Digital optical processing of optical communications: towards an Optical Turing Machine

3.1.1 Density

Communication over long distances requires symbols with a high density, i.e. where each symbol is one of a large set; thus, each symbol encodes many bits [9], [23]. Commercial modulating electronics typically achieves rates up to 40 G symbols/s, and a binary encoding would limit an optical channel to 40 Gb/s. Parallel channels (WDM over one waveguide or one wavelength over multiple waveguides) can be used over short distances, but variation of dispersion, loss, and latency between different channels or fibers typically limits their use to datacenter scales or low data rates (10 Gb/s per channel).

Germanium electronics can modulate optics at higher frequencies, up to the serial electronic limit of 600 GHz. Unfortunately, use of such signals at the necessary voltage ranges (e.g. to drive a Pockels cell) often results in the driver circuit becoming a (very inefficient) transmission line because the drive signal wavelength approaches the length of the interconnect. At 600 GHz, the 1/10 wavelength rule of thumb indicates that traces longer than 30 μm become transmission lines. As a result, there are only two ways to achieve high density – either natively convert parallel electronics into multibit symbols (e.g. quadrature phase-shift keying – QPSK) or optically multiplex binary-modulated streams. OTM assumes the former may be possible, but explores the latter in Section 5.2.3.

3.1.2 Regeneration

Regeneration is needed to support communication over large geographic distances. It enables long-distance transmission by recovering symbols before they become ambiguous by both increasing the OSNR and restoring power. This is already a very active area of current optical processing research [24], [25], [26], [27].

3.2.1 Processing

Computational processing requires functions that support the processing operations required for a field [2]. Although simple operations support basic counting, the full power of a field is required for error detecting/correcting checksums, encryption, and authentication.

In discrete mathematics, a field is a set of symbols and two binary operators (i.e. two-input functions). The symbol set is closed under both operators, each operator has an identity element (a·I=a), and every element of the set an inverse under each operator (a·a⁻¹=I). Both operators are commutative (a·b=b·a), and one operator is distributive over the other [a·(b°c)=(a·b)°(b·c)].

A field defines common arithmetic. It is also the foundation of most mechanical and electronic computing, whether in high-density symbols (e.g. decimal for the Eniac) or binary (Boolean logic). Because these are all based on the same abstract concept, they all easily support the same common arithmetic and logic operations. Other, more obscure mathematics have been considered, including residue arithmetic [28] and directed logic (which replaces scalars with vectors) [29]; however, neither provides a sufficient advantage for optics over that of a basic field.

Support for a field requires considering how its symbols are represented and how they are processed by its binary operations. Information is represented as a set of discrete symbols and a value mapping (a value assigned to each symbol). Candidate encodings include optical phase (e.g. PSK; Figure 8, right) and {phase, amplitude} pairs (e.g. QAM; Figure 8, left). Value maps assign specific information to each symbol (e.g. numbers in Figure 8).

Figure 8:

Encoding impact on state transition properties.

Binary operations can be performed by switching or transformation, and optics can support high symbol rates only through the use of wave mixing transformations. Transformation processing is simpler with continuous, uniform transitions between its states (Hamiltonian paths). Such processing strictly requires unambiguous Hamiltonian paths; otherwise, on the way between transitions, the transformation device would enter a state with multiple outcomes, and the result of the computation would be ambiguous.

Different encodings can enable or impede these binary operations [30]. Consider the “+1” Hamiltonian path whose values increase by 1 (shown as the dashed paths in Figure 8). The PSK path is continuous, uniform, and unambiguous; the transitions are in the same relative direction, each transition is the same relative phase shift, and the path never crosses itself. The QAM path has discontinuities – short jumps (3–4, 7–8, 11–12), and a large jump (15–0). None of the transitions can be represented as a single transform of either absolute or relative amplitude-phase pairs. The QAM path also crosses itself in five different places. This is why M-PSK encodings can support field operations, whereas QAM cannot.

3.2.2 Composition

A field also relies on the ability to chain its operations, where the output of one operation is cascaded into others. This enables creating complex functions through the composition of simpler ones [17]. Composition requires that information be regenerated, to avoid the accumulation of noise during this cascade.

There are a variety of ways to regenerate symbols, i.e. to restore power levels and OSNR, so the information can be distinguished from background noise. Some methods rely on pilot signals that experience the same noise as the data; others remove noise by taking the differential of the signal (the difference between symbols). In the latter case, relatively stationary noise accumulated through transmission or processing can be removed because it cancels out between adjacent symbols.

3.2.3 State

All computations beyond combinatorial logic require a state that persists, even if temporarily [1]. A single state is required for an FSM, many states accessed in a limited way (the value on the top of a “stack”) for a PDA, or arbitrary access to a “tape” of many states for TMs. In all cases where the state exists, that state depends on previous input data and affects the interpretation of subsequent input – i.e. it is effectively a time-delayed recirculation of information. Without a persistent state, only combinatorial functions can be generated; all feedback would be prohibited. This feedback enables recursion, a key requirement for general-purpose computation.

There are various forms of storage that can be used for optical data. Permanent storage, with arbitrary persistence, requires conversion of the optical signal to another form (e.g. electronic) because photons cannot be “stopped”. Ephemeral storage, such as fiber loops, can be used instead, as long as the data can be recirculated if needed. There is a large body of work in using ephemeral storage, beginning with acoustic waves in mercury delay lines in early electronic computers and in recent reservoir computing [31].

It may be important to also assume a complete reconsideration of computation architecture based on these capabilities combined with the serial nature of communication. Current architectures focus on increased parallelism and synchronous, phased operation due to the use of switched, highly integrated transistor systems. Digital processing of optical communication streams is better matched to asynchronous serial processing.

3.2.4 Control/programmability

A computational device can be fixed, supporting only a single algorithm, or can be reconfigurable to support the entire variety of algorithms available for a given level of complexity. For in-transit computation, reconfigurable devices are much more useful because the specific forwarding, data filtering, or cryptographic operation is very likely to vary. This reconfiguration can be accomplished either by changing the signal path directly (known as “rewiring”, even for optical systems) or by using some portion of the data (known as a “program”) to control the signal path. The latter falls into two general classes: using program data that is distinct from the processed data (called the “Harvard” architecture) and treating program and processed data as co-mingled (called the “von Neumann” architecture). It is important to appreciate that all three of these variants – rewiring, Harvard, and von Neumann – have equivalent capabilities.

Rewiring is easy to achieve in an optical system using any type of deflection switch controlled by a configurable state [1]. The state need not be represented optically, as it applies only to reprogramming. The deflection switch need not be fast or lossless (i.e. it can interrupt the signal flow), as it can be used only when reconfiguring an entire system. This allows the use of a variety of optical switches for reconfigurability, including MEMS.

5.1.1 Hop-count decrement and checksums

The simplest network function is hop-count processing. Packets contain a hop count (a.k.a. “time to live”) field to ensure that forwarding loops and misdirected traffic does not overload the network [36]. Each packet is given an initial count (e.g. 255), which is decremented at each hop visited. When the count reaches zero, the packet is silently discarded. This avoids the need for a coordinated mechanism to flush out stale packets.

Hop-count processing is currently implemented using either a general-purpose CPU or complex, dedicated bit-parallel arithmetic hardware. Subtraction is typically implemented as addition of “−1”, a complex operation cascading “carries” across the bit field in parallel, similar to the approach shown for parallel addition in Figure 9 (left).

A simpler approach is possible when processing the data serially, using only three active components (Figure 10). Subtraction of an unsigned bit field involves inverting the “0” values (starting at the low-order bit) until the first “1” value is encountered. That value is inverted, and all subsequent inputs are copied (Figure 10, left). The entire system can be implemented using only three active elements (Figure 10, right) – an inverter, a 2×2 switch, and a set-reset (S/R) flip-flop (FF). The switch is set to select the inverted input until the first “1” bit arrives. That bit sets the flip-flop, whose output is delayed by one symbol to change the switch just before the next symbol. After the change, the input is copied to the output without inversion.

Figure 10:

Serial ones-complement subtraction.

Our team implemented this mechanism for a binary OOK encoding, using an electronic S/R FF (Figure 11) [36]. All-optical OOK micro-ring S/R FFs have been demonstrated [37], but were too costly to replicate.

Figure 11:

Optical packet hop-count decrement.

The mechanism has been extended to support M-PSK multibit encoding, replacing inversion by a “−1” transformation, and all of the optical components already exist for M-PSK encodings. For example, “−1” transform for 8PSK encoding is a −π/4 phase shift that can be accomplished using a fixed difference in signal path, e.g. of 187.5 nm for a 1500 nm wavelength signal. The OOK micro-ring flip-flop can be extended to support M-PSK encoding using phase interference with a reference signal as input, and a Mach-Zehnder modulator can serve as an optical switch that can be controlled using an independent M-PSK input (i.e. the flip-flop output).

Internet packet routers support hop-count processing, but also rely on other, more complicated functions. One such function is a checksum, a mathematical function that validates that the contents of a message have not been corrupted in transit. There are a wide variety of such checksums used in various protocol layers, including cyclic redundancy checks (CRCs, as for Ethernet and Bluetooth), parity (a 1-bit CRC, as for memory checks), and very complex hash functions (e.g. MD5, SHA-1) that also detect deliberate tampering. Parity and CRCs are very simple operations using position-based symbol feedback and serial modular arithmetic (shown as an XOR symbol), and are already well suited to all-optical implementation (Figure 12). The key challenge to their computation is maintaining signal integrity through the feedback of state, i.e. regeneration. Note that Figure 12 depicts a binary implementation using XOR gates; multibit encoding would use optical adders for modular arithmetic [38].

Figure 12:

Parity and CRC via simple serial feedback circuits.

The Internet checksum is of particular interest as it is used for IP version 4 packet header error detection and as a check on the entire end-to-end message at higher protocol layers, e.g. TCP and UDP [6]. This checksum is a 16-bit one’s complement sum of the message, i.e. the entire message is added as adjacent byte pairs of 16 bits. The summation function is one’s complement, which differs from the more familiar two’s complement arithmetic by looping its high-order (most significant bit) carry-out back around as a low-order (least significant bit) carry-in. This feature of one’s complement summation enables a simple serial design.

When computed on two’s complement hardware, a one’s complement sum is typically computed using a larger accumulation register (e.g. 32 bits). As values are added into the accumulator (in bit-parallel), the high-order carry-out bits accumulate in the top half of the register. When the computation is complete, the carries are “folded over” and added back into the bottom half of the register. This operation is simple in typical two’s complement hardware; however, it is even easier in one’s complement, where the entire checksum can be computed using a single “full adder”, i.e. one device that adds two symbols and a carry-in, and generates the sum and a carry-out (Figure 13). This serial circuit relies on delay and recirculation to overcome the need for one adder per bit position and complex carry-look-ahead, as is needed in the corresponding parallel circuit (Figure 9). Because one’s complement accumulates carries through wrap around, there is no need to reset the circuit as bits are summed in series; instead, the carries wrap around (from Co to Ci) the same way as the partial sum (from S to Yi).

Figure 13:

Serial, optics-friendly Internet checksum.

The primary challenge in implementing a CRC or the Internet checksum using serial optics is the need to recirculate state, which requires regeneration. An additional challenge for the Internet checksum is the need for a full adder, which is significantly complex in optics.

5.1.2 Modular arithmetic

Support for the mathematical field that is the basis of computation typically requires support for modular arithmetic, as this is the basis of the operations in the most familiar fields. In binary logic, the corresponding field is Boolean algebra, which includes addition (OR), multiplication (AND), and complementation (NOT). For fields with more than two symbols, modular operators are needed, whose outputs “wrap around”.

Members of our group previously developed modular arithmetic for M-PSK symbols [39], as depicted in Figure 14. Three symbols encoded as QPSK were added and subtracted in a non-degenerative FWM process in an HNLF (Figure 15). Three-input operations are often more useful than two-input operations, as they natively support the combination of two new values as well as a carry-in from either a previous or adjacent stage. A similar mechanism was used to extend this QPSK method to 8PSK and 16PSK encodings [38].

Figure 14:

Modular arithmetic via wave mixing concept.

Figure 15:

Modular arithmetic system design.

5.1.3 Extension to a full adder

Although modular arithmetic is useful on its own, e.g. for CRC calculations, most computing relies on the ability to extend the symbol space of a field using positional notation, so that a fixed set of symbols can represent an indefinitely large number of values. Support for positional notation requires the extension of modular arithmetic to carry-based arithmetic. This evolution typically requires the design of a half-adder and full-adder, the former combining two symbols to generate a sum and carry-out symbols and the latter combining three symbols: two input symbols and a carry-in symbol. It is a basic exercise to extend binary half-adders to create a full adder, using two half-adders and an OR to merge the carry-out values (Figure 16, left). A less typical design can combine multivalued (i.e. so-called “multibit”) half-adders to create a corresponding full-adder; however, this design requires three half-adders (Figure 16, right). The final carry-out (Co) of the last half-adder is never active and can be ignored.

Figure 16:

Full adders via half-adder composition.

Half-adder and full-adder designs rely on both modular arithmetic (for the sum) and carry generation. Modular addition loses the information needed to indicate whether a carry is needed or not, e.g. for 8PSK, 1+2=3 but also 6+5=3 (Figure 17). In M-PSK modular addition, no part of the FWM “remembers” whether the phase simply rotates as needed (1+3) or “wraps around” (6+5).

Figure 17:

Loss of carry context during modular add.

Our team has proposed a method to determine whether a carry is generated or not. The goal is to keep track of whether the accumulation of phase would have “wrapped” or not. This approach first halves the original values, so that instead of adding 1+3 or 5+6, the values of 0.5+1.5 and 2.5+3 are computed (as shown in Figure 18).

Figure 18:

Carry context via adding half-phase.

The resulting value cannot wrap around because the inputs are at most half the maximum symbol value. The half-sum ends up either on the bottom or top half of the phase diagram (Figure 19, left). The bottom half indicates no carry and the top half indicates carry. The key is to then squeeze the phase of the half-sum to represent two distinct values (Figure 19, middle) and then shift those values to represent the appropriate carry symbols (Figure 19, right).

Figure 19:

Half-phase add transformed into encoded carry out.

The circuit for accomplishing this method is based on shifting the input symbols using a CW pump, summing the result using modular addition, and then squeezing and transforming the result (Figure 20). It demonstrates the way in which carry generation relies on phase squeezing. This circuit has been proposed and analyzed, but it is currently difficult to implement using benchtop equipment due to the number of cascaded components and the constraint that signals cannot be regenerated between the intermediate stages (as this would defeat the overall goal).

Figure 20:

Generating the carry of the sum of QPSK symbols (A) and (B) via half-sum and phase squeezing.

5.1.4 Need for recirculating state

Computation beyond simple combinatorial logic requires both retaining state and recirculating that state back into the combinatorial logic together with the input. As noted earlier, various levels of computational complexity hold state in different forms (a single value for an FSM, a stack for a PDA, or an arbitrary-access “tape” for a TM) and for different lengths of time. Even some of the simplest functions, including hop-count decrement, CRCs, and Internet checksums, all require this type of state recirculation.

This state either needs to be continually recirculated (as with an FSM) or held in a way that emulates persistent storage, which may itself require recirculation (e.g. in a delay loop). Optical signals can be delayed off-chip using fiber loops and on-chip using convoluted waveguide paths. On-chip delays are limited in length to a few centimeters; however, the capacity of that delay increases as baud rate increases, e.g. at 1 T baud, each 1 cm of waveguide can store 33 symbols.

There are many forms of “limited lookback” computation that restrict the amount of time a state is held, notably linearly bounded TMs that can leverage such limited storage. These approaches assume that state is recirculated only a limited number of times or expires after a fixed period (whether recirculated or not), which can limit the kinds of computation that they can perform.

Regeneration can be coupled with delay-based storage to extend its lifetime and/or enable increased recirculation. This is critical because most examples of computation assume arbitrary recirculation of state through the combinatorial logic and/or indefinite storage of state. A simple 8-bit binary hop count requires seven such cycles; the Internet checksum, over a typical 1500B Internet packet, could require as many as 750 such recirculation cycles. Optical signals tolerate traversing only a very small number of devices before signal integrity cannot be recovered, so regeneration is critical to supporting these advanced levels of computation for even the most basic operations. Similarly, the limitations of on-chip delays require regeneration to recycle state over longer periods.

5.2.1 Phase squeezing

Signal regeneration begins with restoring the distinctness of the symbol representations. There are a variety of methods that have been used to restore M-PSK symbols, including differential regeneration and PSA. Note that phase restoration focuses on reducing accumulated phase noise and does not address other noise sources (e.g. amplitude noise).

One of the most effective methods is differential regeneration, often referred to as “non-PSA” squeezing, in which a symbol stream is processed with a one-symbol delayed copy of itself [40] (Figure 21). This method assumes that phase noise is mostly stationary compared to the symbol stream, i.e. that adjacent symbols experience similar noise, irrespective of their symbol values. This might occur if a symbol stream is noisily amplified or if it experiences phase-insensitive transmission loss.

Figure 21:

Non-PSA phase squeezing system design.

In non-PSA squeezing, harmonics are generated in a non-linear medium (a PPLN or HNLF) using wave mixing injected pumps. In two different stages, the signal is first copied as a conjugate and then the third harmonics are generated. The conjugate and third harmonic of the original signal are delayed by one symbol, and combined using SFG/DFG processes in a final non-linear device. The resulting output is the differential of the input, i.e. it represents the difference of adjacent symbols. Because the phase noise is relatively stationary, it cancels out of this difference and OSNR is improved, as shown in Figure 22.

Figure 22:

Non-PSA phase squeezing results.

The challenge with using non-PSA squeezing is that the output is semantically different from the input. Even though both are represented using the same symbols, the meaning has changed. Computation requires that each symbol be independent, so it can be manipulated without needing adjacent context. Differential output lacks this property, and cannot support computation. Further, it is impossible to recover a non-differential equivalent, e.g. by “integrating” the output signal [32]. Doing so requires inserting reference symbols in the data stream (to provide the “constant” needed to perform integration); however, those reference values would have needed to be kept separate from the data and not participate in computation.

A different approach is to amplify signals that are close to valid symbol values and attenuate signals that are not. This is known as PSA; it does not actually correct any phase variation directly, but rather it tries to discard the portion of the signal that is slightly phase misaligned and to copy or reinforce the portion that is aligned. The particular variant explored by our team is non-degenerate PSA, which uses a distinct idler to amplify and select the desired portion of the signal [27] (Figure 23). Degenerate PSA overlaps the idler with the signal, but is more difficult to control.

Figure 23:

Non-degenerate PSA phase squeeze system design.

This system uses pumps to generate harmonics in a non-linear medium (an HNLF) and combines those pumps and signals in a SFG/DFG process in another non-linear medium (a PPLN). There are two complications to this approach – the system requires generating the harmonic in direct proportion to the number of distinct symbols – e.g. QPSK requires the fourth harmonic, 8PSK requires the eighth, and the system implementation includes an interferometer as a side effect, which is very difficult to stabilize.

The harmonic required depends on the number of symbols. Our experiments showed a 3.6 dB OSNR gain for BPSK using the second harmonic, but only a 0.4 dB OSNR gain for QPSK using the fourth harmonic (Figure 24). As symbol density increases, the harmonics become more difficult to generate and are generated less efficiently, rapidly reducing the system impact.

Figure 24:

Non-degenerate PSA phase squeezing results.

The system design includes an interferometer created because of how the signals are processed. The first non-linear process converts the signal and pump to generate the needed harmonic. An injection-locked pump is added to amplify the harmonic; however, the harmonic has a much lower power, so the harmonic needs to be separated from the other signals for the injection-locked laser to synchronize to the desired signal. This creates an interferometer – one arm where the harmonic is coupled to the injection-locked laser and another where other signals bypass that laser. This device is very difficult to implement macroscopically on an optical bench using fibers, because the system is sensitive to vibration and thermal disturbances, and the result requires active phase stabilization.

In an attempt to avoid the need for this stabilization, our group explored PSA based on Brillouin amplification [41] (Figure 25). It replaced the interferometer and injection-locked laser with a Brillouin amplifier, which has an inherently narrow band and is able to selectively amplify the harmonic only. This method achieves 11 dB OSNR gain at 1E-5 BER for 10 Gb/s BPSK, 9.1 dB OSNR for 20 Gb/s BPSK, as shown in Figure 26. Brillouin PSA remains compatible with computation because it neither changes the signal semantics nor uses reference signals.

Figure 25:

Brillouin phase squeezing system design.

Figure 26:

Brillion phase squeezing results.

5.2.2 Amplification

In addition to differentiating the symbols, it is important that each symbol be detectable. Improving the power level of the symbol is known as amplification. For M-PSK symbols, each symbol should have the same power level, so nearly any efficient amplification should suffice and will also reduce amplitude noise. However, it is important that amplification should not decrease intersymbol OSNR, i.e. it should not “spread” the phase of the symbols at the same time.

Our team explored using saturation amplification in an HNLF [40]. The results show improved signal power at the expense of an increase in phase noise. Figure 27 shows the noisy input signal, where the noisy input (left) is phase squeezed (right) using differential noise reduction (although already indicated as not viable for computation, the phase squeezing method used in this experiment is not critical to the next step), and then saturation amplified (right). This type of amplification was able to compensate for power lost during the squeezing operation; however, it also introduced phase dispersion (the right signal is “wider” than the middle). The phase noise introduced by amplification was lower than in the noisy input signal, but the overall result did not squeeze enough.

Figure 27:

Saturation amplification results.

Our team also explored using Raman amplification in an attempt to increase the signal power without introducing phase dispersion [42]. The concept is similar to the saturation amplifier, replacing the HNLF with a Raman amplifier (shown in Figure 28). The result had similar performance, resulting in a 19.3 dB gain for a −26 dBm input signal but had no significant impact on phase noise.

Figure 28:

Raman-assisted PSA system design.

5.2.3 Aggregation and deaggregation

Because phase squeezing requires harmonics linearly proportional to the number of symbols, it may not be feasible to assume symbol regeneration for very dense encodings. It may be useful to consider long-distance transmission using aggregates of less dense encodings, where signals are deaggregated for computation. This is similar to the OEO/OOO conversion that should generally be avoided, but might be necessary and useful if limited to conversions that are feasible in all-optical devices. Note that this refers to combining or splitting multiple lower-baud-rate streams (on separate waveguides or different wavelengths in a single waveguide) into a single higher-baud-rate stream on a single wavelength.

Our team explored aggregating and deaggregating (multiplexing and demultiplexing) M-PSK signals. The aggregation method (Figure 29) uses an apparatus based on phase-coherent addition (Figure 30) [43]. Both BPSK and QPSK signals were combined to generate QPSK (via two BPSKs). The approach depends on the availability of phase-locked comb sources.

Figure 29:

Aggregation concept.

Figure 30:

Aggregation system design.

Deaggregation of an M-PSK was achieved by separating the I and Q planes of the source signal, resulting in BPSK for QPSK inputs and PAM for higher-density inputs [44] (Figure 31). This system uses the apparatus shown in Figure 32, with results as shown in Figure 33. For computation, only the QPSK to BPSK conversion would be useful; the 8PSK to 4PAM output would require subsequent conversion from 4PAM to QPSK.

Figure 31:

Deaggregation concept.

Figure 32:

Deaggregation system design.

Figure 33:

Deaggregation results.

6.1.1 Phase encodings

Phase-based encoding is the only multibit optical representation that supports the operations of a mathematical field with transformations that are continuous, uniform, and unambiguous. The lack of ambiguity is needed to allow operations to have deterministic consequences. Having continuous and uniform transforms means that a single device can process a single operation, without need for conditional (value-dependent) processing.

Phase encoding is attractive for other reasons. It allows use of other encoding dimensions (such as polarization) as independent channels, potentially enabling a single device to process multiple channels concurrently. It also simplifies amplification because all symbols are represented using the same power. Receivers require phase recovery, but this is already mature and efficient.

Binary encodings also support the operations needed to implement a field but are very inefficient for communication. Their use would necessitate the same very high level of aggregation and deaggregation that would be required for OEO conversion and would render an optical computing solution uncompetitive with one using conventional electronics.

6.1.2 Digital encodings

The need for digital encodings is driven by the desire to cascade processing functions and to support state feedback. Analog systems can cascade functions, but only through a limited number of levels due to signal degradation, which constrains the computational complexity and prevents any but the most basic computational model of combinatorial logic.

Regeneration is the key to supporting digital encodings and is the largest impediment to developing effective optical computation. Current methods are complex, consume significant power, and have limited impact. There are a wide variety of approaches to regeneration, but the more efficient and effective methods – such as differential processing – fail to preserve the semantics of the symbol stream, rendering them useless for computation.

6.1.3 Wave mixing

Although phase encodings and digitization are more obviously needed, the need to use wave mixing is less so. It is driven primarily by the need to support field operations on symbols at rates that exceed that of electronics.

Wave mixing has the benefit of being able to support transformational processing transparently to the symbol coding rate. Some functions (i.e. some field operations) are completely transparent, depending only on the frequency over which the symbols are encoded. Others, such as regeneration, can depend on the symbol density (i.e. the number of distinct phase values used for encoding), but remain transparent to the symbol rate.

6.1.4 Need for state

The desire to use digital phase encoding and mixing is not uncommon for optical computation, but there is less consideration for state. The amount of state and the complexity of its state access patterns determine the computational capabilities of the resulting processing system.

A combinatorial system can never be used to identify context-dependent patterns, as are needed for the most basic packet forwarding operations or even basic data filtering beyond exact match. An FSM cannot count or support AI backtracking, so it cannot be used for triggers based on threshold levels, compression, or encryption. A PDA cannot compute recursive functions, as are sometimes needed for hash functions used for authentication.

State is the key to supporting these higher levels of computation. Many optical signal processing systems are only combinatorial, using no state feedback at all. Others have a single state, either as direct feedback or encoded in the device itself; some systems use a single such device, others an array, but all are limited to the capability of an FSM. Most in-transit operations require more than just a single state, e.g. either PDA or TM capabilities. This is why our focus is on seeking a viable approach to an OTM.

The key to supporting state for such a TM is the use of optical delays. Implemented in on-chip waveguides, these may be limited to tens-hundreds of symbols, recirculated with phase restoration. That should be sufficient for many of the kinds of algorithms that are useful for in-transit processing. Additional storage may be possible off-chip, e.g. using board-level fiber “spools”. The amount of recirculation is limited by the efficiency of symbol restoration and access to state needs to be coordinated with the symbol’s position in the delay line. The latter may require splitters and configurable delays to align stored state with incoming data. These issues are under active investigation by our team.

6.1.5 Need for hybrid integration

The desire to encode data using phase and to use wave mixing drives the need for hybrid nanophotonic integration. Benchtop systems are too difficult to stabilize because the optical paths often create multiple overlapping interferometers. Although a single interferometer can be stabilized, multiple overlapping interferometers cannot.

This extreme phase sensitivity can be avoided through nanoscale integration. Distances between components can be engineered as needed, often within <1% of a wavelength (e.g. 14-nm fabrication resolution used to implement 1400-nm-wide devices).

Passive optics can be easily fabricated on a silicon substrate, including filters, couplers/splitters, and vias. Silicon can also be used to implement detectors and some forms of wave mixing. Full processing requires pumps (to support mixing), generation, and modulation, all of which require other substrates. Integration supports stability and efficiency only when all these devices are implemented on a single underlying substrate, to enable environment control (temperature, vibration) and to avoid the coupling loss of chip-to-chip interfaces.

6.1.6 Some additional caveats

This discussion began with an assumption that optical computation should focus on in-transit operations because that might be where it would be most useful. The corollary is that optical computation is likely not useful as an end system alternative to electronics.

Optical processing already requires the use of exotic materials to do anything beyond limited passive processing. It is unfair to compare it to silicon electronics, whose frequencies have recently plateaued near 4 GHz. A more appropriate comparison would be to GaAs, germanium, or other more exotic materials, which already support switching upwards of 600 GHz.

Fast optical processing, at rates competitive with electronics, requires wave mixing, which, in turn, requires (and consumes) pumps. The power needed for these pumps suggests that optical computation should never be considered as power efficient. There is no optical equivalent of adiabatic (zero heat or friction loss) or reversible (zero energy) computing, as there is for electronics.

As a result, it seems less useful to consider optical processing as a replacement for electronics in the end system, or to seek an optical solution as a power-efficient alternative to an electronic approach.

6.2.1 Computation

Computation relies on two capabilities: the operations of a mathematical field (for combinatorial logic) and support for state recirculation (for all higher levels). Wave mixing already natively supports some of the functions that correspond to the needed field operations, including addition, subtraction, and multiplication. These functions require substantial signal manipulation, including frequency conversion, harmonics generation, conjugate generation, and the need for phase-aligned pump sources.

Carry generation is required to support positional representations. Current approaches to carry generation require a cascade of several wave mixing operations, including phase division (via phase-amplitude offset), symbol addition, phase squeezing, and output normalization. The challenge of these cascaded operations is that regeneration cannot be supported between the first three (division, addition, squeezing) operations.

6.2.2 Regeneration

Regeneration is known as the most significant challenge for optical computation. It is widely understood as needed to support function composition, to cascade processing operations, and to allow single-state feedback (to support the computational complexity of an FSM).

The need for regeneration to support state is also widely appreciated. State is a form of delayed signal recirculation and recirculation is easily seen as amplifying signal distortion. Given regeneration, state can be supported using delay, as was done in the earliest electronic computers.

Regeneration is also critical for carry generation. Carries are inherently a type of digitization, taking a set of symbols and returning either a 0 (no carry) or 1 (carry). In this case, regeneration needs to be even more powerful, collapsing previously distinguishable states.

Efficient regeneration is difficult to achieve. The power needed for phase-sensitive amplification or phase squeezing via wave mixing processes can be substantial. Denser encodings require correspondingly higher harmonics, which are increasingly inefficient to generate. This density-harmonic relationship may place an effective upper bound on the encoding density, requiring some aggregation/deaggregation to support efficient communication, but it may still retain enough symbol density to remain competitive as an alternative to binary electronics.