Wavetrains and Coherency

© 2006 Walter Fendt Beats Animation

y(x) = Sin x © SPK

y(x) = [Sin x + Sin (1.08 x)]/2 © SPK

y(x) = [Sin x + Sin(1.04 x) + Sin (1.08 x)]/3 © SPK 0 < x < 200

y(x) = [Sin x + Sin(1.02 x) + Sin (1.04 x) + Sin(1.06 x) + Sin (1.08 x)]/5 © SPK 0 < x < 400

y(x) = [Sin x + Sin(1.01 x) + Sin (1.02 x) + Sin(1.03 x) + Sin (1.04 x) + Sin (1.05 x) + Sin (1.06 x) + Sin (1.07 x) + Sin (1.08 x)]/9 © SPK 0 < x < 400

y(x) = [Sin x + Sin(1.01 x) + Sin (1.02 x) + Sin(1.03 x) + Sin (1.04 x) + Sin (1.05 x) + Sin (1.06 x) + Sin (1.07 x) + Sin (1.08 x)]/9 © SPK

Solitary pulse

For -L +L E0E0

Fourier integral

k p =2

Wave packet or Wave group for k p =k

Frequency Bandwidth Range of frequency k (or ) in wavetrain ( k) (or

Temporal coherence: Coherence time: Coherence length: © SPK

Spectral lines from helium gas tube

A characteristic Spectral line

Spectral line broadening 1.Natural linewidth 2.Doppler broadening 3.Collision broadening 4.Pressure broadening

Red Cadmium= 6438 Å = Hz, 30 cm Yellow Sodium = cm = 5893 Å He-Ne Laser 6328 Å 300 m = 10 6 Hz, © SPK

Kr discharge lamp has roughly the following intensity distribution at various wavlengths, (in nm), Estimate the coherence length of the Kr source.

Coherence time Coherence length