Control of dispersion in photonic crystal waveguides using group symmetry theory

Abstract

Abstract:We demonstrate dispersion tailoring by coupling the even and the odd modes in a line-defect photonic crystal waveguide. Coupling is determined ab-initio using group theory analysis, rather than by trial and error optimisation of the design parameters. A family of dispersion curves is generated by controlling a single geometrical parameter. This concept is demonstrated experimentally on a 1.5mm-long waveguide with very good agreement with theory.

Integrable microwave filter based on a photonic crystal delay line

“…The waveguide design is characterized by an anti-symmetric shift of the first row of holes [34][35][36] , as indicated in Fig. 2c (see details in Methods).…”

“…2d). Details are discussed in Colman et al 36 The group delays for both TE (defined as the E field parallel to the membrane and perpendicular to the direction of propagation) and TM modes have been measured with an interferometric technique (see Methods). The calculated dispersion for both TE and TM modes is also plotted, with excellent agreement.…”

Giant anomalous self-steepening in photonic crystal waveguides

“…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.…”

“…For that purpose we consider typical parameters found in recent nonlinear experiments [12,22,23,31,32]. We take γ eff = 1600 (W m) −1 (n g = 15, n o = 3.17 for GaInP), an anomalous dispersion of β 2 = −7.7 ps 2 /mm, n 2 = 6 × 10 −18 m 2 /W, and modal area A eff = 0.34 μm 2 [6]. The dispersive nonlinearity is τ NL = −220 fs as detailed above.…”

“…More recently, it has been shown that gas-filled hollow-core fibers can activate or suppress nonlinearities such as the Raman effect [4]. In parallel, rapid advances in integrated semiconductor devices have pushed the forefront of optical science by reducing nonlinear thresholds to subfemtojoule energy levels [5] while simultaneously incorporating dispersion control [6]. Among nanostructures, photonic crystal waveguides (PhCWGs) are of extreme interest due to the link between geometric fabrication and direct modulation of the electric field, giving rise to exciting physical phenomena such as slow light and enhanced nonlinearity.…”