Coherence 1 Concept of coherence is related to

Coherence 1

Concept of coherence is related to stability or predictability of phase Spatial coherence describes the correlation between signals at different points in space. Temporal coherence describes the correlation between signals at different moments of time. 2

Electric field distribution around the focus of a laser beam with perfect spatial and temporal coherence. A laser beam with high spatial coherence, but poor temporal coherence. A laser beam with poor spatial coherence, but high temporal coherence. 3 3

Quantifying Coherence Physically, monochromatic sources are fictitious. Band of frequencies = Wave train Many sinusoidal nearby frequencies are needed to construct the above 4

y(t) = [Sin t + Sin(1. 01 t) + Sin (1. 02 t) + Sin(1. 03 t) + Sin (1. 04 t) + Sin (1. 05 t) + Sin (1. 06 t) + Sin (1. 07 t) + Sin (1. 08 t)]/9 0 < t < 800 5

Quantifying Coherence Temporal coherence: Coherence time: The coherence time is the time over which a propagating wave may be considered coherent. In other words, it is the time interval within which its phase is, on average, predictable. : Spectral width of the source in units of frequency. Coherence length: The coherence length is the coherence times the vacuum velocity of light, and thus also characterizes the temporal (not spatial!) coherence via the propagation length (and thus propagation time) over which coherence is lost. 6

Red Cadmium = 10 9 Hz, Yellow Sodium 10 = 10 Hz, He-Ne Laser = 10 6 = 6438 Å 30 cm = 5893 Å 3 cm = 6328 Å Hz, 300 m 7

A plane wave with an infinite coherence length. Since there are two transverse dimensions, we can define a coherence area (Ac). 8

A wave with a varying profile (wavefront) and infinite coherence length. 9

A wave with a varying profile and finite coherence length. The spatial coherence depends on the emitter size and its distance. where d is the diameter of the light source and D is the distance. 10

The wave with finite coherence length is passed through a pinhole. The emerging wave has infinite coherence area. The coherence length (or coherence time) are unchanged by the pinhole. 11

Double slit: A closer look Curves of equal-path difference are Hyperboloids of revolution

http: //fp. optics. arizona. edu/milster/505%20 Lecture/Lecture%20 Notes%20 and%20 Slides/Chapter%204%20 Basic%20 Interference/OLD%20 NOTES/Basic%20 Interference%20 -%20 Part%20 B%20. pdf

Transverse Section: Straight fringes

Longitudinal section: Circular fringes