Slow-light Waveguides Research Articles

Sporadic-Slot Photonic-Crystal Waveguide for All-Optical Buffers With Low-Dispersion, Distortion, and Insertion Loss

A novel structure is studied with implanting sporadic slots inside a photonic crystal waveguide (PCW) to form sporadic-slot PCW (SSPCW) for realizing compact, all-optical buffers with low-dispersion, distortion, and attenuation (DDA). We implement the first demonstration that, to the best of our knowledge, the SSPCW works for both TE- and TM-modes all-optical buffers and slow-light waveguides. High buffer performance and wider transmission bandwidth in telecommunication band are obtained, which are guaranteed through bit rate optimization that exceeded 2 Tb/s for both TE and TM modes in ultra-low dispersion region which is 20 times greater than that required for 5G mobile communications and it is also useful for all-optical signal processing. The storage length of 1 bit is obtained as $4.5202~\mu \text {m}$ for TE mode and $6.0525~\mu \text {m}$ for TM mode. Moreover, a low relative pulse distortion of 0.0801% $\mu \text{m}^{-1}$ along the propagation path per unit length is acquired for a 0.63 ps pulse. Besides, the attenuation coefficient of the optical power pulse between the input and output is $0.0170~\text {dB}/\mu \text {m}$ . Additionally, the deigned SSPCW is insensitive for small variations of waveguide parameters and the deviation is virtually negligible between the simulated results and that of the fabricated structures with totally acceptable tolerance below ±3 nm, which is the challenge in the fabrication process of conventional PCW and PCW-cavity.

Conical Swiss Roll Metamaterial Application for Slow-Light Waveguides

The framework for designing and fabricating a slow-light waveguide structure with conical Swiss roll metamaterial core at Terahertz frequencies has been carried out in this article. In the earliest work, theoretical backgrounds based on Maxwell’s equations have been developed for anisotropic single-negative permeability slab waveguides and anisotropic metamaterial slab waveguides. Subsequently, simulation results fulfilled by the MATLAB programming tool verify extremely low group velocities in the aforementioned slab waveguides in the Terahertz regime frequency. A volumetric conical Swiss roll metamaterial has been proposed as a practical achievement for slow-light waveguides. Dispersion characteristics of the electromagnetic waves in the proposed conical Swiss roll metamaterial have been investigated using the CST simulation tool in Terahertz frequencies. Furthermore, a 2-D dispersion diagram fulfilled by CST and MATLAB validates highly electromagnetic field concentration as well as the presence of backward waves in the conical Swiss roll configuration.

Double-layer graphene on photonic crystal waveguide electro-absorption modulator with 12 GHz bandwidth

Abstract Graphene has been widely used in silicon-based optical modulators for its ultra-broadband light absorption and ultrafast optoelectronic response. By incorporating graphene and slow-light silicon photonic crystal waveguide (PhCW), here we propose and experimentally demonstrate a unique double-layer graphene electro-absorption modulator in telecommunication applications. The modulator exhibits a modulation depth of 0.5 dB/μm with a bandwidth of 13.6 GHz, while graphene coverage length is only 1.2 μm in simulations. We also fabricated the graphene modulator on silicon platform, and the device achieved a modulation bandwidth at 12 GHz. The proposed graphene-PhCW modulator may have potentials in the applications of on-chip interconnections.

Dispersion Engineering With Photonic Inverse Design

Dispersion engineering, such as the design of slow light waveguide systems, is an effective tool for a wide range of photonic applications, but presents a difficult optical design challenge. Most applications require a slow light waveguide design that mitigates group velocity dispersion, and efficient coupling solutions over the slow light operating bandwidth. In this work, we optimize the slow light dispersion relation of a photonic crystal waveguide with three dimensional (3D) inverse design methods. In addition, we design mode couplers for the photonic crystal waveguide. The optimized waveguide supports a slow light mode with a group index of n <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">g</sub> = 25 and a normalized bandwidth group index product of of 0.38. A compact mode coupler to a strip waveguide is designed with an average efficiency of 92.7% within the slow light operating bandwidth. Lastly, we design a fully etched grating which couples directly to the slow light mode with a 32.5% average efficiency.

Front-induced transitions

Refractive index fronts propagating in waveguides are special spatiotemporal perturbations. The interaction of light with such fronts can be described in terms of an indirect transition where the frequency and wavenumber of a guided mode both are changed. In recent years, front-induced transitions have been used in dispersion-engineered waveguides for frequency conversion, optical delays, and bandwidth and pulse duration manipulation. These concepts have originated from different research areas of photonics, such as nonlinear fibre optics, slow-light waveguides, plasma physics, moving media and relativistic effects. Here, we discuss these concepts, providing a unifying theoretical description and highlight the potential of this exciting research field for light manipulation in guided optics. Front-induced transitions have been used in dispersion-engineered waveguides for frequency conversion, optical delays, and bandwidth and pulse duration manipulation. This Review provides a theoretical description of the subject and highlights the potential for light manipulation in guided optics.

Broadband delay lines and nonreciprocal resonances in unidirectional waveguides

Slow-light waveguides play an important role in optical pulse delay lines, but are practically limited by disorder-induced attenuation. Topological edge states, unidirectional and robust against disorder, have been proposed as a way to address this issue. Here, we study the transmission phase and pulse propagation dynamics through unidirectional systems in the presence of strong discontinuities. We first investigate a magnetically biased slow-light channel, demonstrating broadband pulse delays in small footprints. We uncover a nonreciprocal etalonlike resonance, sustained by propagating forward and evanescent backward modes, affecting pulse propagation and delay. We then show the existence of these features in topologically protected edge states, highlighting their universality. These exotic resonances provide a new degree of freedom in unidirectional waveguides to engineer their response, and they may therefore prove highly useful in various nanophotonic applications.

Demonstration of slow-light effect in silicon-wire waveguides combined with metamaterials.

We demonstrated a novel slow-light Si-wire waveguide combined with metamaterials, which can be easily integrated with other Si photonics devices. The slow-light effect can be produced simply by placing metamaterials at an appropriate position on a Si-wire waveguide. It was confirmed that the large group index of more than 40 could be obtained because of a steep and discontinuous change of dispersion relation near the resonance frequency of metamaterials.

Broadband Topological Slow Light through Higher Momentum-Space Winding.

Slow-light waveguides can strongly enhance light-matter interaction, but suffer from a narrow bandwidth, increased backscattering, and Anderson localization. Edge states in photonic topological insulators resist backscattering and localization, but typically cross the bulk band gap over a single Brillouin zone, meaning that slow group velocity implies narrow-band operation. Here we show theoretically that this can be circumvented via an edge termination that causes the edge state to wind many times around the Brillouin zone, making it both slow and broadband.

Slow light performance enhancement of graphene-based photonic crystal waveguide

We propose a graphene-based photonic crystal (PC) slow light waveguide, which is realized by creating periodical air holes in a silicon layer to achieve spatially varying chemical potentials of graphene. The structure is optimized around 30 THz, and a large group index of 166.6 is obtained, with a very low propagation loss of −2.1 dB/um. The corresponding normalized delay-bandwidth product reaches as high as 4.00. Furthermore, the slow light performance can be dynamically tuned by changing a bias voltage. The center frequency of the slow light waveguide can be tuned between 19.1 THz and 27.4 THz. Our results suggest that graphene-based PC structures are very promising for slow light devices.

Slow light in ultracompact photonic crystal decoder.

In this study, merging two photonic crystal-based structures, a new design for an all-optical 2-to-4 decoder has been proposed. The switching operation is based on the Kerr effect and refractive index modification. The structure consists of one nonlinear ring resonator and three nonlinear cavities that have been modified for entering the slow-light regime in order to enhance coupling through waveguides. The maximum group index of 94 has been obtained for the proposed slow-light waveguides. With this approach, the maximum and minimum normalized output powers for logic 0 and 1 are 4% and 82%, respectively. The data transfer rate of the decoder is 220GHz, and the size of the structure is 24×9.5 μm2. The maximum insertion loss and cross talk are -7.45 dB and -16.38 dB, respectively. Considering the above characteristics, the proposed decoder can be qualified as a part of optical integrated circuits.

Dispersion engineering and thermo-optic tuning in mid-infrared photonic crystal slow light waveguides on silicon-on-insulator.

In this Letter, the design, fabrication, and characterization of slow light devices using photonic crystal waveguides (PhCWs) in the mid-infrared wavelength range of 3.9-3.98μm are demonstrated. The PhCWs are built on the silicon-on-insulator platform without undercut to leverage its well-developed fabrication process and strong mechanical robustness. Lattice shifting and thermo-optic tuning methods are utilized to manipulate the slow light region for potential spectroscopy sensing applications. Up to 20nm wavelength shift of the slow light band edge is demonstrated. Normalized delay-bandwidth products of 0.084-0.112 are obtained as a result of dispersion engineering. From the thermo-optic characterization results, the slow light enhancement effect of thermo-optic tuning efficiency is verified by the proportional relationship between the phase shift and the group index. This work serves as a proof of concept that the slow light effect can strengthen light-matter interaction and thereby improve device performance in sensing and nonlinearity applications.

Mid-Infrared Slow Light Engineering and Tuning in 1-D Grating Waveguide

The design, fabrication, and characterization of 1-D grating waveguide as slow light structure working in mid-infrared (MIR) region are demonstrated for the first time. The effects of various structural parameters on slow light properties are investigated through theoretical analysis, simulation and experimental verification, providing guidance on slow light engineering in 1-D grating waveguide. By adjusting structural parameters, average group indices of 9.4–15.5 with bandwidths of 23–66 nm and normalized delay-bandwidth products of 0.093–0.164 are obtained. Thermo-optic tuning is also demonstrated with π phase shift and group index tuning from 23 to 33 at the wavelength of 3.9024 μm by applying 1.4 mA current. The proposed tunable 1-D grating slow light waveguide provides a promising platform for various MIR applications such as on-chip absorption-based biochemical sensors, tunable optical buffers, and thermo-optic modulators.

Unidirectional light transport in dynamically modulated waveguides

Unidirectional light propagation, as in the emerging field of topological photonics, offers robust transport of light in devices despite the presence of fabrication flaws. This highly nontrivial effect, however, can only be achieved in correspondingly nontrivial structures. The authors present a significantly simplified paradigm in which dynamic modulation of a photonic waveguide conducts light in one direction, even through structural defects. This approach opens an avenue to exploring topological photonics, and to slow-light waveguides unhindered by their imperfections, which is exciting for applications in integrated optics.

Unidirectional Slow Light Transmission in Heterostructure Photonic Crystal Waveguide

In conventional photonic crystal systems, extrinsic scattering resulting from random manufacturing defects or environmental changes is a major source of loss that causes performance degradation, and the backscattering loss is amplified as the group velocity slows down. In order to overcome the limitations in slow light systems, we propose a backscattering-immune slow light waveguide design. The waveguide is based on an interface between a square lattice of magneto-optical photonic crystal with precisely tailored rod radii of the first two rows and a titled 45 degrees square lattice of Alumina photonic crystal with an aligned band gap. High group indices of 77, 68, 64, and 60 with the normalized frequency bandwidths of 0.444%, 0.481%, 0.485%, and 0.491% are obtained, respectively. The corresponding normalized delay-bandwidth products remain around 0.32 for all cases, which are higher than previously reported works based on rod radius adjustment. The robustness for the edge modes against different types of interfacial defects is observed for the lack of backward propagation modes at the same frequencies as the unidirectional edge modes. Furthermore, the transmission direction can be controlled by the sign of the externally applied magnetic field normal to the plane.

Bend Coupling Through Near-Zero GVD Slow Light Photonic Crystal Waveguides

Slow light propagation through photonic crystal (PhC) slab devices has great potential to reduce the size and power consumption of silicon photonic optical circuits. Most commonly, slow light routing through photonic crystals is achieved by using W1 waveguide bends operating near their cutoff frequencies. Unfortunately, this leads to optical pulse distortion due the high group velocity dispersion (GVD) associated with these designs. In this letter, however, we study the coupling between slow light waveguides optimized for near-zero GVD and 60 $^{\circ }$ PhC bends. Using numerical methods and the temporal coupled mode theory, we assess the performance of single bends coupled to input/output waveguides, and S-bends composed of two cascaded bends. In this latter, we observe that the bend-waveguide quality factor has great impact over transmission and dispersion. We propose a novel 60 $^{\circ }$ PhC bend design for routing optical modes while maintained reduced dispersion. This is achieved over a -3 dB bandwidth of around 50 nm in devices with slowdown factor up to 40. We show that this 60 $^{\circ }$ PhC bend has good stability under changes in S-bend length and fabrication induced disorder. These results can lead to great improvements in the design of monolithically integrated modulators, switches, (de)multiplexers, and filters based on photonic crystals, as well as on the routing of long optical buffers and delay lines.

Thermally controlled Si photonic crystal slow light waveguide beam steering device.

The doubly periodic Si photonic crystal waveguide radiates the guided slow light into free space as an optical beam. The waveguide also functions as a beam steering device, in which the steering angle is changed substantially by a slight variation in the wavelength generated due to the large angular dispersion of the slow light. A similar function is obtained when the wavelength is fixed and the refractive index of the waveguide is changed. In this study, we tested two kinds of integrated heater structures and observed the beam steering using the thermo-optic effect. For a p-i-p doped waveguide, the heating current was made to flow directly across the waveguide and a beam steering range of 21° was obtained with a relatively low heating power and high-speed response of the order of 100 kHz, maintaining a narrow beam divergence of 0.1-0.3° and a 120 resolution points. We also performed a preliminary life test of the device but did not observe any severe degradation in the temperature variation of 80-430 K for the duration up to 20‒40 h. For a TiN heater device, we obtained the comparable beam steering characteristics, but the required heating power increased, and the response speed decreased drastically.

Analysis of Kerr nonlinearity enhancement in silicon nitride waveguides using one-dimensional slow light structure

A corrugated based slow-light silicon nitride waveguide is studied numerically to enhance Kerr nonlinearity by increasing the group index of the waveguide at the band edge. The structure is optimized taking into account the limitations existing in CMOS-compatible platforms. Bandwidth limitations of the structure are investigated at different wavelengths for various slow-down factors. Finite size realizations of the structure are studied using transfer matrix method to obtain the desired transmission and group velocity at the band edge. Optical loss corresponding to slow-light effect is modeled, and the limitations imposed by the slow-light loss on the nonlinear phase shift saturation are considered. It is shown that by employing slow-down factor of 3, the nonlinear phase shift is improved by a factor of 5. Also, in comparison with a straight waveguide, shorter corrugated waveguides (up to nine times) can provide the same accumulated nonlinear phase shift.

Wideband slow short-pulse propagation in one-thousand slantingly coupled L3 photonic crystal nanocavities

Coupled cavities have been used previously to realize on-chip low-dispersion slow-light waveguides, but the bandwidth was usually narrower than 10 nm and the total length was much shorter than 1 mm. Here we report long (0.05-2.5 mm) slow-light coupled cavity waveguides formed by using 50, 200, and 1,000 L3 photonic crystal nanocavities with an optical volume smaller than (λ/n)3, slanted from Γ-K orientation. We demonstrate experimentally the formation of a single-mode wideband coupled cavity mode with a bandwidth of up to 32nm (4THz) in telecom C-band, generated from the ultra-narrow-band (~300 MHz) fundamental mode of each L3 nanocavity, by controlling the cavity array orientation. Thanks to the ultrahigh-Q nanocavity design, coupled cavity waveguides longer than 1 mm exhibited low loss and allowed time-of-flight dispersion measurement over a bandwidth up to 22 nm by propagating a short pulse over 1,000 coupled L3 nanocavities. The highly-dense slanted array of L3 nanocavity demonstrated unprecedentedly high cavity coupling among the nanocavities. The scheme we describe provides controllable planar dispersion-managed waveguides as an alternative to W1-based waveguides on a photonic crystal chip.

Energy Consumption Enhancement of Reverse-Biased Silicon-Based Mach–Zehnder Modulators Using Corrugated Slow Light Waveguides

The energy efficiency of silicon modulators can be enhanced by increasing the doping level. As an alternative solution, slow light modulators based on corrugated waveguides can also be used for improving the energy efficiency. Using numerical and analytical tools, we show that for the same level of energy consumption reduction, the loss coefficient and the loss-modulation efficiency for the slow-light modulators are smaller than those for the modulators with an increased doping level. It is shown that the slow light structures with medium slow down factors (specifically slowdown factors of less than 6) can be reasonable candidates for enhancing the modulator's energy efficiency. For example, an energy consumption of less than 100 fJ/bit can be achieved at a slow-down factor of 6, using a doping level of 5 × 1017 cm-3 for acceptors and 1 × 1018 cm-3 for donors.

Anderson Localization in Disordered LN Photonic Crystal Slab Cavities

We present a detailed theoretical study of the effects of structural disorder on LN photonic crystal slab cavities, ranging from short to long length scales, using a fully-3D Bloch mode expansion technique. We compute the optical density of states, quality factors and effective mode volumes of the cavity modes, with and without disorder, and compare with the localized modes of the corresponding disordered photonic crystal waveguide. We demonstrate how the quality factors and effective mode volumes saturate at a specific cavity length and become bounded by the corresponding values of the Anderson modes appearing in the disordered waveguide. By means of the intensity fluctuation criterion, we observe Anderson localization for cavity lengths larger than around L31, and show that the field confinement in the disordered LN cavities is mainly determined by the local characteristics of the structural disorder as long as the confinement region is far enough from the cavity mirrors and the effective mode localization length is much smaller than the cavity length; under this regime, the disordered cavity system becomes insensitive to changes in the cavity boundaries and a good agreement with the intensity fluctuation criterion is found for localization. Surprisingly, we find that the Anderson localized modes do not appear as new disorder-induced resonances in the main spectral region of the LN cavity modes, and, moreover, the disordered DOS enhancement is largest for the disordered waveguide system with the same length. These results are fundamentally interesting for applications such as lasing and cavity-QED, and provide new insights into the role of the boundary condition on finite-size slow-light waveguides. They also point out the clear failure of using models based on the cavity boundaries/mirrors and a single slow-light Bloch mode to describe cavity systems with large N.