L08 · Synthesis and measurement

Laser Diagnostic Bench

Connect an unknown source to six instruments. Acquire a pump sweep, finite-resolution spectrum, beam caustic, polarization scan, Michelson visibility and fast photodiode trace, then classify the evidence.

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

For an unknown case, collect the pump sweep, spectrum, coherence and either beam or fast trace before classifying. Acquired readouts persist across instruments; changing a setting clears them.

Four phenomenological source families at 1064 nm, not material-calibrated devices. One source law supplies every instrument: normalized Lorentzian lines, Gaussian-Schell beam propagation and linear/unpolarized polarization mixture. The spectrometer convolves a Lorentzian instrument response; its measured peak width can remain unresolved. Beam quality comes from a multi-plane caustic fit, not one image, and is a teaching proxy rather than an ISO measurement. Michelson assumes balanced arms and perfect spatial/polarization overlap; optical path difference is twice mirror travel. The photodiode samples classical complex fields with finite bandwidth; RF bins are not calibrated noise PSD or quantum correlations. No finite set of these measurements uniquely identifies every real source.

Start with the essentials

Focus question: Which evidence distinguishes a narrow ASE source from a laser oscillator, or a multimode laser from a single-mode laser?
One-sentence intuition: A threshold slope change, resolved modal structure, coherence revivals and propagation quality tell complementary stories. Treat unresolved linewidth as a bound.

Core mathematical model

Finite spectral resolution

S_{\mathrm{rec}}(\nu)=(S*K)(\nu),\quad \Delta\nu_{\mathrm{rec}}=\Delta\nu_s+\Delta\nu_{\mathrm{inst}}

The width sum applies to a single Lorentzian line and Lorentzian instrument kernel. Overlapping multimode peaks need not obey that single-line inference.

The spectrum predicts coherence

g^{(1)}(t)=\sum_j p_j e^{-\pi\Delta\nu_j|t|}e^{2\pi i\nu_jt}

The same normalized Lorentzian mixture drives the interferometer and the sampled complex fields. A multimode comb creates visibility dips and revivals.

Balanced Michelson measurement

V(\delta)=|g^{(1)}(\delta/c)|,\quad P_d=\frac{P}{2}[1+V\cos\phi]

The selected optical path difference is twice mirror travel. The phase scan records one output port; both output ports together conserve input power.

Measure a caustic, not one image

w^2(z)=w_0^2+\theta^2z^2,\quad M^2=\frac{\pi w_0\theta}{\lambda}

The model uses a circular Gaussian-Schell source with second-moment radius. The propagation fit determines the beam-quality proxy; the displayed image represents the selected camera plane.

Analyzer transmission

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

A linear polarized fraction is mixed with an unpolarized fraction. Highly polarized ASE is included deliberately: polarization alone cannot prove oscillation.

Common difficulties

First crossing is not always coherence length

Typical misconceptionEvery visibility dip defines a unique coherence length.

Better mental modelThe readout reports the first e-fold crossing within a finite scan. Multimode revivals and unresolved long coherence prevent a universal one-number description.

Detector noise is conditional

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

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

Run the experiment

01
Learn four known families
Compare the known-source presets. Acquire the pump sweep, spectrum and coherence for each.
What to observe: Fluorescence and ASE have smooth pump response. The laser cases have a teaching threshold kink; multimode coherence revives rather than simply decaying.
02
Expose instrument limits
Choose a single-mode source and broaden the spectrometer response. Acquire again, then reduce the response width.
What to observe: A resolution-limited peak does not establish the true linewidth. Changing a setting clears all measurements to preserve a consistent preparation.
03
Test 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. Narrow electrical bandwidth suppresses resolved beating; strong polarization can also occur in ASE.
04
Classify an unknown
Load an unknown source. Acquire pump, spectrum, coherence and either beam or fast data, then submit a source class.
What to observe: The challenge requires converging evidence. A correct answer matches this teaching family, not a universal proof of every possible real source.