1

Waveguide Superlattices for High Density Photonic Integration

Weiwei Song1, Robert Gatdula1, Siamak Abbaslou1, Ming Lu2, Aaron Stein2, Warren Y.-C. Lai1,3, J. Provine4, R. Fabian W. Pease4, Demetrios N. Christodoulides5, and Wei Jiang1,3*

1Department of Electrical and Computer Engineering, Rutgers University, Piscataway, NJ 08854, USA

2Center for Functional Nanomaterials, Brookhaven National Laboratory, Upton, NY 11973, USA

3Institute for Advanced Materials, Devices, and Nanotechnology, Rutgers University, Piscataway, NJ 08854, USA

4Department of Electrical Engineering, Stanford University, Stanford, CA 94305, USA

5School of Optics/CREOL, University of Central Florida, Orlando, Florida 32816-2700, USA

(December 17, 2013)

*Email: wjiangnj@rci.rutgers.edu

2

Abstract

Silicon photonics holds great promise towards low-cost large-scale photonic integration. In its

future development, integration density will play an ever increasing role in a way similar to that

witnessed in silicon integrated circuits. Waveguides are perhaps the most ubiquitous component

in silicon photonics. As such, the ultimate density of waveguide elements is expected to have a

profound impact on the integration density of a silicon photonic chip. A solution to high density

waveguide integration with minimal impact on other performance metrics associated with

crosstalk remains a central problem in many silicon photonics platforms. Here we propose and

demonstrate a waveguide superlattice that enables high-density waveguide integration on a half-

wavelength scale. Such waveguide superlattices can lead to a significant reduction in on-chip

estate and cost especially for large-scale photonic device arrays and systems, and further open up

possibilities for half-waveguide-pitch optical phased arrays and ultra-dense space division

multiplexing schemes. It may also provide a novel arrangement for exploring a host of intriguing

scientific problems such as Anderson localization.

3

Silicon photonics has made great strides in developing a wide range of devices [1-12].

Built upon these advances, this technology now offers a low-cost platform for building large-

scale optical systems [13-15]. Arrays of waveguides are among the cornerstones of such systems.

For example, optical phased arrays [16-18], space-division multiplexing configurations [19], and

common optical switching fabrics may comprise massive waveguide arrays for large-scale

systems. On the other hand, a waveguide lattice can be viewed [20] as fully analogous to a

periodic chain of atoms, which lends itself to a broad spectrum of fascinating scientific

possibilities ranging from Anderson localization of light [21] to parity-time symmetric effects

[22]). Thus far, in most studies, the pitch associated with such relatively simple waveguide

arrays/lattices has been typically large, ranging from a few microns to tens of microns (or a

multiple of wavelengths) [17,23,24]. As such, the inter-coupling between waveguides can be

generally weak, which helps to reduce crosstalk. On the other hand, the subwavelength or

submicron regime of such systems has not been adequately explored for practical applications,

mainly because of an intolerable surge in crosstalk usually occurring at these length scales. Here

we introduce a superlattice of waveguides (Fig. 1), whose supercell comprises a sub-array of

waveguides, and explore intricate light inter-coupling and scattering in such a system. Guided by

advanced simulations, we demonstrate the possibility for very weak crosstalk even as the

waveguide pitch approaches the half wavelength mark. This not only enables high-density

integration of silicon waveguides with significant reduction in on-chip estate and cost, but also

opens up opportunities for half-wavelength-pitch optical phased arrays and ultra-dense space-

division multiplexing that have long been sought.

Before we explore more sophisticated superlattices, we first consider the simplest

possible superlattice cell (supercell) consisting of two dissimilar units or atoms, i.e. two

4

waveguides with different propagation constants., Within such a single “diatomic” supercell, the

normalized optical power P12 that is transferred from one waveguide to another is given by [25],

),)2/((sin1)2/(

1 2222

1

21 LP

P

where represents the propagation constant

difference (or phase mismatch) between two waveguides, the coupling strength, and L the

propagation distance. One readily sees that if the phase mismatch is significantly stronger

than the corresponding coupling strength , the transferred power (waveguide crosstalk) is

extremely weak. Several methods exist in establishing a mismatch between adjacent

waveguide elements. For practical fabrication considerations, here we choose to vary the

waveguide widths so as to induce an appropriate . Detailed theoretical calculations are shown

in Fig. 2a for pairs of waveguides in which the first waveguide has a fixed width of w1=450nm

and the second waveguide width, w2, is varied. Evidently, the crosstalk between the waveguide

pair can be reduced to far below 20 dB with sufficient even for a pitch of a~0.8 m.

However, when such a waveguide pair is periodically replicated in space to form a waveguide

superlattice, the power transfer between adjacent waveguide supercells (separated by a

superlattice period as=2a) remains high (e.g. crosstalk ~ 14 dB for as=2m, see Fig. S3 in the

Supplementary Information). To deter such coupling beyond nearest neighbors, non-trivial

waveguide superlattices must be explored.

To explore non-trivial superlattice structures beyond simple pairs, we need to first

understand the physics of light transport in such coupled systems. First, to build a superlattice,

we need different species of “atoms,” namely, waveguides of different widths w. More types of

such units are clearly desirable for more sophisticated superlattice designs. However, there are

two physical constraints that limit the range of available waveguide widths. On the one hand, the

5

maximum waveguide width is constrained by the single-mode condition (wmax ~ 450 nm here).

On the other hand, for a very narrow waveguide, the width of the optical mode increases

significantly as the waveguide width decreases. This in turn enlarges the mode overlap between

adjacent waveguides, and enhances their inter-coupling strength n,n+1. Eventually, at a

sufficiently narrow w, crosstalk starts to increase (see Fig. 2a, and Supplementary Information

for more details) because the increase in n,n+1 cancels out any benefit introduced by increasing

. By considering this limit and by also noting that narrow waveguides tend to have higher loss,

the narrowest waveguide used in the superlattices is set to be around 330 nm wide. Second, in a

sophisticated superlattice many effects come up due to complex light transport/coupling. For

example, the inter-coupling causes the effective phase constant of a superlattice mode to

deviate from the intrinsic of an isolated waveguide. Furthermore, light transport may also

comprise contribution from inter-waveguide scattering due to structure imperfections (e.g.

waveguide sidewall roughness), which will be discussed later as a secondary effect. Hence, a

rigorous theory is needed to model light transport in a superlattice. Note that approximate

theories based on small index contrast cannot be applied to silicon waveguides. Here a fully-

vectorial waveguide mode theory previously developed for a high-index-contrast photonic

crystal waveguide [26,27] is employed. It can be shown that the amplitude of the mode, 'nc , can

be obtained from

,0'

)('

mnn

nn

mnn

n Bz

ciAzc

where n is the propagation constant of the original mode of the n-th waveguide, Bmn is related to

the overlap integral between modes m and n, and mnA is the perturbation potential matrix

6

element (see detailed derivation in the Supplementary Information). In addition, nsuper denotes

the number of waveguides in a supercell, and the superlattice period is given by as=nsupera. Third,

despite the complexity of superlattice coupling, some qualitative guidelines can be followed to

design the superlattices. Detailed theory and simulation results show that for mnA <<(mn),

the crosstalk between waveguide #m and #n remain small, which indicates qualitatively that the

strategy for minimizing / remains useful. Furthermore, the off-diagonal matrix element is

given to a good approximation by mnA ~ mnfanm )||exp( , where is a constant and fmn a

periodic function (period=nsuper) of (m, n). Thus, mnA decays almost exponentially with

waveguide separation ( anm || ); and the nearest-neighbor coupling 1, nnA is generally much

more pronounced than the coupling to all other neighbors.

As a first step, we designed a superlattice with three waveguides in each supercell (called

“SC3” hereafter). By spreading the waveguide widths sparsely between the upper and lower

bounds set above, we choose the waveguide widths to be 450, 380, and 330 nm. Simulations

showed that the SC3 superlattice can achieve <30dB crosstalk between nearest neighbors at

1m pitch, as depicted in Fig. 2b. Such a SC3 superlattice with a pitch of 1m and a length of

L=200m was fabricated on a silicon-on-insulator chip (fabrication processes, waveguide

structure details, and measurement schemes are described in Methods). The measured

transmission spectra are shown in Fig. 3a. As a starting point, only 2 superlattice periods (plus

one extra #7 for a rough estimate of crosstalk over 2as) were studied to save time in simulation,

fabrication and measurement. For light input into a given waveguide i, output spectra of all seven

waveguides Tij(), j=1, 2, …, 7, were measured (77=49 spectra in total for different i). For a

visual comparison of crosstalk between different channels, the transmission spectra originating

7

from one input waveguide are normalized with respect to the peak transmission of the

corresponding direct through channel [e.g. T3j() all normalized by the peak of T33()] so that

each direct through channel has its peak aligned at 0 dB. Note that by defining the maximum

crosstalk from channel i to channel j as )]()([max),(max iiij TTjiXT , the crosstalk value is

not affected by the normalization scheme of Tij. To avoid a heavily cluttered presentation, for

each input, only the two nearest-neighbors (Ti,i1) plus the worst crosstalk channel are plotted in

Fig. 3a. Evidently, the crosstalk was fairly low. For ease of visual comparison, the statistics

(mean and standard deviation) of each transmission spectrum Tij() is plotted in Fig. 3b. Note

that the true crosstalk for most non-adjacent channels (e.g. T24) should be small (e.g. T24<50dB,

T24<80dB) and are below the noise floor of our measurement setup (see noise floor discussion

in Methods). The values of these channels were measured and shown in Fig. 3b just for verifying

that its crosstalk was low enough for most applications. The overall crosstalk level of the leading

crosstalk channels in Fig. 3b was several dB higher than the theoretical results in Fig. 2b, but it

was still within a reasonable range considering the noise floor of our measurement setup and the

noise due to scattering from sidewall roughness, which will be discussed later. The peaks of all

crosstalk channels were in the range of 24dB to 20dB. However, when the pitch a is reduced

below 1m, this SC3 structure produces significantly higher crosstalk. For example, for a SC3

superlattice with a=0.8 m that we fabricated, the peak crosstalk channel XTmax(2,5) can surge

above 10dB.

To further compress the waveguide density to the submicron-pitch regime, more

sophisticated superlattices are considered. Due to the constraint of the waveguide width range

discussed above, a trivial insertion of an extra waveguide in this width range into a supercell will

8

likely reduce minimum w in the superlattice and hence the phase mismatch between certain

waveguides (e.g. inserting a w=420nm waveguide into the SC3 supercell above reduces the

minimum w to 30nm). Fortunately, for nsuper>3, the order of the waveguides in a supercell can

be effectively utilized as a new route for minimizing the crosstalk (Note that nsuper3, after

classifying all configurations that are equivalent by symmetry, there is essentially one unique

order once the set of waveguide widths are decided.). Consider the case of nsuper=5. In this case, a

simple decreasing (or increasing) order of the waveguide widths (assuming wa>wb>wc>wd>we) in

a supercell is not optimal for crosstalk reduction. Instead, an interlacing configuration (wa wc we

wb wd) maximizes the phase mismatch between adjacent waveguides and therefore

significantly reduces the crosstalk. In this interlacing configuration, any two waveguides that

have the least width difference (e.g. wc and wb) are separated by 2a rather than a. This larger

separation significantly reduces the crosstalk between these two waveguides that have the least

phase mismatch , as shown in Fig. 2c. A SC5 superlattice whose supercell comprises 200m

long waveguides of widths 450, 390, 330, 420, and 360 nm at pitch a=0.8m was fabricated. Its

measured spectra are shown in Fig. 3c and its spectral statistics (all 121 spectra) in Fig. 3d.

Compared to the statistics of the SC3 superlattice at a=1m in Fig. 3b, the overall crosstalk level

rose, substantially spreading into the 30 to 20 dB range. The trend is consistent with the

theoretical results in Fig. 2b and c. Note that the overall maximum crosstalk XTmax(7,6)=18.8

dB is substantially above the theoretical prediction.

The high maximum channel crosstalk in Fig. 3c can be attributed in part to the random

light scattering between different waveguide modes due to sidewall roughness. Roughness

induced scattering loss has been studied in single Si waveguides (e.g. ref. [28]). In a waveguide

superlattice, scattering can cause additional crosstalk and noise. As the propagation length

9

increases, the scattering effect may accumulate substantially to produce much higher peak

crosstalk. For example, in a longer (L=500m) SC5 superlattice we fabricated, the peak crosstalk

of several channels spread into the range of 15dB to 10dB. Detailed simulations show that the

crosstalk fluctuation can be much reduced (see Fig. S2 and related discussions in Supplementary

Information) if the sidewall roughness can be reduced. Hence we switched to an ultrafine-

resolution e-beam resist hydrogen silsesquioxane (HSQ), instead of the previous moderate-

resolution resist (ma-N, see more details in Methods), to fabricate a 500m long SC5 superlattice.

The measured spectra are depicted in Fig. 3e and their statistics in Fig. 3f. Compared to the SC5

superlattice in Fig. 3c, d, the standard deviations of the direct transmission spectra Tii are

substantially reduced. This signifies a reduction of scattering-induced spectral noise (despite a

longer L). The diminishing scattering also helps to suppress the overall maximum crosstalk of

the entire superlattice to XTmax(10,9)=21.1 dB at ~1565nm.

To further demonstrate the characteristics of the waveguide superlattice beyond two

supercells, we have fabricated a 500m long superlattice of five SC5 supercells using HSQ e-

beam resist. The transmission from each of the five waveguides in the center supercell to its

neighboring 11 waveguides within one superlattice period was measured and plotted in Fig. 4

(for example, for input waveguide #12, output spectra from #7 to #17 were measured). Evidently,

the crosstalk remains low (<20dB) across the entire spectrum for all channels, with the worst

case being XTmax(15,10)=21 dB. We have also checked the crosstalk for identical waveguides

separated by two superlattice periods (2as=10a), their crosstalk spectra were generally sheer

noise (~ 30 dB or lower). To further analyze the wavelength dependence of the crosstalk

statistics, the transmission of all 50 crosstalk channels Tij (ji) is plotted against the direct

10

transmission channel Tii in Fig. 4b in three wavelength bands, 1530nm (green), 1530 ~

1560nm (blue), and 1560 ~ 1570nm (red). Note that for each direct transmission channel, there

are 10 crosstalk channels. Evidently, the crosstalk was less than 25dB for 1530nm while it

increased for longer wavelength bands.

To assess the width control in fabrication, the waveguide widths of a SC5 superlattice

fabricated by HSQ resist have been characterized by high-resolution SEM as shown in Fig. 5.

The width statistics of five waveguides in a supercell are shown in Fig. 5b. In reference to the

mean width <w1> of the widest waveguide, the mean width differences (<wn><w1>) of the

other waveguides are 60, 119, 26, and 87nm, respectively, in good agreement with the

designed values of 60, 120, 30, and 90nm. The standard deviations of all waveguide widths

are less than 2.7nm. Note that the mean values of all waveguide widths had an overall shift

~12nm from the designed values. However, simulations show that as long as the width difference

is retained, this overall shift does not change the crosstalk significantly (see Fig. S1 in

Supplementary Information).

Discussion

The waveguide superlattice demonstrated here can drastically improve the integration

density of silicon photonic devices, thereby enabling higher level of integration, and more

complex functionality in a given chip area and reducing the on-chip estate and cost of waveguide

elements. In Si microelectronics, continual reduction of size and cost of transistors and increase

of transistor density have driven the technology growth for decades (as encapsulated by Moore’s

law). In photonics, increasing the density of waveguides has been challenging due to significant

11

crosstalk at small pitches. This work shows that pronounced increase in integration density can

be achieved by designing sophisticated superlattices that drastically suppress crosstalk. Further

down-scaling of the waveguide pitch can potentially be achieved through more sophisticated

superlattice structures, tighter control of the waveguide width and roughness, and even

modification of individual waveguide height. Note that the dimension control required in the

current work is within the reach of the state-of-the-art silicon foundries [29] and therefore is

amenable to mass production. Extension of this idea to 3D is also possible and it can be

facilitated by membrane transfer technology [30]. Note that plasmonic waveguides have the

potential of achieving high waveguide density, but significant loss and short propagation

distance fundamentally limit their use in most practical applications.

Note that this approach offers a broadband solution (covering ~65nm bandwidth) to the

waveguide integration density. For chip-scale optical interconnects, such a dense waveguide

superlattice can be used for space-division multiplexing (SDM) [19,31], while employing

wavelength-division multiplexing (WDM) in each waveguide. Combining SDM and WDM, the

spatial density of data bandwidth of a waveguide superlattice can potentially reach 10THz/m

(with 65nm bandwidth and a pitch of a=0.8 m), opening up unprecedented opportunities for

optical interconnects in future high-performance computer chips (e.g. comprising >100 cores).

For less demanding interconnect applications, SDM may be preferred to substitute for WDM

because WDM devices are more complex and sensitive to temperature. Note that in fiber-based

SDM, the spatial density of waveguide channels is much lower (typical core spacing >10 m).

Our results suggest that this can be significantly improved by using high index core materials

(e.g. Si [32]) in fibers. This may benefit longer-reach (e.g. inter-chip) optical interconnects [33-

36] that use fibers.

12

The waveguide superlattice demonstrated here can potentially transform the optical

phased array (OPA) technology [37,38]. For an OPA, a smaller pitch will increase the angular

separation between the primary beam and the unwanted secondary beams. As the pitch decreases

below /2, the angle separation is so large that no secondary beams appear in the range of –90o

to +90o. Such an OPA is considered ideal [37,38] and has long been pursued. The waveguide

superlattice demonstrated in Fig. 4 enables us to squeeze phase-modulated signals into emitters

at /2-pitch (in an OPA structure like ref. [17]) and shows, for the first time to our knowledge,

that such a /2-pitch OPA is feasible. Extension to 2D OPA is also possible with the help of

membrane transfer and stacking technology [30]. Another important benefit of a smaller pitch is

that it can significantly reduce the power consumption of phase-tuning elements of an OPA (see

detailed discussion in the Supplementary Information).

The waveguide superlattice can also stimulate new directions in scientific studies. By

introducing optical nonlinearity, waveguide superlattices may provide a playground for studying

a rich spectrum of phenomena in nonlinear optics, disordered systems, and their interplay

[20,39,40]. For example, with nonlinear self-focusing in a discrete system, we can further

enhance light “localization” in each “atom” (waveguide), which will effectively reduce crosstalk

and may enable even smaller pitches. As another example, phonon scattering of electrons in

atomic crystals can be emulated by roughness-induced light scattering. The results of this work

suggest that such random scattering plays two contrasting roles: it frustrates coherent coupling

between identical atoms whereas induces incoherent scattering into non-identical atoms,

resulting into two opposite localization trends. Such a complex localization behavior in a

precisely designed superlattice may shed new light on metal-insulator transition in complex

crystals. Note that many scientific studies may use different characterization schemes, such as

13

imaging the optical field of an entire lattice, rather than characterizing the crosstalk between

individual waveguides. The latter is more common for optical device applications of interest here.

Also note that the structures considered in this study resemble an insulator with hopping-type

transport, and is better described in the basis of individual waveguide modes rather than periodic

Bloch modes [20,41].

Conclusions

In summary, high density waveguide superlattices with half-wavelength pitches have been

demonstrated with low crosstalk. Such waveguide superlattices could have important

applications in optical phased arrays and space-division multiplexing techniques. The fine

waveguide pitch and low crosstalk can lead to a quantum leap in integration density, signal

quality, beam steering range, and power efficiency in such applications. Ultimately, high density

integration holds the key to reducing on-chip estate and cost of waveguide elements and enabling

more complex functionality and will be the driving force for silicon photonics, as Moore’s law

has driven silicon microelectronics for decades. Last but not the least, waveguide optical

superlattices may also provide a playground for exploring an array of fundamental scientific

problems in solid state physics.

Methods

The waveguide superlattice structures in this work were fabricated by processes for

making high-quality silicon nanophotonic structures [42]. Starting from a silicon-on-insulator

14

wafer with a 2 m buried oxide layer and a 260 nm top Si layer, a JEOL JBX-6300FS high-

resolution e-beam lithography system was employed to pattern the waveguide structures. E-beam

resists we used were either ma-N 2405 (Micro Resist Technology) or hydrogen silsesquioxane

(Dow Corning). The effects of the resist choice on sidewall roughness and light scattering are

discussed in detail in the Supplementary Information. Then the pattern was transferred to the top

silicon layer of the wafer by reactive ion etching in an Oxford Plasmalab 100 ICP etcher. Finally,

a 2 m thick silicon oxide cover was deposited by plasma-enhanced chemical vapor deposition

(PECVD). To facilitate measurement, the input and output ends of the waveguide superlattices

were spread out to a large spacing through waveguide bends with radii 100 m (radii = 50 m

for the 5-period superlattice to reduce the lateral pattern size), followed by a 100 m taper to a

450 nm wide access waveguide. The propagation loss of the silicon waveguides fabricated by

HSQ resist ranges from ~0.6 dB/mm to ~0.9 dB/mm as the width decreases from 450 nm to 330

nm. The loss difference (propagation, taper loss) between waveguides of different widths is

estimated <0.8dB for the superlattices patterned by HSQ (actual loss had random fluctuation up

to 2dB). The propagation loss of waveguides made by ma-N is higher (about twice of those made

by HSQ). To characterize the transmission spectra of a waveguide superlattice, light from a

superluminescent LED with a spectral range of about 80 nm was coupled to the TE mode of a

waveguide in the superlattice via a lensed fiber. The spectra of the output light from this

waveguide and other waveguides were measured by an optical spectrum analyzer. Owing to

mode-size mismatch between the lensed fiber (Gaussian spot size ~2.5m) and silicon

waveguides, a portion of light from the input fiber did not enter the silicon waveguides but

strayed outside. A small fraction of the stray light reached the output edge of the chip and

entered the output lensed fiber. The amount of stray light entering the output lensed fiber was

15

estimated around –60dB, in reference to the input light from the lensed fiber, in typical

experiments. For long wavelengths far from the peak of the broadband source we used, the

source intensity could be fairly low (e.g. ~10 dB down from the peak). Adding an effective

attenuation of 40~50 dB (>20 dB due to propagation and coupling loss, 20~25 dB due to relative

crosstalk), the crosstalk signal of the output waveguides at long wavelengths could diminish to a

level comparable to the noise floor of the optical spectrum analyzer (OSA). The above factors

(relatively weak crosstalk signal, stray light, and noise floor of the OSA) limited the lowest

crosstalk that can be measured.

References

1 Liu, A.S. et al., A high-speed silicon optical modulator based on a metal-oxide-semiconductor capacitor. Nature 427, 615-618 (2004).

2 Xu, Q.F., Schmidt, B., Pradhan, S., & Lipson, M., Micrometre-scale silicon electro-optic modulator. Nature 435, 325-327 (2005).

3 Gu, L.L., Jiang, W., Chen, X.N., Wang, L., & Chen, R.T., High speed silicon photonic crystal waveguide modulator for low voltage operation. Appl. Phys. Lett. 90, 071105 (2007).

4 Xia, F., Sekaric, L., & Vlasov, Y., Ultracompact optical buffers on a silicon chip. Nat Photon 1, 65-71 (2007).

5 Liu, J. et al., Waveguide-integrated, ultralow-energy GeSi electro-absorption modulators. Nature Photonics 2, 433-437 (2008).

6 Kang, Y. et al., Monolithic germanium/silicon avalanche photodiodes with 340 GHz gain-bandwidth product. Nat Photon 3, 59-63 (2009).

7 Assefa, S., Xia, F., & Vlasov, Y.A., Reinventing germanium avalanche photodetector for nanophotonic on-chip optical interconnects. Nature 464, 80-84 (2010).

8 Reed, G.T., Mashanovich, G., Gardes, F.Y., & Thomson, D.J., Silicon optical modulators. Nature Photonics 4, 518-526 (2010).

9 Yu, Z. & Fan, S.H., Complete optical isolation created by indirect interband photonic transitions. Nat Photon 3, 91-94 (2009).

10 Fan, L. et al., An All-Silicon Passive Optical Diode. Science 335, 447-450 (2011). 11 Foster, M.A. et al., Broad-band optical parametric gain on a silicon photonic chip. Nature

441, 960-963 (2006). 12 Liu, X. et al., Bridging the mid-infrared-to-telecom gap with silicon nanophotonic

spectral translation. Nat Photon 6, 667-671 (2012).

16

13 Soref, R., The past, present, and future of silicon photonics. IEEE Journal of Selected Topics in Quantum Electronics 12, 1678-1687 (2006).

14 Jalali, B. & Fathpour, S., Silicon photonics. Journal of Lightwave Technology 24, 4600-4615 (2006).

15 Hochberg, M. & Baehr-Jones, T., Towards fabless silicon photonics. Nature Photon. 4, 492-494 (2010).

16 Van Acoleyen, K. et al., Off-chip beam steering with a one-dimensional optical phased array on silicon-on-insulator. Opt. Lett. 34, 1477-1479 (2009).

17 Kwong, D., Hosseini, A., Zhang, Y., & Chen, R.T., 1 x 12 Unequally spaced waveguide array for actively tuned optical phased array on a silicon nanomembrane. Appl. Phys. Lett. 99, 051104 (2011).

18 Sun, J., Timurdogan, E., Yaacobi, A., Hosseini, E.S., & Watts, M.R., Large-scale nanophotonic phased array. Nature 493, 195-199 (2013).

19 Richardson, D.J., Fini, J.M., & Nelson, L.E., Space-division multiplexing in optical fibres. Nature Photonics 7, 354-362 (2013).

20 Christodoulides, D.N., Lederer, F., & Silberberg, Y., Discretizing light behaviour in linear and nonlinear waveguide lattices. Nature 424, 817-823 (2003).

21 Segev, M., Silberberg, Y., & Christodoulides, D.N., Anderson localization of light. Nature Photonics 7, 197-204 (2013).

22 Regensburger, A. et al., Parity-time synthetic photonic lattices. Nature 488, 167-171 (2012).

23 Doany, F.E. et al., Multichannel High-Bandwidth Coupling of Ultradense Silicon Photonic Waveguide Array to Standard-Pitch Fiber Array. Journal of Lightwave Technology 29, 475-482 (2011).

24 Fleischer, J.W., Segev, M., Efremidis, N.K., & Christodoulides, D.N., Observation of two-dimensional discrete solitons in optically induced nonlinear photonic lattices. Nature 422, 147-150 (2003).

25 Saleh, B.E.A. & Teich, M.C., Fundamentals of Photonics. (Wiley, Hoboken, NJ, 2007). 26 Povinelli, M.L., Johnson, S.G., Lidorikis, E., Joannopoulos, J.D., & Soljacic, M., Effect

of a photonic band gap on scattering from waveguide disorder. Appl. Phys. Lett. 84, 3639-3641 (2004).

27 Song, W., Integlia, R.A., & Jiang, W., Slow light loss due to roughness in photonic crystal waveguides: An analytic approach. Phys. Rev. B 82, 235306 (2010).

28 Lee, K.K. et al., Effect of size and roughness on light transmission in a Si/SiO2 waveguide: Experiments and model. Appl. Phys. Lett. 77, 1617-1619 (2000).

29 ITRS Roadmap: Lithography Table, Available at http://www.itrs.net, (2011). 30 Rogers, J.A., Lagally, M.G., & Nuzzo, R.G., Synthesis, assembly and applications of

semiconductor nanomembranes. Nature 477, 45-53 (2011). 31 Winzer, P.J. & Foschini, G.J., MIMO capacities and outage probabilities in spatially

multiplexed optical transport systems. Opt. Express 19, 16680-16696 (2011). 32 Ballato, J. et al., Silicon optical fiber. Opt. Express 16, 18675-18683 (2008). 33 Vlasov, Y.A., Silicon CMOS-integrated nano-photonics for computer and data

communications beyond 100G. IEEE Comm. Magazine 50, s67-s72 (2012). 34 Zheng, X. et al., Ultralow Power 80 Gb/s Arrayed CMOS Silicon Photonic Transceivers

for WDM Optical Links. Journal of Lightwave Technology 30, 641-650 (2012).

17

35 Urino, Y. et al., Demonstration of 12.5-Gbps optical interconnects integrated with lasers, optical splitters, optical modulators and photodetectors on a single silicon substrate. Opt. Express 20, B256-B263 (2012).

36 Miller, D.A.B., Device Requirements for Optical Interconnects to Silicon Chips. Proceedings of the IEEE 97, 1166-1185 (2009).

37 McManamon, P.F. et al., Optical phased array technology. Proceedings of the IEEE 84, 268-298 (1996).

38 McManamon, P.F. et al., A Review of Phased Array Steering for Narrow-Band Electrooptical Systems. Proceedings of the IEEE 97, 1078-1096 (2009).

39 Christodoulides, D.N. & Joseph, R.I., Discrete self-focusing in nonlinear arrays of coupled waveguides. Opt. Lett. 13, 794-796 (1988).

40 Keil, R. et al., Perfect imaging through a disordered waveguide lattice. Opt. Lett. 37, 809-811 (2012).

41 Martins, E.R., Li, J., Liu, Y., Zhou, J., & Krauss, T.F., Engineering gratings for light trapping in photovoltaics: The supercell concept. Phys. Rev. B 86, 041404 (2012).

42 Tan, J., Lu, M., Stein, A., & Jiang, W., High-purity transmission of a slow light odd mode in a photonic crystal waveguide. Opt. Lett. 37, 3189-3191 (2012).

Acknowledgement

The authors are grateful to George K. Celler, Philip E, Batson, and Roy Yates for helpful

discussions. This work is supported in part by U.S. Air Force Office of Scientific Research under

Grant No. FA9550-08-1-0394 and by the DARPA Young Faculty Award under Grant No.

N66001-12-1-4246. This research was carried out in part at the Center for Functional

Nanomaterials, Brookhaven National Laboratory, which is supported by the U.S. Department of

Energy, Office of Basic Energy Sciences, under Contract No. DE-AC02-98CH10886.

Author contributions

W. J. conceived the idea of the project, conducted the simulation, and guided the project. W. S.

conducted the fabrication and characterization, and contributed to the simulation. R. G. and S. A.

contributed to the fabrication and characterization. M. L., A. S., W. Y-C. L., J. P. and R. F. W. P.

18

contributed to solving crucial fabrication issues and structural characterization. D. N. C.

contributed to understanding the physics of light transport in superlattices and optical

characterization.

19

Figure Captions

Figure 1. Schematic drawing of a waveguide superlattice.

Figure 2. Crosstalk simulation results. a, crosstalk between a pair of waveguides of different

widths (w1=450nm, w2 and pitch a vary). b, SC3 superlattice, a=1m, L=200m. c, SC5

superlattice, a=0.8m, L=200m. In b and c, transmission spectra Ti,j() from a given input

waveguide (WG) i to different output waveguides are plotted in the i-th plane (e.g. T1,j all in the

first plane). The color/symbol for each output channel j is shown in the legend.

Figure 3. Measured transmission spectra and their statistics for a-b SC3 superlattice; c-d

and e-f SC5 superlattice. The superlattices in a-d were patterned by the ma-N resist; and the one

in e-f by HSQ. Only adjacent channels Ti,i1 plus the worst crosstalk channel are shown in a, c,

and e. Different colors mark different output ports, whose indices are shown in the legends. The

spectral statistics of all transmission channels are shown by error bars in b, d, and f, respectively.

The color/symbol for each output channel is shown in the legend.

Figure 4. Transmission spectra of a large-scale SC5 superlattice for 5 input waveguides in a

representative supercell (Ti,j, i=11~15, j=i5, i4, … i+4, i+5). L=500m. The color for each

output channel is shown in the legend. a, Spectra. To avoid cluttered view, only Ti,i1() plus the

worst are shown for each i. b, scatter plot of Ti,i vs. Ti,j for all 50 crosstalk spectra ( ji), for three

bands: 1530nm (green), 1530 ~1560nm (blue), and 1560 ~ 1570nm (red). The lines of

Ti,jTi,i=20, 25dB are delineated (to demark relative crosstalk levels).

Figure 5. Width statistics. a, SEM micrograph of one supercell in a SC5 superlattice made by

HSQ (scale bar: 2m); b, width distribution in reference to <w1>.

1

Fig. 1

a as

super-cell super-cell z

x

y

2

Fig. 2

a b c

1.52 1.54 1.56 1 3 5 7 9 11-60

-40

-20

0

input WG index

(m)

Tra

nsm

issi

on

(d

B)

1

2

3

4

5

6

7

8

9

10

11

1.52 1.54 1.56 13

57

-60

-40

-20

0

input WG index

(m)

Tra

nsm

issi

on (

dB)

1

2

3

45

6

7

3

Fig. 3

15001520

15401560 1

35

79

11-40

-30

-20

-10

0

input WG index

(nm)

Tra

nsm

issi

on (

dB)

15001520

15401560 1

35

7-40

-30

-20

-10

0

input WG index

(nm)

Tra

nsm

issi

on (

dB)

15001520

15401560 1

35

79

11-40

-30

-20

-10

0

input WG index

(nm)

Tra

nsm

issi

on

(d

B)

a c e

1 3 5 7 9 11-50

-40

-30

-20

-10

0

input WG index

Tra

nsm

issi

on (

dB)

1 2 3 4 5 6 7 8 91011

1 3 5 7 9 11-50

-40

-30

-20

-10

0

input WG index

Tra

nsm

issi

on (

dB)

f d b

1 3 5 7-50

-40

-30

-20

-10

0

input WG index

Tra

nsm

issi

on

(d

B)

1234567

1 2

3

4

5

6 7

8

9

1011

12

3

4

5

67

4

Fig. 4

-4 -3 -2 -1 0-50

-40

-30

-20

Transmission (dB)

Cro

ssta

lk (

dB)

15001520

15401560 11

13

15-40

-30

-20

-10

0

input WG index

(nm)

Tra

nsm

issi

on (

dB)

a

20dB

25dB 1

2

34

5

mod(j,5)

b

5

Fig. 5

-120 -90 -60 -30 00

500

1000

w (nm)

a b

wn <w1>