Resonant Nonlinear Dielectric Response in a Photonic Band Gap Material (original) (raw)
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Dipole-dipole interaction in photonic-band-gap materials doped with nanoparticles
Physical Review A, 2007
A theory of linear susceptibility has been developed in the presence of dipole-dipole interaction for photonicband-gap ͑PBG͒ 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 dipoledipole 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.
Optical bistability and phase transitions in a doped photonic band-gap material
Physical Review A, 1996
We discuss the nonlinear response of impurity two-level atoms in a pseudophotonic band gap ͑PBG͒ to an applied laser field. It is shown that in the case when the variance of resonant dipole-dipole interaction ͑RDDI͒ 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.
Photonic band gap enhancement in frequency-dependent dielectrics
Physical Review E, 2004
We illustrate a general technique for evaluating photonic band structures in periodic d-dimensional microstructures in which the dielectric constant ͑͒ exhibits rapid variations with frequency. This technique involves the evaluation of generalized electromagnetic dispersion surfaces ͑k ជ , ͒ in a ͑d +1͒-dimensional space consisting of the physical d-dimensional space of wave vectors k ជ and an additional dimension defined by the continuous, independent, variable. The physical band structure for the photonic crystal is obtained by evaluating the intersection of the generalized dispersion surfaces with the "cutting surface" defined by the function ͑͒. We apply this method to evaluate the band structure of both two-and three-dimensional (3D) periodic microstructures. We consider metallic photonic crystals with free carriers described by a simple Drude conductivity and verify the occurrence of electromagnetic pass bands below the plasma frequency of the bulk metal. We also evaluate the shift of the photonic band structure caused by free carrier injection into semiconductor-based photonic crystals. We apply our method to two models in which ͑͒ describes a resonant radiation-matter interaction. In the first model, we consider the addition of independent, resonant oscillators to a photonic crystal with an otherwise frequency-independent dielectric constant. We demonstrate that for an inhomogeneously broadened distribution of resonators impregnated within an inverse opal structure, the full 3D photonic band gap (PBG) can be considerably enhanced. In the second model, we consider a coupled resonant oscillator mode in a photonic crystal. When this mode is an optical phonon, there can be a synergetic interplay between the polaritonic resonance and the geometrical scattering resonances of the structured dielectric, leading to PBG enhancement. A similar effect may arise when resonant atoms that are coupled radiatively through resonance dipole-dipole interaction are placed in a photonic crystal.
Self-induced transparency solitary waves in a doped nonlinear photonic band gap material
Physical Review E, 1998
We derive the properties of self-induced transparency ͑SIT͒ solitary waves in a one-dimensional periodic structure doped uniformly with resonance two-level atoms. In our model, the electromagnetic field is treated classically and the dopant atoms are described quantum mechanically. The resulting solitary waves take the form of ultrashort ͑picosecond͒ laser pulses which propagate near the band edge of the nonlinear photonic band gap ͑PBG͒ material doped with rare-earth atoms such as erbium. Solitary wave formation involves the combined effects of group velocity dispersion ͑GVD͒, nonresonant Kerr nonlinearity, and resonant interaction with dopant atoms. We derive the general Maxwell-Bloch equations for a nonlinear PBG system and then demonstrate the existence of elementary solitary wave solutions for frequencies far outside the gap where GVD effects are negligible and for frequencies near the photonic band edge where GVD effects are crucial. We find two distinct new types of propagating SIT solitary wave pulses. Far from Bragg resonance, we recapture the usual McCall-Hahn soliton with hyperbolic secant profile when the nonlinear Kerr coefficient (3) ϭ0. However, when the host nonresonant Kerr coefficient is nonzero, we obtain the first new type of soliton. In this case, the optical soliton envelope function deviates from the hyperbolic secant profile and pulse propagation requires nontrivial phase modulation ͑chirping͒. We derive the dependence of the solitary wave structure on the Kerr coefficient (3) , the resonance impurity atom density, and the detuning of the average laser frequency from the atomic transition. When the laser frequency and the atomic transition frequencies are near the photonic band edge we obtain the second type of soliton. To illustrate the second type of soliton we consider two special cases. In the first case, GVD facilitates the propagation of an unchirped SIT-gap soliton moving at a velocity fixed by the material's parameters. The soliton structure changes dramatically as the laser frequency is tuned through the atomic resonance. In the second illustrative case we set the Kerr coefficient (3) ϭ0. In this case, the solution is a chirped pulse which arises from the balance between GVD and the resonance interaction with the dopant atoms. Finally, we show that under certain circumstances, these solitary wave solutions may persist even in the presence of ͑subpicosecond͒ dipolar dephasing of the dopant atoms and absorption losses of the host PBG material, provided that the system is incoherently pumped. These results may be relevant to the application of PBG materials as optical devices in fiber-optic networks. ͓S1063-651X͑98͒08409-8͔
Controlling spontaneous emission in photonic-band-gap materials doped with nanoparticles
Physical Review A, 2007
The phenomenon of spontaneous emission cancellation has been investigated in photonic-band-gap materials in the presence of dipole-dipole interaction. The material is densely doped with an ensemble of five-level nanoparticles. The mean field theory is used to calculate the effect of the dipole-dipole interaction whereas the linear response theory is used to calculate the expressions for the real and imaginary susceptibilities. Numerical simulations are performed for an isotropic photonic-band-gap material. Interesting results are predicted such as the control of the spontaneous emission cancellation by moving the resonance energies between the energy band and energy gap. It is also found that the photonic-band-gap material can be switched between absorptive and nonabsorptive states by changing the strength of the dipole-dipole interaction and the resonance energies in the energy band.
Anomalous electromagnetically induced transparency in photonic-band-gap materials
Physical Review A, 2004
The phenomenon of electromagnetically induced transparency has been studied when a four-level atom is located in a photonic band gap material. Quantum interference is introduced by driving the two upper levels of the atom with a strong pump laser field. The top level and one of the ground levels are coupled by a weak probe laser field and absorption takes place between these two states. The susceptibility due to the absorption for this transition has been calculated by using the master equation method in linear response theory. Numerical simulations are performed for the real and imaginary parts of the susceptibility for a photonic band gap material whose gap-midgap ratio is 21%. It is found that when resonance frequencies lie within the band, the medium becomes transparent under the action of the strong pump laser field. More interesting results are found when one of the resonance frequencies lies at the band edge and within the band gap. When the resonance frequency lies at the band edge, the medium becomes nontransparent even under a strong pump laser field. On the other hand, when the resonance frequency lies within the band gap, the medium becomes transparent even under a weak pump laser field. In summary, we found that the medium can be transformed from the transparent state to the nontransparent state just by changing the location of the resonance frequency. We call these two effects anomalous electromagnetically induced transparency.
Physics Letters A, 2007
We have investigated the switching mechanism due to the spontaneous emission cancellation in a photonic band gap (PBG) material doped with an ensemble of four-level nano-particles. The effect of the dipole-dipole interaction has also been studied. The linear susceptibility has been calculated in the mean field theory. Numerical simulations for the imaginary susceptibility are performed for a PBG material which is made from periodic dielectric spheres. It is predicted that the system can be switched between the absorbing state and the non-absorbing state by changing the resonance energy within the energy bands of the photonic band gap material.
Polariton stark effect in dispersive and photonic band gap materials
Physica B: Condensed Matter, 2003
The polariton stark effect has been studied in dispersive and photonic band gap materials doped with a two-level atom in the presence of a monochromatic driving laser field. The driven atom gets excited to the higher state and the system spontaneously decays to the ground state by emitting polaritons. The power spectrum of polaritons emitted by the atom is calculated by using the master equation for the density matrix in the presence of the damping. It is found that when the excitation frequency of the atom lies outside the energy gap and the Rabi frequency associated with the driving field becomes comparable to or larger than the atomic line width, the polaritons spontaneous decay spectrum splits into three peaks. We call this phenomena the stark effect. The central peak has a line width smaller than that of the two side peaks. Numerical calculations are performed for GaAs and SiC semiconductors.
Thresholdless dressed-atom laser in a photonic band-gap material
Physical Review A, 2009
We demonstrate the capability of complete thresholdless lasing operation between dressed states of a twolevel atom located inside a microscopic cavity engineered in a photonic band-gap material. We distinguish between threshold and thresholdless behaviors by analyzing the Mandel's Q parameter for the cavity field. We find that the threshold behavior depends on whether the spontaneous emission is or is not present on the lasing transition. In the presence of the spontaneous emission, the mean photon number of the cavity field exhibits threshold behavior indicating that the system may operate as an ordinary laser. When the spontaneous emission is eliminated on the lasing transition, no threshold is observed for all values of the pumping rate indicating the system becomes a thresholdless laser. Moreover, we find that under a thresholdless operation, the mean photon number can increase nonlinearly with the pumping rate, and this process is accompanied by a sub-Poisson statistics of the field. This suggests that the nonclassical statistics can be used to distinguish a nonlinear operation of the dressed-atom laser.
Quantum optics of localized light in a photonic band gap
Physical Review B, 1991
We describe the quantum electrodynamics of photons interacting with hydrogenic atoms and molecules in a class of strongly scattering dielectric materials. These dielectrics consist of an ordered or nearly ordered array of spherical scatterers with real positive refractive index and exhibit a complete photonic band gap or pseudogap for all directions of electromagnetic propagation. For hydrogenic atoms with a transition frequency in the forbidden optical gap, we demonstrate both the existence and stability of a photon-atom bound state. For a band gap to center frequency ratio Aco/too-5%, the photon localization length g~") 10L, where L is the lattice constant of dielectric array. This strong self-dressing of the atom by its own localized radiation field leads to anomalous Lamb shifts and a splitting of the excited atomic level into a doublet when the transition frequency lies near a photonic band edge. We estimate the magnitude of this splitting to be 10 at the vacuum transition energies. The stability of this photon-bound state with respect to electromagnetic as well as vibrational decay mechanisms is examined. For an isolated molecule embedded in the solid fraction of the dielectric structure, the dominant mechanism for absorption and spontaneous emission is via optically driven electron-phonon interactions and the resulting phonon-absorption and-emission sidebands. Raman or Brillouin scattering of a localized photon into a propagating mode, or vice versa, directly by photon-phonon interaction is forbidden. For atoms not in contact with the solid fraction of the dielectric host, the electromagnetic two-photon spontaneous emission rate is on the scale of several days. For two identical atoms separated by a distance R within the photonic band gap, energy transfer from an excited atom to an unexcited atom occurs by a phase-shifted resonance dipole-dipole interaction which vanishes exponentially for R) g~". This leads to the formation of a narrow photonic impurity band within the gap when a finite density of atoms is present. This impurity band exhibits a difterent kind of nonlinear optical properties. When two neighboring atoms are both excited, single-photon spontaneous emission at-2%co occurs by a third-order electromagnetic process with rate I-a'coo(ao/R)', where ao is the atomic Bohr radius and e is the fine-structure constant.