The quantum optics of metamaterials starts with the question of whether the same effective-medium theories apply as in classical optics. In general, the answer is negative. For active plasmonics but also for some passive metamaterials, we show that an additional effective-medium parameter is indispensable besides the effective index, namely, the effective noise-photon distribution. Only with the extra parameter can one predict how well the quantumness of states of light is preserved in the metamaterial. The fact that the effective index alone is not always sufficient and that one additional effective parameter suffices in the quantum optics of metamaterials is both of fundamental and practical interest. Here, from a Lagrangian description of the quantum electrodynamics of media with both linear gain and loss, we compute the effective noise-photon distribution for quantum light propagation in arbitrary directions in layered metamaterials, thereby detailing and generalizing our previous work. The effective index with its direction and polarization dependence is the same as in classical effective-medium theories. As our main result, we derive both for passive and for active media how the value of the effective noise-photon distribution too depends on the polarization and propagation directions of the light. Interestingly, for s-polarized light incident on passive metamaterials, the noise-photon distribution reduces to a thermal distribution, but for p-polarized light it does not. We illustrate the robustness of our quantum optical effective-medium theory by accurate predictions both for power spectra and for balanced homodyne detection of output quantum states of the metamaterial.
The quantum optics of metamaterials starts with the question of whether the same effective-medium theories apply as in classical optics. In general, the answer is negative. For active plasmonics but also for some passive metamaterials, we show that an additional effective-medium parameter is indispensable besides the effective index, namely, the effective noise-photon distribution. Only with the extra parameter can one predict how well the quantumness of states of light is preserved in the metamaterial. The fact that the effective index alone is not always sufficient and that one additional effective parameter suffices in the quantum optics of metamaterials is both of fundamental and practical interest. Here, from a Lagrangian description of the quantum electrodynamics of media with both linear gain and loss, we compute the effective noise-photon distribution for quantum light propagation in arbitrary directions in layered metamaterials, thereby detailing and generalizing our previous work. The effective index with its direction and polarization dependence is the same as in classical effective-medium theories. As our main result, we derive both for passive and for active media how the value of the effective noise-photon distribution too depends on the polarization and propagation directions of the light. Interestingly, for s-polarized light incident on passive metamaterials, the noise-photon distribution reduces to a thermal distribution, but for p-polarized light it does not. We illustrate the robustness of our quantum optical effective-medium theory by accurate predictions both for power spectra and for balanced homodyne detection of output quantum states of the metamaterial.
A quantum theory of the optical field in presence of a linear dispersive medium with losses representing a passive optical device is given. The medium is modelled by quantum oscillators coupled to thermal reservoirs. Time-ordered correlation functions of the optical field can be expressed by integrals of time-ordered source operators multiplied by classical field propagators which are influenced by dispersion and loss effects. Additionally correlation functions of thermal source quantities are needed. For a dielectric layer the propagator is derived, and some simple applications are discussed.
The study of optical effects in active media is rich with unexpected consequences. For instance, one may imagine that absorption and amplification in a dielectric medium will exhibit some sort of symmetry because both are related to the same imaginary part of the dielectric constant, except for a sign change. It turns out that such a symmetry does not exist [1]. This issue has also been investigated in detail for random or disordered gain media, with varying viewpoints [2]. Traditionally, much of the research on amplifying media has considered the interaction of light within the entire volume of such a medium. Recent interest in metamaterials and other esoteric structures in which plasmons are used to manipulate optical signals has brought attention to the role of surface waves in active dielectrics [3, 4]. From a fundamental perspective, the main difference between active and passive media is that spontaneous emission cannot be avoided in gain media. As a result, a rigorous analysis of gain media demands a quantum-mechanical treatment. Spontaneous emission in a gain medium depends not only on the material properties of that medium but also on the optical modes supported by the structure containing that material [5]. By a clever design of this structure (e.g., photonic crystals or microdisk resonators with a metallic cladding), it is possible to control the local density of optical modes and the spontaneous emission process itself. In Chapter 4, we discuss how to model a gain medium under such conditions by deploying optical Bloch equations.
We present results of our theoretical research on collective emission of photons (super- and subradiance) and photon propagation in photonic environments.Just like the single-atom emission, collective emission depends on the photonic environment. For quantum emitters in layered media, we study whether surface plasmons can enhance collective emission, especially for emitters at distances smaller than an optical wavelength.A common approximation in quantum optics is the rotating-wave approximation in the light-matter interaction. We show that in general multi-atom emission rates depend on the approximation, but exceptions exist. Interatomic interactions induced by the electromagnetic field are given by the classical Green tensor, but only when not making the rotating-wave approximation.As a final example of quantum electromagnetics, we describe photons propagating through a layered medium with alternating loss and gain, so-called loss-compensated media. There is no analogous compensation of the quantum noise associated with loss and gain media.
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.
In this dissertation we introduce a quantum theory of propagation of light in integrated photonic devices. The necessity of this theory is justi ed 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 ux of Momentum and derive Heisenberg equations. We apply it to coupling devices with di erent 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 eld-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 di erent-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 con nement in particular regions of the optical eld space of the probability distributions of quantum states. Likewise, we propose a consistent polarization degree, a gure which measures how di erent 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 e ect 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 eld of integrated quantum photonics.
Two independent significant developments have challenged our understanding of light-matter interaction, one, involves the artificially structured materials known as metamaterials, and the other, relates to the coherent control of quantum systems via the quantum interference route. We theoretically demonstrate that one can engineer the electromagnetic response of composite metamaterials using coherent quantum interference effects. In particular, we predict that these composite materials can show a variety of effects ranging from dramatic reduction of losses to switchable ultraslow-to-superluminal pulse propagation. We propose parametric control of the metamaterials by active tuning of the capacitance of the structures, which is most efficiently engineered by embedding the metamaterial structures within a coherent atomic/molecular medium. This leads to dramatic frequency dependent features, such as significantly reduced dissipation accompanied by enhanced filling fraction. For a Split-ring resonator medium with magnetic properties, the associated splitting of the negative permeability band can be exploited for narrow band switching applications at near infrared frequencies involving just a single layer of such composite metamaterials.