Noise and pulse dynamics in backward stimulated Brillouin scattering.

We theoretically and numerically study the effects of thermal noise on pulses in backwards stimulated Brillouin scattering (SBS). Using a combination of stochastic calculus and numerical methods, we derive a theoretical model that can be used to quantitatively predict noise measurements. We study how the optical pulse configuration, including the input powers of the pump and Stokes fields, pulse durations and interaction time, affects the noise in the output Stokes field. We investigate the effects on the noise of the optical loss and waveguide length, and we find that the signal-to-noise ratio can be significantly improved, or reduced, for specific combinations of waveguide properties and pulse parameters.

Spontaneous parametric down conversion in a doubly resonant one-dimensional photonic crystal.

We study spontaneous parametric down conversion (SPDC) in a one-dimensional photonic crystal designed to operate in a doubly resonant configuration, where the frequencies of the pump and the generated photons are both tuned to band-edge resonances. We investigate the spectral correlations of the generated photons as a function of the spectral width of the pump, and demonstrate that the SPDC generation rate can scale with the fifth power of the structure length in the limit of a quasi-continuous-wave pump. We show that such an unusual scaling can be simply connected with the scaling of second-harmonic generation in the same structure, illustrating the general link between spontaneous and stimulated parametric nonlinear processes.

Suspended mid-infrared waveguides for Stimulated Brillouin Scattering.

We theoretically investigate a new class of silicon waveguides for achieving Stimulated Brillouin Scattering (SBS) in the mid-infrared (MIR). The waveguide consists of a rectangular core supporting a low-loss optical mode, suspended in air by a series of transverse ribs. The ribs are patterned to form a finite quasi-one-dimensional phononic crystal, with the complete stopband suppressing the transverse leakage of acoustic waves, confining them to the core of the waveguide. We derive a theoretical formalism that can be used to compute the opto-acoustic interaction in such periodic structures, and find forward intramodal-SBS gains up to 1750 m-1W-1, which compares favorably with the proposed MIR SBS designs based on buried germanium waveguides. This large gain is achieved thanks to the nearly complete suppression of acoustic radiative losses.

Elastic Purcell Effect.

In this work, we introduce an elastic analog of the Purcell effect and show theoretically that spherical nanoparticles can serve as tunable and robust antennas for modifying the emission from localized elastic sources. This effect can be qualitatively described by introducing elastic counterparts of the familiar electromagnetic parameters: local density of elastic states, elastic Purcell factor, and effective volume of elastic modes. To illustrate our framework, we consider the example of a submicron gold sphere as a generic elastic GHz antenna and find that shear and mixed modes of low orders in such systems offer considerable elastic Purcell factors. This formalism opens pathways towards extended control over dissipation of vibrations in various optomechanical systems and contributes to closing the gap between classical and quantum-mechanical treatments of phonons localized in elastic nanoresonators.

Digital waveguide adiabatic passage part 1: theory.

Spatial adiabatic passage represents a new way to design integrated photonic devices. In conventional adiabatic passage, designs require smoothly varying waveguide separations. Here we show modelling of adiabatic passage devices where the waveguide separation is varied digitally. Despite digitisation, our designs show robustness against variations in the input wavelength and refractive index contrast of the waveguides relative to the cladding. This approach to spatial adiabatic passage opens new design strategies and hence the potential for new photonics devices.

Lasing in ring resonators by stimulated Brillouin scattering in the presence of nonlinear loss.

We theoretically investigate lasing due to stimulated Brillouin scattering in integrated ring resonators. We give analytic expressions and numerical calculations for the lasing threshold for rings in the presence of for both linear and nonlinear loss. We demonstrate the operation of the ring in the different regimes of amplification and lasing, and show how these regimes depend on the coupling to the ring and on the nonlinear parameters. In the case of nonlinear losses, we find that there can exist an upper threshold to the lasing regime where the losses are dominated by free-carrier absorption. We also find that nonlinear losses can inhibit Brillouin lasing entirely for certain ranges of coupling parameters, and we show how the correct ranges of coupling parameters can be calculated and optimized for the design of integrated Brillouin lasers.

Digital waveguide adiabatic passage part 2: experiment.

Using a femtosecond laser writing technique, we fabricate and characterise three-waveguide digital adiabatic passage devices, with the central waveguide digitised into five discrete waveguidelets. Strongly asymmetric behaviour was observed, devices operated with high fidelity in the counter-intuitive scheme while strongly suppressing transmission in the intuitive. The low differential loss of the digital adiabatic passage designs potentially offers additional functionality for adiabatic passage based devices. These devices operate with a high contrast (>90%) over a 60 nm bandwidth, centered at ∼ 823 nm.

Effect of dark counts on single-photon heralding with quasi-number-resolving detection schemes.

We consider photon heralding with quasi-number-resolving detection schemes and account for detection efficiencies and dark count probabilities. With a straightforward formalism, we develop closed-form expressions for the heralding probability, photon number distribution of the resulting heralded state, and fidelity of this heralded state to a single-photon state. We calculate that this fidelity has a maximum as a function of the number of multiplexed detection modes and that, for experimental configurations in which the maximum is reached for quite a large number of detection modes, it can still be highly beneficial to multiplex fewer modes.

Parasitic Photon-Pair Suppression via Photonic Stop-Band Engineering.

We calculate that an appropriate modification of the field associated with only one of the photons of a photon pair can suppress generation of the pair entirely. From this general result, we develop a method for suppressing the generation of undesired photon pairs utilizing photonic stop bands. For a third-order nonlinear optical source of frequency-degenerate photons, we calculate the modified frequency spectrum (joint spectral intensity) and show a significant increase in a standard metric, the coincidence to accidental ratio. These results open a new avenue for photon-pair frequency correlation engineering.

Domain engineering algorithm for practical and effective photon sources.

We introduce a method for shaping the spectral response of nonlinear light sources by tailoring the quasi-phase matching. Our algorithm relies on engineering the poling to accurately trace a generated target signal field amplitude to determine the desired nonlinearity profile. The proposed poling algorithm results in a poling pattern that is more robust to manufacture, as all domain inversions are of equal width. The poling pattern is verified using a nonlinear beam propagation method simulation. This approach is applied to achieve Gaussian-shaped phase matching along a potassium titanyl phosphate (KTP) crystal in order to generate pure heralded single photons of spectral purity ~0.996-this is highly desirable for heralded single photon quantum optics.

Stimulated Brillouin scattering in silicon/chalcogenide slot waveguides.

We study slot waveguide geometries, comprising a combination of soft glasses and high-index guiding structures, for enhancing stimulated Brillouin scattering (SBS). We show that strong optical and acoustic mode confinement in these waveguides can lead to a substantial increase in SBS gain, comparable to or greater than recently proposed suspended silicon nanowire structures. We compute the optimal parameters of the structure and examine the physics of optical and acoustic confinement within slot waveguides. Finally, we compute the effects of linear and nonlinear loss mechanisms on optimum pump/Stokes powers and waveguide lengths.

Power limits and a figure of merit for stimulated Brillouin scattering in the presence of third and fifth order loss.

We derive a set of design guidelines and a figure of merit to aid the engineering process of on-chip waveguides for strong Stimulated Brillouin Scattering (SBS). To this end, we examine the impact of several types of loss on the total amplification of the Stokes wave that can be achieved via SBS. We account for linear loss and nonlinear loss of third order (two-photon absorption, 2PA) and fifth order, most notably 2PA-induced free carrier absorption (FCA). From this, we derive an upper bound for the output power of continuous-wave Brillouin-lasers and show that the optimal operating conditions and maximal realisable Stokes amplification of any given waveguide structure are determined by a dimensionless parameter ℱ involving the SBS-gain and all loss parameters. We provide simple expressions for optimal pump power, waveguide length and realisable amplification and demonstrate their utility in two example systems. Notably, we find that 2PA-induced FCA is a serious limitation to SBS in silicon and germanium for wavelengths shorter than 2200nm and 3600nm, respectively. In contrast, three-photon absorption is of no practical significance.

Effect of scattering loss on connections between classical and quantum processes in second-order nonlinear waveguides.

We show that a useful connection exists between spontaneous parametric downconversion (SPDC) and sum frequency generation in nonlinear optical waveguides with arbitrary scattering loss, while the same does not hold true for SPDC and difference frequency generation. This result refines the relationship between these quantum and classical second-order nonlinear optical processes in waveguides, and identifies the most accurate characterization of a waveguide's quantum performance in the presence of loss based solely on classical measurements.

Measurement and Shaping of Biphoton Spectral Wave Functions.

In this work we present a simple method to reconstruct the complex spectral wave function of a biphoton, and hence gain complete information about the spectral and temporal properties of a photon pair. The technique, which relies on quantum interference, is applicable to biphoton states produced with a monochromatic pump when a shift of the pump frequency produces a shift in the relative frequencies contributing to the biphoton. We demonstrate an example of such a situation in type-II parametric down conversion allowing arbitrary paraxial spatial pump and detection modes. Moreover, our test cases demonstrate the possibility to shape the spectral wave function. This is achieved by choosing the spatial mode of the pump and of the detection modes, and takes advantage of spatiotemporal correlations.

Formal selection rules for Brillouin scattering in integrated waveguides and structured fibers.

We derive formal selection rules for Stimulated Brillouin Scattering (SBS) in structured waveguides. Using a group-theoretical approach, we show how the waveguide symmetry determines which optical and acoustic modes interact for both forward and backward SBS. We present a general framework for determining this interaction and give important examples for SBS in waveguides with rectangular, triangular and hexagonal symmetry. The important role played by degeneracy of the optical modes is illustrated. These selection rules are important for SBS-based device design and for a full understanding the physics of SBS in structured waveguides.

Competition of Faraday rotation and birefringence in femtosecond laser direct written waveguides in magneto-optical glass.

We consider the process of Faraday rotation in femtosecond laser direct-write waveguides. The birefringence commonly associated with such waveguides may be expected to impact the observable Faraday rotation. Here, we theoretically calculate and experimentally verify the competition between Faraday rotation and birefringence in two waveguides created by laser writing in a commercial magneto-optic glass. The magnetic field applied to induce Faraday rotation is nonuniform, and as a result, we find that the two effects can be clearly separated and used to accurately determine even weak birefringence. The birefringence in the waveguides was determined to be on the scale of Δn = 10(-6) to 10(-5). The reduction in Faraday rotation caused by birefringence of order Δn = 10(-6) was moderate and we obtained approximately 9° rotation in an 11 mm waveguide. In contrast, for birefringence of order 10(-5), a significant reduction in the polarization azimuth change was found and only 6° rotation was observed.

Mode conversion using stimulated Brillouin scattering in nanophotonic silicon waveguides.

We theoretically and numerically investigate Stimulated Brillouin Scattering generated mode conversion in high-contrast suspended silicon nanophotonic waveguides. We predict significantly enhanced mode conversion when the linked effects of radiation pressure and motion of the waveguide boundaries are taken into account. The mode conversion is more than 10 times larger than would be predicted if the effect of radiation pressure is not taken into account: we find a waveguide length of 740 µm is required for 20dB of mode conversion, assuming a total pump power of 1W. This is sufficient to bring the effect into the realm of chip-scale photonic waveguides. We explore the interaction between the different types of acoustic modes that can exist within these waveguides, and show how the presence of these modes leads to enhanced conversion between the different possible optical modes.

Detuning in apodized point-by-point fiber Bragg gratings: insights into the grating morphology.

Point-by-point (PbP) inscription of fiber Bragg gratings using femtosecond laser pulses is a versatile technique that is currently experiencing significant research interest for fiber laser and sensing applications. The recent demonstration of apodized gratings using this technique provides a new avenue of investigation into the nature of the refractive index perturbation induced by the PbP modifications, as apodized gratings are sensitive to variation in the average background index along the grating. In this work we compare experimental results for Gaussian- and sinc-apodized PbP gratings to a coupled-mode theory model, demonstrating that the refractive index perturbation induced by the PbP modifications has a negative contribution to the average background index which is small, despite the presence of strong reflective coupling. By employing Fourier analysis to a simplified model of an individual modification, we show that the presence of a densified shell around a central void can produce strong reflective coupling with near-zero change in the average background index. This result has important implications for the experimental implementation of apodized PbP gratings, which are of interest for a range of fiber laser and fiber sensing technologies.

Theoretical modeling and experiments on a DBR waveguide laser fabricated by the femtosecond laser direct-write technique.

We present a model for a Yb-doped distributed Bragg reflector (DBR) waveguide laser fabricated in phosphate glass using the femtosecond laser direct-write technique. The model gives emphasis to transverse integrals to investigate the energy distribution in a homogenously doped glass, which is an important feature of femtosecond laser inscribed waveguide lasers (WGLs). The model was validated with experiments comparing a DBR WGL and a fiber laser, and then used to study the influence of distributed rare earth dopants on the performance of such lasers. Approximately 15% of the pump power was absorbed by the doped "cladding" in the femtosecond laser inscribed Yb doped WGL case with the length of 9.8 mm. Finally, we used the model to determine the parameters that optimize the laser output such as the waveguide length, output coupler reflectivity and refractive index contrast.

Bidirectional multiplexing of heralded single photons from a silicon chip.

We demonstrate integrated spatial multiplexing of heralded single photons generated from a single 96 µm long silicon photonic crystal waveguide in a bidirectional pump configuration. By using a low-loss fiber-coupled opto-ceramic switch, the multiplexing technique enhances the brightness of the single photon source by 51.2±4.0% while maintaining the coincidence-to-accidental ratio. Compared with the demonstration of multiplexing two individual sources, the bidirectional pump scheme represents a twofold reduction in the footprint of nonlinear devices for future large-scale integration of on-chip single photon sources. The 51.2±4.0% gain will make any quantum operation requiring n photons 1.5(n) times faster.