Radiation from sources of difference states of coherence

Yan Joe Lee, ENGN2912Q

Introduction/Contents

Sources with different coherence properties

Correlations and spectral density in the far field

Radiation from model sources

Conclusion

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Sources with different (spatial) coherence properties

Lambertian source Spatially coherent source

https://upload.wikimedia.org/wikipedia/commons/1/14/Incandescent_light_bulb_on_db.jpg https://en.wikipedia.org/wiki/Laser#/media/File:LASER.jpg

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Correlations and the spectral density in the far field

Mandel and Wolf, Optical Coherence and Quantum Optics, Fig. 5.6

Planar secondary source, far field

= 2 2 0 21

12cos 1 cos 2

= , =

Low and high spatial frequency components?

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Spectral density

, =2

2 0 , , cos

2

Radiant intensity

Spectral degree of coherence

Two cases:

1. 2 = 1 (two points in same direction) => complete longitudinal spectral coherence at each frequency regardless of coherence of the source

2. Two points located at same distance (r1 = r2) => transverse degree of coherence, independent of the distance r, depends only the directions

Mandel and Wolf, Optical Coherence and Quantum Optics, Fig. 5.7

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Radiation from model sources

Quasi-homogeneous sources (subclass of Schell-model sources)

Schell-model source: (0) 1, 2, = (0)(2 1, )

Quasi-homogeneous: Spectral density is a slow function of p, spectral degree of coherence is a fast function of p=p2-p1 (varies much faster than the spectral density)

Example: Gaussian spectral intensity and spectral degree of coherence

(0)Source plane Far zone

Spectral Density Spectral degree of coherence

Spectral Degree of Coherence

Radiant intensity

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Conclusion Sources of different states of spatial coherence have different radiation and

coherence properties

Can derive properties of far field using the cross-spectral density of the far field (in our case defined for planar, statistically stationary sources of any state of coherence)

Far field has complete longitudinal spectral coherence at each frequency regardless of the state of coherence of the source

Transverse degree of coherence is independent of distance from source

For quasi-homogeneous sources:

1. Generated radiant intensity (far field) is independent of the shape of the source and spatial distribution of spectral intensity across the source.

2. Spectral degree of coherence (far field) is the Fourier transform of spectral density across the source.

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References

Wolf, Emil. Introduction to the Theory of Coherence and Polarization of Light. Cambridge: Cambridge University Press, 2007.

Mandel, Leonard and Emil Wolf. Optical Coherence and Quantum Optics. Cambridge: Cambridge University Press, 1995.

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