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Advances in Optical and Mechanical Technologies for Telescopes and Instrumentation IV

Crossing the diffraction limit with an optical amplifier

Gal Gumpel, Erez N. Ribak

Published Dec 10, 2020• 0 citations
Publisher

Abstract

Heisenberg's uncertainty principle tells us that it’s impossible to determine simultaneously the position of a photon crossing a telescope's aperture as well as the angle of its momentum. A new technique suggests to overcome the diffraction limit via optical amplification. A number of entangled photons, created by amplification of a single photon, behaves as a single quantum system with respect to the uncertainty principle. Unfortunately, spontaneous emission contributes noise and negates the possible gain from this stimulated emission. The spontaneous photons guarantee the uncertainty principle. Thus the problem of low resolution is replaced by the problem of low SNR. The detection of spontaneous photons follows the same Poisson statistics in time and space. However, the stimulated photons are spatially and temporally coherent with the incoming photons. A pixel with additional hidden thermal signal will slightly modify the Poisson statistics, and only within the diffraction pattern of the photon packets. We characterise the average number of spontaneous photons in all pixels, and subtract it from the stimulated photons. This algorithm is applied on simulated detection events of an amplified signal. The reconstructed image is resolved beyond the limit of the same optical system in the absence of amplification. We produced a number of samples of a wide-band solid-state dye (DCM within PMMA), because the expected number of (stellar) photons is small, and a solid-state dye is easier to handle compared to a dye solution. Initial results with a white light source and a laser pump depict the parameters of the method.

DOI
10.1117/12.2559434

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Heisenberg's uncertainty principle tells us that it’s impossible to determine simultaneously the position of a photon crossing a telescope's aperture as well as the angle of its momentum. A new technique suggests to overcome the diffraction limit via optical amplification. A number of entangled photons, created by amplification of a single photon, behaves as a single quantum system with respect to the uncertainty principle. Unfortunately, spontaneous emission contributes noise and negates the possible gain from this stimulated emission. The spontaneous photons guarantee the uncertainty principle. Thus the problem of low resolution is replaced by the problem of low SNR. The detection of spontaneous photons follows the same Poisson statistics in time and space. However, the stimulated photons are spatially and temporally coherent with the incoming photons. A pixel with additional hidden thermal signal will slightly modify the Poisson statistics, and only within the diffraction pattern of the photon packets. We characterise the average number of spontaneous photons in all pixels, and subtract it from the stimulated photons. This algorithm is applied on simulated detection events of an amplified signal. The reconstructed image is resolved beyond the limit of the same optical system in the absence of amplification. We produced a number of samples of a wide-band solid-state dye (DCM within PMMA), because the expected number of (stellar) photons is small, and a solid-state dye is easier to handle compared to a dye solution. Initial results with a white light source and a laser pump depict the parameters of the method.
In a previous article [Astron. Astrophys.561, A118 (2014)], we suggested a method to overcome the diffraction limit behind a telescope. We discuss and extend recent numerical simulations and test whether it is indeed possible to use photon amplification to enhance the angular resolution of a telescope or a microscope beyond the diffraction limit. An essential addition is the proposal to select events with an above-average ratio of stimulated to spontaneous photons. The analysis shows that the diffraction limit of a telescope is surpassed by a factor of 10 for an amplifier gain of 200, if the analysis is restricted to a tenth of the incoming astronomical photons. A gain of 70 is sufficient with a hundredth of the photons. More simulations must be performed to account for the bunching of spontaneous photons.
Introduction Most of the lightwave transmission systems operating today benefit fully from extensive deployment of optical amplifiers (OA). These components perform the amplification of optical intensity directly in the optical domain, without resorting to any electrical-domain regeneration. Optical amplifiers increase the average number of output photons per unit time by several orders of magnitude compared with the incoming signal intensity. However, as with every amplifying process, optical amplification cannot be achieved without paying back for the unavoidable noise power added to the signal intensity. As we will see in detail in Chapter 6, the optical amplification process comes with optical noise generated by spontaneous emission inside the active medium. The intensity of the optical signal is represented by the flux of the signal photon population. Conversely, the photons generated by the spontaneous emission process inside the optical cavity represent the noise photon population. The fundamental phenomenon supporting optical amplification is stimulated emission. The basic property of stimulated emission, making the great difference from spontaneous emission and enabling optical amplification, is the coherent nature of the photon generation process. Accordingly, both signal and noise photons go through the same multiplication process by means of stimulated emission. Unless the optical cavity where the stimulated emission takes place (the active cavity) presents selective features for enhancing the signal photon population relative to the spontaneous one, there is no way to avoid noise photons going through stimulated emission, filling most of the cavity population. As a consequence, both photon populations increase, leading respectively to amplified signal intensity and to amplified spontaneous emission intensity. It should be apparent that every noise photon can create a new identical noise photon as a result of stimulated emission, effectively increasing the noise intensity in the active optical cavity. This is the well-known mechanism of amplified spontaneous emission (ASE) noise in optical amplification. Any improvement in the optical amplifier structure devoted to increasing stimulated over spontaneous emission will probably increase the optical signal-to-noise ratio (OSNR) at the cavity output. The spectrum of gain characteristic of the optical active medium is usually wide enough to support an efficient amplification of the broadband spontaneous emission spectrum, leading to the broadband ASE noise power spectral density.
The classical optical diffraction limit can be overcome by exploiting the quantum properties of light in several theoretical studies; however, they mostly rely on an entangled light source. Recent experiments have demonstrated that quantum properties are preserved in many fluorophores, which makes it possible to add a new dimension of information for super-resolution fluorescence imaging. Here, we developed a statistical quantum coherence model for fluorescence emitters and proposed a new super-resolution method using fluorescence quantum coherence in fluorescence microscopy. In this study, by exploiting a single-photon avalanche detector (SPAD) array with a time-correlated single-photon-counting technique to perform spatial-temporal photon statistics of fluorescence coherence, the subdiffraction-limited spatial separation of emitters is obtained from the determined coherence. We numerically demonstrate an example of two-photon interference from two common fluorophores using an achievable experimental procedure. Our model provides a bridge between the macroscopic partial coherence theory and the microscopic dephasing and spectral diffusion mechanics of emitters. By fully taking advantage of the spatial-temporal fluctuations of the emitted photons as well as coherence, our quantum-enhanced imaging method has the significant potential to improve the resolution of fluorescence microscopy even when the detected signals are weak.
The fundamental understanding of biological pathways requires minimally invasive nanoscopic optical resolution imaging. Many approaches to high-resolution imaging rely on localization of single emitters, such as fluorescent molecules or quantum dots. Additionally, the exact determination of the number of such emitters in an imaging volume is essential for a number of applications; however, in standard intensity-based microscopy it is not possible to determine the number of individual emitters within a diffraction limited spot without initial knowledge of system parameters. Here we explore how quantum measurements of the emitted photons using photon number resolving detectors can be used to address this challenging task. In the proposed new approach, the problem of counting emitters reduces to the task of determining differences between the emitted photon distribution and the Poisson limit. We show that quantum measurements of the number of photons emitted from an ensemble of emitters enable the determination of both the number of emitters and the probability of emission. This method can be applied for any type of single-photon emitters. The scaling laws of this new approach are presented by the Cramer-Rao Lower Bounds, and this technique has great potential in quantum optical imaging with nanoscopic resolution.
The basic equations governing noise phenomena are derived from first principles and applied to examples in optical communications. Quantum noise arises from two sources, the momentum fluctuations of electrons at optical frequencies and the uncertainty-related fluctuations of the electromagnetic field. Shot noise results from the beating of the noise sources with the signal field. In high-gain amplifiers, the spontaneous-emission noise dominates shot noise and results in a noise figure of at least 3 dB. It is shown explicitly how, at high power, both the laser field and the laser noise source become classical. The increase in noise in lasers with open cavities is not due to enhanced spontaneous emission as once thought, but to single-pass amplification. The noise fields and spontaneous currents have Gaussian distributions, while nonlasing modes have exponential photon-number distributions. Low-frequency intensity fluctuations arise from the electric current driving the laser and can be sub-Poissonian, in contrast to shot noise, which has a Poissonian distribution. The calculational tools are a wave equation for the field operator and a rate equation for the carrier-number operator, each containing spontaneous current noise sources. The correlation functions of these sources are determined by the fluctuation-dissipation theorem. [S0034-6861(96)00503-X]