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Soviet Journal of Quantum Electronics

Nonlinear optics methods in conversion of spatially modulated signals

N. D. Ustinov, I. N. Matveev

Published Dec 31, 1977• 2 citations
Publisher

Abstract

The interaction of light waves in crystals with a quadratic nonlinearity is considered. It is shown that when one of the interacting waves carries information on the image of an object, such information can be transferred to a different wavelength, providing the basis for a parametric image converter. The results are given of experimental measurements of the noise and sensitivity of parametric-conversion detectors. It is shown that when both interacting waves carry information on an object, the interaction in a nonlinear crystal allows us to obtain correlation functions of the initial images of the objects. Suitable systems make it possible to determine experimentally the correlation function of the images of simple objects. By way of example, a description is given of a system which makes it possible to remove phase distortions introduced by an optical system in the far-field zone.

DOI
10.1070/qe1977v007n12abeh008271

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The interaction of light waves in crystals with a quadratic nonlinearity is considered. It is shown that when one of the interacting waves carries information on the image of an object, such information can be transferred to a different wavelength, providing the basis for a parametric image converter. The results are given of experimental measurements of the noise and sensitivity of parametric-conversion detectors. It is shown that when both interacting waves carry information on an object, the interaction in a nonlinear crystal allows us to obtain correlation functions of the initial images of the objects. Suitable systems make it possible to determine experimentally the correlation function of the images of simple objects. By way of example, a description is given of a system which makes it possible to remove phase distortions introduced by an optical system in the far-field zone.
We develop for the first time a quantum theory of simultaneous amplification and frequency up-conversion of optical images in two coupled three-wave processes. The theory developed takes into account the diffraction effect and the difference of the group velocities of the interacting waves. Due to the degenerate parametric process involved in the nonlinear optical interactions, the up-conversion also possesses phase sensitivity. As a result, the statistical characteristics of the amplified image and the converted one depend on the phase relation between the signal and the pump waves. It is shown that at the output of the nonlinear crystal the signal-to-noise ratios for the amplified image and the converted one may be same as those for the initial image, i.e. transformation of the optical image may be 'noiseless'.
We experimentally show that, by using spatial correlations of photon pairs produced by Spontaneous Parametric Down-Conversion, it is possible to increase the Signal to Noise Ratio in images of objects illuminated with those photons; in comparison, objects illuminated with light from a laser present a minor ratio. Our simple experimental set-up was capable to produce an average improvement in signal to noise ratio of 11dB of Parametric Down-Converted light over laser light. This simple method can be easily implemented for obtaining high contrast images of faint objects and for transmitting information with low noise.
Quantum properties of parametric amplification and frequency conversion of an optical image in coupled parametric interactions are analyzed for the case of a remote object. The coupled-wave interaction consists of a traditional process of parametric amplification in the high-frequency pump field accompanied by the frequency mixing of generated and pump waves. The photon number density and signal-to-noise ratio at the interacting frequencies are studied in the image plane at the output of the nonlinear frequency converter in the fixed pump field approximation. The degree of entanglement of optical images at frequencies above and below the pump frequency is investigated.
Imaging is the estimation of the spatial distribution of a physical object by measuring the optical radiation it emits, or by making use of an optical wave that interacts with the object, via reflection or transmission, for example, before being measured by a detector. The resolution of an imaging system is limited by the inability to localize the optical field at points of the object. Under otherwise ideal conditions, resolution is limited by diffraction. The sensitivity of an imaging system is limited by the uncertainty in the measurement. Under ideal conditions, this is determined by photon noise, which depends on the statistical fluctuations of the light. In conventional imaging systems, an extended detector, such as a CCD camera or an array detector, measures the spatial distribution of the optical intensity, which is proportional to the photon flux density. In interferometric systems, the spatial distribution of the optical field is inferred from measurements of the optical intensity. With the emergence of coherence theory, imaging systems based on measurements of the second-order coherence function at pairs of points in the detection plane were developed. An example is the imaging of an incoherent object based on the van Cittert-Zernike theorem. Imaging systems based on measurement of intensity correlation, or the photon coincidence rate, at pairs of points, were developed in the 1960s. A classic example of the photon-correlation imaging of an object emitting thermal light is stellar imaging using a Hanbury-Brown-Twiss intensity-correlation interferometer. More recently, two-photon light, which may be generated via spontaneous parametric downconversion in a second-order nonlinear optical crystal, has been used for imaging. This type of two-photon (or biphoton) imaging, which has come to be called quantum imaging, is also based on the measurement of photon coincidence by the use of photon-counting array detectors or by scanning two photon-counting detectors at pairs of points. To compare the resolution and sensitivity of imaging systems based on the aforementioned types of measurements, it is necessary to derive expressions for the measured quantities in terms of the object distribution. The point-spread functions based on such expressions can be used to assess the resolution. One measure of the sensitivity of the imaging process is the signal-to-noise ratio (SNR) of the measured variables. The statistical nature of the light source must be known in order to determine the SNR. The purpose of this chapter is to compare the resolution and sensitivity of photon-correlation imaging systems that make use of thermal light and two-photon light. We will henceforth refer to these two imaging modalities as classical and quantum photon-correlation imaging, or simply classical and quantum imaging, respectively. Clearly, light in other quantum states can also be used for imaging.
A quantum theory of parametric amplification and frequency conversion of an optical image in coupled nonlinear optical processes that include one parametric amplification process at high-frequency pumping and two up-conversion processes in the same pump field is developed. The field momentum operator that takes into account the diffraction and group velocities of the waves is used to derive the quantum equations related to the spatial dynamics of the images during the interaction. An optical scheme for the amplification and conversion of a close image is considered. The mean photon number density and signal-to-noise ratio are calculated in the fixed-pump-field approximation for images at various frequencies. It has been established that the signal-to-noise ratio decreases with increasing interaction length in the amplified image and increases in the images at the generated frequencies, tending to asymptotic values for all interacting waves. The variance of the difference of the numbers of photons is calculated for various pairs of frequencies. The quantum entanglement of the optical images formed in a high-frequency pump field is shown to be converted to higher frequencies during the generation of sum frequencies. Thus, two pairs of entangled optical images are produced in the process considered.