En aquest treball s'ha estudiat la dinàmica dels làsers de classe A i de classe B en termes del potencial de Lyapunov. En el cas que s'injecti un senyal al làser o es modulin alguns dels paràmetres, apareix un comportament moltmés complex i s'estudia el conjunt de bifurcacions.1) Als làsers de classe A, la dinàmica determinista s'ha interpretat com el moviment damunt el potencial de Lyapunov. En la dinàmica estocàstica s'obté un flux sostingut per renou per a la fase del camp elèctric.2) Per als làsers de classe A amb senyal injectat, s'ha descrit el conjunt de bifurcacions complet i s'ha determinat el conjunt d'amplituds i freqüències en el quals el làser responajustant la seva freqüència a la del camp extern. 3) S'ha obtingut un potencial de Lyapunov pels làsers de classe B, només vàlid en el cas determinista, que inclou els termes de saturació de guany i d'emissió espontània.4) S'ha realitzat un estudi del conjunt de bifurcacions parcial al voltant del règim tipus II de la singularitat Hopf--sella--node en un làser de classe B amb senyal injectat.5) S'han identificat les respostes òptimes pels làsers de semiconductor sotmesos a modulació periòdica externa. S'han obtingut les corbes que donen la resposta màxima per cada tipus de resonància en el pla definit per l'amplitud relativa de modulació i la freqüència de modulació. / In this work we have studied the dynamics of both class A and class B lasers in terms of Lyapunov potentials. In the case of an injected signal or when some laser parameters are modulated, and more complex behaviour is expected, the bifurcation set is studied. The main results are the following:1) For class A lasers, the deterministic dynamics has been interpreted as a movement on the potential landscape. In the stochastic dynamics we have found a noise sustained flow for the phase of the electric field. 2) For class A lasers with an injected signal, we have been able to describe the whole bifurcation set of this system and to determine the set of amplitudes frequencies for which the laser responds adjusting its frequency to that of the external field. 3) In the case of class B lasers, we have obtained a Lyapunov potential only valid in the deterministic case, including spontaneous emission and gain saturation terms. The fixed point corresponding to the laser in the on state has been interpreted as a minimum in this potential. Relaxation to this minimum is reached through damped oscillations. 4) We have performed a study of the partial bifurcation set around the type II regime of the Hopf-saddle-node singularity in a class B laser with injected signal. 5) We have identified the optimal responses of a semiconductor laser subjected to an external periodic modulation. The lines that give a maximum response for each type of resonance are obtained in the plane defined by the relative amplitude modulation and frequency modulation.

The discovery of the Higgs boson by the LHC provided the last piece of the puzzle neces- sary for the Standard Model (SM) to be a successful theory of electroweak scale physics. However there exist various phenomenological reasons which serve as pointer towards the existence of physics beyond the Standard Model. For example the explanation for the smallness of the neutrino mass, baryon asymmetry of the universe, the presence of dark matter and dark energy etc. are not within purview of the Standard Model. Con- ceptual issues like the gauge hierarchy problem, weakness of gravity provide some of the theoretical motivation to pursue theories beyond the SM. We consider scenarios with warped extra-dimensions (Randall-Sundrum (RS) Model ) as our preferred candidate to answer some of the questions raised above. RS model gives an elegant geometric solution to address the hierarchy between the two fundamental scales of nature i.e. Planck scale and electroweak scale. In addition to this, the geometry of RS serves as a useful setup wherein the fermion mass hierarchy problem can also be solved. The goal of this thesis is to investigate whether RS model can be an acceptable theory of avour while at the same time serving as a solution to the hierarchy problem. In Chapter[1] we begin with a brief introduction of the SM, highlighting issues which pro- vides the necessary motivation for constructing new physics models. Various candidates of Beyond Standard Model (BSM) physics are introduced and a few preliminaries es- sential to understand frameworks with additional spatial-dimensions ( at and warped) is provided. In Chapter[2] we specialize to the case of warped extra-dimensions and motivate the need to have the SM elds in the bulk. Mathematical details related to the analysis of various spin elds (0; 12; 1 and 2) in a warped background necessary to understand relevant phenomenology is provided. The lack of knowledge of Dirac or Majorana nature of the neutrino leads to a wide variety of possibilities as far as neutrino mass generation is concerned. In Chapter[3] we focus on the leptonic sector where three cases of neutrino mass generation are consid- ered: a)Planck Scale lepton number violation (LLHH case) b) Dirac neutrinos c) Bulk Majorana mass terms. We then study the implications of each case on the charged lepton mass tting. The case with Planck scale lepton number violation in normal RS scenario requires large and negative values for the bulk mass parameters for the charged singlets cE. Dirac neutrinos and the case with Bulk Majorana mass terms give good t to data. For completeness, the ts for the hadronic sector is provided in the appendix. In Chapter[4] avour violation for each of three cases introduced in Chapter[3] is studied. For the case with Planck scale lepton number violation, the non-perturbative Yukawa coupling between the SM singlets and the KK states render the higher order diagrams incalculable. Lepton avour violation (LFV) is particularly large for the Dirac case and the bulk Majorana case for low Kaluza-Klein(KK) mass scales. We then invoke the ansatz of Minimal Flavour violation to suppress LFV with low lying KK scales and examples of avour group is provided for both cases. In Chapter[5] we present an example with a type II two Higgs doublet model applied to the LLHH case. The setup o ers a solution where LLHH scenario can be consistently realized in RS model, where the masses and mixing angles in the leptonic sector can bet with O(1) choice of bulk parameters. Assumption of global lepton number conservation (like in Dirac neutrinos) could lead to problems in theories of quantum gravity where it does not hold. This leads us to the question whether Dirac neutrinos can be naturally realized in nature. In Chapter[6] we consider the special case of bulk Majorana mass encountered in Chapter[3] where the bulk Dirac mass terms for the right handed neutrino is set to zero. We nd that this leads to a case where the e ective zero mode neutrino mass is of Dirac type with negligible e ects from the tower of Majorana states. In Chapter[7] we consider RS at the GUT scale which no longer serves as a solution to the hierarchy problem. SUSY is introduced in the bulk and the low energy SUSY serves as a solution to the hierarchy problem. Such models serve as a useful alternative to SUSY models with family symmetries (e.g. Froggatt-Nielsen Model). However the solutions to the Yukawa hierarchy problem are constrained due to anomaly cancellation conditions. In Chapter[8] supersymmetry breaking due to radion mediation in addition to brane localized sources is considered and detailed analysis of the running of soft masses and the low energy avour observables is considered for both cases separately. In Chapter[9] we conclude and present future directions.