NUMERICAL MODELING OF OPTICAL PARAMETRIC FREQUENCY CONVERSION

for temporally confined pulses and spatially confined modes

Abstract

This thesis analyses Parametric Frequency Conversion arising from second order non-linear effects in crystals, namely a 5% Mg-doped PPLN crystal.


The analysis starts with a detailed analytical framework discussing the simplifications and approximations used in developing the governing equations later simulated. The theoretical framework constitutes the fundamental backbone of the simulations presented afterwards and the validity of several assumptions is analysed with the simulations as a basis. The effect of accounting for spatial and temporal confinement and depletion are all analysed.


The simulations include; quasi-monochromatic continuous plane waves, quasi-monochromatic continuous Gaussian waves and quasi-monochromatic plane wave} pulses. Simulation results are compared to analytical results, to previously published numerical results and to new experimental results.


Results show that the computation time of the simple plane wave theory is significantly less than that of the Gaussian basis model used to describe spatially confined CW field and the Split-step Fourier method used to describe plane wave pulses. The plane wave theory is seen to be applicable for spatially confined pulses in the slightly confined, weak coupling regime and for temporally long pulses.

Supervisors

Peter Tidemand-Lichtenberg

DTU Fotonik, Department of Photonics Engineering

Associate Professor

Optical Sensor Technology

Lasse Høgstedt

DTU Fotonik, Department of Photonics Engineering

PhD Student

Optical Sensor Technology

Matlab Scripts

DFG simulation of plane wave CW fields

RunPowerPlaneWave.m

Simulation of DFG for plane wave CW fields.

Single DFG simulation

ScalarDFG.m

Subscript to calculate single DFG simulation.

Governing differential equations

ode45equation.m

Governing differential equations that is solved using Runge-Kutte 45.

DFG simulation of Gaussian CW fields

GaussianBasisComplete.m

Simulation of DFG for Gaussian CW fields.

Gaussian basis transformation matrix

GaussianBasis.m

Subscript to create a basis transformation matrix.

Gaussian mode

GaussianMode.m

Subscript to create a Gaussian mode as a vector.

Plot simulation results

GaussianBasisPlot.m

Subscript to plot the relevant results.

DFG simulation of plane wave pulses

RUNpower.m

Simulation of DFG for plane wave pulses.

Single DFG simulation

SplitStepDFG.m

Subscript to calculate single DFG simulation.

Fourier transform

FourierT.m

Function to Fourier transform.

Inverse Fourier transform

IFourierT.m

Function to inverse Fourier transform.

Plotting propagation

RUNpowerPlotPropagation.m

Subscript to plot the calculated propagation.

Plotting waterfall

RUNpowerPlotWaterfall.m

Subscript to plot the temporal form as function of pump powers.

Anders Bilfeldt — Anders.Bilfeldt.dk — (+45) 3116 4000