Dispersion tailoring of the quarter-wave Bragg reflection waveguide

Abstract

We present analytical formulae for the polarization dependent first-and second-order dispersion of a quarter-wave Bragg reflection waveguide (QtW-BRW). Using these formulae, we develop several qualitative properties of the QtW-BRW. In particular, we show that the birefringence of these waveguides changes sign at the QtW wavelength. Regimes of total dispersion corresponding to predominantly materialdominated and waveguide-dominated dispersion are identified. Using this concept, it is shown that the QtW-BRW can be designed so as to provide anomalous group velocity dispersion of large magnitude, or very small GVD of either sign, simply by an appropriate chose of layer thicknesses. Implications on nonlinear optical devices in compound semiconductors are discussed. ©2006 Optical Society of America

Coupled interface modes for nonlinear interaction in periodic layered media

“…In the comparison of table 3.1,each design aims at maximizing the conversion efficiency. and hence greater GVM [40]. While operation away from the quarter-wave point appears to be a favorable alternative in order to avoid these limitations, the lack of closed-form Chapter 3.…”

The quarter-wave Bragg reflection waveguide: analytical solutions and properties

“…The matrix elements for TE polarization are (8) The periodicity of E K,TE (x) requires that (9) which, by (7), leads to the eigenequation (10) The eigenvalues and corresponding eigenvectors of (10) are, using (8), (11) multiplied by an arbitrary constant which will be absorbed into C 2 TE . The last term in (11) follows from repeated application of (9).…”

“…Within a unit cell of the cladding the field components in adjacent slabs are related by the transfer matrix 7 (13) Inserting (11) and (6) into (4) gives the complete form of the mode profile, Finally, enforcing continuity of E y and H z (proportional to ∂E y /∂x) at the core -cladding interface leads, via (11) and (14), to the mode dispersion equation …”

Broadband mid-infrared generation using one-dimensional photonic bandgap waveguides

“…1 [7]. Due to the strong spectral dependence of reflectioncoefficient for the periodic cladding geometry, the ID-PCWs exhibit strong phase-and group-velocity dispersion characteristics which can be favorably exploited to maintain quasi phase matching (,1f3=f3p-f3s-j3,-2rrJA QPM =0 where f3p, f3s, {3; are modal propagation constants at pump (Ap), signal (As) and idler (A;) wavelengths respectively and A QPM is the QPM grating period)) over a broad range of wavelengths [8]. We analyze a DFG process in a planar high-index core symmetric ID-PCW comprised of a periodically-poled GaN (PPGaN) core (n c ) to facilitate QPM and periodic layers of AloOlGao.99N (nJ) and AloAoGao.60N (n2) as Bragg cladding (Fig.l ), The thicknesses of layers with refractive indices n.; ni and n2 are d-, d, and d: respectively.…”

“…We choose the idler to be a TM-po1arized Bragg mode of the lD-PCW [7]. The waveguide design is such that the quarter-wave stack (QWS) condition [8] is satisfied at a design wavelength (I"d) longer than the idler wavelength (Ai = 3.26 11m). This choice is governed by the fact that a slight shift of the idler towards the band edges entails stronger waveguide dispersion to the idler mode without any substantial fall in modal confinement which eventually would counter the strong material dispersion of near-IR signal mode.…”