Photonics · 13 min
Linewidth, spectral width, RIN, M², coherence length — five numbers that answer five different questions, all quoted in units your experiment does not use. This guide translates each into what your measurement actually pays for.
The governing ideas
Most laser-buying mistakes are unit mistakes: a number read in the wrong domain, or a spec that answers a question the experiment never asks. Three conversions cover almost everything.
one mode: Δν (kHz–MHz) · whole output: Δλ (up to ~0.5 nm)
A multimode laser can quote a narrow per-mode linewidth while its full emission spans half a nanometre of comb. For spectroscopy, the envelope is what convolves onto every band you measure — always ask for the width of the whole output.
L_c ≈ c / (π·Δν) → 1 MHz ≈ 95 m · 0.1 nm @ 532 ≈ 1 mm
The same number in a different unit — and it follows the whole envelope, not one mode. A multimode laser has millimetre coherence regardless of how narrow each mode is, which is why holography setups care about a spec Raman setups can ignore.
RMS ≈ √(RIN × BW) → −120 dB/Hz × 1 MHz ≈ 0.1%
Relative intensity noise is a density, so it only becomes a number your detector feels after integrating over your measurement band. The same laser is quiet for a slow imaging camera and loud for a 100 kHz trap — a RIN figure without a frequency range attached is not a specification.
spot Ø ∝ M² · peak intensity ∝ 1/M⁴
M² measures how much worse than a perfect Gaussian the beam focuses: the spot diameter grows linearly with it and the peak intensity collapses with its fourth power. Going from M² = 1.05 to 3 turns a diffraction-limited focus into the same power spread nine times thinner — the difference between trapping a bead and gently warming it, or between 80% and 20% coupling into a single-mode fibre.
It is also the spec that matters least when no focus is involved. Wide-field illumination, absorption measurements, and bathing a sample in light are all blissfully indifferent to beam quality — which makes M² the clearest example of a specification you should sometimes decline to pay for.
Interactive
Five laser constructions, with every specification converted live into the units experiments are actually designed in. Switch from the fibre laser to the free-running diode and watch a kilometre of coherence become half a millimetre.
Pick a laser construction and see its emission spectrum with the numbers translated: nanometres, gigahertz, wavenumbers, and metres of coherence — plus what your RIN and M² budgets buy at the detector and the focus.
detuning from centre (nm)
Spectral width
< 0.001 pm
1000 kHz
Raman broadening
≈ 0 cm⁻¹
added to every band at 532 nm
Coherence length
95 m
L_c ≈ c / (π·Δν)
Fringe visibility
100%
at 10.0 cm path difference
RIN, integrated
0.10% RMS
-120 dB/Hz over 1 MHz
Focused spot
19 µm
Ø, f = 50 mm lens, 2 mm beam
Peak intensity
68%
vs a perfect M² = 1 beam
M²
1.10
beam quality factor
10.0 cm
-120 dB/Hz — good DPSS territory
M² 1.10 — diffraction-limited class
What this construction buys
The MSL single-frequency class: one longitudinal mode, ~100 m coherence — everything most coherent experiments need.
The unit conversions are exact; the spectra are schematic archetypes with widths typical of each construction. Coherence length uses the Lorentzian convention L_c = c/(π·Δν) — other definitions differ by factors of order one. The RIN integral assumes a flat spectrum over a 1 MHz detection band, and the focus assumes an f = 50 mm lens on a 2 mm beam. Real datasheets quote each number under their own conditions — the point of this lab is knowing which number to ask for.
At a glance
| Specification | What it measures | Typical good value | When it binds | Red flag |
|---|---|---|---|---|
| Linewidth | The frequency width of one longitudinal mode | <20 kHz fibre · <1 MHz DPSS | Heterodyne detection, DLS, velocimetry, long-path interferometry | A kHz number quoted for a laser whose full output is a multimode comb |
| Spectral width | The width of the entire emission envelope | <0.03 nm for 532 nm Raman work | Every kind of spectroscopy — it is instrumental broadening on every band | “Linewidth” on the datasheet with the envelope width nowhere to be found |
| Coherence length | How far the phase survives: L_c ≈ c / (π·Δν) | Metres to kilometres, single frequency | Interferometry, holography, OCT reference arms, speckle behaviour | Computed from the single-mode linewidth of a laser that runs many modes |
| RIN | Intensity noise density vs frequency, dB/Hz | −120 dB/Hz solid · −150 dB/Hz fibre-quiet | Optical trapping, balanced detection, anything reading small AC signals | A single number with no frequency range attached to it |
| Power stability | Slow drift of mean power over minutes to hours | <1–2% over 8 h | Quantitative imaging, mapping, any measurement compared across time | Confused with RIN — a laser can be RIN-quiet and still drift 5% per hour |
| M² | How close the beam is to a perfect Gaussian (1.0 = perfect) | <1.2 for focusing work | Tight focusing, single-mode fibre coupling, trapping, nonlinear pumping | Quoted at low power for a laser you will run at maximum |
Each application is ruled by one or two specifications and genuinely indifferent to the rest. Knowing which is which is most of the negotiation.
| Application | Ruling spec | Typical requirement | Forgiving of |
|---|---|---|---|
| Raman spectroscopy | Spectral width + wavelength stability | Whole envelope <1 cm⁻¹ (0.03 nm at 532; 0.06 nm at 785) and a centre that does not drift | kHz-class linewidth — 1 MHz is already 3×10⁻⁵ cm⁻¹, five orders below anything you can resolve |
| Interferometry & holography | Coherence length | L_c comfortably beyond the largest path difference — metres for holography of real objects | Moderate RIN, absolute wavelength accuracy |
| DLS, heterodyne, velocimetry | True linewidth + RIN | kHz-class single-frequency operation; the beat spectrum is the measurement | M² and a few percent of slow power drift |
| Optical trapping | RIN in the trap band + pointing | Quiet from ~0.1 Hz to 100 kHz, where intensity noise shakes the trap stiffness | Linewidth almost entirely — trapping is incoherent detection |
| Quantitative fluorescence & mapping | Long-term power stability | <1–2% drift over the acquisition, or intensities cannot be compared across the map | Linewidth, coherence — fluorescence forgets the phase instantly |
| Fibre coupling & nonlinear pumping | M² + polarization | M² < 1.2 for efficient single-mode coupling; conversion efficiency rides on focused intensity | Coherence length beyond millimetres |
A defensible order
The goal is not the best laser — it is the laser that is exactly good enough on every axis your measurement feels, and unremarkable on the ones it cannot.
Every experiment compares the light against something: a phase (interferometry), a frequency (heterodyne, DLS), an intensity level (trapping, imaging), or a geometry (focusing, coupling). That single question routes you to coherence, linewidth, RIN, or M² — and the other specs become secondary.
Specifications only bind in your units: nm of envelope into cm⁻¹ at your excitation, dB/Hz integrated over your detection band, coherence length against your actual path difference. The lab above does the arithmetic — a spec you cannot state in your own units is a spec you cannot verify.
kHz linewidth for fluorescence excitation, kilometre coherence for Raman, M² = 1.05 for bathing a sample — each is real money for capability the measurement physically cannot feel. The best value laser is the one that is exactly good enough on every axis that matters and unremarkable on the rest.
Spectral width of the whole output, not one mode. RIN over your band, not at one flattering frequency. M² at your operating power. Stability over your acquisition time and your lab’s temperature swing. A good supplier answers in a day; the datasheet alone rarely does.
The source families
Every laser family in the catalog is a different answer to which specification deserves the money. Read them that way and the range stops being a wall of part numbers.
The specification ceiling: kilometre-scale coherence and the lowest RIN in the catalog, at watt-class powers. Bought for heterodyne detection, interferometry, and measurements where the laser must vanish from the noise budget.
One longitudinal mode and ~100 m of coherence — the workhorse single-frequency class that covers almost every spectroscopy and coherent-imaging need at a fraction of fibre-laser cost.
The pragmatic spectroscopy answer: the envelope is 0.08 nm but the centre cannot drift, which is the spec that keeps a Raman axis calibrated. Milliwatts per euro far beyond single-frequency.
The stability specialist: a published long-term power-stability grade plus a built-in modulator for shuttering and lock-in schemes — the card to play when the measurement is quantitative intensity.
The same families run from the UV to 1064 nm and beyond, at powers from milliwatts to tens of watts. If you know which specification rules your measurement, we can shortlist the wavelength and power variants in a single email.
Going deeper
The companion guides apply this vocabulary to specific measurements, and the accessories are how specs survive contact with a real optical bench.
The application deep-dive where RIN and pointing stability rule: what laser noise costs in piconewtons.
Where spectral width and wavelength drift decide the measurement — the guide this one generalises from.
The instrument that either resolves your laser’s envelope or is broadened by it.
The full catalog — single-frequency, locked, low-noise, and multimode — filterable by wavelength and power.
Set power optically instead of turning the drive current down into the noisy, drifting low end of its range.
Laser clean-up filters strip the broadband pedestal and side modes that a spectral-width figure quietly includes.
Every specification is quoted under the manufacturer's conditions: after full warm-up, at a favourable power setpoint, over a stated (or unstated) timescale. A linewidth over 1 ms and over an hour are different physical claims; power stability in a ±0.1 °C lab does not transfer to a ±2 °C one. None of this is dishonesty — it is convention — but it means the question “under what conditions?” belongs in every quote request.
Common questions
Linewidth is the frequency width of a single longitudinal mode — for a good single-frequency laser, kilohertz to a megahertz, which at 532 nm is far less than a millionth of a nanometre. Spectral width is the width of everything the laser emits. A multimode laser can honestly quote a narrow per-mode linewidth while its full output spans half a nanometre of comb. The two numbers differ by up to eight orders of magnitude, they are both called “linewidth” in careless catalogues, and confusing them is the most expensive misunderstanding in laser buying.
You need a narrow total spectral width — which in practice usually means buying single-frequency, but for the envelope, not the coherence. Every band in a Raman spectrum is convolved with the laser’s emission profile, so a 0.3 nm diode adds 1.6 cm⁻¹ of broadening at 785 nm while a single-frequency laser adds effectively zero. What you do not need is kilohertz-class linewidth: 1 MHz and 1 kHz are equally invisible to any spectrograph on earth. Pay for the narrow envelope and stable centre wavelength; do not pay extra for coherence you cannot use.
L_c ≈ c / (π·Δν) for a Lorentzian lineshape — other conventions (c/Δν, Gaussian factors) differ by factors of order one that rarely change a decision. The useful anchors: 1 MHz → about 95 m; 20 kHz → nearly 5 km; a 0.1 nm multimode envelope at 532 nm → about a millimetre. That last one is the trap: coherence follows the whole envelope, so a multimode laser has millimetre coherence no matter how narrow each mode is. If your interferometer arms differ by a metre, that laser will show you no fringes at all.
Relative intensity noise is a spectral density: the noise power in a 1 Hz slice, relative to the mean optical power, at a given frequency. To get a number your detector feels, integrate over your measurement bandwidth: RMS ≈ √(RIN × bandwidth). At −120 dB/Hz over a 1 MHz band that is 0.1% RMS; a fibre laser at −150 dB/Hz over the same band gives 0.003%. Two consequences: a RIN number without a frequency range is meaningless, and the bandwidth that matters is your detection band — a laser can be noisy at 100 kHz and irrelevantly so if you only measure below 1 kHz.
Only if a focus or a fibre is involved. The focused spot diameter scales with M² and the peak intensity falls as M⁴, so 1.3 versus 1.05 costs about 25% in spot size and 50% in peak intensity — decisive for single-mode fibre coupling, trapping stiffness, and nonlinear conversion, invisible if the beam just needs to illuminate a sample. Also check the fine print: M² is often specified at modest power, and thermal lensing can degrade it exactly at the maximum power you bought the laser for.
Because for spectroscopy the centre wavelength drifting matters more than the envelope width. A free-running diode moves about 0.3 nm per °C of case temperature; at 785 nm every 0.1 nm of drift shifts the entire Raman axis by 1.6 cm⁻¹, silently recalibrating the instrument between morning and afternoon. A volume Bragg grating pins the centre so it cannot wander and compresses the envelope to ~0.08 nm — not as narrow as single-frequency, but stable, powerful, and much cheaper per milliwatt. It is the pragmatic 785 nm answer, which is why the locked variant is the Raman workhorse.
Describe the measurement — what it compares, over what bandwidth, at what wavelength — and we will tell you which two numbers matter and which laser meets them without charging you for the other four.