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Temporal, spectral, and spatial coherence of optical pulse trains

Rahul Dutta

Published Jun 17, 2016• 0 citations
OpenAlex

Abstract

The work presented in this thesis deals with the coherence of optical pulse trains in time, frequency, and space domains.This thesis, based on the second-order coherence theory of nonstationary light, primarily consists of theoretical investigations which result in useful insights in the coherence characterization of pulsed optical sources.Analytical models that physically represent supercontinuum pulse trains, broadband axicon fields, and slightly disturbed mode-locked pulse trains are proposed.Numerically simulated realizations of supercontinuum pulse trains are also considered in this study.In addition, an experimental setup with corresponding analytical analysis is presented to illustrate the evaluation of the two-time coherence function of pulse trains and it is shown that for that one needs to perform time-resolved measurements of the interference fringes.Moreover, information conveyed by the timeintegrated measurements of the interference fringes produced by supercontinuum light and slightly perturbed mode-locked laser is explained through analytical and numerical investigations.An experimental demonstration of the time-integrated measurements is reported for an almost fully coherent femtosecond pulse train.

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The work presented in this thesis deals with the coherence of optical pulse trains in time, frequency, and space domains.This thesis, based on the second-order coherence theory of nonstationary light, primarily consists of theoretical investigations which result in useful insights in the coherence characterization of pulsed optical sources.Analytical models that physically represent supercontinuum pulse trains, broadband axicon fields, and slightly disturbed mode-locked pulse trains are proposed.Numerically simulated realizations of supercontinuum pulse trains are also considered in this study.In addition, an experimental setup with corresponding analytical analysis is presented to illustrate the evaluation of the two-time coherence function of pulse trains and it is shown that for that one needs to perform time-resolved measurements of the interference fringes.Moreover, information conveyed by the timeintegrated measurements of the interference fringes produced by supercontinuum light and slightly perturbed mode-locked laser is explained through analytical and numerical investigations.An experimental demonstration of the time-integrated measurements is reported for an almost fully coherent femtosecond pulse train.
We examine the temporal coherence properties of trains of nonidentical short optical pulses in the framework of the second-order coherence theory of nonstationary light. Considering Michelson's interferometric measurement of temporal coherence, we demonstrate that time-resolved interferograms reveal the full two-time temporal coherence function of the partially coherent pulse train. We also show that the result given by the time-integrated Michelson interferogram equals the true degree of temporal coherence only when the pulse train is quasi-stationary, i.e., the coherence time is a small fraction of the pulse duration. True two-time and integrated coherence functions produced by specific models representing perturbed trains of mode-locked pulses and supercontinuum pulse trains produced in nonlinear fibers are illustrated.
We consider temporally integrating interferometric measurements and their relation to the coherence properties of nonstationary light. We find that performing such experiments as a function of time delay is equivalent to spectrally resolving the interference patterns, and time-domain coherence information can be obtained from field autocorrelation only if the source is of the Schell-model type. In an analogy to autocorrelation, we introduce field cross-correlation, which can be used to determine the complete complex field of unknown signal pulses if suitable probe pulses are available. We demonstrate our findings with simulated supercontinuum and free-electron laser ensembles, and discuss the prospect of carrying out experiments.
The coherence properties of broadband down converted light are investigated theoretically and experimentally in both the classical and quantum mechanical frameworks. Although broadband down converted light is one-photon incoherent noise, it possesses unique two-photon coherence. Thus, for performing two-photon processes, down-converted light is equivalent to coherent ultrashort pulses in some aspects and to coherent CW laser radiation in others. This equivalence is theoretically established and experimentally demonstrated in the classical, high-power regime. Two applications that take advantage of multi-photon coherence are then described in detail; one for optical spread spectrum communication and the other for sub-diffraction limit optical lithography. A key part of this research is the design and implementation of an efficient source that generates high-power broadband down conversion in a cavity. A broadband oscillation in the cavity is ensured by a mechanism very similar to passive mode-locking of ultrashort pulse laser sources, which we term as pair-wise mode locking, thus extending the equivalence to ultrashort pulses to the light generating sources also. Finally, the quantum mechanical properties of broadband down-conversion are explored experimentally, by performing a two-photon process (sum frequency generation) at the low power level of entangled photon pairs. The non-classical nature of the light is expressed by a linear intensity dependence of the non-linear process. Temporal shaping with femtosecond resolution of the entangled photon pairs is demonstrated using this non-linear interaction.
The experimental work in this thesis is divided into two distinct parts. In both parts, broadband femtosecond laser pulses are "shaped" by adjusting the relative phase and amplitude of spectral components. In the first set of experiments, time-dependent perturbation theory is used to show that the probability of a quantum transition in atomic rubidium can be substantially enhanced or suppressed using pulse shaping, compared to the probability of transition observed when a transform-limited or "flat phase" optical pulse is used. These enhancement or suppression effects are also demonstrated experimentally. As quantum interference (the material phase having been transferred from the optical phase) is used to enhance or diminish a particular final quantum state, this can be classified as a quantum coherent control experiment. In the second set of experiments, an optical pulse is scattered into a train of pulses by a layered structure. The layered structure is used to simulate the effect of optical pulses travelling through certain types of complex media. One consequence of the disruption of a single pulse into a train of pulses is lower per-pulse peak intensity, and thus a greatly diminished nonlinear signal. It is shown that spectral pulse shaping (in phase only) is sufficient to pre-compensate for the scattering structure, allowing a single transform-limited pulse to be obtained at the output.
This thesis contains research related to random light fields.In particular, novel constructions of electromagnetic coherence in beam fields are introduced, and certain fundamental notions concerning the spectrum of light are assessed in the context of nonstationary fields.The singular-value decomposition (SVD) of the cross-spectral density matrix (CSDM) is analysed and interpreted for electromagnetic beams.In addition, the Gram matrix of the CSDM is invoked and combined with the SVD formalism.The Gram matrix shares the essential properties of the polarization matrix, thus appearing as a particularly potential descriptor of electromagnetic coherence.The SVD and the Gram matrix yield results analogous to those traditionally met in polarization theory of beam fields, but in the context of two-point spatial coherence analysis.In particular, two-point analogies of the usual decompositions of the polarization matrix are introduced by applying the SVD.In addition, the Poincaré sphere representation of electromagnetic coherence is established, which is analogous to the traditional Poincaré sphere in polarization optics.Cross-spectral purity and spectral invariance of light are two fundamental concepts concerning stationary random light fields, which were recently generalized to nonstationary fields.In this thesis, a reduction formula for time-integrated coherence functions of cross-spectrally pure nonstationary scalar fields is established.This reduction formula is an equivalent condition for the physical definition of crossspectral purity in nonstationary fields, similarly to the reducibility met in the case of cross-spectrally pure stationary light.In addition, optical systems consisting of hybrid refractive-diffractive lens designs which transform partially coherent isodiffracting pulsed beams into cross-spectrally pure or spectrally invariant nonstationary fields are developed.Furthermore, polarimetric measurement of temporal coherence in electromagnetic beam fields is performed.It is shown that the electromagnetic temporal degree of coherence can be deduced from these measurements, thus without the need for visibility detection or optical elements in the arms of the device, in contrast to earlier studies.
A supercontinuum (SC) laser pulse, which is generated through third-order nonlinear process, is valuable light for various applications such as optical coherence tomography (OCT), and spectral measurement. Coherence of a SC pulse is one of the most important properties because the accuracy and sensitivity of these measurements are determined by its noise property. Recently, the second-order coherence property has been revealed by some numerical simulations and experiments [1, 2]. According to these previous reports, the coherence of the SC pulse has been almost lost through the spectral broadening process. However, the depletion of the coherence has been studied only in two bases: time and frequency. Thus, we experimentally study the coherent basis from noisy modes of the SC pulse by utilizing multimode quantum theory [3, 4].