Structural disorder results in multiple scattering in real photonic crystals, which have been widely used for applications and studied for fundamental interests. The interaction of light with such complex photonic media is expected to show interplay between disorder and order. For a completely disordered medium, the intensity statistics is well-known to obey Rayleigh statistics with a negative exponential distribution function, corresponding to absence of correlations. Intensity statistics is unexplored however for complex media with both order and disorder. We study experimentally the intensity statistics of light reflected from photonic crystals with various degree of disorder. We observe deviations from the Rayleigh distribution and the deviations increase with increasing long-range order.
Structural disorder results in multiple scattering in real photonic crystals, which have been widely used for applications and studied for fundamental interests. The interaction of light with such complex photonic media is expected to show interplay between disorder and order. For a completely disordered medium, the intensity statistics is well-known to obey Rayleigh statistics with a negative exponential distribution function, corresponding to absence of correlations. Intensity statistics is unexplored however for complex media with both order and disorder. We study experimentally the intensity statistics of light reflected from photonic crystals with various degree of disorder. We observe deviations from the Rayleigh distribution and the deviations increase with increasing long-range order.
The irradiation of a dilute cloud of cold atoms with a coherent light field produces a random intensity distribution known as laser speckle. Its statistical fluctuations contain information about the mesoscopic scattering processes at work inside the disordered medium. Following up on earlier work by Assaf and Akkermans [Phys. Rev. Lett. 98, 083601 (2007)], we analyze how static speckle-intensity correlations are affected by an internal Zeeman degeneracy of the scattering atoms. It is proven on general grounds that the speckle correlations cannot exceed the standard Rayleigh law. On the contrary, because which-path information is stored in the internal atomic states, the intensity correlations suffer from strong decoherence and become exponentially small in the diffusive regime applicable to an optically thick cloud.
We study the angular correlation function of speckle patterns that result from multiple scattering of photons by cold atomic clouds. We show that this correlation function becomes larger than the value given by Rayleigh law for classical scatterers. These large intensity fluctuations constitute a new mesoscopic effect specific to atom-photon interactions, that could not be observed in other systems such as weakly disordered metals. We provide a complete description of this behavior and expressions that allow for a quantitative comparison with experiments.
Light transmission measurements and frequency-delay reflectometry maps for GaAs photonic crystal membranes are presented and analyzed, showing the transition from propagation with a well-defined group velocity to a regime completely dominated by disorder-induced coherent scattering. Employing a self-consistent optical scattering theory, with only statistical functions to describe the structural disorder, we obtain excellent agreement with the experiments using no fitting parameters. Our experiments and theory together provide clear physical insight into naturally occurring light localization and multiple coherent-scattering phenomena in slow-light waveguides.
Understanding the complex interactions of the quantum light with different media provides valuable insights into potential applications in quantum tomography, microscopy, circuit and network design, and imaging. This thesis investigates quantum light interaction with two types of media: I. Random media entailing multiple scattering (Chapters 2-5), and II. Structured media, specifically designed to control quantum interferences (Chapters 6 and 7). In the first part of the thesis, and through solving the Lippmann-Schwinger equation for collections of small scatterers, a first principle scalar model for multiple scattering in finite-sized random media is developed. This efficient numerical model serves as the basis for investigating the coherent backscattering, a manifestation of weak localization in random media, for several bounded random media and various illuminations. Through employing mode expansion, next, the developed model is adapted to a general class of quantum-optical studies and quantum correlations are successfully derived and analyzed in scattering from finite disordered structures as well as systems of few scatterers. In multiple scattering of two-photon states in weak localization regime, the emergence of coherent two-photon backscattering is presented for the first time in coincidence detection, and it is demonstrated that quantum correlations can be used as a probe of entanglement dimensionality. Multiple scattering of two-photon states results in granular patterns known as speckle patterns. The statistical properties of single- and two-photon speckle patterns in scattering of different states are numerically calculated and the speckle visibilities and relevant parameters are derived. Specifically, the deviation of the probability density functions from negative exponential distributions, traditionally recognized as Rayleigh statistics in classical scattering, is identified, and shown to significantly depend on the presence of entanglement. Lastly, a different numerical implementation (based on COMSOL Multiphysics package) is used to consolidate our findings by incorporating the polarization effects. Coherent backscattering and coherent two-photon backscattering are observed for co-polarized fields in scattering from synthesized disordered media. It is demonstrated that depending on the particle exchange symmetry in polarization entangled excitation, the photons can exhibit statistical tendency to bunch together in the same mode, appear in separate modes (antibunching), or show a mixed response after multiple scattering. These bosonic-, fermionic-, and anyonic-like behaviors are studied in connection with coherent backscattering phenomenon, and it is demonstrated that the degree of enhancement in backscattering depends on the exchange symmetries. The simplicity and effectiveness of the implemented scattering analysis and the significance of the consequent conclusions suggest our approach as a promising platform for ‘numerical experiments’ without the limitations of analytical or semi-analytical models, and a practical tool prior to experiments. In the second part of the thesis, the random media operating as multimode platforms are replaced with engineered surfaces, i.e., metasurfaces, to realize targeted quantum interferences. First, a design roadmap for general lossy, asymmetric, and unbalanced coupling networks is presented, allowing to achieve maximum programmability in two-photon interferences. Next, two switchable metasurface-based coupling networks are designed to control nonclassical two-photon interferences via thermally driven crystallographic phase transitions. Numerical simulations confirm smooth transition between coalescence and anti-coalescence, aiming to address the current need in quantum optics for free-space compact devices creating tunable quantum interferences and acting as fast modulators for the second order quantum correlations. Our proposed compact and rapidly controllable devices pave the way towards new quantum applications as well as improving the current free-space quantum systems.
We investigated several types of random lasing modes against frequency and the excitation of active medium. Random lasing occurring from multiple light scatterings and the interference effect of the scattered light has various complex lasing states in disordered structures, in which light waves are localized in various forms. Modes of random lasing are generally classified into localized, extended and transition modes based on their localization types. Numerical methods are used for analysing such complex phenomena. In this paper, a finite-element method is used to investigate the relationship among lasing modes, frequency and population inversion density of active medium for random lasing. Light amplification defined as the ratio of radiative powers between excited and non-excited states of the active medium is computed by changing both the frequency and the population inversion density of the active medium, which is modelled by the negative imaginary part of relative permittivity. The distributions of random lasing modes is strongly influenced by the lasing frequency. We also found that the localized modes that are strongly confined lasing modes in disordered structures do not appear in the frequency ranges in which mean free paths are approximately equal to the half-wavelength.
Long-range correlation characterizes the nondiffusive scattering paths of light through disordered media, playing an important role in the coherent control of multiply scattered light. Here, we report the long-range correlation of subsets of coherently interacting scattering paths, known as transmission eigenchannels. We find that the high-transmission eigenchannels exhibit a negative long-range correlation, in contrast to conventional positive long-range correlation. Moreover, when the transmission decreases, a prominent negative-to-positive transition of long-range correlation emerges for these eigenchannels. Finally, we demonstrate that this intriguing negative-to-positive transition originates from the characteristic transmission fluctuations of the eigenchannels. Our study provides valuable insights into the long-range correlation of scattered light in disordered media, constituting an important step toward advanced control of scattered light by manipulating the long-range correlation.