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# Calculating with light using a chip-scale all-optical abacus

Nature Communicationsvolume 8, Article number: 1256 (2017) | Download Citation

## Abstract

Machines that simultaneously process and store multistate data at one and the same location can provide a new class of fast, powerful and efficient general-purpose computers. We demonstrate the central element of an all-optical calculator, a photonic abacus, which provides multistate compute-and-store operation by integrating functional phase-change materials with nanophotonic chips. With picosecond optical pulses we perform the fundamental arithmetic operations of addition, subtraction, multiplication, and division, including a carryover into multiple cells. This basic processing unit is embedded into a scalable phase-change photonic network and addressed optically through a two-pulse random access scheme. Our framework provides first steps towards light-based non-von Neumann arithmetic.

## Introduction

In this work, we demonstrate a key component in this quest, namely an integrated all-optical abacus-like arithmetic calculating unit. Our approach is based on the progressive crystallization of nanoscale phase-change materials (PCMs) embedded with nanophotonic waveguides. PCMs have been the subject of intense research and development in recent decades, mainly in the context of re-writable optical disks and non-volatile electronic memories8,9,10. A key feature for such applications is the high contrast in both the electrical (resistivity) and optical (refractive index) properties of PCMs between their amorphous and crystalline states8,9,10. The high refractive index contrast means that if we place PCMs onto nanophotonic waveguides, we can switch them between states using optical pulses sent down the waveguide, and readout the resulting state optically too. Previous work has used such an approach to demonstrate integrated all-optical memories11, 12. Here we show that processing and storage is in fact possible, demonstrating an on-chip abacus-like photonic device that simultaneously combines calculation and memory. We carry out base-10 additions and subtractions (including carryover) in a single PCM-cell using picosecond optical pulses and energies in the sub-nano-Joule range. We also demonstrate successful random user-selective access to each PCM-cell in a two-dimensional array. Moreover, our approach is scalable and could provide photonic integrated circuits with devices that are reconfigurable, namely can be operated as memory, switches, and calculation units, perhaps providing the first steps towards the optical equivalent of electronic field-programmable gate arrays (FPGAs).

## Results

### A phase-change material nanophotonic abacus

In our all-optical approach which mimics the central element of a non-von Neumann arithmetic calculator, the abacus beads are represented by ‘quanta’ of crystallization in a phase-change material (PCM) cell8, 13. Sliding of a bead to the left/right is thus represented by stepwise amorphization/crystallization14 which can be triggered by nanosecond, picosecond or even femtosecond optical pulses15,16,17. Due to the large refractive index contrast between the amorphous and crystalline phase of PCMs18, the crystallinity and thus the stored quanta can be conveniently read-out by optical means. This concept is sketched in Fig. 1a which illustrates the addition ‘7 + 3 = 10’ as a simple example of a calculation in base ten with carryover. Two phase-change cells are used to represent the first (depicted red) and second (depicted blue) digit of the used base-10 system used. Initially, both cells are in the amorphous phase which represents the number 0. In the first step, as many recrystallization steps as the first summand, seven in this case, are initiated in the red PCM-cell by appropriately designed optical pulses. Subsequently, recrystallization steps equivalent to the second summand, 3, are carried out which eventually result in full crystallization. In analogy to the abacus where at this point all the red beads are shifted back to the left and one blue bead is slid to the right (a carryover), the red PCM-cell is now amorphized (by a single more intense optical pulse) and in the blue PCM-cell one crystallization step is performed. Arithmetic calculations and data storage are therefore carried out simultaneously in the self-same PCM-cell. This allows us to avoid the well-known von Neumann bottleneck that plagues conventional computers, in which data has to be continually transferred between memory and CPU during and after a calculation19, 20.

We implement the abovementioned photonic abacus out of phase-change devices12, 21 integrated into the chip-scale photonic networks sketched in Fig. 1b. Integrated optics provides a scalable platform to implement a fast and random-access architecture that can also eliminate heating and latency issues associated with electrical interconnects22, 23. The rectangular waveguide array with a PCM-cell realized at every waveguide crossing point enables selective addressing and manipulation of each of these basic arithmetic units with the sketched two-pulse switching method (described in more detail below). This crossed-waveguide approach is potentially scalable and thus readily leads to on-chip arrays capable of efficient and powerful computation. The overall size of the array is eventually limited by absorption within the PCM cells, which can be alleviated using multi-pulse addressing schemes. Figure 1c shows an atomic force microscopy image of a single waveguide crossing with its integral PCM-cell on top (red). We operate our on-chip photonic circuits at telecom C-band wavelengths (1530−1565 nm) and use picosecond optical pulses, that here for simplicity are electronically generated off-chip, to switch the PCM-cells. We note that in principle the pulse routing and generation could also be realized on-chip using heterogeneous integration with light sources and through combination with active elements available in photonic foundries24, 25. Details on the device design and the experimental set-up are given in methods section. Using this platform, we first demonstrate the operation of one basic arithmetic unit, including a carryover. We then proceed to the operation of multiple units within an array of PCM-cells, illustrating photonic random memory access.

### All-optical arithmetic processing

As shown in Fig. 2a, the single processing unit comprises a straight waveguide with a phase-change cell of 7 µm length on top (in this first demonstration we use AgInSbTe (AIST)). Due to the substantial refractive index contrast between the amorphous and crystalline state18, the optical absorption (and thus optical transmission) for light traveling down the waveguide depends sensitively on the phase-state of the cell11. This is demonstrated in Fig. 2a where the transmission through such a waveguide is plotted as the PCM-cell is taken through a full switching cycle. Starting from the amorphized state (low absorption, thus high transmission), stepwise crystallization is carried out with identical picosecond pulses with pulse energies of 12 pJ each. In the presented operation, five consecutive pulses are used for every crystallization step. Subsequently, the device is reset (reamorphization) with ten 19 pJ pulses. Single pulse mode is also possible, resulting in faster and lower energy operation, but with lower optical contrast (Supplementary Note 3).

The first all-optical arithmetic operation we demonstrate is base-10 addition of ʻ6 + 6ʼ, cf. Fig. 2b. Starting from state 0, pulse sequences equivalent to the first summand are sent into the waveguide which sets the PCM-cell to level six. Then the second summand is added by sending in the corresponding pulses. When reaching the tenth level, the PCM-cell is reset to level 0 before the rest of the input sequence is applied. While resetting the cell, one pulse sequence is sent to a second PCM-cell representing the next highest order multiple of the base to store the carryover information (not shown in the graph). At the end of the calculation, the shown PCM-cell is at level 2 while the second PCM-cell is at level 1, revealing the expected answer of ‘12’. Next, in Fig. 2c we demonstrate multiplication of ʻ4 × 3ʼ. Since this operation can be implemented by successive addition, the scheme is analog to the already presented procedure. As expected, the final states of the PCM-cells after 4 successive pulse sequences and one carryover are ‘2’ and ‘1’, thus representing the correct result ‘12’.

As mentioned above, the carryover is stored in a second PCM-cell and arithmetic operations with more than a single digit can be performed using multiple cells and exploiting the additional computational power and efficiency that comes with operating directly in base ten. Each cell represents a single place value (ones, tens, hundreds, and so on) corresponding to the different rods of an abacus. Figure 3a shows the experimental pump-probe set-up used for two-digit operations including the carryover to the second PCM cell. To detect the cell-states a continuous wave probe laser is used and the optical transmission through the PCM-cell is monitored with a photodetector. As in the previous experiments (above), the pump pulse to switch the cells is picked from a picosecond-laser. The pulse which was formerly used to operate the first phase-change cell is now split in two (here off-chip, but this could in the future also be carried out on-chip, for example with a Y-splitter) and guided to both PCM-cells. If the splitting ratio is adjusted in an appropriate way (which we accomplish by using optical amplifiers), the part of the energy of the crystallization pulse for the first element which is sent to the second cell does not induce a phase transition. In contrast, if the high energy amorphization pulse is sent to the first element, a crystallization step is induced in parallel in the second cell and thus it directly stores a carryover. Figure 3b now shows a subtraction example carried out directly in base-10 and with two digits (see Supplementary Notes 5, 6 for additional information). Here we use the numbers complements approach which requires addition routines only26. We subtract ʻ17ʼ from ʻ74ʼ (which of course should yield the answer ‘57’) by adding ʻ17ʼ to the nine’s complement of the minuend ʻ74ʼ, which is ʻ25ʼ. In a first step, we set the state of the two PCM-cells corresponding to the minuend. Because we use the nine’s complement we switch the first cell (ones) to ‘5’ and the second cell (tens) to ‘2’, so that the phase states of the two elements now hold the value ‘25’. Now the subtrahend ‘17’ is added, consisting of a single crystallization pulse in the second cell and seven pulses sent to the first cell. After five of these seven pulses, the ‘full’ crystalline level in the first cell is reached and storage of the carryover is performed. The reset pulse for cell one is now utilized to induce a crystallization step in the second cell (representing the tens), as described above. After sending all the required pulses, as above, the phase states of the PCM-cells represent the value ‘42’ which is the nine’s complement of ‘57’, the correct result of the subtraction. In this example only single pulses per step with energies of 10 pJ for crystallization and 20 pJ for amorphization were used, showing that in total 15 steps were needed for the calculation with an accumulated calculation time of less than 15 ns, assuming that a single switching event for picosecond pulses takes place in less than a nanosecond as shown in ref. 12. The speed of operation is only limited by the crystallization and cooling time of the phase-change material and approaches the GHz-regime when using picosecond pulses. In our experiments, the pulses were generated with an electronically triggered pulse picker and were sent, for ease of demonstration, manually to the photonic abacus device. This led to artificially long overall operation times (for the completion of calculations) of the order of seconds. However, we note that the ancillary circuit needed to perform the necessary signal generation, as well as the detection of the carryover, can be envisaged and implemented on chip as well in future work to exploit the speedup potential of the PCM-based photonic abacus.

Assuming that division is repeated subtraction, all four basic arithmetic operations can thus be executed with our on-chip device. As shown in Supplementary Note 4, we can also use other number bases should this be desirable and/or suited to a particular problem.

## Discussion

Our on-chip abacus-like all-photonic calculator simultaneously combines calculation and memory in a single PCM cell and can operate directly in arbitrary bases using picosecond pulses. Convenient stepwise calculations can be performed using single-optical pulses with the same pulse energies for each step, leading to potential GHz operation speeds. Such multistate compute-and-store capability can set the stage for a new generation of fast and efficient Turing-complete arithmetic processors. The extraordinary properties of PCMs, e.g., stability of the phase-state for years13, sub-ns crystallization times33, sub-pJ switching energies34, and endurance potentially up to 1015 cycles35, hold promise for ultra-fast, low-energy all-optical processing. Our concepts are scalable so as to deliver large-scale photonic processing networks, for example by using the crossed-waveguide array approach that we have demonstrated here. In the current work the signal generation and detection of a carryover was achieved off-chip but can be envisaged to be completely integrated on a photonic chip, removing the need for time and energy sapping electrical-optical conversions, as well as leveraging the significant benefits of light-based systems, such as ultra-fast, ultra-high bandwidth, and low-energy signaling. Taken in tandem with the rapid progress being made in the silicon photonics field, our work presages a new generation of light-based arithmetic processors.

## Methods

### Device fabrication

The phase-change photonic devices presented in this work are fabricated using a three-step electron-beam (e-beam) lithography (EBL) procedure with a 50 kV EBL system (JEOL 5300). In the first step, alignment markers are deposited on top of a commercially purchased silicon wafer (Rogue Valley Microdevices) with a 330 nm Si3N4, 3334 nm fused silica layer stack. The marker areas are defined by EBL in the positive tone e-beam resist Polymethylmethacrylat (PMMA). After 2 min development in 1:3 MIBK:Isopropanol, ~5 nm chromium and ~120 nm gold are e-beam evaporated to achieve good contrast for high-precision alignment. The PMMA is then removed by lift-off in acetone. In the second step, photonic circuitry is defined in the negative-tone e-beam resist ma-N 2403. The resist is developed in MF-319 for 60 s and then placed on a hotplate at 110 °C for 2 min to reduce the surface roughness. Afterwards, the mask pattern is transferred into the silicon nitride layer by reactive ion etching in CHF3/O2 plasma and the remaining resist is removed by oxygen plasma subsequently. In all devices the silicon nitride layer is fully etched down to the underlying silicon dioxide. Finally, masking windows for the PCM-cells are opened in another PMMA-based EBL-step. Then 10 nm of PCM are sputter deposited and subsequently capped with another 10 nm indium tin oxide (ITO) film to prevent oxidation. The deposition was carried out with a Nordiko sputter system from commercially purchased targets. The GST (2.5″ solid target purchased from Super Conductor Materials, USA) was deposited at 30 W DC with a rate of approximately 3.6 nm/min, the AIST (2.5″ target purchased from Super Conductor Materials, USA) at 30 W DC with approximately 3.4 nm/min and the ITO (3″ target purchased from Testbourne, UK) at 120 W DC with ~11 nm/min. Finally, the PMMA is removed in another aceton-based lift-off and the PCMs are crystallized by placing the chip on a hotplate at 250 °C for more than 10 min.

The on-chip optical devices are fabricated with a waveguide width of 1.2 µm and therefore operated in single mode at a wavelength of 1550 nm. Focusing grating couplers are used as input and output ports for transmission and switching experiments.

### Measurement set-up

The set-up used to switch and characterize the phase-change photonic circuits is shown in Supplementary Fig. 1 and consists of two optical paths. The first path contains the probe light (colored red) which is used to perform transmission measurements and therefore allows us to monitor the phase state of a PCM-cell. Light from a continuous wave (CW) laser (Santec, TSL 510) is coupled into the on-chip waveguide via focusing grating couplers inscribed at the ends of each waveguide. Before coupling into the waveguide the polarization is adjusted to match the desired mode profile within the on-chip waveguide. After passing the on-chip device, the transmitted light is detected by a low-noise photodetector (New Focus, Model 2011).

The second measurement path is the one for the pump light (colored blue) and is used to generate optical pulses to switch the PCM-cells. A pulse picker, consisting of an acousto-optic modulator (Gooch and Housego, Fibre-Q T-M200) controlled by an electrical pulse generator (Agilent, HP 8131 A) and a computer is used to select optical pulses on demand from a modelocked picosecond laser (Pritel, FFL Series) working at a repetition rate of 40 MHz with a pulse length of about 1 ps. Behind the pulse picker, the selected pulses are split by a 50:50 beam splitter and separately amplified by low-noise erbium-doped amplifiers (Pritel, LNHPFA-33). To control the time delay at which the pulses arrive at a PCM-cell an optical delay line (OZ Optics, ODL-300) is inserted into one optical path. Separation of the pump pulses and the probe light for independent off-chip detection is achieved by means of optical circulators which are used to guide pump and probe light to different detectors. The picosecond pulses are recorded with a 12 GHz photodetector (New Focus, Model 1554-B) and a high bandwidth 6 GHz oscilloscope (Agilent infiniium, 54855 A). This allows us to measure the time delay between the two pump pulses and thus to match their arrival time at a PCM-cell in the two-pulse switching scheme described in the main text.

Prior to arithmetic operations, the PCM-cell is conditioned by repeating the switching cycle several times to achieve good reproducibility, as already described in previous work12.

### Data availability

All relevant data are available from the authors.

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## Acknowledgements

Additional data supporting the conclusions are available in Supplementary Materials. The authors acknowledge support by Deutsche Forschungsgemeinschaft (DFG) grants PE 1832/2-1 and EPSRC grant EP/J018783/1. M.S. acknowledges support from the Karlsruhe School of Optics and Photonics (KSOP) and the Stiftung der Deutschen Wirtschaft (sdw). C.R. is grateful to JEOL UK and the Clarendon Fund for funding his graduate studies. H.B. acknowledges support from the John Fell Fund and the EPSRC (EP/J00541X/2 and EP/J018694/1). The authors also acknowledge support from the DFG and the State of Baden-Württemberg through the DFG-Center for Functional Nanostructures (CFN). The authors thank S. Diewald for assistance with device fabrication.

## Author information

### Author notes

1. J. Feldmann and M. Stegmaier contributed equally to the work.

### Affiliations

1. #### Institute of Physics, University of Muenster, Heisenbergstr. 11, 48149, Muenster, Germany

• J. Feldmann
• , M. Stegmaier
• , N. Gruhler
•  & W. H. P. Pernice
2. #### Department of Materials, University of Oxford, Parks Road, Oxford, OX1 3PH, UK

• C. Ríos
•  & H. Bhaskaran
3. #### Department of Engineering, University of Exeter, Exeter, EX4 QF, UK

• C. D. Wright

### Contributions

W.H.P.P., H.B., and C.D.W. conceived the experiments. N.G. and C.R. fabricated the samples with the help of M.S. and J.F. J.F. and M.S. performed the measurements. All authors discussed the results and wrote the manuscript.

### Competing interests

The authors declare no competing financial interests.

### Corresponding author

Correspondence to W. H. P. Pernice.

## Electronic supplementary material

### DOI

https://doi.org/10.1038/s41467-017-01506-3