We introduce a theoretical formalism to describe disorder-induced extrinsic scattering in slow-light photonic crystal waveguides. This work details and extends the optical scattering theory used in a recent \emph{Physical Review Letter} [M. Patterson \emph{et al.}, \emph{Phys. Rev. Lett.} \textbf{102}, 103901 (2009)] to describe coherent scattering phenomena and successfully explain complex experimental measurements. Our presented theory, that combines Green function and coupled mode methods, allows one to self-consistently account for arbitrary multiple scattering for the propagating electric field and recover experimental features such as resonances near the band edge. The technique is fully three-dimensional and can calculate the effects of disorder on the propagating field over thousands of unit cells. As an application of this theory, we explore various sample lengths and disordered instances, and demonstrate the profound effect of multiple scattering in the waveguide transmission. The spectra yield rich features associated with disorder-induced localization and multiple scattering, which are shown to be exasperated in the slow light propagation regime.
We introduce a polariton-waveguide structure, comprised of a nanowire-based photonic crystal waveguide with a quantum dot embedded in each unit cell. Using realistic designs and parameters, we derive and calculate the fundamental electromagnetic properties of these polariton waveguides, with an emphasis on the photon Green function and local optical density of states (LDOS). Both infinite and finite-size waveguides are considered, where the latter's properties are calculated using a Dyson equation approach without any approximations. We demonstrate dramatic increases, and rich fundamental cont…
We theoretically investigate the magnitude and range of the photon-mediated interaction between two quantum dots embedded in a photonic crystal waveguide, including fabrication disorder both in the crystal and in the dot positioning. We find that disorder-induced light localization has a drastic effect on the excitation transfer rate - as compared to an ideal structure - and that this rate varies widely among different disorder configurations. Nevertheless, we also find that significant rates of 50 micro-eV at a range of 10 micro-meters can be achieved in realistic systems.
We report an ultrafast optical tuning of the reflectivity of AlGaAs/InAlGaAs multiple quantum well photonic crystal waveguides using a reflection geometry, pump-probe technique.
Using finite difference time domain and band structure computer simulations, we show that it is possible to construct optical cavities and waveguide architectures in hyperuniform disordered photonic solids that are unattainable in photonic crystals. The cavity modes can be classified according to the symmetry (monopole, dipole, quadrupole,etc.) of the confined electromagnetic wave pattern. Owing to the isotropy of the band gaps characteristic of hyperuniform disordered solids, high-quality waveguides with freeform geometries (e.g., arbitrary bending angles) can be constructed that have no anal…
We report a valley photonic crystal (VPhC) waveguide in a GaAs slab with InAs quantum dots (QDs) as an internal light source exploited for experimental characterization of the waveguide. A topological interface state formed at the interface between two topologically-distinct VPhCs is used as the waveguide mode. We demonstrate robust propagation for near-infrared light emitted from the QDs even under the presence of sharp bends as a consequence of the topological protection of the guided mode. Our work will be of importance for developing robust photonic integrated circuits with small footprint…
We present a graphene photodetector for telecom applications based on a silicon photonic crystal defect waveguide. The photonic structure is used to confine the propagating light in a narrow region in the graphene layer to enhance light-matter interaction. Additionally, it is utilized as split-gate electrode to create a pn-junction in the vicinity of the optical absorption region. The photonic crystal defect waveguide allows for optimal photo-thermoelectric conversion of the occurring temperature profile in graphene into a photovoltage due to additional silicon slabs on both sides of the waveg…
The authors investigate the spontaneous emission dynamics of self-assembled InGaAs quantum dots embedded in GaAs photonic crystal waveguides. For an ensemble of dots coupled to guided modes in the waveguide we report spatially, spectrally, and time-resolved photoluminescence measurements, detecting normal to the plane of the photonic crystal. For quantum dots emitting in resonance with the waveguide mode, a ~21x enhancement of photoluminescence intensity is observed as compared to dots in the unprocessed region of the wafer. This enhancement can be traced back to the Purcell enhanced emission …
Using a polaron master equation approach we investigate the resonance fluorescence spectra from coherently driven quantum dots (QDs) coupled to an acoustic phonon bath and a photonic crystal waveguide with a rich local density of photon states (LDOS). Resonance fluorescence spectra from QDs in semiconductor crystals are known to show strong signatures of electron-phonon interactions, but when coupled to a structured photonic reservoir, the QD emission properties are also determined by the frequency dependence of the LDOS of the photon reservoir. Here, we investigate the simultaneous role of co…
We introduce a new coupled mode theory to model nonlinear Schrödinger equations for contra- propagating Bloch modes that include disorder-induced multiple scattering effects on nonlinear soliton propagation in photonic crystal waveguides. We also derive sub unit-cell coupling coefficients and use these to introduce a generalized length scale associated with each coupling effect. In particular, we define a multiple-scattering length scale that quantifies the spatial extent of a disorder- induced cavity mode. Our numerical simulations of nonlinear pulse propagation are in excellent qualitative a…
We introduce a weakly coupled photonic crystal waveguide as a promising and realistic model for all-optical amplification. A symmetric pillar type coupled photonic crystal waveguide consisting of dielectric rods periodically distributed in a free space is proposed as all-optical amplifier. Using the unique features of the photonic crystals to control and guide the light, we have properly chosen the frequency at which only one mode (odd mode) becomes the propagating mode in the coupled photonic crystal waveguide, whereas another mode (even mode) is completely reflected from the guiding structur…
We introduce a theory to describe disorder-induced scattering in photonic crystal waveguides, specifically addressing the influence of local field effects and scattering within high-index-contrast perturbations. Local field effects are shown to increase the predicted disorder-induced scattering loss and result in significant resonance shifts of the waveguide mode. We demonstrate that two types of frequency shifts can be expected, a mean frequency shift and a RMS frequency shift, both acting in concert to blueshift and broaden the nominal band structure. For a representative waveguide, we predi…
In this paper, the non-Markovian dynamics of a microcavity coupled to a waveguide in photonic crystals is studied based on Fano-type tight binding model. Using the exact master equation, we solve analytically and numerically the temporal evolution of the cavity coherent state and the associated physical observables. A critical transition is revealed when the coupling increase between the cavity and the waveguide. In particular, the cavity field becomes dissipationless when the coupling strength goes beyond a critical value, as a manifestation of strong non-Markovian memory effect. The result a…
We propose a new scheme for quantum computation using flying qubits--propagating photons in a one-dimensional waveguide--interacting with matter qubits. Photon-photon interactions are mediated by the coupling to a three- or four-level system, based on which photon-photon π-phase gates (Controlled-NOT) can be implemented for universal quantum computation. We show that high gate fidelity is possible given recent dramatic experimental progress in superconducting circuits and photonic-crystal waveguides. The proposed system can be an important building block for future on-chip quantum networks.
We study both theoretically and experimentally the effects of introducing deliberate disorder in a slow-light photonic crystal waveguide on the photon density of states. We first introduce a theoretical model that includes both deliberate disorder through statistically moving the hole centres in the photonic crystal lattice and intrinsic disorder caused by manufacturing imperfections. We demonstrate a disorder-induced mean blueshift and an overall broadening of the photonic density of states for various amounts of deliberate disorder. By comparing with measurements from a GaAs photonic crystal…
We demonstrate the in-plane emission of highly-polarized single photons from an InAs quantum dot embedded into a photonic crystal waveguide. The spontaneous emission rates are Purcell-enhanced by the coupling of the quantum dot to a slow-light mode of the waveguide. Photon-correlation measurements confirm the sub-Poissonian statistics of the in-plane emission. Under optical pulse excitation, single photon emission rates of up to 19 MHz into the guided mode are demonstrated, which corresponds to a device efficiency of 24%. These results herald the monolithic integration of sources in photonic q…
We report a study of the quantum dot emission in short photonic crystal waveguides. We observe that the quantum dot photoluminescence intensity and decay rate are strongly enhanced when the emission energy is in resonance with Fabry-Perot cavity modes in the slow-light regime of the dispersion curve. The experimental results are in agreement with previous theoretical predictions and further supported by three-dimensional finite element simulation. Our results show that the combination of slow group velocity and Fabry-Perot cavity resonance provides an avenue to efficiently channel photons from…
Cavities embedded in photonic crystal waveguides offer a promising route towards large scale integration of coupled resonators for quantum electrodynamics applications. In this letter, we demonstrate a strongly coupled system formed by a single quantum dot and such a photonic crystal cavity. The resonance originating from the cavity is clearly identified from the photoluminescence mapping of the out-of-plane scattered signal along the photonic crystal waveguide. The quantum dot exciton is tuned towards the cavity mode by temperature control. A vacuum Rabi splitting of ~ 140 \mueV is observed a…
We present measurements of the beta-factor, describing the coupling efficiency of light emitted by single InAs/GaAs semiconductor quantum dots into a photonic crystal waveguide mode. The beta-factor is evaluated by means of time-resolved frequency-dependent photoluminescence spectroscopy. The emission wavelength of single quantum dots is temperature tuned across the band edge of a photonic crystal waveguide and the spontaneous emission rate is recorded. Decay rates up to 5.7 ns^(-1), corresponding to a Purcell factor of 5.2, are measured and beta-factors up to 85% are extracted. These results …
In this paper, we develop a quantum transport theory to describe photonic transport in photonic networks. The photonic networks concerned in the paper consist of all-optical circuits incorporating photonic bandgap waveguides and driven resonators. The photonic transport flowing through waveguides are entirely determined from the exact master equation of the driven resonators. The master equation of the driven resonators is obtained by explicitly eliminating all the waveguide degrees of freedom while the back-reactions between resonators and waveguides are fully taken into account. The relation…
We explore the dynamics and directionality of spontaneous emission from self-assembled In(Ga)As quantum dots into TE-polarised guided modes in GaAs two-dimensional photonic crystal waveguides. The local group velocity of the guided waveguide mode is probed, with values as low as $\sim 1.5\%\times c$ measured close to the slow-light band edge. By performing complementary continuous wave and time-resolved measurements with detection along, and perpendicular to the waveguide axis we probe the fraction of emission into the waveguide mode ($β$-factor). For dots randomly positioned within the unit c…
Local control of the generation and interaction of indistinguishable single photons is a key requirement for photonic quantum networks. Waveguide-based architectures, in which embedded quantum emitters act as both highly coherent single photon sources and as nonlinear elements to mediate photon-photon interactions, offer a scalable route to such networks. However, local electrical control of a quantum optical nonlinearity has yet to be demonstrated in a waveguide geometry. Here, we demonstrate local electrical tuning and switching of single photon generation and nonlinear interaction by embedd…
Interfacing single emitters and photonic nanostructures enables modifying their emission properties, such as enhancing individual decay rates or controlling the emission direction. To achieve full control, the single emitter must be positioned in the nanostructures deterministically. Here, we use spectroscopy to gain spectral and spatial information about individual quantum dots in order to position each emitter in a pre-determined location in a unit cell of a photonic-crystal waveguide. Depending on the spatial and spectral positioning within the structured nanophotonic mode, we observe that …
We experimentally demonstrate topological slow light waveguides in valley photonic crystals (VPhCs). We employed a bearded interface formed between two topologically-distinct VPhCs patterned in an air-bridged silicon slab. The interface supports both topological and non-topological slow light modes below the light line. By means of optical microscopy, we observed light propagation in the topological mode in the slow light regime with a group index $n_{\rm g}$ over $30$. Furthermore, we confirmed light transmission via the slow light mode even under the presence of sharp waveguide bends. In com…
Slow light propagation in structured materials is a highly promising approach for realizing on-chip integrated photonic devices based on enhanced optical nonlinearities. One of the most successful research avenues consists in engineering the band dispersion of light-guiding photonic crystal (PC) structures. The primary goal of such devices is to achieve slow-light operation over the largest possible bandwidth, with large group index, minimal index dispersion, and constant transmission spectrum. Here, we report on the experimental demonstration of to date record high GBP in silicon-based couple…
We present an analytical theory of topologically protected photonic states for the two-dimensional Maxwell equations for a class of continuous periodic dielectric structures, modulated by a domain wall. We further numerically confirm the applicability of this theory for three-dimensional structures.
