Invited Correlation-induced spectral (and other) changes

1. InvitedCorrelation-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

2. average over random ensemble (or a time average) components of the E/M field (i,j =x,y,z) Coherence Theory: unified theory of the optical field Correlation function: all the (linear) properties of the field: Properties of Classical Fields • Local properties • -Intensity/spectrum • Polarization • Flux/momentum Non-local properties -Interference

3. -Intensity -Stokes parameters u =unit vector normal to the plane of the field components -Fringe visibility • can be measured by interference experiments Correlation Functions are our Friends • All the “interesting” quantities can be got from :

4. Scalar representation of the E/M field obeys the pair of equations- The Wolf Equations* Field Correlation function - (scalar approximation) - * E. Wolf, Proc. R. Soc A230, 246-65 (1955)

5. The Wolf Equations (II) • Correlation functions are dynamic quantities, which obey exact propagation laws. • Quantities dependent on correlation functions do not obey simple 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.

6. • van Cittert - Zernike Theorem in pictures solid angle incoherent planar source radiated field acquires transverse coherence • coherence and radiometry in pictures partially coherent planar source radiation pattern has solid angle

7. The Wolf Equations (II) • Correlation functions are dynamic quantities, which obey exact propagation laws. • Quantities dependent on correlation functions do not obey simple 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. – Change of spectrum on propagation (“The Wolf Effect”). – Change of polarization on propagation. – Change of what else on propagation?

8. obeys the equations - Space-Frequency Domain The cross-spectral density

9. A Solution (secondary sources)

10. Far Zone • Remember Fraunhofer diffraction theory....

11. spectrum (spatially invariant) spectral degree of coherence intensity slow function fast function Quasi-Homogeneous Model Source* *J. W. Goodman, Proc. IEEE53, 1688 (1965); W. H. Carter and E. Wolf, J. Opt. Soc. Amer.67, 785 (1977)

12. Spectral degree of coherence - fringe visibility Spectrum – spectrum is different from the source! Far Zone Field Properties – spectral analogue of the van Cittert - Zernike theorem. – measure visibility then invert Fourier transform - synthetic aperture imaging

13. excess red light off axis excess blue light on 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). Spectral Changes in Pictures

14. • Fractional shift of central frequency of a spectral line Spectral Shifts* • 3D primary source * E. Wolf, Nature (London)326, 363 (1986)

15. Applications to Date* •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) * E. Wolf and D.F.V. James, Rep. Prog. Phys.59, 771 (1996)

16. axis of strong anisotropy scattered light incident light Doppler-Like Shifts* • Broad-spectrum temporal fluctuating scatterer, with anisotropic spatial coherence *D.F.V. James, M. P. Savedoff and E. Wolf, Astrophys.J. 359, 67 (1990).

17. Model AGN ?* *D.F.V. James, Pure Appl. Opt.7, 959 (1998)

18. Applications to Date* •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?) * E. Wolf and D.F.V. James, Rep. Prog. Phys.59, 771 (1996)

19. Spatial Coherence Spectroscopy* • Interferometry and imaging are equivalent. • Use spectral measurements to determine the coherence. *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).

20. Polarization Changes on Propagation* • Different polarizations have different spatial coherence properties • Need to be very careful about using vector diffraction theory *A.K. Jaiswal, et al. Nuovo Cimento15B, 295 (1973) [claims about thermal source are not correct] D.F.V. James, J. Opt. Soc. Am. A11, 1641 (1994); Opt. Comm. 109, 209 (1994).

21. Solve the Wolf Equations Source Correlation function Field Correlation function 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 source Properties of the Field