SUPPLEMENTARY INFORMATION

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1 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 1

2 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

3 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 nm, which generates a wavelength shift Δλ of ~0.25 nm. Here, the maximum NATURE PHOTONICS 3

4 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 and , 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 and , 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

5 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 and subsequent fine-tuning in another sample increased the experimental Q of the Si L3 cavity to 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 (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 5

6 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, modified L3 (Si) 408 1, L3 (InP-BH) 434 1, modified L3 (InP-BH) 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

7 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 7

8 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 µw, fj, and fj, respectively. The wavelength detuning of the bias light, write pulse, and read pulse were in the , , and nm ranges, respectively. In contrast, 8 NATURE PHOTONICS

9 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 µw, fj, and fj, respectively. The wavelength detuning of the bias light, write pulse, and read pulse were in the , , and 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) Table S3. Bias light wavelengths in the 105bit Si nanocavity DRAM operation shown in Fig. 6. NATURE PHOTONICS 9

10 SUPPLEMENTARY INFORMATION Reference 1 Nozaki, K. et al., Ultralow-power all-optical RAM based on nanocavities, Nature Photon. 6, (2012). 10 NATURE PHOTONICS