Many essential processes and interactions on atomic and molecular scales occur at ultrafast timescales. The ability to measure and manipulate ultrashort pulses hold the key to probing and understanding these key processes that physicists, engineers, chemists and biologists study today. Measuring ultrashort pulses means that we measure both the intensity (which is a function of time) and the phase of the pulse in time. Or alternately we might measure spectrum and spectral phase (in the corresponding Fourier domain). In the early 1990's, the invention of FROG opened up the field of ultrashort measurement with it's ability to measure the complete pulse. Since then, there have been a whole host of pulse measurement techniques that have been invented to measure all sorts of ultrashort pulses. However, no variation of FROG nor any other fs pulse measurement technique, for that matter, has yet been able to completely measure arbitrary ultraweak femtosecond light pulses such as those found in nature. In this thesis, we will explore a couple of highly sensitive methods in a quest to measure ultraweak ultrashort pulses. We explore the use of Spectral Interferometry, a known sensitive technique as one possibility. We find that it has certain drawbacks that make it not necessarily suitable to tackle this problem. But in the course of our quest, we find that this technique is highly suitable for measuring 10s of picosecond-long shaped pulses. We discuss a couple of developments which make SI highly practical to use for such shaped pulse-measurements. We also develop a new technique which is a variation of FROG, based on the non-linearity of Difference Frequency Generation and Optical Parametric Amplification, which can amplify pulses as weak as a few hundred attojoules to be able to spectrally resolve them and measure the full intensity and phase of these pulses. This technique offers great potential to measure generalized ultraweak ultrashort pulses.

Spectral interferometry, also known as spectral-domain white light or low coherence interferometry, has seen numerous applications in sensing and metrology of physical parameters. It can provide phase or optical path information of interest in single shot measurements with exquisite sensitivity and large dynamic range. As fast spectrometer became more available in 21st century, spectral interferometric techniques start to dominate over time-domain interferometry, thanks to its speed and sensitivity advantage. In this work, a dual-modality phase/birefringence imaging system is proposed to offer a quantitative approach to characterize phase, polarization and spectroscopy properties on a variety of samples. An interferometric spectral multiplexing method is firstly introduced by generating polarization mixing with specially aligned polarizer and birefringence crystal. The retardation and orientation of sample birefringence can then be measured simultaneously from a single interference spectrum. Furthermore, with the addition of a Nomarski prism, the same setup can be used for quantitative differential interference contrast (DIC) imaging. The highly integrated system demonstrates its capability for noninvasive, label-free, highly sensitive birefringence, DIC and phase imaging on anisotropic materials and biological specimens, where multiple intrinsic contrasts are desired. Besides using different intrinsic contrast regime to quantitatively measure different biological samples, spectral multiplexing interferometry technique also finds an exquisite match in imaging single anisotropic nanoparticles, even its size is well below diffraction limit. Quantitative birefringence spectroscopy measurement over gold nanorod particles on glass substrate demonstrates that the proposed system can simultaneously determine the polarizability-induced birefringence orientation, as well as the scattering intensity and the phase differences between major/minor axes of single nanoparticles. With the anisotropic nanoparticles' spectroscopic polarizability defined prior to the measurement with calculation or simulation, the system can be further used to reveal size, aspect ratio and orientation information of the detected anisotropic nanoparticle. Alongside developing optical anisotropy imaging systems, the other part of this research describes our effort of investigating the sensitivity limit for general spectral interferometry based systems. A complete, realistic multi-parameter interference model is thus proposed, while corrupted by a combination of shot noise, dark noise and readout noise. With these multiple noise sources in the detected spectrum following different statistical behaviors, Cramer-Rao Bounds is derived for multiple unknown parameters, including optical pathlength, system-specific initial phase, spectrum intensity as well as fringe visibility. The significance of the work is to establish criteria to evaluate whether an interferometry-based optical measurement system has been optimized to its hardware best potential. An algorithm based on maximum likelihood estimation is also developed to achieve absolute optical pathlength demodulation with high sensitivity. In particular, it achieves Cramer-Rao bound and offers noise resistance that can potentially suppress the demodulation jump occurrence. By simulations and experimental validations, the proposed algorithm demonstrates its capability of achieving the Cramer-Rao bound over a large dynamic range of optical pathlengths, initial phases and signal-to-noise ratios. / PHD / Optical imaging is unique for its ability to use light to provide both structural and functional information from microscopic to macroscopic scales. As for microscopy, how to create contrast for better visualization of detected objects is one of the most important topic. In this work, we are aiming at developing a noninvasive, label-free and quantitative imaging technique based on multiple intrinsic contrast regimes, such as intensity, phase and birefringence. Spectral multiplexing interferometry method is firstly introduced by generating spectral interference with polarization mixing. Multiple parameters can thus be demodulated from single-shot interference spectrum. With Jones Matrix analysis, the retardation and orientation of sample birefringence can be measured simultaneously. A dual-modality phase/birefringence imaging system is proposed to offer a quantitative approach to characterize phase, polarization and spectroscopy properties on a variety of samples. The high integrated system can not only deliver label-free, highly sensitive birefringence, DIC and phase imaging of anisotropic materials and biological specimens, but also reveal size, aspect ratio and orientation information of anisotropic nanoparticles of which the size is well below diffraction limit. Alongside developing optical imaging systems based on spectral interferometry, the other part of this research describes our effort of investigating the sensitivity limit for general spectral interferometry based systems. The significance of the work is using Cramer-Rao Bounds to establish criteria to evaluate whether an optical measurement system has been optimized to its hardware best potential. An algorithm based on maximum likelihood estimation is also developed to achieve absolute optical pathlength demodulation with high sensitivity. In particular, it achieves Cramer-Rao bound and offers noise resistance that can potentially suppress the demodulation jump occurrence.

<p dir="ltr">Accurately locating a radio-frequency (RF) emitter is imperative in the defense sector, and passive direction finding systems are intriguing due to relatively low cost. This approach involves using the time difference between a signal’s impact at equispaced antennas to determine the location of the emitter, a particular challenge for wideband waveforms operating near the noise floor. Microwave photonic systems have been demonstrated for passive direction finding. These techniques possessed drawbacks, such as reliance on the incoming signal’s bandwidth, dependence on laser power, or the inability to recover an angle from wideband pulses. This thesis presents a novel approach to passive direction finding by translating the methods of spectral interferometry from the optical domain to RF. Spectral interferometry involves interfering a time-delayed reference pulse with a “signal” pulse that has passed through an unknown system. By removing the spectral phase of the reference pulse from the resulting interferogram, the spectral phase of the uncharacterized system is recovered. This enables direction-finding for many waveforms, including the wideband low peak power chirps frequently used in radar. Incorporating an analog optical delay line into both a hard-wired RF interferometer and a two-element antenna array demonstrated spectral interferometric processing of chirped signals with up to 1 GHz instantaneous bandwidth. The technique extracted accurate delays and angles to within 2$\degree$ throughout testing. This approach only requires the imposed delay be longer than the autocorrelation of the bandwidth limited pulses. With additional backend processing, this method could simultaneously determine the angle and classify the incoming signal.</p>

This thesis describes methods for using spectral interferometry for the complete space-time characterisation of few-cycle near-infrared femtosecond pulses and extreme ultraviolet (XUV) attosecond pulses produced via high harmonic generation (HHG). Few-cycle pulses tend to exhibit one or more of the following: (1) an octave-spanning bandwidth, (2) a highly modulated spectrum and (3) space-time coupling. These characteristics, coupled with the desire to measure them in a single-shot (to characterise shot-to-shot fluctuations) and in real-time (for online optimisation and control) causes problems for conventional characterisation techniques. The first half of this thesis describes a method, based on a spatially encoded arrangement for spectral phase interferometry for direct electric-field reconstruction (SEA-SPIDER). SEA-SPIDER is demonstrated for sub-10fs pulses with a central wavelength near 800nm, a bandwidth over 350nm, and a pulse energy of several nano-Joules. In addition, the pulses exhibit a modulated spectrum and space-time coupling. The spatially-dependent temporal intensity of the pulse is reconstructed and compared to other techniques: interferometric frequency-resolved optical gating (IFROG) and spectral phase interferometry for direct electric field reconstruction (SPIDER). SEA-SPIDER will prove useful in both femtoscience, which requires accurate knowledge of the space-time character of few-cycle pulses, and in HHG, which requires the precise knowledge of the driving pulse for seeding into simulations and controlling the generation process itself. Pulses arising from HHG are known to exhibit significant space-time coupling. The second half of this thesis describes how spectral interferometry may be performed to obtain the complete space-time nature of these fields via the use of lateral shearing interferometry. Finally, it is shown, via numerical simulations, how to extend the SPIDER technique for temporal characterisation of XUV pulses from HHG by driving the process with two spectrally-sheared driving pulses. Different experimental configurations and their applicability to different laser systems are discussed. This method recovers the space-time nature of the harmonics in a single shot, thus reducing the stability constraint currently required for photoelectron based techniques and may serve as a complimentary method for studying interactions of XUV attosecond pulses with matter.

La décohérence dans les solides est un problème majeur vers la réalisation d'un processeur quantique basé sur l'utilisation de boîtes quantiques (BQs) semiconductrices comme qubits optiquement actifs. Mesurer et contrôler la cohérence optique de tels qubits s'avère donc primordial, tant d'un point de vue technologique que fondamental. Cependant, leurs tailles nanométriques, associées aux temps de vie sub-nanosecondes de leurs transitions optiques, rendent les mesures expérimentales très délicates.Ce travail de thèse propose une étude détaillée des mécanismes de déphasage et de couplage cohérent de complexes excitoniques fortement confinés dans des BQs InAs/GaAs individuelles. Pour réaliser ces mesures, j'ai développé une expérience de mélange à quatre ondes hétérodyne sensible à l'amplitude et à la phase du champ électrique émis par une BQ unique. Ce dispositif permet de mesurer le temps de vie et de cohérence d'un exciton unique, même en présence d'élargissement inhomogène. Pour augmenter l'interaction lumière-matière et l'efficacité d'extraction du signal, l'utilisation de nanostructures photoniques s'est avérée indispensable. La sensibilité optique du dispositif m'a permis d'étudier en détail les mécanismes d'interaction exciton-phonon, source importante de décohérence dans les solides, comme la formation du polaron acoustique, le couplage quadratique aux phonons acoustiques, et le déphasage induit pendant l'excitation. Par ailleurs, la réalisation de spectres bidimensionnels m'a permis de révéler le couplage cohérent entre différentes transitions excitoniques. Enfin, je présente un nouveau protocole de mélange multi-ondes permettant de contrôler la réponse cohérente d'un exciton unique que je propose d'appliquer sur une paire de BQs pour contrôler le couplage radiatif longue distance, étape fondamentale vers la réalisation d'une porte logique quantique dans les solides. / Decoherence in solids is a major issue towards the realization of a quantum processor based on semiconductor quantum dots (QDs) as optically active qubits. Measuring and controlling the optical coherence of such qubits is required in their fundamental studies, paving a way for technological applications. However, their nanometer size combined to the sub-nanosecond lifetime of their optical transitions, render experimental measurements very challenging.This thesis presents a detailed study of the dephasing mechanisms and the coherent coupling of excitonic complexes strongly confined in individual InAs/GaAs QDs. To achieve these measurements, I developed an heterodyne four-wave mixing experiment sensitive to the amplitude and phase of the electric field emitted by a single QD. With this setup one can measure the lifetime and the coherence time of a single exciton, even in the presence of inhomogeneous broadening. To increase the light-matter interaction and the extraction efficiency of the signal, the use of photonic nanostructures has proved to be necessary. The optical sensitivity of the setup allowed me to study in detail the mechanisms of exciton-phonon interaction, which is an important source of decoherence in solids, like the acoustic polaron formation, the quadratic coupling to acoustic phonons, and the excitation-induced dephasing. Furthermore, by inferring two-dimensional spectra, I demonstrate coherent couplings between various exciton complexes. Finally, I highlight a new multi-wave mixing protocol to control the coherent response of a single exciton, and I propose to employ it to control long-range radiative coupling between two QDs, which is a fundamental step towards achieving a quantum logic gate in solids.