**4. Tunability of zero-n gap**

Next, in order to demonstrate the tunable character of the zero- n bandgaps, we performed transmission experiments on four sets of binary superlattices, with each set having different superlattice ratios: *d2/d1*=0.74 (Figure 9a), *d2/d1*=0.76 (Figure 9b), *d2/d1*=0.78 (Figure 9d), and *d2/d1*=0.8 (Figure 9e). In all our experiments the negative index PhC has the same parameters as those given above. Each set has three devices of different periods , with the negative index PhC layer in the superlattice spanning 7, 9, and 11 unit cells along the *z*-axis similar to the numerical study in 3.1, so that the thickness of this layer is d 3.5 3 a <sup>1</sup> (2.564 μm), d 4.5 3 a <sup>1</sup> (3.297 μm), and d 5.5 3 a <sup>1</sup> (4.029 μm), respectively. The corresponding thickness of the PIM layer is determined by requiring that the average index is zero [ \_ 11 22 n nd nd / Λ 0 ], while keeping the ratio *d*2/*d*1 unchanged for all devices in each set (see Table 2). Here, *n*1 and *n*2 are the effective mode indices in the PhC and homogeneous layers respectively at the corresponding wavelengths. For the three devices in each set, we designed 7 super-periods (SPs) for the devices with 7 unit cells of PhC and 5 SPs for those with 9 and 11 unit cells of PhC (these designs ensure a sufficient signal-to-noise ratio for the transmission measurements). In these experiments we have tested both the existence of the zero- n bandgap as well as its tunability. For the three devices belonging to each set, we observed the zero- n bandgap at the same frequency whereas the spectral locations of the other bandgaps were observed to shift with the frequency – this confirms the zero- n bandgap does not depend on the total superperiod length gap existence dependent only


Table 2. **Calculated parameters of the devices in the Figure 9 (units in m).** 

Next, in order to demonstrate the tunable character of the zero- n bandgaps, we performed transmission experiments on four sets of binary superlattices, with each set having different superlattice ratios: *d2/d1*=0.74 (Figure 9a), *d2/d1*=0.76 (Figure 9b), *d2/d1*=0.78 (Figure 9d), and *d2/d1*=0.8 (Figure 9e). In all our experiments the negative index PhC has the same parameters

index PhC layer in the superlattice spanning 7, 9, and 11 unit cells along the *z*-axis similar to the numerical study in 3.1, so that the thickness of this layer is d 3.5 3 a <sup>1</sup> (2.564 μm), d 4.5 3 a <sup>1</sup> (3.297 μm), and d 5.5 3 a <sup>1</sup> (4.029 μm), respectively. The corresponding thickness of the PIM layer is determined by requiring that the average index is zero

11 22 n nd nd / Λ 0 ], while keeping the ratio *d*2/*d*1 unchanged for all devices in each set (see Table 2). Here, *n*1 and *n*2 are the effective mode indices in the PhC and homogeneous layers respectively at the corresponding wavelengths. For the three devices in each set, we designed 7 super-periods (SPs) for the devices with 7 unit cells of PhC and 5 SPs for those with 9 and 11 unit cells of PhC (these designs ensure a sufficient signal-to-noise ratio for the transmission measurements). In these experiments we have tested both the existence of the zero- n bandgap as well as its tunability. For the three devices belonging to each set, we observed the zero- n bandgap at the same frequency whereas the spectral locations of the other bandgaps were observed to shift with the frequency – this confirms the zero- n
