Seminarium Optyczne

The autocorrelation, or the Wiener-Khintchine, theorem plays a pivotal role in optical coherence theory. The proof of the theorem derives from the time-frequency Fourier theorem. The derivation requires either dropping the cross-products (interference terms) between the different field amplitudes corresponding to different frequencies, or taking a time integration over the entire duration of the signal [1]. The physical interpretation of these mathematical steps implies, either (i) non-interference (non-interaction) between different frequencies, or (ii) the registered data is valid for interpretation when the detector is set for long time integration. We have already proposed [2] the generic principle of Non-Interaction Waves (NIW), or the absence of interference between light beams irrespective of their phases, frequencies or polarizations. In the linear domain, the waves do not exert any force of interaction between themselves. So they cannot exchange energy or induce energy distribution between themselves, which usually is a quadratic process. All the complex amplitudes continue to propagate through each other unperturbed, following the Huygens-Fresnel diffraction integral, without modifying each other’s energy distribution. Observed energy re-distribution can take place only in the presence of some interacting material medium.

The hypothesis of non-interaction between different frequencies was used by Michelson to frame the theory behind his Fourier Transform Spectroscopy, which is correct only when the detector possesses a long integrating time constant like a human eye, a photographic plate, or a photo detector circuit with a long LCR time constant. We now know that a fast detector gives heterodyne signal (light beating spectroscopy). So, the correlation factor derived by the prevailing coherence theory, and measured through fringe visibility, is essentially the quantum property of the detecting molecules compounded by the response time of the follow-on instrumentation. Low visibility fringes (low correlation factor) do not imply that the intrinsic property of light is partially coherent. The fringes correspond to a joint light-matter response characteristic. So, we re-define coherence by directly referring to the key characteristics of light beams, which are responsible for reducing the visibility of fringes registered by our detecting instruments. These are: (i) spectral correlation (presence of multi frequency), (ii) temporal correlation (time varying amplitude of light), (iii) spatial correlation (independent multi-point source), and (iv) complex correlation (mixture of previous characteristics).

[1] C. Roychoudhuri, “Re-interpreting coherence in light of Non-Interaction of Waves, or the NIW-Principle”; SPIE Conf. Proc. Vol.8121-44 (2011).

[2] C. Roychoudhuri, “Principle of non-interaction of waves”, doi:10.1117/1.3467504; J. Nanophotonics, Vol.4, 043512 (2010).