Slow-light Photonic Crystal Waveguides Research Articles

Theory of disorder-induced coherent scattering and light localization in slow-light photoniccrystal waveguides

We introduce a theoretical formalism to describe disorder-induced extrinsic scattering inslow light photonic crystal waveguides. This work details and extends the optical scatteringtheory used in a recent issue of Physics Review Letters (Patterson et al 2009 Phys. Rev.Lett. 102 253903) to describe coherent scattering phenomena and successfully explainrelated experimental measurements. Our presented theory, which combines Green functionand coupled mode methods, allows us to self-consistently account for arbitrary multiplescattering for the propagating electric field and recover experimental features such asresonances near the band edge. The technique is fully three-dimensional and can calculatethe effects of disorder on the propagating field over thousands of unit cells. As anapplication of this theory, we explore various sample lengths and disordered instances, anddemonstrate the profound effect of multiple scattering in the waveguide transmission.The spectra yield rich features associated with disorder-induced localization andmultiple scattering, which are shown to be exacerbated in the slow light propagationregime.

Electro-optic polymer infiltrated silicon photonic crystal slot waveguide modulator with 23 dB slow light enhancement

A silicon/organic hybrid modulator integrating photonic crystal (PC) waveguide, 75 nm slot, and electro-optic (EO) polymer is experimentally demonstrated. Slow light in PC waveguide and strong field confinement in slot waveguide enable ultraefficient EO modulation with a record-low Vπ×L of 0.56 V mm and an in-device effective r33 of 132 pm/V. This result makes it the most efficient EO polymer modulator demonstrated to date. The modulated signal shows strong wavelength dependence and peak enhancement of 23 dB near the band edge of defect mode, which confirms the signature of the slow light effect.

Improvement of delay-bandwidth product in photonic crystal slow-light waveguides

We report new results about the improvement of delay-bandwidth product in photonic crystal slow light waveguides. Previous studies have obtained large delay-bandwidth product at the price of small average group index. It is pointed out here that the radius and the distance between the two boundary rows of holes have a key contribution for delay-bandwidth product. We show the possibility of improving this factor of merit meanwhile maintaining the same group index. We succeed in improving normal delay-bandwidth product from 0.15 to 0.35, keeping at the same time the group index unchanged at high value of 90. This optimization approach may be applicable for previous flat band slow light devices.

Observation of four-wave mixing in slow-light silicon photonic crystal waveguides

Four-wave mixing is observed in a silicon W1 photonic crystal waveguide. The dispersion dependence of the idler conversion efficiency is measured and shown to be enhanced at wavelengths exhibiting slow group velocities. A 12-dB increase in the conversion efficiency is observed. Concurrently, a decrease in the conversion bandwidth is observed due to the increase in group velocity dispersion in the slow-light regime. The experimentally observed conversion efficiencies agree with the numerically modeled results.

Statistical fluctuations of transmission in slow light photonic-crystal waveguides

We report statistical fluctuations for the transmissions of a series of photonic-crystal waveguides (PhCWs) that are supposedly identical and that only differ because of statistical structural fabrication-induced imperfections. For practical PhCW lengths offering tolerable -3dB attenuation with moderate group indices (n(g) approximately 60), the transmission spectra contains very narrow peaks (Q approximately 20,000) that vary from one waveguide to another. The physical origin of the peaks is explained by calculating the actual electromagnetic-field pattern inside the waveguide. The peaks that are observed in an intermediate regime between the ballistic and localization transports are responsible for a smearing of the local density of states, for a rapid broadening of the probability density function of the transmission, and bring a severe constraint on the effective use of slow light for on-chip optical information processing. The experimental results are quantitatively supported by theoretical results obtained with a coupled-Bloch-mode approach that takes into account multiple scattering and localization effects.

Nonlinear loss dynamics in a silicon slow-light photonic crystal waveguide

We directly investigate both experimentally and numerically the influence of optical nonlinear loss dynamics on a silicon waveguide based all-optical device. The dynamics of these nonlinear losses are explored through the analysis of optical limiting of an amplitude distorted 10 Gbit/s signal in a slow-light silicon photonic crystal waveguide. As the frequency of the distortion approaches the free-carrier recombination rate, free-carrier absorption reaches a steady state, leaving two-photon absorption the dominant dynamic nonlinear loss. Our results highlight the importance of engineering the free-carrier lifetime in silicon waveguides for high speed all-optical processing applications.

Investigation of phase matching for third-harmonic generation in silicon slow light photonic crystal waveguides using Fourier optics

Using Fourier optics, we retrieve the wavevector dependence of the third-harmonic (green) light generated in a slow light silicon photonic crystal waveguide. We show that quasi-phase matching between the third-harmonic signal and the fundamental mode is provided in this geometry by coupling to the continuum of radiation modes above the light line. This process sustains third-harmonic generation with a relatively high efficiency and a substantial bandwidth limited only by the slow light window of the fundamental mode. The results give us insights into the physics of this nonlinear process in the presence of strong absorption and dispersion at visible wavelengths where bandstructure calculations are problematic. Since the characteristics (e.g. angular pattern) of the third-harmonic light primarily depend on the fundamental mode dispersion, they could be readily engineered.

Novel slow light waveguide with controllable delay-bandwidth product and utra-low dispersion

We demonstrate a novel type of slow light photonic crystal waveguide which can produce unusual "U" type group index - frequency curves with constant group index n(g) over large bandwidth. By shifting the boundaries of this waveguide, flexible control of n(g) (10 <n(g)< 210) with large bandwidth (1nm<Deltalambda<43nm centered at 1550nm) and normalized Delay-Bandwidth Product (0.1363<DBP<0.3143) are achieved. Additionally, depending on the chosen waveguide geometry, extremely low group velocity dispersion (GVD<0.5 ps x nm(-1) x mm(-1)), with controllable group velocity dispersion of both signs is obtained.

Bistability by Slow Light Photonic Crystal Waveguide

We study theoretically and numerically optical bistability in photonic crystal waveguide-cavity system with cavity holding multipole mode patterns. The elimination of dominant component of the radiation in cavity can reduce dramatically the scattering of light by cavity and can be used to achieve bistability at band edge. Numerical results performed by the finite-difference time-domain method indicate that the switch power can be reduced greatly that can be regarded as the improvement of quality-factor in cavity.

Longitudinal and Angular Dispersions in Photonic Crystals: A Synergistic Perspective on Slow Light and Superprism Effects

The slow-light effect and the superprism effect are two important effects in photonic crystal structures. In this paper, we will review some of our recent works on the fundamental physics and device applications of these two effects. We will present a synergistic perspective that examines these two effects as a whole. Apparently, the slow light effect is due to the dispersion of a photonic crystal along the direction of light propagation, namely the longitudinal direction, and the superprism effect is related to angular dispersion. However, a deep analysis will show that the superprism effect has an elusive dependence on the longitudinal dispersion as well. Some subtle connections and distinctions between the slow-light effect and the superprism effect will be revealed through our physical analysis. This allows us to treat these two effects under a common theoretical framework. As an example, we will apply this framework to make a direct comparison of the slow-light optical phase array approach and the superprism approach to beam steering applications. Dispersive effects are frequently accompanied by high optical loss and/or narrow bandwidths. We will discuss these issues for both longitudinal and angular dispersions. For the slow light effect, we will give a simple proof of the scaling of fabrication-imperfection related random scattering losses in a slow-light photonic crystal waveguide. Similar to the bandwidth-delay product for the longitudinal dispersion, we will introduce a simple, yet fundamental, limit that governs the bandwidth and angular sensitivities of the superprism effect. We will also discuss the application of the slow-light effect to making compact silicon optical modulators and switches.

Enhanced Raman Scattering in Slow-Light Photonic Crystals for Chip-Scale Frequency Conversion and Optical Amplification

We present measurements of enhanced Raman scattering in silicon slow-light photonic crystal waveguides. By utilizing both the Bragg gap edge dispersion of TM-like modes for pump enhancement and the TE-like fundamental mode onset for Stokes enhancement, a six-fold increase in the spontaneous Raman scattering was observed in the double slow-light regime. Both forward and backward Stokes signals are examined, with continuous-wave measurements, in our low-loss photonic crystal membranes. The measured nonlinear enhancement matches well with our numerical model and simulations, and are described in detail in this paper. These observations support the development of chip-scale frequency conversion and optical amplification in silicon nanophotonics.

Non-trivial scaling of self-phase modulation and three-photon absorption in III-V photonic crystal waveguides

We investigate the nonlinear response of photonic crystal waveguides with suppressed two-photon absorption. A moderate decrease of the group velocity (approximately c/6 to c/15, a factor of 2.5) results in a dramatic (x 30) enhancement of three-photon absorption well beyond the expected scaling, proportional, variant 1/v3g. This non-trivial scaling of the effective nonlinear coefficients results from pulse compression, which further enhances the optical field beyond that of purely slow-group velocity interactions. These observations are enabled in mm-long slow-light photonic crystal waveguides owing to the strong anomalous group-velocity dispersion and positive chirp. Our numerical physical model matches measurements remarkably.

Disorder-induced incoherent scattering losses in photonic crystal waveguides: Bloch mode reshaping, multiple scattering, and breakdown of the Beer-Lambert law

Through a combined theoretical and experimental study of disorder-induced incoherent scattering losses in slow-light photonic crystal slab waveguides, we show the importance of Bloch mode reshaping and multiple scattering. We describe a convenient and fully three-dimensional theoretical treatment of disorder-induced extrinsic scattering, including the calculation of backscatter and out-of-plane losses per unit cell, and the extrapolation of the unit-cell loss to the loss for an entire disordered waveguide. The theoretical predictions, which are also compared with recent measurements on dispersion engineered silicon waveguides, demonstrate the failure of the Beer-Lambert law due to multiple scattering. We also explain why the previously assumed group velocity scalings of disorder-induced loss break down in general.

Light transport regimes in slow light photonic crystal waveguides

The dispersive properties of waves are strongly affected by inevitable residual disorder in man-made propagating media, in particular in the slow wave regime. By a direct measurement of the dispersion curve in $k$ space, we show that the nature of the guided modes in real photonic crystal waveguides undergoes an abrupt transition in the vicinity of a band edge. Such a transition that is not highlighted by standard optical transmission measurement, defines the limit where $k$ can be considered as a good quantum number. In the framework of a mean-field theory we propose a qualitative description of this effect and attribute it to the transition from the ``dispersive'' regime to the diffusive regime. In particular we prove that a scaling law exists between the strength of the disorder and the group velocity. As a result, for group velocities ${v}_{g}$ smaller than $c/25$ the diffusive contribution to the light transport is predominant. In this regime the group velocity ${v}_{g}$ loses its relevance and the energy transport velocity ${v}_{E}$ is the proper light speed to consider.

A proposal for enhancing four-wave mixing in slow light engineered photonic crystal waveguides and its application to optical regeneration

In this paper, we investigate both analytically and numerically four-wave mixing (FWM) in short (80 microm) dispersion engineered slow light photonic crystal waveguides. We demonstrate that both a larger FWM conversion efficiency and an increased FWM bandwidth (approximately 10 nm) can be achieved in these waveguides as compared to dispersive PhC waveguides. This improvement is achieved through the net slow light enhancement of the FWM efficiency (almost 30dB as compared to a fast nanowire of similar length), even in the presence of slow light increased linear and nonlinear losses, and the suitable dispersion profile of these waveguides. We show how such improved FWM operation can be advantageously exploited for designing a compact 2R and 3R regenerator with the appropriate nonlinear power transfer function.

Efficient coupling into slow light photonic crystal waveguide without transition region: role of evanescent modes

We show that efficient coupling between fast and slow photonic crystal waveguide modes is possible, provided that there exist strong evanescent modes to match the waveguide fields across the interface. Evanescent modes are required when the propagating modes have substantially different modal fields, which occurs, for example, when coupling an index-guided mode and a gap-guided mode.

Enhanced parametric amplification in slow-light photonic crystal waveguides

We demonstrate both theoretically and numerically that slow light can enhance the parametric process of silicon in photonic crystal line-defect waveguides. Specifically, to get the desired gain, the pump power for a given gain medium length or the gain medium length for given pump power can be reduced by (c/v g n)2 when slow light waveguides are used, where n is the material index of conventional waveguide, v g is the group velocity of the slow light waveguide and c is the light velocity in vacuum.

Disorder-Induced Coherent Scattering in Slow-Light Photonic Crystal Waveguides

Light transmission measurements and frequency-delay reflectometry maps for GaAs photonic crystal membranes are presented and analyzed, showing the transition from propagation with a well-defined group velocity to a regime completely dominated by disorder-induced coherent scattering. Employing a self-consistent optical scattering theory, with only statistical functions to describe the structural disorder, we obtain excellent agreement with the experiments using no fitting parameters. Our experiments and theory together provide clear physical insight into naturally occurring light localization and multiple coherent-scattering phenomena in slow-light waveguides.

Backscattering and disorder limits in slow light photonic crystal waveguides

It is known that slow light propagation in disordered photonic crystal channel waveguides leads to backscattering and localization phenomena. The knowledge of the reflection of a slow light mode at a single disorder defect of the periodical structure can help to estimate the backscattering intensity and the localization length. Here, this Bloch-mode reflection is calculated in a simplified slow light waveguide using an eigenmode-expansion approach. We show that by properly engineering the waveguide, backscattering can be significantly reduced while maintaining the same low group velocity. A strong effect of the mode's anticrossing taking place in photonic crystal line-defects is demonstrated on backscattering. The localization length of slow light waveguides is estimated, which provides fundamental limits for the applicability of slow light waveguides.

Spectrally narrow polarisation conversion in a slow-light photonic crystal waveguide

A narrow-band (3dB bandpass < 2 nm) transmission notch based on polarisation conversion within a SOI photonic crystal waveguide is demonstrated. Signal contrast between quasi- TE and TM eigenstates exceeding 40 dB is achieved. Further, multiple resonant wavelength coupling between the two eigenstates is also observed.