**3.3 Device nanofabrication and experiments**

Our theoretical predictions are validated by a series of experiments. Thus, we have fabricated in a single-crystal silicon-on-insulator substrate samples with 3, 5 and 8 stacks whose PhC layers have thickness of d 3.5 3 a <sup>1</sup> . The silicon device height is 320 nm and the silicon oxide cladding thickness is 1 m. The PhC superlattice is lithographically patterned with a 248-nm lithography scanner, and the Si is plasma-etched. Figure 1b shows an example of a fabricated photonic crystal superlattice with 8 stacks. The fabrication disorder in the PhC slab was statistically parameterized [37], with resulting hole radius 122.207 1.207 nm, lattice period 421.78 1.26 nm (~ 0*:*003*a*), and ellipticity 1.21 nm 0.56 nm. These small variations are below ~0*:*05*a* disorder theoretical target [46].

Incident light from tunable lasers between 1480 nm to 1690 nm (0.248 to 0.284 in normalized frequency of *a/2c*) is coupled into the chip *via* tapered lensed fibers with manual fiber polarization control. The transmission for the TM polarization is measured, with each transmission measurement averaged over three scans. Figure 8a shows the transmission spectrum for design 1 (with *d2/d1* = 0.746); it shows two distinct spectral dips, centered at 1520 nm (*a/2c* 0.276) and 1585 nm (*a/2c* 0.265). We then repeat these transmission measurements for a second design (design 2; *d2/d1* = 0.794); the corresponding results are shown in Figure 8b. Similar to the spectra in Figure 8a, this figure shows a distinct spectral dip, located near the normalized frequency *a/2c* 0.272, *i.e.* at =1543 nm. Furthermore, the frequency spectral dip at *a/2c* 0.262 is weaker than in design 1, which is due to the fact that below a certain frequency, *a/2c* 0.265, the detected power is not high enough for observing the spectral features.

Figure 8c shows the near-infrared image captured with incident laser at 1550 nm and corresponds to the design 1. The spatially alternating vertical stripes show radiation scattered at the interfaces between the PhC and the homogeneous layers and confirm the transmission of the light through the superlattice. The near-infrared images also confirm the existence of the dip in the transmission spectrum, with most of the light being reflected and only a small amount propagating out of the output facet of the third stack (in this figure , the incident laser is tuned to the zero- n gap frequency).

To better understand the results of these measurements, we repeated the FDTD simulations for the case of the fabricated devices. A good match between the results of the measurements and those of simulations, in terms of *absolute* values of the frequencies, has been observed for both values of the ratio *d2/d1* (design 1 and 2) and varying stack numbers (design 1). The theoretical predictions are shown as the dotted lines in Figure 8a and 3.8b.

Figure 8d further shows the results of a series of experiments for PhC superlattices of design 1, each with 7 unit cells but with increasing number of stacks, from 3 to 5 and 8. As observed, both gaps become deeper with increasing number of stacks. It should be noted that by improving the impedance matching between the negative and positive index materials, transmission spectrum for even larger number of stacks in the PhC superlattice can be observed. The center-frequency of the gaps does not change when the number of stacks increases, the slight deviations in the gap frequency being attributable to small variations in the dimensions of the fabricated superlattice structures. This series of measurements further reinforce the observation of the zero- n gap in cascaded negative- and positive-refraction superlattices.

Our theoretical predictions are validated by a series of experiments. Thus, we have fabricated in a single-crystal silicon-on-insulator substrate samples with 3, 5 and 8 stacks whose PhC layers have thickness of d 3.5 3 a <sup>1</sup> . The silicon device height is 320 nm and the silicon oxide cladding thickness is 1 m. The PhC superlattice is lithographically patterned with a 248-nm lithography scanner, and the Si is plasma-etched. Figure 1b shows an example of a fabricated photonic crystal superlattice with 8 stacks. The fabrication disorder in the PhC slab was statistically parameterized [37], with resulting hole radius 122.207 1.207 nm, lattice period 421.78 1.26 nm (~ 0*:*003*a*), and ellipticity 1.21 nm 0.56

Incident light from tunable lasers between 1480 nm to 1690 nm (0.248 to 0.284 in normalized

polarization control. The transmission for the TM polarization is measured, with each transmission measurement averaged over three scans. Figure 8a shows the transmission spectrum for design 1 (with *d2/d1* = 0.746); it shows two distinct spectral dips, centered at

measurements for a second design (design 2; *d2/d1* = 0.794); the corresponding results are shown in Figure 8b. Similar to the spectra in Figure 8a, this figure shows a distinct spectral

> *a/2*

Figure 8c shows the near-infrared image captured with incident laser at 1550 nm and corresponds to the design 1. The spatially alternating vertical stripes show radiation scattered at the interfaces between the PhC and the homogeneous layers and confirm the transmission of the light through the superlattice. The near-infrared images also confirm the existence of the dip in the transmission spectrum, with most of the light being reflected and only a small amount propagating out of the output facet of the third stack (in this figure , the

To better understand the results of these measurements, we repeated the FDTD simulations for the case of the fabricated devices. A good match between the results of the measurements and those of simulations, in terms of *absolute* values of the frequencies, has been observed for both values of the ratio *d2/d1* (design 1 and 2) and varying stack numbers (design 1). The theoretical predictions are shown as the dotted lines in Figure 8a and 3.8b.

Figure 8d further shows the results of a series of experiments for PhC superlattices of design 1, each with 7 unit cells but with increasing number of stacks, from 3 to 5 and 8. As observed, both gaps become deeper with increasing number of stacks. It should be noted that by improving the impedance matching between the negative and positive index materials, transmission spectrum for even larger number of stacks in the PhC superlattice can be observed. The center-frequency of the gaps does not change when the number of stacks increases, the slight deviations in the gap frequency being attributable to small variations in the dimensions of the fabricated superlattice structures. This series of measurements further reinforce the observation of the zero- n gap in cascaded negative- and

*a/2*

*c*) is coupled into the chip *via* tapered lensed fibers with manual fiber

*c* 0.265). We then repeat these transmission

*c* 0.262 is weaker than in design 1, which is due to the

*c* 0.265, the detected power is not high enough

*c* 0.272, *i.e.* at =1543 nm. Furthermore,

nm. These small variations are below ~0*:*05*a* disorder theoretical target [46].

*a/2*

*c* 0.276) and 1585 nm (

incident laser is tuned to the zero- n gap frequency).

*a/2*

dip, located near the normalized frequency

**3.3 Device nanofabrication and experiments** 

frequency of

1520 nm (

*a/2*

the frequency spectral dip at

fact that below a certain frequency,

for observing the spectral features.

positive-refraction superlattices.

*a/2*

Fig. 8. (a) Measured transmission for a superlattice with *d2/d1*= 0.746, with 7 unit cells in the PhC layers and 5 stacks; for comparison, results of numerical simulations are also shown. (b) The same as in a), but for a superlattice with 0.794. (c) Example of near-infrared top-view image of a device with 3 stacks, from transmission measurement at 1550 nm. Superimposed are the locations of the negative refraction PhC and positive index material in the superlattice. Scale bar: 2 m. (d) Measured transmission for a superlattice with *d2/d1*= 0.746, with 3, 5 and 8 stacks and 7 unit cells in the PhC layers. Both gaps become deeper as the number of stacks increases.

It has been pointed out that zero- n gaps can be omnidirectional [28, 41]; however, in our case, due to the anisotropy of the index of refraction of the PhC, the zero- n gap is not omnidirectional. Moreover, varying the lattice period, radius, and the thickness of the superlattice, and thus changing the frequency at which the average effective index of refraction is equal to zero, the frequency of the zero- n gap can be easily tuned as we show in the next section. Importantly, we note the demonstration of these zero- n gap structures can have potential applications as delay lines with zero phase differences which we also show later in this chapter.

Negative Index Photonic Crystals Superlattices and Zero Phase Delay Lines 341

on the condition of path-averaged zero index: *n1d1* + *n2d2* = 0) while the frequency of the

invariant, zero- n , bandgap is located at 1525.5 nm, 1535.2 nm, 1546.3 nm, and 1556.5 nm, respectively (averaged over the three devices in each set). The slight red-shift with increasing number of unit cells in each set is due to effects of edge termination between the

Fig. 9. **Experimental verification of period-invariance and tunability of zero-** n **bandgaps. a,** Experimental verification of the zero- n bandgap in superlattices with varying period (

for green (dotted) curves (*a.u.* arbitrary units). The lightly shaded regions in all panels

(solid), 5.80 μm for red (dashed), and 7.09 μm for green (dotted) curves. **c,** Transmission spectra for superlattices with *d*2/*d*1 =0.76, containing 5, 6, and 7 unit cells (UC). Each PhC

and 7.25 μm for green (dotted) curves. **f,** Calculated effective index of refraction for the superlattices with the ratios in **a**, **b**, **d**, and **e**. The wavelengths at which the average index of

=4.56 μm for black (solid), 5.87μm for red (dashed), and 7.17 μm for green (dotted) curves.

Furthermore, when we tuned the ratio *d*2/*d*1 and repeated these same experiments we observed a redshift of the zero- n mid-gap frequency as we increased the ratio *d*2/*d*1. This result is explained by the fact that for the negative index band the refractive index of the 2D hexagonal PhC decreases with respect to the wavelength (see Figure 3c) and therefore when the length of the PIM layer in the 1D binary superlattice increases (higher *d*2/*d*1), the wavelength at which the effective index cancels is red-shifted. The effective index of the PIM

denote the negative index regions. **b,** Same as in **a**, but for *d*2/*d*1 =0.76.

refraction cancels agree very well with the measured values.

=4.46 μm for black (solid), 5.74 μm for red (dashed), and 7.01 μm

=4.51μm). **d,** Same as in **a**, but for *d*2/*d*1 =0.78.

=4.61 μm for black (solid), 5.93 μm for red (dashed),

=4.51 μm for black

. Our measurements show that the

).

regular 1D PhC Bragg bandgaps does depend on

PhC and the homogeneous slab.

The ratio *d*2/*d*1 =0.74 and

layer contains 7 unit cells (*d1*=2.564 μm *,* 

**e,** Same as in **a**, but for *d*2/*d*1 =0.80.
