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Physical Review A

Optical bistability and phase transitions in a doped photonic band-gap material

Sajeev John, Tran Quang

Published Nov 1, 1996• 35 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.54.4479

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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 dielectric response of impurity two-level atoms in a photonic band gap (PBG) to an applied laser field. In this system, the atoms may exchange energy coherently by resonance dipole-dipole interaction (RDDI) which is assumed to be strong compared to the spontaneous emission rate. When the applied Rabi frequency exceeds the RDDI energy scale, nonlinear saturation of the absorptive part of the susceptibility occurs while the real part of the nonlinear susceptibility remains large. This suggests that doped PBG materials may act as nearly lossless, but highly nonlinear dielectrics.
Summary form only given. Unlike semiconductors which facilitate the coherent propagation of electrons, photonic band gap (PBG) materials execute their novel functions through the coherent localization of photons. When a PBG material is doped with impurity atoms which have an electronic transition that lies within the gap, spontaneous emission of light from the atom is inhibited. Inside the gap, the photon forms a bound state to the atom. Outside the gap, radiative dynamics in the colored vacuum is highly nonMarkovian. I discuss the influence of these memory effects on laser action. When spontaneous emission is absent, the next order radiative effect (resonance dipole-dipole interaction between atoms) must be incorporated, leading to anomalous nonlinear optical effects which occur at a much lower threshold than in ordinary vacuum. I describe the collective switching of two-level atoms near a photonic band edge, by external laser field, from a passive stare to one exhibiting population inversion. This effect is forbidden in ordinary vacuum. Finally, I discuss the prospects for a phase sensitive, single (3-level) atom quantum memory device, onto which information may be written by an external laser pulse. By scattering polarized photons (flying qubit) this system may execute certain quantum logic operations.
A method of dynamic control of absorption and dispersion of a two-level quantum system (atoms, ions or quantum dots) doping a photonic band gap (PBG) material via variation of the intensity and frequency of an external laser field is proposed. The frequency of an optical transition should be inside a PBG and located near or at a photonic band edge. In this case the laser field 'dresses' the quantum system (Mollow splitting) while the decay rates of the dressed states become very different due to a photonic band edge and depend on the form of spectral density of electromagnetic modes as well as intensity and frequency of the laser field. This enables us to control absorption and dispersion of a signal laser field, which is near resonant to the quantum transition of a dopant.
Summary form only given. Photonic band gap (PBG) materials are a new class of dielectrics which represent a major new frontier in quantum, nonlinear, and classical optics. They also represent a new technology platform for the optical networking industry. Unlike semiconductors which facilitate the coherent propagation of electrons, PBG materials execute their novel functions through the coherent localization of photons. When a PBG material is doped with impurity atoms (or other two-level systems) which have an electronic transition that lies within the gap, spontaneous emission of light from the atom is inhibited. Instead, the photon forms a bound state to the atom. This has dramatic consequences for collective light emission from a large number of atoms and for the interaction of such atoms with an external laser field. I describe the design of an all optical micro-transistor based on collective switching of two-level atoms near a photonic band edge, by an external laser field. I discuss tunable PBG materials whose band structure can be modulated by means of an external field. This effect enables the steering of light in a manner similar to the steering of electrons by an electric field in a semiconductor.
We describe all-optical transistor action in photonic band gap materials doped with active atoms. In the presence of a photonic band gap (PBG) material, a coherent laser beam with the frequency slightly detuned from the resonant atomic transition frequency can drive a collection of two-level atoms to an almost totally inverted state, a phenomenon strictly forbidden in ordinary vacuum. By changing the laser field intensity in the neighborhood of a threshold value, it is possible to drive the atomic system through a transition from states in which the atoms populate preferentially the ground level to almost totally inverted states. In this process, the atomic system switches from a passive medium (highly absorptive) to a active medium (highly amplifying). The switching action in a PBG material is not associated with operating near a narrow cavity resonance with conventional trade-off between switching time and switching threshold intensity. Rather it is associated with an abrupt discontinuity in the engineered broad band electromagnetic density of states of the PBG material. We demonstrate all-optical transistor action in PBG materials by analyzing the absorption spectrum of a second probe laser beam and we show that the probe beam experience a substantial differential gain by slight intensity modulations in the control laser field.
A theory of linear susceptibility has been developed in the presence of dipole-dipole interaction for photonic-band-gap (PBG) materials doped with an ensemble of five-level nanoparticles. An external probe laser induces dipole moments in nanoparticles. When the concentration of the particles is high, the induced dipoles interact with one another through dipole-dipole interaction. Mean-field theory is used to include the effect of dipole-dipole interaction in the calculation of susceptibility. Numerical simulations are performed for the real and imaginary susceptibilities and it is found that the system switches between inversionless and noninversionless states. In addition the system switches between absorptionless and nonabsorptionless states. These occur when the resonance energy lies near the valence-band edge of the photonic-band-gap material. The theory also predicts a polarization catastrophe in PBG materials doped with nanoparticles.