Capstone: photonics at work — telecommunications, lidar, laser manufacturing, medicine and quantum photonics

The first eleven lessons built the physics of lasers and photonic devices piece by piece. This capstone puts the pieces to work in five areas that shape modern life: optical communications, lidar and sensing, laser materials processing, medicine, and the emerging field of quantum photonics. In each we use the tools of the course to estimate what is possible and what limits it, and we end with laser safety, which every user of a laser must understand. The program at the end of the lesson gathers the key calculations in one place.

Optical communications

The modern internet is a photonic system. A long-haul link combines everything from lessons 5 to 11: distributed-feedback lasers (lesson 6) or narrow-linewidth tunable lasers as sources; Mach–Zehnder modulators (lesson 11) imposing amplitude and phase on both polarizations; single-mode fiber (lesson 9) with a loss of about 0.2 dB/km; erbium-doped fiber amplifiers every 50 to 100 km; and coherent receivers that mix the signal with a local laser and use fast digital signal processing to undo chromatic dispersion and polarization effects.

Capacity comes from wavelength-division multiplexing (WDM): many independent channels at different wavelengths share one fiber. The C band from 1530 to 1565 nm spans about 4.4 THz, enough for about 87 channels on the standard 50 GHz grid, or about 58 on a 75 GHz grid that suits 400 Gb/s channels. Each channel uses advanced modulation formats that encode several bits per symbol. The ultimate limit is set by Shannon's theorem, \(C = B\log_2(1 + \mathrm{SNR})\) per polarization, and by fiber nonlinearity (lesson 10): raising the launched power improves the signal-to-noise ratio until the Kerr effect starts to distort the signals, so there is an optimum power and a maximum capacity for each link. To go further, systems add the L band (about 1565 to 1625 nm) and, in new submarine cables, more fiber pairs and fibers with several cores.

Inside data centers, the problem is different: enormous numbers of short links, where cost and power per bit matter more than reach. Here vertical-cavity lasers and multimode fiber serve the shortest links, and silicon photonic transceivers the longer ones, increasingly placed right beside the switching chips to save the electrical power spent on copper connections. Artificial intelligence workloads, which move vast amounts of data between processors, have made optical interconnects one of the fastest-growing parts of photonics.

Lidar and sensing

Lidar measures distance by the time a light pulse takes to travel to a target and back. A target at range \(R\) returns the pulse after \(t = 2R/c\), about 6.7 ns per meter, and two targets can be distinguished if their ranges differ by more than \(c\tau/2\), where \(\tau\) is the pulse length. The weak return from a diffuse surface is estimated with the lidar equation: a Lambertian target of reflectance \(\rho\) at range \(R\) scatters light into a hemisphere, and a receiver aperture of area \(A_r\) collects a fraction \(\rho A_r/(\pi R^2)\) of the transmitted energy, ignoring atmospheric loss. The return therefore falls as \(1/R^2\), and at long range only a few thousand photons, or fewer, come back.

Lidar maps terrain and forests from aircraft, measures wind and aerosols in the atmosphere, surveys buildings and mines, and is used by many automated vehicles to build a three-dimensional picture of their surroundings. Common wavelengths are 905 nm, where cheap silicon detectors work, and 1550 nm, where the eye tolerates more power because the light is absorbed before it reaches the retina. Frequency-modulated continuous-wave lidar, which sweeps the laser frequency and measures the beat between outgoing and returning light, also gives each point's velocity through the Doppler shift.

Other photonic sensors exploit interference and resonance. Fiber-optic gyroscopes in aircraft and ships measure rotation through the Sagnac phase shift between light traveling both ways around a fiber coil. Fiber Bragg gratings strung along bridges, pipelines and wind turbine blades measure strain and temperature from shifts in their reflected wavelength. Interferometers with kilometer-long arms and cavities of extreme finesse (lesson 4) detect gravitational waves, and optical frequency combs (lesson 10) underpin optical atomic clocks.

Laser materials processing

Lasers cut, weld, drill, mark and additively build parts in nearly every manufacturing industry. The key quantity is the intensity at the work surface. A 4 kW fiber laser focused to a 50 µm radius delivers about \(5 \times 10^7\ \mathrm{W/cm^2}\), far above the roughly \(10^6\ \mathrm{W/cm^2}\) at which steel melts and begins to vaporize. In cutting, a jet of gas blows the molten metal out of the kerf; in keyhole welding, vapor pressure opens a narrow cavity that lets the beam penetrate deep into the joint. The small spot needs good beam quality (lesson 7), which is why fiber lasers with \(M^2\) close to one dominate thin-sheet cutting, while multimode lasers with larger spots suit thick sections and welding. Metal additive manufacturing, or 3D printing, melts metal powder layer by layer with a scanned laser beam.

Ultrashort pulses (lesson 8) change the physics. A femtosecond pulse deposits its energy before heat can diffuse away from the focus, so material is ablated with almost no melted zone. This allows clean micromachining of glass, ceramics and heat-sensitive materials, the drilling of fuel-injector nozzles and the cutting of the thin glass used in phone screens. In transparent materials, nonlinear absorption at the focus (lesson 10) lets the beam write structures inside the bulk without touching the surface.

Medicine

Medicine was one of the first fields to adopt lasers and remains one of the most inventive. Because tissue absorbs different wavelengths very differently, the choice of laser controls the effect. Water absorbs strongly at the CO₂ wavelength of 10.6 µm and near 3 µm, so these lasers vaporize a thin layer of tissue and seal small blood vessels as they cut. Hemoglobin absorbs green and yellow light strongly, which is used to treat vascular lesions and to seal leaking vessels in the retina. Near-infrared light between about 650 and 1350 nm penetrates furthest, the so-called therapeutic window, and is used for imaging and photodynamic therapy, in which light activates a drug concentrated in the target tissue.

Ophthalmology shows the full range of laser technology. Argon-ion and later frequency-doubled solid-state lasers have treated diabetic damage to the retina for decades. Excimer lasers at 193 nm reshape the cornea in refractive surgery by removing tissue with sub-micrometer precision, and femtosecond lasers, made possible by chirped pulse amplification, cut the corneal flap and are used in cataract surgery. Optical coherence tomography, which uses the short coherence length of a broadband source (lesson 7) to produce cross-sectional images of the retina with micrometer depth resolution, has become a routine eye examination. Optical tweezers, the other half of the 2018 Nobel Prize, hold and manipulate single cells and molecules with the force of focused light.

Quantum photonics

Light is the natural carrier for quantum information over distance, because photons interact only weakly with their surroundings and travel fast. Quantum key distribution (QKD) uses single photons, or very weak laser pulses, in randomly chosen polarization or phase states to establish a shared secret key; any eavesdropper disturbs the states and reveals herself through an increased error rate. The first protocol, BB84, was published in 1984 by Charles Bennett and Gilles Brassard of the Université de Montréal. Fiber QKD networks operate over tens to a hundred or so kilometers, and satellites have distributed keys over intercontinental distances. In the United States, the National Quantum Initiative supports quantum research at national laboratories and universities, NIST develops single-photon sources and detectors, and companies such as PsiQuantum are building photonic quantum computers.

An attenuated laser is not a true single-photon source. Its photon number per pulse follows a Poisson distribution, so if the mean is 0.1 most pulses are empty and a small fraction contain two or more photons, which an eavesdropper could in principle split off. Practical systems counter this with decoy-state protocols, which vary the pulse intensity to detect such attacks. True single-photon sources based on quantum dots, defects in diamond or pairs of photons produced by spontaneous parametric down-conversion (the reverse of sum-frequency generation, lesson 10) are an active field of research. Photonic quantum computers use squeezed light and interferometers on integrated chips (lesson 11), and quantum-enhanced sensors already use squeezed light to improve the sensitivity of gravitational-wave detectors.

Laser safety

Every laser application depends on handling light safely. The eye is the most vulnerable organ: for visible and near-infrared light between about 400 and 1400 nm, the lens focuses a collimated beam to a spot of a few micrometers on the retina, increasing the intensity by a factor of up to about \(10^5\). Retinal damage can be instant and painless. Outside this band, the cornea and lens absorb the light, and the main hazards are burns to the front of the eye and to the skin.

The international standard IEC 60825-1, on which product rules in both Canada and the United States draw, together with workplace standards such as ANSI Z136.1 for laser safety programs, defines the maximum permissible exposure (MPE), the level of exposure below which no damage is expected, as a function of wavelength and exposure time, and groups lasers into classes. Class 1 lasers are safe under all normal conditions; class 2 lasers are visible lasers of at most 1 mW, considered safe for accidental exposure because the blink reflex limits viewing to about 0.25 s; class 3R lasers, up to 5 mW visible, carry a small risk; class 3B lasers, up to 0.5 W, are hazardous to the eye directly; and class 4 lasers, above 0.5 W, are hazardous even by diffuse reflection and can cause skin burns and fires. Laser pointers sold to the public are meant to be class 2 or below, but many imported pointers exceed their labeled power.

For a given beam, the nominal ocular hazard distance (NOHD) is the distance beyond which the beam has spread enough that its irradiance falls below the MPE. For a beam of power \(P\), initial diameter \(a\) and full divergence \(\phi\),

Control measures follow from the class: enclosures and interlocks, controlled areas, beam stops at the end of every beam path, keeping beams below or above eye level, and eyewear with the right optical density at the laser wavelength. Aiming any laser at aircraft is a criminal offense in both Canada and the United States, because even a few milliwatts spread over a cockpit windshield at night can dazzle a pilot.

Computing photonics at work

The program counts WDM channels in the C band and compares the capacity with the Shannon limit, computes lidar timing, range resolution and the photon return from a diffuse target, evaluates the intensity of a cutting laser, checks the class 2 limit against the MPE for the blink reflex, computes nominal ocular hazard distances, and simulates the photon statistics of an attenuated laser used for quantum key distribution.

import math, random
c, h = 2.99792458e8, 6.62607015e-34
# 1. Telecommunications: channels in the C band on a 50 GHz grid, and capacity
f_lo, f_hi = c / 1565e-9, c / 1530e-9
ch = int((f_hi - f_lo) // 50e9)
print(f"C band 1530-1565 nm spans {(f_hi-f_lo)/1e12:.2f} THz: {ch} channels at 50 GHz spacing")
print(f"at 100 Gb/s per channel: {ch*100/1000:.1f} Tb/s; with 400 Gb/s channels on a 75 GHz grid: {int((f_hi-f_lo)//75e9)*400/1000:.1f} Tb/s")
snr_db = 15; se = math.log2(1 + 10 ** (snr_db / 10))
print(f"Shannon limit at an SNR of {snr_db} dB: {se:.2f} b/s per Hz -> {se*(f_hi-f_lo)/1e12:.1f} Tb/s per polarization")
# 2. Lidar: time of flight, range resolution and the returned signal
for R_m in (10, 100, 200):
    print(f"lidar target at {R_m:3d} m: round trip {2*R_m/c*1e9:.0f} ns")
for tau in (5e-9, 1e-9):
    print(f"pulse {tau*1e9:.0f} ns -> range resolution c tau / 2 = {c*tau/2*100:.0f} cm")
# received energy from a diffuse (Lambertian) target: E_r = E_t * rho * A_r / (pi R^2)
E_t, rho, A_r = 1e-6, 0.10, math.pi * 0.0125 ** 2      # 1 uJ pulse, reflectance 0.1, 25 mm aperture
for R_m in (50, 200):
    E_r = E_t * rho * A_r / (math.pi * R_m ** 2)
    n_ph = E_r / (h * c / 905e-9)
    print(f"  {R_m:3d} m, reflectance 0.1: {E_r:.2e} J back = {n_ph:.0f} photons at 905 nm")
# 3. Laser materials processing: intensity at the focus
P, w = 4000.0, 50e-6
print()
print(f"4 kW focused to a 50 um radius: {P/(math.pi*w*w)/1e4:.2e} W/cm^2 (steel melts and vaporizes above about 1e6 W/cm^2)")
# 4. Laser safety (textbook values): MPE for a visible CW beam viewed for 0.25 s is about 2.5 mW/cm^2
MPE = 25.4                     # W/m^2
pupil = math.pi * (3.5e-3) ** 2
print(f"power through a 7 mm pupil at the 0.25 s visible MPE: {MPE*pupil*1e3:.2f} mW (the class 2 limit is 1 mW)")
# nominal ocular hazard distance: NOHD = (sqrt(4P/(pi MPE)) - a) / phi
for P_w, a, phi in [(0.005, 1e-3, 1e-3), (1.0, 2e-3, 1e-3)]:
    nohd = (math.sqrt(4 * P_w / (math.pi * MPE)) - a) / phi
    print(f"{P_w*1e3:6.0f} mW beam, 1 mrad divergence: NOHD = {max(0.0, nohd):.0f} m")
# 5. Quantum photonics: an attenuated laser is not a single-photon source
mu = 0.1
p0, p1 = math.exp(-mu), mu * math.exp(-mu)
p2 = 1 - p0 - p1
print()
print(f"attenuated laser, mean 0.1 photon per pulse: P(0) = {p0:.4f}, P(1) = {p1:.4f}, P(2 or more) = {p2:.4f}")
print(f"of the non-empty pulses, {p2/(1-p0):.3f} contain two or more photons")
rng = random.Random(460)
def poisson(lam):
    L, k, p = math.exp(-lam), 0, 1.0
    while True:
        p *= rng.random()
        if p < L: return k
        k += 1
counts = [poisson(mu) for _ in range(200000)]
print(f"simulated, 200000 pulses: multi-photon fraction of non-empty = {sum(1 for x in counts if x >= 2)/sum(1 for x in counts if x >= 1):.3f}")

C band 1530-1565 nm spans 4.38 THz: 87 channels at 50 GHz spacing
at 100 Gb/s per channel: 8.7 Tb/s; with 400 Gb/s channels on a 75 GHz grid: 23.2 Tb/s
Shannon limit at an SNR of 15 dB: 5.03 b/s per Hz -> 22.0 Tb/s per polarization
lidar target at  10 m: round trip 67 ns
lidar target at 100 m: round trip 667 ns
lidar target at 200 m: round trip 1334 ns
pulse 5 ns -> range resolution c tau / 2 = 75 cm
pulse 1 ns -> range resolution c tau / 2 = 15 cm
   50 m, reflectance 0.1: 6.25e-15 J back = 28474 photons at 905 nm
  200 m, reflectance 0.1: 3.91e-16 J back = 1780 photons at 905 nm

4 kW focused to a 50 um radius: 5.09e+07 W/cm^2 (steel melts and vaporizes above about 1e6 W/cm^2)
power through a 7 mm pupil at the 0.25 s visible MPE: 0.98 mW (the class 2 limit is 1 mW)
     5 mW beam, 1 mrad divergence: NOHD = 15 m
  1000 mW beam, 1 mrad divergence: NOHD = 222 m

attenuated laser, mean 0.1 photon per pulse: P(0) = 0.9048, P(1) = 0.0905, P(2 or more) = 0.0047
of the non-empty pulses, 0.049 contain two or more photons
simulated, 200000 pulses: multi-photon fraction of non-empty = 0.048

The C band holds 87 channels at 50 GHz spacing, about 8.7 Tb/s at 100 Gb/s per channel, or about 23 Tb/s with 400 Gb/s channels on a 75 GHz grid. The Shannon limit at a signal-to-noise ratio of 15 dB is about 5 bits per second per hertz, 22 Tb/s per polarization over the C band, so modern dual-polarization systems are approaching the fundamental limit and further growth must come from more bandwidth or more fibers.

The lidar numbers show why automotive and surveying systems need sensitive detectors. A target at 200 m returns its echo after 1.33 µs. A 1 ns pulse resolves ranges to 15 cm. A 1 µJ pulse at 905 nm scattered from a dark target of reflectance 0.1 returns about 28,000 photons from 50 m but only about 1,800 from 200 m into a 25 mm aperture, before any atmospheric loss or detector inefficiency. Single-photon avalanche diodes and arrays of them are therefore common in lidar receivers.

The safety calculation shows where the class 2 limit comes from: the MPE for a 0.25 s exposure to visible light, about 2.5 mW/cm² averaged over a 7 mm pupil, corresponds to 0.98 mW, essentially the 1 mW limit. A 5 mW pointer with 1 mrad divergence remains above the MPE for about 15 m, and a 1 W beam for more than 200 m. Finally, the attenuated laser with a mean of 0.1 photon per pulse is empty about 90 times in 100, and among pulses that contain any light, about 1 in 20 contains two or more photons, as both the formula and the 200,000-pulse simulation show.

Looking back and ahead

The course began with Einstein's 1917 insight that stimulated emission must exist. From that, we built the cross section and gain of a medium, the stability and modes of a resonator, the rate equations of a laser, the Gaussian beams it emits, the pulses it can make, the fibers that carry its light, the nonlinear crystals that change its color, and the devices that detect and modulate it. The same few ideas recur everywhere: gain must exceed loss; a resonator selects modes spaced by \(c/2nL\); bandwidth and duration are reciprocal; diffraction ties beam size to divergence; and phase matching governs every wave interaction. These ideas, combined with careful engineering, have made photonics one of the foundations of modern technology, and they will remain the language of its future developments, from optical computing and quantum networks to new lasers for fusion energy and medicine.