Transparent expressions for group velocity and sensitivity to index changes of
Photonic Crystal Waveguide modes
Hugo J.W.M. Hoekstra1 and Theo P. Valkering2
1
University of Twente, MESA+ Institute of nanotechnology, P.o. box 217, 7500 AE Enschede, The Netherlands
h.j.w.m.hoekstra@utwente.nl
2
University of Twente, Faculty of Science and Technology, P.o. box 217, 7500 AE Enschede, The Netherlands
On the basis of Maxwell’s equations and Bloch’s theorem basic relations for modes propagating in photonic crystal waveguides are derived. The physical meaning and possible experimental implications are discussed. Summary
Slow light propagation of photonic crystal waveguide (PhC-WG) modes is currently widely investigated to study the strong matter-light interaction for among others nonlinear effects [1], time delays [2] and sensors [3, 4]. Hereby the group velocity is often considered to be a key parameter. For such studies and also for a better understanding of the underlying physics it is quite relevant to have simple, explicit expressions for the modal group velocity and the sensitivity to index changes in terms of the corresponding modal field or intensity pattern.
Such expressions will be derived in a straightforward way from Maxwell’s equations and Bloch’s theorem. In particular it will be established, in the frequency domain and including the effect of material dispersion, that the modal group velocity equals the ratio of the spatially averaged energy flow and energy density. The relations will be applied on a number of relatively simple structures. In addition to that, the potential of the derived relations for the interpretation of experimental results will be discussed.
Acknowledgements
This work was supported by NanoNed, a national nanotechnology program coordinated by the Dutch ministry of Economic Affairs and the STW Technology Foundation project TOE.6596.
References
[1] D.M. Beggs, T.P. White, L. O'Faolain and T.F. Krauss, Optics Lett., 33, 147-149 (2008) [2]M.L. Povinelli, S.G. Johnson and J.D. Joannopoulos, Optics Express 13, 7145-7159 (2005) [3] X.Y. Mao et al., Chinese Phys. Lett., 25, 141-143 (2008)
