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Optics Letters

In-fiber frequency-domain measurement of ultrashort second-order correlations of incoherent light

Carlos R. Fernández‐Pousa, Juan P. Torres

Published May 25, 2010• 2 citations
Publisher

Abstract

The second-order correlation function of incoherent light, which is usually measured in the time domain, can be alternatively measured in the frequency domain. Here, we use an all-optical technique in a highly nonlinear fiber for measuring the full spectrum of the fluctuations of the photocurrent (rf spectrum) generated by broadband radiation with different spectral coherence properties. Our experiments reveal that the rf spectrum of a light signal depends strongly on its spectral coherence properties. From a practical perspective, this ultrafast technique constitutes an alternative for measuring the intensity correlations of spectrally incoherent radiation.

DOI
10.1364/ol.35.001850

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The second-order correlation function of incoherent light, which is usually measured in the time domain, can be alternatively measured in the frequency domain. Here, we use an all-optical technique in a highly nonlinear fiber for measuring the full spectrum of the fluctuations of the photocurrent (rf spectrum) generated by broadband radiation with different spectral coherence properties. Our experiments reveal that the rf spectrum of a light signal depends strongly on its spectral coherence properties. From a practical perspective, this ultrafast technique constitutes an alternative for measuring the intensity correlations of spectrally incoherent radiation.
We measure experimentally the second-order coherence properties of supercontinuum generated in a photonic crystal fiber. Our approach is based on measuring separately the quasicoherent and quasistationary contributions to the cross-spectral density and mutual coherence functions using a combination of interferometric and nonlinear gating techniques. This allows us to introduce two-dimensional coherence spectrograms which provide a direct characterization and convenient visualization of the spectrotemporal coherence properties. The measured second-order coherence functions are in very good agreement with numerical simulations based on the generalized nonlinear Schrödinger equation. Our results pave the way towards the full experimental characterization of supercontinuum coherence properties. More generally, they provide a generic approach for the complete experimental measurement of the coherence of broadband sources.
The second-order correlation function of light g(2)(τ) constitutes a pivotal tool to quantify the quantum behavior of an emitter and in turn its potential for quantum information applications. The experimentally accessible time resolution of g(2)(τ) is usually limited by the jitter of available single-photon detectors. Here, we present a versatile technique allowing g(2)(τ) to be measured from a large variety of light signals with a time resolution given by the pulse length of a mode-locked laser. The technique is based on frequency upconversion in a nonlinear waveguide, and we analyze its properties and limitations by modeling the pulse propagation and the frequency conversion process. We measure g(2)(τ) from various signals including light from a quantum emitter—a confined exciton-polariton structure—revealing its quantum signatures at a scale of a few picoseconds and demonstrating the capability of the technique.
Abstract In recent years, electro-optic sampling, which is based on Pockel’s effect between an electromagnetic mode and a copropagating, phase-matched ultrashort probe, has been largely used for the investigation of broadband quantum states of light, especially in the mid-infrared and terahertz frequency range. The use of two mutually delayed femtosecond pulses at near-infrared frequencies allows the measurement of quantum electromagnetic radiation in different space-time points. Their correlation allows therefore direct access to the spectral content of a broadband quantum state at terahertz frequencies after Fourier transformation. In this work, we will prove experimentally and theoretically that when using strongly focused coherent ultrashort probes, the electro-optic sampling technique can be affected by the presence of a third-order nonlinear mixing of the probes’ electric field at near-infrared frequencies. Moreover, we will show that these third-order nonlinear phenomena can also influence correlation measurements of the quantum electromagnetic radiation. We will prove that the four-wave mixing of the coherent probes’ electric field with their own electromagnetic vacuum at near-infrared frequencies results in the generation of a higher-order nonlinear correlation term. The latter will be characterized experimentally, proving its local nature requiring the physical overlap of the two probes. The parameters regime where higher order nonlinear correlation results predominant with respect to electro-optic correlation of terahertz radiation is provided.
The coherence properties of broadband down converted light are investigated theoretically and experimentally in both the classical and quantum mechanical frameworks. Although broadband down converted light is one-photon incoherent noise, it possesses unique two-photon coherence. Thus, for performing two-photon processes, down-converted light is equivalent to coherent ultrashort pulses in some aspects and to coherent CW laser radiation in others. This equivalence is theoretically established and experimentally demonstrated in the classical, high-power regime. Two applications that take advantage of multi-photon coherence are then described in detail; one for optical spread spectrum communication and the other for sub-diffraction limit optical lithography. A key part of this research is the design and implementation of an efficient source that generates high-power broadband down conversion in a cavity. A broadband oscillation in the cavity is ensured by a mechanism very similar to passive mode-locking of ultrashort pulse laser sources, which we term as pair-wise mode locking, thus extending the equivalence to ultrashort pulses to the light generating sources also. Finally, the quantum mechanical properties of broadband down-conversion are explored experimentally, by performing a two-photon process (sum frequency generation) at the low power level of entangled photon pairs. The non-classical nature of the light is expressed by a linear intensity dependence of the non-linear process. Temporal shaping with femtosecond resolution of the entangled photon pairs is demonstrated using this non-linear interaction.
We have discussed the possibilities of correlation spectroscopy (light beating spectroscopy) technique if squeezed light is used as a probe radiation for medium monitoring. The dispersion of the fluctuation of photocurrent spectrum measured in this method is expressed in terms of fourth order photocurrent correlation function. This correlation function is considered and evaluated in assumptions of photodetection theory developed by Glauber in first nonvanishing orders in interaction of probe light with the atoms of a photodetector. We show that fourth order correlation function is determined by all field TN-ordered amplitude correlation functions up to the fourth order. In case of heterodyne detection, when the light incident on photodetector surface is the mix of strong coherent modes of local oscillator wave and weak non-coherent (squeezed) modes, the observable (photocurrent spectrum) as well as its fluctuation (noise of photocurrent spectrum) is expressed in terms of spectrum-dependent Mandel parameter. We have discussed possible improvement of sensitivity limit for correlation spectroscopy in this case.
In recent years, electro-optic sampling, which is based on Pockel's effect between an electromagnetic mode and a copropagating, phase-matched ultrashort probe, has been largely used for the investigation of broadband quantum states of light, especially in the mid-infrared and terahertz frequency range. The use of two mutually delayed femtosecond pulses at near-infrared frequencies allows the measurement of quantum electromagnetic radiation in different space-time points. Their correlation allows therefore direct access to the spectral content of a broadband quantum state at terahertz frequencies after Fourier transformation. In this work, we will prove experimentally and theoretically that when using strongly focused coherent ultrashort probes, the electro-optic sampling technique can be affected by the presence of a third-order nonlinear mixing of the probes' electric field at near-infrared frequencies. Moreover, we will show that these third-order nonlinear phenomena can also influence correlation measurements of the quantum electromagnetic radiation. We will prove that the four-wave mixing of the coherent probes' electric field with their own electromagnetic vacuum at near-infrared frequencies results in the generation of a higher-order nonlinear correlation term. The latter will be characterized experimentally, proving its local nature requiring the physical overlap of the two probes. The parameters regime where higher order nonlinear correlation results predominant with respect to electro-optic correlation of terahertz radiation is provided.