CW Laser

Emits a steady monochromatic collimated beam at one wavelength.

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In the real world

Laser technology occupies a central position within photonics because laser light exhibits several properties that distinguish it from conventional light sources, beyond simple monochromaticity. A laser beam is characterized by high spatial coherence, which permits propagation over considerable distances with minimal divergence — frequently limited only by diffraction — and allows the beam to be focused to a very small spot, yielding a correspondingly high intensity.

This coherence typically extends to the temporal domain as well: a continuous-wave laser emits within a very narrow spectral bandwidth, in contrast to sources such as incandescent or gas-discharge lamps, which radiate across a broad spectral range. Emission is steady rather than pulsed: the output power a detector reads is the same at every instant.

The theoretical foundation for the laser predates its experimental realization: Townes, Schawlow, Basov, and Prokhorov independently developed the theory of stimulated emission as a mechanism for light amplification, building on the microwave maser Townes had demonstrated in 1953 — the concept was initially termed the "optical maser" before "laser" became standard usage. Theodore Maiman first realized this theory experimentally in 1960, constructing the first laser: a pulsed, lamp-pumped ruby crystal. The same year saw two further milestones: the helium–neon laser, the first to operate with a gaseous gain medium, and the first semiconductor laser diode.

Real laser beams are not perfectly collimated: they exhibit Gaussian propagation and diverge with distance. For a beam of waist radius w₀, the far-field half-angle divergence is given by

\theta \approx \frac{\lambda}{\pi w_0}

Far-field divergence half-angle of a Gaussian beam (small-angle, TEM₀₀ mode).

E_{\text{photon}} = \frac{hc}{\lambda}

Photon energy — why shorter wavelengths (blue, UV) carry more energy per photon than longer ones (red, IR).

These properties originate from stimulated emission within a resonant cavity: a gain medium bounded by two mirrors amplifies a specific wavelength on each round trip, while losses — mirror transmission, absorption, scattering — deplete it. Above threshold, the pump rate at which round-trip gain first equals round-trip loss, the cavity sustains the stable, highly monochromatic, spatially coherent beam described above.

Coherence length

No real laser is perfectly monochromatic. The emission occupies a finite linewidth, and the physical meaning of that linewidth is that the optical phase drifts: predict the phase far enough ahead and the prediction stops being right. Coherence length is the distance over which the phase stays predictable — formally the coherence time times the vacuum speed of light^[1].

It matters because it decides whether an experiment sees fringes. Split a beam, send the halves down two arms and recombine them: the two waves can only interfere if the one arriving from the long arm still remembers the phase of the one from the short arm. Make the arms differ by much more than the coherence length and the fringes vanish, leaving the ports simply to add their powers^[1]. The same constraint sets how deep a hologram can be recorded, and how far apart the two arms of an interferometric sensor may be.

Linewidth and coherence length are inversely related, though the exact prefactor depends on the lineshape and is not universal^[1,2]. For the Lorentzian spectrum produced by a random walk of the optical phase, the expression is^[1]

L_{\text{coh}} = c\,\tau_{\text{coh}} = \frac{c}{\pi\,\Delta\nu}

Lorentzian lineshape: the distance at which the coherence function falls to 1/e, for a FWHM linewidth Δν. The literature often quotes this without the π when only an order of magnitude is wanted.

The span across real sources is enormous. A stabilised single-frequency solid-state laser at 10 kHz linewidth reaches roughly 9.5 km; systems built for optical clocks, stabilised below 1 Hz, exceed 300 000 km. A laser diode is far shorter, limited by phase noise from spontaneous emission in a short, strongly out-coupled resonator. At the opposite extreme, the superluminescent diodes used for optical coherence tomography are made deliberately broadband — tens of nanometres — precisely because a coherence length of a few micrometres is what gives that technique its axial resolution: only light returning from one narrow depth can still interfere with the reference^[1].

Two cautions are worth carrying. The shape and width of a spectrum do not by themselves fully determine coherence: a frequency comb has a broad spectrum and excellent long-range coherence, and no single-number coherence length describes it^[1]. And “coherence length” is not one quantity but a family of them — several inequivalent definitions are in use, and which is meant matters as soon as a real source departs from an idealised lineshape^[2].

In OpticalSetup

The CW Laser emits either a single collimated ray or, in Beam with size mode, a fan of 25 parallel rays sampling a finite beam width — this is what lets the tracer show a lens actually focusing a beam of nonzero extent, rather than a single infinitesimal ray that can never miss an aperture.

Its spectrum is monochromatic by construction: the beam carries one wavelength and is drawn and detected as one colour. That is the point of the split between the three laser sources — a bench that needs real spectral width, with distinct wavelengths propagating and dispersing separately, needs the Pulsed Laser or the Supercontinuum laser instead, both of which model where that width comes from. Polarization is set directly as a Stokes vector rather than emerging from a modeled cavity.

What the CW Laser does carry is a coherence length, and it is the one place a linewidth enters this source. It changes no ray and no colour; it decides how far the two arms of an interferometer may differ before their fringes fade. Fields recombining at a beamsplitter are weighted, pair by pair, by a Gaussian visibility in their path difference.

V(\Delta L) = \exp\!\left[-4\ln 2\left(\frac{\Delta L}{l_c}\right)^{2}\right]

Fringe visibility against arm mismatch. The coherence length l_c is the full width at half maximum of this envelope, so ΔL = l_c/2 halves the contrast.

l_c = \frac{2\ln 2}{\pi}\,\frac{\lambda^{2}}{\Delta\lambda}

The linewidth the inspector reports as implied by a given coherence length — the Gaussian convention standard in optical coherence tomography, where l_c is the axial resolution.

Zero, the default, means the idealised source: the arms interfere perfectly however far apart they are, which is how every scene behaved before this parameter existed. Give it a finite value and the bench becomes a ruler — sweep the delay line and fringes appear only where the arms match, which is the measurement an interferometer is actually for. The inspector reports the linewidth that coherence length implies, so the two ways of describing the same source stay visible together: 50 nm at 840 nm gives 6.2 µm, the familiar axial resolution of a broadband OCT source.

Note the convention. This model uses the Gaussian form standard in optical coherence tomography, in which l_c is the full width at half maximum of the visibility envelope. The Lorentzian expression quoted above^[1] is a different definition — the 1/e point of a differently shaped coherence function — and the two disagree by a numerical factor. Neither is more correct: they describe different lineshapes under different conventions, and real source spectra are non-Gaussian often enough that the choice of definition is itself a documented source of disagreement^[2].

Energy is conserved at every visibility: the self-powers of the recombining fields always add, and only their cross term is scaled by V. The two ports of an interferometer therefore always sum to the input, whether they are fringing hard or have washed out to a flat half each.

Simplified vs. reality

There is no modeled gain medium, cavity round trip, or threshold — wavelength, polarization, and power are configured directly as source parameters, not derived from first principles. Divergence and M² are not modeled: a collimated beam stays perfectly parallel over any distance.

Coherence length is a visibility envelope applied at recombination, not a simulated phase-noise process: the beam carries no actual linewidth, so the source stays exactly one wavelength for colour, dispersion, and every spectral readout, and the implied linewidth is reported rather than propagated. Spatial coherence is not modelled at all — only the temporal kind — and the envelope is Gaussian by assumption, so a lineshape that behaves differently, a frequency comb above all, cannot be represented by this single number.

CW Laser

In the real world

Coherence length

In OpticalSetup

Related components

References

Further reading