Mapping the optical properties of slab-type two-dimensional photonic crystal waveguides

We report on systematic experimental mapping of the transmission properties of two-dimensional silicon-on-insulator photonic crystal waveguides for a broad range of hole radii, slab thicknesses, and waveguide lengths for both TE and TM polarizations. Detailed analysis of numerous spectral features allows a direct comparison of experimental data with three-dimensional plane-wave and finite-difference time-domain calculations. We find that the bandwidth for low-loss propagation completely vanishes for structural parameters where the photonic band gap is maximized. Our results demonstrate that in order to maximize the bandwidth of low-loss waveguiding the hole radius must be significantly reduced. While the photonic band gap considerably narrows, the bandwidth of low-loss propagation in PhC waveguides is increased up to $125\mathrm{nm}$ with losses as low as $8\pm 2\mathrm{dB}∕\mathrm{cm}$.

Figure 1

Comparison of experimental TE transmission spectra of PhC waveguides with large hole radii against 3D plane-wave band structure calculations. (a) Band structure for a PhC waveguide with $r∕a=0.348$. (b) Set of transmission spectra for PhC waveguides, equal in length $(l=29\mu \mathrm{m})$ but with increasing hole radius $r∕a=0.348–0.379$. The grey curve illustrates the spectral merge of lower photonic band edge (LBE) and waveguiding onset for the PhC with $r∕a=0.379$ (slab modes for $r∕a=0.348$ shifted with respect to the normalized frequency for comparison with the modes for $r∕a=0.379$). (c) Band structure for a PhC waveguide with a hole radius of $r∕a=0.379$.

Figure 2

Experimentally determined TE map of spectral positions of lower band edge (LBE), waveguiding onset, light line, and stop band as a function of the normalized hole radius for $r∕a=0.348–0.384$. The grey shaded area shows the frequency region for low-loss propagation (lines are guides for the eye).

Figure 3

Length series of TE transmission spectra of PhC waveguides $(29–2000\mu \mathrm{m})$ for two different hole radii: (a) $r∕a\sim 0.34$ and (b) $r∕a\sim 0.23$. The transmission dip marked with an asterisk corresponds to the $x$-odd TE-like mode (see text for details).

Figure 4

(a) Experimental TE transmission spectra (black line) of a $29\text{−}\mu \mathrm{m}$ PhC waveguide with $r∕a=0.22$ compared with 3D FDTD calculations (grey line). Inset: normalized transmission at $1650\mathrm{nm}$ of PhC waveguides as a function of the length. From the slope, the losses of the whole photonic circuit (PhC and strip waveguides) are determined as $3\pm 2\mathrm{dB}∕\mathrm{cm}$. This corresponds to $8\pm 2\mathrm{dB}∕\mathrm{cm}$ loss for the PhC waveguide (see text for details). (b) 3D plane-wave band structure calculations with the same structural input parameters as for the FDTD calculations in (a).

Figure 5

Experimentally derived TE map depicting spectral positions of stop band (triangles up), UBE (asterisks), light line (circles), WG onset (squares), and LBE (triangles down) as a function of the hole radius $r∕a=0.22–0.38$. Solid lines represent 3D plane-wave band structure calculations with input parameters determined from SEM measurements for hole radii with $r∕a=0.32–0.34$.

Figure 6

(a) Length series of TM transmission spectra of PhC waveguides $(29–700\mu \mathrm{m})$ with hole radii $r∕a\sim 0.33$. The transmission dip marked with an asterisk corresponds to the $x$-odd TE-like mode (see text for details). (b) 3D plane-wave band structure calculations. The dotted line indicates the fundamental TM-like waveguiding mode.

Figure 7

Experimental TM map of the spectral positions of light line (squares), band edge (triangles), and stop band (circles) as a function of the hole radius $r∕a=0.32–0.38$. Solid lines represent 3D plane-wave band structure calculations (black and grey) with input parameters according to the experimental SEM results for hole radii of $r∕a=0.32–0.34$ and $r∕a=0.35–0.38$, respectively. Inset: TM spectra of two PhC waveguides, identical in length $\left(29\mu \mathrm{m}\right)$, but with different hole radii ($0.348a$ and $0.371a$). The transmission dips marked with an asterisk correspond to the $x$-odd TE-like mode (see text for details).

Figure 8

Experimental map of the $x$-odd TE-like waveguiding mode as a function of the hole radius. Solid lines represent 3D plane-wave band structure calculations with input parameters according to SEM measurements for hole radii of $r∕a=0.32–0.34$. The black line plots the $x$-odd TE mode while the grey lines represent the UBE, light line, WG onset (even TE mode), stop band, and LBE from Fig. 5.