An analysis of the coherent mode decomposition of an optical field after propagation through atmospheric turbulence is presented. The coherent modes represent an ideal basis by which to decompose the field for design of mode-limited optical systems. Due to rotational symmetry of the Fredholm integral operator for Kolmogorov optical turbulence, the decomposition yields separable solutions classified by a radial and azimuthal mode index. The study of the coherent modes is then reduced to that of the radial functions determined by the coherence ratio D/r0 and obscuration ratio ϵ. Analysis of the spectrum of eigenvalues yields sharp bounds on the efficiency of receivers using incoherent or coherent combining with mode-limited photonic devices in the presence of Kolmogorov turbulence. The effective number of modes needed to represent Kolmogorov optical turbulence is studied via the von Neumann entropy, purity, and largest eigenvalue, and the differences in the different definitions is discussed. The similarity of the coherent modes to linearly polarized (LP) fiber modes is quantified yielding a precise characterization of the maximum gain that can be achieved in mode-limited systems via mode shaping techniques. As a final application, a mode sorting technique is presented for optimally splitting power from atmospherically degraded light into a finite number of modes simultaneously maximizing total coupling efficiency and minimizing the difference in average power between channels.
NASA Glenn Research Center’s quantum metrology approach is to combine measurements and models. Measurement results and models are subsequently integrated with NASA’s aerospace competency needs to provide an understanding of how spaceflight components work together in quantum network architectures. Trade studies and device measurements are performed within NASA’s Quantum Metrology Laboratory (NQML) whereas dynamic quantum network modeling occurs via the NASA Quantum Communications Analysis Suite (NQCAS) simulation tool. In illustrating the synthesis of the network model and metrology for quantum network development, we have focused on the evaluation of a degenerate Spontaneous Parametric Down Conversion (SPDC) source. Here we present an overview of Hong-Ou-Mandel and Joint Spectral Intensity measurements of the degenerate SPDC source. Results of these experiments are input into NQCAS to evaluate source suitability for entanglement swapping. This demonstrates the technology development approach of coupling of quantum measurement and free space quantum network models.
Free-space optical communication links with terrestrial ground stations experience fading due to atmospheric scintillation and beam pointing. Fiber-coupled receiver systems experience additional fading at the interface between the fiber and free-space optics of the telescope. The National Aeronautics and Space Administration (NASA) Glenn Research Center (GRC) has characterized a real-time photon-counting optical ground receiver system with an atmospheric fade emulation system. The receiver system is comprised of a fiber interconnect, an array of Superconducting Nanowire Single Photon Detectors (SNSPDs), and a Field Programmable Gate Array (FPGA) based receive modem. Two fiber interconnect/detector architectures have been studied. One architecture uses a 70-mode photonic lantern coupled to seven single pixel SNSPDs. The other architecture uses a 10-mode Few-Mode Fiber (FMF) coupled to a 15-pixel SNSPD array. The receiver system complies with the Consultative Committee for Space Data Systems (CCSDS) optical communications high photon efficiency coding and synchronization standard, which uses Serially Concatenated convolutionally coded Pulse-Position Modulation (SCPPM). The CCSDS standard is designed for use in low photon flux missions, including the Orion Artemis-II Optical (O2O) communications demonstration. The standard utilizes a convolutional symbol interleaver which can be resized to mitigate different fades. The fade emulation system employed in this work emulates scintillation-induced, pointing-induced, and coupling-induced fading. This paper gives an overview of the real-time optical receiver system and the fade emulation system. It presents tests results which show the impact of fading on the performance on the receiver. The test results show that in the presence of channel fading, the 70-mode photonic lantern outperforms the 10-mode FMF under higher (𝐷/𝑟0 = 9) turbulence conditions due to high fiber-coupling-induced fading and fiber coupling loss on the 10-mode FMF. When operating in lower turbulence (𝐷/𝑟0 = 4), the 10-mode FMF outperforms the 70-mode photonic lantern. The paper also shows a larger convolutional interleaver improves the system performance as long as the receiver does not lose acquisition.
KEYWORDS: Scintillation, Optical fibers, Free space optical communications, Receivers, Analytic models, Turbulence, Statistical modeling, Monte Carlo methods, Single mode fibers, Linear filtering, Statistical analysis
The design and testing of a free-space optical communication system requires assessment of the impact of random fluctuations in received power from a laser beam transmitted over an atmospheric channel. A number of methods for generating fading power vectors for in-lab emulation of an atmospheric channel have previously been reported. These techniques include spectral shaping and filtering of a signal from a normally distributed pseudo-random number generator, full wave optics simulations with random phase screens, and pre-recorded measurements from experimental free-space links. In this work, a statistical analysis of atmospheric fading is presented with the goal of producing a practical engineering model suitable for generating synthetic fade vectors in real-time for long-duration receiver testing with channel interleaving. Specifically, a parametric model is developed for turbulence-induced fade on space-to-ground links with large-aperture receivers, including aperture-averaging and the effects of aperture size on the instantaneous coupling efficiency for mode-limited receivers. In particular, we analyze the probability density function and temporal power spectrum for fluctuations of the coupling efficiency for few-mode fibers in a range of turbulence conditions.
Atmospheric emulators based on spatial light modulators offer the ability to test atmospheric propagation effects on a laser communication component’s performance in the laboratory setting. To create a high-fidelity atmospheric emulator, details of the optical design are key. This paper discusses the optical design choices and refinements that enabled the creation of a system that was verified to recreate multi-layer turbulence with high fidelity up to D/r0 =50. Optical design choices that affect the fidelity discussed in this paper include the characteristics of the input laser, the spatial light modulator, the holograms, the image relay optical components, and the spatial filter. Also included in this paper is a comparison of the chosen folded optical layout to an alternative angled layout.
A fundamental requirement of free-space optical communication is the ability to efficiently couple atmospherically distorted light from a telescope to a detector. A numerical method is presented for modeling fiber-based receiver performance in atmospheric conditions based on phase space optics which does not rely on Monte Carlo methods. This method is employed to analyze the waveguide insertion loss and optimal coupling geometry in atmospheric conditions for step-index fibers, graded-index fibers, and photonic lanterns with and without tilt compensation and central obscurations in the telescope.
A key challenge of photon counting optical communication is delivering light with atmospherically distorted wavefronts from the telescope to detectors efficiently. When using fiber coupled single photon detectors, the efficiency of the transmittance is constrained by the modes supported by the fiber. The number of modes supported by a fiber depends on the size of the core. The larger the core, the more modes supported. However, commercial off the shelf superconducting nanowire single photon detectors (SNSPDs) are currently limited in area, which limits the core size of the fibers that can efficiently couple to the detectors. To increase the amount of light that can be delivered to the detectors, NASA Glenn Research Center is considering many different fiber/detector architectures. This paper compares insertion loss of the fiber device for two different architectures:
• a multi-plane light conversion device to split the light from a 30 µm core diameter fiber into 7 separate, 15 μm core diameter few-mode fibers butt-coupled to 7 single-element SNSPDs, and
• a 30 μm core diameter multimode fiber butt-coupled to a 16 multi-element, SNSPD array.
The measured insertion loss for each fiber device under emulated atmospheric conditions with D/r0 between 2 and 30 is presented. The multi-plane light conversion device shows a consistent ~1 dB loss more than the multimode fiber. Also presented is the measured uneven power splitting of the multiplane light conversion device, especially at lower D/r0. How this uneven power splitting contributes to system loss called blocking loss is discussed.
An analysis of optical scintillation and fade on long slant-path atmospheric channels is presented via a direct comparison between wave-optics-based numerical simulations and experimental flight data from a ground-to-aircraft optical communication link. In addition to physically modeling the propagation through slant-path atmospheric turbulence, the numerical simulations include simultaneously the effects of mechanical pointing jitter, aperture-averaging, and first-order scattering/absorption models. The power spectral density, fade probability, and mean fade time of the simulated power fluctuations are studied and validated against measurements taken at slant-path distances ranging from 60 to 113 km and aircraft speeds up to 70 m / s.
Photonic lanterns are being evaluated as a component of a scalable photon counting real-time optical ground receiver for space-to-ground photon-starved communication applications. The function of the lantern as a component of a receiver is to efficiently couple and deliver light from the atmospherically distorted focal spot formed behind a telescope to multiple small-core fiber-coupled single-element super-conducting nanowire detectors. This architecture solution is being compared to a multimode fiber coupled to a multi-element detector array. This paper presents a set of measurements that begins this comparison. This first set of measurements are a comparison of the throughput coupling loss at emulated atmospheric conditions for the case of a 60 cm diameter telescope receiving light from a low earth orbit satellite. The atmospheric conditions are numerically simulated at a range of turbulence levels using a beam propagation method and are physically emulated with a spatial light modulator. The results show that for the same number of output legs as the single-mode fiber lantern, the few-mode fiber lantern increases the power throughput up to 3.92 dB at the worst emulated atmospheric conditions tested of D/r0=8.6. Furthermore, the coupling loss of the few-mode fiber lantern approaches the capability of a 30 micron graded index multimode fiber chosen for coupling to a 16 element detector array.
This report presents our model for atmospheric turbulence fade for an Earth/Space system, and our physical emulation test bed components. For modeling the atmosphere, we have used the Hufnagel-Valley model, in combination with Cn2 measurement parameters and MATLAB software. From these models, power fluctuation time series were generated and subsequently converted to voltages that were uploaded into an acousto-optic modulator and signal generator. The acousto-optic modulator is a compact, fiber-based device that has a maximum 55 MHz response and 45 dB of range, making it a viable component for future integration into a laboratory atmospheric emulation test bed. Results from our fade model implementation with the acousto-optic modulation system will be offered and discussed.
Modeling the effects of atmospheric turbulence on optical beam propagation is a key element in the design and analysis of free-space optical communication systems. Numerical wave optics simulations provide a particularly useful technique for understanding the degradation of the optical field in the receiver plane when the analytical theory is insufficient for characterizing the atmospheric channel. Motivated by such an application, we use a splitstep method modeling the turbulence along the propagation path as a series of thin random phase screens with modified von Karman refractive index statistics using the Hufnagel-Valley turbulence profile to determine the effective structure constant for each screen. In this work, we employ a space-to-ground case study to examine the irradiance and phase statistics for both uniformly and non-uniformly spaced screens along the propagation path and compare to analytical results. We find that better agreement with the analytical theory is obtained using a non-uniform spacing with the effective structure constant for each screen chosen to minimize its contribution to the scintillation in the receiver plane. We evaluate this method as a flexible alternative to other standard layered models used in astronomical imaging applications.
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