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Measuring spatial correlations of photon pairs by automated raster scanning with spatial light modulators.

Paul EC, Hor-Meyll M, Ribeiro PH, Walborn SP - Sci Rep (2014)

Bottom Line: We demonstrate the use of a phase-only spatial light modulator for the measurement of transverse spatial distributions of coincidence counts between twin photon beams, in a fully automated fashion.This is accomplished by means of the polarization dependence of the modulator, which allows the conversion of a phase pattern into an amplitude pattern.We also present a correction procedure, that accounts for unwanted coincidence counts due to polarization decoherence effects.

View Article: PubMed Central - PubMed

Affiliation: Instituto de Física, Universidade Federal do Rio de Janeiro, Caixa Postal 68528, Rio de Janeiro, RJ 21941-972, Brazil.

ABSTRACT
We demonstrate the use of a phase-only spatial light modulator for the measurement of transverse spatial distributions of coincidence counts between twin photon beams, in a fully automated fashion. This is accomplished by means of the polarization dependence of the modulator, which allows the conversion of a phase pattern into an amplitude pattern. We also present a correction procedure, that accounts for unwanted coincidence counts due to polarization decoherence effects.

No MeSH data available.


Related in: MedlinePlus

Phase slits on the SLM for measurement of coincidences N11.
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f2: Phase slits on the SLM for measurement of coincidences N11.

Mentions: Let us first describe our model for the simplified case where the SLM surface is divided in 3 slit regions for each light beam, as shown in Fig. 2. We denote Cij as the ideal () number of coincidence counts when slit 1 is at position i and slit 2 is at position j. Here 1 and 2 refer to signal and idler, respectively. We define Nij as the measured number of coincidence counts between these two regions. Ideally, for a perfect SLM and perfect polarization optics, we would detect coincidence counts only between photons incident on the phase slits, so that Nij = Cij. However, due to the imperfections discussed above, we detect coincidence counts that originate from other regions of the SLM. The probability that a photon is detected when coming from a zero phase region, implementing the equivalent of a slit, is given by the p obtained from the visibility measurements, as explained above. Likewise (1 − p) is the probability that a photon is detected when coming from a region modulated with phase π. Then, we see a decrease in signal, since instead of detecting all ideal counts C11 we detect pspiC11 ≤ C11 of them. In addition, we detect unwanted counts coming from different combinations of π-phase regions of the SLM. For example, it is possible that photon s reflected from region 1 and photon i from region 2 or 3, contributing to a background term. Then, we expect a contribution from terms C12 and C13 that is proportional to ps(1 − pi). Similarly, terms like C22 and C23 appear with a proportionality constant (1 − ps)(1 − pi). Summing up all these events, we can relate the measured count rate N11 to the ideal count rates as Let us arrange the measured and ideal coincidence counts as column vectors: We can write the measured coincidence counts N as a function of the ideal coincidence counts C as where the symmetric matrix and α = pspi, β = (1 − ps)(1 − pi), γ = ps(1 − pi), δ = (1 − ps)pi. Finding the inverse of this matrix E−1, we can find the ideal coincidence counts as a function of the measured counts In the more general case of d slit positions, we follow the same procedure as outlined above, to obtain and the matrices E and E−1 are described accordingly.


Measuring spatial correlations of photon pairs by automated raster scanning with spatial light modulators.

Paul EC, Hor-Meyll M, Ribeiro PH, Walborn SP - Sci Rep (2014)

Phase slits on the SLM for measurement of coincidences N11.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4061558&req=5

f2: Phase slits on the SLM for measurement of coincidences N11.
Mentions: Let us first describe our model for the simplified case where the SLM surface is divided in 3 slit regions for each light beam, as shown in Fig. 2. We denote Cij as the ideal () number of coincidence counts when slit 1 is at position i and slit 2 is at position j. Here 1 and 2 refer to signal and idler, respectively. We define Nij as the measured number of coincidence counts between these two regions. Ideally, for a perfect SLM and perfect polarization optics, we would detect coincidence counts only between photons incident on the phase slits, so that Nij = Cij. However, due to the imperfections discussed above, we detect coincidence counts that originate from other regions of the SLM. The probability that a photon is detected when coming from a zero phase region, implementing the equivalent of a slit, is given by the p obtained from the visibility measurements, as explained above. Likewise (1 − p) is the probability that a photon is detected when coming from a region modulated with phase π. Then, we see a decrease in signal, since instead of detecting all ideal counts C11 we detect pspiC11 ≤ C11 of them. In addition, we detect unwanted counts coming from different combinations of π-phase regions of the SLM. For example, it is possible that photon s reflected from region 1 and photon i from region 2 or 3, contributing to a background term. Then, we expect a contribution from terms C12 and C13 that is proportional to ps(1 − pi). Similarly, terms like C22 and C23 appear with a proportionality constant (1 − ps)(1 − pi). Summing up all these events, we can relate the measured count rate N11 to the ideal count rates as Let us arrange the measured and ideal coincidence counts as column vectors: We can write the measured coincidence counts N as a function of the ideal coincidence counts C as where the symmetric matrix and α = pspi, β = (1 − ps)(1 − pi), γ = ps(1 − pi), δ = (1 − ps)pi. Finding the inverse of this matrix E−1, we can find the ideal coincidence counts as a function of the measured counts In the more general case of d slit positions, we follow the same procedure as outlined above, to obtain and the matrices E and E−1 are described accordingly.

Bottom Line: We demonstrate the use of a phase-only spatial light modulator for the measurement of transverse spatial distributions of coincidence counts between twin photon beams, in a fully automated fashion.This is accomplished by means of the polarization dependence of the modulator, which allows the conversion of a phase pattern into an amplitude pattern.We also present a correction procedure, that accounts for unwanted coincidence counts due to polarization decoherence effects.

View Article: PubMed Central - PubMed

Affiliation: Instituto de Física, Universidade Federal do Rio de Janeiro, Caixa Postal 68528, Rio de Janeiro, RJ 21941-972, Brazil.

ABSTRACT
We demonstrate the use of a phase-only spatial light modulator for the measurement of transverse spatial distributions of coincidence counts between twin photon beams, in a fully automated fashion. This is accomplished by means of the polarization dependence of the modulator, which allows the conversion of a phase pattern into an amplitude pattern. We also present a correction procedure, that accounts for unwanted coincidence counts due to polarization decoherence effects.

No MeSH data available.


Related in: MedlinePlus