L01 · Laser foundations

Laser vs Lamp vs LED

Move a detector along the beam, then inspect the same source with a spectrometer, double slit, polarizer and fast photodiode. Separate power, directionality and coherence with a controlled counterexample.

Detector beam radius $\text{—}$

Far-field half-angle $\text{—}$

Peak irradiance $\text{—}$

Fringe visibility $\text{—}$

Temporal correlation $\text{—}$

Slit spatial correlation $\text{—}$

Finite-screen collected power $\text{—}$

Power after analyzer $\text{—}$

Actual path difference $\text{—}$

Counterexample challenge $\text{—}$

Configure the source

Properties are not synonyms

Beam expanderExpand the waist tenfold; reduce angular spread consistently.High spatial coherenceChange transverse coherence width, also changing divergence.Narrow spectral linesSwitch between 5 MHz and 2 THz line widths; temporal coherence follows.Five longitudinal modesEqual weights separated by 500 MHz; inspect coherence revivals.Linear polarizationOtherwise use an unpolarized ensemble.Technical intensity variation20 MHz field-envelope modulation adds spectral sidebands.Equal optical pathsSet temporal delay to zero without changing spatial coherence.Mean source power

P

10\,\mathrm{mW}

Detector distance

z

250\,\mathrm{cm}

Path difference, logarithmic scale

\log_{10}(\Delta L/\mathrm{mm})

2

Analyzer rotation

\theta

0\,\mathrm{^\circ}

Challenge: expand the beam, raise mean power to at least 80 mW, and keep fringe visibility below 0.1. Can brightness and directionality fail to buy coherence?

Source presets are teaching examples. Edits configure a synthetic source; they do not redefine every real lamp, LED or laser.

Idealized conditioned beams at 633 nm, not complete lamp or LED spectra. Gaussian-Schell propagation; equal-power longitudinal modes with Lorentzian lines. Beam expansion changes both beam and coherence width. The screen uses relative brightness with square-root display gamma. Ideal diagnostics have no measurement noise; the photodiode passes frequencies below 100 MHz and shows technical amplitude modulation, not photon statistics.

Start with the essentials

Focus question: Can increased power make the normalized fringe visibility improve?
One-sentence intuition: Power scales the signal. Coherence controls interference contrast. Temporal coherence must agree with the spectrum, while spatial coherence describes correlations across the beam.

Core mathematical model

Power and irradiance

I(r,z)=\frac{2P}{\pi w^2(z)}e^{-2r^2/w^2(z)}

Integrating over the transverse plane returns mean power. The screen spans 40 mm and may miss weak tails; the displayed peak irradiance remains a linear physical quantity.

A consistent conditioned beam

w^2(z)=w_0^2+\theta_d^2z^2,\quad\theta_d=\frac{\lambda}{\pi}\sqrt{w_0^{-2}+\xi^{-2}}

The Gaussian-Schell model couples coherence width to angular spread. Beam expansion multiplies both waist and coherence width by ten, conserving power. The envelope geometry is schematic and does not simulate a lens train.

Spectrum determines temporal coherence

g^{(1)}(\tau)=e^{-\pi\Delta\nu|\tau|}\sum_j p_j e^{2\pi i\nu_j\tau},\quad\sum_jp_j=1

Each component has the same Lorentzian frequency FWHM. Five longitudinal modes can produce revivals. Technical field-envelope modulation adds sidebands to this same component list, rather than independently changing the time trace.

Equal-intensity slits

V=e^{-d^2/(2\xi^2)}|g^{(1)}(\Delta L/c)|,\qquad d=0.5\,\mathrm{mm}

The two slits sample the source exit plane after any beam expansion. The fringe coordinate is in periods, with equal arm intensities. Equal optical paths remove temporal delay but cannot repair low spatial coherence.

Common difficulties

Source labels are not definitions

Typical misconceptionEvery laser is perfectly monochromatic and every LED is completely incoherent.

Better mental modelThese presets are idealized comparisons. Real sources have finite coherence, may be multimode, and can be filtered or spatially conditioned.

Display brightness is not a measurement

Typical misconceptionA similar-looking detector spot means the same irradiance.

Better mental modelThe screen uses relative brightness and display gamma. Compare calibrated irradiance readouts and profiles, not screen brightness alone.

Run the experiment

01
Power is not contrast
Choose Lamp, enable the beam expander, and raise power to 80 mW or more. Inspect Double slit and check the counterexample.
What to observe: Irradiance increases while normalized visibility stays low. Collimation changes the spatial coherence sampled by fixed slits, but does not narrow the spectrum.
02
Separate space from time
Choose Single mode. Turn off high spatial coherence and balance the optical paths. Then restore spatial coherence and broaden the spectral lines at nonzero delay.
What to observe: Either spatial decorrelation or temporal decorrelation can wash out fringes. The readouts identify which one limits this measurement.
03
A spectrum is more than one width
Choose Multiple modes and inspect Spectrum. Sweep path difference and look for correlation revivals. Toggle technical intensity variation and compare the photodiode with spectral sidebands.
What to observe: The five modes are separated by 500 MHz. The ideal photodiode rejects intermode beats above its 100 MHz cutoff while retaining the technical 20 MHz modulation and its intensity harmonic.
04
Inspect polarization independently
Use Polarizer and rotate the analyzer. Repeat with linear polarization disabled, then drag the detector in the apparatus.
What to observe: Unpolarized light transmits half its mean power at every analyzer angle. Moving the detector changes beam size and peak irradiance without changing total source power. A broad beam can spill beyond the finite screen, reducing collected power.