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Physical Review A

Optical wavelength converters for photonic band gap microcircuits

Dragan Vujić, Sajeev John

Published May 18, 2009• 4 citations
Publisher

Abstract

We demonstrate compact optical wavelength conversion architecture for picosecond laser pulses and data streams within photonic band gap waveguides. These multimode waveguides are seeded with resonantly driven, inhomogeneously broadened, distributions of quantum dots whose optical transition center frequency is placed near a sharp discontinuity in the local (electromagnetic) density of states (LDOS). This discontinuity is provided by a cutoff in one of the waveguide modes. Wavelength conversion of an optical pulse propagating in the single-mode spectral range of the waveguide, near the LDOS jump, is provided by a steady-state holding field with frequency matched to the center frequency of the quantum dot distribution. In the absence of an incident laser pulse, the holding field is absorbed by the quantum dots. When the incident pulse intensity is sufficient to cause population inversion of a suitable fraction of the quantum dots, the holding field is amplified and the incident pulse profile is imprinted on to the holding field, leading to wavelength conversion in the range of 3--20 nm at wavelengths near $1.5\text{ }\ensuremath{\mu}\text{m}$. Larger wavelength shifts typically require higher power levels for operation (milliwatt scale) but enable conversion of shorter (picosecond) pulses. Small wavelength shifts typically require narrower distribution of quantum dot resonance frequencies. Using finite-difference time-domain simulations, we show that an optical pulse (Gaussian in time) can create another equivalent optical pulse with either higher or lower center frequency inside the photonic band gap of the structure. Optical pulses of a given center frequency can also be selectively amplified or absorbed depending on the coincident arrival of another laser pulse with different center frequency, enabling all-optical logic operations within a multiwavelength-channel optical circuit.

DOI
10.1103/physreva.79.053836

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We demonstrate compact optical wavelength conversion architecture for picosecond laser pulses and data streams within photonic band gap waveguides. These multimode waveguides are seeded with resonantly driven, inhomogeneously broadened, distributions of quantum dots whose optical transition center frequency is placed near a sharp discontinuity in the local (electromagnetic) density of states (LDOS). This discontinuity is provided by a cutoff in one of the waveguide modes. Wavelength conversion of an optical pulse propagating in the single-mode spectral range of the waveguide, near the LDOS jump, is provided by a steady-state holding field with frequency matched to the center frequency of the quantum dot distribution. In the absence of an incident laser pulse, the holding field is absorbed by the quantum dots. When the incident pulse intensity is sufficient to cause population inversion of a suitable fraction of the quantum dots, the holding field is amplified and the incident pulse profile is imprinted on to the holding field, leading to wavelength conversion in the range of 3--20 nm at wavelengths near 1.5 \ensuremathμm1.5\text{ }\ensuremath{\mu}\text{m}1.5 \ensuremathμm. Larger wavelength shifts typically require higher power levels for operation (milliwatt scale) but enable conversion of shorter (picosecond) pulses. Small wavelength shifts typically require narrower distribution of quantum dot resonance frequencies. Using finite-difference time-domain simulations, we show that an optical pulse (Gaussian in time) can create another equivalent optical pulse with either higher or lower center frequency inside the photonic band gap of the structure. Optical pulses of a given center frequency can also be selectively amplified or absorbed depending on the coincident arrival of another laser pulse with different center frequency, enabling all-optical logic operations within a multiwavelength-channel optical circuit.
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 demonstrate dynamical near-complete inversion switching of a two-level quantum dot driven by picosecond optical pulses in a bimodal photonic band gap (PBG) waveguide at microwatt power levels. This is enabled by a sharp steplike discontinuity in the local (electromagnetic) density of states (LDOS) provided by a cutoff in one of the two waveguide modes. The atomic Bloch vector equations in this colored vacuum are derived using dressed state description of the atomic density operator in the presence of phonon-mediated dephasing. Instead of assuming phenomenological decay rates, we derive explicit expressions for decay terms of bare state atomic dipole moments and population in the Born-Markov approximation from a master equation approach. Giant Mollow splitting of the atom level due to subwavelength light localization of strong driving pulse causes the time-dependent Mollow bands to straddle the LDOS jump, leading to different radiative decay rates in the upper and lower Mollow sidebands. This results in remarkable field-dependent spontaneous emission and dipolar dephasing rates, combined with a novel ``vacuum structure'' term in the Bloch equations. Our Bloch equations predict ultrafast high-contrast inversion switching that is activated and deactivated by picosecond pulse trains detuned below and above the atomic resonance, respectively. This dynamic inversion is due to the rapid rise in relaxation rates as the pulse amplitude rises, causing the Bloch vector to switch from antiparallel to parallel alignment with the pulse ``torque vector.'' Subsequent near-complete inversion occurs through an adiabatic following process retained long after the pulse amplitude subsides and the system reverts to slow relaxation. For a 1% inhomogeneously broadened distribution of quantum dot with average of 100 D dipole moment, driven by $1.5\text{ }\ensuremath{\mu}\text{m}$ picosecond pulses and coupled to a cutoff mode LDOS jump with radiative emission rates of ${\ensuremath{\gamma}}_{high}=2.5\text{ }\text{THz}$ and ${\ensuremath{\gamma}}_{low}=5\text{ }\text{GHz}$, a large average population switching contrast of 0.5 is demonstrated with a phonon dephasing rate ${\ensuremath{\gamma}}_{p}=0.5\text{ }\text{THz}$. A 1.6 fJ control pulse is required per switching operation and a $30\text{ }\ensuremath{\mu}\text{W}$ pulse train is sufficient to maintain the inversion. This switchable gain (loss) segment of the PBG waveguide can be used to controllably amplify (absorb) signal pulses conveying optical information. This provides a robust mechanism for ultrafast multiwavelength channel all-optical logic in PBG microchips.
We demonstrate a trimodal waveguide architecture in a three-dimensional (3D) photonic-band-gap (PBG) material, in which the local electromagnetic density of states (LDOS) within and adjacent to the waveguide exhibits a forklike wavelength filter characteristic. This facilitates the control and switching of one laser beam with other laser beams ( $\ensuremath{\sim}1\phantom{\rule{0.3em}{0ex}}\ensuremath{\mu}\mathrm{W}$ steady-state holding power and $\ensuremath{\sim}5\phantom{\rule{0.3em}{0ex}}\mathrm{nW}$ switching power) through mutual coherent resonant interaction with quantum dots. Two waveguide modes provide narrow spectral windows where the electromagnetic LDOS is enhanced by a factor of 100 or more relative to the background LDOS of a third air-waveguide mode with nearly linear dispersion. This ``engineered vacuum'' can be used for frequency-selective, atomic population inversion and switching (by coherent resonant optical pumping) of an inhomogeneously broadened collection of ``atoms'' situated adjacent to the waveguide channel. The ``inverted'' atomic system can then be used to coherently amplify fast optical pulses propagating through the third waveguide mode. This coherent ``control of light with light'' occurs without recourse to microcavity resonances (involving long cavity buildup and decay times for the optical field). Our architecture facilitates steady-state coherent pumping of the atomic system (on the lower-frequency LDOS peak) to just below the gain threshold. The higher-frequency LDOS peak is chosen to coincide with the upper Mollow sideband of the same atomic resonance fluorescence spectrum. The probing laser is adjusted to the lower Mollow sideband, which couples to the linear dispersion (high group velocity part) of the third waveguide mode. This architecture enables rapid modulation (switching) of light at the lower Mollow sideband frequency through light pulses conveyed by the linear dispersion mode at frequencies corresponding to the central Mollow component (lower LDOS peak). We demonstrate that LDOS jumps of order 100 can occur on frequency scales of $\ensuremath{\Delta}\ensuremath{\omega}\ensuremath{\approx}{10}^{\ensuremath{-}4}{\ensuremath{\omega}}_{c}$ (where ${\ensuremath{\omega}}_{c}$ is the frequency of the jump) in a finite-size 3D photonic crystal (PC) consisting of only $10\ifmmode\times\else\texttimes\fi{}10\ifmmode\times\else\texttimes\fi{}20$ unit cells. When the semiconductor backbone of the PC has a refractive index of 3.5 and ${\ensuremath{\omega}}_{c}$ corresponds to a wavelength of $1.5\phantom{\rule{0.3em}{0ex}}\ensuremath{\mu}\mathrm{m}$, this vacuum engineering may be achieved in a sample whose largest dimension is about $12\phantom{\rule{0.3em}{0ex}}\ensuremath{\mu}\mathrm{m}$.
In this thesis, we demonstrate a new type of resonant, nonlinear, light-matter interaction facilitated by the unique electromagnetic vacuum density-of-state (DOS) structure of Photonic Band Gap (PBG) materials. Strong light localization inside PBG waveguides allows extremely strong coupling between laser fields and embedded two-level quantum dots (QD). The resulting Mollow splitting is large enough to traverse the precipitous DOS jump created by a waveguide mode cutoff. This allows the QD Bloch vector to sense the non-smoothness of the vacuum structure and evolve in novel ways that are forbidden in free space. These unusual strong-coupling effects are described using a "vacuum structure term" of the Bloch equation, combined with field-dependent relaxation rates experienced by the QD Bloch vector. This leads to alternation between coherent evolution and enhanced relaxation. As a result, dynamic high-contrast switching of QD populations can be realized with a single beam of picosecond pulses. During enhanced relaxation to a slightly inverted steady state at the pulse peak, the Bloch vector rapidly switches from anti-parallel to parallel alignment with the pulse torque vector. This then leads to a highly inverted state through subsequent coherent "adiabatic following" near the pulse tail, providing a robust mechanism for picosecond, femto-Joule all-optical switching. The simultaneous input of a second, weaker (signal) driving beam at a different frequency on top of the stronger (holding) beam enables rich modulation effects and unprecedented coherent control over the QD population. This occurs through resonant coupling of the signal pulse with the Mollow sideband transitions created by the holding pulse, leading to either augmentation or negation of the final QD population achieved by the holding pulse alone. This effect is applied to ultrafast all-optical logic AND, OR and NOT gates in the presence of significant (0.1 THz) nonradiative dephasing and (about 1%) inhomogeneous broadening. Further numerical studies of pulse evolutions inside the proposed devices demonstrate satisfactory population contrast within a PBG waveguide length of about 10 micro meter. These results provide the building blocks for low-power, ultrafast, multi-wavelength channel, on-chip, all-optical computing.
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.
Quantum frequency converters are key enabling technologies in photonic quantum information science to bridge the gap between quantum emitters and telecom photons. Here, we report a coherent frequency converter scheme combining a fiber-coupled nonlinear optical Lithium Niobate waveguide with a fiber-pigtailed single-photon source based on semiconductor quantum dots. Single and indistinguishable photons are converted from 925.7 nm to the telecommunication C-band, with a 48.4% end-to-end efficiency and full preservation of single-photon purity and indistinguishability. The integration of the two fiber-based modules achieving top-level performance represents an important step toward the practical interconnection of future quantum information processing systems operating at different wavelengths.