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JSAP-OSA Joint Symposia

Coherence Synthesis in Nonlinear Optics

Zihao Pang, Ady Arie

Published Jan 1, 2025• 0 citations
Publisher

Abstract

Nonlinear frequency conversion has traditionally relied on highly coherent light sources. This assumption has deeply shaped the field, yet it overlooks the broader role that spatial incoherence can play in nonlinear optics. In this work, we break that paradigm by demonstrating, for the first time, that second harmonic generation (SHG) can be performed with spatially incoherent light, and more importantly, that the spatial coherence of the generated second harmonic field can be customized with precision. Our work unlocks spatial coherence as an active and designable parameter in nonlinear optics.

DOI
10.1364/jsapo.2025.7p_n204_7

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Scientific Reports•Sep 11, 2020•4 citations
Nonlinear frequency conversion has traditionally relied on highly coherent light sources. This assumption has deeply shaped the field, yet it overlooks the broader role that spatial incoherence can play in nonlinear optics. In this work, we break that paradigm by demonstrating, for the first time, that second harmonic generation (SHG) can be performed with spatially incoherent light, and more importantly, that the spatial coherence of the generated second harmonic field can be customized with precision. Our work unlocks spatial coherence as an active and designable parameter in nonlinear optics.
Nonlinear optical interactions are typically driven by coherent sources. Recently, however, incoherent sources have also been shown to offer new opportunities in nonlinear optics. Here we study the effects of the source incoherence in second harmonic generation. We derive and experimentally validate an analytic expression for the far-field coherence function at the second harmonic frequency, which is a generalization of the well-known van Cittert-Zernike theorem. Unlike the linear optics case, here the results depend not only on the source spatial distribution, but also on the nonlinear structure of the crystal. We further show, by performing Young's double-slit measurement, that the coherence at the second harmonic increases as the light propagates inside the nonlinear crystal. Our results establish nonlinearity as a degree of freedom for optical coherence, opening a new research area at the interface of statistical optics and nonlinear optics.
In this Letter, we study the second-harmonic (SH) generation of temporally low-coherence light using the statistical optics method. By introducing the statistical characteristics of low-coherence light into the nonlinear coupled wave equation, we predict the self-convolution relationship between the power spectral density of the second-harmonic and that of the fundamental wave and demonstrate it in experiments. The effects of phase matching and group velocity matching on the second-harmonic bandwidth and conversion efficiency are analyzed, which is beneficial to improve the efficiency of low-coherent SH light. Combining the statistics optics and nonlinear optics, our research provides a suitable mathematical model for the study of nonlinear frequency conversion processes of temporally low-coherence light. Due to its statistical characteristics and temporal incoherence, low-coherence SH light would have further applications in uniform illumination, quantum optics, metrology, and so on.
The recent advent of optical metasurfaces, ultra-thin structures composed of nanoresonators facilitating strong light concentration [1–3], opens the path towards efficient \nfrequency conversion [4–7] in a material thousand times thinner than a human hair [8]. \nThere is a remarkable capacity to individually shape each nanoresonator of the metasurface to spatially and spectrally control the conversion process with unprecedented \nnanoscale resolution, facilitating an ultimate flexibility to selectively convert, focus, \nand image different colours with a single metasurface. The strong enhancement of the \nnonlinear processes in dielectric nanoresonators is largely due to the absence of material \nabsorption and the excitation of Mie-type bulk resonances [2]. The highest conversion \nefficiency to date has been achieved employing III-V semiconductor nanostructures, \nsuch as AlGaAs which is a non-centrosymmetric material with high quadratic nonlinear \nsusceptibility. In particular, second-harmonic generation efficiencies up to 10−4 have \nbeen recently demonstrated [8–12], six orders of magnitude higher than in plasmonics. \nSuch capabilities can make an immense fundamental and practical impact, including \nthe quantum state generation in nonlinear metasurfaces as we discuss in this chapter. \nThe quantum state of correlated photon-pairs is the essential building block for photon entanglement [13, 14], which underpins many quantum applications, including secure networks, enhanced measurement and lithography, and quantum information processing [15]. One of the most versatile techniques for the generation of correlated photons is the process of spontaneous parametric down-conversion (SPDC) [16, 17], see \nFig. 1. It allows for an arbitrary choice of energy and momentum correlations between \nthe generated photons, robust operation at room temperature, as well as for spatial and \ntemporal coherence between simultaneously pumped multiple SPDC sources. Alternative approaches based on atom-like single photon emitters, such as solid-state fluorescent atomic defects [18], quantum dots [19, 20], and 2D host materials [21, 22], have \nreached a high degree of frequency indistinguishability, purity and brightness [19, 20]. \nHowever, this comes with the expense of operation at cryogenic temperatures and lack \nof spatial coherence between multiple quantum emitters. These features might limit \npossible applications and reduce the potential for device scalability. Furthermore, the \nsmall size of the atomic sources often requires complex schemes aimed at coupling to \noptical nanoantennas and improving the photon extraction efficiency [21]. \nThe miniaturization of SPDC quantum-light sources to micro and nanoscale dimensions is a continuing quest, as it enables denser integration of functional quantum \ndevices. Traditionally, bulky cm-sized crystals were utilized for SPDC, entailing the \ndifficulty of aligning multiple optical elements after the SPDC crystal, while offering \nrelatively low photon-pair rates [17]. As a first step of miniaturization, SPDC was \nrealized in low-index-contrast waveguides, which allowed confining light down to several square micrometers transversely to the propagation direction, significantly enhancing the conversion efficiency [23]. However, this approach still requires centimetres \nof propagation length, which makes the on-chip integration with other elements challenging [24]. The introduction of high-index contrast waveguides and ring resonators \nallowed for shrinking the sizes necessary for SPDC to millimetres [25], and to tens \nof micrometers [26]. However, further miniaturisation down to the metasurfaces composed of nanoresonators requires conceptually different approaches.
English: In this project has been designed and implemented a setup to produce the nonlinear process of the second harmonic generation (SHG) in Bragg reflection waveguides (BRW). Starting with the adjustment of a tunable single frequency laser at 1550 with an external cavity configuration. Two diferent types of SHG have been observed, we measured their spectrum and its shifting caused by temperature variations. Finally, it has also been observed the spatial shape of the Bragg mode guided along the BRW, which is the responsible for reaching the phase-matching condition between all the waves involved in this non-linear process. The results obtained in this project will be used in a future experiments, specially, in the implementation of a monolithic integrated source of entangled photon pairs generated by using the spontaneous parametric down-conversion (SPDC) process.
We demonstrate supermode-based second harmonic generation in an integrated nonlinear interferometer made of linear and nonlinear directional couplers. We use a fully-fibered pump shaper to demonstrate second harmonic generation pumped by the symmetric or anti-symmetric fundamental spatial modes. The selection of the pumping mode and thus of a specific SHG spectral profile is achieved through the selection of the fundamental wavelength and via a robust phase setting scheme. We use two methods: either post-selecting or actively setting the pumping mode. Such modal phase matching paves the way for classical and quantum applications of coupled nonlinear photonic circuits, where multimode excitation, encoding and detection are a route for multiplexing and scaling up light-processing.
Nonlinear parametric processes involving ultrashort pulses are typically carried out in time domain, which mathematically corresponds to a convolution of their frequency spectra. In contrast, this spectral convolution changes into a multiplication operation when performing the nonlinear interaction in frequency domain. Here, we extend the scope of frequency-domain nonlinear optics by demonstrating its ability to perform a temporal convolution. Through this approach, nonlinear optical operations that are inaccessible in time domain can be realised: specific optical information can be coherently advanced by picoseconds within a pulse sequence-a newly generated second harmonic pulse carries the amplitude and phase information of two input pulses. This central pulse is isolated when using an input field consisting of two cross-polarized input pulses in combination with type-II second harmonic generation. The effects of nonlinear temporal convolution can be viewed from the aspect of signal processing and pulse shaping, where the nonlinear interaction in the parametric crystal plays the role of a dynamic linear optical filter-in contrast to conventional static filters-with a shaping mask instantaneously adapting to the laser field.