Polarization control and sensing with two-dimensional coupled photonic crystal microcavity arrays

We have experimentally studied polarization properties of the two-dimensional coupled photonic crystal microcavity arrays, and observed a strong polarization dependence of the transmission and reflection of light from the structures - the effects that can be employed in building miniaturized polarizing optical components. Moreover, by combining these properties with a strong sensitivity of the coupled bands on the surrounding refractive index, we have demonstrated a detection of small refractive index changes in the environment, which is useful for construction of bio-chemical sensors.Comment: 8 pages text and 4 figures on 4 pages. Submitted for publication on 07/14/0

Solution of Effective-Mass Dirac Equation with Scalar-Vector and Pseudoscalar Terms for Generalized Hulth\'en Potential

We find the exact bound-state solutions and normalization constant for the Dirac equation with scalar-vector-pseudoscalar interaction terms for the generalized Hulth\'{e}n potential in the case where we have a particular mass function $m(x)$. We also search the solutions for the constant mass where the obtained results correspond to the ones when the Dirac equation has spin and pseudospin symmetry, respectively. After giving the obtained results for the non-relativistic case, we search then the energy spectra and corresponding upper and lower components of Dirac spinor for the case of $PT$-symmetric forms of the present potential.Comment: 21 pages, 1 Tabl

Relativistic Approximate Solutions for a Two-Term Potential: Riemann-Type Equation

Approximate analytical solutions of a two-term potential are studied for the relativistic wave equations, namely, for the Klein-Gordon and Dirac equations. The results are obtained by solving of a Riemann-type equation whose solution can be written in terms of hypergeometric function $\,_{2}F_{1}(a,b;c;z)$. The energy eigenvalue equations and the corresponding normalized wave functions are given both for two wave equations. The results for some special cases including the Manning-Rosen potential, the Hulth\'{e}n potential and the Coulomb potential are also discussed by setting the parameters as required.Comment: 6 page

Approximate Analytical Solutions of a Two-Term Diatomic Molecular Potential with Centrifugal Barrier

Approximate analytical bound state solutions of the radial Schr\"odinger equation are studied for a two-term diatomic molecular potential in terms of the hypergeometric functions for the cases where $q\geq1$ and $q=0$. The energy eigenvalues and the corresponding normalized wave functions of the Manning-Rosen potential, the 'standard' Hulth\'{e}n potential and the generalized Morse potential are briefly studied as special cases. It is observed that our analytical results are the same with the ones obtained before.Comment: 13 page

Exact Solutions of Effective Mass Dirac Equation with non-PT-Symmetric and non-Hermitian Exponential-type Potentials

By using two-component approach to the one-dimensional effective mass Dirac equation bound states are investigated under the effect of two new non-PT-symmetric, and non-Hermitian, exponential type potentials. It is observed that the Dirac equation can be mapped into a Schr\"{o}dinger-like equation by rescaling one of the two Dirac wave functions in the case of the position dependent mass. The energy levels, and the corresponding Dirac eigenfunctions are found analytically.Comment: 10 page

Exact Analytical Solution of the N-dimensional Radial Schrodinger Equation with Pseudoharmonic Potential via Laplace Transform Approach

The second order $N$-dimensional Schr\"odinger equation with pseudoharmonic potential is reduced to a first order differential equation by using the Laplace transform approach and exact bound state solutions are obtained using convolution theorem. Some special cases are verified and variation of energy eigenvalues $E_n$ as a function of dimension $N$ are furnished. To give an extra depth of this letter, present approach is also briefly investigated for generalized Morse potential as an example.Comment: 16 pages.Published version has some figure

Approximate analytical solutions of the Dirac equation for Yukawa potential plus Tensor Interaction with any κ\kappa-value

Approximate analytical solutions of the Dirac equation are obtained for the Yukawa potential plus a tensor interaction with any $\kappa$-value for the cases having the Dirac equation pseudospin and spin symmetry. The potential describing tensor interaction has a Yukawa-like form. Closed forms of the energy eigenvalue equations and the spinor wave functions are computed by using the Nikiforov-Uvarov method. It is observed that the energy eigenvalue equations are consistent with the ones obtained before. Our numerical results are also listed to see the effect of the tensor interaction on the bound states.Comment: 15 page