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Classical and quantum nonlinear optics in confined photonic structures

Mohamadreza Ghafari Banaee

Published Jan 1, 2008• 0 citations
Publisher

Abstract

Nonlinear optical phenomena associated with high-order soliton breakup in photonic crystal fibres and squeezed state generation in three dimensional photonic crystal microcavities are investigated. In both cases, the properties of periodically patterned, high-index contrast dielectric structures are engineered to control the dispersion and local field enhancements of the electromagnetic field. Ultra-short pulse propagation in a polarization-maintaining microstructured fibre (with 1 um core diameter and 1.1 m length) is investigated experimentally and theoretically. For an 80 MHz train of 130 fs pulses with average propagating powers in the fibre up to 13.8 mW, the output spectra consist of multiple discrete solitons that shift continuously to lower energies as they propagate in the lowest transverse mode of the fibre. The number of solitons and the amount that they shift both increase with the launched power. All of the data is quantitatively consistent with solutions of the nonlinear Schrodinger equation, but only when the Raman nonlinearity is treated without approximation, and self-steepening is included. The feasibility of using a parametric down-conversion process to generate squeezed electromagnetic states in 3D photonic crystal microcavity structures is investigated for the first time. The spectrum of the squeezed light is theoretically calculated by using an open cavity quantum mechanical formalism. The cavity communicates with two main channels, which model vertical radiation losses and coupling into a single-mode waveguide respectively. The amount of squeezing is determined by the correlation functions relating the field quadratures of light coupled into the waveguide. All of the relevant model parameters are realistically estimated using 3D finite-difference time-domain (FDTD) simulations. Squeezing up to ~20% below the shot noise level is predicted for reasonable optical excitation levels. To preserve the squeezed nature of the light generated in the microcavity, a unidirectional coupling geometry from the microcavity to a ridge waveguide in a slab photonic crystal structure is studied. The structure was successfully fabricated in a silicon membrane, and experimental measurements of the efficiency for the signal coupled out of the structure are in good agreement with the result of FDTD simulations. The coupling efficiency of the cavity mode to the output channel is ~60%.

DOI
10.14288/1.0066274

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Nonlinear optical phenomena associated with high-order soliton breakup in photonic crystal fibres and squeezed state generation in three dimensional photonic crystal microcavities are investigated. In both cases, the properties of periodically patterned, high-index contrast dielectric structures are engineered to control the dispersion and local field enhancements of the electromagnetic field. Ultra-short pulse propagation in a polarization-maintaining microstructured fibre (with 1 um core diameter and 1.1 m length) is investigated experimentally and theoretically. For an 80 MHz train of 130 fs pulses with average propagating powers in the fibre up to 13.8 mW, the output spectra consist of multiple discrete solitons that shift continuously to lower energies as they propagate in the lowest transverse mode of the fibre. The number of solitons and the amount that they shift both increase with the launched power. All of the data is quantitatively consistent with solutions of the nonlinear Schrodinger equation, but only when the Raman nonlinearity is treated without approximation, and self-steepening is included. The feasibility of using a parametric down-conversion process to generate squeezed electromagnetic states in 3D photonic crystal microcavity structures is investigated for the first time. The spectrum of the squeezed light is theoretically calculated by using an open cavity quantum mechanical formalism. The cavity communicates with two main channels, which model vertical radiation losses and coupling into a single-mode waveguide respectively. The amount of squeezing is determined by the correlation functions relating the field quadratures of light coupled into the waveguide. All of the relevant model parameters are realistically estimated using 3D finite-difference time-domain (FDTD) simulations. Squeezing up to ~20% below the shot noise level is predicted for reasonable optical excitation levels. To preserve the squeezed nature of the light generated in the microcavity, a unidirectional coupling geometry from the microcavity to a ridge waveguide in a slab photonic crystal structure is studied. The structure was successfully fabricated in a silicon membrane, and experimental measurements of the efficiency for the signal coupled out of the structure are in good agreement with the result of FDTD simulations. The coupling efficiency of the cavity mode to the output channel is ~60%.
The feasibility of using a parametric down-conversion process to generate squeezed electromagnetic states in three dimensional photonic crystal microcavity structures is investigated for the first time. The spectrum of the squeezed light is theoretically calculated by using an open cavity quantum mechanical formalism. The cavity communicates with two main channels, which model vertical radiation losses and coupling into a single-mode waveguide respectively. The amount of squeezing is determined by the correlation functions relating the field quadratures of light coupled into the waveguide. All of the relevant model parameters are realistically estimated for structures made in Al0.3Ga0.7As, using finite-difference time-domain simulations. Squeezing up to approximately 30% below the shot noise level is predicted for 10 mW average power, 80 MHz repetition, 500 ps excitation pulses using in a [111] oriented wafer.
Entangled multi-mode squeezed states of light have a wide variety of applications in quantum information systems, particularly in the generation of non-Gaussian states of light, which are central to continuous-variable quantum computing. Although theoretical approaches exist to model the nonlinear generation of one- and two-mode entangled states of light in ring resonator systems, these approaches are difficult to implement in modeling more complicated many-cavity systems. In this work, we present an efficient and accurate theoretical approach to modeling the generation and propagation of quantum states of light in lossy coupled-cavity systems containing a two- or three-mode nonlinear resonant structure. Our approach is general and computationally viable even in systems with hundreds of modes. We apply our method to the design and modeling of a multimode photonic crystal coupled-cavity system for the generation of entangled squeezed states of light on-chip. The system consists of a three-mode resonant structure coupled to three coupled-resonator optical waveguides (CROWs) in a square lattice silicon photonic crystal slab. The computational speed of the method allows us to efficiently optimize the system such that the signal and idler light in the two output CROWs remains entangled even after propagating tens of cavities down the CROWs.
Non-classical states of light, such as squeezed states, enable a wide variety of scientific and engineering applications in optical communication, precision measurements and quantum computing. Therefore, engineering non-classical states of light in different systems for different purposes is interesting and appealing. Non-classical states of light, particularly squeezed states, can be generated from light in a coherent state or vacuum state by using certain optical nonlinear interactions. To efficiently introduce such optical nonlinear interactions, a high nonlinear coefficient of the medium and high intensity of light in the medium are the key factors, where the hollow core photonic crystal fibers filled with atomic vapor shows their great benefits. In this thesis, we report on our approach to apply hollow core photonic crystal fibers (HCPCFs) with the goal to generate squeezed states using strong optical nonlinearities of atomic vapor. In a HCPCF, light with high intensity has a well confined mode over long distances along the fiber. To apply the HCPCF in squeezed state generation, we experimentally investigated unexpected noise properties of the HCPCF and determined the parameter range to reduce excess noise from the fiber. Furthermore, we have filled the hollow core of a piece of HCPCF with rubidium vapor, which provides a high nonlinearity when the confined light is on resonance with the rubidium dipole transition. Fundamentally, our planned approach relies on self induced transparency (SIT), which offers high nonlinearity and absorption-free propagation at the same time. We have theoretically investigated SIT solitons in rubidium vapor to analyze the required parameters to achieve SIT solitons in our rubidium filled HCPCF. The experimental and theoretical approach presented in this thesis suggests an efficient method for generating squeezed light.
Generation of light with nonclassical properties, such as squeezed light, has gathered a lot of attention because of possible uses in such areas as quantum state engineering, quantum imaging, continuous variable quantum computing, and detection of gravitational waves. Squeezed light is generally produced by transporting light through a nonlinear medium. One such media is Kerr-nonlinear optical fibres. We aim to find the parameters for a fibre polarization squeezing setup by studying the dependencies of quantum noise suppression on the duration of the pulse and the input power. This is performed by modeling the light field propagation using the split-step Fourier method to numerically solve the stochastic nonlinear Schrödinger equation obtained by using the Wigner representation. This equation includes such physical effects as damping, quantum loss noise, dispersion, Kerr and Raman nonlinearities, and stochastic Raman noise.
Squeezing is a fundamental quantum optical phenomenon - induced by various nonlinear optical processes - in which a special state of the electromagnetic field is generated, for which quantum noise fluctuations are reduced below the shot noise level for certain frequency ranges. Two qualitatively different kinds of squeezing are currently known to take place in optical fibers. The first is the four-wave mixing (FWM) induced quadrature squeezing, in which an intense continuous wave (CW) pump initiates a spontaneous emission of signal and idler waves from vacuum fluctuations at symmetric detunings from the pump. The noise components at the signal and idler frequencies become correlated via the fiber nonlinearity, leading to a reduction of the noise power spectrum below the shot noise level. All the waves participating to the FWM-induced squeezing are monochromatic waves. The second kind of squeezing is the so called self-phase modulation (SPM) induced squeezing, in which the spectral components of an intense short pulse in a coherent state become correlated via the SPM during propagation. We demonstrate theoretically that a third kind of squeezing is possible in optical fibers, in which the noise spectrum of the quasi-monochromatic resonant radiation (RR) emitted by optical solitons when subject to perturbations shows evidence of photon correlation and a reduction of noise below the shot-noise level.
This thesis presents a comprehensive numerical investigation of polarisation squeezing in photonic crystal fibre. Squeezing is the reduction of quantum noise in one variable beyond the Heisenberg limit at the expense of increased noise in the conjugate. The greater confinement of light that is possible in photonic crystal fibres leads to a greater effective nonlinearity, which promises to yield greater quantum squeezing than is possible in standard optical fibre. There are two dominant noise sources that limit the degree of polarisation squeezing. Raman noise is the interaction of photons with phonons in the fibre medium the degree of which is characteristic of the fibre medium and scales inversely with pulse width. And guided acoustic wave Brillouin scattering is due to thermally excited mechanical eigenmodes which scales with fibre length. The larger nonlinearity of photonic crystal fibres allows shorter fibre lengths with larger pulse widths providing a means to significantly reduce the dominant noise sources and obtain polarisation squeezing beyond that of ordinary silica fibre. This thesis presents an extensive quantum treatment using the truncated Wigner method that includes loss, a non-instantaneous Raman response, excess phase-noise, second- and third- order dispersion and self-steepening to identify the physical factors that limit current photonic crystal fibre squeezing experiments and demonstrate the optimal parameters to obtain the best squeezing.