Characterisation of polarised supercontinuum generation and its focal field

Since the first investigation of supercontinuum generation in microstructured optical fibre almost a decade ago, an enormous interest has developed in its application. Supercontinuum generation, the construction of broadband light from nonlinear and dispersive optical processes is a unique type of radiation that has the design functionality to enhance a broad range of applications. The temporal and spectral characteristics of a supercontinuum make it an ideal source in microscopy, as these features can provide a means to simultaneously optically image with different carrier frequencies or simultaneously optical record in a spectrally selective storage medium. These applications all involve the diffraction and interference of the supercontinuum field and what needs to be understood is how such a field behaves under these conditions. The investigation in this thesis identifies the supercontinuum characteristics which are important to the diffraction by a lens and how these characteristics will affect the measurement of the optical properties in microscopic applications. To achieve this goal there are two major areas of investigation; supercontinuum generation and optical diffraction theory. A theoretical and experimental investigation into supercontinuum generation is first presented, which investigates the polarisation properties of supercontinuum generation in highly birefringent photonic crystal fibre with two zero dispersion wavelengths. It is shown that the polarisation state of the incident ultrashort optical pulse maintains its polarisation state as it propagates through the optical fibre. The temporal and spectral properties of the principal axes are determined not only by the phase mismatch and the group velocity mismatch between the two fundamental linear polarised modes, but are affected by the different higher order dispersion coefficients. The balance between the nonlinearity induced by the Kerr effect and the second order dispersion initiates the formation of a high order soliton which then shifts spectrally toward the infrared frequencies. This formation sets the condition for the emission of dispersive waves which shifts toward the lower visible frequencies. However, the dispersion parameters associated with the two fundamental modes produces different high order solitons and phase matching conditions, which determine the wave-numbers for the dispersive waves. The larger of the two dispersion terms enlarges the initial compression of the ultrashort pulse creating a high order soliton with a significantly smaller temporal width, which under conditions of Raman scattering the shift of the soliton is further. Experimentally, it is confirmed that the two fundamental modes of the photonic crystal fibre have different spectral and temporal features. The degree of polarisation also confirms that the supercontinuum spectrum is highly polarised with the degradation attributed to the depolarisation caused by the objective lens. The processes of nonlinearity and dispersion act as phase shifts onto an ultrashort pulse. When superimposed through the diffraction by a lens of low numerical aperture, the temporal phase associated with the field couples with the spatial phase incurred by the lens. This coupling changes the way the field correlates, which is analysed through the degree of coherence of the field. Fluctuations occur in the temporal coherence of the field because of enlarged variations in spatial phase, which are associated with the conditions of destructive interference, which imposes zero intensity locations in the focal region of the lens. These variations are quantified through the coherence time of the field and is most dramatic for a nonstationary observation frame which is affected by the path difference between the rays at the extremities of the lens and the rays along the optical axis. The significant phase contribution that affects the temporal coherence of the SC field is the initial formation of the high order soliton. The compression of the ultrashort pulse and the formation of the high order soliton increases the bandwidth of the field altering the coherence time. After this point in the evolution the coherence is constructed by the interference from dispersive waves and the fission of the high order solitary waves. The two dominant processes which influence the temporal coherence in the focal region are the third order dispersion effect and the Raman scattering. However, the interference of the temporal phase from these effects and the other higher order dispersion and third order nonlinear effects couple with the spatial phase from the diffraction by the lens increasing the complexity of the degree of coherence. Specifically, the coherence time in the case of a nonstationary observation frame can be enhanced by a factor of 3 and occurs at the zero intensity locations within the focal region. Furthermore, it is shown that such an enhancement in the degree of coherence can be controlled by the pulse evolution through the photonic crystal fibre, in which nonlinear and dispersive effects such as the soliton fission process provides the key phase evolution necessary for dramatically changing the coherence time of the focused electromagnetic wave. An extension to this theory can be developed by an investigation into vectorial effects in polarisation, which are achieved through vectorial diffraction theory. This theoretical treatment gives insight into the coherence fluctuations introduced by a supercontinuum in a high numerical diffraction system. Under such conditions and due to the increased refraction at the extremities of the lens the incident polarisation state rotates to transfer energy from this state to the orthogonal transverse field and the longitudinal field, which is known as depolarisation. For a supercontinuum with a horizontal polarisation state the coherence times along the x-, y- and z-axes are different and change with increased numerical aperture. The coherence time for the x-axis increases with numerical aperture and the y-axis decreases with numerical aperture, which is due to the transfer of energy because of depolarisation. The influence of numerical aperture is evident along the optical axis (z), which shows the most significant change in coherence time. The mean coherence time as a function of numerical aperture decreases by an order of magnitude and is due to the superposition conditions no longer forming points of destructive interference. Since the field is a vector field containing three polarisation components, the theory for the degree of coherence is extended to incorporate cross correlation effects within these vectorial components which is calculated through a coherency matrix. The use of this matrix provides insight into interesting correlation effects between co-propagating vector fields such as the coupled modes (linear polarised modes) of a photonic crystal fibre. An investigation is presented on the coherence times for the supercontinuum field generated by cross coupling into the photonic crystal fibre. The coherence times under cross coupling conditions show that the degree of coherence of the two coupled modes from the fibre are different, which is due to the difference in phase associate with each mode. The effect of temporal phase from a supercontinuum and the spatial phase inherent from diffraction by a lens, are important to many experimental applications of supercontinuum generation. The manifestation of these temporal and spatial phase effects result in a modification of the focal region and the bandwidth of the field. Applications involving supercontinuum generation must first understand the generation of the supercontinuum and the modification imposed by the optical system.