Spatial & Temporal Coherence - NTUA

1 Spatial & Temporal Coherence Optical Engineering Prof. Elias N. Glytsis School of Electrical & Computer Engineering National Technical University of Athens 12/03/2022 Prof. Elias N. Glytsis, School of ECE, NTUA 2 Coherence Concept Coherence Incoherence Partial Coherence Spatial and Temporal Coherence B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics, 2nd Ed., J. Wiley 2007 3 Prof. Elias N. Glytsis, School of ECE, NTUA Coherence is a measure of the correlation between the phases measured at different ( Temporal and Spatial ) points on a wave. Temporal Coherence is a measure of the correlation of light wave s phase at different points along the direction of propagation it tells us how monochromatic a source is.

2 Spatial Coherence is a measure of the correlation of a light wave s phase at different points transverse to the direction of propagation - it tells us how uniform the phase of a wavefront is. Temporal Coherence Time, c Temporal Coherence Length, c = c c Spatial Coherence Length, xc xc Spatial and Temporal Coherence 4 Prof. Elias N. Glytsis, School of ECE, NTUA Spatial and Temporal Coherence Temporal Coherence ; Spatial Incoherence Spatial Coherence ; Temporal Incoherence Spatial and Temporal Incoherence Spatial and Temporal Coherence 5 Prof. Elias N. Glytsis, School of ECE, NTUA Temporal Coherence Temporal Coherence Time, c Temporal Coherence Length, c = 2d = c c 6 Prof.

3 Elias N. Glytsis, School of ECE, NTUA Spatial Coherence Spatial Coherence Area, Ac= d2 7 Prof. Elias N. Glytsis, School of ECE, NTUA Temporal Coherence Temporal Coherence Function (Autocorrelation) Degree of Temporal Coherence Coherence Time and Coherence Length B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics, 2nd Ed., J. Wiley 2007 8 Prof. Elias N. Glytsis, School of ECE, NTUA Temporal Coherence Power Spectral Density B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics, 2nd Ed., J. Wiley 2007 9 Prof. Elias N. Glytsis, School of ECE, NTUA Temporal Coherence B. E. A. Saleh and M.

4 C. Teich, Fundamentals of Photonics, 2nd Ed., J. Wiley 2007 10 Prof. Elias N. Glytsis, School of ECE, NTUA Temporal Coherence Power Spectral Density B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics, 2nd Ed., J. Wiley 2007 11 Prof. Elias N. Glytsis, School of ECE, NTUA Young s Experiment to Demonstrate Spatial Coherence 12 Prof. Elias N. Glytsis, School of ECE, NTUA Spatial Coherence Mutual Coherence Function Mutual Degree of Coherence B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics, 2nd Ed., J. Wiley 2007 13 Prof. Elias N. Glytsis, School of ECE, NTUA Spatial Coherence Function Spatial Coherence Area, Ac B.

5 E. A. Saleh and M. C. Teich, Fundamentals of Photonics, 2nd Ed., J. Wiley 2007 14 Prof. Elias N. Glytsis, School of ECE, NTUA Coherence area Thermal source Sun (500nm filter) Betelgeuse (500nm filter) A 1mm2 10-3 mm2 6m2 Spatial Coherence 222cDd =The van Cittert- zernike Theorem states that the Spatial Coherence area Ac is given by: where d is the diameter of the light source and D is the distance away. Basically, wave-fronts smooth out as they propagate away from the source. 15 Prof. Elias N. Glytsis, School of ECE, NTUA Prof. Elias N. Glytsis, School of ECE, NTUA 16 Spatial Coherence Example 1: Spatial Coherence of the Sun = m D = 150 106 km = 1011 m d = 106 km = 109 m Ac 10-3 mm2 Example 2: Spatial Coherence of the Betelguese = m D 548 light years = 548 1012 km = 1018 m d 764 dsun = 764 106 km = 1011 m Ac m2 222cDd = Spatial and Spectral Filtering to Produce Coherence Radiation 17 Prof.

6 Elias N. Glytsis, School of ECE, NTUA temporally