Slow light enhancement of nonlinear effects in silicon engineered photonic crystal waveguides

A generic model for the study of supercontinuum generation in graphene-covered nanowires

We study supercontinuum (SC) generation in graphene-covered nanowires based on a generic model that correctly accounts for the evolution of the photon number under Kerr and two-photon absorption processes, and the influence of graphene is treated within the framework of saturable photoexcited-carrier refraction. We discuss the role of the various effects on the generation of SC by a thorough analysis of short-pulse propagation in two different kinds of graphene-covered nanowires, one made of silicon nitride and the other made of silicon. Finally, we discuss the effect of stacking graphene layers as a means to enhance SC generation with pulse powers compatible with those in integrated optical devices.

Si photonic crystal slow-light waveguides optimized through informatics technology

We modeled the photonic bands of SiO₂-cladded Si lattice-shifted photonic crystal waveguides via machine learning and found a structure that generates low-dispersion slow light with a group index of approximately 20 in the full C-band at telecom wavelengths. The normalized delay-bandwidth product is as large as 0.45, which is close to the theoretical upper limit. The transition structure between this waveguide and a Si-channel waveguide was designed using an evolutional optimization, and a C-band average loss of 0.116 dB/transition was calculated. These results prove the possibility of further enhancing the versatility of slow light.

Figures of merit for mid-IR evanescent-wave absorption sensors and their simulation by FEM methods

Proper optimization of a photonic structure for sensing applications is of extreme importance for integrated sensor design. Here we discuss on the definition of suitable parameters to determine the impact of photonic structure designs for evanescent-wave absorption sensors on the achievable resolution and sensitivity. In particular, we analyze the most widespread quantities used to classify photonic structures in the context of sensing, namely the evanescent-field ratio (or evanescent power factor) and the confinement factor Γ. We show that, somewhat counterintuitively, the confinement factor is the only parameter that can reliably describe the absorption of the evanescent-field in the surrounding medium, and, by quantifying the discrepancy between the two parameters for a set of realistic photonic structures, we demonstrate that using the evanescent-field ratio can lead to a wrong classification of the performance of different structures for absorption sensing. We finally discuss the most convenient simulation strategies to retrieve the confinement factor by FEM simulations.

Nonlinear acoustic metamaterial for efficient frequency down-conversion

Frequency conversion is one of the most important nonlinear wave phenomena that has been widely used in the field of electromagnetic waves for changing signal frequencies. Recently, studies on frequency conversion have been actively performed in the field of acoustics owing to its importance in nonlinear ultrasonic nondestructive evaluation and directional speakers. However, acoustic frequency conversion presents relatively poor efficiency owing to the small amplitudes of the converted frequencies and undesired intermodulation. Herein, we propose an acoustic metamaterial to achieve an efficient frequency down-conversion of acoustic waves. Based on background theory, we discovered that the amplitudes of the converted frequencies are inversely proportional to the cube of the speed of sound. Accordingly, we amplify the converted frequency components by reducing the effective speed of sound by coiling up space while suppressing undesired intermodulation by the Bragg gap. Numerical simulation and analytical results show that efficient frequency down-conversion is possible using the corresponding metamaterial. Additionally, dissipation due to viscosity and boundary layer effects is considered. We expect our study results to facilitate research regarding acoustic frequency conversion.

Quantifying the Robustness of Topological Slow Light

The backscattering mean free path ξ, the average ballistic propagation length along a waveguide, quantifies the resistance of slow light against unwanted imperfections in the critical dimensions of the nanostructure. This figure of merit determines the crossover between acceptable slow-light transmission affected by minimal scattering losses and a strong backscattering-induced destructive interference when the waveguide length L exceeds ξ. Here, we calculate the backscattering mean free path for a topological photonic waveguide for a specific and determined amount of disorder and, equally relevant, for a fixed value of the group index n_{g} which is the slowdown factor of the group velocity with respect to the speed of light in vacuum. These two figures of merit, ξ and n_{g}, should be taken into account when quantifying the robustness of topological and conventional (nontopological) slow-light transport at the nanoscale. Otherwise, any claim on a better performance of topological guided light over a conventional one is not justified.

Design of ultra-small mode area all-dielectric waveguides exploiting the vectorial nature of light

The wave nature and diffraction of light pose a significant bottleneck to the continued performance and efficiency scaling of a wide variety of integrated photonic devices, often necessitating solutions based on resonance, slow-light, or plasmonics to derive enhanced light-matter interaction. Here, we introduce all-dielectric waveguides that exploit the vectorial nature of light to achieve strong subdiffraction confinement in high index dielectrics, enabling characteristic mode dimensions below λ02/1000 without metals or plasmonics. We further show how these ultra-small mode areas may coincide or diverge from the nonlinear effective mode area. The work opens the door to new types of waveguide-based devices featuring strong near-field confinement, Purcell factors, and nonlinear effects, with broad applications spanning classical and quantum optics.

Non-Hermitian Dirac Cones

Non-Hermitian systems containing gain or loss commonly host exceptional point degeneracies, not the diabolic points that, in Hermitian systems, play a key role in topological transitions and related phenomena. Non-Hermitian Hamiltonians with parity-time symmetry can have real spectra but generally nonorthogonal eigenstates, impeding the emergence of diabolic points. We introduce a pair of symmetries that induce not only real eigenvalues but also pairwise eigenstate orthogonality. This allows non-Hermitian systems to host Dirac points and other diabolic points. We construct non-Hermitian models exhibiting three exemplary phenomena previously limited to the Hermitian regime: Haldane-type topological phase transition, Landau levels without magnetic fields, and Weyl points. This establishes a new connection between non-Hermitian physics and the rich phenomenology of diabolic points.

Four Wave Mixing control in a photonic molecule made by silicon microring resonators

Four Wave Mixing (FWM) is the main nonlinear interaction in integrated silicon devices, which finds diffuse use in all-optical signal processing and wavelength conversion. Despite the numerous works on coupled resonator devices, which showed record conversion efficiencies and broadband operation, the possibility to coherently control the strength of the stimulated FWM interaction on a chip has received very limited attention. Here, we demonstrate both theoretically and experimentally, the manipulation of FWM in a photonic molecule based on two side coupled silicon microring resonators. The active tuning of the inter-resonator phase and of their eigenfrequencies allows setting the molecule in a sub-radiant state, where FWM is enhanced with respect to the isolated resonators. On the other hand, we can reconfigure the state of the photonic molecule to have energy equipartition among the resonators, and suppress FWM by making the two Signal waves to interfere destructively in the side coupled waveguides. This work constitutes an experimental demonstration of the control of a nonlinear parametric interaction via coherent oscillation phenomena in an integrated optical device.

Physical origin of higher-order soliton fission in nanophotonic semiconductor waveguides

Supercontinuum generation in Kerr media has become a staple of nonlinear optics. It has been celebrated for advancing the understanding of soliton propagation as well as its many applications in a broad range of fields. Coherent spectral broadening of laser light is now commonly performed in laboratories and used in commercial “white light” sources. The prospect of miniaturizing the technology is currently driving experiments in different integrated platforms such as semiconductor on insulator waveguides. Central to the spectral broadening is the concept of higher-order soliton fission. While widely accepted in silica fibers, the dynamics of soliton decay in semiconductor waveguides is yet poorly understood. In particular, the role of nonlinear loss and free carriers, absent in silica, remains an open question. Here, through experiments and simulations, we show that nonlinear loss is the dominant perturbation in wire waveguides, while free-carrier dispersion is dominant in photonic crystal waveguides.

Z2 topological edge state in honeycomb lattice of coupled resonant optical waveguides with a flat band

Two-dimensional (2D) coupled resonant optical waveguide (CROW), exhibiting topological edge states, provides an efficient platform for designing integrated topological photonic devices. In this paper, we propose an experimentally feasible design of 2D honeycomb CROW photonic structure. The characteristic optical system possesses two-fold and three-fold Dirac points at different positions in the Brillouin zone. The effective gauge fields implemented by the intrinsic pseudo-spin-orbit interaction open up topologically nontrivial bandgaps through the Dirac points. Spatial lattice geometries allow destructive wave interference, leading to a dispersionless, near-flat energy band in the vicinity of the three-fold Dirac point in the telecommunication frequency regime. This nontrivial structure with a near-flat band yields topologically protected edge states. These characteristics underpin the fundamental importance as well as the potential applications in various optical devices. Based on the honeycomb CROW lattice, we design the shape-independent topological cavity and the beam splitter, which demonstrate the relevance for a wide range of photonic applications.

Pulse propagation in the slow and stopped light regime

Electromagnetic pulse propagation in the slow light regime and near a zero group velocity point is relevant to a plethora of potential applications, and has analogies in numerous other wave systems. Unfortunately, the standard frequency-based formulation for pulse propagation is unsuitable for describing the dynamics in such regimes, due to the divergence of the dispersion coefficients. Moreover, in the presence of absorption, it is not clear how to interpret the propagation dynamics due to the drastic change induced by absorption upon the dispersion curves. As a remedy, we present an alternative momentum-based formulation, which is rapidly converging in these regimes, and naturally suitable for lossy and nonlinear media. It is specialized to a waveguide geometry which provides a significant simplification with respect to existing momentum-based schemes. Doing so, we provide a somewhat alternative, yet intuitive picture of the seeming enhanced absorption and nonlinear response in these regimes, and show that light-matter interactions are not enhanced in the slow/stopped light regimes.

High-performance on-chip autocorrelator using a rib waveguide loaded with two-photon absorption diodes

We report an on-chip autocorrelator comprising a Si rib waveguide and two-photon-absorption photodiodes in which two pulses simultaneously propagate in opposite directions, and their correlation is acquired. The rib waveguide's broadband guiding mode and moderately low group index allow the device to operate over a wide wavelength range with high resolution. We confirm that the waveguide has a transmission band of at least 1300-1630 nm and observed correlation waveforms for pulses of the order of several hundred femtoseconds to several picoseconds, with a range of at least the entire C band region.

Dynamic modulation of wideband slow light with continuous group index in polymer-filled photonic crystal waveguide

The dynamic modulation of wide bandwidth and low-dispersion slow light with continuous variation of group index n_g is realized in a polymer-filled photonic crystal waveguide (PF-PCW) with optimal structure. By adjusting the unified radius of air holes under a different refractive index of polymer in the first two rows of holes adjacent to the defect, the structure optimization of PF-PCW is first studied, then the fixed optimal structure is obtained. In the optimal photonic crystal waveguide with hole radius r₀=0.328a, a fixed refractive index n₁=1.74 of polymer in the first-row holes, and by adjusting refractive index n₂, the flattened wideband slow light with large normalized delay bandwidth product of group index from 17.15 to 55.65 has been demonstrated. Then, by filling polymer with electro-optic effect into the second-row holes, the dynamic modulation of the optimized slow light in PF-PCW is investigated. The simulation shows that the center operating frequency slightly shifts linearly to a higher one, and the average group index increases exponentially from 33.943 to 75.546 with a normalized delay bandwidth product larger than 0.3089 as the applied voltage increases. The modulation sensitivity of the average group index is about 0.3467/V when applied voltages vary from 0 V to 120 V. These results open the possibility for the dynamic control of slow light according to the practical requirements of flexibility and tunability.

Soliton Pulse Propagation in the Presence of Disorder-Induced Multiple Scattering in Photonic Crystal Waveguides

We introduce a new coupled mode theory to model nonlinear Schrödinger equations for counterpropagating Bloch modes that include disorder-induced multiple scattering effects on nonlinear soliton propagation in photonic crystal waveguides. We also derive subunit-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 agreement with recent experiments and provide insight into how structural disorder inhibits soliton propagation and other nonlinear propagation effects in photonic crystal waveguides.

GaInP on oxide nonlinear photonic crystal technology

Heat dissipation is improved in nonlinear III-V photonic crystal waveguides owing to the hybrid III-V/Silicon integration platform, allowing efficient four-wave mixing in the continuous-wave regime. A conversion efficiency of -17.6  dB is demonstrated with a pump power level below 100 mW in a dispersion-engineered waveguide with a flat group index of 28 over a 10 nm bandwidth.

Integrated nonlinear interferometer with wavelength multicasting functionality

Nonlinear interference based on four wave mixing (FWM) is extremely attractive due to its phase sensitivity. On the other hand, wavelength multicasting, which supports data point-to-multipoint connections, is a key functionality to increase the network efficiency and simplify the transmitter and receiver in the wavelength-division multiplexing systems. We propose and experimentally demonstrate a nonlinear interferometer with wavelength multicasting functionality based on single-stage FWM in an integrated silicon waveguide. With a three-pump and dual-signal input, four phase sensitive idlers are obtained at the interferometer output. For a proof-of-concept application, we further theoretically demonstrate the multicasting logic exclusive-OR (XOR) gate for both intensity and phase modulated signals. The proposed scheme would be potentially applied in various on-chip applications for future optical communication system.

Free-carrier-induced soliton fission unveiled by in situ measurements in nanophotonic waveguides

Solitons are localized waves formed by a balance of focusing and defocusing effects. These nonlinear waves exist in diverse forms of matter yet exhibit similar properties including stability, periodic recurrence and particle-like trajectories. One important property is soliton fission, a process by which an energetic higher-order soliton breaks apart due to dispersive or nonlinear perturbations. Here we demonstrate through both experiment and theory that nonlinear photocarrier generation can induce soliton fission. Using near-field measurements, we directly observe the nonlinear spatial and temporal evolution of optical pulses in situ in a nanophotonic semiconductor waveguide. We develop an analytic formalism describing the free-carrier dispersion (FCD) perturbation and show the experiment exceeds the minimum threshold by an order of magnitude. We confirm these observations with a numerical nonlinear Schrödinger equation model. These results provide a fundamental explanation and physical scaling of optical pulse evolution in free-carrier media and could enable improved supercontinuum sources in gas based and integrated semiconductor waveguides.

Solitons are nonlinear waves that exist in diverse forms of matter. Here, Husko et al. use near-field measurements to observe the spatio-temporal evolution of optical pulses in a nanophotonic semiconductor waveguide, demonstrating that nonlinear photo-carrier generation can induce fission of solitons.

Degenerate band edge resonances in periodic silicon ridge waveguides

We experimentally demonstrate degenerate band edge resonances in periodic Si ridge waveguides that are compatible with carrier injection modulation for active electro-optical devices. The resonant cavities are designed using a combination of the plane-wave expansion method and the finite difference time domain technique. Measured and simulated quality factors of the first band edge resonances scale to the fifth power of the number of periods. Quality factor scaling is determined to be limited by fabrication imperfections. Compared to resonators based on a regular transmission band edge, degenerate band edge devices can achieve significantly larger quality factors in the same number of periods. Applications include compact electro-optical switches, modulators, and sensors that benefit from high-quality factors and large distributed electric fields.

Unambiguous demonstration of soliton evolution in slow-light silicon photonic crystal waveguides with SFG-XFROG

We demonstrate the temporal and spectral evolution of picosecond soliton in the slow light silicon photonic crystal waveguides (PhCWs) by sum frequency generation cross-correlation frequency resolved optical grating (SFG-XFROG) and nonlinear Schrödinger equation (NLSE) modeling. The reference pulses for the SFG-XFROG measurements are unambiguously pre-characterized by the second harmonic generation frequency resolved optical gating (SHG-FROG) assisted with the combination of NLSE simulations and optical spectrum analyzer (OSA) measurements. Regardless of the inevitable nonlinear two photon absorption, high order soliton compressions have been observed remarkably owing to the slow light enhanced nonlinear effects in the silicon PhCWs. Both the measurements and the further numerical analyses of the pulse dynamics indicate that, the free carrier dispersion (FCD) enhanced by the slow light effects is mainly responsible for the compression, the acceleration, and the spectral blue shift of the soliton.

Observation of soliton compression in silicon photonic crystals

Solitons are nonlinear waves present in diverse physical systems including plasmas, water surfaces and optics. In silicon, the presence of two photon absorption and accompanying free carriers strongly perturb the canonical dynamics of optical solitons. Here we report the first experimental demonstration of soliton-effect pulse compression of picosecond pulses in silicon, despite two photon absorption and free carriers. Here we achieve compression of 3.7 ps pulses to 1.6 ps with <10 pJ energy. We demonstrate a ~1-ps free-carrier-induced pulse acceleration and show that picosecond input pulses are critical to these observations. These experiments are enabled by a dispersion-engineered slow-light photonic crystal waveguide and an ultra-sensitive frequency-resolved electrical gating technique to detect the ultralow energies in the nanostructured device. Strong agreement with a nonlinear Schrödinger model confirms the measurements. These results further our understanding of nonlinear waves in silicon and open the way to soliton-based functionalities in complementary metal-oxide-semiconductor-compatible platforms.

Nonlinear optical response of low loss silicon germanium waveguides in the mid-infrared

We have investigated the nonlinear optical response of low loss Si(0.6)Ge(0.4) / Si waveguides in the mid-infrared wavelength range from 3.25- 4.75μm using picosecond optical pulses. We observed and measured the three and four-photon absorption coefficients as well as the Kerr nonlinear refractive index. The dynamics of the spectral broadening suggests that, in addition to multiphoton absorption, the corresponding higher order nonlinear refractive phenomena also needs to be included when high optical pulse intensities are used at mid-infrared wavelengths in this material.

Designing photonic crystal waveguides for broadband four-wave mixing applications

We present photonic crystal waveguide designs which exhibit large four-wave mixing efficiencies over a wide wavelength region. These designs are identified using an optimization process taking into account sophisticated figure-of-merits that depend on the pump bandwidth and the signal/pump tunability. The obtained designs achieve up to -18.9  dB conversion efficiency, tunable over a 10 nm tunability range. We also present alternative designs that are less efficient but have smaller power requirements and are far more compact.

Triply resonant four-wave mixing in silicon-coupled resonator microring waveguides

Silicon photonic four-wave mixing (FWM) devices intended for telecommunications applications must satisfy three requirements: achieve conversion efficiencies close to the detection threshold of typical receivers, while keeping pump power requirements modest and providing enough bandwidth for typical signal formats. Here, we report a continuous-wave FWM efficiency of -21.3  dB at 100 mW pump power and demonstrate wavelength conversion at 10 Gbps in a coupled-resonator optical-waveguide device.

Dynamic wavelength conversion in copropagating slow-light pulses

Dynamic wavelength conversion (DWC) is obtained by controlling copropagating slow-light signal and control pulse trajectories. Our method is based on the understanding that conventional resonator-based DWC can be generalized, and is linked to cross-phase modulation. Dispersion-engineered Si photonic crystal waveguides produce such slow-light pulses. Free carriers generated by two-photon absorption of the control pulse dynamically shift the signal wavelength. Matching the group velocities of the two pulses enhances the shift, elongating the interaction length. We demonstrate an extremely large wavelength shift in DWC (4.9 nm blueshift) for the signal wavelength. Although DWC is similar to the Doppler effect, we highlight their essential differences.

Phase-sensitive amplification in silicon photonic crystal waveguides

We experimentally demonstrate phase-sensitive amplification in a silicon photonic crystal waveguide based on pump-degenerate four-wave mixing. An 11 dB phase-extinction ratio is obtained in a record compact 196 μm nanophotonic device due to broadband slow light, in spite of the presence of two-photon absorption and free carriers. Numerical calculations show good agreement with the experimental results.

Ultracompact (3 μm) silicon slow-light optical modulator

Wavelength-scale optical modulators are essential building blocks for future on-chip optical interconnects. Any modulator design is a trade-off between bandwidth, size and fabrication complexity, size being particularly important as it determines capacitance and actuation energy. Here, we demonstrate an interesting alternative that is only 3 μm long, only uses silicon on insulator (SOI) material and accommodates several nanometres of optical bandwidth at 1550 nm. The device is based on a photonic crystal waveguide: by combining the refractive index shift with slow-light enhanced absorption induced by free-carrier injection, we achieve an operation bandwidth that significantly exceeds the shift of the bandedge. We compare a 3 μm and an 80 μm long modulator and surprisingly, the shorter device outperforms the longer one. Despite its small size, the device achieves an optical bandwidth as broad as 7 nm for an extinction ratio of 10 dB, and modulation times ranging between 500 ps and 100 ps.

Unravelling nonlinear spectral evolution using nanoscale photonic near-field point-to-point measurements

We demonstrate nanoscale photonic point-to-point measurements characterizing a single component inside an all-optical signal-processing chip. We perform spectrally resolved near-field scanning optical microscopy on ultrashort pulses propagating inside a slow light photonic crystal waveguide, which is part of a composite sample. A power study reveals a reshaping of the pulse's spectral density, which we model using the nonlinear Schrödinger equation. With the model, we are able to identify the various physical processes governing the nonlinear pulse propagation. Finally, we contrast the near-field measurements with transmission measurements of the complete composite sample to elucidate the importance of gaining local information about the evolution of the spectral density.

All-optical tunable slow light achievement in photonic crystal coupled-cavity waveguides

In this paper, a tunable low power slow light photonic crystal device with a silicon-on-insulator platform is proposed based on the combination of an asymmetric defects coupled-cavity waveguide and the electromagnetically induced transparency (EIT) phenomenon. Modulating the refractive index of special regions in the suggested structure by the EIT phenomenon leads to a relatively wideband slow light device with adjustable group index in the same structure. Using this feature, a small and compact delay line is introduced that has many applications in optical telecommunications, especially in buffers. The numerical calculations show that the group index of 80-98 over the slow light bandwidth from 3.2 to 2.6 nm is achievable for the central wavelength of 1546-1555 nm, respectively. The device malfunction, due to fabrication errors, is modeled, and the tunable characteristics of the proposed structure are verified.

Coupling light into a slow-light photonic-crystal waveguide from a free-space normally-incident beam

We present a coupler design allowing normally-incident light coupling from free-space into a monomode photonic crystal waveguide operating in the slow-light regime. Numerical three-dimensional calculations show that extraction efficiencies as high as 80% can be achieved for very large group indices up to 100. We demonstrate experimentally the device feasibility by coupling and extracting light from a photonic crystal waveguide over a large group-index range (from 10 to 60). The measurements are in good agreement with theoretical predictions. We also study numerically the impact of various geometrical parameters on the coupler performances.

High-frequency self-induced oscillations in a silicon nanocavity

We show that self-induced oscillations at frequencies above GHz and with a high spectral purity can be obtained in a silicon photonic crystal nanocavity under optical pumping. This self-pulsing results from the interplay between the nonlinear response of the cavity and the photon cavity lifetime. We provide a model to analyze the mechanisms governing the onset of self-pulsing, the amplitudes of both fundamental and harmonic oscillations and their dependences versus input power and oscillation frequency. Theoretically, oscillations at frequencies higher than 50 GHz could be achieved in this system.

Design of large-bandwidth single-mode operation waveguides in silicon three-dimensional photonic crystals using two guided modes

We report on the design of silicon three-dimensional (3D) photonic crystal (PC) waveguides with a combination of acceptor-type and donor-type line defects. Tuning the width of the acceptor-type line defect allows the waveguide to support two guided modes, which enable single-mode propagation over 98.7% of the complete photonic bandgap (cPBG). In addition, we demonstrate that the frequency ranges for single-mode propagation can be extended to the entire range of the cPBG by further tuning the thickness of the layers in which the donor-type line defects are located. The wide ranges of available frequencies for single mode propagation enable flexible design of 3D PC components and will provide a route towards future 3D photonic circuits.

Fabrication and characterization of photonic crystal slow light waveguides and cavities

Slow light has been one of the hot topics in the photonics community in the past decade, generating great interest both from a fundamental point of view and for its considerable potential for practical applications. Slow light photonic crystal waveguides, in particular, have played a major part and have been successfully employed for delaying optical signals(1-4) and the enhancement of both linear(5-7) and nonlinear devices.(8-11) Photonic crystal cavities achieve similar effects to that of slow light waveguides, but over a reduced band-width. These cavities offer high Q-factor/volume ratio, for the realization of optically(12) and electrically(13) pumped ultra-low threshold lasers and the enhancement of nonlinear effects.(14-16) Furthermore, passive filters(17) and modulators(18-19) have been demonstrated, exhibiting ultra-narrow line-width, high free-spectral range and record values of low energy consumption. To attain these exciting results, a robust repeatable fabrication protocol must be developed. In this paper we take an in-depth look at our fabrication protocol which employs electron-beam lithography for the definition of photonic crystal patterns and uses wet and dry etching techniques. Our optimised fabrication recipe results in photonic crystals that do not suffer from vertical asymmetry and exhibit very good edge-wall roughness. We discuss the results of varying the etching parameters and the detrimental effects that they can have on a device, leading to a diagnostic route that can be taken to identify and eliminate similar issues. The key to evaluating slow light waveguides is the passive characterization of transmission and group index spectra. Various methods have been reported, most notably resolving the Fabry-Perot fringes of the transmission spectrum(20-21) and interferometric techniques.(22-25) Here, we describe a direct, broadband measurement technique combining spectral interferometry with Fourier transform analysis.(26) Our method stands out for its simplicity and power, as we can characterise a bare photonic crystal with access waveguides, without need for on-chip interference components, and the setup only consists of a Mach-Zehnder interferometer, with no need for moving parts and delay scans. When characterising photonic crystal cavities, techniques involving internal sources(21) or external waveguides directly coupled to the cavity(27) impact on the performance of the cavity itself, thereby distorting the measurement. Here, we describe a novel and non-intrusive technique that makes use of a cross-polarised probe beam and is known as resonant scattering (RS), where the probe is coupled out-of plane into the cavity through an objective. The technique was first demonstrated by McCutcheon et al.(28) and further developed by Galli et al.(29).

Optimization of the storage capacity of slow light photonic crystal waveguides

The storage capacity of slow light photonic crystal waveguides is maximized using a systematic procedure based on the optimization of various parameters of the structure. Both optical loss and dispersion-induced broadening are incorporated into the model. The results indicate that this procedure can provide up to a threefold increase in storage capacity.

Modal theory of slow light enhanced third-order nonlinear effects in photonic crystal waveguides

In this paper, we derive the couple-mode equations for third-order nonlinear effects in photonic crystal waveguides by employing the modal theory. These nonlinear interactions include self-phase modulation, cross-phase modulation and degenerate four-wave mixing. The equations similar to that in nonlinear fiber optics could be expanded and applied for third-order nonlinear processes in other periodic waveguides. Based on the equations, we systematically analyze the group-velocity dispersion, optical propagation loss, effective interaction area, slow light enhanced factor and phase mismatch for a slow light engineered silicon photonic crystal waveguide. Considering the two-photon and free-carrier absorptions, the wavelength conversion efficiencies in two low-dispersion regions are numerically simulated by utilizing finite difference method. Finally, we investigate the influence of slow light enhanced multiple four-wave-mixing process on the conversion efficiency.

Four-wave mixing in slow light photonic crystal waveguides with very high group index

We report efficient four-wave mixing in dispersion engineered slow light silicon photonic crystal waveguides with a flat band group index of n(g) = 60. Using only 15 mW continuous wave coupled input power, we observe a conversion efficiency of -28 dB. This efficiency represents a 30 dB enhancement compared to a silicon nanowire of the same length. At higher powers, thermal redshifting due to linear absorption was found to detune the slow light regime preventing the expected improvement in efficiency. We then overcome this thermal limitation by using oxide-clad waveguides, which we demonstrate for group indices of n_g = 30. Higher group indices may be achieved with oxide clad-waveguides, and we predict conversion efficiencies approaching -10 dB, which is equivalent to that already achieved in silicon nanowires but for a 50x shorter length.

Design of an ultracompact low-power all-optical modulator by means of dispersion engineered slow light regime in a photonic crystal Mach-Zehnder interferometer

We present the design procedure for an ultracompact low-power all-optical modulator based on a dispersion-engineered slow-light regime in a photonic crystal Mach-Zehnder interferometer (PhC MZI), selectively infiltrated by nonlinear optical fluids. The dispersionless slow-light regime enhancing the nonlinearities enabled a 22 μm long PhC MZI to operate as a modulator with an input power as low as 3 mW/μm. Simulations reveal that the switching threshold can be controlled by varying the optofluidic infiltration.

Reconfigurable photonic crystal waveguides created by selective liquid infiltration

We experimentally demonstrate reconfigurable photonic crystal waveguides created directly by infiltrating high refractive index (n≈2.01) liquids into selected air holes of a two-dimensional hexagonal periodic lattice in silicon. The resulting effective index contrast is large enough that a single row of infiltrated holes enables light propagation at near-infrared wavelengths. We include a detailed comparison between modeling and experimental results of single line defect waveguides and show how our infiltration procedure is reversible and repeatable. We achieve infiltration accuracy down to the single air hole level and demonstrate control on the volume of liquid infused into the holes by simply changing the infiltration velocity. This method is promising for achieving a wide range of targeted optical functionalities on a "blank" photonic crystal membrane that can be reconfigured on demand.

Design of an optofluidic biosensor using the slow-light effect in photonic crystal structures

The authors propose a biosensor architecture based on the selective infiltration of photonic crystal (PhC) structures. The proposed sensor consists of a ring cavity coupled to an optofluidic slow-light waveguide in a PhC platform. A high potential sensitivity of 293 nm/refractive index unit is numerically demonstrated, while maintaining an ultracompact footprint.

Slow pulses in disordered photonic-crystal waveguides

Using a 3D fully-vectorial coupled Bloch-mode method, we present a systematic study of the transport of slow-light pulses in single-mode photonic-crystal waveguides (PhCW) with a realistic disorder model. For the intermediate regime corresponding to waveguide lengths of the order of the mean-free path (3 dB attenuation), we show that the group-velocity has a strong impact on the pulse broadening and distortion, limiting the practical use of PhCW to group indices below ≈50. For smaller group velocities, the pulse experiences an additional delay and the group-velocity is no longer a meaningful quantity.

Slow light enhanced optical nonlinearity in a silicon photonic crystal coupled-resonator optical waveguide

We demonstrate highly enhanced optical nonlinearity in a coupled-resonator optical waveguide (CROW) in a four-wave mixing experiment. Using a CROW consisting of 200 coupled resonators based on width-modulated photonic crystal nanocavities in a line defect, we obtained an effective nonlinear constant exceeding 10,000 /W/m, thanks to slow light propagation combined with a strong spatial confinement of light achieved by the wavelength-sized cavities.

Ultracompact all-optical XOR logic gate in a slow-light silicon photonic crystal waveguide

We demonstrate an ultracompact, chip-based, all-optical exclusive-OR (XOR) logic gate via slow-light enhanced four-wave mixing (FWM) in a silicon photonic crystal waveguide (PhCWG). We achieve error-free operation (<10⁻⁹) for 40 Gbit/s differential phase-shift keying (DPSK) signals with a 2.8 dB power penalty. Slowing the light to vg = c/32 enables a FWM conversion efficiency, η, of -30 dB for a 396 μm device. The nonlinear FWM process is enhanced by 20 dB compared to a relatively fast mode of vg = c/5. The XOR operation requires ≈ 41 mW, corresponding to a switching energy of 1 pJ/bit. We compare the slow-light PhCWG device performance with experimentally demonstrated XOR DPSK logic gates in other platforms and discuss scaling the device operation to higher bit-rates. The ultracompact structure suggests the potential for device integration.

Slow-light enhanced correlated photon pair generation in a silicon photonic crystal waveguide

We report the generation of correlated photon pairs in the telecom C-band at room temperature from a dispersion-engineered silicon photonic crystal waveguide. The spontaneous four-wave mixing process producing the photon pairs is enhanced by slow-light propagation enabling an active device length of less than 100 μm. With a coincidence to accidental ratio of 12.8 at a pair generation rate of 0.006 per pulse, this ultracompact photon pair source paves the way toward scalable quantum information processing realized on-chip.

Third-harmonic generation in slow-light chalcogenide glass photonic crystal waveguides

We demonstrate third-harmonic generation (THG) in a dispersion-engineered slow-light photonic crystal waveguide fabricated in AMTIR-1 chalcogenide glass. Owing to the relatively low loss and low dispersion in the slow-light (c/30) regime, combined with the high nonlinear figure of merit of the material (∼2), we obtain a relatively large conversion efficiency (1.4×10(-8)/W(2)), which is 30× higher than in comparable silicon waveguides, and observe a uniform visible light pattern along the waveguide. These results widen the number of applications underpinned by THG in slow-light platforms, such as the direct observation of the spatial evolution of the propagating mode.

Effect of multiphoton absorption and free carriers in slow-light photonic crystal waveguides

We examine the effects of multiphoton absorption, free carriers, and disorder-induced linear scattering in slow-light photonic crystal waveguides. We derive an analytic formulation for self-phase modulation including the group velocity scaling of the nonlinear phase shift in materials limited by three-photon absorption as a representative nonlinear process. We investigate the role of free carriers and derive an approximate critical intensity at which these effects begin to strongly modify the optical field. This critical intensity is employed to determine an optimal group index for the self-phase modulation in the slow-light devices. These observations are confirmed with numerical modeling.

Light propagation in a resonantly absorbing waveguide array

Light propagation behavior in a resonantly absorbing waveguide array is analyzed. Both a Lorentzian line shape and an inhomogeneous broadened absorbing line shape are considered, with their imaginary and real part of the refractive index determined by a Kramers-Kronig relationship. The diffracted wave is shown to have the frequency spectra determined by the material absorption, dispersion as well as the waveguide structure. An interesting phenomenon is that a spectral hole is produced and becomes deeper in the diffraction spectrum as the thickness of the resonantly absorbing waveguide array increases. The experimental measurements conducted in a waveguide array are found to be in good agreement with the numerical results.

Four-wave mixing in photonic crystal waveguides: slow light enhancement and limitations

We demonstrate continuous wave four-wave mixing in silicon photonic crystal waveguides of 396 μm length with a group index of ng=30. The highest observed conversion efficiency is -24 dB for 90 mW coupled input pump power. The key question we address is whether the predicted fourth power dependence of the conversion efficiency on the slowdown factor (η≈S4) can indeed be observed in this system, and how the conversion efficiency depends on device length in the presence of propagation losses. We find that the expected dependencies hold as long as both realistic losses and the variation of mode shape with slowdown factor are taken into account. Having achieved a good agreement between a simple analytical model and the experiment, we also predict structures that can achieve the same conversion efficiency as already observed in nanowires for the same input power, yet for a device length that is 50 times shorter.

Loss engineered slow light waveguides

Slow light devices such as photonic crystal waveguides (PhCW) and coupled resonator optical waveguides (CROW) have much promise for optical signal processing applications and a number of successful demonstrations underpinning this promise have already been made. Most of these applications are limited by propagation losses, especially for higher group indices. These losses are caused by technological imperfections ("extrinsic loss") that cause scattering of light from the waveguide mode. The relationship between this loss and the group velocity is complex and until now has not been fully understood. Here, we present a comprehensive explanation of the extrinsic loss mechanisms in PhC waveguides and address some misconceptions surrounding loss and slow light that have arisen in recent years. We develop a theoretical model that accurately describes the loss spectra of PhC waveguides. One of the key insights of the model is that the entire hole contributes coherently to the scattering process, in contrast to previous models that added up the scattering from short sections incoherently. As a result, we have already realised waveguides with significantly lower losses than comparable photonic crystal waveguides as well as achieving propagation losses, in units of loss per unit time (dB/ns) that are even lower than those of state-of-the-art coupled resonator optical waveguides based on silicon photonic wires. The model will enable more advanced designs with further loss reduction within existing technological constraints.

Nonlinear light propagation in chalcogenide photonic crystal slow light waveguides

Optical nonlinearity can be enhanced by the combination of highly nonlinear chalcogenide glass and photonic crystal waveguides (PCWs) providing strong optical confinement and slow-light effects. In a Ag-As(2)Se(3) chalcogenide PCW, the effective nonlinear parameter γeff reaches 6.3 × 10(4) W(-1)m(-1), which is 200 times larger than that in Si photonic wire waveguides. In this paper, we report the detailed design, fabrication process, and the linear and nonlinear characteristics of this waveguide at silica fiber communication wavelengths. We show that the waveguide exhibits negligible two-photon absorption, and also high-efficiency self-phase modulation and four-wave mixing, which are assisted by low-dispersion slow light.

Four-wave mixing in slow light engineered silicon photonic crystal waveguides

We experimentally investigate four-wave mixing (FWM) in short (80 μm) dispersion-engineered slow light silicon photonic crystal waveguides. The pump, probe and idler signals all lie in a 14 nm wide low dispersion region with a near-constant group velocity of c/30. We measure an instantaneous conversion efficiency of up to -9dB between the idler and the continuous-wave probe, with 1W peak pump power and 6 nm pump-probe detuning. This conversion efficiency is found to be considerably higher (>10 × ) than that of a Si nanowire with a group velocity ten times larger. In addition, we estimate the FWM bandwidth to be at least that of the flat band slow light window. These results, supported by numerical simulations, emphasize the importance of engineering the dispersion of PhC waveguides to exploit the slow light enhancement of FWM efficiency, even for short device lengths.