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We study the short pulse dynamics in the deterministic and stochastic environment in this thesis. The integrable short pulse equation is a modelling equation for ultra-short pulse propagation in the infrared range in the optical fibers. We…
This paper is concerned with topology optimization based on a level set method using (doubly) nonlinear diffusion equations. Topology optimization using the level set method is called level set-based topology optimization, which is possible…
To add the detailed information to the existed knowledge of nonlinear optics field, the nonlinear optical processes of the second and third order have been discussed in their respective susceptibility tensors in the presence of degenerate…
This work developed a numerical procedure for a system of partial differential equations (PDEs) describing the propagation of solitons in ideal optical fibers. The validation of the procedure was implemented from the numerical comparison…
Nonlinear optical wave propagation manifests in a multitude of frequencies generated from quantum-noise, and selecting desired nonlinear products usually requires seeding the medium with extraneous waves, employing spatial or spectral…
The short pulse equation provides a model for the propagation of ultra-short light pulses in silica optical fibers. It is a nonlinear evolution equation. In this paper the wellposedness of bounded solutions for the homogeneous initial…
Nonlinear optical processing of ambient natural light is highly desired in computational imaging and sensing applications. A strong optical nonlinear response that can work under weak broadband incoherent light is essential for this…
An optical pulse asymptotically reaching zero group velocity in tapered waveguides can ultimately stop at a certain position in the taper accompanied by a strong spatial compression. This phenomenon can be also observed in spatio-temporal…
The system of equations describing an ultrashort optical pulses propagation in semiconductor superlattice with applied magnetic field was obtained based on Boltzmann equation in the relaxation-time approximation for the single electron…
The Transfer Matrix Method (TMM) is a widely used technique for modeling linear propagation of electromagnetic waves through stratified layered media. However, since its extension to inhomogeneous and nonlinear systems is not…
In this paper, the trial function method is employed to find the exact solutions for high-order nonlinear Schr\"odinger equations with time-dependent coefficients. This system describes the propagation of ultrashort light pulses in…
We show that the duration of broadband universal control pulses can be halved by choosing control targets with a quadratic function of phase dispersion. This class of control pulses perform a broadband universal rotation around an axis, in…
Determined polarization state of light is required in nonlinear optics applications related to ultrashort and single-cycle light pulse generation. Such short time scales require up to full octave of spectral width of light. Fiber-based,…
We present an analytical approach to the theory of nonlinear propagation in gases of femtosecond optical pulses with broad-band spectrum . The vector character of the nonlinear third-order polarization of the electrical field in air is…
We investigate the interplay of diffraction and nonlinear effects during propagation of very short light pulses. Adapting the factorization approach to the problem at hand by keeping the transverse-derivative terms apart from the residual…
Nonlinear spectroscopy employs a series of laser pulses to interrogate dynamics in large interacting many-body systems, and has become a highly successful method for experiments in chemical physics. Current quantum optical experiments…
Light propagation in optical waveguides with periodically modulated index of refraction and alternating gain and loss are investigated for linear and nonlinear systems. Based on a multiscale perturbation analysis, it is shown that for many…
A novel approach to study transmission through waveguides in terms of optical streamlines is presented. This theoretical framework combines the computational performance of beam propagation methods with the possibility to monitor the…
Modal expansions are useful to understand wave propagation in an infinite electromagnetic transmission line or waveguide. They can also be used to construct generalized Dirichlet-to-Neumann maps that can be used to provide artificial…
Optical time-domain reflectometry (OTDR) is the basis for distributed time-domain optical fiber sensing techniques. By injecting pulse light into an optical fiber, the distance information of an event can be obtained based on the time of…