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Quantum photonic devices are candidates for realizing practical quantum computers and networks. The development of integrated quantum photonic devices can greatly benefit from the ability to incorporate different types of materials with complementary, superior optical or electrical properties on a single chip. Semiconductor quantum dots (QDs) serve as a core element in the emerging modern photonic quantum technologies by allowing on-demand generation of single-photons and entangled photon pairs. During each excitation cycle, there is one and only one emitted photon or photon pair. QD photonic devices are on the verge of unfolding for advanced quantum technology applications. In this review, we focus on the latest significant progress of QD photonic devices. We first discuss advanced technologies in QD growth, with special attention to droplet epitaxy and site-controlled QDs. Then we overview the wavelength engineering of QDs via strain tuning and quantum frequency conversion techniques. We extend our discussion to advanced optical excitation techniques recently developed for achieving the desired emission properties of QDs. Finally, the advances in heterogeneous integration of active quantum light-emitting devices and passive integrated photonic circuits are reviewed, in the context of realizing scalable quantum information processing chips.

The anisotropy of hexagonal boron nitride (hBN) gives rise to hyperbolic phonon-polaritons (HPhPs), notable for their volumetric frequency-dependent propagation and strong confinement. For frustum (truncated nanocone) structures, theory predicts five, high-order HPhPs, sets, but only one set was observed previously with far-field reflectance and scattering-type scanning near-field optical microscopy. In contrast, the photothermal induced resonance (PTIR) technique has recently permitted sampling of the full HPhP dispersion and observing such elusive predicted modes; however, the mechanism underlying PTIR sensitivity to these weakly-scattering modes, while critical to their understanding, has not yet been clarified. Here, by comparing conventional contact- and newly developed tapping-mode PTIR, we show that the PTIR sensitivity to those weakly-scattering, high-Q (up to ≈280) modes is, contrary to a previous hypothesis, unrelated to the probe operation (contact or tapping) and is instead linked to PTIR ability to detect tip-launched dark, volumetrically-confined polaritons, rather than nanostructure-launched HPhPs modes observed by other techniques. Furthermore, we show that in contrast with plasmons and surface phonon-polaritons, whose Q-factors and optical cross-sections are typically degraded by the proximity of other nanostructures, the high-Q HPhP resonances are preserved even in high-density hBN frustum arrays, which is useful in sensing and quantum emission applications.

The deterministic integration of quantum emitters into on-chip photonic elements is crucial for the implementation of scalable on-chip quantum circuits. Here, we report on the deterministic integration of single quantum dots (QD) into tapered multimode interference beam splitters using in-situ electron beam lithography (EBL). We demonstrate the functionality of the deterministic QD-waveguide structures by µPL spectroscopy and by studying the photon cross-correlation between the two MMI output ports. The latter confirms single-photon emission and on-chip splitting associated with g(2)(0) << 0.5. Moreover, the deterministic integration of QDs enables the demonstration and controlled study of chiral light-matter effects and directional emission in QD-WGs, and the realization of low-loss heterogenous QD-WG systems with excellent quantum optical properties.

Semiconductor quantum dots are excellent emitters of single photons. Often, the same mode is used to resonantly excite a QD and to collect the emitted single-photons, requiring cross polarization to separate out scattered laser light. This reduces the source brightness to ≤50%, and potentially eliminates their use in some quantum applications. We demonstrate a resonant-excitation approach to creating single photons that is free of any filtering whatsoever. This integrated device allows us to resonantly excite single quantum-dot states in several cavities in the plane of the device using connected cavity-waveguides, while the cavity-enhanced single-photon fluorescence is directed vertically (off-chip) in a Gaussian mode.

We demonstrate hybrid quantum photonic circuits comprising Si3N4 waveguides featuring losses in the dB/m range, with directly integrated quantum dot based single-photon sources.

We report progress in bi-directional microwave-to-optical conversion mediated by a resonant mechanical super-mode in a coupled piezo-optomechanical system with theoretically predicted high conversion efficiency and potential in quantum networks.

We demonstrate integrated Si3N4 waveguides containing single-photon emitters based on single InAs quantum dots that were deterministically positioned in a GaAs nanowaveguide via a low-temperature in-situ electron-beam lithography.

Semiconductor quantum dots embedded in micro-pillar cavities are excellent emitters of single photons when pumped resonantly. Often, the same spatial mode is used to both resonantly excite a quantum dot and to collect the emitted single photons, requiring cross-polarization to reduce the uncoupled scattered laser light. This inherently reduces the source brightness to 50 %. Critically, for some quantum applications the total efficiency from generation to detection must be over 50 %. Here, we demonstrate a resonant-excitation approach to creating single photons that is free of any cross-polarization, and in fact any filtering whatsoever. It potentially increases single-photon rates and collection efficiencies, and simplifies operation. This integrated device allows us to resonantly excite single quantum-dot states in several cavities in the plane of the device using connected waveguides, while the cavity-enhanced single-photon fluorescence is directed vertical (off-chip) in a Gaussian mode. We expect this design to be a prototype for larger chip-scale quantum photonics., 6 pages, 5 figures

Silicon photonics enables scaling of quantum photonic systems by allowing the creation of extensive, low-loss, reconfigurable networks linking various functional on-chip elements. Inclusion of single quantum emitters onto photonic circuits, acting as on-demand sources of indistinguishable photons or single-photon nonlinearities, may enable large-scale chip-based quantum photonic circuits and networks. Towards this, we use low-temperature $\textit{in situ}$ electron-beam lithography to deterministically produce hybrid GaAs/Si$_3$N$_4$ photonic devices containing single InAs quantum dots precisely located inside nanophotonic structures, which act as efficient, Si$_3$N$_4$ waveguide-coupled on-chip, on-demand single-photon sources. The precise positioning afforded by our scalable fabrication method furthermore allows observation of post-selected indistinguishable photons. This indicates a promising path towards significant scaling of chip-based quantum photonics, enabled by large fluxes of indistinguishable single-photons produced on-demand, directly on-chip.

Optomechanical cavities have been studied for applications ranging from sensing to quantum information science. Here, we develop a platform for nanoscale cavity optomechanical circuits in which optomechanical cavities supporting co-localized 1550 nm photons and 2.4 GHz phonons are combined with photonic and phononic waveguides. Working in GaAs facilitates manipulation of the localized mechanical mode either with a radio frequency (RF) field through the piezo-electric effect, which produces acoustic waves that are routed and coupled to the optomechanical cavity by phononic crystal waveguides, or optically through the strong photoelastic effect. Along with mechanical state preparation and sensitive readout, we use this to demonstrate an acoustic wave interference effect, similar to atomic coherent population trapping, in which RF-driven coherent mechanical motion is cancelled by optically-driven motion. Manipulating cavity optomechanical systems with equal facility through both photonic and phononic channels enables new architectures for signal transduction between the optical, electrical, and mechanical domains.

We demonstrate stable microresonator Kerr soliton frequency combs in a III-V platform (AlGaAs on SiO$_2$) through quenching of thermorefractive effects by cryogenic cooling to temperatures between 4~K and 20~K. This cooling reduces the resonator's thermorefractive coefficient, whose room-temperature value is an order of magnitude larger than that of other microcomb platforms like Si$_3$N$_4$, SiO$_2$, and AlN, by more than two orders of magnitude, and makes soliton states adiabatically accessible. Realizing such phase-stable soliton operation is critical for applications that fully exploit the ultra-high effective nonlinearity and high optical quality factors exhibited by this platform.

Nanophotonics is enabling for photonic quantum technologies, providing means to effectively control light-matter interactions on chip. This talk will describe the use of nanophotonics for the creation of efficient and versatile chip-based quantum light sources.

The development of ${\text{Si}}_{\text{3}}{\text{N}}_{\text{4}}$ nanobeam optomechanical crystals is reviewed. These structures consist of a 350-nm thick, 700-nm wide doubly-clamped ${\text{Si}}_{\text{3}}{\text{N}}_{\text{4}}$ nanobeam that is periodically patterned with an array of air holes to which a defect region is introduced. The periodic patterning simultaneously creates a photonic bandgap for 980 nm band photons and a phononic bandgap for 4 GHz phonons, with the defect region serving to colocalize optical and mechanical modes within their respective bandgaps. These optical and mechanical modes interact dispersively with a coupling rate $g_{0}/2\pi \approx$ 100 kHz, which describes the shift in cavity mode optical frequency due to the zero-point motion of the mechanical mode. Optical sidebands generated by interaction with the mechanical mode lie outside of the optical cavity linewidth, enabling possible use of this system in applications requiring sideband-resolved operation. Along with a review of the basic device design, fabrication, and measurement procedures, we present new results on improved optical quality factors (up to $4\times 10^5$ ) through optimized lithography, measurements of devices after HF acid surface treatment, and temperature dependent measurements of mechanical damping between 6 and 300 K. A frequency-mechanical quality factor product $\left(f\,{\times }\,Q_m\right)$ as high as $\approx 2.6\times 10^{13}$ Hz is measured.

Deterministic techniques enabling the implementation and engineering of bright and coherent solid-state quantum light sources are key for the reliable realization of a next generation of quantum devices. Such a technology, at best, should allow one to significantly scale up the number of implemented devices within a given processing time. In this work, we discuss a possible technology platform for such a scaling procedure, relying on the application of nanoscale quantum dot imaging to the pillar microcavity architecture, which promises to combine very high photon extraction efficiency and indistinguishability. We discuss the alignment technology in detail, and present the optical characterization of a selected device which features a strongly Purcell-enhanced emission output. This device, which yields an extraction efficiency of $\eta=(49\pm4)~\%$, facilitates the emission of photons with $(94\pm2.7)~\%$ indistinguishability., Comment: 8 pages, 5 figures. arXiv admin note: text overlap with arXiv:1512.07453

Photonic integration is as an enabling technology for photonic quantum science, providing great experimental scalability, stability, and functionality. Although the increasing complexity of quantum photonic circuits has allowed proof-of-principle demonstrations of quantum computation, simulation, and metrology[1], further development is severely limited by the on-chip photon flux that can be made available from external quantum light sources[2]. Overcoming such limitations would allow a significant scaling of quantum photonic experiments, and enable quantum-level investigation of many physical processes observable on-chip through nanophotonic and nanoplasmonic structures (e.g., Kerr, optomechanical, single-photon nonlinearities). Towards such goals, we have developed a scalable, heterogeneous III-V/Si 3 N 4 integration platform for quantum photonic circuits based on passive Si 3 N 4 waveguides which directly incorporate nanophotonic single-photon sources based on self-assembled InAs quantum dots (QDs)[3]. InAs quantum dots constitute the most promising solid-state triggered single-photon sources to date[4], while SI3N4 waveguides offer low-loss propagation, tailorable dispersion and high Kerr nonlinearities which can be used for linear and nonlinear optical signal processing down to the quantum level. In our platform, the building blocks of which are shown in Fig. 1(a), active GaAs waveguide-based geometries containing InAs QDs are designed to efficiently capture QD-emitted single-photons. Captured photons, confined within the GaAs core, are then transferred with high efficiency into a passive Si 3 N 4 waveguide network via adiabatic mode transformers. Figure 1(b) shows an example device fabricated with our platform: a GaAs microring resonator containing InAs quantum dots, evanescently coupled to a GaAs bus waveguide, which is in turn coupled to an underlying Si 3 N 4 waveguide through adiabatic mode-transformers. The photoluminescence spectrum for this device, in Fig. 1(b), shows that a single QD exciton near 1125 nm, coupled to a microring whispering-gallery mode, acts as a source of single-photons that are launched directly into the Si3N4 waveguide. This geometry also allows us to effectively control the QD spontaneous emission decay lifetime by spectrally detuning the WGM with respect to the QD, as shown in Fig. 1(d).

Acoustic wave devices provide a promising chip-scale platform for efficiently coupling radio frequency (RF) and optical fields. Here, we use an integrated piezo-optomechanical circuit platform that exploits both the piezoelectric and photoelastic coupling mechanisms to link 2.4 GHz RF waves to 194 THz (1550 nm) optical waves, through coupling to propagating and localized 2.4 GHz acoustic waves. We demonstrate acousto-optic modulation, resonant in both the optical and mechanical domains, in which waveforms encoded on the RF carrier are mapped to the optical field. We also show opto-acoustic gating, in which the application of modulated optical pulses interferometrically gates the transmission of propagating acoustic pulses. The time-domain characteristics of this system under both pulsed RF and pulsed optical excitation are considered in the context of the different physical pathways involved in driving the acoustic waves, and modelled through the coupled mode equations of cavity optomechanics.

We present a wide-field, high-throughput optical technique for locating solid-state quanutm emitters with

Monolayers of transition metal dichalcogenide materials emerged as a new material class to study excitonic effects in solid state, since they benefit from enormous coulomb correlations between electrons and holes. Especially in WSe2, sharp emission features have been observed at cryogenic temperatures, which act as single photon sources . Tight exciton localization has been assumed to induce an anharmonic excitation spectrum, however, the evidence of the hypothesis, namely the demonstration of a localized biexciton, is elusive. Here, we unambiguously demonstrate the existence of a localized biexciton in a monolayer of WSe2, which triggers an emission cascade of single photons. The biexciton is identified by its time-resolved photoluminescence, superlinearity and distinct polarization in micro-photoluminescence experiments. We evidence the cascaded nature of the emission process in a cross-correlation experiment, which yields a strong bunching behavior. Our work paves the way to a new generation of quantum optics experiments with two-dimensional semiconductors., Comment: 13 pages, 3 Figures

We develop a heterogeneous III-V/Si3N4 integration platform for photonic integrated circuits incorporating on-chip, InAs quantum dot-based single-photon sources.

We report a photoluminescence imaging system for locating single quantum emitters with respect to alignment features. Samples are interrogated in a 4~K closed-cycle cryostat by a high numerical aperture (NA=0.9, 100$\times$ magnification) objective that sits within the cryostat, enabling high efficiency collection of emitted photons without image distortions due to the cryostat windows. The locations of single InAs/GaAs quantum dots within a $>50$~$��$m~$\times$~50~$��$m field of view are determined with $\approx4.5$~nm uncertainty (one standard deviation) in a 1~s long acquisition. The uncertainty is determined through a combination of a maximum likelihood estimate for localizing the quantum dot emission, and a cross-correlation method for determining the alignment mark center. This location technique can be an important step in the high-throughput creation of nanophotonic devices that rely upon the interaction of highly confined optical modes with single quantum emitters., 8 pages, 4 figures, two tables. Comments are welcome

We demonstrate an optomechanical circuit platform in GaAs in which optomechanical cavities are interfaced with interdigitated-transducers using phononic crystal waveguides. We use this platform to demonstrate phonon routing, acousto-optic and opto-acoustic modulation, and sensitive motion detection.

We demonstrate a flexible slot-mode architecture for cavity optomechanics that supports mechanical frequencies between 400 MHz and 3.5 GHz, multimode operation coupling multiple optical and mechanical resonances, and an electrostatic actuation scheme for wavelength tuning/stabilization.

We demonstrate an optomechanical circuit platform in GaAs in which optomechanical cavities are interfaced with interdigitated-transducers using phononic crystal waveguides. We use this platform to demonstrate phonon routing, acousto-optic and opto-acoustic modulation, and sensitive detection.

Optical frequency conversion has applications ranging from tunable light sources to telecommunications-band interfaces for quantum information science. Here, we demonstrate efficient, low-noise frequency conversion on a nanophotonic chip through four-wave-mixing Bragg scattering in compact (footprint < 0.5 x 10^-4 cm^2) Si3N4 microring resonators. We investigate three frequency conversion configurations: (1) spectral translation over a few nanometers within the 980 nm band, (2) upconversion from 1550 nm to 980 nm, and (3) downconversion from 980 nm to 1550 nm. With conversion efficiencies ranging from 25 % for the first process to > 60 % for the last two processes, a signal conversion bandwidth > 1 GHz, < 60 mW of continuous-wave pump power needed, and background noise levels between a few fW and a few pW, these devices are suitable for quantum frequency conversion of single photon states from InAs quantum dots. Simulations based on coupled mode equations and the Lugiato-Lefever equation are used to model device performance, and show quantitative agreement with measurements.

Cavity optomechanical systems are being studied for their potential in areas such as metrology, communications, and quantum information science. For a number of recently proposed applications in which multiple optical and mechanical modes interact, an outstanding challenge is to develop multimode architectures that allow flexibility in the optical and mechanical sub-system designs while maintaining the strong interactions that have been demonstrated in single-mode systems. To that end, we demonstrate slot-mode optomechanical crystals, devices in which photonic and phononic crystal nanobeams separated by a narrow slot are coupled via optomechanical interactions. These nanobeam pairs are patterned to confine a mechanical breathing mode at the center of one beam and a low-loss optical mode in the slot between the beams. This architecture affords great design flexibility towards multimode optomechanics, as well as substantial optomechanical coupling rates. We show this by producing slot-mode devices in stoichiometric Si3N4, with optical modes in the 980 nm band coupled to mechanical modes at 3.4 GHz, 1.8 GHz, and 400 MHz. We exploit the Si3N4 tensile stress to achieve slot widths down to 24 nm, which leads to enhanced optomechanical coupling, sufficient for the observation of optomechanical self-oscillations at all studied frequencies. We then develop multimode optomechanical systems with triple-beam geometries, in which two optical modes couple to a single mechanical mode, and two mechanical modes couple to a single optical mode. Taken together, these results demonstrate great flexibility in the design of multimode chip-scale optomechanical systems with large optomechanical coupling.

Self-assembled, epitaxially grown InAs/GaAs quantum dots (QDs) are promising semiconductor quantum emitters that can be integrated on a chip for a variety of photonic quantum information science applications. However, self-assembled growth results in an essentially random in-plane spatial distribution of QDs, presenting a challenge in creating devices that exploit the strong interaction of single QDs with highly confined optical modes. Here, we present a photoluminescence imaging approach for locating single QDs with respect to alignment features with an average position uncertainty, Self-assembled quantum dots are good emitters, but lack emission control prior to device fabrication. Here a photoluminescence imaging technique to characterize position and emission properties of such quantum dots is demonstrated, enabling the realization of high-performance single-photon sources.

We present simulations and measurements examining moving boundary and photoelastic contributions to the optomechanical coupling rate in GaAs microdisks, and discuss nanobeam optomechanical crystal geometries with the potential for enhanced coupling rates.

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We review recent experiments demonstrating quantum frequency conversion (QFC) of single photon states of light and discuss perspectives for combining QFC with temporal wavepacket shaping. Progress in developing nanophotonic geometries for QFC is also presented.

Photon correlations measured over 12 decades in time reveal multiple-time-scale blinking in InAs/GaAs microcavity-quantum dot single-photon sources and enable estimation of quantum dot radiative efficiency. Non-unity efficiencies suggest nanofabrication may produce traps responsible for blinking.

We use photon correlation measurements to study blinking in single, epitaxially grown self-assembled InAs quantum dots situated in circular Bragg grating and microdisk cavities. The normalized second-order correlation function ${g}^{(2)}(\ensuremath{\tau})$ is studied across 11 orders of magnitude in time, and shows signatures of blinking over time scales ranging from tens of nanoseconds to tens of milliseconds. The ${g}^{(2)}(\ensuremath{\tau})$ data is fit to a multilevel system rate equation model that includes multiple nonradiating (dark) states, from which radiative quantum yields significantly less than 1 are obtained. This behavior is observed even in situations for which a direct histogramming analysis of the emission time-trace data produces inconclusive results.

We describe different experiments demonstrating quantum frequency conversion of single photons produced by a quantum dot, and present efforts at developing new frequency converters using four-wave-mixing and cavity optomechanics in the Si3N4 platform.

Single photon sources based on a self-assembled quantum dot in nanophotonic waveguides, gratings, and cavities are interfaced with nonlinear media and electro-optic modulators to demonstrate quantum frequency conversion and amplitude modulation of single photon states.

We demonstrate heralded single photon generation in a CMOS-compatible silicon nanophotonic device. The strong modal confinement and slow group velocity provided by a coupled resonator optical waveguide (CROW) produced a large four-wave-mixing nonlinearity coefficient gamma_eff ~4100 W^-1 m^-1 at telecommunications wavelengths. Spontaneous four-wave-mixing using a degenerate pump beam at 1549.6 nm created photon pairs at 1529.5 nm and 1570.5 nm with a coincidence-to-accidental ratio exceeding 20. A photon correlation measurement of the signal (1529.5 nm) photons heralded by the detection of the idler (1570.5 nm) photons showed antibunching with g^(2)(0) = 0.19 \pm 0.03. The demonstration of a single photon source within a silicon platform holds promise for future integrated quantum photonic circuits.

We demonstrate a single photon source based on a single quantum dot in a circular grating microcavity and measure a collection efficiency of 10%. Tradeoffs between suppressed multi-photon probability and Purcell enhancement are investigated.

A highly nonlinear (γ≈3700/W·m) silicon coupled-resonator-optical-waveguide generated heralded single photons (g(2) (0) ≤ 0.19 ±0.03) and widely-spaced photon pairs with coincidences-to-accidentals ratio >10 (cw) and >23 (pulsed), and outperformed a 54× longer silicon nanophotonic waveguide.

We leverage the high spontaneous four-wave-mixing nonlinearity (γ≈4150/W·m) of silicon coupled-resonator optical waveguides to demonstrate a telecommunications-band, heralded single photon source. The generated light is antibunched with g(2)(0) ≈ 0.19 ±0.03 at low power.

Hybrid quantum information devices that combine disparate physical systems interacting through photons offer the promise of combining low-loss telecommunications wavelength transmission with high fidelity visible wavelength storage and manipulation. The realization of such systems requires control over the waveform of single photons to achieve spectral and temporal matching. Here, we experimentally demonstrate the simultaneous wavelength translation and amplitude modulation of single photons generated by a quantum dot emitting near 1300 nm with an exponentially-decaying waveform (lifetime $\approx$1.5 ns). Quasi-phase-matched sum-frequency generation with a pulsed 1550 nm laser creates single photons at 710 nm with a controlled amplitude modulation at 350 ps timescales., 5 pages, 4 figures

Telecommunications-band single photons from a quantum dot are upconverted using

Fiber-coupled waveguides are realized for broadband spectroscopy of InAs quantum dots. Above-band and p-shell excitation of individual dots is performed, with fluorescence collection into the fiber exceeding free-space collection by one order of magnitude.

A general relation is derived between the band structure of an arbitrary low-loss unit cell and its effective index of refraction. In addition, we determine the maximum unit cell size that defines the ''metamaterial regime'' (D.R. Smith et al., Phys. Rev. E 71, 036617 (2005)). Furthermore, these general rules allow for the design of a subwavelength near-infrared negative-index material, where the negative refractive index is verified by band calculations to be a bulk property. Full-wavelength simulations of prisms consisting of these unit cells suggest behavior consistent with Snell's law in the negative-index regime. does not play a role. The EMW is obliquely incident on the hypotenuse from within the prism, and the refracted beam is detected in the far field. Negative refraction occurs due to the negative phase index, i.e., antiparallel energy velocity and wave vector, rather than anisotropy of the material, accompanied by a positive phase index (13). In Ref. (10), the index determined by the S-parameter method was shown to agreewith Snell's law. In Ref. (11), refractive indices measured on two different prisms (i.e., at two different incidence angles) consisting of the same unit cells were shown to be equal. In this work, we apply photonic band calculations to a near-infrared NIM structure with subwavelength dimen- sions. The negative index obtained from a monolayer of the structure is verified to be a bulk property. We then derive a general relationship between the band structure of an arbi- trary 1D low-loss unit cell and its effective index exhibited in refraction experiments similar to Refs. (10,11). This relationship confirms the negative index for our structure. Full-wavelength simulations on NIM prisms consisting of our structure show negative refraction consistent with pre- dictions from Snell's law. Finally, the role of the small lateral unit cell size unique to the structure is discussed. The NIM unit cell is shown in the inset in Fig. 1(a) .I t consists of 20-nm-thick � 100-nm-wide Au strips, sepa- rated from a 20-nm-thick central continuous Au layer (14) by 15-nm-thick polymer dielectric spacers. The unit cell extends infinitely along the ^ z direction and is replicated in

The propagation characteristics of a subwavelength plasmonic crystal are studied based on its complex Bloch band structure. Photonic crystal bands are generated with an alternative 2D Finite Element Method formulation in which the Bloch wave problem is reduced to a quadratic eigenvalue system for the Bloch wavevector amplitude k. This method constitutes an efficient and convenient alternative to nonlinear search methods normally employed in the calculation of photonic bands when dispersive materials are involved. The method yields complex wavevector Bloch modes that determine the wave-scattering characteristics of finite crystals. This is evidenced in a comparison between the band structure of the square-lattice plasmonic crystal and scattering transfer-functions from a corresponding finite crystal slab. We report on a wave interference effect that leads to transmission resonances similar to Fano resonances, as well as on the isotropy of the crystal's negative index band. Our results indicate that effective propagation constants obtained from scattering simulations may not always be directly related to individual crystal Bloch bands.