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arXiv:2403.12746 · Optica

Super-resolution of ultrafast pulses via spectral inversion

Michał Lipka, Michal P. Parniak

Published Jul 30, 2024• 3 citations
arXivHTMLPDF

Abstract

The resolution limits of classical spectroscopy can be surpassed by quantum-inspired methods leveraging the information contained in the phase of the complex electromagnetic field. Their counterpart in spatial imaging has been widely discussed and demonstrated; however, the spectral-domain implementations are few and scarce. We experimentally demonstrate a spectroscopic super-resolution method aimed at broadband light (tens to hundreds of GHz), and based on the spectral-domain analog of image inversion interferometry. In a proof-of-principle experiment, we study the paradigmatic problem of estimating a small separation between two incoherent spectral features of equal brightness, with a small number of photons per coherence time. On the grounds of asymptotic estimation theory, more than a two-fold improvement over the spectral direct imaging is demonstrated in terms of required resources (photons) for a given estimator variance. The setup is based on an actively stabilized Mach–Zehnder-type interferometer with electro-optic time lenses and passive spectral dispersers implementing the inversion. As such, the method promises on-chip integration, good scalability, and further applications, e.g., for mode sorting.

DOI
10.1364/optica.522555

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The resolution limits of classical spectroscopy can be surpassed by quantum-inspired methods leveraging the information contained in the phase of the complex electromagnetic field. Their counterpart in spatial imaging has been widely discussed and demonstrated; however, the spectral-domain implementations are few and scarce. We experimentally demonstrate a spectroscopic super-resolution method aimed at broadband light (tens to hundreds of GHz), and based on the spectral-domain analog of image inversion interferometry. In a proof-of-principle experiment, we study the paradigmatic problem of estimating a small separation between two incoherent spectral features of equal brightness, with a small number of photons per coherence time. On the grounds of asymptotic estimation theory, more than a two-fold improvement over the spectral direct imaging is demonstrated in terms of required resources (photons) for a given estimator variance. The setup is based on an actively stabilized Mach–Zehnder-type interferometer with electro-optic time lenses and passive spectral dispersers implementing the inversion. As such, the method promises on-chip integration, good scalability, and further applications, e.g., for mode sorting.
Existing super-resolution methods of optical imaging hold a solid place as an application in natural sciences, but many new developments allow for beating the diffraction limit in a more subtle way. One of the recently explored strategies to fully exploit information already present in the field is to perform a quantum-inspired tailored measurements. Here we exploit the full spectral information of the optical field in order to beat the Rayleigh limit in spectroscopy. We employ an optical quantum memory with spin-wave storage and an embedded processing capability to implement a time-inversion interferometer for input light, projecting the optical field in the symmetric-antisymmetric mode basis. Our tailored measurement achieves a resolution of 15 kHz and requires 20 times less photons than a corresponding Rayleigh-limited conventional method. We demonstrate the advantage of our technique over both conventional spectroscopy and heterodyne measurements, showing potential for application in distinguishing ultra-narrowband emitters, optical communication channels, or signals transduced from lower-frequency domains.
Existing super-resolution methods of optical imaging hold a solid place as an application in multiple sciences, but many new developments allow beating of diffraction limit in better and more subtle ways. An avenue was opened by suggesting to fully exploit information already present in the field by performing quantum-inspired tailored measurements. Here we exploit the full spectral information of the optical field in order to beat the Rayleigh limit in spectroscopy. We employ optical quantum memory with spin-wave storage and an embedded processing capability to implement a timeinversion interferometer for input light, projecting the optical field in the symmetricanti-symmetric mode basis. Our tailored measurement achieves a resolution of 15 kHz and requires 20.1 times less photons than a corresponding Rayleigh-limited conventional method. We demonstrate the advantage of our technique over both conventional spectroscopy and heterodyne measurements, showing potential for application in distinguishing ultra-narrowband emitters, optical communication channels, or signals transduced from lower-frequency domains.
Quantum-inspired superresolution methods surpass the Rayleigh limit in imaging, or the analogous Fourier limit in spectroscopy. This is achieved by carefully extracting the information carried in the emitted optical field by engineered measurements. An alternative to complex experimental setups is to use simple homodyne detection and customized data analysis. We experimentally investigate this method in the time-frequency domain and demonstrate the spectroscopic superresolution for two distinct types of light sources: thermal and phase-averaged coherent states. The experimental results are backed by theoretical predictions based on estimation theory.
The inherent non-linearity of intensity correlation functions can be used to spatially distinguish identical emitters beyond the diffraction limit, as achieved, for example, in super-resolution optical fluctuation imaging (SOFI). Here, we propose a complementary concept based on spectral correlation functions, termed spectral fluctuation super-resolution (SFSR) imaging. Through theoretical and computational analysis, we show that spatially resolving time-frequency correlation functions in the image plane can improve the imaging resolution by a factor of 2 in most cases and up to twofold for strictly two emitters. This improvement is achieved by quantifying the degree of correlation in spectral fluctuations across the spatial domain. Experimentally, SFSR can be implemented using a combination of interferometry and photon-correlation measurements. The method works for non-blinking emitters and stochastic spectral fluctuations with arbitrary temporal statistics. This suggests its utility in super-resolution microscopy of quantum emitters at low temperatures, where spectral diffusion is often more pronounced than emitter blinking.
The method of optical centroid measurement (OCM) has shown to exhibit spatial super-resolution with enhancements at the Heisenberg limit in plane wave interference experiments. In this work, the OCM method is for the first time used in an imaging setting where actual object features are observed. The OCM result is rederived in a near-field imaging formalism for a general imaging system and in full 2-D treatment. Analogies to coherent and incoherent imaging are shown Moreover, coherent OCM imaging is experimentally implemented for photon number N = 2, where an experimental setup is presented which allows to generate the desired entangled two-photon state containing the super-resolved image. This state is then imaged by an imaging system with a finite resolution defined by its point spread function (PSF). The centroid measurement of the two-photon states delivers then an image with a width of the PSF reduced by a factor 2 corresponding to the Heisenberg limit. In the experiment, the object is illuminated by a continuous-wave pump laser centred at 405nm with an output power of 30mW. A 4-f lens system images the object to the state preparation output plane. In the far-field plane between the lenses, a 5mm long periodically poled KTiOPO4 non-linear crystal generates photon pairs at 810nm by type-0, frequency-degenerate and collinear spontaneous parametric down-conversion. This generated OCM state is then imaged by a single lens and detected in coincidence by a fully digital 2-D sensor array with single-photon sensitivity and per-pixel sub-nanosecond time resolution. The OCM state is spectrally filtered at 810nm. Its imaging capability is compared to classical light sources including spatially coherent, monochromatic illumination at 405nm and 810 nm, as well as spatially incoherent light at 810 nm. The former is implemented using collimated lasers, the latter is a thermal light source spectrally filtered at 810 nm. The PSF of the different light sources are compared at low numerical aperture by imaging a focal point of 25μm Gaussian waist radius.
Sensing with undetected photons has become a vibrant, application-driven research domain with a special focus on the mid-infrared (mid-IR) wavelength region. Since the mid-IR contains spectral bands with highly specific and strong molecular absorbance signatures, often referred to as fingerprints, a multitude of different samples and their compositions can be detected and quantified spectroscopically. Enhancing this spectroscopic method with imaging capabilities leads to a powerful technique for environmental monitoring and biomedical applications that enables automated diagnostics while omitting time-consuming and non-reversible labeling steps. To evade the shortcomings of state-of-the-art instruments for mid-IR hyperspectral microscopy—namely cost, complexity, power consumption, and performance, which stem from technological challenges in mid-IR detection and light sources—we construct a proof-of-concept nonlinear interferometer in a wide-field imaging arrangement. This nominally narrowband imaging technique is then expanded to acquire broadband spectral information through capturing images for varying interferometer displacement and applying a pixelwise Fourier-transform of the resulting interferograms, yielding high-resolution infrared spectra for each camera pixel. For the broadband range of 2300−3100cm −1 , covering the important CH-stretch band, we perform hyperspectral imaging that simultaneously resolves 3500 spatial modes, each with a spectral resolution of 10cm −1 , leveraging in total around 10 5 spatio-spectrally entangled photon modes. Our image acquisition uses a commercial sCMOS camera, while a medium-power and compact continuous-wave pump laser is the only necessary light source. For a moderate speed of 360 voxel/s, we obtain a predominantly shot-noise-influenced signal-to-noise ratio (SNR) of 50. We further demonstrate the practicality of our novel hyperspectral imaging technique for microplastics detection and bio-imaging tasks and outline engineering solutions to increase its speed by several orders of magnitude. This shows that our quantum imaging technique is highly promising for applications requiring compact, cost-effective label-free analyses.