Large second order dispersion in periodical and aperiodical photonic crystal waveguides

Abstract

The second order dispersion is proportional to the difference of time delays accumulated by waves of two adjacent wavelengths. This time delay difference can be obtained when the group velocity or the propagation distance is changing with wavelength. In both cases, a decrease of the smallest available group velocity leads to a proportional size reduction given a fixed dispersion value. In conventional waveguides the smallest group velocity is close to the speed of light in the core material, whereas in photonic crystal line-defect waveguides orders of magnitude smaller group velocities can be obtained within a certain bandwidth. Based on these waveguides, different concepts are proposed and evaluated. A large difference in group velocities for different wavelengths is obtained by anti-crossing of modes in single and coupled line-defect waveguides. Alternatively, in chirped photonic crystal waveguides the path difference, hence the group delay, is strongly varied for adjacent wavelengths. Positive and negative dispersion of approximately hundred ps/nm on millimeter scale over the bandwidth of a single WDM channel (0.8nm) are theoretically predicted and demonstrated using finite integration simulations.