Abstract Here we use approaches and concepts from quantum mechanics in order to analyze the propagation of classical electromagnetic waves in the elements of integrated optical circuits. These waveguide circuits are considered as potential wells between complex-shapes barriers formed by opaque media. This allowed us to construct in the framework of the slow-varying amplitude approximation for the wave equation an analogy between coherent oscillations in a quantum system and the redistribution in space of the field strength of a classical wave. We also demonstrated the methods to control the mode composition of a classical light in a spatially inhomogeneous waveguide structure. The proposed description was based on the analogy with Rabi-type oscillations in quantum mechanics.
Abstract Here we use approaches and concepts from quantum mechanics in order to analyze the propagation of classical electromagnetic waves in the elements of integrated optical circuits. These waveguide circuits are considered as potential wells between complex-shapes barriers formed by opaque media. This allowed us to construct in the framework of the slow-varying amplitude approximation for the wave equation an analogy between coherent oscillations in a quantum system and the redistribution in space of the field strength of a classical wave. We also demonstrated the methods to control the mode composition of a classical light in a spatially inhomogeneous waveguide structure. The proposed description was based on the analogy with Rabi-type oscillations in quantum mechanics.
We have determined conditions when a pair of coupled waveguides, a common element for integrated room-temperature photonics, can act as a qubit based on a system with a double-well potential. Moreover, we have used slow-varying amplitude approximation (SVA) for the "classical" wave equation to study the propagation of electromagnetic beams in a couple of dielectric waveguides both analytically and numerically. As a part of an extension of the optical-mechanical analogy, we have considered examples of "quantum operations" on the electromagnetic wave state in a pair of waveguides. Furthermore, we have provided examples of "quantum-mechanical" calculations of nonlinear transfer functions for the implementation of the considered element in optical neural networks.
Abstract Quantum Mechanics and classical optics feature similar phenomena such as superposition, interference and even entanglement. Hence, techniques from optics can be used in quantum mechanics and vice versa. In this article I address the question: What can we learn from formulating optics in the language of quantum mechanics? It is argued that the solutions of the wave equations for the electromagnetic field form a tensor product of Hilbert spaces corresponding to the degrees of freedom of classical light. Therefore, it comprises non-separable solutions reminiscent of entanglement. Moreover, the two spatial degrees of freedom each carry non-commuting position and momentum variables forming a Heisenberg algebra like quantum particles moving in a two dimensional space. An analogy between the dynamics of a quantum harmonic oscillator and paraxial light propagating through a converging lens is drawn. This article presents a modern formulation of optics in the language of state vectors and operators (based on Dirac’s notation) along the lines of an earlier contribution [1], specifying and explaining its results.
In this dissertation we introduce a quantum theory of propagation of light in integrated photonic devices. The necessity of this theory is justified due to the conceptual and formal inconsistencies the Hamiltonian theory presents when dealing with propagation problems. Taking into account the orthonormalization property and the modal norms, we carry out a canonical quantization of the flux of Momentum and derive Heisenberg equations. We apply it to coupling devices with different features of the refractive index: inhomogeneities, nonlinear response and losses; like N × N linear and nonli- near directional couplers and spontaneous parametric down conversion and spontaneous four wave mixing-based nonlinear inhomogeneous waveguides.
Likewise, we introduce the optical field-strength space and the amplitude probability distributions in this representation, and by means of a spatial- type Lagrangian theory we derive by path integration propagators in this space for different-media based devices. In this way we solve the propagation for discrete and continuous variables.
Next, we present a new method of characterization of quantum states introducing a generalized quantum polarization, based on the confinement in particular regions of the optical field space of the probability distributions of quantum states. Likewise, we propose a consistent polarization degree, a figure which measures how different a state is from a full unpolarized one, showing its application to the characterization of various examples of stationary and dynamic quantum states.
The last aim of this dissertation is to measure quantum states of light propagating in integrated photonic devices. We designe a versatile and relia- ble electro-optic integrated device to accomplish this goal. This device allows carrying out any SU(2) unitary transformation and is able to be nested as well, allowing its extension to SU(N) transformations. Likewise, it outper- forms other current schemes based on pasive directional couplers due to its ability to reduce the effect produced by fabrication errors, a very important fact when complex circuits are involved. We perform simulations and show possible applications.
In summary, in this thesis we develop tools to design and simulate the performance of photonic devices, as well as propose a characterization me- thod for quantum states propagating within, with interest in the conti- nuously growing field of integrated quantum photonics.
We study the propagation of quantum states of light in separable longitudinally inhomogeneous waveguides based on the momentum operator. This is carried out in the optical field-strength space E by means of the optical propagator obtained by the path integral formalism. We analyze virtual squeezing appearing in these media and its effect on quantum states of light, that is, Gouy’s quantum phases depending on both the longitudinal inhomogeneity and the quantum state. In addition, it is justified that these media perform unitary Infeld–Plebanski transformations, thus avoiding real squeezing. Likewise, WKB and exact results are presented for the propagation of coherent and squeezed states of light and, additionally, Bessel–Gauss quantum states of light propagating in a power-law parametric family of longitudinally inhomogeneous waveguides are studied in detail.
In the electromagnetic field formed by coaxial cables, electromagnetic waves of different frequencies are shown to propagate at the same speed (the speed of light c). Therefore, the variational method, which is based on the fact that electromagnetic waves of different frequencies have different propagation speeds, cannot be applied. In this session, the characteristics of light propagating through an electromagnetic field of glass, suitable for applying the variational method and for constructing lenses, are determined. Although the electromagnetic field is derived from the properties of dielectrics, it has been demonstrated to be equivalent to a circuit that represents the Schrödinger equation used in quantum mechanics. In other words, it may be possible to apply electromagnetic fields from classical physics (circuit theory) to quantum mechanics. Quaternions and wave functions that are considered to be related to complex functions will be the topic of future studies because the Schrödinger equation is a complex function.
Using quantum theory, we study the propagation of an optical field in an inhomogeneous dielectric, and apply this scheme to traveling optical fields in a waveguide. We introduce a field-atom interaction Hamiltonian and derive the refractive index using quantum optics. We show that the transmission and reflection of optical fields at an interface between different materials can be described with normalized Fresnel coefficients and that this representation is related to the beam splitter operator. We then study the propagation properties of the optical fields for two types of slab waveguides: step-index and graded-index. The waveguides are divided into multiple layers to represent the spatial dependence of the optical field. We can evaluate the number of photons in an arbitrary volume in the waveguide using this procedure. Using the present method, the quantum properties of weak optical fields in a waveguide are revealed, while coherent states with higher amplitudes reduces to representation of classical waveguide optics.