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Dr. Daniel F.V. James MS B283, PO Box 1663, Los Alamos NM 87545 1 Invited Correlation-induced spectral (and other) changes Daniel F. V. James, Los Alamos National Laboratory Frontiers in Optics Rochester NY JMA3 10:00 a.m. Monday 11 October

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Dr. Daniel F.V. James MS B283, PO Box 1663, Los Alamos NM 87545 2 Properties of Classical Fields Local properties -Intensity/spectrum -Polarization -Flux/momentum Non-local properties -Interference Coherence Theory: unified theory of the optical field components of the E/M field (i,j =x,y,z) average over random ensemble (or a time average) Correlation function: all the (linear) properties of the field:

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Dr. Daniel F.V. James MS B283, PO Box 1663, Los Alamos NM 87545 3 Correlation Functions are our Friends All the “interesting” quantities can be got from : u = unit vector normal to the plane of the field components -Intensity -Stokes parameters -Fringe visibility can be measured by interference experiments

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Dr. Daniel F.V. James MS B283, PO Box 1663, Los Alamos NM 87545 4 The Wolf Equations* * E. Wolf, Proc. R. Soc A 230, 246-65 (1955) Field Correlation function - (scalar approximation) - Scalar representation of the E/M field obeys the pair of equations-

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Dr. Daniel F.V. James MS B283, PO Box 1663, Los Alamos NM 87545 5 The Wolf Equations (II) Correlation functions are dynamic quantities, which obey exact propagation laws. Coherence properties change on propagation. – van Cittert - Zernike theorem: spatial coherence in the far zone of an incoherent object. – laws of radiometry and radiative transfer. Quantities dependent on correlation functions do not obey simple laws.

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Dr. Daniel F.V. James MS B283, PO Box 1663, Los Alamos NM 87545 6 incoherent planar source radiated field acquires transverse coherence solid angle van Cittert - Zernike Theorem in pictures partially coherent planar source radiation pattern has solid angle coherence and radiometry in pictures

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Dr. Daniel F.V. James MS B283, PO Box 1663, Los Alamos NM 87545 7 The Wolf Equations (II) Correlation functions are dynamic quantities, which obey exact propagation laws. Coherence properties change on propagation. – van Cittert-Zernike theorem: spatial coherence in the far zone of an incoherent object. – Laws of radiometry and radiative transfer. Quantities dependent on correlation functions do not obey simple laws. – Change of spectrum on propagation (“The Wolf Effect”). – Change of polarization on propagation. – Change of what else on propagation?

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Dr. Daniel F.V. James MS B283, PO Box 1663, Los Alamos NM 87545 8 Space-Frequency Domain The cross-spectral density obeys the equations -

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Dr. Daniel F.V. James MS B283, PO Box 1663, Los Alamos NM 87545 9 Solution (secondary sources) A

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Dr. Daniel F.V. James MS B283, PO Box 1663, Los Alamos NM 87545 10 Far Zone Remember Fraunhofer diffraction theory....

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Dr. Daniel F.V. James MS B283, PO Box 1663, Los Alamos NM 87545 11 Quasi-Homogeneous Model Source* *J. W. Goodman, Proc. IEEE 53, 1688 (1965); W. H. Carter and E. Wolf, J. Opt. Soc. Amer. 67, 785 (1977) intensity spectral degree of coherence spectrum (spatially invariant) slow function fast function

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Dr. Daniel F.V. James MS B283, PO Box 1663, Los Alamos NM 87545 12 – spectrum is different from the source! Far Zone Field Properties Spectrum Spectral degree of coherence - fringe visibility – spectral analogue of the van Cittert - Zernike theorem. – measure visibility then invert Fourier transform - synthetic aperture imaging

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Dr. Daniel F.V. James MS B283, PO Box 1663, Los Alamos NM 87545 13 Spectral Changes in Pictures excess blue light on axis excess red light off axis What if ? All wavelengths have same solid angle, and spectrum is the same. Rigorously:. (The Scaling Law for spectral invariance*) *E. Wolf, Phys. Rev. Lett. 56, 1370 (1986).

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Dr. Daniel F.V. James MS B283, PO Box 1663, Los Alamos NM 87545 14 Spectral Shifts* 3D primary source * E. Wolf, Nature (London) 326, 363 (1986) Fractional shift of central frequency of a spectral line

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Dr. Daniel F.V. James MS B283, PO Box 1663, Los Alamos NM 87545 15 Applications to Date* * E. Wolf and D.F.V. James, Rep. Prog. Phys. 59, 771 (1996) Primary sources (i.e. random charge-current distributions). Secondary sources (i.e. illuminated apertures). Weak scatterers (First Born Approximation). Atomic systems (correlations induced by radiation reaction). Twin-pinholes (application to synthetic aperture imaging)

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Dr. Daniel F.V. James MS B283, PO Box 1663, Los Alamos NM 87545 16 Doppler-Like Shifts* *D.F.V. James, M. P. Savedoff and E. Wolf, Astrophys.J. 359, 67 (1990). Broad-spectrum temporal fluctuating scatterer, with anisotropic spatial coherence axis of strong anisotropy incident light scattered light

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Dr. Daniel F.V. James MS B283, PO Box 1663, Los Alamos NM 87545 17 Model AGN ?* *D.F.V. James, Pure Appl. Opt. 7, 959 (1998)

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Dr. Daniel F.V. James MS B283, PO Box 1663, Los Alamos NM 87545 18 Applications to Date* * E. Wolf and D.F.V. James, Rep. Prog. Phys. 59, 771 (1996) Primary sources (i.e. random charge-current distributions). Secondary sources (i.e. illuminated apertures). Weak scatterers (First Born Approximation). Atomic systems (correlations induced by radiation reaction). Twin-pinholes (application to synthetic aperture imaging) Dynamic scattering (Doppler-like shifts: cosmological implications?)

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Dr. Daniel F.V. James MS B283, PO Box 1663, Los Alamos NM 87545 19 *D.F.V. James, H. C. Kandpal and E. Wolf, Astrophys. J. 445, 406 (1995). H.C. Kandpal et al, Indian J. Pure Appl. Phys. 36, 665 (1998). Interferometry and imaging are equivalent. Spatial Coherence Spectroscopy* Use spectral measurements to determine the coherence.

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Dr. Daniel F.V. James MS B283, PO Box 1663, Los Alamos NM 87545 20 Polarization Changes on Propagation* Different polarizations have different spatial coherence properties *A.K. Jaiswal, et al. Nuovo Cimento 15B, 295 (1973) [claims about thermal source are not correct] D.F.V. James, J. Opt. Soc. Am. A 11, 1641 (1994); Opt. Comm. 109, 209 (1994). Need to be very careful about using vector diffraction theory

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Dr. Daniel F.V. James MS B283, PO Box 1663, Los Alamos NM 87545 21 Conclusions Shifts happen. Get used to it. - Spatial Coherence (van Cittert - Zernike) - Temporal Coherence/ Spectra - Polarization - Fourth-order (& higher) effects (e.g. photon counting statistics) Wolf equations are the only way to analyze the field! Properties of the sourceProperties of the Field Solve the Wolf Equations Source Correlation function Field Correlation function

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