Marek Izdebski

Kinetic Monte Carlo study of crystal growth from solution

A study of both surface micromorphology and growth kinetics of the (001) face of a crystal growing from solution is performed on the basis of Monte Carlo simulations taking into account surface diffusion. Special attention is paid to growth simulations performed for layer-by-layer growth mechanism. An influence of the size of two-dimensional array describing crystal surface on simulation results is also discussed. The presented results show that the size of the surface array affects both growth mechanism and growth rate. The simulation results are confronted with predictions of crystal growth theories. The influence of surface diffusion on growth process is compared with some results reported for vapor growth, and it is found that for solution growth, the influence is much weaker. An implementation of fast simulation algorithm with explicit growth time is presented. It is revealed that calculations of the average crystal growth rate using time proportional to the number of events fail in the case of the perfect face growing at low supersaturations.

Analysis of accuracy of measurement of quadratic electro-optic coefficients in uniaxial crystals: a case study of KDP

Taking KDP as an example of a uniaxial crystal, we analyze contributions to its quadratic electro-optic response with a view to explaining differences in published values of certain quadratic coefficients. In an eigenvalue theory of light propagation we show that the linear electro-optic coefficient contributes to the quadratic response, even under ideal laboratory conditions. In addition, the effect of imperfect crystal cutting and alignment is investigated by means of computer calculations based on the Jones calculus. It is found that, for relatively small inaccuracies, the calculated values of the quadratic coefficient g(xyxy) are approximately two orders of magnitude greater when measured with a static field than with a dynamic one. This finding could explain the observed spread in some results for KDP-type crystals.

Application of the Jones calculus for a modulated double-refracted light beam propagating in a homogeneous and nondepolarizing electro-optic uniaxial crystal

The Jones matrix calculus is applied to an electro-optic crystal with uniaxial symmetry when the light beam is incident nearly normally on the crystal face. The approach allows one to treat refracted waves and rays that diverge in the crystal and are modulated by an external low-frequency field. The effect of partial interference of overlapping refracted beams is allowed for and calculated for the case of uniform intensity of the beam over its cross section. The method is employed to analyze optical systems containing an imprecisely cut and aligned electro-optic crystal plate.

Effect of beam divergence from the optic axis in an electro-optic experiment to measure an induced Jones birefringence

Certain optical properties can be described in terms of two linear birefringences existing in separate Jones platelets of a medium. One of these, known as Jones birefringence, although occurring naturally in some crystals is too small to be measurable. However, the two birefringences can be induced by an electric field in 4 and 6 crystals for propagation along the optic axis. For an even slightly divergent light beam, natural birefringence may affect accuracy of measurement. Calculations show that in an experiment with a static field the error depends critically on beam divergence, whereas with a modulated field this is not so.

Application of the Jones calculus for Gaussian beams in uniaxial crystals

Following our recent approach in which the Jones matrix calculus was applied to a modulated double-refracted and partially interfering light beam propagating in a homogeneous electro-optic crystal [J. Opt. Soc. Am. A21, 132 (2004)], we generalize the method for any distribution of the light intensity. Special attention is paid to Gaussian, flat-topped Gaussian, and quasi-Gaussian beams for which the intensity of the light emerging from the optical system is found analytically. Application of the method to an optical system with an electro-optic crystal is described.

Systematic approach for finding configurations for measuring quadratic electro-optic coefficients in noncentrosymmetric crystals.

A new approach for finding configurations for measuring quadratic electro-optic effect in noncentrosymmetric crystals without any background of a linear electro-optic response is presented. This approach utilizes a generalized form of Fresnels wave vectors equation. The method allows the modulation of the fast and slow waves in the crystal to be considered separately. An example is given for the lithium niobate crystal.

Ray and wave tracing in uniaxial crystals perturbed by an external field

Uniaxial crystals may become biaxial in an external field. The general and exact law of double refraction on the boundary of an isotropic medium and a biaxial crystal lead to an unwieldy set of involved formulas. Rotations of the principal axes of the optical permittivity tensor in the crystal subjected to the field lead to further difficulties in ray and wave tracing. Therefore, we propose a calculus in which the directions of refracted rays and waves in an unperturbed uniaxial crystal are taken as the first approximation, and then small perturbations of rays and waves due to the applied field are considered. Our approach is based on Huygenss principle and a generalized form of Fresnels ray equation. As an example, the method is applied to the electro-optic modulation of ray and wave directions in a BaTiO(3) crystal of 4mm symmetry.

Effect of divergence of light wave and alignment of crystal on the response of electro-optic modulators

In this work we report on numerical investigations of the effect of the light beam divergence or imperfect crystal alignment on the response of electrooptic modulators. Resulting non linearities are discussed both in terms of nonlinear distortion of modulators and as related to errors in measurements of quadratic electrooptic coefficients. Our calculations based on the Jones calculus have been performed for uniaxial crystals including KDP, and its isomorphs, and LiNbO3. The results obtained confirm that either the response of the modulators or results of electrooptic measurements can be significantly affected by the light divergence or imperfections in the crystals alignment.

Application of the general Jacobi diagonalization method to the optical properties of a medium perturbed by an external field

An analytical approach is presented for studying the convergence of the general Jacobi method applied to diagonalizing the second-rank tensors that describe the optical properties of a medium subjected to an external field. This approach utilizes the fact that the components of such tensors are usually given in field-free principal axes as power series in the field strength, neglecting terms beyond a chosen power of the field. It is shown that for a biaxial or uniaxial medium, the finite number of iterations, which guarantees exact reduction of all the initial terms up to the required power in the series expansions of all off-diagonal elements, can always be found. Moreover, a fixed sequence of rotations in the Jacobi algorithm can be predicted. These findings allow one to derive analytical formulas in noniterative form for a given highest order of the effects being considered and also to optimize numerical iterative diagonalization procedures. Formulas for eigenvalues and eigenvectors applicable to biaxial and uniaxial mediums perturbed by the linear and quadratic effects are presented. Illustrations are given of the electro-optic and piezo-optic effects for the point group 3m. Conditions for biaxial and uniaxial perturbation of a uniaxial crystal are discussed.

Analysis of some limitations of Monte Carlo crystal growth simulations

Monte Carlo simulations with the use of a new, efficient algorithm have been performed for a wide range of supersaturation values. The influence of both the method of calculation of the average growth rate and the size of an array on the simulation results are analyzed. It is revealed that calculations of the average growth rate without the use of explicitly defined growth time lead to systematic errors and inconsistency with observed growth process, especially at low supersaturations. On the other hand, the size of an array affects not only value of the average growth rate but also operating growth mechanism. Therefore, the average growth rate increases non-linearly with increasing size of an array, tending to a constant value. This effect has been observed for growth of a perfect face as well as for growth of a face consisting steps.