All-Optical Switches and Gates

The last lesson left us with a problem of arithmetic: the Kerr effect lets light switch light, but only at gigawatts per square centimetre. From the late 1970s to the 2000s, some of the best physicists and engineers alive attacked that arithmetic from every angle, and this lesson is their parts catalogue. The strategies all reduce to one of three moves: borrow a stronger nonlinearity from semiconductor carriers instead of bound electrons; stretch the interaction over kilometres of fibre so a feeble nonlinearity has time to add up; or trap the light in a resonant box a wavelength across until modest powers become enormous intensities. Each move works. Each exacts a price — in speed, in size, or in fragility — and the pattern of those prices is the real syllabus here. Read this catalogue the way a sceptical engineer would: not "does it switch?" (they all switch) but "what did the switching cost, and what did it break?"

Semiconductor optical amplifiers: carriers do the heavy lifting

A semiconductor optical amplifier (SOA) is a laser diode with the mirrors removed: a current-pumped stripe of gain material that amplifies whatever passes through. Its population of excited carriers is a shared, exhaustible resource — and that is exploitable. Send in a strong "control" pulse and it eats the available gain; a weak probe arriving at the same moment finds the larder bare and emerges dimmed. That is cross-gain modulation (XGM): control on → probe off, an inverting gate for free. Subtler and better: the depleted carriers also change the refractive index (carrier density and index are locked together in a semiconductor), so the control writes a phase onto the probe — cross-phase modulation (XPM). Put one SOA in each arm of a Mach–Zehnder and push them differentially, and the interferometer converts that phase into a clean on/off output — the SOA-MZI gate, the workhorse of 1990s–2000s all-optical logic demonstrations, running AND, XOR and wavelength conversion at 10–40 Gb/s with control energies of order 10–100 fJ.

The price is time. Depleting carriers is fast (picoseconds); replenishing them waits on the injection current, with recovery times of tens to hundreds of picoseconds. Drive the gate faster than it recovers and each bit sees a gain that depends on what the previous bits were — the dreaded pattern effect, a data-dependent error source with no analogue in a clocked CMOS gate. Carrier devices bought their sensitivity by storing energy in matter, and stored energy has a memory.

The loop mirror: pure Kerr, stretched over kilometres

If you insist on the instantaneous Kerr nonlinearity of silica — femtosecond response, no carriers, no pattern effects — you must compensate for n_2 = 2.6\times 10^{-20}\ \mathrm{m^2/W} with sheer distance. The classic vehicle is the nonlinear optical loop mirror: a Sagnac interferometer made by joining the two output ports of a coupler into a single loop of fibre. Both copies of the input traverse the same loop in opposite directions, so every slow perturbation — temperature, vibration, drift — cancels identically. Only something that distinguishes the two directions can unbalance it, and that something is a control pulse riding alongside one copy:

The switching condition is exactly the arithmetic of last lesson: \Delta\varphi = 2\pi n_2 I L/\lambda = \pi, achievable with watt-scale peak powers and hundreds of metres to kilometres of fibre. The response is essentially instant — loop mirrors demultiplexed 640 Gb/s data streams in the lab, far beyond anything electronics could then touch — but look at the footprint: a "gate" the size of a spool of fibre, consuming picojoules per switching event. A refinement called the TOAD put an SOA inside the loop, offset from centre: the strong carrier nonlinearity shrank the loop to metres and the control energy to ~100 fJ, at the cost of re-importing the SOA's slow recovery. The two knobs — fast/weak versus slow/strong — refuse to turn independently.

Photonic-crystal cavities: trap the light instead

The third strategy attacks intensity directly. Recall from reciprocal-lattice diffraction that a periodic structure reflects waves whose wavevector hits the Bragg condition; a photonic crystal — a slab of semiconductor drilled with a wavelength-scale lattice of holes — does to photons what a crystal's periodic potential does to electrons, opening a photonic band gap: a range of frequencies that cannot propagate at all. Omit a few holes and you create a defect state in the gap — a cavity that light physically cannot leave, with mode volume V approaching the theoretical minimum of (\lambda/n)^3 and quality factors Q up to 10^6.

Both numbers multiply your nonlinearity. A photon entering the cavity recirculates for a lifetime \tau = Q/\omega, so the circulating intensity is boosted by a factor \propto Q; and squeezing the mode into V \sim (\lambda/n)^3 concentrates whatever energy is present. The figure of merit for nonlinear light–matter interaction scales as Q/V — and photonic-crystal cavities hold the record by orders of magnitude. The payoff was real: InGaAsP photonic-crystal switches around 2010 achieved all-optical switching with control energies of a few femtojoules — into the energy neighbourhood of contemporary CMOS gates — in a footprint of square microns. The price, once more: the strong nonlinearity used was carrier-based (recovery tens of picoseconds), the resonance drifts with temperature (a cavity that stores light for a million cycles is exquisitely sensitive to being detuned), and a high-Q resonance is intrinsically narrowband — photon lifetime and switching bandwidth are the same number wearing two hats.

The scoreboard: energy versus speed

DeviceNonlinearitySwitching energyResponse / recoveryThe catch
SOA-MZI gatecarriers (XGM/XPM)~10–100 fJps / 25–100 ps pattern effects; amplified noise
Fibre NOLMsilica Kerr (χ⁽³⁾)~1–10 pJfs / fs metres-to-kilometres of fibre
TOAD (SOA-in-loop)carriers~100 fJps / ~100 ps SOA recovery returns
Photonic-crystal cavitycarriers, cavity-enhanced~1–10 fJ~10 ps / ~10–100 ps thermal drift; narrowband
Microcavity "optical transistor"cavity QED~single photons (aJ)ns-scale cryogenics, vacuum, one-off
CMOS gate (for shame)electrons~0.1–1 fJ~10 ps none of the above

Squint at the table and a law emerges: fast and weak, or strong and slow. The instantaneous Kerr response is too feeble to use compactly; every nonlinearity strong enough to switch at femtojoules stores its state in carriers or cavities, whose relaxation time then caps the speed. Nothing in the catalogue is simultaneously as small, as fast, as cheap and as well-behaved as the transistor it aims to replace — each entry wins one column and concedes the rest. Whether any of them could anchor a computer is not a question about a single switching event at all, and the next lesson makes that precise.

How far can "trap the light" be pushed? To the very end, it turns out. In cavity quantum electrodynamics, a single atom parked in a small enough, good enough cavity couples so strongly to the field that one photon saturates it — the ultimate nonlinearity, at the ultimate energy. In 2013, groups at MIT and the Max Planck Institute demonstrated exactly this: a cavity-trapped atomic gas in which a single stored "gate" photon toggled the cavity's transparency for hundreds of subsequent photons — a genuine optical transistor with gain, switched by one quantum of light. It is a magnificent rebuttal to any claim that optical switching is fundamentally energy-hungry. It is also an apparatus of lasers, magnetic traps and ultra-high vacuum occupying an optical table, operating at kilohertz-to-megahertz rates, at microkelvin temperatures. As a physics result: profound — nonlinear optics has no floor above the single photon. As a computing technology: a reminder that "possible" and "practical" are separated by the roughly fifteen orders of magnitude between one optical table and one square millimetre of silicon. These single-quantum tools found their true calling elsewhere — in the quantum computing module at the end of this course.

Every device on this page has a landmark paper with an eye-catching contrast ratio, and it is easy to read "10 dB switching at 40 Gb/s" as "logic gate achieved". Resist. A demonstration typically shows one switching event, driven by a strong, clean, lab-groomed control pulse, measured with a sensitive receiver, under conditions (bias, temperature, polarization, timing) tuned by a graduate student in real time. A logic gate in a computer must instead be driven by the battered output of another identical gate, must feed several more, must not care that its input is 3 dB low, and must do this 10^{15} times without a human in the loop. None of those requirements appear in a switching-energy table — they are system properties, not device properties. The gap between the two is precisely the subject of the next lesson, and it is where, historically, every entry in today's catalogue ran aground. When you read an "optical transistor" press release — they still appear yearly — this vignette is the checklist to reach for.

Where this goes next

We now own a drawer full of working optical switches spanning six orders of magnitude in energy and nine in size. The question that decides the fate of optical computing is not whether any of them works — it is what a technology must provide beyond switching to be the substrate of a computer: gain, restoration, isolation, cascadability. Those criteria — Keyes' famous checklist, sharpened by Miller for optics — are the next lesson, and they are the most transferable ideas in this entire module: they apply to every "beyond-CMOS" device you will ever be pitched.