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Physical Review A

Resonance fluorescence in photonic band gap waveguide architectures: Engineering the vacuum for all-optical switching

Marian Florescu A, Sajeev John

Published May 11, 2004• 69 citations
Publisher

Abstract

We describe the spectral characteristics of the radiation scattered by two-level atoms (quantum dots) driven by a strong external field, and coupled to a photonic crystal radiation reservoir. We show that in the presence of strong variations with the frequency of the photonic reservoir density of states, the atomic, Mollow, sideband components of the scattered intensity can be strongly modified. Consequently, a weak optical probe field experiences a substantial differential gain in response to slight variations in the intensity of an optical driving field. We suggest that these effects may be of relevance to all-optical transistor action in photonic crystals. Using a specific photonic crystal heterostructure, we suggest that an all-optical microtransistor based on photonic crystals may operate at less than $100\phantom{\rule{0.3em}{0ex}}\text{nW}$ switching threshold power. Collective $N$-atom effects substantially enhance this optical switching effect. Near the switching threshold intensity, collective effects are manifest in the ${N}^{2}$ scaling of the intensity spectrum (reminiscent of superradiance). Above and below this critical region, the gain spectrum widens (linearly with $N$). This correspondingly reduces the switching time scales of the atomic system in response to external fields. Furthermore, the quantum degree of second-order coherence exhibits unusual features. Scattered photons display a variable degree of antibunching as function of driving laser field intensity and the photonic density of states discontinuity. We analyze the effects of the inhomogeneous atomic line broadening on the amplification process. We show, using suitable photonic density of states engineering, that it is possible to select a narrow spectral range around the central frequency of the atomic frequency distribution over which amplification and switching occur. This is done either by spectral decoupling of the active elements from the electromagnetic field (through the introduction of band gaps at specified spectral locations) or through incoherent pumping to selectively saturate atoms outside the spectral region chosen for amplification.

DOI
10.1103/physreva.69.053810

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Physical Review Letters•Mar 10, 1997•171 citations
We describe the spectral characteristics of the radiation scattered by two-level atoms (quantum dots) driven by a strong external field, and coupled to a photonic crystal radiation reservoir. We show that in the presence of strong variations with the frequency of the photonic reservoir density of states, the atomic, Mollow, sideband components of the scattered intensity can be strongly modified. Consequently, a weak optical probe field experiences a substantial differential gain in response to slight variations in the intensity of an optical driving field. We suggest that these effects may be of relevance to all-optical transistor action in photonic crystals. Using a specific photonic crystal heterostructure, we suggest that an all-optical microtransistor based on photonic crystals may operate at less than 100nW100\phantom{\rule{0.3em}{0ex}}\text{nW}100nW switching threshold power. Collective NNN-atom effects substantially enhance this optical switching effect. Near the switching threshold intensity, collective effects are manifest in the N2{N}^{2}N2 scaling of the intensity spectrum (reminiscent of superradiance). Above and below this critical region, the gain spectrum widens (linearly with NNN). This correspondingly reduces the switching time scales of the atomic system in response to external fields. Furthermore, the quantum degree of second-order coherence exhibits unusual features. Scattered photons display a variable degree of antibunching as function of driving laser field intensity and the photonic density of states discontinuity. We analyze the effects of the inhomogeneous atomic line broadening on the amplification process. We show, using suitable photonic density of states engineering, that it is possible to select a narrow spectral range around the central frequency of the atomic frequency distribution over which amplification and switching occur. This is done either by spectral decoupling of the active elements from the electromagnetic field (through the introduction of band gaps at specified spectral locations) or through incoherent pumping to selectively saturate atoms outside the spectral region chosen for amplification.
In this thesis we demonstrate that the photonic band edge facilitates fundamental switching effects for resonant two-level atomic systems. In a photonic crystal, a coherent laser beam can drive a two-level atom to inverted atomic states, a phenomenon forbidden in ordinary vacuum. In this process, the atomic system switches from a passive medium to a gain medium as a function of the driving field intensity. We show that the large differential gain exhibited by the atomic medium is robust against non-radiative relaxation and dephasing mechanisms. This switching effect exhibits collective enhancement for a large number of two-level atoms within a cubic wavelength. In this case, the ensemble of atoms sharply switches to a highly inverted state at a very well defined threshold value of the laser field intensity. We next demonstrate that a probe laser field of prescribed wavelength experiences a substantial differential gain by slight modulations in the control laser field. We suggest that a doped photonic band gap material may, in this sense, be used as an all-optical micro-transistor. We analyze the effects of inhomogeneous line broadening on the probe beam spectrum and demonstrate that further electromagnetic density of states engineering combined with photo-bleaching techniques can be used to both offset the deleterious effects of inhomogeneous broadening and to enlarge the switching bandwidth. We investigate the prospects and challenges in designing microstructures with characteristics required by our proposal. We further show that the switching power and the response time of an all-optical transistor can be dramatically reduced by including collective effects, which also provide a natural mechanism of broadening of the gain spectrum. Finally, we develop an exact multi-photon scattering theory of resonance fluorescence in frequency-dependent photonic reservoirs. We show that, in the limit of weak driving field, the scattering cross section becomes strongly non-Lorentzian, reflecting the non exponential character of the atomic decay. As the driving field intensity increases, the scattered field acquires new features, consistent with predictions of a dynamical decoupling of the atomic system from the photonic reservoir.
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.
We describe all-optical transistor action in photonic bandgap (PBG) materials doped with active atoms and analyse the advantages of this system over other all-optical transistor proposals. In the presence of a 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 varying the laser field intensity in the neighbourhood 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 large differential gain exhibited by the atomic medium is very robust with respect to nonradiative relaxation and dephasing mechanisms. The switching action in a PBG material is not associated with operation 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 analysing the absorption spectrum of a second probe laser beam and we show that the probe beam experiences a substantial differential gain by slight intensity modulations in the control laser field. Under certain conditions, the fluctuations in the number of totally inverted atoms that contribute to the amplification process are strongly diminished (the statistics of the excited atoms becomes sub-Poissonian), which, in turn, determines a very low-noise regime of amplification.
We study the detailed propagative characteristics of optical pulses in photonic band-gap (PBG) waveguides, coupled near resonantly to inhomogeneously broadened distributions of quantum dots. The line centers of the quantum-dot (QD) distributions are placed near a sharp discontinuity in the local electromagnetic density of states. Using finite-difference time-domain (FDTD) simulations of optical pulse dynamics and independent QD susceptibilities associated with resonance fluorescence, we demonstrate subpicosecond switching from pulse absorption to pulse amplification using steady-state optical holding and gate fields with power levels on the order of 1 milliwatt. In the case of collective response of QDs within the periodic dielectric microstructure, the gate power level is reduced to 200 microwatt for room temperature operation. In principle, this enables 200 Gbits per second optical information processing at wavelengths near 1.5 microns in various wavelength channels. The allowed pulse bandwidth in a given waveguide channel exceeds 0.5 THz allowing switching of subpicosecond laser pulses without pulse distortion. The switching contrast from absorption to gain is governed by the QD oscillator strength and dipole dephasing time scale. We consider dephasing time scales ranging from nanoseconds (low-temperature operation) to one picosecond (room-temperature operation). This all-optical transistor action is based on simple Markovian models of single-dot and collective-dot inversion and switching by coherent resonant pumping near the photon density of states discontinuity. The structured electromagnetic vacuum is provided by two-mode waveguide architectures in which one waveguide mode has a cutoff that occurs, with very large Purcell factor, near the QDs resonance, while the other waveguide mode exhibits nearly linear dispersion for fast optical propagation and modulation. Unlike optical switching based on Kerr nonlinearities in an optical cavity resonator, switching power levels and switching speeds for our QD device are not inversely proportional to cavity quality factors.
We describe the role of first non-Markovian corrections to resonance fluorescence in photonic crystals, using a perturbative expansion of the Heisenberg equations of motion in powers of the atom-field reservoir coupling strength. Non-Markovian effects arise from the rapid variation of the photonic density of states with frequency. Our method recaptures the physics of the photon-atom bound state in the presence of a full photonic band gap. For the anisotropic three-dimensional photonic band gap, it predicts remarkable features in the resonance fluorescence, such as atomic population inversion and switching behavior in a two-level atom for moderate values of the applied laser field. The magnitude of the switching effect depends sensitively on the external laser intensity and its detuning frequency from the atomic transition. The robustness of this effect against nonradiative decay and dephasing mechanisms is also investigated.
We demonstrate population inversion and sub-Poissonian excitation statistics of NNN two-level atoms in the context of collective resonance fluorescence. This occurs within photonic band gap and other confined photonic systems that exhibit sharp features in the optical density of states. When the deviation in the photon density of states between the Mollow spectral components is considerable, the atoms switch collectively from ground to excited states at a critical value of the applied laser field. This suggests a new mechanism of sub-Poissonian pumping of lasers, fast optical switching, and optical transistor action.