L08 · Synthesis and measurement

Laser Diagnostic Bench

Which measurements tell laser light apart from fluorescence and amplified spontaneous emission? It takes several; no single one settles it. Output that suddenly climbs faster once the pump passes a threshold, separate cavity modes in the spectrum, Michelson fringe contrast that fades and then returns as the path difference grows, and a beam that propagates well together make the case. A linewidth too narrow for the spectrometer to resolve is only an upper limit.

Connect an unknown source to six instruments. Record a pump sweep, a spectrum at finite resolution, the beam caustic, a polarization scan, Michelson visibility and a fast photodiode trace, then decide from the evidence what the source is.

Source identity $\text{—}$

Acquired instruments $\text{—}$

Power meter $\text{—}$

Local pump-output slope $\text{—}$

Recorded dominant peak FWHM $\text{—}$

Instrument response FWHM $\text{—}$

Caustic-fit beam quality $\text{—}$

Selected camera-plane radius $\text{—}$

Analyzer transmitted power $\text{—}$

Linear polarization degree $\text{—}$

Visibility at selected delay $\text{—}$

First e-fold visibility crossing $\text{—}$

Recorded relative intensity RMS $\text{—}$

Evidence for classification $\text{—}$

L08 · Diagnostic challenge

Measure first, then identify the source

Source pump setting

r

1.8

Spectrometer response width

\Delta\nu_{\mathrm{inst}}

0.1\,\mathrm{GHz}

Camera distance from waist

z

30\,\mathrm{cm}

Analyzer axis angle

\theta

0\,\mathrm{{}^\circ}

Michelson optical path difference

\delta

15\,\mathrm{cm}

Photodiode electrical bandwidth

B

1.5\,\mathrm{GHz}

Recorded time window

t_w

10\,\mathrm{ns}

Random realization seed

s

13

Before classifying an unknown source, collect the pump sweep, spectrum and coherence, plus either the beam caustic or the fast trace. The demonstration acquires all six instruments automatically. Unknown challenges keep only the selected instrument after a setting changes; acquire the other evidence again.

The four source families at 1064 nm are phenomenological models, not devices calibrated to real materials. One source description feeds every instrument: normalized Lorentzian lines, Gaussian-Schell beam propagation and a mix of linearly polarized and unpolarized light. The spectrometer convolves the spectrum with a Lorentzian instrument response, so a measured peak width may still be unresolved. Beam quality comes from fitting the caustic across several planes, not from one image, and it is a teaching proxy, not an ISO measurement. The Michelson interferometer assumes balanced arms and perfect spatial and polarization overlap; the optical path difference is twice the mirror travel. The photodiode samples classical complex fields with a finite bandwidth, and its RF bins are not a calibrated noise power spectral density or quantum correlations. No finite set of these measurements can identify every real source uniquely.

Physics tutorial

Identify a source from converging evidence

BackgroundFluorescence, amplified spontaneous emission (ASE) and laser output can look alike in brightness, directionality or polarization. To tell them apart, combine the response to the pump with spectral, spatial and time measurements.

Why it mattersReal instruments have limited resolution and bandwidth, so what a detector records is not the ideal property of the source. Several kinds of source can also give similar results in any single measurement.

Start with the essentials

Focus question: What evidence tells a narrow ASE source from a laser oscillator, or a multimode laser from a single-mode one?
One-sentence intuition: A kink in the pump response, resolved mode structure, revivals in coherence and beam quality each add a different piece of evidence. A linewidth the instrument cannot resolve is only a bound.

Core mathematical model

Finite spectral resolution

\begin{aligned}S_{\mathrm{rec}}(\nu)&=(S*K)(\nu)\\\Delta\nu_{\mathrm{rec}}&=\Delta\nu_s+\Delta\nu_{\mathrm{inst}}\end{aligned}

Adding the widths works only for a single Lorentzian line measured with a Lorentzian instrument response. Overlapping multimode peaks need not follow this rule.

The spectrum predicts coherence

\begin{aligned}g^{(1)}(t)&=\sum_j p_j e^{-\pi\Delta\nu_j|t|}\\&\qquad\cdot e^{2\pi i\nu_jt}\end{aligned}

The same normalized mix of Lorentzian lines drives both the interferometer and the sampled complex fields. Each spectral component accumulates its own phase as the delay increases. The components can cancel and later align again, so a multimode comb makes visibility dip and revive.

Michelson interferometer with balanced arms

\begin{aligned}V(\delta)&=|g^{(1)}(\delta/c)|\\P_d&=\frac{P}{2}[1+V\cos\phi]\end{aligned}

The optical path difference is twice the mirror travel. The phase scan records one output port; the two ports together carry all the input power.

Beam quality from a caustic, not one image

\begin{aligned}w^2(z)&=w_0^2+\theta^2z^2\\M^2&=\frac{\pi w_0\theta}{\lambda}\end{aligned}

The model uses a circular Gaussian-Schell source with a second-moment radius. A wider beam in one plane can be either a large waist or rapid divergence. A fit along the propagation direction separates these and gives the beam-quality proxy; the image shows only the chosen camera plane.

Analyzer transmission

P_\theta=P[(1-p)/2+p\cos^2\theta]

The light is part linearly polarized and part unpolarized. Highly polarized ASE is included on purpose, because polarization alone cannot prove that a laser is oscillating.

Common difficulties

The first dip is not always the coherence length

Typical misconceptionEvery dip in visibility marks a unique coherence length.

Better mental modelThe readout reports where the visibility first drops to one over e within the finite scan. Multimode revivals and long coherence that the scan cannot resolve mean no single number describes every case.

Detector noise depends on how you measure

Typical misconceptionThe recorded relative RMS is an intrinsic noise specification of the laser.

Better mental modelIt depends on the bandwidth, the time window and the random realization. The RF bins from the finite window are a transform of the same trace, not calibrated RIN or a quantum photon-statistics result.

Run the experiment

01
Learn the four known sources
Predict which source will show a threshold kink, then compare the four known-source presets. All six instruments are acquired automatically; switch between Pump sweep, Spectrum and Coherence.
What to observe: Fluorescence and ASE respond smoothly to the pump. The lasers show a threshold kink in this teaching model, and multimode coherence revives instead of simply decaying.
02
Find the instrument limits
Choose Known single-mode laser, select Spectrum and widen the response. It updates as you drag; narrow the response again.
What to observe: A peak limited by resolution does not give the true linewidth. The demonstration reacquires all instruments at the new setting. In an unknown challenge, only the selected instrument is reacquired; the other records are hidden until measured again.
03
Add independent measurements
Acquire the beam caustic and polarization. For a multimode source, compare fast traces at broad and narrow detector bandwidth.
What to observe: The beam-quality proxy uses several planes. A narrow electrical bandwidth hides the resolved beating between modes. ASE can also be strongly polarized.
04
Classify an unknown source
In Advanced controls, load an unknown source. One instrument is acquired at entry; use the instrument buttons to collect the pump sweep, spectrum and coherence, plus either the beam or the fast trace, then submit a class.
What to observe: The challenge needs several pieces of evidence that agree. A correct answer matches this teaching family; it is not a proof that would hold for every possible real source.