Orientador: Edmundo Capelas de Oliveira / Dissertação (mestrado profissional) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Cientifica / Made available in DSpace on 2018-08-11T17:01:55Z (GMT). No. of bitstreams: 1 Rosendo_DaniloCastro_M.pdf: 1231397 bytes, checksum: 33e1a80ea06fa615b7b7aec7917bbbe2 (MD5) Previous issue date: 2008 / Resumo: Neste trabalho abordamos um estudo da equação diferencial ordinária, linear, homogênea de segunda ordem com três singularidades regulares, incluindo uma no infinito de onde obtivemos a equação hipergeométrica e, através do método de Frobenius, introduzimos a função hipergeométrica com singularidade na origem. Por um conveniente processo de limite na equação hipergeométrica obtivemos a equação hipergeométrica confluente, bem como a função hipergeométrica confluente. Apresentamos a função de Mittag-Le²er como uma generalização da função exponencial e suas relações com outras funções, em especial com a função hipergeométrica confluente. Abordamos o conceito de integral e derivada de ordens fracionárias de algumas funções conhecidas. Através da metodologia da transformada de Laplace discutimos uma equação diferencial fracionária com coeficientes constantes de onde emergem as funções de Mittag-Leffler. Por fim, definimos as equações diferenciais fracionárias e, como aplicação, efetuamos um estudo sistemático do oscilador harmônico fracionário. / Abstract: This work presents an introductory study of a second order, linear and homogeneous, ordinary differential equation with three singular regular points, including a singularity at the infinity. We obtain the hypergeometric equation and, by means of the Frobenius method, we introduce the hypergeometric function which is regular at the origin. By a convenient limit process we obtain the confluent hypergeometric equation which has the confluent hypergeometric function as a regular solution at the origin. We introduce the Mittag-Leffler function as a generalization of the exponential function and present a relation with the confluent hypergeometric function. Finally, we present the so-called fractional ordinary differential equation and as an application we discuss the fractional harmonic oscillator / Mestrado / Mestre em Matemática

This diploma thesis deals with numerical simulations of the optical response of plasmonic infrared antennas placed on silicon substrates with thin film of silicon dioxide and subsequently with fitting of scattering spectra by model of coupled harmonic oscillators. In this work, we study an influence of length of antennas on the strength of coupling of localized surface plasmons in the antennas with phonons in silicon dioxide film. Also, the influence of silicon dioxide film thickness on this coupling is investigated.

Made available in DSpace on 2016-06-02T20:16:52Z (GMT). No. of bitstreams: 1 5357.pdf: 11039751 bytes, checksum: 1534d2a0d9db4a8e8f0feb6c57f55080 (MD5) Previous issue date: 2013-08-01 / Financiadora de Estudos e Projetos / The simultaneously incidence of two light beams on one or more atoms causes destructive interference of these beams in atomic states causing cancellation of the absorption of one of the incident beams and this phenomenon is called Electromagnetically Induced Transparency (EIT). The main objective of this work is to show that the Electromagnetically Induced Transparency, which is usually studied in the quantum context, can be modeled classically as a function of coupled harmonic oscillators subject to an external force and dissipation. To will establish the classical equivalence, it will be presented the theory of the EIT in diferent quantum systems and also the theory of classic harmonic oscillators. Analogies will be performed comparing the classical and quantum equations of motion obtained for each scheme. For this, we perform the equivalence of EIT in quantum systems as atoms in three levels in Λ configuration, two-level atoms plus a cavity mode and the cavity optomechanics with the classical system of two coupled harmonics oscillator forced and damped. We also analyze the equivalence of two diferent quantum systems: three level atoms plus one cavity mode and four levels atoms in free space with a classical system composed by three coupled harmonic oscilators, forced and damped, in diferent configurations. / A incidência simultânea de dois feixes luminosos em um ou mais átomos provoca a interferência destrutiva desses feixes em um dos estados atômicos causando o cancelamento da absorção de um dos feixes incidentes e esse fenômeno é denominado Transparência Eletromagneticamente Induzida (\Electromagnetically Induced Transparency", EIT). O objetivo principal deste trabalho é mostrar que a Transparência Eletromagneticamente Induzida, que é normalmente estudada no contexto quântico, pode ser modelada classicamente em função de osciladores harmônicos amortecidos forçados e acoplados. Para que a equivalência clássica seja bem fundamentada, será apresentada a teoria da EIT em diversos sistemas quânticos e também a teoria dos osciladores harmônicos clássicos. As equivalências serão realizadas comparando as equações de movimento clássicas e quânticas obtidas para cada regime. Para isso, vamos realizar a equivalência da EIT em sistemas quânticos de átomos de três níveis em configuração Λ, dois níveis atômicos mais um modo da cavidade e a optomecânica de cavidades com o sistema clássico de dois osciladores harmônicos amortecidos forçados e acoplados. Logo após, será analisada a equivalência de dois sistemas quânticos compostos por átomos de três níveis mais um modo da cavidade e átomos de quatro níveis com os sistemas clássicos de três osciladores harmônicos amortecidos forçados e acoplados em diferentes configurações.

CoordenaÃÃo de AperfeiÃoamento de Pessoal de NÃvel Superior / Nesse trabalho apresentamos as soluÃÃes clÃssicas e quÃnticas de duas classes de osciladores harmÃnicos dependentes de tempo, a saber: (a) o oscilador log-periÃdico e (b) o oscilador tipo Caldirola-Kanai. Para a classe (a) estudamos os seguintes osciladores: (I) $m(t)=m_0frac{t}{t_0}$, (II) $m(t)=m_0$ e (III) $m(t)=m_0ajust{frac{t}{t_0}}^2$. Nesses trÃs casos $omega(t)=omega_0frac{t_0}{t}$. Para a classe (b) estudamos o oscilador (IV) de Caldirola-Kanai onde $omega(t)=omega_0$ e $m(t)=m_0 ext{Exp}ajust{gamma t}$ e osciladores com $omega(t)=omega_0$ e $m(t)=m_0ajust{1+frac{t}{t_0}}^alpha$, para (V) $alpha=2$ e (VI) $alpha=4$. Para obter as soluÃÃes clÃssicas de cada oscilador resolvemos suas respectivas equaÃÃes de movimento e analisamos o comportamento de $q(t)$, $p(t)$ assim como do diagrama de fase $q(t)$ vs $p(t)$. Para obter as soluÃÃes quÃnticas usamos uma transformaÃÃo unitÃria e o mÃtodo dos invariantes quÃnticos de Lewis e Riesenfeld. A funÃÃo de onda obtida à escrita em termos de uma funÃÃo $ ho$, que à soluÃÃo da equaÃÃo de Milne-Pinney. Ainda, para cada sistema resolvemos a respectiva equaÃÃo de Milne-Pinney e discutimos como o produto da incerteza evolui no tempo. / In this work we present the classical and quantum solutions of two classes of time-dependent harmonic oscillators, namely: (a) the log-periodic and (b) the Caldirola-Kanai-type oscillators. For class (a) we study the following oscillators: (I) $m(t)=m_0frac{t}{t_0}$, (II) $m(t)=m_0$ and (III) $m(t)=m_0ajust{frac{t}{t_0}}^2$. In all three cases $omega(t)=omega_0frac{t_0}{t}$. For class (b) we study the Caldirola-Kanai oscillator (IV)where $omega(t)=omega_0$ and $m(t)=m_0 ext{exp}ajust{gamma t}$ and the oscillator with $omega(t)=omega_0$ and $m(t)=m_0ajust{1+frac{t}{t_0}}^alpha$, for $alpha=2$ (V) and $alpha=4$ (VI). To obtain the classical solution for each oscillator we solve the respective equation of motion and analyze the behavior of $q(t)$, $p(t)$ as well as the phase diagram $q(t)$ vs $p(t)$. To obtain the quantum solutions we use a unitary transformation and the Lewis and Riesenfeld quantum invariant method. The wave functions obtained are written in terms of a function ($ ho$) which is solution of the Milne-Pinney equation. Futhermore, for each system we solve the respective Milne-Pinney equation and discuss how the uncertainty product evolves with time.

The field of coupled resonant systems is a rich research area with enumerable real-world applications, including the fields of neural computing and pattern recognition, energy harvesting, and even modeling the behavior of certain types of biological systems. This work is primarily focused on the study of the behaviors of two subsets of this field: large networks of globally coupled resonators (which, in this work, refers to passive, damped resonant elements which require external stimulus) and smaller networks of oscillators (referring to active devices capable of self-sustained motion), which are coupled through a network of light-sensitive resistive elements. In the case of the former, we begin by developing an analytical and experimental framework to examine the behaviors of this system under various conditions, such as different coupling modalities and element-level parametric mistunings. Once a proper understanding of the dynamics of these systems has been established, we go on to develop the system into a single-input, single-output, multi-analyte volatile organic compound sensor. For the study of oscillator networks, we begin by building a device which utilizes a network of Colpitts oscillators, coupled through a series of color-filtered CdSe photocells. We then establish that through the analysis of particular emergent behaviors (most notably, frequency locking within the network), this type of system may show promise as a threshold color sensor. By exploiting these behaviors, this type of system may find applications in neuromorphic computing (particularly in optical pattern recognition).

Path integral approaches have been widely used for long in both quantum mechanics as well as statistical mechanics. In addition to being a tool for obtaining the probability distributions of interest(wave functions in the case of quantum mechanics),these methods are very instructive and offer great insights into the problem. In this thesis, path integrals are extensively employed to study some very interesting problems in both equilibrium and non-equilibrium statistical mechanics. In the non-equilibrium regime, we have studied, using a path integral approach, a very interesting class of anomalous diffusion, viz. the L´evy flights. In equilibrium statistical mechanics, we have evaluated the partition function for a class of molecules referred to as the hindered rotors which have a barrier for internal rotation. Also, we have evaluated the exact quantum statistical mechanical propagator for a harmonic potential with a time-dependent force constant, valid under certain conditions. Diffusion processes have attracted a great amount of scientific attention because of their presence in a wide range of phenomena. Brownian motion is the most widely known class of diffusion which is usually driven by thermal noise. However ,there are other classes of diffusion which cannot be classified as Brownian motion and therefore, fall under the category of Anomalous diffusion. As the name suggests, the properties of this class of diffusion are very different from those for usual Brownian motion. We are interested in a particular class of anomalous diffusion referred to as L´evy flights in which the step sizes taken by the particle during the random walk are obtained from what is known as a L´evy distribution. The diverging mean square displacement is a very typical feature for L´evy flights as opposed to a finite mean square displacement with a linear dependence on time in the case of Brownian motion. L´evy distributions are characterized by an index α where 0 <α ≤ 2. When α =2, the distribution becomes a Gaussian and when α=1, it reduces to a Cauchy/Lorentzian distribution. In the overdamped limit of friction, the probability density or the propagator associated with L´evy flights can be described by a position space fractional Fokker-Planck equation(FFPE)[1–3]. Jespersen et al. [4]have solved the FFPE in the Fourier domain to obtain the propagator for free L´evy flight(absence of an external potential) and L´evy flights in linear and harmonic potentials. We use a path integral technique to study L´evy flights. L´evy distributions rarely have a compact analytical expression in the position space. However, their Fourier transformations are rather simple and are given by e−D │p│α where D determines the width of the distribution. Due to the absence of a simple analytical expression, attempts in the past to study L´evy flights using path integrals in the position space [5, 6] have not been very successful. In our approach, we have tried to make use of the elegant representation of the L´evy distribution in the Fourier space and therefore, we write the propagator in terms of a two-dimensional path integral –one over paths in the position space(x)and the other over paths in the Fourier space(p). We shall refer to this space as the ‘phase space’. Such a representation is similar to the Hamiltonian path integral of quantum mechanics which was introduced by Garrod[7]. If we try to perform the path integral over Fourier variables first, then what remains is the usual position space path integral for L´evy flights which is rather difficult to solve. Instead, we perform the position space path integral first which results in expressions which are rather simple to handle. Using this approach, we have obtained the propagators for free L´evy flight and L´evy flights in linear and harmonic potentials in the over damped limit [8]. The results obtained by this method are in complete agreement with those obtained by Jesepersen et al. [4]. In addition to these results, we were also able to obtain the exact propagator for L´evy flights in a harmonic potential with a time-dependent force constant which has not been reported in the literature. Another interesting problem that we have considered in the over damped limit is to obtain the probability distribution for the area under the trajectory of a L´evy particle. The distributions, again, were obtained for free L´evy flight and for L´evy flights subjected to linear and harmonic potentials. In the harmonic potential, we have considered situations where the force constant is time-dependent as well as time-independent. Like in the case of the over damped limit, the probability distribution for L´evy flights in the under damped limit of friction can also be described using a fractional Fokker-Planck equation, although in the full phase space. However, this has not yet been solved for any general value of α to obtain the complete propagator in terms of both position and velocity. Using our path integral approach, the exact full phase space propagators have been obtained for all values of α for free L´evy flights as well as in the presence of linear and harmonic potentials[8]. The results that we obtain are all exact when the potential is at the most harmonic. If the potential is higher than harmonic, like the cubic potential, we have used a semi classical evaluation where, we extremize the action using an optimal path and further, account for fluctuations around this optimal path. Such potentials are very useful in describing the problem of escape of a particle over a barrier. The barrier crossing problem is very extensively studied for Brownian motion (Kramers problem) and the associated rate constant has been calculated in a variety of methods, including the path integral approach. We are interested in its L´evy analogue where we consider the escape of a particle driven by a L´evy noise over a barrier. On extremizing the action which depends both on phase space variables, we arrived at optimal paths in both the position space as well as the space of the conjugate variable, p. The paths form an infinite hierarchy of instant on paths, all of which have to be accounted for in order to obtain the correct rate constant. Care has to be taken while accounting for fluctuations around the optimal path since these fluctuations should be independent of the time-translational mode of the instant on paths. We arrived at an ‘orthogonalization’ scheme to perform the same. Our procedure is valid in the limit when the barrier height is large(or when the diffusion constant is very small), which would ensure that there is small but a steady flux of particles over the barrier even at very large times. Unlike the traditional Kramers rate expression, the rate constant for barrier crossing assisted by L´evy noise does not have an exponential dependence on the barrier height. The rate constant for wide range of α, other than for those very close to α = 2, are proportional to Dμ where, µ ≈ 1 and D is the diffusion constant. These observations are consistent with the simulation results obtained by Chechkin et al. [9]. In addition, our approach when applied to Brownian motion, gives the correct dependence on D. In equilibrium statistical mechanics we have considered two problems. In the first one, we have evaluated the imaginary time propagator for a harmonic oscillator with a time-dependent force constant(ω2(t))exactly, when ω2(t) is of the form λ2(t) - λ˙(t)where λ(t) is any arbitrary function of t. We have made use of Hamiltonian path integrals for this. The second problem that we considered was the evaluation of the partition function for hindered rotors. Hindered rotors are molecules which have a barrier for internal rotation. The molecule behaves like free rotor when the barrier is very small in comparison with the thermal energy, and when the barrier is very high compared to thermal energy, it behaves like a harmonic oscillator. Many methods have been developed in order to obtain the partition function for a hindered rotor. However, most of them are some what ad-hoc since they interpolate between free-rotor and the harmonic oscillator limits. We have obtained the approximate partition function by writing it as the trace of the density matrix and performing a harmonic approximation around each point of the potential[10]. The density matrix for a harmonic potential is in turn obtained from a path integral approach[11]. The results that we obtain using this method are very close to the exact results for the problem obtained numerically. Also, we have devised a proper method to take the indistinguishability of particles into account in internal rotation which becomes very crucial while calculating the partition function at low temperatures.

There is a growing consensus among physicists that the classical notion of spacetime has to be drastically revised in order to nd a consistent formulation of quantum mechanics and gravity. One such nontrivial attempt comprises of replacing functions of continuous spacetime coordinates with functions over noncommutative algebra. Dynamics on such noncommutative spacetimes (noncommutative theories) are of great interest for a variety of reasons among the physicists. Additionally arguments combining quantum uncertain-ties with classical gravity provide an alternative motivation for their study, and it is hoped that these theories can provide a self-consistent deformation of ordinary quantum field theories at small distances, yielding non-locality, or create a framework for finite truncation of quantum field theories while preserving symmetries. In this thesis we study the gauge theories on noncommutative Moyal space. We nd new static solitons and instantons in terms of the so-called generalized Bose operators (GBO). GBOs are constructed to describe reducible representation of the oscillator algebra. They create/annihilate k-quanta, k being a positive integer. We start with giving an alternative description to the already found static magnetic flux tube solutions of the noncommutative gauge theories in terms of GBOs. The Nielsen-Olesen vortex solutions found in terms of these operators also reduce to the ones known in the literature. On the other hand, we nd a class of new instanton solutions which are unitarily inequivalent to the ones found from ADHM construction on noncommutative space. The charge of the instanton has a description in terms of the index representing the reducibility of the Fock space representation, i.e., k. After studying the static soliton solutions in noncommutative Minkowski space and the instanton solutions in noncommutative Euclidean space we go on to study the implications of the time-space noncommutativity in Minkowski space. To understand it properly we study the time-dependent transitions of a forced harmonic oscillator in noncommutative 1+1 dimensional spacetime. We also provide an interpretation of our results in the context of non-linear quantum optics. We then shift to the so-called DSR theories which are related to a different kind of noncommutative ( -Minkowski) space. DSR (Doubly/Deformed Special Relativity) aims to search for an alternate relativistic theory which keeps a length/energy scale (the Planck scale) and a velocity scale (the speed of light scale) invariant. We study thermodynamics of an ideal gas in such a scenario. In first chapter we introduce the subjects of the noncommutative quantum theories and the DSR. Chapter 2 starts with describing the GBOs. They correspond to reducible representations of the harmonic oscillator algebra. We demonstrate their relevance in the construction of topologically non-trivial solutions in noncommutative gauge theories, focusing our attention to flux tubes, vortices, and instantons. Our method provides a simple new relation between the topological charge and the number of times the basic irreducible representation occurs in the reducible representation underlying the GBO. When used in conjunction with the noncommutative ADHM construction, we nd that these new instantons are in general not unitarily equivalent to the ones currently known in literature. Chapter 3 studies the time dependent transitions of quantum forced harmonic oscillator (QFHO) in noncommutative R1;1 perturbatively to linear order in the noncommutativity . We show that the Poisson distribution gets modified, and that the vacuum state evolves into a \squeezed" state rather than a coherent state. The time evolutions of un-certainties in position and momentum in vacuum are also studied and imply interesting consequences for modelling nonlinear phenomena in quantum optics. In chapter 4 we study thermodynamics of an ideal gas in Doubly Special Relativity. We obtain a series solution for the partition function and derive thermodynamic quantities. We observe that DSR thermodynamics is non-perturbative in the SR and massless limits. A stiffer equation of state is found. We conclude our results in the last chapter.

This work deals with using modern active functional blocks in electronic circuits. These blocks have better features than classical operational amplifiers and are characterized especially by working in current mode. Therefore these blocks can be used in higher frequencies. Using those blocks it is possible to design e.g. electronically variable-frequency filters of types low-pass filter, high-pass filter, band-pass filter, etc. Then it is also possible to easily realize electronically variable-frequency oscillators. This work is focused on some of these blocks, their basic characteristics and principles. Also three oscillators with current conveyors of second generation are designed. Its made simulation, sensitivity and tolerance analysis and magnitude stabilization. Everything is performed in OrCAD PSpice program. These made oscillators are electronic tunable in the band frequency ones of MHz.

[ES] La optomecánica de cavidades se ocupa de la interacción entre la luz y la materia a través del efecto de presión de radiación cuando las ondas ópticas y mecánicas implicadas están confinadas en una cavidad. En estos sistemas optomecánicos, la interacción entre fotones y fonones da lugar a multitud de fenómenos en función de las condiciones en las que se excita el sistema. En particular, se pueden obtener dos regímenes distintos en los que se puede, o bien absorber fonones (denominado como enfriamiento de la cavidad), o bien éstos se pueden amplificar (régimen conocido como calentamiento de la cavidad). El primer régimen puede usarse, por ejemplo, para reducir la ocupación térmica del sistema y se usa comúnmente para aplicaciones relativas al procesado de información cuántica. Sin embargo, la amplificación de fonones, que puede ser desarrollada a temperatura ambiente, ha permitido conseguir alcanzar incluso las condiciones necesarias para obtener láseres de fonones, lo cual permite poder usar esta característica como elemento de referencia en aplicaciones relativas al procesado de señales de radiofrecuencia (RF). En esta tesis se aborda el confinamiento simultáneo y la interacción de fotones y fonones en estructuras periódicas y en guías no suspendidas desarrolladas en sistemas CMOS compatibles basados en tecnología de silicio. A través del estudio experimental de estas estructuras periódicas, hemos demostrado que las cavidades optomecánicas pueden actuar como elementos clave en el dominio de la fotónica de microondas, donde todo el procesado de la información puede ser realizado en el dominio óptico a través de la manipulación de fonones en este sistema. En particular, mostramos que un solo oscilador optomecánico puede actuar tanto como un oscilador local y un mezclador de RF, y éste puede operar como un conversor de frecuencias de señales de cadenas de datos reales. Para mejorar esta funcionalidad, también se demuestra que es posible obtener tanto peines de frecuencias ópticos así como múltiples modos mecánicos confinados, aumentando así su rendimiento. Por otro lado, con el objetivo de poder solventar las posibles limitaciones de estos sistemas, en esta tesis también se exploran diferentes configuraciones que permiten la interacción acusto-óptica simultánea en la misma estructura. Específicamente, se analiza la interacción optomecánica en discos de alto índice que soportan estados cuasi-ligados en el continuo así como una propuesta de guías no suspendidas que soportan altas ganancias de Brillouin. Este último estudio debería permitir el desarrollo de sistemas optomecánicos no suspendidos donde el problema de la pérdida de fonones hacia el sustrato se resuelva, hecho que permitiría enormemente simplificar la fabricación de estos sistemas optomecánicos en chips de silicio así como su uso en múltiples aplicaciones. / [CA] L'optomecànica de cavitats s'ocupa de la interacció entre la llum i la matèria a través de l'efecte de pressió de radiació quan les ones òptiques i mecàniques implicades estan confinades en una cavitat. En aquests sistemes optomecànics, la interacció entre fotons i fonons dona lloc a multitud de fenòmens en funció de les condicions de les condicions en les quals s'excita el sistema. En particular, es poden obtindre dos règims diferents en els quals es pot, o bé, absorbir fonons (denominat com a refredament de la cavitat), o bé, es poden amplificar (règim conegut com a calfament de la cavitat). El primer règim pot usar-se, per exemple, per a reduir l'ocupació tèrmica del sistema i s'usa comunament per a aplicacions relatives al processament d'informació quàntica. No obstant això, l'amplificació de fonons, que pot ser desenvolupada a temperatura ambient, ha permés aconseguir fins i tot les condicions necessàries per a obtindre làsers de fonons, la qual cosa permet poder usar aquesta característica com a element de referència en aplicacions relatives al processament de senyals de radiofreqüència (RF). En aquesta tesi s'aborda el confinament simultani i la interacció de fotons i fonons en estructures periòdiques i en guies no suspeses en sistemes CMOS compatibles basats en tecnologia de silici. A través de l'estudi experimental d'aquestes estructures periòdiques, hem demostrat que les cavitats optomecàniques poden actuar com a elements clau en el domini de la fotònica de microones, on tot el processament de la informació pot ser realitzat en el domini òptic a través de la manipulació de fonons en aquest sistema. En particular, vam mostrar que només un oscil·lador optomecànic pot actuar tant com un oscil·lador local i un mesclador de RF, i aquest pot operar com un convertidor de freqüències de senyals de cadenes de dades reals. Per a millorar aquesta funcionalitat, també es demostra que és possible obtindre tant tren de freqüències òptics així com múltiples modes mecànics confinats, augmentant així el seu rendiment. D'altra banda, amb l'objectiu de poder solucionar les possibles limitacions d'aquests sistemes, en aquesta tesi també s'exploren diferents configuracions que permeten la interacció acusto-òptica simultània en la mateixa estructura. Específicament, s'analitza la interacció optomecànica en discos d'alt índex que suporten estats quasi-lligats en el continu així com una proposta de guies no suspeses que suporten altes ganancies de Brillouin. Aquest últim estudi hauria de permetre el desenvolupament de sistemes optomecànics no suspesos on el problema de la pèrdua de fonons cap al substrat es resolga, fet que permetria enormement simplificar la fabricació d'aquests sistema optomecànics en xips de silici així com el seu ús en diverses aplicacions. / [EN] Cavity optomechanics deals with the interaction of light and matter through the radiation pressure effect, when the involved optical and mechanical waves are confined in a cavity. In optomechanical systems, photon and phonon interaction give rise to a plethora of phenomena as a function of the driving conditions of the system. Relative to that, two distinctive regimes can be obtained which enable either the absorption of phonons (cavity cooling) or their amplification (cavity heating). The first regime can be used to reduce the thermal occupancy of the system and it is commonly used for quantum processing information applications. However, the amplification of phonons, which can be performed at room temperature, has enabled to even reach phonon lasing conditions, a feature that could be used as a reference element for RF processing applications. In this thesis, we address the simultaneous confinement and interaction of photons and phonons in periodic structures and unreleased waveguides on CMOS-compatible silicon-based technology. Throughout the experimental study of those periodic structures, we demonstrate that optomechanical cavities can perform as key blocks in the microwave photonics domain where all the information processing can be performed in the optical domain through phonon manipulation. In particular, we show that a single optomechanical oscillator can perform as both a local oscillator and an RF mixer, and it can operate as a frequency-converted of real data stream signals. To improve its performance, it is also demonstrated that optical frequency combs can be obtained by means of this system and multiple mechanical mode confinement can also be achieved, thus improving the functionality of the system. On the other hand, in order to fulfill the possible limitations of those systems, we explore different configurations enabling the simultaneous acousto-optic interaction together into the same structure. Especially, optomechanical interaction in high-index disks supporting quasi-bound states in the continuum is addressed, as well as a proposal of unreleased waveguides supporting strong Brillouin gains is also reported. The last one should lead to unreleased optomechanical interacting systems where the issue of phonon leakage into the substrate is solved, which could enormously simplify the fabrication of optomechanical systems in silicon chips as well as their practical use in multiple applications. / This work has been carried out under the framework of the H2020 FET-Open EU project PHENOMEN. This Thesis was also supported by the Programa de Ayudas de Investigación y Desarrollo (PAID-01-16) de la Universitat Politècnica de València / Mercadé Morales, L. (2021). Phonons Manipulation in Silicon Chips Using Cavity Optomechanics [Tesis doctoral]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/171461