Room temperature Interferometry to measure the momentum space of light from a long distance away

What is it about?

Usual spectroscopic techniques reveal the energy distribution of light by dispersing it with a grating or a prism. However, the momentum (k) space distribution of photons coming out of any light source also provides critical information about its underlying physical origin. Conventional methods of determining such properties using high numerical aperture based objective lenses are somewhat challenging to probe light sources which are kept within a low temperature cryostat as well as placed far away from the measurement set up. There were past reports to measure spatial coherence of light which could then be used for extracting the momentum space information. However, all of these are experimentally challenging and somewhat complex in nature. So, here we propose a much simpler optical interferometry setup based on a modified Michelson interferometer which – (i) can be kept at room temperature and placed outside any low temperature cryostat and (ii) also at a long distance away from the source of light. We initially measure the two dimensional (2D) spatial coherence function of emitted light, which can then be used to directly estimate the 2D in-plane momentum space distribution by calculating its fast Fourier transform. We also discuss how this experimental method can overcome as well as simplify instrumentational difficulties encountered in the past. Most interestingly, similar optical interferometry based instrumentations can also be extended for momentum space resolved detection of light for astronomical studies as well as for futuristic telecommunication networks involving distant light sources.

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Why is it important?

There were past studies of momentum (k) space distribution of light using spatial coherence measurements but only in one dimension. However, in this paper we measured the full two dimensional (2D) map of coherence function over a selected cross-sectional area of the light beam and then used that directly to determine its 2D momentum space distribution, which was not explored earlier in this particular way. We have also used this new experimental setup to measure the 2D coherence function as well as the 2D momentum space distribution of light from a laser diode as a function of its bias voltage and observed the evolution of the momentum space during the onset of lasing. This will be very useful for optical communications based on momentum space information of photons. The optical elements used in our interferometry setup are much simpler components compared to previously proposed setups and can be aligned much more easily. The surfaces of planar retroreflectors used in our setup has ‘no discernible’ obliquity other than the right angle maintained between two internal reflecting surfaces. So, polarization dependent phase shifts in the light beam are prevented. Also, there is no spherical surfaces used in our optical set up which can introduce additional asymmetric/non uniform path lengths or phase differences. Moreover, we have a control over the additional phase which we introduce to the beam. This can help whenever one is trying to image smaller sized micro/nano structures. Nevertheless, additional phase correction methods can also provide further information about the k-space structure of a light beam. This is, however, beyond the aim and scope of this study and not executed here. As a control experiment, we compared the results of our set-up based on spatial coherence with the standard one using back-focal plane imaging. Results demonstrates that all essential peaks from the theoretical simulation are not only nicely measured, but also better captured with significantly more details by our coherence method as compared to the usual Back-focal plane method. This certainly highlights the strength of this coherence method in revealing these intricate k-space features of light much more effectively. Our experimental setup also has an advantage in its capacity to control the fringe width by simply tilting only one mirror, thus enabling us to study even smaller light emission pattern(s) over a 2D area. It doesn’t have problems associated with the use of Cat-Eye retroreflector (CER), dove prisms and also with those studies where only 2D coherence function was studied but not the momentum space. Moreover, this method is certainly easier to implement and advantageous in cases where the sample under study is kept at a low temperature, but k-space distributions of light emission can still be measured using optical instrumentations placed totally outside the low temperature cryostat. Therefore, this experimental design will certainly be helpful to probe Bose-Einstein Condensate of excitons, polaritons, photons by detecting the narrowing of momentum space of emitted light as evidence of the underlying long-range spatial coherence or order. Most importantly, such optical set up can also have a much wider applicability in astronomy and optical communications based on k-space resolved detection and imaging of light signals from distant light sources in future.

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