Slow-light Regime Research Articles

Bit-error ratio calculation for single-channel silicon optical interconnects utilizing return-to-zero pulsed signals

We introduce an accurate and efficient approach to compute the transmission bit-error ratio (BER) of single-channel silicon photonic interconnects when the optical signal consists of arbitrarily shaped optical pulses. The silicon photonic systems investigated in this study contain an optical transmitter, a silicon optical interconnect, which can be either a strip single-mode silicon photonic waveguide (Si-PhW) or a silicon photonic crystal (PhC) waveguide (Si-PhCW), and a direct-detection receiver. The input signal consists of a superposition of a train of Gaussian pulses and white noise, its propagation in the silicon waveguide being described by a rigorous theoretical model based on a modified nonlinear Schrodinger equation, which captures all relevant linear and nonlinear optical effects. The statistical properties of the output signal and the corresponding BER were determined using the Fourier series Karhunen–Loeve expansion method. Our analysis reveals that in the case of Si-PhWs the pulse width is the parameter that most strongly influences the BER, whereas for Si-PhCWs the main factor affecting BER is the pulse group velocity. Finally, we show that similar values of BER are achieved in Si-PhCWs with length of about 2 orders of magnitude smaller than that of Si-PhWs, a further reduction of the silicon interconnect footprint being possible if the Si-PhCW is operated in the slow-light regime.

Fine tuning of the center frequency of the slow light regime in an infiltrated W09 photonic crystal waveguide

We report the tuning process of center frequency in a dispersion engineered slow light regime in W09 photonic crystal slab waveguide (W09-PhCSW). The W09-PhCSW consists of hexagonal lattice of air holes of radii r = 0.3ɑ in a Si substrate with a reduced waveguide width. This end is achieved by means of simultaneous infiltration of magneto and opto-fluidics in first and second rows adjacent to the waveguide. In particular, change in infiltration of opto-fluidics (1.5 ≤ nf ≤ 2.1) is used for selecting the optimized group index with low group velocity dispersion. Concurrently, the center frequency in the constant group index regime (Δng = ±5%) get tuned with an external magnetic field. This course of external controllability originated from the field dependent refractive index of magneto-fluidic. After all, this design leads to a considerable low group velocity dispersion of |β2| ≤ 2000 (ɑ/2πc2), the group index values in the range of 23 ≤ ng ≤ 103 and reasonable group index-bandwidth product values (0.114 ≤ ng × Δω/ωc ≤ 0.26).

Schottky graphene/Si photodetector based on metal-dielectric hybrid hollow-core photonic crystal fibers.

This Letter presents a new family of Schottky graphene/silicon (Si) photodetectors (PDs) based on hollow-core photonic crystal fibers (HPCFs), working at both optical communication and room temperature. The proposed structure has the advantage of plasmonic HPCFs in a slow-light regime, and the absorption mechanism is based on an internal photoemission effect. The main feature of this structure is that the enhanced electric field is strongly localized in the hollow core of the guided core mode with the surface plasmon modes at the surface metal wires embedded in the photonic crystal structure. For the proposed graphene/silicon Schottky PD, numerical simulation predicts responsivity of ∼0.39 A/W, and continuous-wave sensitivity of -59 dBm, which reveals substantial improvements compared to that of typical metal/Si Schottky PDs.

BER in Slow-Light and Fast-Light Regimes of Silicon Photonic Crystal Waveguides: A Comparative Study

In this letter, we present an in-depth comparison between the bit-error ratio (BER) of optical systems containing silicon photonic crystal (Si-PhC) waveguides (Si-PhCWs) operating in the slow- and fast-light regimes. Our analysis of these optical interconnects employs the time domain Karhunen–Loève expansion method for the statistical analysis of the optical signal and relies on a full theoretical model and its linearized form to describe the propagation of noisy optical signals in Si-PhCWs. These models incorporate all key linear and nonlinear optical effects and the mutual interaction between free-carriers and the optical field, as well as the influence of slow-light effects on the optical field and carriers dynamics. Using these tools and employing a 512-b pseudorandom bit sequence, we have studied the dependence of BER on the key system parameters, including group-velocity, input power, and signal-to-noise ratio.

Statistics of Anderson-localized modes in disordered photonic crystal slab waveguides

We present a fully three-dimensional Bloch mode expansion technique and photon Green function formalism to compute the quality factor, mode volume, and Purcell enhancement distributions of a disordered W1 photonic crystal slab waveguide in the slow-light Anderson localization regime. By considering fabrication (intrinsic) and intentional (extrinsic) disorder we find that the quality factor and Purcell enhancement statistics are well described by log-normal distributions without any fitting parameters. We also compare directly the effects of hole size fluctuations as well as fluctuations in the hole position. The functional dependence of the mean and standard deviation of the quality factor and Purcell enhancement distributions is found to decrease exponentially on the square root of the extrinsic disorder parameter. The strong coupling probability between a single quantum dot and an Anderson-localized mode is numerically computed and found to exponential decrease with the squared extrinsic disorder parameter, where low disordered systems give rise to larger probabilities when state-of-art quantum dots are considered. The optimal regions to position quantum dots in the W1 waveguide are also discussed. These theoretical results are fundamental interesting and connect to recent experimental works on photonic crystal slab waveguides in the slow-light regime.

MODELLING of a two-dimensional photonic crystal with line defect for a laser gas sensor application

Abstract We present the results of a numerical analysis of a two-dimensional photonic crystal with line defect for a laser gas sensor working in a slow light regime. The geometrical parameters of photonic crystals with three different line defects were numerically analyzed: a missing row of holes, a row of holes with changed diameter and air channel. Antireflection sections were also analyzed. The simulations were carried out by MEEP and MPB programs, with the aim to get the values of a group refractive index, transmission and a light-gas overlap as high as possible. The effective refractive index method was used to reduce the simulation time and required computing power. We also described numerical simulation details such as required conditions to work in the slow light regime and the analyzed parameters values’ dependency of the simulation resolution that may influence the accuracy of the results.

Exploiting high-order phase-shift keying modulation and direct-detection in silicon photonic systems.

A computational approach to evaluate the bit-error ratio (BER) in silicon photonic systems employing high-order phase-shift keying (PSK) modulation formats is presented. Specifically, the investigated systems contain a silicon based optical interconnect, namely a strip silicon photonic waveguide or a silicon photonic crystal waveguide, and direct-detection receivers suitable to detect PSK and amplitude-shaped PSK signals. The superposition of a PSK signal and complex additive white Gaussian noise passes through the optical interconnect and subsequently through two detection-branch receivers. To model the signal propagation in the silicon optical interconnects we used a modified nonlinear Schrödinger equation, which incorporates all relevant linear and nonlinear optical effects and the mutual interaction between free-carriers and the optical field. Finally, the BER is calculated by applying a frequency-domain approach based on the Karhunen-Loève series expansion method. Our computational studies of the BER reveal that the optical power, type of PSK modulation, waveguide length, and group-velocity are key factors characterizing the system BER, their influence on BER being more significant in a photonic system with larger nonlinearity. In particular, our analysis shows that the system performance is affected to a much larger extent when the signal propagates in the slow-light regime, despite the fact that this regime allows for a significantly reduced length of optical interconnects.

Hybrid silicon slotted photonic crystal waveguides: how does third order nonlinear performance scale with slow light?

We investigate in this paper the influence of slow light on the balance between the Kerr and two-photon absorption (TPA) processes in silicon slotted hybrid nonlinear waveguides. Three typical silicon photonic waveguide geometries are studied to estimate the influence of the light slow-down factor on the mode field overlap with the silicon region, as well as on the complex effective nonlinear susceptibility. It is found that slotted photonic crystal modes tend to focalize in their hollow core with increasing group index (nG) values. Considering a hybrid integration of nonlinear polymers in such slotted waveguides, a relative decrease of the TPA process by more factor of 2 is predicted from nG=10 to nG=50. As a whole, this work shows that the relative influence of TPA decreases for slotted waveguides operating in the slow light regime, making them a suitable platform for third-order nonlinear optics.

Time-reversal constraint limits unidirectional photon emission in slow-light photonic crystals.

Photonic crystal waveguides are known to support C-points-point-like polarization singularities with local chirality. Such points can couple with dipole-like emitters to produce highly directional emission, from which spin-photon entanglers can be built. Much is made of the promise of using slow-light modes to enhance this light-matter coupling. Here we explore the transition from travelling to standing waves for two different photonic crystal waveguide designs. We find that time-reversal symmetry and the reciprocal nature of light places constraints on using C-points in the slow-light regime. We observe two distinctly different mechanisms through which this condition is satisfied in the two waveguides. In the waveguide designs, we consider a modest group velocity of vg≈c/10 is found to be the optimum for slow-light coupling to the C-points.This article is part of the themed issue 'Unifying physics and technology in light of Maxwell's equations'.

Performance Enhancement of Cavity Assisted Photonic Crystal De-Multiplexerin Slow Light Regime

This study first proposes a new version of a photonic crystal based de-multiplexer operating under the slow light regime, secondly analyses the structure numerically to demonstrate de-multiplexing operation and finally studies the impact of light speed on the performance of the proposed structure. The operation wavelength is 1.55 µm. The study indicates that, by adjusting the speed of light, around 0.1C, in the main waveguide and in the output channels’ waveguides, an enhancement in the performance of the de-multiplexer will be gained.

Controlling slow and fast light and dynamic pulse-splitting with tunable optical gain in a whispering-gallery-mode microcavity

We report controllable manipulation of slow and fast light in a whispering-gallery-mode microtoroid resonator fabricated from Erbium (Er3+) doped silica. We observe continuous transition of the coupling between the fiber-taper waveguide and the microresonator from undercoupling to critical coupling and then to overcoupling regimes by increasing the pump power even though the spatial distance between the resonator and the waveguide was kept fixed. This, in turn, enables switching from fast to slow light and vice versa just by increasing the optical gain. An enhancement of delay of two-fold over the passive silica resonator (no optical gain) was observed in the slow light regime. Moreover, we show dynamic pulse splitting and its control in slow/fast light systems using optical gain.

Theoretical Comparative Analysis of BER in Multi-Channel Systems With Strip and Photonic Crystal Silicon Waveguides

We present a comparative analysis of the performance of multi-channel photonic systems containing strip or photonic crystal (PhC) silicon (Si) waveguides in the presence of white Gaussian noise. Specifically, we consider a multi-wavelength optical signal propagating either in a strip single-mode Si photonic waveguide (Si-PhW) or in a Si PhC waveguide (Si-PhCW), each channel consisting of a CW nonreturn-to-zero ON–OFF keying modulated signal. The output signal is demultiplexed and the signal in each channel is analyzed using direct-detection optical receivers. We describe the propagation of the optical signal in the Si-PhW and Si-PhCW using a linearized model and validate our main results by employing a rigorous theoretical model that incorporates all relevant linear and nonlinear optical effects and the mutual interaction between free-carriers and the optical field. The bit error rate (BER) of the transmitted signal is calculated by using both a time- and frequency-domain Karhunen–Loeve expansion method. Our analysis suggests that due to enhanced nonlinear effects, for comparable optical power, a similar BER is achieved in a PhC waveguide about $100\times$ shorter than a strip one, with a particularly strong signal degradation being observed in the slow-light regime of the Si-PhCW.

Threshold Characteristics of Slow-Light Photonic Crystal Lasers.

The threshold properties of photonic crystal quantum dot lasers operating in the slow-light regime are investigated experimentally and theoretically. Measurements show that, in contrast to conventional lasers, the threshold gain attains a minimum value for a specific cavity length. The experimental results are explained by an analytical theory for the laser threshold that takes into account the effects of slow light and random disorder due to unavoidable fabrication imperfections. Longer lasers are found to operate deeper into the slow-light region, leading to a trade-off between slow-light induced reduction of the mirror loss and slow-light enhancement of disorder-induced losses.

Pathological scattering by a defect in a slow-light periodic layered medium

Scattering of electromagnetic fields by a defect layer embedded in a slow-light periodically layered ambient medium exhibits phenomena markedly different from typical scattering problems. In a slow-light periodic medium, constructed by Figotin and Vitebskiy, the energy velocity of a propagating mode in one direction slows to zero, creating a “frozen mode” at a single frequency within a pass band, where the dispersion relation possesses a flat inflection point. The slow-light regime is characterized by a 3 × 3 Jordan block of the log of the 4 × 4 monodromy matrix for EM fields in a periodic medium at special frequency and parallel wavevector. The scattering problem breaks down as the 2D rightward and leftward mode spaces intersect in the frozen mode and therefore span only a 3D subspace V˚ of the 4D space of EM fields. Analysis of pathological scattering near the slow-light frequency and wavevector is based on the interaction between the flux-unitary transfer matrix T across the defect layer and the projections to the rightward and leftward spaces, which blow up as Laurent-Puiseux series. Two distinct cases emerge: the generic, non-resonant case when T does not map V˚ to itself and the quadratically growing mode is excited and the resonant case, when V˚ is invariant under T and a guided frozen mode is resonantly excited.

A Proposal for Loss Engineering in Slow-Light Photonic Crystal Waveguides

The authors present a loss engineering method for slow-light photonic crystal (PhC) waveguides. Our proposed method for engineering the loss is based on optofluidic techniques to produce low propagation loss in the low dispersions slow-light regime. We numerically demonstrate that this approach allows one to control the propagation loss (from 180 to 120 dB/cm) by selective infiltration of suitable fluids into air holes of a PhC waveguide around the group velocity of c/55 to c/70. It is proposed that fabrication imperfections, i.e., roughness and other deviations from an ideal structure that lead to propagation losses, can be compensated by a selective nanoinfiltration method. A loss of 150 dB/cm for loss-engineered waveguides, compared to 230 dB/cm for conventional waveguides, is numerically demonstrated, while both waveguide structures maintain the same group index-bandwidth product.

Designing Tunable Microstructure Spectroscopic Gas Sensor Using Optofluidic Hollow-Core Photonic Crystal Fiber

A tunable slow-light hollow-core photonic crystal fiber (HPCF), applicable to miniaturized microstructure spectroscopic gas sensors is proposed. In the proposed structure, we have taken the advantage of the microfluidic infiltration technique to tune the slow-light regime so as to match the reference absorption line of the target gas sample, which is required for designing miniaturized gas sensors with reconfigurable detection sensitivity. The main feature of this structure is that the enhanced electrical field is strongly localized in the hollow-core of a photonic crystal fiber for any gas samples due to tunability of slow-light modes. We discuss the potential of slow light in HPCF for realizing compact and tunable gas sensor devices with low and high loss material. In particular, we present numerical results showing how this optofluidic microstructure can be used for detecting CO, CO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> , H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> S, CH <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">4</sub> , SO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> , and N <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> O gases.

Lateral lattice shift engineered slow light in elliptical photonics crystal waveguides

A photonics crystal (PhC) waveguide that operates in the slow-light regime is reported in this paper. A second line of circular air holes from the PhC waveguide in a triangular lattice is replaced by a line of elliptical air holes. Based on a three-dimensional plane wave expansion, the lateral shift of elliptical air holes is conducted to enhance the slow-light characteristics. A group index of 166 and a delay-bandwidth product of 0.1812 are derived from an optimized PhC using elliptical air holes with a lateral shift of 160 nm according to the simulation results. A Mach–Zehnder interferometer (MZI) is integrated with the above-mentioned PhC waveguide with a 17 μm length in one of its arms. The measured transmission spectrum of the fabricated MZI embedded with a PhC waveguide shows slow-light interference patterns.

Design and analysis of slow light regime in silicon carbide 2D photonic crystal waveguides

We theoretically demonstrate the slow light capabilities of 2D silicon carbide based photonic crystal W1 waveguides (SiC-PhC-W1Ws) with numerical simulations. The PhC is assumed to be created by devising air-holes with hexagonal lattice in a standard SiC substrate having oscillator type ordinary refractive index. Numerical simulations show that by means of selective optofluidic infiltration and varying the air-holes radii, SiC-PhC-W1Ws are capable of slowing light down by about 473 times while their group velocity dispersions are tailored to near zero values. Our numerical study also suggests the possibility of slow-light guiding with ng×Δλ/λc values as high as 0.42 in SiC-PhC-W1Ws at optical telecommunications wavelengths.

Reducing disorder-induced losses for slow light photonic crystal waveguides through Bloch mode engineering

We present theory and measurements of disorder-induced losses for low loss 1.5mm long slow light photonic crystal waveguides. A recent class of dispersion engineered waveguides increases the bandwidth of slow light and shows lower propagation losses for the same group index. Our theory and experiments explain how Bloch mode engineering can substantially reduce scattering losses for the same slow light group velocity regime.

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.