Optical Science Laboratory
Recently, the two-dimensional photonic crystal slab (PCS)
has attracted great interest because it has led to the development of high
quality-factor photonic nanocavities and low-loss waveguides [1]. It has been
revealed that a guided mode induced by a line defect in ideal PCS is theoretically
lossless when it is designed to be inside the photonic band gap and under
the light line. However, current nanolithography technology allows nanometer-order
disorder and it is believed that such disorder causes a considerable loss
increase due to out-of-plane scattering.
One aim of our research is to demonstrate that waveguide loss can be reduced
by reducing fabrication disorder. We patterned PCSs by using a precise electron
beam lithography system with 1-nm position accuracy and 100-kV acceleration,
where we paid great effort to minimizing the proximity effect. We observed
the fabricated Si PCS with scanning electron microscopes and found that disorder
(σ, RMS) was about 3 nm (Fig. 1). We measured the propagation loss of PCS
waveguides by the cut-back method. The minimum loss measured was 5dB/cm (Fig.
2), which is record loss for photonic crystal waveguides [2].
Another aim of our research is to reveal the physics of PCS waveguide loss.
We applied the photon Green function tensor (GFT) formalism [3] to disorder-related
scattering in the guided mode. We derived the loss formula as a simple product
of the disorder and local density of states of light between the initial state
and final state. We calculated the loss assuming σ of 3nm, and the result
showed surprisingly good agreement with the experimental data (Fig. 2). This
loss calculation by our GFT method is the most detailed ever achieved. We
investigated the scattering-loss mechanism in detail by theory and experiment.
We revealed for the first time that the loss characteristics of PCS waveguides
are unique and complex because the loss mechanisms (out-of-plane scattering,
intermode scattering, and backward scattering) are tightly bound with photonic
band structure.
In conclusion, by experiment and theory, we successfully revealed the detailed
physics of scattering loss in PCS waveguides caused by fabrication disorder.
[1] M. Notomi et al., Optics Express 12, 1551 (2004).
[2] E. Kuramochi et al., LEOS2004, WF6 (2004).
[3] S. Hughes et al., Phys. Rev. Lett. 94, 033903 (2005).
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| Fig. 1. SEM images of Si
PCSs fabricated in this study. |
Fig. 2. Measured and calculated loss
spectra of PCS waveguides. |
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