Hanbury Brown and Twiss interferometry with twisted light. O. Magaña-Loaiza, M. Mirhosseini, R. Cross, S. Rafsanjani and R. Boyd in Science Advances 2 (2016). What the paper says!?
This text is a pioneering work on angular correlations from LG beams, as such it is extremely related to bosoc. They work with angular momentum moments, $\ell$, but also with angles:
Here, we show that random fluctuations give rise to the formation of intensity correlations among the OAM components and among the angular positions of pseudothermal light. Furthermore, we show that the presence of these correlations leads to a variety of complex interference structures that correspond to the azimuthal analog of the HBT effect.
They speak specifically of the azimuthal analog of the HBT effect.
We identify two key signatures of the azimuthal HBT effect.
These are:
- «HBT interference can show features in the OAM-mode distribution both at the frequency and at twice the frequency of the first-order coherence produced by coherent light.»
- «a shift of the interference structure when plotted as a function of OAM.»
Their approach is completely different than ours as they have broadband light with a lot of $\ell$ (up to $\pm15$) and they consider correlations as genuine, even almost quantum:
throughout this article, we highlight the similarities and differences between thermal and quantum correlations as manifested in the azimuthal degree of freedom.
They rightly comment:
The random nature of light is an essential element of the HBT effect.
Yes, but in which capacity?
More comments on classical/quantum relationships:
The interplay between Gℓ and G2ℓ might be useful to the study of the relationship between coherence and the quantum nature of light.
or:
As we have shown throughout this paper, the HBT correlations of pseudothermal light lead to effects that show resemblance to those previously observed with entangled photons (8, 9, 29–31). The reason for this behavior is that, in contrast to the degree of second-order coherence that describes coherent light, the functions that describe second-order correlations in angular position and OAM for random fields are nonseparable.
This unquenchable thirst for making thermal correlations "similar" to quantum ones:
Intensity correlations in the OAM components and angular positions of pseudothermal light show similarities with the azimuthal EPR effect, observed in photons entangled in angular position and OAM (9).
The difference being that thermal ones are not perfect, but still with hope that it could get there:
if background subtraction is performed, the variance product for Dℓ and Df is similar to that achieved for nonclassical light
Their model for the field is also far from our refined Eduardo Zubizarreta Casalengua et al.[1]'s treatment:
ϵ(r) represents the coherent optical field produced by a laser, Φ(r, ϕ) is a particular realization of a random phase screen, and A(ϕ) describes the transmission function of the angular slits.
They deal with thermal light, using Kolmogorov phase scrambling (DMD, SLM, etc.)
As a particular case of random light, they point us to «speckled light, intimately related to pseudothermal light». The technical details on spatial coherence are interesting, e.g., they recourse to «the Fried coherence length» to quantify spatial coherence.
One of their most illustrative results, the $g^{(2)}$ as function of $\ell$ on the left and as function of angle on the right:
This reduces to a moot autocorrelation bunching peak! Compare to our case with structured correlations delocalised on the vortices, namely, two peaks for $\ell=\pm1$.
I would summarize it as a very complicated, sunk in broadband fields platform to evidence our spatial correlations of vortices, which we have put on a pedestal of simplicity and strong phenomenology. Also disconnecting the classical from quantum character completely,[2] unlike here where they try very much to be merged (never to the point of claiming EPR correlations, though).
