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Photonics

Analysis of the Spatial Properties of Correlated Photon in Collinear Phase-Matching

Lin Yin, Jianjun Li, Wenchao Zhai, Maopeng Xia, Youbo Hu, Xiaobing Zheng

Published Jan 7, 2021• 5 citations
Publisher

Abstract

In this paper, the spatial properties of correlated photon in collinear phase-matching in the process of spontaneous parametric down conversion (SPDC) are researched. Based on the study of the phase-matching angle, non-collinear angle, and correlated photon wavelength, a theoretical model of non-collinear angular variation is derived, which can be used to estimate and predict the width of the correlated photon ring. The experimental measurement is carried out with CMOS camera, and the measurement results are consistent with the theoretical simulation results, which verifies the rationality of theoretical reasoning. Meanwhile, the change of the correlated photon divergence angle outside the crystal is studied, the closer the wavelength is to the degenerate, the smaller the measurement value of the divergence angle, which is agreement with the theoretical simulation. The results of the study play a reference role in the evaluation of the spatial properties of correlated photon and lay a foundation for the measurement of the correlated photon number rate and the calibration of a photodetector.

DOI
10.3390/photonics8010012

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Acta Physica Sinica•Jan 1, 2016•1 citation
In this paper, the spatial properties of correlated photon in collinear phase-matching in the process of spontaneous parametric down conversion (SPDC) are researched. Based on the study of the phase-matching angle, non-collinear angle, and correlated photon wavelength, a theoretical model of non-collinear angular variation is derived, which can be used to estimate and predict the width of the correlated photon ring. The experimental measurement is carried out with CMOS camera, and the measurement results are consistent with the theoretical simulation results, which verifies the rationality of theoretical reasoning. Meanwhile, the change of the correlated photon divergence angle outside the crystal is studied, the closer the wavelength is to the degenerate, the smaller the measurement value of the divergence angle, which is agreement with the theoretical simulation. The results of the study play a reference role in the evaluation of the spatial properties of correlated photon and lay a foundation for the measurement of the correlated photon number rate and the calibration of a photodetector.
The correlated photon technique makes it possible to achieve a radiation calibration processing without chain transferring. The study of the spectral radiation character and time correlation of the photon is of great significance for broad-band radiometric calibration. To absolutely calibrate quantum efficiency of photoelectric detector, it is necessary to extend calibration band from single band to more bands. According to the phase-matching condition of the spontaneous parametric down-conversion, non-collinear angle formula of correlated photon in the crystal is derived. The distribution of the photon spectrum is simulated. Meanwhile, the phase-matching angle of the crystal is optimized. The photon generated by the spontaneous parameters down-conversion has a broad spectral distribution and the correlated photon wavelength is corresponding to its emission angle. Based on the result of the simulation, the experimental measurement system of the spectral distribution and time-correlation of the correlated photon is established. The spectral distribution, the time-correlation and the polarization properties of the four pair photon were measured by using this system. The experimental results show that, (1) the spectral distribution of the measurements is 633~808 nm, where the maximum spectral distribution measurement bias is 1.51 mm. The experiment result is highly consistent with theoretical ones; (2) the correlation time of four pairs correlated photon is measured, during which “three coincidence-peaks” is observed and the minimum correlation time was 0.32 ns; (3) single photon count rate along with coincidence count rate of correlated photon vary with the polarization direction of the pump as sine function. The experimental result is shown that the correlated photon pairs are ranging from the visible to near infrared band distribution, and that the spectrum has time-correlation and polarization characteristic. The research result is firstly reported at home and abroad, and the results are promising for the application of the photoelectric detector in the multi-band radiometric calibration.
In this paper, we report on the collinear spontaneous parametric down conversion (SPDC) with quantum theory in angle picture. Based on angle-dependent refractive index of biaxial crystal and the dielectric dispersion, we numerically simulate the effective nonlinear coefficients of BiB 3 O 6 (BIBO) crystal in principle planes. The results indicate that the most effective phase matching scheme is the type I in yz plane, while the secondary options are the type I, type II in xz plane. Considering the derivation of angular phase matching conditions, the calculation is convenient, and it is superior in determination of the spatial distribution of entangled photons.
As a tutorial to the spatial aspects of Spontaneous Parametric Downconversion (SPDC), we present a detailed first-principles derivation of the transverse correlation width of photon pairs in degenerate collinear SPDC. This width defines the size of a biphoton birth zone, the region where the signal and idler photons are likely to be found when conditioning on the position of the destroyed pump photon. Along the way, we discuss the quantum-optical calculation of the amplitude for the SPDC process, as well as its simplified form for nearly collinear degenerate phase matching. Following this, we show how this biphoton amplitude can be approximated with a Double-Gaussian wavefunction, and give a brief discussion of the measurement statistics (and subsequent convenience) of such Double-Gaussian wavefunctions. Next, we use this approximation to get a simplified estimation of the transverse correlation width, and compare it to more accurate calculations as well as experimental results. We then conclude with a discussion of the concept of a biphoton birth zone, using it to develop intuition for the tradeoff between the first-order spatial coherence and bipohoton correlations in SPDC.
Abstract As a tutorial to the spatial aspects of spontaneous parametric downconversion (SPDC), we present a detailed first-principles derivation of the transverse correlation width of photon pairs in degenerate collinear SPDC. This width defines the size of a biphoton birth zone, the region where the signal and idler photons are likely to be found when conditioning on the position of the destroyed pump photon. Along the way, we discuss the quantum-optical calculation of the amplitude for the SPDC process, as well as its simplified form for nearly collinear degenerate phase matching. Following this, we show how this biphoton amplitude can be approximated with a double-Gaussian wavefunction, and give a brief discussion of the measurement statistics (and subsequent convenience) of such double-Gaussian wavefunctions. Next, we use this approximation to get a simplified estimation of the transverse correlation width, and compare it to more accurate calculations as well as experimental results. We then conclude with a discussion of the concept of a biphoton birth zone, using it to develop intuition for the tradeoff between the first-order spatial coherence and bipohoton correlations in SPDC.
The spectral properties of entangled photon pairs generated via quasi-phased matching in spontaneous parametric down-conversion are proposed and demonstrated experimentally.A general mathematical model for evaluating the spectral properties is developed to obtain the spectrum shape and range of down-converted photons.The model takes into account the effects of phase mismatching due to non-ideal pumping and the relationship between crystal periodic modulation function and the incidence angle of the pump beam.The spectrum curve shape is determined by the discrete Fourier transform of a Gaussian pump beam and the integration of parametric down-conversion generated by an individual plane wave.An experiment is carried out with a PPLN non-linear crystal and dispersing optics, which shows a good consistency in their spectral ranges and shapes with our model predictions within the spectrum of 600-633 nm.This therefore illustrates that both the simulation model and the experimental process are reasonable.This novel method has potential applications in high-accuracy calibration in the wide spectrum using correlated photons.
The optical radiometric calibration method based on correlated photons generated by spontaneous parametric down-conversion (SPDC) is a promising method,because it is based on the basic physical phenomena and does not need radiometric traceability.At the present,the SPDC calibration technology is applicable for the photon-counting detector with a highest calibration accuracy of 0.18%.More and more researchers are making effort to improve its calibration accuracy and expand its applicable targets to analog detectors.Correlated photon circles have the high photon rate characteristic.The photon rates of signal and idle light can be improved significantly by using correlated photon circles in calibration.It has very important significance to study the time-correlation characteristic of correlated photon circles. In this paper,the spatial distribution of emission angle of the broadband (450-1000 nm) correlated photons generated by type-I spontaneous parametric down-conversion is presented through the theoretical calculations.The ZEMAX optical software is used to design the optical system which can receive the broadband correlated photon circles and remove the pump laser which is the main source of stray light.The 355 nm wavelength laser is used to pump -barium borate (BBO) crystal to generate the broadband correlated photon circles.A low-light-level CMOS camera is used to adjust and align the opt-mechanical system.Finally,the 430 nm-860 nm correlated photon circles are received by the optical system and detected by the low-light-level CMOS camera.An experimental measurement system is established to measure the time-correlation characteristics of 685 nm and 736.89 nm correlated photon circles.Using 1.0 mW continuous-wave laser to pump BBO crystal,a coincidence peak is observed evidently.The results show that the correlated photon circles generated by type-I SPDC have the characteristics of time-correlation and high photon rates.It can be conductive to improving optical radiometric calibration accuracy based on correlated photons and promoting the development and application in analog detector calibration.