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Physical Review A

Dipole lasing phase transitions in media with singularities in polarizabilities

Игорь Евгеньевич Проценко, Eoin P. O’Reilly

Published Sep 20, 2006• 10 citations
Publisher

Abstract

We show that a divergence in the optical polarizability of a heterogeneous medium with nonlinear amplification and a strong dipole-dipole interaction between particles can lead to a phase transition, for which the dipole momentum of the particles or the dipole radiation rate can be taken as order parameters. The ``dipole laser'' [Phys. Rev. A 71, 063812 (2005)] can be used both as a simple example of such a second-order phase transition and to provide a recipe for its analysis. We show that similar phase transitions may be possible for a nanoparticle on the surface of an optically active medium and at the ``Clausius-Mossotti'' catastrophe in a bulk heterogeneous medium.

DOI
10.1103/physreva.74.033815

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•Dec 1, 2015•0 citations
We show that a divergence in the optical polarizability of a heterogeneous medium with nonlinear amplification and a strong dipole-dipole interaction between particles can lead to a phase transition, for which the dipole momentum of the particles or the dipole radiation rate can be taken as order parameters. The dipole laser'' [Phys. Rev. A 71, 063812 (2005)] can be used both as a simple example of such a second-order phase transition and to provide a recipe for its analysis. We show that similar phase transitions may be possible for a nanoparticle on the surface of an optically active medium and at the Clausius-Mossotti'' catastrophe in a bulk heterogeneous medium.
We study a single-mode laser system, whose active medium consists of molecules with a large difference between excited and ground electrical permanent-dipole moments. In this case, the Maxwell-Bloch equations are further coupled by nonlinear terms involving the ratio between this difference between the dipoles and the transition dipole moment. It is found that these new terms lead to multiple stationary solutions. From the linear stability analysis, we demonstrate the bistable (or multistable) character of the lasing solutions.
An interaction of an atomic/molecular medium with two strong electric fields E L (t) and E M (t) is investigated. The frequency omega L of the first (laser) field E L (t) is close to a transition frequency omega 21 between an upper (2) and a lower (1) atomic levels while the second field E M (t) is of a much lower frequency omega M << omega 21 . The medium is a dipole gas characterized by a nonzero averaged value of electric dipole moment in the states 1 and/or 2. As analytical solution of equations for the density matrix of a dipole atom/molecule interacting with the fields E L (t) and E M (t) is found using the second approximation of the averaging method by Krylov-Bogoliubov-Mitropolskii. The solution obtained is valid in a much broader range of field strengths than an analogous solution that could have been found by the usual time-dependent perturbation theory. Using the solution obtained for the density matrix, polarization of a dipole gas interacting with the fields E L (t) and E M (t) is analytically calculated. This analytical expression for polarization of such media can be utilized for study of various nonlinear optical phenomena. One of the phenomena is a generation of waves at frequencies omega L +or-p omega M and (p+1) omega M (where p=1,2,3,...) in a dipole gas. Another phenomenon is an amplification of the incident wave of the lower frequency omega M due to a stimulated scattering in a dipole gas.
Polarizable dipoles, such as atoms, molecules, or nanoparticles, subject to laser radiation may attract or repel each other. We derive a general formalism in which such laser-induced dipole-dipole interactions (LIDDIs) in any geometry and for any laser strength are described in terms of the resonant dipole-dipole interaction (RDDI) between dipoles dressed by the laser. This approach provides a simple route towards the analysis of LIDDI in a general geometry. Our general results reveal LIDDI effects due to nonlinear dipolar response to the laser, previously unaccounted for. The origin of these nonlinear effects is discussed. Our general formalism is illustrated for LIDDI between atoms in a cavity.
Theoretically predicted ''dipole lasing'', i.e., spontaneous excitation of coherent metal nano-particle dipole oscillations through interaction with a quantum-dot two-level system subject to population inversion is demonstrated. Equations for dipole lasing are the same as equations for ordinary laser, where the dipole momentum of nano-particle stands for the electromagnetic field cavity mode. Dipole lasing frequency corresponds to the localized plasmon resonance of the nano-particle. Dipole momentum of nano-particle leads to coherent dipole radiation. Optical cavity is not necessary, the size of the dipole laser can be smaller than the optical wavelength, i.e. it is dipole nano-laser. Threshold conditions and optical bistability in dipole nano-lasers are considered.
We discuss the nonlinear response of impurity two-level atoms in a pseudophotonic band gap (PBG) to an applied laser field. It is shown that in the case when the variance of resonant dipole-dipole interaction (RDDI) is much larger than its average value and the spontaneous emission rate, a nonequilibrium second-order phase transition occurs when the applied field strength parameter exceeds the variance of RDDI. This situation arises when the atomic density is low and the resonance frequency is near the center of a wide PBG. At this threshold the system changes from glassy phase to ferroelectric phase. In the case when the average value of RDDI is larger than its variance and spontaneous emission decay rate, this phase transition becomes first order, leading to optical bistability. This situation arises when the atomic density is high or when the photon localization length within the PBG extends over many optical wavelengths. The influence of RDDI fluctuation on bistability is discussed. These results suggest that disordered, impurity-doped, PBG materials may exhibit very low threshold switching properties. \textcopyright{} 1996 The American Physical Society.
We study the behavior of electric fields in and around dielectric and metal nanoparticles, and prepare the ground for their applications to a variety of systems viz. photovoltaics, imaging and detection techniques, and molecular spectroscopy. We exploit the property of nanoparticles being able to focus the radiation field into small regions and study some of the interesting nonlinear, and quantum coherence and interference phenomena near them. The traditional approach to study the nonlinear light-matter interactions involves the use of the slowly varying amplitude approximation (SVAA) as it simplifies the theoretical analysis. However, SVVA cannot be used for systems which are of the order of the wavelength of the light. We use the exact solutions of the Maxwell's equations to obtain the fields created due to metal and dielectric nanoparticles, and study nonlinear and quantum optical phenomena near these nanoparticles. We begin with the theoretical description of the electromagnetic fields created due to the nonlinear wavemixing process, namely, second-order nonlinearity in an nonlinear sphere. The phase-matching condition has been revisited in such particles and we found that it is not satisfied in the sphere. We have suggested a way to obtain optimal conditions for any type and size of material medium. We have also studied the modifications of the electromagnetic fields in a collection of nanoparticles due to strong near field nonlinear interactions using the generalized Mie theory for the case of many particles applicable in photovoltaics (PV). We also consider quantum coherence phenomena such as modification of dark states, stimulated Raman adiabatic passage (STIRAP), optical pumping in 444-level atoms near nanoparticles by using rotating wave approximation to describe the Hamiltonian of the atomic system. We also considered the behavior of atomic and the averaged atomic polarization in 777-level atoms near nanoparticles. This could be used as a prototype to study any n−n-n−level atomic system experimentally in the presence of ensembles of quantum emitters. In the last chapter, we suggested a variant of a pulse-shaping technique applicable in stimulated Raman spectroscopy (SRS) for detection of atoms and molecules in multiscattering media. We used discrete-dipole approximation to obtain the fields created by the nanoparticles.