In the paper propagation of two overlapping light pulses in saturable nonlinear medium of Kerr type is analyzed. During
their interaction higher order effects are taken into account. The total field of both pulses satisfies Higher Order
Nonlinear Schrödinger Equation (HONSE). This equation is being solved analytically and numerically for the field
describing sum of two concentric solitons - one high and narrow and the second low but very wide. The approximate
analytical solution of HONSE is obtained by means of canonical method. The derived ten Euler-Lagrange equations can
be solved analytically if parameters of considered solitons significantly differ. The obtained solution describes
oscillations of altitude and width of the narrow soliton and monotonous change of parameters of the wide component -
its width increases and altitude decreases during propagation. The correspondence between numeric and analytical
solutions is analyzed.
In this paper a quantum description of degree of polarization (DOP) is presented. The analysis includes differences
between quantum and quasi-classic description of photons and what they are in comparison with coherent states of
electric field. In the end a possible interpretation for single-photon experiments is given to allow DOP calculation for
photons.
In the paper we consider propagation of (3+1)D ultra-short spatio-temporal light pulses (bullets) in saturable nonlinear
medium of Kerr type. The envelope of the complex amplitude describing such pulse is a solution of (3+1)D Nonlinear
Schrödinger Equation. In order to obtain possibility of stationary and stable transmission along the z-axis we assume
dielectric permittivity with square graded index linear profile and saturable nonlinearity of cubic-quintic type. The
corresponding Higher Order Nonlinear Schrödinger Equation (HONSE) can be solved approximately by means of
variational method. Following after the solutions in linear medium we predict existence of the whole series of solution in
a form of higher-order modes. Assuming the trial function with appropriate spatial profile we obtain corresponding
Euler-Lagrange equations. We solve these equations analytically in stationary case obtaining parameters of stationary
light pulses. Assuming small deviations from stationary pulse parameters we obtain and solve equations of oscillatory
type that describe non-stationary propagation of bullets. We compare the exact numerical and approximate analytical
solutions. We analyze coupling between oscillations with different frequencies in the evolution of higher-order light
bullets.
Propagation of (3+1)D short light bullets in media with Kerr-like saturable nonlinearity is considered. The influence of higher-order terms - third order dispersion, nonlinear dispersion and self frequency shift are taken into account. A trial function corresponding to the product of (2+1)D gaussian beam and approximate solution of (1+1)D generalized nonlinear Schrodinger equation is applied. The Euler-Lagrange equations for varying temporal and spatial widths of the bullet are obtained. A stationary corresponding to small higher-order terms of these equations is found. The influence of material nonlinear coefficients for the stationary widths is discussed. The linearized form of Euler-Lagrange equations is obtained. The periods of oscillations of temporal and spatial width are found.
In the paper propagation of stationary hybrid TE-TM electromagnetic fields through nonlinearly anisotropic Kerr layer is considered. For arbitrary phase shift between TE and TM components the permittivity tensor describing different mechanisms of nonlinearity is obtained. The system of Maxwell's equations, nonlinear material equations and boundary conditions are solved numerically in the three-layered structure. For the weak field approximation the analytical expressions approximating fields of nonlinear fundamental mode and its power are derived.
In this paper propagation of stationary hybrid TE-TM electromagnetic fields through nonlinear Kerr dielectric is considered. The nonlinear material equations are generalized to contain the phase shift between TE and TM components. The resulting system of Maxwell's and material equation is solved numerically. The shape of the field as function of the mechanism of Kerr nonlinearity, propagation constant, quotient of the TE to TM component and phase shift between them is discussed. The solutions of spatial soliton form are thoroughly analyzed. The approximate solution of the equations describing fundamentals hybrid solitons is obtained. The accuracy of the approximation is discussed.
The numerical solutions of hybrid modes equations describing monochromatic electromagnetic fields propagating along the boundary between the nonlinear Kerr medium and linear dielectric are obtained. The dependence of the mode structure on the nonlinearity mechanism and the propagation constant is discussed. The analytical expressions approximating the fields of the lowest order mode are reported. These expressions are applied to the boundary problem at the interface between the Kerr medium and the linear cover. The approximate formula describing power flow along the boundary is derived. The accuracy of the applied approximation is analyzed.
In the paper a Y-cut Ti--diffused lithium niobate planar waveulde
is considered. The field propagates in the direction inclined to the
optic axis, so instead of pure TE or TM modes hybrid modes occur. As
TE-like modes leak into the substrate we deal with TM-like hybrid
modes only. By using WKB method we obtain approximate formulae
expressing fields both inside the waveguide and in the substrate. We
calculate coefficients of coupling between modes of perturbed and
unperturbed area. We analyze transmission characteristic of such
modulator and discuss effects playing significant role in device
effaciericy.
Access to the requested content is limited to institutions that have purchased or subscribe to SPIE eBooks.
You are receiving this notice because your organization may not have SPIE eBooks access.*
*Shibboleth/Open Athens users─please
sign in
to access your institution's subscriptions.
To obtain this item, you may purchase the complete book in print or electronic format on
SPIE.org.
INSTITUTIONAL Select your institution to access the SPIE Digital Library.
PERSONAL Sign in with your SPIE account to access your personal subscriptions or to use specific features such as save to my library, sign up for alerts, save searches, etc.