Optical solitons due to quadratic nonlinearities: from basic physics to futuristic applications

This paper presents some of the most important features of the MirO code, which is a laser propagation program for high-peak-power laser setups. The main propagation models are discussed: the paraxial nonlinear Schrodinger approximation, broadband computation including dispersion effects, and spatial and temporal Talanov transforms are described, as well as the main optical components: a four-level multipass amplifier including both saturation and narrowing effects; broadband and noncollinear frequency conversion; the grating, including high-order dispersion effects; and laser damage effects. Some elementary examples of MirO computation are also provided.

Miro: Complete modeling and software for pulse amplification and propagation in high-power laser systems

We present an analytic simplified form for the 4 × 4 propagation matrix of a general homogeneous biaxial layer. The expression is applicable to any linear homogeneous, absorbing, biaxial, gyrotropic, magneto-optic, arbitrarily oriented anisotropic structure. Its simple form speeds up the calculation of the optical properties of inhomogeneous anisotropic media and allows real-time analysis of ellipsometric experimental data. A simplified analytic expression for the propagation matrix is also derived for the case of mode degeneration such as for propagation at certain angles and for the isotropic case. Using this analytic method it is found that the time required for calculating the propagation matrix is shorter by a factor of two than that using direct numerical calculation.

https://iopscience.iop.org/article/10.1088/1464-4258/1/5/311/pdf

Analytic propagation matrix method for linear optics of arbitrary biaxial layered media

Diffraction of a 3D optical beam on a multilayer phase-shifted Bragg grating (PSBG) is considered. It is shown that the PSBG enables optical computation of the spatial Laplace operator of the electromagnetic field components of the incident beam. The computation of the Laplacian is performed in reflection at normal incidence. As a special case, the parameters of the PSBG transforming the incident Gaussian beam into a Laguerre-Gaussian mode of order (1,0) are obtained. Presented numerical results demonstrate high quality of the Laplace operator computation and confirm the possibility of the formation of Laguerre-Gaussian mode. We expect the proposed applications to be useful for all-optical data processing.

Optical computation of the Laplace operator using phase-shifted Bragg grating.

Nondegenerate four-wave mixing is demonstrated in Ti in-diffused lithium niobate waveguides. The second-order nonlinear interaction between two oppositely propagating guided modes was observed to generate a radiation field at the sum frequency into a direction perpendicular to the surface during the overlap of the incident waves.

Nondegenerate four wave mixing in integrated optics (A)

The general case of monochromatic plane-wave reflection and refraction at oblique incidence from a planar biaxial–biaxial interface is presented for arbitrary principal-axes orientation in each region. A complete, systematic methodology is provided for calculating all properties of the transmitted and reflected light waves. The singularities that arise when one or both regions are taken to be isotropic are addressed, to our knowledge for the first time. Example calculations are presented for all cases. Finally, the methodology yields all wave parameters, including phase-velocity indices of refraction, angles of refraction and reflection, polarization angles, walk-off angles, and Poynting-vector relative magnitudes. Some common applications of this theory include multilayer structure analysis and the determination of internal angles for second-harmonic generation.

Complete method to determine transmission and reflection characteristics at a planar interface between arbitrarily oriented biaxial media

Transmission and reflection of Gaussian beams from a general anisotropic multilayer structure are investigated. The principal axes of the layers are oriented arbitrarily with respect to each other and with respect to a fixed reference coordinate system. The Gaussian beam is assumed to have an arbitrary angle of incidence and linear polarization orientation. Two numerical examples are presented: a single slab of uniaxial calcite and a multilayer structure of biaxial 4-(N, N-dimethylamino)-3-acet amidonitrobenzene with antireflection coatings on the input and output faces. Results show the distortions of the beam caused by the anisotropy of the structure.

Gaussian beam transmission and reflection from a general anisotropic multilayer structure.

A counterpropagating quasi-phase-matched configuration is examined that is capable of efficiently producing second-order cascaded nonlinear phase shifts with minimal power lost to the second harmonic. For all-optical switching in a nonlinear Mach–Zehnder interferometer, the calculated minimum input power needed for switching (i.e., to yield a ±π/2 phase shift) is 40 times smaller than the power needed in the standard type I copropagating configuration. The throughput of this counterpropagating device is 96% at the optimum switching point.

Efficient nonlinear phase shifts due to cascaded second-order processes in a counterpropagating quasi-phase-matched configuration.

Numerical solutions to the nonlinear coupled-wave equations of a
counterpropagating quasi-phase-matched device are analyzed by numerical
methods for both second-harmonic generation and cascaded
processes. Normalized derivations for second-harmonic generation
efficiency are also presented. The nonlinear phase shifts acquired
in this device by cascaded second-order processes are promising in
all-optical-switching applications. Specifically, a π/2 phase
shift is shown to be achievable with 42 times less input intensity than
the standard Type I configuration and 100% throughput. The effects
of metallic mirrors are also presented. Careful use of the phase
mismatch is shown to compensate for nonideal mirrors. Finally,
conservation of power in this configuration is briefly
investigated.

Second-harmonic generation and cascaded second-order processes in a counterpropagating quasi-phase-matched device.

A wave-vector zigzag analysis is developed to investigate the complicated interference effects among the four extraordinary waves in a biaxial slab with general principal-axes orientation; the four corresponding zigzag Poynting vectors have distinct walk-off directions. Expressions for transmission and reflection coefficients, analogous to Airy’s summation for isotropic slabs, are determined for an arbitrarily oriented linearly polarized monochromatic plane wave at oblique incidence. A KTP slab is analyzed with the derived method, and the results are compared with those obtained with the 4 × 4 matrix method. Some common applications of this theory include analysis of multilayer structures and waveguides.

Gary D. Landry

Papers

Complete method to determine transmission and reflection characteristics at a planar interface between arbitrarily oriented biaxial media

Gaussian beam transmission and reflection from a general anisotropic multilayer structure.

Efficient nonlinear phase shifts due to cascaded second-order processes in a counterpropagating quasi-phase-matched configuration.

Second-harmonic generation and cascaded second-order processes in a counterpropagating quasi-phase-matched device.

Zigzag analysis of interference effects in an arbitrarily oriented biaxial single layer