EEEL Measures High-Order Coherences of Chaotic and Coherent Light

Researchers in the Optoelectronics Division of EEEL, in collaboration with colleagues at MIT and MIT Lincoln Laboratory, have demonstrated a new way to measure second-,third- and fourth-order temporal coherences, g⁽²⁾, g⁽³⁾, and g⁽⁴⁾. Temporal coherence measurements are especially useful for understanding the fast dynamics of novel optical sources such as low-threshold lasers and single photon sources. Coherences higher than second order are not routinely measured, even though they can reveal information not contained in g⁽²⁾, in part because they are generally thought to require a complex apparatus in which multiple beamsplitters direct light to several discrete detectors.

The new, more direct method developed by Marty Stevens, Burm Baek, Sae Woo Nam, and Rich Mirin relies on a four-element superconducting nanowire single-photon detector (SNSPD), in which four independent, single-photon-sensitive elements are interleaved over a single spatial mode of the optical beam. The outputs of these four SNSPD elements are fed to fourchannel timing electronics that record the arrival times of all detected photons. These arrival times are postprocessed and normalized to compute n^th-order coherences for n = 2, 3, 4. The researchers studied a chaotic, pseudo-thermal source, which exhibited strong photon bunching, reaching peak values of 1.985±0.019 for g⁽²⁾, 5.87±0.17 for g⁽³⁾, and 23.1±1.8 for g⁽⁴⁾, consistent with the expected peak values (g⁽ⁿ⁾ = n!) of 2, 6, and 24. For a coherent source (an attenuated laser), they observed mean values of 1.0018±0.0008 for g⁽²⁾, 1.006±0.002 for g⁽³⁾, and 1.011±0.005 for g⁽⁴⁾, all close to the prediction g⁽ⁿ⁾ = 1. In the past, measurements of g⁽³⁾ and g⁽⁴⁾ were limited to investigating correlations where at least one of the time delays was fixed and nonzero. By contrast, the EEEL team has now measured them for continuous ranges of all delays, offering fresh insight into higher order photon bunching. These results demonstrate that using multiple detector elements to sample an optical beam over dimensions smaller than the minimum diffraction—limited spot size can be equivalent—and in some cases advantageous-to using beamsplitters and discrete detectors that each sample the entire mode.

High-order coherence measurements can be used to study fundamental properties of optical sources such as single-photon sources and low-threshold lasers, as well as a wide range of time-dependent scattering media including foams, particles in solution, and biological specimens. Under certain conditions, visibility or signal-to-noise ratio could be improved by measuring higher order coherences. The technique could even be used to test the long-held assertion that laser light is coherent to all orders (g⁽ⁿ⁾ = 1), since the experimental record contains limited data for coherences higher than second order.

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