Why lasers and photonics: light as a technology

Few inventions have moved from laboratory curiosity to everyday infrastructure as quickly as the laser. When Theodore Maiman switched on the first ruby laser at Hughes Research Laboratories on 16 May 1960, newspapers called it a solution looking for a problem. Within a few decades lasers were reading prices at supermarket checkouts, carrying telephone calls and internet traffic through glass strands under the oceans, cutting steel in car factories, reshaping corneas, measuring the distance to the Moon to a few millimeters and cooling atoms to within a millionth of a degree of absolute zero. Today the word photonics describes the whole technology of generating, guiding, switching and detecting light, much as electronics describes the technology of electric charge.

This course explains how lasers and photonic devices work, starting from the physics you already know. PHYS-230 introduced interference, diffraction, polarization and the Fabry–Pérot interferometer, and ended with a short tour of optical instruments, lasers and optical fibers. PHYS-372 and PHYS-373 developed the quantum mechanics of two-level systems, Rabi oscillations and Fermi's golden rule. PHYS-382 treated electromagnetic waves in matter, dispersion and waveguides, and PHYS-410 explained band structure and the p–n junction. Here those threads are tied together into a working engineering science: we will be able to calculate how much gain a laser medium provides, whether a cavity is stable, how short a pulse can be, how far a signal can travel in a glass guide and how efficiently a crystal can double the frequency of light.

What makes laser light special

Ordinary light sources, from the Sun to a filament bulb to a light-emitting diode, emit by spontaneous emission: each excited atom or electron–hole pair releases a photon at a random time, in a random direction, with a random phase. The result is light that spreads in all directions, contains a broad range of frequencies and has phase relationships that survive only over very short distances. A laser works differently. Its light is produced mainly by stimulated emission, a process in which an incoming photon causes an excited atom to emit a second photon that is an exact copy of the first: same frequency, same direction, same polarization and same phase. When stimulated emission dominates, light builds up in a single pattern of the electromagnetic field, a mode of an optical cavity, and the output inherits the properties of that mode.

Four properties follow, and every application in this course exploits at least one of them.

The word laser is an acronym for light amplification by stimulated emission of radiation. The name describes the physics exactly. A laser is an optical amplifier, a medium in which stimulated emission outweighs absorption, placed inside an optical resonator, two or more mirrors that send the light back through the amplifier many times. Amplification plus feedback makes an oscillator, just as an electronic amplifier with feedback makes a radio-frequency oscillator. The ingredients are therefore a gain medium, a pump that supplies energy to the gain medium, and a resonator. Lessons 2 and 3 deal with the gain medium, lesson 4 with the resonator and lesson 5 with what happens when they are combined.

Photons, power and brightness

A useful way to get a feel for laser light is to count photons. The energy of one photon is \(E = h\nu = hc/\lambda\). In electronvolts, a convenient form is

A beam of power \(P\) therefore carries \(P/(h\nu)\) photons per second. Radiance \(L\) is power per unit area per unit solid angle. For a beam of waist radius \(w_0\) and divergence half-angle \(\theta\), a rough estimate is \(L \approx P/(\pi w_0^2 \cdot \pi\theta^2)\). The surface of the Sun is a blackbody at about 5,772 K, whose radiance is \(\sigma T^4/\pi\), where \(\sigma\) is the Stefan–Boltzmann constant. The program below computes photon energies and photon rates for six common lasers, compares the radiance of a 1 mW helium–neon laser with that of the Sun, and turns a few typical spectral widths into coherence lengths using \(\ell_c \approx c/\Delta\nu\).

import math
h, c, e, kB = 6.62607015e-34, 2.99792458e8, 1.602176634e-19, 1.380649e-23
# Photon energy and photon rate for some common lasers
lasers = [('violet diode', 405e-9, 0.005), ('green pointer', 532e-9, 0.001),
          ('HeNe', 632.8e-9, 0.001), ('Nd:YAG', 1064e-9, 1.0),
          ('telecom diode', 1550e-9, 0.010), ('CO2', 10.6e-6, 100.0)]
print(f"{'laser':14s}{'lambda':>11s}{'power':>9s}{'E (eV)':>9s}{'photons/s':>12s}")
for name, lam, P in lasers:
    E = h * c / lam
    lam_s = f"{lam*1e9:.1f} nm" if lam < 2e-6 else f"{lam*1e6:.1f} um"
    print(f"{name:14s}{lam_s:>11s}{P:>8g}W{E/e:9.3f}{P/E:12.3e}")
# Radiance: a 1 mW HeNe beam against the surface of the Sun
w0 = 0.4e-3                      # beam waist radius (m)
theta = 632.8e-9 / (math.pi * w0)   # far-field half-angle divergence (rad)
area = math.pi * w0**2
solid = math.pi * theta**2
L_laser = 1e-3 / (area * solid)
sigma = 5.670374e-8
L_sun = sigma * 5772**4 / math.pi  # blackbody radiance, W m^-2 sr^-1
print()
print(f"HeNe divergence half-angle = {theta*1e3:.2f} mrad")
print(f"HeNe radiance  = {L_laser:.2e} W/(m^2 sr)")
print(f"Sun radiance   = {L_sun:.2e} W/(m^2 sr)")
print(f"ratio laser/Sun = {L_laser/L_sun:.0f}")
# Spectral narrowness: linewidths and coherence lengths
print()
for name, dnu in [('white light (300 THz wide)', 3e14), ('LED (30 nm at 600 nm)', c*30e-9/(600e-9)**2),
                  ('multimode HeNe (1.5 GHz)', 1.5e9), ('single-frequency laser (1 MHz)', 1e6)]:
    print(f"{name:32s} coherence length = {c/dnu:.3g} m")

laser              lambda    power   E (eV)   photons/s
violet diode     405.0 nm   0.005W    3.061   1.019e+16
green pointer    532.0 nm   0.001W    2.331   2.678e+15
HeNe             632.8 nm   0.001W    1.959   3.186e+15
Nd:YAG          1064.0 nm       1W    1.165   5.356e+18
telecom diode   1550.0 nm    0.01W    0.800   7.803e+16
CO2               10.6 um     100W    0.117   5.336e+21

HeNe divergence half-angle = 0.50 mrad
HeNe radiance  = 2.50e+09 W/(m^2 sr)
Sun radiance   = 2.00e+07 W/(m^2 sr)
ratio laser/Sun = 125

white light (300 THz wide)       coherence length = 9.99e-07 m
LED (30 nm at 600 nm)            coherence length = 1.2e-05 m
multimode HeNe (1.5 GHz)         coherence length = 0.2 m
single-frequency laser (1 MHz)   coherence length = 300 m

The photon rates are enormous: \(3 \times 10^{15}\) photons per second for a 1 mW helium–neon laser and more than \(10^{21}\) for a 100 W carbon dioxide laser. Light at these levels behaves very much like a classical electromagnetic wave, and most of this course treats it that way. Single-photon effects appear only at very low powers or in carefully engineered quantum light sources, the subject of part of the capstone.

The radiance comparison is striking. The Sun delivers about 1 kW to each square meter of the Earth, far more power than a laser pointer, yet the 1 mW beam is more than a hundred times brighter in radiance because all of its power comes from a tiny area into a tiny cone. Radiance cannot be increased by passive optics: no arrangement of lenses and mirrors can make an image brighter than its source. That is why a magnifying glass can focus sunlight to set paper alight only modestly, while a laser of modest power focused by the same lens can drill steel. It is also the root of laser hazards to the eye, discussed in lesson 12: the lens of the eye focuses a collimated laser beam to a spot a few micrometers across on the retina.

The coherence lengths span nine orders of magnitude. White light, with a bandwidth of a few hundred terahertz, is coherent over about a micrometer, which is why soap-film colors appear only for films thinner than a few micrometers. A light-emitting diode is coherent over tens of micrometers, a multimode helium–neon laser over about 20 cm, and a single-frequency laser with a 1 MHz linewidth over 300 m. Lesson 7 makes these estimates precise.

A short history

The physics of the laser was in place long before the device. In 1917 Albert Einstein, analyzing how atoms come to thermal equilibrium with blackbody radiation, showed that there must be a process of stimulated emission in addition to absorption and spontaneous emission; lesson 2 repeats his argument. For decades stimulated emission seemed a theoretical curiosity, because in thermal equilibrium it is always outweighed by absorption. In 1954 Charles Townes and his students at Columbia University built the maser, which amplified microwaves at 24 GHz using ammonia molecules, and Nikolay Basov and Aleksandr Prokhorov in Moscow developed the same ideas; the three shared the 1964 Nobel Prize in Physics. In 1958 Arthur Schawlow and Townes published a proposal for an optical maser using a Fabry–Pérot resonator, the key idea that made lasers practical.

Maiman's ruby laser of 1960 was followed within months by the helium–neon laser of Ali Javan, William Bennett and Donald Herriott at Bell Laboratories, the first continuous laser and the first gas laser. The semiconductor diode laser followed in 1962 from Robert Hall's group at General Electric and others, the carbon dioxide laser in 1964 from Kumar Patel at Bell Labs, and the neodymium-doped yttrium aluminum garnet (Nd:YAG) laser in the same year. In 1966 Charles Kao and George Hockham, working in England, argued that glass fibers could carry light over long distances if impurities were removed; Corning made a fiber with a loss below 20 dB/km in 1970, and Kao received the Nobel Prize in Physics in 2009. That same 2009 prize was shared with Willard Boyle, born in Amherst, Nova Scotia, and George Smith for the charge-coupled device, the light sensor in digital cameras and telescopes.

The past two decades have brought more Nobel Prizes for laser physics than for almost any other field. The 2018 prize went to Arthur Ashkin for optical tweezers and to Gérard Mourou and Donna Strickland for chirped pulse amplification, the technique behind today's most intense lasers; Strickland, who did the work as a doctoral student and later joined the University of Waterloo, was the first woman to win the physics prize in 55 years. The 2023 prize went to Pierre Agostini, Ferenc Krausz and Anne L'Huillier for attosecond pulses of light, building on work in which Paul Corkum of the National Research Council in Ottawa played a central part. Lesson 8 explains both techniques. In December 2022 the National Ignition Facility at Lawrence Livermore National Laboratory used 192 laser beams to produce, for the first time, more fusion energy (3.15 MJ) than the laser energy delivered to the target (2.05 MJ), a milestone for fusion energy research.

Photonics as an industry

Photonics is now a large industry. Lasers for cutting, welding and marking metals are standard in manufacturing. Fiber-optic links carry almost all long-distance data traffic, and the data centers that host cloud computing use millions of short optical links. Lidar, light detection and ranging, measures distances by timing laser pulses and is used in surveying, forestry, atmospheric science and driver-assistance systems. Medicine uses lasers for eye surgery, dermatology, dentistry and the removal of cancers, and uses optical imaging for diagnosis. Displays, solid-state lighting and solar cells are photonic technologies too.

The United States has a long tradition in photonics. Bell Laboratories in New Jersey produced the helium–neon and carbon dioxide lasers and much of the early theory; Corning in New York made the first low-loss optical fibers; MIT Lincoln Laboratory and university groups developed semiconductor lasers and laser radar; and national laboratories such as Lawrence Livermore operate the largest lasers in the world, including the National Ignition Facility. Regional clusters in places such as Rochester, Tucson and central Florida grew around optics companies and university programs.

The plan of the course

The course has three parts. Lessons 2 to 5 build the physics of a laser from the inside out: how light interacts with atoms (lesson 2), how spectral lines are broadened and how a population inversion produces gain (lesson 3), how mirrors form a resonator with well-defined modes (lesson 4), and how gain and loss balance to set the threshold and output power (lesson 5). Lessons 6 to 8 look at real lasers and their beams: the main types of laser (lesson 6), the Gaussian beams and coherence properties they produce (lesson 7), and the techniques for making short, intense pulses (lesson 8). Lessons 9 to 12 turn to photonics: guiding light in optical fibers (lesson 9), nonlinear optics (lesson 10), light-emitting diodes, photodetectors, modulators and integrated photonic circuits (lesson 11), and finally a capstone on photonics at work in communications, sensing, manufacturing, medicine and quantum technology (lesson 12).

Each lesson has a runnable Python program, using only the standard library, that turns the formulas into numbers. The programs are short enough to read in a few minutes, and you are encouraged to change their parameters. Many of the most useful skills in photonics are estimation skills: knowing that a beam of a given size will diffract by a given angle, that a cavity of a given length will have modes spaced by a given frequency, or that a link of a given length will lose a given number of decibels. The programs make those estimates quick and reliable.