A comparative study on dual colour soft aperture cascaded second-order mode-locking with different nonlinear optical crystals

A comparative study in terms of optimized output power and stability is made on cascaded second-order nonlinear optical mode-locking with KTP, BBO and LBO crystals for both 1064 nm and 532 nm. Large nonlinear optical phase shift achieved in a non-phase-matched second harmonic generating crystal, is transformed into amplitude modulation through soft aperturing the nonlinear cavity mode variation at the laser gain medium to mode-lock a Nd:YVO4 laser. The laser delivers stable dual wavelength cw mode-locked pulse train with pulse duration 10.3 ps and average power of 1.84 W and 255 mW at 1064 nm and 532 nm respectively for the optimum performance in type-II KTP crystal. The exceptional stability achieved with KTP is accounted by simulating the mode-size variation with phase mismatch.     

Perturbation theory for discotic nematic liquid crystals of axially symmetric molecules: effect of dispersion interaction

We investigate the influence of dispersion interaction on a variety of thermodynamic properties of discotic nematic liquid crystals at the discotic nematic-isotropic transition. We report calculations for a hard oblate ellipsoidal system, superposed with an attractive interaction represented by dispersion interaction subjected to different external pressures ranging from 1 to 300 bar. We consider a model system (which simulates a discotic nematic liquid crystal) in which molecules are assumed to interact via a pair potential having both repulsive and attractive parts. The repulsion part is represented by a repulsion between hard oblate ellipsoids of revolution and is a short range, rapidly varying potential. The attractive potential, a function of centre of mass distance and relative orientation between two molecules, is represented by dispersion interaction. The properties of the reference system and first order perturbation term are evaluated using a decoupling approximation which decouples orientational from translational degrees of freedom. The inclusion of fourth and sixth rank orientational order parameters in the calculation slightly improves the result. The role of pressure on phase transition parameters has also been studied.     

Bias expansion of spatial statistics and approximation of differenced lattice point counts

Investigations of spatial statistics, computed from lattice data in the plane, can lead to a special lattice point counting problem. The statistical goal is to expand the asymptotic expectation or large-sample bias of certain spatial covariance estimators, where this bias typically depends on the shape of a spatial sampling region. In particular, such bias expansions often require approximating a difference between two lattice point counts, where the counts correspond to a set of increasing domain (i.e., the sampling region) and an intersection of this set with a vector translate of itself. Non-trivially, the approximation error needs to be of smaller order than the spatial region’s perimeter length. For all convex regions in 2-dimensional Euclidean space and certain unions of convex sets, we show that a difference in areas can approximate a difference in lattice point counts to this required accuracy, even though area can poorly measure the lattice point count of any single set involved in the difference. When investigating large-sample properties of spatial estimators, this approximation result facilitates direct calculation of limiting bias, because, unlike counts, differences in areas are often tractable to compute even with non-rectangular regions. We illustrate the counting approximations with two statistical examples.     

Quantum Jarzynski equality with multiple measurement and feedback for isolated system

In this paper, we derive the Jarzynski equality (JE) for an isolated quantum system in three different cases: (i) the full evolution is unitary with no intermediate measurements, (ii) with intermediate measurements of arbitrary observables being performed, and (iii) with intermediate measurements whose outcomes are used to modify the external protocol (feedback). We assume that the measurements will involve errors that are purely classical in nature. Our treatment is based on path probability in state space for each realization. This is in contrast with the formal approach based on projection operator and density matrices. We find that the JE remains unaffected in the second case, but gets modified in the third case where the mutual information between the measured values with the actual eigenvalues must be incorporated into the relation.