Resampling the transmission matrix in an aberration-corrected Bessel mode basis

The study of the optical transmission matrix (TM) of a sample reveals important statistics of light transport through it. The accuracy of the statistics depends strongly on the orthogonality and completeness of the basis in which the TM is measured. While conventional experimental methods suffer from sampling effects and optical aberrations, we use a basis of Bessel modes of the first kind to faithfully recover the singular values, eigenvalues and eigenmodes of light propagation through a finite thickness of air

Modal Analysis of Millimetre-wave and Terahertz Imaging Systems

This thesis presents the theory and applications of electromagnetic field calculation using orthogonal Gaussian beam modes within the context of far-infrared imaging systems. Laguerre and Hermite-Gaussian modes have been frequently reported in the analysis of paraxial millimetre-wave propagation in astronomical optical systems. Here the method of Gaussian beam mode analysis (GBMA) is extended to fields of optical research that have until recently been associated with wavelengths in the visible band. Using recently derived expressions for the non-paraxial diffraction of Hermite-Gaussian modes, the author demonstrates the modal calculation of far-field intensity distributions with less angular restriction on the accuracy of the method compared to the conventional paraxial description of orthogonal Gaussian modes. This method shows excellent agreement with predictions from more rigourous fullwave numerical methods such as the finite-difference time-domain algorithm, which is also described as a software tool in the modelling of horn and lens antennas. The properties of diffraction limited Bessel beams is described using the Laguerre-Gaussian expansion of conical lenses, and experimental measurements of a conical lens is presented to explore the validity of the use of these optical elements as horn coupled devices in millimetre wave imaging systems. A study of diffractive Fresnel lenses has been undertaken with a comparison of experimentally measured fields with those predicted by the modal techniques. The effects of such lenses on ultrashort paraxial pulses are also investigated using a novel numerical description of few-cycle fields as a superposition of pulsed Laguerre- Gaussian modes. The application of digital holography in the far-infra red band has the prospect of diffraction limited imaging systems without creating distortions and aberrations which is a common problem in conventional techniques using lenses and mirrors. The author presents results from a simple proof-of-concept system which exhibits the potential of this technique for application in, for example, mm-wave security imaging

Modal Analysis of Millimetre-wave and Terahertz Imaging Systems

This thesis presents the theory and applications of electromagnetic field calculation using orthogonal Gaussian beam modes within the context of far-infrared imaging systems. Laguerre and Hermite-Gaussian modes have been frequently reported in the analysis of paraxial millimetre-wave propagation in astronomical optical systems. Here the method of Gaussian beam mode analysis (GBMA) is extended to fields of optical research that have until recently been associated with wavelengths in the visible band. Using recently derived expressions for the non-paraxial diffraction of Hermite-Gaussian modes, the author demonstrates the modal calculation of far-field intensity distributions with less angular restriction on the accuracy of the method compared to the conventional paraxial description of orthogonal Gaussian modes. This method shows excellent agreement with predictions from more rigourous fullwave numerical methods such as the finite-difference time-domain algorithm, which is also described as a software tool in the modelling of horn and lens antennas. The properties of diffraction limited Bessel beams is described using the Laguerre-Gaussian expansion of conical lenses, and experimental measurements of a conical lens is presented to explore the validity of the use of these optical elements as horn coupled devices in millimetre wave imaging systems. A study of diffractive Fresnel lenses has been undertaken with a comparison of experimentally measured fields with those predicted by the modal techniques. The effects of such lenses on ultrashort paraxial pulses are also investigated using a novel numerical description of few-cycle fields as a superposition of pulsed Laguerre- Gaussian modes. The application of digital holography in the far-infra red band has the prospect of diffraction limited imaging systems without creating distortions and aberrations which is a common problem in conventional techniques using lenses and mirrors. The author presents results from a simple proof-of-concept system which exhibits the potential of this technique for application in, for example, mm-wave security imaging

Propagation of generalized vector Helmholtz-Gauss beams through paraxial optical systems

We introduce the generalized vector Helmholtz-Gauss (gVHzG) beams that constitute a general family of localized beam solutions of the Maxwell equations in the paraxial domain. The propagation of the electromagnetic components through axisymmetric ABCD optical systems is expressed elegantly in a coordinate-free and closed-form expression that is fully characterized by the transformation of two independent complex beam parameters. The transverse mathematical structure of the gVHzG beams is form-invariant under paraxial transformations. Any paraxial beam with the same waist size and transverse spatial frequency can be expressed as a superposition of gVHzG beams with the appropriate weight factors. This formalism can be straightforwardly applied to propagate vector Bessel-Gauss, Mathieu-Gauss, and Parabolic-Gauss beams, among others

Transverse modes in porro prism resonators

Thesis (M.Sc.)-University of KwaZulu Natal, Westville, 2008.This dissertation consists of two main sections. The first is a review of laser resonators using spherical mirrors, and incorporates a physical optics numerical model of a Fabry-Perot laser resonator without gain. The output of this model, which includes spot sizes, loss, and transverse mode formation, is compared to the parameters calculated using published analytical results. This comparison serves as a verification of the numerical methods used, as well as a frame of reference for the model of a Porro prism resonator which follows in the second section. The second section proposes a new method for analysing Porro prism resonators. The analysis incorporates both geometric as well as physical optics concepts, with the prisms modelled as rotating elements with amplitude and phase distortions. This yields expressions for the orientation of the loss at the apex of each prism, and as well as the number of petals in the “petal-pattern” beam structure commonly observed from Porro prism lasers. These expressions are included in a numerical model, which is first used to verify the development of the characteristic petal-pattern. Next, the numerical model is used to investigate the development of the beam structure, in both time and space, in crossed Porro resonators with a range of Fresnel numbers and stability parameters. This leads to some new insight into the transverse modes of these lasers

Control and characterization of nano-structures with the symmetries of light

Light beams can be symmetric under different transformations: translations, rotations, mirror symmetries, duality transformations, etc. In this thesis, a systematic way of characterizing these symmetries is presented. Then, it is shown that light beams symmetric under different transformations can be used to control light-matter interactions at the nano-scale. Particular applications are developed, both theoretically and experimentally. Inducing a dual behaviour on a non-dual sample, the excitation of high multipolar order resonances and the measurement of circular dichroism using vortex beams are among them.Comment: PhD Thesis, Department of Physics and Astronomy, Macquarie University. PhD Supervisor: Gabriel Molina-Terriz

Topics in Three-Dimensional Imaging, Source Localization and Super-resolution

The realization that twisted light beams with helical phasefronts could carry orbital angular momentum (OAM) that is in excess of the photon\u27s spin angular momentum (SAM) has spawned various important applications. One example is the design of novel imaging systems that achieve three-dimensional (3D) imaging in a single snapshot via the rotation of point spread function (PSF). Based on a scalar-field analysis, a particular simple version of rotating PSF imagery, which was proposed by my advisor Dr. Prasad, furnishes a practical approach to perform 3D source localization using a spiral phase mask that generates a combination of Bessel vortex beams. For a special annular design of the mask, with the spiral-phase winding number in successive annuli changing by a fixed quantum number, this Bessel-beam combination can yield a shape and size invariant PSF that rotates as a function of the axial position of the source, and possesses a superior depth of field (DOF) when compared to other rotating PSFs. In the first part of this dissertation, we present a vector-field analysis of an improved rotating PSF design that encodes both the 3D location and polarization state of a monochromatic point dipole emitter for high numerical aperture (NA) microscopy, in which non-paraxial propagation of the imaging beam and the associated vector character of light fields are properly accounted for. By examining the angle of rotation and the spatial form of the PSF, one can simultaneously localize point sources and determine the polarization state of light emitted by them over a 3D field in a single snapshot. We also propose a more advanced approach for doing joint polarimetry and 3D localization using a SAM-OAM conversion device without the need for high NA is also proposed. A recent paradigm-shifting research proposal has focused on employing the toolbox of quantum parameter estimation for the problem of super-resolution of two incoherent point sources. Surprisingly, the quantum Fisher information (QFI) and associated quantum Cram\\u27er-Rao bound (QCRB) for estimating the one-dimensional transverse separation of the source pair are both finite constants that are achievable with purely classical measurements that utilize coherent projections of the optical wavefront. A second important contribution of this dissertation is the generalization of the previous quantum limited transverse super-resolution work to full 3D imaging with more general PSF. Under the assumption of known centroid, we first derive the general expression of $3\times 3$ QFI matrix with respect to (w.r.t.) the 3D pair separation vector, in terms of the correlation of the wavefront phase gradients in the imaging aperture. For a clear circular aperture, the QFI matrix turns out to be a separation-independent diagonal matrix. Coherent-projection bases that can attain the corresponding QCRB in special cases and small separation limits are also proposed with confirmation by numerical simulations. We next extend our 3D analysis to treat the more general 6-parameter problem of jointly estimating the 3D pair-centroid location and pair-separation vectors. We also present the results of computer simulation of an experimental protocol based on the use of Zernike-mode projections to attain these quantum estimation-limited bounds of performance

Entanglement enhanced communication and sensing

Entanglement has been an extremely active field of research both from a theoretical and an experimental point of view. As the understanding of the phenomena grows, so does the interest in using it to advance different technological fields: communica- tion, computing and sensing being just some examples. It is now well known that entangled photon pairs can be generated through a process known as spontaneous parametric down-conversion (SPDC). In this thesis I therefore integrate the SPDC generated photons in a variety of experiments each exploiting a different charac- teristic of this quantum effect. In particular, both chapter 3 and chapter 4 utilise the spatial degree of freedom of SPDC generated entangled photons to enhance the quantity of information that can be transmitted in quantum communication systems. In particular, in chapter 3 the information capacity of two of the best known spa- tial modal sets is analysed in the context of real life finite-aperture communication systems, while chapter 4 proposed a new approach for imparting information onto photons. On the other hand, both chapters 5, and 6 rely on the ability of SPDC to generate completely indistinguishable photon pairs, which, when made to interfere, bunch together in what is known as N00N state. In particular, chapter 5 demon- strates that the recently discovered “Coherent Perfect Absorption” process (CPA) can be used to coherently control and absorb two-photon N00N states and therefore can be employed in the generation of quantum gates, while in chapter 6, the quantum interference process that produces the N00N states is used to test the role of relativity in quantum mechanics through the construction of a “quantum gyroscope”

Experimental study of a non-gaussian Fabry-Perot resonator to depress mirror thermal noise for gravitational waves detectors

This thesis is a study of a new kind of Fabry-Perot long-baseline optical resonator proposed for gravitational waves interferometric detectors: the Mesa beam profile Fabry-Perot cavity. A detailed experimental work has been performed on a prototype built in the LIGO laboratories of the California Institute of Technology. The aim of this experiment is to explore all of the main properties of such an optical cavity including: the reliability of its control; beam distortions due to surface imperfections and misalignments; the efficiency of the coupling to a gaussian input beam. The advantage to use a non-spherical optics resonator consists in the possibility to significantly reduce test masses thermal noise which is expected to be the fundamental limit for advanced gravitational waves interferometric detectors, such as Advanced LIGO. It is possible to generate a flat-top, wider laser beam probe of such a detector just reshaping the profile of its mirrors. The characteristic ``Mexican hat' mirror profile has been designed to support a flat-top beam, the so-called Mesa beam. Three test mirrors have been manufactured by the LMA laboratory (Lyon, France) in order to study the behavior of this new family of laser beams in our Fabry Perot prototype. A brief introduction about the problem of estimating mirror thermal noises, their physical sources and how to treat them formally, using, for example, Levin's direct approach is presented. After that, this thesis deals with all the physical characteristic of finite size optical resonators and the related experimental issues like the lock acquisition techniques. A overview of the Mesa beam design and related theoretical issues is included. The second part of this thesis treats all the experimental issues of our experiment: a Fabry-Perot, folded, suspended optical resonator 7 meters long conceived to store Nd:YAG laser light with optics sizes scaled down from the Advanced LIGO baseline parameters. It is placed inside a vacuum pipe and the spacing between the mirrors is determined by three INVAR rods. A cavity finesse of about 100 is achieved by tuning the reflectivity of the input (flat) mirror. The other two mirrors, the folding mirror, and the end mirror, which can be either a spherical or a Mexican hat mirror, have high reflectivity coatings. During this year of operations, the cavity was always operated in air. The stability of the mechanics has been tested with a spherical mirror, 8 meters radius of curvature. The input and output optics layout has been developed to match and study this preliminary cavity configuration. The control electronics, necessary to keep the cavity locked on a resonance, has been made and assembled so that it is possible to use either a side-lock feedback on the laser frequency or the cavity length dithering technique. A high voltage driver circuit has been designed and assembled to drive the mirror piezo actuators. A preliminary study of the cavity beam profile was performed for the spherical optics configuration: several beam profile samples of the fundamental mode and higher order modes were compared to the theoretical predictions. The last part of this work was the characterization of the cavity behavior with the first Mexican hat mirror. Since spherical symmetry is lost for such a resonator, the resonant beam depends on the particular mirrors and input beam alignment. Beam profiles recorded were compared with realistic simulations based on the Fast Fourier Transform implementation of the beam propagation and using the actual Mexican hat mirror map. Finally, the first Mesa beam fundamental mode was acquired and analyzed