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Attojoule Optoelectronics for Low-Energy Information Processing and Communications: a Tutorial Review

David A. B. Miller

arXiv:1609.05510v3physics.optics

TL;DR

The paper examines how optics and optoelectronics can reduce interconnect energy, focusing on operating-energy scaling, optical concentration, integration, and system-level approaches. It concludes that sub-femtojoule devices are physically possible and that optics offers substantial opportunities for reducing information-processing and communication energy.

  • Problem

    Most energy in information processing and communications is spent sending information, especially through local electrical interconnects, creating energy-per-bit and bandwidth-density challenges inside machines.

  • Method

    The paper reviews scaling approaches for low-energy optoelectronics, including device mechanisms, optical concentration, photodetector integration, wavelength-dependent arrays, and system interconnect strategies.

  • Results

    Sub-femtojoule optoelectronic output devices are physically possible, with active volumes around (300 nm)^3 considered quite possible and (100 nm)^3 potentially viable without drastic technological efforts.

  • Takeaways & Limitations

    Optics offers substantial opportunities to reduce energy and improve performance in information systems, and may provide the only viable approach to current interconnect energy and density problems.

Abstract

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Optics offers unique opportunities for reducing energy in information processing and communications while resolving the problem of interconnect bandwidth density inside machines. Such energy dissipation overall is now at environmentally significant levels; the source of that dissipation is progressively shifting from logic operations to interconnect energies. Without the prospect of substantial reduction in energy per bit communicated, we cannot continue the exponential growth of our use of information. The physics of optics and optoelectronics fundamentally addresses both interconnect energy and bandwidth density, and optics may be the only scalable solution to such problems. Here we summarize the corresponding background, status, opportunities, and research directions for optoelectronic technology and novel optics, including sub-femtojoule devices in waveguide and novel 2D array optical systems. We compare different approaches to low-energy optoelectronic output devices and their scaling, including lasers, modulators and LEDs, optical confinement approaches (such as resonators) to enhance effects, and the benefits of different material choices, including 2D materials and other quantum-confined structures. Beyond the elimination of line charging by the use optical connections, the next major interconnect dissipations are in the electronic circuits for receiver amplifiers, timing recovery and multiplexing. We can address these through the integration of photodetectors to reduce or eliminate receiver circuit energies, free-space optics to eliminate the need for timing and multiplexing circuits (while solving bandwidth density problems), and using optics generally to save power by running large synchronous systems. One target concept is interconnects from ~ 1 cm to ~ 10 m that have the same energy (~ 10fJ/bit) and simplicity as local electrical wires on chip.

I. INTRODUCTION

Energy dissipation in information systems is shifting from logic toward interconnects, while optics is being considered for reducing both communication energy and bandwidth-density constraints. The review frames goals and research directions for optical links spanning roughly 1 cm to 10 m.

  • Motivation: Interconnect energy is becoming a dominant constraint because logic energy has fallen faster than the energy required to send information inside machines.The paper notes that 50–80% of gates on silicon chips can serve as repeater amplifiers for long interconnects.
  • Motivation: Optics is being examined for shorter links because it already supports high-capacity long-distance communication and increasingly dense links inside data centers.The review asks whether optics can reduce energy in interconnects inside cabinets and machines, not merely increase communication density.
  • Goals for this review: The review targets optical interconnects from ~1 cm to ~10 m, with energies near ~10 fJ/bit or lower and the simplicity of short electrical wires.The proposed approach also seeks enough connection density to eliminate current bandwidth bottlenecks.
  • How optics can reduce interconnect energy: Optics can reduce energy by avoiding electrical-line charging and by eliminating receiver, timing-recovery, line-coding, and multiplexing circuitry.Low-capacitance photodetectors, dense parallel optical channels, and large synchronous zones are identified as enabling mechanisms.
  • Scope: The review surveys promising device and system directions while emphasizing that its broad scope makes its references representative rather than comprehensive.It is intended to provide context and background rather than detailed coverage of every research area.

6) General conclusions on energies in information processing and communication

Electrical interconnect energy is tied to line capacitance and becomes especially costly over longer distances, whereas optics can avoid line charging and exploit photodetection, parallelism, and timing precision. These properties motivate optical interconnects as a route toward lower energy and higher density.

  • General conclusions: Most energy in information processing and communications is spent sending information rather than performing logic, with local electrical interconnects accounting for most of that energy outside wireless links.The paper therefore identifies optics as the only currently viable approach it sees for jointly addressing interconnect energy and density problems inside machines.
  • Physics of electrical interconnect energies: ~2 pF/cm (200 aF/μm) is a typical capacitance per unit length for both 50Ω coaxial cable and densely spaced on-chip interconnects.The similarity follows despite large differences in physical scale because interconnect geometries trade density against capacitance only weakly.
  • Physics of electrical interconnect energies: A wire extending only ~3 transistor widths can require as much charging energy as switching the transistor itself.Because most signals travel farther, communication rather than logic dominates dynamic energy dissipation.
  • Energies for electrical off-chip communications: Picojoules per bit are typical for off-chip electrical interconnects, with longer links reaching multiple picojoules because of more sophisticated transmitter and receiver circuits.The cited circuits include amplification, timing recovery, line coding, and serialization or deserialization.
  • Physics of optical interconnect energies: Optical links avoid charging the communication line and instead charge the detector and connected load, enabling quantum impedance conversion.A photodiode converts power in a low-impedance optical medium into power in a high-impedance electrical load.
  • Physics of optical interconnect energies: ~0.8 V output swing and optical energies below 1 fJ can be sufficient to switch a logic gate in receiverless operation.This requires low-capacitance photodetectors connected to low-capacitance loads such as CMOS inverter inputs.
  • Additional physical benefits of optics: Dense optical channels can avoid serialization and line coding, while stable optical timing can avoid clock-and-data recovery circuits.Optics also supports high-density connections and low-jitter timing over system-scale distances.

III. SCALING OPTOELECTRONICS INTO THE ATTOJOULE RANGE

The review separates optoelectronic operating energy into capacitive voltage-swing energy and other device-operation energies. It uses this decomposition to assess whether sub-femtojoule, or attojoule-range, devices are physically plausible.

  • Conclusions for scaling to attojoule optoelectronic devices: Sub-femtojoule optoelectronic output devices are physically possible using mechanisms already widely exploited technologically.The review treats the conclusion as optimistic but distinguishes physical possibility from practical implementation.
  • Energy components: Optoelectronic device operating energy is separated into electrostatic energy for voltage swings and other energies associated with running the device.The second category includes carrier injection in emitters and carrier-density changes in some modulators.

A. Electrostatic energies

Sub-femtojoule optoelectronic devices require micron-scale or smaller active dimensions and close integration with their electronics to keep electrostatic energies low. Optical concentration and scaling of established laser and modulator mechanisms offer routes toward still lower operating energies, although practical losses and device constraints remain.

  • Capacitance scaling: 1 μm semiconductor cubes have ~100 aF capacitance and ~100 aJ charging energy at 1 V, while 100 nm cubes require ~10 aJ.The estimate uses the cube capacitance scaling with dielectric constant and dimensions.
  • Device-size requirement: Micron or sub-micron optoelectronic devices are required for single-femtojoule or sub-femtojoule operation at typical logic voltages.The conclusion assumes integrated semiconductor devices are not more than ~1 μm thick.
  • Integration requirement: Connecting wires must also be only a few microns long or smaller in scale, because their capacitance can otherwise dominate the device capacitance.Photodetector connections are especially sensitive to added input capacitance.
  • Optical concentration: Optical concentration can reduce operating energy when increased electromagnetic energy density accompanies a proportional reduction in active volume.Resonators, slower group velocity, and reduced waveguide cross-sections are identified as concentration approaches.
  • Scaling outlook: Known laser and modulator mechanisms support sub-femtojoule output devices physically, with ~300 nm active volumes viewed as plausible and 10 nm cases remaining speculative.The scaling arguments include demonstrated-device energy scales and compare laser and quantum-well electroabsorption-modulator approaches.

D. Conclusions for scaling to attojoule optoelectronic devices

The scaling analysis concludes that sub-femtojoule optoelectronic output devices are physically possible using established mechanisms, but achieving their benefits requires nanoscale fabrication, intimate electronic integration, and careful management of optical concentration losses. The review compares emitter and modulator architectures as system-level design choices rather than by a single device metric.

  • Conclusions for scaling to attojoule optoelectronic devices: Sub-femtojoule optoelectronic output devices are physically possible using mechanisms already widely exploited technologically.The (300 nm)^3 active-volume range is considered quite possible, while the (10 nm)^3 case is speculative.
  • Conclusions for scaling to attojoule optoelectronic devices: Achieving the full energy benefit requires active devices in the hundreds of nanometers or smaller and very close integration with associated electronics.Optical-field concentration methods must also be assessed critically because associated loss can undermine the energy benefit.
  • Optoelectronic output device approaches: The reviewed architectures include conventional waveguides, ring or disk resonators, surface-normal devices, vertical cavities, and Mach-Zehnder interferometers.These configurations support laser, electroabsorptive, and electrorefractive output-device implementations.
  • Qualitative comparison of light-emitters and modulators: Emitter and modulator choices involve system-level benefits and drawbacks, so a single parameter is insufficient for selecting between them.The comparison includes device configurations, optical distribution, and synchronization considerations.

B. Efficiency

Low-energy optical outputs must combine low operating energy with efficient, single-mode delivery, while the best device mechanism depends on the surrounding system. Modulators span a wide energy range: electroabsorption can be especially strong, whereas weaker electrorefractive mechanisms require longer devices or greater optical concentration.

  • Efficiency: Low-energy optical output devices must minimize total operating energy while efficiently delivering modulated optical power to the receiver.Low emitter efficiency, modulator background loss, or compensating receiver sensitivity can increase total dissipation.
  • Efficiency: Single-spatial-mode operation is important because emitted power must be efficiently delivered to the photodetector.Lasers require controlled spatial modes, while sufficiently small LEDs may make predominantly single-mode emission more feasible.
  • Light emitters: Laser designs may need nanoresonators or other optical-concentration structures, but metallic confinement can raise loss and operating energy.Small size alone is not beneficial if confinement losses compromise efficiency.
  • Modulators: 2D materials may enable large absorption changes in small volumes, but they do not currently appear to offer substantially lower device energies than quantum-well structures.Band-filling mechanisms have broadly similar energy strengths in 2D materials and quantum wells.
  • Modulators: ~10–100× weaker electrorefractive mechanisms generally require longer devices or higher optical concentration than electroabsorptive mechanisms.The comparison identifies free-carrier-plasma modulation in silicon as ~1000× weaker than QCSE electroabsorption, with a few pJ/bit versus a few fJ/bit or less in cited examples.
  • Modulators: Modulator mechanisms range from somewhat worse than laser energies to much better, including the lowest-energy microscopic output-device mechanisms.The strongest examples include QCSE and, somewhat more weakly, FKE electroabsorption effects.

V. PHOTODETECTORS AND RECEIVER CIRCUITS

Short-distance optical links must minimize total system energy, making detector capacitance and receiver-circuit dissipation central design constraints. Very low-capacitance detectors enable receiverless or near-receiverless operation, but integration and gain must be optimized together.

  • <1 fJ optical energy can switch a logic gate when low-capacitance photodetectors drive low-capacitance loads without electronic amplification.This is termed receiverless operation.
  • 170 fJ/bit at 25 Gb/s was achieved by a photodiode and receiver with approximately 30 fF total capacitance.The example operated at -14.9 dBm noise-limited sensitivity.
  • ~300 aF total receiver capacitance could convert the example’s 260 aC optical charge into a ~0.8 V logic swing, eliminating 170 fJ/bit receiver energy.The detector, wiring, and transistor input capacitances are assumed to total approximately 300 aF.
  • Near-receiverless designs balance added receiver-gain energy against the optical-source energy saved by requiring less transmitted power.About one simple, non-noise-limited gain stage might be advantageous for low-loss links with low detector capacitance.
  • Very low-capacitance photodetectors with reasonable efficiency are viable, especially with moderate optical concentration and integration within approximately 1 μm of electronics.The cited wiring scale is approximately 200 aF/μm, so longer connections can dominate input capacitance and operating energy.

VI. COMPARISON OF LONG, MEDIUM AND SHORT DISTANCE SYSTEMS

Optical-system requirements change with distance: long links prioritize information capacity, medium links emphasize connection density, and short links require low energy per bit alongside dense interconnection. Short-link designs therefore favor whole-system optimization, simple receiver paths, and optics that preserve channel density without unnecessary electronic overhead.

  • Comparison of long, medium and short distance systems: Electrical interconnects remain inadequate for problems such as the supercomputer “byte per FLOP” gap, motivating optical approaches at medium and short distances.The passage describes this problem as difficult to resolve using electrical approaches.
  • Comparison of long, medium and short distance systems: Short-distance interconnects require both very low energy per bit and very high connection density, unlike longer-distance systems with different dominant requirements.The review emphasizes that technologies for long distances cannot simply be transferred to the shortest links.
  • Short-distance interconnects: Short links can reduce overhead through moderate clock rates, large synchronous zones, and elimination of retiming, coding, CDR, and SERDES circuitry.These system choices are presented as key benefits or opportunities for short-distance optics.
  • Short-distance interconnects: For a receiverless detector collecting N spatial modes, detector area and capacitance grow by N, increasing required system energy per bit by N.The voltage swing falls by N unless transmitted optical energy is increased correspondingly.
  • Short-distance interconnects: Receiverless operation favors a single spatial mode because power scattered into other modes is unusable, while multimode systems can collect many modes with receiver amplification.This creates a direct trade-off between low detector capacitance and mode-collection flexibility.

B. Beam couplers

Beam coupling in low-energy, high-density optical interconnects must preserve the desired spatial mode while supporting compact arrays and many channels. Free-space optics offers substantial channel density, but multiplexing precision, scattering, and coupling efficiency remain practical constraints.

  • B. Beam couplers: Mode-matched or diffraction-limited couplers are required when coupling into a single-mode waveguide or minimum-sized detector.The input beam shape and alignment must match the accepted spatial mode to avoid power loss.
  • B. Beam couplers: Grating couplers, inverse tapers, and computational nanophotonic mode converters are candidate approaches for improving compact coupling efficiency.Self-aligning couplers could compensate for fabrication imperfections, misalignment, aberrations, and some modal mixing.
  • C. Large numbers of channels: Dense WDM for large-scale short-distance interconnects remains an open question because many wavelength channels require high fabrication or tuning precision.A 100 GHz channel spacing near 200 THz corresponds to approximately one part in 2000 precision.
  • C. Large numbers of channels: Scattering between overlapping modes or loosely coupled cores can be unpredictable and can vary with temperature, bending, or vibration.Complex coherent cross-coupling may be difficult to undo in practical systems.
  • C. Large numbers of channels: A 32×32 array of 10×10 μm^2 spots occupies 320×320 μm^2 side by side or approximately 1×1 mm^2 when spaced on 31.25 μm centers.Lenslet arrays can focus larger, spaced spots onto the smaller chip areas.
  • C. Large numbers of channels: 1024 free-space channels in a 2×2 mm^2 area could provide 1 Tb/s at a ~2 GHz clock rate and 25 Tb/cm^2 bandwidth density.The estimate allows two physical beams per data channel.

VIII. CLOCKING, DATA RETIMING, AND TIME-MULTIPLEXING

Electrical interconnects incur substantial power for clock recovery, retiming, line coding, and time multiplexing. Optical pulse timing, modulo-synchronous links, and dual-rail signaling offer routes to remove much of this circuitry.

  • Timing problems and resulting power dissipation: Long interconnects introduce unpredictable, noninteger-cycle delays and potentially different endpoint clock frequencies, requiring phase and frequency recovery.These functions can require phase- or delay-locked loops and buffering for retiming.
  • Timing problems and resulting power dissipation: Time multiplexing adds serialization and deserialization power while worsening clock-recovery precision requirements.The link must recover a higher-frequency clock with tighter timing precision.
  • Timing problems and resulting power dissipation: ~2 pJ/bit is consumed by line coding, CDR, and SERDES together for a 10 Gb/s channel.More than half is attributed to SERDES, while CDR alone exceeds 100 fJ/bit.
  • Optical approaches to eliminating line coding, CDR and SERDES: Optical pulses can provide sub-picosecond clocking and remove timing skew, jitter, data registers, and their clocking.The optical path sets fixed delays, while pulse arrival within the clock window can enable electronic-free retiming.
  • Optical approaches to eliminating line coding, CDR and SERDES: Modulo-synchronous optical volumes make propagation delays equal to integer clock cycles, eliminating clock phase and frequency recovery across ~1 cm to ~10 m.Signals arrive within a known portion of the clock window throughout the volume.
  • Optical approaches to eliminating line coding, CDR and SERDES: Dual-rail signaling avoids AC coupling and associated line coding by representing one signal with complementary bright and dark beams.Stacked photodetectors recover the differential output and can also avoid high optical on/off contrast and gain control.

IX. AN EXAMPLE PHYSICAL ARCHITECTURE FOR ATTOJOULE OPTOELECTRONICS

The paper sketches a straw-man optical architecture spanning transistor-scale integration to meter-scale free-space arrays. Its assumptions combine near-receiverless detection, dual-rail channels, optical pulses, and low-energy modulators to target sub-10-fJ/bit interconnects.

  • Optical platform concept: The proposed architecture targets elimination of receiver amplifiers, line coding, CDR, SERDES, and part of clock-distribution power while maintaining high bandwidth density.It is explicitly presented as an illustrative architecture rather than an optimized design.
  • System interconnect energies: The example assumes a 2 GHz system clock and optical modulo-synchronous pulses for predominantly off-chip, and some longer on-chip, interconnects.The architecture is intended to operate across a shared synchronous system.
  • Optical platform concept: ~100 aF is the assumed total capacitance of the integrated photodetector pair, input transistors, and connecting wiring.The photodetectors are presumed to be receiverless or near-receiverless and integrated close to minimum-sized transistors.
  • Optical platform concept: 1024 spatial channels can be configured as 512 dual-rail logical channels, corresponding to ~1 Tb/s at 2 GHz.Free-space arrays provide the spatial-channel count assumed by the architecture.
  • System interconnect energies: <10 fJ/bit is the projected total system energy, including 8 fJ/bit for the laser and sub-1-fJ/bit modulator and drive energies.The calculation assumes 19 dB optical loss, 30% wall-plug efficiency, and a 1 Tb/s, 512-channel unit.
  • System interconnect energies: ~2 orders of magnitude or more is the projected interconnect-energy reduction relative to current approaches.The same energy per bit is proposed across the entire modulo-synchronous volume, including longer on-chip links.
  • Optical platform concept: Photodetectors are integrated in the transistor layer and connected through short waveguides to avoid the capacitance of micron-spaced electrical wiring.The design goal is efficient optical coupling with low parasitic capacitance at the transistor input.
  • Optical platform concept: Meter-scale free-space optics can support thousands of channels, with diffraction and system alignment treated as engineering constraints.The passage notes that imaging optics routinely handle millions of resolution elements and may require autofocus and autoalignment.

X. CONCLUSIONS

The review argues that optics can reduce interconnect energy by eliminating line charging and much of the circuitry associated with longer links, while also increasing bandwidth density. It presents an existence-proof system targeting ~10 fJ/bit links but emphasizes substantial integration, device, coupling, and scaling challenges.

  • Optical interconnects can avoid electrical line charging, shifting the main technical challenge to reducing the energy of photodetectors, modulators, lasers, and LEDs.
  • ~100 aF detector capacitance could enable receiverless or near-receiverless operation by largely eliminating receiver-amplifier dissipation currently of the order of 100’s of fJ/bit or higher.
  • Optical timing precision and high channel counts could eliminate line coding, CDR, and SERDES circuits, which can dissipate picojoules or more per bit.
  • ~10 fJ/bit is proposed as a stretch goal for links from chip-to-chip connections to longer connections, potentially 2 to 3 orders of magnitude below current approaches.
  • Free-space optics may provide very high interconnect bandwidth densities and help break byte-per-flop limits that constrain current architectures.
  • Replacing CMOS logic is not the focus: optical logic faces qualitative system requirements, while the review identifies stronger near-term prospects in interconnects.
  • Key research directions include nanoscale detector-electronics integration, low-loss nanostructured coupling, free-space micro-array optics, and sub-femtojoule devices with scalable fabrication.
  • The proposed platform is an existence proof rather than a unique solution, and useful progress could come from solving individual challenges without complete success in every aspect.

APPENDIX A – MICROSCOPIC MECHANISMS FOR OPTICAL MODULATION AND THEIR ENERGY REQUIREMENTS

The appendix reviews microscopic electroabsorption and electrorefraction mechanisms, emphasizing how quantum confinement and carrier filling alter optical absorption. It identifies QCSE as a particularly strong, compact, and energy-efficient modulation mechanism while noting dependence on absorption-edge abruptness and temperature.

  • Electro-optic modulation mechanisms fall into electroabsorption, based on absorption changes, and electrorefraction, based on refractive-index changes.
  • Quantum-confined Stark effect: The QCSE arises in quantum wells where confinement quantizes the allowed states and produces excitonic peaks associated with absorption steps.
  • Quantum-confined Stark effect: An applied field shifts the lowest electron and highest hole states toward one another, lowering the lowest absorption step, while reducing wavefunction overlap and absorption-step height.
  • Quantum-confined Stark effect: 100’s to 1000’s of cm-1 absorption shifts of up to ~100 meV can be produced with fields of 10^4–10^5 V/cm.
  • Comparison with FKE: QCSE generally offers larger on/off absorption contrasts than FKE, an important device criterion, although both can produce changes from ~100 cm-1 to nearly ~1000 cm-1.
  • Quantum-confined Stark effect: A 10 μm-long waveguide QCSE modulator without a resonant cavity has demonstrated sub-femtojoule operation.
  • Quantum-confined Stark effect: QCSE operation has been confirmed to picosecond time scales, with a likely speed limit below one picosecond.

E. Electrorefraction mechanisms and approaches

Electrorefraction changes refractive index through electrically controlled polarization or carrier-density effects, with energy efficiency shaped by absorption, device length, and optical concentration. The review compares Pockels, QCSE, band-filling, and free-carrier approaches, highlighting resonator-assisted operation and demonstrated low-energy devices.

  • Electrorefraction mechanisms fall into electric-field effects from microscopic polarization and band-filling effects from changed carrier density.
  • Near absorption resonances, refractive-index and absorptive changes are comparable, but high absorption forces operation farther from resonance and generally lengthens refractive devices.
  • ~25 fJ/bit was demonstrated in a 10 μm plasmonic-waveguide modulator using a 90 nm gap, ±3 V drive, and estimated 2.8 fF capacitance.
  • ~100 fJ operation was estimated for a 330 μm QCSE electrorefractive device in a 200 nm × 300 nm waveguide with ~2 V drive.
  • ~1 fJ/bit was obtained in a 4.8 μm microdisk resonator with Q ~10,000, while feedback and control electronics project ~10 fJ/bit overall.
  • Silicon free-carrier plasma devices without resonators require ~10 times greater length than band-filling or QCSE electrorefractive devices, motivating strong optical concentration for low energy.

F. Comparison of quantum wells and 2D materials

The review compares graphene and MoS2 with quantum wells as low-energy electro-optic materials, emphasizing carrier-density requirements, excitonic absorption, and practical modulation limits. It also explains how resonator concentration relates to finesse, Q, and Purcell enhancement.

  • Comparison of quantum wells and 2D materials: Quantum wells provide strong excitonic absorption near the bandgap, with a single well measuring >2% absorption and a double-pass device showing >4% transmission change.
  • Comparison of quantum wells and 2D materials: ~1.2 × 10^13 cm^-2 graphene carrier density is required for transparency at 0.8 eV, versus <10^12 cm^-2 for the compared quantum well.
  • Comparison of quantum wells and 2D materials: Graphene’s absorption edge has ~0.15 eV width for a factor-2 absorption change near a 0.8 eV transparency edge.
  • Comparison of quantum wells and 2D materials: 2D materials may offer qualitative integration advantages, but currently show no basic energy advantage over quantum wells and may require larger operating energies.
  • Optical concentration factor: A cavity increases optical concentration because photons make multiple passes before loss, with mirror transmission contributing to round-trip loss.
  • Optical concentration factor: Finesse is a more direct measure than Q of the optical concentration increase from a cavity, while Purcell enhancement and the concentration factor are essentially equivalent for resonators.

H. Use of high-Q resonators

High-Q resonators increase optical interaction in small devices but impose tighter fabrication, wavelength, temperature, and tuning requirements. For modulators, electroabsorptive approaches can avoid some high-Q burdens, while electrorefractive devices retain stringent material criteria.

  • Resonator requirements: High-Q resonators require cavity-length precision of approximately 1/Q, making fabrication or operational tuning necessary as Q increases.The cavity resonance width is approximately f/Q, so the cavity length must be set within a fractional precision of about 1/Q.
  • Resonator requirements: Per-device trimming, feedback, and thermal tuning can make large arrays of high-Q modulators financially, energetically, or operationally impractical.The paper therefore advises caution about using Q values beyond 1000 for modulators deployed in large numbers.
  • Resonator requirements: Temperature drift can exceed the linewidth of high-Q resonators, whereas Q ≈ 30 may tolerate a 100°C variation without tuning.For Q ≈ 30 or smaller, the corresponding fractional resonance shift is significantly below the fractional linewidth.
  • Modulator material criteria: At least a factor-of-2 absorption-coefficient contrast is needed for a modulator to use optical power with reasonable efficiency above 25%.Lower contrast causes a steep efficiency penalty, and insufficient contrast rules out several electroabsorptive mechanisms.
  • Modulator material criteria: Electrorefractive modulators face a difficult high-speed material criterion: achieving Δn much greater than about 10^-3 while maintaining low loss.A 90 nm plasmonic-waveguide device using organic electro-optic material operated over 10 μm at approximately 25 fJ/bit.
  • Modulator material criteria: Adding a resonator does not remove the underlying material requirement for electrorefractive modulators, because the relevant factors divide out.The resonator can enhance interaction, but the material criterion remains unchanged.

APPENDIX D – EXAMPLE ANALYSIS OF “NEAR-RECEIVERLESS” OPERATION

Near-receiverless operation shifts the energy trade-off toward photodetector capacitance and transmitter energy, potentially making small receiver gain stages worthwhile. The supplied analysis finds ordinary thermal and shot noise generally manageable at the discussed energy levels, with caution near 10 aJ/bit.

  • Energy trade-offs: A receiver gain stage is energetically beneficial only when its energy per bit is less than the transmitter energy saved by adding gain.For gain g significantly above 1, the saved transmitter energy is approximately ET, giving Egain < ET = ERLSP/ηS.
  • Energy trade-offs: Low-capacitance photodetectors reduce receiverless optical input energy and therefore reduce the receiver-gain energy that can be spent while retaining a net benefit.Even so, the transmitter energy may remain tens of femtojoules per bit, allowing a gain stage costing a few femtojoules per bit in the hypothetical system considered.
  • Noise: At approximately 100 aJ/bit with 1 eV photons, the received signal corresponds to about 600 photons/bit, well above the 20–100 photons typically needed to avoid photon-statistics errors.Shot noise may require renewed consideration if operation approaches approximately 10 aJ/bit.
  • Noise: Thermal noise is estimated at approximately 2 mV for 1 fF and 20 mV for 10 aF, both below a logic swing.With modest amplification of about 3–5, these noise sources are still unlikely to dominate, although amplified cases should be analyzed.

I. Diffraction limit to the number of free-space channels

Diffraction limits the number of separable free-space communication channels between finite apertures. Simple lenslet and free-space systems can nevertheless support thousands to tens of thousands of channels over centimeter-to-meter distances.

  • Channel limit: Diffraction limits the practical number of orthogonal spatial channels between parallel surfaces to NC ≈ ATAR/(λ^2L^2).The limit follows from the transmitting and receiving apertures, their separation L, and the wavelength λ.
  • Channel limit: The same channel count can be interpreted as the number of approximately non-overlapping diffraction-limited spots or optimally coupled communications modes.A rigorous singular-value decomposition of the diffraction operator gives the same count as the intuitive spot argument.
  • Channel limit: Changing to orbital-angular-momentum beams does not increase the available number of spatial channels, because these beams are merely another basis for spatial modes.Ring-like beams can also use the aperture inefficiently unless the relevant radial forms are included.
  • Example systems: 17,800 channels are available for a 2 × 2 mm cross-section over centimeters, making 1024 channels readily viable and 4096 channels potentially viable through the same free-space link.The example uses lenslet couplers on 62.5 μm or 31.25 μm centers and a single imaging lens.
  • Example systems: 110,000 channels are available in the example using two 25 cm-aperture telephoto lenses separated by 5 m.The paper presents this as a hypothetical cabinet-to-cabinet link carrying tens of thousands of channels.
  • Wavelength dependence: A 32 × 32 spot array requires approximately 1/226 relative wavelength precision, corresponding to about 7 nm at 1550 nm.The tolerance is described as relatively slack when wavelength is set by a centralized laser.
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