Systematic design of flat band slow light in photonic crystal waveguides

Li, Juntao; White, Thomas P.; O’Faoláin, Liam; Gomez‐Iglesias, Alvaro; Krauss, Thomas F.

doi:10.1364/oe.16.006227

Cited by 535 publications

(397 citation statements)

References 22 publications

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“…In order to obtain the good fit displayed in the figure, the calculated spectrum was redshifted by 1.6% in wavelength compared to the experimental results, which is a reasonable deviation given experimental uncertainties. 17 The numerically obtained Q-factor is approximately three times higher than the one obtained in our experiments, which is most likely due to fabrication imperfections.…”

contrasting

confidence: 51%

Electro-optic modulation in slotted resonant photonic crystal heterostructures

Wülbern¹,

Hampe²,

Petrov³

et al. 2009

Applied Physics Letters

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Two dimensional photonic crystal waveguides in high index materials enable integrated optical devices with an extremely small geometrical footprint on the scale of micrometers. Slotted waveguides are based on the guiding of light in low refractive index materials and a field enhancement in this particular region of the device. In this letter we experimentally demonstrate electro-optic modulation in slotted photonic crystal waveguides based on silicon-on-insulator substrates covered and infiltrated with nonlinear optical polymers. A photonic crystal heterostructure is used to create a cavity, while simultaneously serving as an electrical connection from the slot to the metal electrodes that carry the modulation signal. © 2009 American Institute of Physics. ͓DOI: 10.1063/1.3156033͔Electrically driven optical modulation in silicon photonics typically relies on interactions between the optical mode and a free carrier plasma via either carrier depletion, injection, or accumulation. 1-3 The achievable modulation speed using these methods is limited by the time constants related to the injection or removal of carriers from the optical waveguide. In contrast, modulation via nonlinear optical ͑NLO͒ polymers accesses the electronic polarization of the organic molecules, which allows extremely high modulation speeds extending up to frequencies in the terahertz range. 4 Furthermore, molecular engineering of organic molecules has led to extremely high Pockels-coefficients in polymers exceeding 300 pm/V, 5 which is ten times the value available in lithiumniobate, the standard inorganic material used in electro-optic ͑EO͒ applications. Photonic devices based on a hybrid material system merging silicon and polymer are therefore attractive since they combine the strong light confining abilities of silicon with the superior NLO properties of polymers.All-optical and EO-modulation in such hybrid silicon and NLO-polymer systems has been demonstrated for slotted photonic wire based Mach-Zehnder and ring-resonator modulators. 6-8 Concepts based on slotted photonic crystal ͑PhC͒ waveguides can exploit slow light mechanisms or high quality factor cavities to achieve very compact device dimensions and have been discussed recently. 9-11 We propose a concept using a double heterostructure cavity 11-13 in a slotted silicon PhC waveguide, infiltrated with NLO-polymer to operate as an EO-modulator. Figure 1 shows a scanning electron micrograph of the structure. The 150 nm wide slot in the center of the waveguide is filled with NLO-polymer ͑n poly = 1.63͒ and the strong overlap between the optical field and the polymer makes the effective index of the propagating mode very sensitive to any refractive index changes in EOpolymer. The PhC features a background doping density of 10 15 cm −1 and therefore serves as an electrical conductor from the metallic contact pads to the slot, while keeping the optical field away from the metal regions and hence preventing additional losses. The double heterostructure design of the PhC ͑a = 410 nm, r / a = 0....

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confidence: 51%

Electro-optic modulation in slotted resonant photonic crystal heterostructures

Wülbern¹,

Hampe²,

Petrov³

et al. 2009

Applied Physics Letters

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“…Though near-arbitrary dispersion profiles are possible in periodic media [6,11], here we focus on three specific experimentally demonstrated structures for clarity. Figure 1 shows three group-index curves for PhCWGs with different dispersion relations: (i) a standard line defect waveguide of one missing row of holes in a hexagonal lattice (W1), (ii) a dispersion-engineered waveguide [6] exhibiting a plateau, and (iii) a dispersion with a pronounced group-index peak.…”

Section: Self-steepening In Phcwgsmentioning

confidence: 99%

Giant anomalous self-steepening in photonic crystal waveguides

Husko

Colman

2015

Phys. Rev. A

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Self-steepening of optical pulses arises due the dispersive contribution of the χ (3) (ω) Kerr nonlinearity. In typical structures this response is on the order of a few femtoseconds with a fixed frequency response. In contrast, the effective χ (3) Kerr nonlinearity in photonic crystal waveguides (PhCWGs) is largely determined by the geometrical parameters of the structure and is consequently tunable over a wide range. Here we show self-steepening based on group-velocity (group-index) modulation for the first time, giving rise to a new physical mechanism for generating this effect. Further, we demonstrate that periodic media such as PhCWGS can exhibit self-steepening coefficients two orders of magnitude larger than typical systems. At these magnitudes the self-steepening strongly affects the nonlinear pulse dynamics even for picosecond pulses. Due to interaction with additional higher-order nonlinearities in the semiconductor materials under consideration, we employ a generalized nonlinear Schrödinger equation numerical model to describe the impact of self-steepening on the temporal and spectral properties of the optical pulses in practical systems, including new figures of merit. These results provide a theoretical description for recent experimental results presented in [Scientific Reports 3, 1100) and Phys. Rev. A 87, 041802 (2013]. More generally, these observations apply to all periodic media due to the rapid group-velocity variation characteristic of these structures.

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“…23,24 In the following, all dispersion curves and complex field amplitudes E(r) are calculated using the freely available MIT photonics band (MPB) code, 25 whereas the propagation loss α(S) is estimated with a model based on the code for loss engineering developed in Ref. 14.…”

Section: Srs In Realistic Phc Waveguidesmentioning

confidence: 99%

“…The dispersion of waveguide A has been designed to exhibit a large region of constant group index around n g = 30 by choosing r = 0.282a, s 1 = −0.12a, and s 2 = 0, where s 1 and s 2 are the lateral shifts of the first and second row of holes, respectively. 24 Waveguide B (r = 0.286a, r 2 = 0.26a, s 1 = −0.1a, s 2 = 0.08a, with r 2 the radius of the second row of holes) possibly comes closest to the simplified analysis considered in the preceding section since its loss curve α s (S s ) is very close to linear [ Fig. 2(c)], whereas in waveguide C (same as B, but r 2 = 0.24a), the loss α s is almost constant with S s .…”

Section: Srs In Realistic Phc Waveguidesmentioning

confidence: 99%

Scaling of Raman amplification in realistic slow-light photonic crystal waveguides

et al. 2011

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The prospect for low pump-power Raman amplification in silicon waveguides has recently been boosted by theoretical studies discussing the enhancement of nonlinear phenomena in slow-light structures. In principle, the slowing down of either the pump or the signal beam is equivalent in terms of Raman gain, but in the presence of losses, we show that they play different roles in determining the net signal gain. We also investigate the impact of the mode profile in realistic slow-light waveguides on the total gain, an effect that is usually neglected in the context of stimulated Raman scattering. By taking representative losses and mode shapes into account, we provide a realistic estimation of the achievable performance of slow-light photonic crystal waveguides.

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Systematic design of flat band slow light in photonic crystal waveguides

Cited by 535 publications

References 22 publications

Electro-optic modulation in slotted resonant photonic crystal heterostructures

Electro-optic modulation in slotted resonant photonic crystal heterostructures

Giant anomalous self-steepening in photonic crystal waveguides

Scaling of Raman amplification in realistic slow-light photonic crystal waveguides

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