Adiabatic coupling between conventional dielectric waveguides and waveguides with discrete translational symmetry

Abstract

We study adiabatic transformation in optical waveguides with discrete translational symmetry. We calculate the ref lection and transmission coeff icient for a structure consisting of a slab waveguide that is adiabatically transformed into a photonic crystal waveguide and then back into a slab waveguide. The calculation yields high transmission over a wide frequency range of the photonic crystal waveguide band and indicates efficient coupling between the slab waveguide and the photonic crystal waveguide. Other applications of adiabatic mode transformation in photonic crystal waveguides and the coupled-resonator optical waveguides are also discussed.  2000 Optical Society of America OCIS codes: 230.3120, 230.7370, 130.3120. In quantum mechanics it is well known that, if the Hamiltonian of a system changes slowly, the eigenmode at any one moment is adiabatically transformed into a pure and different eigenmode at any later time. 1Similarly in optoelectronics, if we slowly modify an optical waveguide with distance, the optical mode can be adiabatically changed into another pure mode with different spatial characteristics. By use of this property, many devices such as waveguide fiber couplers 2 and add-drop filters 3 have been constructed. The waveguides that are involved in those applications are all based on guiding as a result of total internal ref lection. The unperturbed waveguides have continuous spatial translation symmetry along the mode propagation direction. As a consequence, one can easily achieve the condition of adiabaticity by slowly and continuously varying the waveguide parameters as the optical modes propagate. 4 However, there are other types of waveguide (for example, the waveguides constructed from photonic crystals 5,6 ) that possess only discrete translational symmetry, for which the optical conf inement is achieved by multiple Bragg ref lections. In these types of geometry, the refractive index of the dielectric medium and the optical modes usually change signif icantly within a single unit cell. Therefore, for these structures it is not clear that we can achieve adiabatic mode transformation or, if we can, how slow the transformation should be to satisfy the adiabaticity condition. This problem is of signif icant practical interest and, until now, has been untreated.As an example of adiabatic mode transformation in waveguides with discrete translational symmetry, we study a geometry shown in Fig. 1(a), where a slab waveguide is tapered and changed into a square-lattice photonic crystal waveguide and then back into a slab waveguide. Because of numerical discretization constraints, we choose the slab waveguide taper to be a simple angled cut, as illustrated in Fig. 1(a). For an arbitrary taper angle u, the slab waveguide mode and the photonic crystal waveguide mode do not couple well to each other, because they have different spatial characteristics and dispersion relations. This mode mismatch will in general cause significant backref lection. However, for a small taper angle it is possible ...

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