Single-Mode Propagation of Light in One-Dimensional All-Dielectric Light-Guiding Systems

Abstract

Abstract-Numerical results are presented for single-mode guidance, which is based on photonic band gap (PBG) effect, in one-dimensional planar all-dielectric light-guiding systems. In such systems there may be two kinds of light-speed point (the intersection of a mode-dispersion curve and the light line of guiding region ambient medium): One is the intrinsic light-speed point that is independent of the guiding region width, and the other is the movable light-speed point that varies with the guiding region width. It is found that the intrinsic lightspeed point plays an important role to form the single-mode regime by destroying the coexistence of the lowest guided TM and TE modes that are born with a degeneration point. A mode-lost phenomenon is exposed and this phenomenon suggests a way of how to identify PBGguided fundamental modes. Quasi-cutoff-free index-guided modes in the PBG guiding structures are examined, which appear when the higher-index layers are adjacent to the guiding region and the guiding region width is small. The transverse resonance condition is derived in the Maxwell optics frame, and it is shown that there is a significant revision to the traditional one in the ray optics model. A sufficient and necessary condition for intrinsic light-speed points is given, which provides strong support to the numerical results.

Light field distributions in one-dimensional photonic crystal fibers

“…The 1D PBG fiber actually is a transversely periodical boundary-value problem in classical electromagnetic theory, where two perfect conducting planes of the parallel-plate waveguide are replaced by two symmetric periodic structures. Ray-optics method based on transverse resonance condition, although it cannot be used to obtain slow-wave modes to provide an overview of the whole mode structure, is an alternative method for finding fast-wave modes, or guided modes; however, there is some inconvenience for this method, because the dispersion property of PBG mirrors makes the transverse resonance condition and mode index not one-to-one corresponding [32]. Field-solution method by matching boundary conditions is a strict method for solving 1D PBG fibers.…”

“…Field-solution method by matching boundary conditions is a strict method for solving 1D PBG fibers. Based on a real translation-matrix method, we have derived a general reflection coefficient expression, which is exactly a description of the PBG-mirror boundary conditions, and this expression can be directly applied for obtaining general dispersion equations for all electromagnetic modes, such as a mode that may provide single-mode guidance [32].…”