the excitation of the metastable electronic states is local. The width of the rocking curve shows that the holographic gratings are written completely over the volume of the crystal. Variations of the wavelengths within the excitation range as well as of the crystal thickness do not influence the maximum photorefractive response. Investigations on the grating vector of the written gratings show unambiguously that charge migration is not responsible for the photorefractive effect. Received: 18 November 1998 / Revised version: 26 January 1999 / Published online: 12 April 1999     

Study of transient photorefractive beam coupling in high- and low-molar-mass liquid crystal mixtures

We observed transient signals of Bragg grating formation in high-performance photorefractive high- and low-molar-mass liquid crystal mixtures (HL-LCMs). These transient signals including oscillation-like behavior can be explained by a complex time constant in the case of a finite applied dc field. The time constant for the space-charge field to reach its steady state and the oscillation frequency are estimated. Received: 30 October 1998 / Revised version: 14 December 1998 / Published online: 24 February 1999     

Adaptive correlation filters for speckle patterns in photorefractive crystals

The experimental study of the in-plain vibration of the speckle pattern in photorefractive GaP and BTO crystals using the polarization self-modulation effect are presented. The simple model based on the propagation of the Gaussian beam through the crystal with recorded space-charge field is proposed to explain main features of the experiment. It is shown that these results allow designing a linear sensor of the speckle-pattern displacement in an effective way. The optical system is very simple and does not include any reference or readout beam. The sensitivity of this system is the same as that of an interferometer. Received: 27 November 1998 / Revised version: 26 January 1999 / Published online: 12 April 1999     

Writing a superlattice with light forces

In atom lithography the conventional roles played by light and matter are reversed. Instead of using a solid mask to pattern a light beam, a mask of light is used to pattern a beam of neutral atoms. In this paper we report the production of different chromium dot arrays with quadratic symmetry. The lattice period depends on the relative polarization and the phase of the two standing waves generating the light mask. A small angular misalignment of the laser beams breaks the high symmetry and a chromium superlattice is written, that is a continuous periodic change between two different quadratic lattices. The structures exhibit lines with a FWHM below 50 nm and clearly separated chromium dots with a FWHM below 70 nm. Received: 30 September 1999 / Revised version: 14 February 2000 / Published online: 5 April 2000     

3D dissipative motion of atoms in a strongly coupled driven cavity

We develop quantum models for the combined external and internal motion of atoms in a strongly coupled driven cavity mode including the transverse degrees of freedom. Using a simplified Gaussian mode function we determine the parameter regimes and prospects of 3D cooling and confinement of one or two atoms in the cavity field. Analysing the field dynamics for slow atoms traversing the cavity, we show that the spectrum of the transmitted and spontaneously scattered light contains ample information on the motional dynamics of the atom and can be nicely used to investigate the cooling properties of the system. Including several atoms in the dynamics we show how motional correlations build up by the common interaction with the cavity field. This can be looked upon as collisions at far distance and can be monitored via the transmitted field dynamics. Received 5 March 1999 and Received in final form 4 May 1999     

Reconstruction of parasitic holograms to characterize photorefractive materials

Photoinduced light scattering is a serious drawback that limits the applicability of thick holographic recording media but provides valuable information on the recording medium. As long as there is no correlation between the scattering centers in the crystal, photoinduced light scattering may be explained to result from the interference pattern of the incident beam and the field scattered from a single point-like scattering center. The hologram of this ellipsoidally scattered wave field will have practically the same structure in the reciprocal space modified by a response function which reflects the anisotropic properties of the recording medium. We studied photoinduced light scattering in LiNbO₃:Fe, a model system for photorefractive materials. The transmitted intensity in the stationary state of the scattering process is investigated as a function of the reconstruction angle at different wavelengths and polarizations of the reconstructing beam. The experimental results are analyzed by a simple phenomenological model based on the Ewald construction and can be used to choose suitable conditions at which holographic scattering can be minimized as well as to extract some physical parameters of the crystal. Received: 27 September 2000 / Revised version: 1 December 2000 / Published online: 21 February 2001     

Analytical solution for the field in photonic structures containing cubic nonlinearity

In this work, we consider the exact solution of the stationary cubic nonlinear equation in a semi-infinite nonlinear medium in contact with a one-dimensional photonic crystal. Two kinds of analytical solutions are found for an arbitrary magnitude of the nonlinearity: a standing-wave-like one containing the inverse elliptic function Eli(?∣m), and a one-wave-type solution for transmitted TE-polarized waves. An approximate two-wave solution is proposed to describe the field propagation through the nonlinear film covering the photonic crystal. It is shown that the problem of a mixed linear-nonlinear structure may be reduced to a transcendental kernel equation determining the field inside the nonlinear part of the medium. The light reflection from a Si/SiO₂ layered structure in contact with an optically nonlinear medium is calculated. The angular-frequency photonic band diagram and power dependency are investigated. Local interface waveguide modes are considered.     

Laser induced self-phase modulation in nematic liquid crystals and effects of applied dc electric field

We investigated the ring-pattern characteristic of self-phase modulation in a homeotropic nematic liquid crystal cell induced by a focused Ar-ion laser beam. Laser induced self-phase retardation versus incident angle was experimentally studied, and good agreement with theory was found. Effects of applied dc electric field on the ring-pattern were studied, to our knowledge, for the first time. When the electric field was below a critical value, laser induced self-phase retardation could be varied by changing the electric field strength. Above this value, irregular shaped diffraction pattern accompanied by intense light scattering was observed, which is attributable to honeycomb-like domain formation.     

Utilizing nonlinear optical pattern formation for a simple image-processing task

A novel scheme for all-optical image processing is suggested, which is based on spontaneous pattern-formation processes. The spatiotemporal instabilities, connected with these self-organization effects, appear in many nonlinear optical systems and mostly obstruct the intended application. We propose to utilize the particular features of pattern formation for parallel image processing, namely the sensitivity to external influences, the selection of well-defined final states, and the rotational and translational invariance. We report here on a single-feedback experiment with a liquid crystal light valve as the optical nonlinearity. In this experiment, the recognition of hexagonal structures is realized. We characterize the response dynamics and study associative properties of this scheme. The extension to square patterns is discussed, and first steps towards a practical implementation are undertaken in providing a simple post-processing scheme and testing the concept on realistic input images. Received: 26 November 2002 / Revised version: 7 February 2003 / Published online: 9 April 2003 RID="*" ID="*"Corresponding author. Fax: +49-6151/16-4123, E-mail: ralph.neubecker@physik.tu-darmstadt.de     

Photo-EMF-based adaptive detectors as optimal photodetectors for detection of light-pattern displacements

It is shown that non-steady-state photo-EMF-based adaptive photodetector operates like an optimal detecting medium when detection of a general spatial shift of a complicated light pattern is needed. This detecting medium can be considered as some spatial distribution of photo-induced p–n junctions matched with the original light pattern and its sensitivity is limited basically by the thermal (Johnson) noise of the detector volume itself. Received: 8 December 1998 / Revised version: 1 February 1999 / Published online: 12 April 1999     

Controlled generation of single photons from a strongly coupled atom-cavity system

We propose a new method for the generation of single photons. Our scheme will lead to the emission of one photon into a single mode of the radiation field in response to a trigger event. This photon is emitted from an atom strongly coupled to a high-finesse optical cavity, and the trigger is a classical light pulse. The device combines cavity-QED with an adiabatic transfer technique. We simulate this process numerically and show that it is possible to control the temporal behaviour of the photon emission probability by the shape and the detuning of the trigger pulse. An extension of the scheme with a reloading mechanism will allow one to emit a bit-stream of photons at a given rate. Received: 7 July 1999 / Revised version: 3 September 1999 / Published online: 20 October 1999     

Surface electric-field-induced instabilities in a homeotropically oriented nematic liquid crystal sample

The effect of a surface electric field produced by ionic adsorption on the molecular orientation of a nematic liquid crystal sample is analyzed. The eigenvalue problem for a semi-infinite medium is analytically solved both for strong and weak anchoring situations. The threshold instabilities are numerically determined and it is shown that the homeotropic pattern can be destabilized also in the situation of strong anchoring. The dependence of the threshold field on the anchoring strength and on the surface polarization is determined by taking into account also the coupling of the quadrupolar component of the flexoelectric coefficient with the field gradient. Received 4 November 1999 and Received in final form 4 April 2000     

Crowdion dynamics in a nonuniformly deformed three-dimensional crystal

The problem of crowdion motion is formulated and analyzed as a dynamical problem of a three-dimensional crystal lattice formed by atoms of several kinds, which interact with each other by means of short-range pair potentials. It is explained that in order for the the crowdion excitations of the close-packed atomic rows to be distinguishable against the background of small dynamic deformations of the crystal as a whole, the microscopic parameters of the crystal structure must meet certain stated requirements. The equation of motion of a crowdion in an arbitrary elastic strain field of the crystal is derived in the Lagrangian formalism. Expressions are obtained which relate the effective mass and the rest energy of a crowdion with the geometric and force parameters of the crystal lattice. Received 4 October 2001 / Received in final form 27 February 2002 Published online 2 October 2002 RID="a" ID="a"e-mail: nazarenko@ksame.kharkov.ua     

4-W and 23-ps pulses from a lamp-pumped Nd:YAG laser passively mode-locked by polarization switching in a KTP crystal

Passive mode-locking of a cw lamp-pumped Nd:YAG laser using nonlinear polarization switching in a type-II SHG crystal is reported. Light pulses with more than 5 W of average power and pulse duration shorter than 25 ps have been obtained at 1064 nm. Received: 29 January 1999 / Revised version: 24 March 1999 / Published online: 1 July 1999