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Supplementary Information "Large-scale integration of wavelength-addressable all-optical memories in a photonic crystal chip" SUPPLEMENTARY INFORMATION Eiichi Kuramochi*, Kengo Nozaki, Akihiko Shinya, Koji Takeda, Tomonari Sato, Shinji Matsuo, Hideaki Taniyama, Hisashi Sumikura, and Masaya Notomi 1. Design of wavelength-addressable optical RAM array in a photonic crystal waveguide In current optical communication technology, a multi-bit signal is transmitted at a unique wavelength, where the signal light is divided in the time domain by many bit signals. Without wavelength addressing, a multi-bit serially integrated memory consists of all-optical RAMs operated at just the signal wavelength. On-chip switching addressor devices should be integrated with every such RAM, which is unrealistic with current technology. With a wavelength addressable multi-bit RAM, the on-chip addressing devices are replaced by external serial-parallel converters, which greatly simplify the serial photonic crystal RAM array. In exchange, the wavelength-addressable RAM requires a finite wavelength band divided for every bit. Clearly, a wider bandwidth is better for increasing the bit number. Figure S1 shows how the RAM band should be engineered in the photonic crystal cavity array. The bandwidth of the photonic crystal waveguide should be the primary consideration. Fortunately, the well-known W1 (one-row missing) waveguide has a relatively wide effective bandwidth of ~100 nm. In the photonic bandgap there are two types of transverse-electronic waveguide modes (TE, or H-polarized mode) depending on the symmetry. These are even and odd modes, respectively. An odd mode is not desirable owing to its poor coupling with external NATURE PHOTONICS www.nature.com/naturephotonics 1

SUPPLEMENTARY INFORMATION Figure S1 Band engineering of W1-based waveguide and a: Si L3 cavity; b: InP-based BH L3 cavity for WDM-compatible ultra-multi-bit optical memory. c. Safe cavity mode spacing to prevent crosstalk between two adjacent memories. optical fibre and poor propagation loss. In addition, almost the entire odd mode band is located above the light line, which results in serious out-of-plane loss. Hence, the usable waveguide band is the band where only an even mode exists. The next critical issue is the relative location of the cavity mode in the even mode band. In an array unit where 2 NATURE PHOTONICS www.nature.com/naturephotonics

SUPPLEMENTARY INFORMATION the lattice constant is a1, a cavity mode with waveguide λ(a1) divides the even mode band (a1) into a shorter wavelength band (S) and a longer wavelength band (L). When units with different a are integrated, the narrowest of S and L determines upper limit of RAM bandwidth. When a normal L3 cavity is combined with a W1 waveguide, the bandwidth of L is less than 10 nm, which results in a poor RAM bandwidth. In our Si RAM array (Fig. S1(a)), where we employ a W1.1 waveguide in which the spacing of the innermost holes sandwiching the waveguide is expanded up to 1.1 a 3 (a 3=W 0 : width of normal W1), the waveguide modes are red-shifted about 50 nm from W1. The S and L bandwidths are now 40 and 60 nm, respectively. We should carefully determine the cavity design because it strongly affects the location of the cavity mode. Moreover, when the cavity is multimode, the free spectrum range (FSR: F) between the fundamental (0 th ) mode and the first higher-order (1 st ) mode may restrict the RAM band since the overlap of the 1 st mode with the 0 th mode of other cavity inhibits the exclusive operation of a wavelength-addressable multi-bit RAM. Since F (~50 nm) of the L3 cavity is wider than S, the effective RAM bandwidth is finally determined by S (40 nm). With an InP-based RAM (Fig. S1b), the InGaAsP BH core (bandgap wavelength: 1.45 µm) strongly red-shifts the cavity mode over 40 nm from the cavity without BH, resulting in a narrow L bandwidth of 15 nm. Further widening of the W1.1 waveguide was found to degrade cavity-waveguide coupling. To expand the RAM bandwidth, we reduced the width of the centre line defect in L3 cavity to 0.95 W 0 (W0.95) to blue shift the cavity mode up to 25 nm. A numerical simulation reveals that the narrowing only changes the cavity wavelength and maintains the Q and V eff of the original L3. Eventually, an effective RAM bandwidth of 40 nm (L) is secured (Fig. S1b). Our fabrication process can realize a minimum lattice pitch variation Δa of 0.125 nm, which generates a wavelength shift Δλ of ~0.25 nm. Here, the maximum NATURE PHOTONICS www.nature.com/naturephotonics 3

SUPPLEMENTARY INFORMATION number of monolithically integrated bits is (RAM bandwidth)/δλ= 40/0.25 =160. To guarantee the completely independent (or exclusive) RAM operation of all bits, any interaction (or crosstalk) between two RAM devices should be excluded. As shown in Fig. S1c, giving an appropriate spacing to two adjacent cavity modes is important. Here a dip-to-top contrast of 10 (10 db) for side coupled cavities is assumed to secure a high bistability contrast. By assuming that the cavity spectrum has a typical Lorentzian waveform, the top (bottom) linewidth is 3Δλ c (λ c : cavity mode wavelength, Δλ c : full width half minimum of the dip = cavity mode linewidth, loaded Q=Δλ c /λ c ). To avoid any interaction the minimum cavity mode spacing without considering dynamic RAM operation should be 3Δλ c as shown in Fig. S1c. When cavity 1 is operated as a bistable RAM, the cavity mode is pumped at λ bias with negative detuning δ from the original cavity wavelength λ c1. Our previous study 1 revealed that at the minimum operation power δ is nearly Δλ c. Hence, when only cavity 1 is operated as a RAM, the cavity spacing should be wider than 4Δλ c and when both cavities 1 and 2 are biased simultaneously for RAM operation the spacing should be wider than 3Δλ c. In our Si multi-bit RAM, the intrinsic Q and loaded Q are 5 10 5 and 5 10 4, respectively, The latter corresponds to a Δλ c of 0.03 nm and a 4Δλ c of 0.12 nm. The 4Δλ c value allows us to set a cavity mode spacing of 0.25 nm and realize a 128-bit integrated RAM. Whereas with an InP-based multi-bit RAM, where the intrinsic Q (including absorption loss in BH) and loaded Q are only 5 10 4 and 1 10 4, respectively, the resulting Δλ c, 3Δλ c, 4Δλ c are 0.155, 0.465, and 0.62 nm, respectively. This is why we employed a 32-bit RAM design with ~1 nm cavity mode spacing. We believe that by further enhancing the cavity Q factor and developing the nanofabrication resolution, we will be able to increase the number of bits in a photonic crystal wavelength-addressable RAM. 4 NATURE PHOTONICS www.nature.com/naturephotonics

SUPPLEMENTARY INFORMATION 2. Details of the empirical tuning model for L3 (Lx) cavity The initial design of an L3 cavity was numerically optimised by finite-difference time-domain simulations. The setting is described in the legend of Fig. 2. Refractive index values of Si (3.46), InP (3.17) and InGaAsP (3.46) were assumed. The essence of our empirical tuning model shown in Fig. 1 is an inward shift of A (s1~0.050a) combined with large outward shifts of B and C. Q is very sensitive to s1 and s2 and, because of the simulation error, the set (s1, s2), which maximizes Q, differs in the simulation and the experiment. So the trial and error fine-tuning of s1 and s2 was performed empirically in the experiment and they were partly optimised when we fabricated a nanocavity memory sample. As described in Methods the loaded Q of L3 cavities in the Si integrated RAM sample (before the post-tuning) was 9 10 5 and subsequent fine-tuning in another sample increased the experimental Q of the Si L3 cavity to 1.0 10 6. The same empirical tuning partially optimised an InP L3 cavity with a BH (size: 300 nm 145 nm 3a) that had a loaded Q of 4.5 10 4 (s 1 :s 2 :s 3 =0.060a, 0.330a, 0) where a was 426 nm and r was 100 nm. The empirical tuning model is commonly available for any Lx cavity (x=1,2,3,4,5,6, ) formed by Si or InP (with or without BH) with significant Q enhancement in experiments, which will be reported elsewhere. Table S1 reports the theoretical Q values for the same hole tuning parameters (s 1 :s 2 :s 3 ) reported in the main text, which were employed in the experimental samples. Figures 2c and 2d report Q values higher than Table S1 since the parameters are different (s 1 :s 2 :s 3 was 0.055a:0.290a:0.030a in Si-L3 and 0.090a:0.320a:0.050a in InP-BH-L3 in the former). The shift of holes denoted B in unmodified L3 was 0.225a both in SI and InP-BH. NATURE PHOTONICS www.nature.com/naturephotonics 5

SUPPLEMENTARY INFORMATION Table S1. Comparison of cavity characteristics. In the L3 cavity, only holes denoted B are tuned and optimised. In the modified L3 cavity, holes denoted A,B,C,D,E, and F are tuned and optimised as described in the main text and Fig. 2. Type of cavity a (nm) λ c (nm) Q V eff (µm 3 ) F (nm) L3 (Si) 408 1,562 1.5 10 5 0.080 49 modified L3 (Si) 408 1,562 1.4 10 6 0.080 49 L3 (InP-BH) 434 1,568 5.6 10 4 0.076 47 modified L3 (InP-BH) 434 1.568 3.9 10 5 0.076 47 3. Detailed experimental setup for Fig. 4a (individual operation of InP-based nanocavity memories) (Figure S2) Detailed experimental setup for Fig. 4a is shown in Fig. S2(a). A part of the description of this setup is given in Method. Here, we add more detailed description which is not given in Method. Optical power of a write pulse was appropriately adjusted with an erbium-doped fibre amplifier (EDFA), a band-pass filter (BPF) with a 0.3-nm spectral width, and a variable optical attenuator (VOA). Input signals were merged by optical couplers. A couple of lensed fibres were used for input/output coupling to waveguides on a PhC chip 11. The waveforms of the optical input which we used for the experiment in Fig. 4a is shown in Figure S2b. These patterns were defined by function generators. 6 NATURE PHOTONICS www.nature.com/naturephotonics

SUPPLEMENTARY INFORMATION Figure S2 Experimental setup for Fig. 4a (individual memory operation). a: Setup configuration. b: Input waveform consisting of the bias light with negative reset pulses (blue), write pulses (red), and read pulses (green). c: Magnified waveform of each light. 4. Detailed experimental setup for Fig. 4b (simultaneous 4-bit RAM operation) (Figure S3) To demonstrate a WDM operation of multi-bit RAM that different 4 bits can be simultaneously addressed as shown in Fig. 4b, we injected multi-wavelength light into the chip. Although a simplified setup is already shown in Fig. 4b and described in Method, here we show a more detailed setup in Fig. S3. In this demonstration, we chose NATURE PHOTONICS www.nature.com/naturephotonics 7

SUPPLEMENTARY INFORMATION Figure S3 Experimental setup for simultaneous 4-bit RAM operation. the sequential resonant channel sets of {λ 2, λ 3, λ 4, λ 5 } and {λ 18, λ 19, λ 20, λ 21 } where the subscript indicates the cavity mode number as shown in Fig. 3b. Four laser sources were used to generate a bias light with a 50-ns-wide reset pulse, and four other laser sources were also used for write pulses having a width of 100 ps. Read pulse train consisting of all four channels with a pulse width of 100 ps were also generated by four other laser sources and were provided 200 ns after the write pulses. Waveform of each light pulses are shown in Fig. 4b. For the channel set {λ 2, λ 3, λ 4, λ 5 }, the bias power, write pulse energy, and read pulse energy were 8.3 12 µw, 160 250 fj, and 50 70 fj, respectively. The wavelength detuning of the bias light, write pulse, and read pulse were in the -0.52-0.38, -0.17-0.13, and -0.08-0.02 nm ranges, respectively. In contrast, 8 NATURE PHOTONICS www.nature.com/naturephotonics

SUPPLEMENTARY INFORMATION for the channel set {λ 18, λ 19, λ 20, λ 21 }, the bias power, write pulse energy, and read pulse energy were 6.5 13 µw, 180 270 fj, and 50 70 fj, respectively. The wavelength detuning of the bias light, write pulse, and read pulse were in the -0.60-0.55, -0.18-0.06, and -0.07-0.03 nm ranges, respectively. All these lights were coupled and injected into the PhC memories. The output read pulse trains were observed by using a sampling oscilloscope with an EDFA and a BPF. The output read pulse trains, as shown in Fig. 4b, clearly demonstrated that only the written channels were stored and regenerated. Therefore, we successfully demonstrated a WDM memory operation for a different set of 4 channels without any crosstalk. 5. Bias light wavelengths in multi-bit nanocavity RAM operations Table S2. Bias light wavelengths in the 28bit InGaAsP/InP BH nanocavity DRAM operation shown in Fig. 4a. Integer numbers shows cavity (memory) number. The fraction immediately below the number shows corresponding bias light wavelength (unit: nm). 1 2 3 4 5 6 7 8 1540.56 1541.20 1542.13 1543.12 1543.95 1544.92 1545.07 1545.59 9 10 11 12 13 14 15 16 1546.74 1548.47 1549.51 1550.02 1550.90 1551.14 1551.67 1552.69 17 18 19 20 21 22 23 24 1553.88 1554.31 1555.02 1555.57 1556.88 1557.77 1559.55 1560.60 25 26 27 28 1561.13 1562.77 1564.51 1565.19 Table S3. Bias light wavelengths in the 105bit Si nanocavity DRAM operation shown in Fig. 6. NATURE PHOTONICS www.nature.com/naturephotonics 9

SUPPLEMENTARY INFORMATION 1 2 3 4 5 6 7 8 9 10 1543.098 1544.196 1544.480 1545.019 1545.493 1546.100 1546.283 1546.283 1546.734 1546.831 11 12 13 14 15 16 17 18 19 20 1546.976 1547.145 1547.357 1548.162 1548.922 1549.248 1549.396 1549.396 1549.744 1549.838 21 22 23 24 25 26 27 28 29 30 1549.933 1550.218 1550.523 1550.639 1550.687 1551.311 1551.464 1551.568 1552.157 1552.659 31 32 33 34 35 36 37 38 39 40 1552.741 1553.320 1553.422 1553.566 1553.642 1553.699 1553.909 1554.487 1554.864 1555.029 41 42 43 44 45 46 47 48 49 50 1555.442 1556.157 1556.330 1556.414 1556.656 1556.790 1557.754 1558.019 1558.092 1558.197 51 52 53 54 55 56 57 58 59 60 1558.386 1558.725 1558.999 1559.055 1559.347 1559.412 1559.866 1560.600 1560.805 1561.073 61 62 63 64 65 66 67 68 69 70 1561.277 1561.320 1561.533 1561.988 1562.163 1562.163 1562.384 1563.120 1563.178 1563.288 71 72 73 74 75 76 77 78 79 80 1563.409 1563.558 1564.157 1564.434 1564.723 1564.930 1565.295 1565.462 1565.686 1566.265 81 82 83 84 85 86 87 88 89 90 1566.425 1566.503 1566.604 1566.996 1567.452 1567.558 1567.990 1568.332 1568.539 1568.803 91 92 93 94 95 96 97 98 99 100 1568.928 1569.075 1569.392 1569.525 1569.693 1570.386 1570.662 1570.908 1571.063 1571.472 101 102 103 104 105 1571.500 1571.847 1571.915 1572.043 1572.262 Reference 1 Nozaki, K. et al., Ultralow-power all-optical RAM based on nanocavities, Nature Photon. 6, 248 252 (2012). 10 NATURE PHOTONICS www.nature.com/naturephotonics