Application of Single-mode Fiber-coupled Receivers in Optical Satellite to High-altitude Platform Communications

Recommended by Shlomi Arnon In a free-space optical communication system employing fiber-optic components, the phasefront distortions induced by atmospheric turbulence limit the efficiency with which the laser beam is coupled into a single-mode fiber. We analyze different link scenarios including a geostationary (GEO) satellite, a high-altitude platform (HAP), and an optical ground station (OGS). Single-mode coupled optically preamplified receivers allow for efficient suppression of background noise and highly sensitive detection. While GEO-to-OGS communication suffers from atmospheric turbulence, we demonstrate that GEO-to-HAP communication allows for close to diffraction-limited performance when applying tip-tilt correction.


INTRODUCTION
Free-space laser communications-with its ability to transmit information via a collimated laser beam at high data rates using compact, low-mass terminals, while avoiding interference problems and without exhausting the radio-frequency bandwidths-are a promising candidate to satisfy the ever increasing bandwidth demand associated with new communication services. While optical intersatellite links are already operable [1], laser communication from ground suffers from cloud coverage, harsh weather conditions, and atmospheric turbulence [2]. To find a remedy, current research concentrates on optical communications from or to high-altitude platforms (HAPs)-aircrafts which are situated well above the clouds at typical heights of 17 to 22 km-where the atmospheric impact on a laser beam is less severe than directly above ground [3,4]. An optical link between satellite and HAP could serve as a broadband communication channel if data from several sensors or RF communication terminals onboard the HAP is to be transmitted to a satellite, or if the HAP works as a data relay station, receiving information from a satellite.
While existing satellite laser communication terminals use AlGaAs semiconductor lasers with wavelengths around 830 nm [1], recent research activities focus on communication wavelengths around λ = 1550 nm. At this wavelength, highly sensitive receivers incorporating Erbium-doped fiber amplifiers (EDFAs) for optical preamplification are available [5,6]. When using such fiber-based technology, coupling into a single-mode fiber (SMF) is required and the reduction of the fiber coupling efficiency due to atmospheric turbulence is an important issue.
The Earth's atmosphere extends approximately 700 km above the surface and consists of several distinct layers [7]. Pronounced density is found within the lowest 20 km, still influencing satellite-to-HAP links. When a laser beam propagates through a turbulent medium like the atmosphere, one observes absorption, scattering, additional beam spreading and beam wander, scintillation, and phasefront distortions. The latter results in a loss of power when the light is coupled into a single-mode fiber and-in the worst case-may lead to a link failure. Knowledge of the efficiency with which random light (i.e., light that produces speckle patterns) can be coupled into optical fibers is therefore important, for example, to assess the feasibility of using single-mode coupled, optically preamplified receivers onboard of HAPs. Other effects of atmospheric turbulence than phasefront distortions are not addressed here as they influence all types of optical  [8,9], angular jitter [10], or atmospheric turbulence [11][12][13] on the single-mode fiber coupling efficiency has been analyzed in the field of optical communications, lidar, or astronomy. In most cases, a Gaussian approximation has been used for the fundamental fiber mode. We calculate the degradation of the mean power coupling efficiency into single-mode fiber coupled devices caused by atmospheric turbulence using the exact field of the fiber's fundamental mode. We analyze different link scenarios, as GEO-to-HAP and GEO-to-OGS, and verify the applicability of fiber coupled receivers onboard HAPs due to the reduced impact of atmospheric turbulence at high altitudes. Additional tip-tilt correction even allows for close to diffraction limited performance. By comparing our calculations with analytical models for the Strehl ratio (a standard indicator of the performance of classical imaging systems), we show that the Strehl ratio is a good approximation for the coupling efficiency into a single-mode fiber.

COMMUNICATION SCENARIO
Optical satellite-to-HAP connections allow establishing broadband (backhaul) links, which are required to globally receive from and distribute data to HAPs. The satellite is located at a height h SAT above ground, which may range from 400 km for a low Earth orbiting satellite (LEO) to 35786 km for a geostationary satellite (GEO). The HAP altitude h HAP gives the height above ground for the high-altitude platform. The telescope diameter D denotes the transmit telescope diameter in the uplink case and the receive telescope diameter in the downlink. Typically, the telescope diameters of optical antennas onboard of HAPs and satellites may vary between 0.05 m and 0.2 m. The zenith angle ζ is defined as the angle between the direction to zenith and the direction of the laser beam towards the satellite. Typical system parameter values used for the calculations in the following sections (assuming the HAP to be positioned in Central Europe) are given in Table 1.
Using a single-mode coupled optical preamplifier (cf., Figure 1) onboard the HAP allows for high sensitivity detection and is of advantage with respect to the suppression of background noise. Like in heterodyning, single-mode coupled receivers are less vulnerable to background light than,  Figure 2: Calculated receiver sensitivity penalty of an optically preamplified receiver using RZ intensity modulation at a bit error probability of 10 −9 as a function of background noise power spectral density.
for example, avalanche photodiode (APD) based receivers because the fiber provides an excellent spatial filter function and only one spatial mode (in two orthogonal directions of polarization) is detected [14] . Figure 2 shows the calculated receiver sensitivity penalty as a function of the background noise power spectral density. The sensitivity penalty is defined as the required number of received photons per bit at a bit error probability (BEP) of 10 −9 relative to the quantum limit of 41 photons per bit [15,16]. For the computation, we assumed return-to-zero (RZ) intensity modulation (with a duty cycle of 33%) using an external modulator with 20-dB extinction and no polarization control at the optically preamplified receiver. Beside an EDFA (gain G = 39 dB and noise figure F = 3.8 dB), the receiver incorporates an optical fiber Bragg grating bandpass filter, a PIN-photodiode module with a sensitivity of S = 0.8 A/W, a transimpedance amplifier with R T = 1800 Ω, and an electrical fifth-order Bessel lowpass filter (cf., Figure 1).
When optimizing the optical and electrical filter bandwidths, the calculated receiver sensitivity is only 1.6 dB above the quantum limit in the absence of background noise. In the case of blue sky as background source, that is, with the receiver onboard the HAP, no degradation of receiver performance is found when compared to the case where there is no background light at all. Even when directly looking into the Sun (with a background noise power spectral density of 4.1 · 10 −20 W/Hz) only an additional deterioration of 1.4 dB has to be expected.
In a HAP-to-satellite uplink, the turbulent eddies forming the atmosphere are right in front of the transmitter and comparatively large relative to the optical beam (cf., Figure 3(a)). The resulting large beam spreading causes the phasefront disturbance to be negligible within the small receiving aperture at the satellite [7]. In the downlink, the turbulent eddies are relatively small when compared to the beam diameter, thus leading to noticeable phasefront distortions (cf., Figure 3(b)).

SINGLE-MODE FIBER COUPLING EFFICIENCY
We model the coupling as shown in Figure 4. The optical input field E-which is collected by the receive telescope of diameter D-is focussed by a thin diffraction limited lens to the bare end of a single-mode fiber, whose field distribution of the fundamental mode F as a function of the radial coordinate r is given by the Bessel function of the first kind and of zero order within the core and by the modified Bessel function of the second kind and of zero order in the cladding [17].
The power coupling efficiency η is defined as the ratio of the average power carried by the fiber mode and the average power available in the focal plane. It is possible-and often more convenient-to calculate the coupling efficiency in the aperture plane A, that is, just in front of the coupling lens (cf., Figure 4). The mean coupling efficiency is given by where the angled brackets represent the ensemble-average operator, E(r) is the incident optical field within plane A normalized to a power of unity within the input aperture, and F(r) is the deterministic fiber mode backpropagated into the aperture plane by means of an inverse spatial Fourier transform. A phase function Φ(r) covers any deviations from an ideal plane wavefront of the input field E. The coupling efficiency depends also on the lens-to-fiber coupling geometry, which can be taken into account via an additional coupling design parameter χ = ρ/r S , with ρ being the core radius of the fiber and r S being the Airy radius. The parameter χ takes into account the properties of the incoming beam and of the coupling optics, while the normalized frequency V = 2πρ/λ(n 2 co − n 2 cl ) 1/2 , with core and cladding refractive indices, n co and n cl , determine the characteristics (e.g., the numerical aperture) of the optical fiber. Without loss of generality, we assume for the calculations to follow the fiber to be operated at single-mode cutoff (V = 2.405) and the lensto-fiber geometry to be optimized for maximum coupling efficiency (χ = 0.5345). In the case of a perfect phasefront, Φ(r) = const., and when approximating the fiber's eigenmode by a Gaussian field distribution a maximum coupling efficiency of η max = 81.5% can be achieved [9]. When using  the exact field of the fiber's fundamental mode the maximum coupling efficiency amounts to η max = 78.6%, corresponding to a minimum power coupling loss of 1.05 dB.

TURBULENCE-INDUCED PHASEFRONT DISTORTIONS
To evaluate the influence of a phasefront disturbance on the fiber coupling efficiency, the phase function Φ(r) is modeled as a normal distribution with zero mean (μ ϕ = 0) and standard deviation σ ϕ . Using (1), the resulting coupling efficiency is calculated by means of a Monte Carlo simulation. Based on the Zernike representation of the Kolmogorov spectrum of turbulence, σ ϕ can be derived depending on the receiving aperture diameter D and the Fried parameter r 0 as [7,18,19] σ ϕ = 1.0299 D/r 0 5/3 .
The Fried parameter can be interpreted as the diameter of an aperture over which there is approximately 1 rad of rms phase distortion σ 2 ϕ . In accordance with [7], we calculate the Fried parameter as using the optical wave number k = 2π/λ in rad/m and the structure parameter C 2 n (h) in m −2/3 at height h. The structure parameter is a measure of turbulence strength and represents the total amount of energy contained in the stochastic field of the refractive index fluctuations. It can be approximated according to the Hufnagle-Valley model [20], The structure constant on ground, C 2 n (0), ranges from 10 −17 m −2/3 (during night and weak turbulence conditions) to 10 −13 m −2/3 (during day and strong turbulence conditions). The required rms wind speed ν RMS is calculated using the Bufton wind model [7,20]: The quantity ν wind is the ground wind speed, ν T is the wind speed at the tropopause, h T is the height of the tropopause, and d T is its thickness. For our calculations, we assume ν wind = 3 m/s, ν T = 30 m/s, h T = 9.4 km, d T = 4.8 km, and a structure constant on ground of C 2 n (0) = 1.7 · 10 −14 m −2/3 , which are typical values for clear sky and weak turbulence conditions.

COMPARISON OF LINK SCENARIOS
A comparison between the single-mode fiber coupling efficiency in a satellite-to-ground communication link and a satellite-to-HAP scenario shows the feasibility of using fiber coupled receivers onboard HAPs due to the reduced impact of atmospheric turbulence at high altitudes. Figure 5 gives the coupling efficiency as a function of the rms phasefront perturbation, RMS λ , expressed in fractions of the wavelength λ. For the calculations (using the methods as described in Sections 3 and 4), we assumed a wavelength of 1550 nm and a standard (telecommunications) single-mode fiber with a  core diameter of 10 μm a core refractive index of 1.46, and a core/cladding refractive indices difference of 0.3%. As expected, the characteristic shown in Figure 5 is rather flat for small perturbations, but drops dramatically to very small values for large disturbances. For typical satellite-to-HAP communication links (i.e., with h HAP > 17 km and D < 20 cm), the mean coupling loss is always less than 1.2 dB, while for communication links to a ground station it significantly increases to values larger than 7 dB. The mean value of the coupling efficiency into a SMF as a function of the zenith angle according to (1) is shown in Figure 6(a) for the following three scenarios: (i) a GEO-to-HAP link with the HAP at h HAP = 20 km and a receive telescope diameter of D = 0.135 m, (ii) a GEO-to-HAP link with D = 0.135 m and h HAP = 2400 m, and (iii) a GEO-to-ground link with a telescope diameter D = 1 m at an optical ground station.
At high altitudes, η is roughly invariant with zenith angle and very close to the maximum possible coupling efficiency of 78.6%. With decreasing height also the coupling efficiency decreases due to increasing turbulence leading to noticeable phasefront perturbations especially at zenith angles ζ > 50 • . The phasefront perturbation over a large aperture like at the OGS is more severe than at a HAP, leading to a poor coupling efficiency which, in practice, excludes the use of a single-mode coupled receiver within a ground station.
If the spatial period of the phasefront perturbation is clearly smaller than the pupil diameter, the normalized mean power coupling efficiency is sometimes estimated by the Strehl ratio SR [13], which is defined as the ratio of peak power in the center of the image plane compared to that of an equivalent unaberrated (diffraction-limited) system. It is useful to have an approximate predictor for the coupling efficiency based on the SR which is also a standard indicator of the performance of classical and adaptive (astronomical) imaging systems. Under general conditions, not limited to Another widely used empirical formula is the Marechal approximation [13,19], where σ 2 ϕ is the variance of the phase aberration across the receiving aperture D. An estimation of the coupling efficiency using these approximations is given in Figure 6(b), showing good agreement with the computationally more intensive calculation of Figure 6(a) in the communication scenarios where HAPs are involved, that is, at high altitudes and when using small telescope diameters.
The phase variance averaged over a circular aperture of diameter D as given in (2) drops to if the tip and tilt components of the atmospheric perturbations are removed by means of active target tracking [18,19]. Thus applying tip-tilt correction reduces the phase variance by a factor of 1.0299/0.134 = 7.7, independent of the diameter of the telescope. Figure 7 compares the coupling loss into an SMF for an untracked beam and for a tip-tilt corrected system in a GEO-to-HAP downlink (at different turbulence conditions and using the parameters as given in Table 1). The coupling loss is normalized to the maximum mean coupling efficiency of 78.6%. When tracking is performed by means of a tiltable mirror, the coupling loss is noticeably reduced compared to the untracked case. The advantage of using large wavelengths and HAP altitudes of more than 15 km, leading to negligible coupling loss, is also shown in Figure 7. Figures 6 and 7 illustrate that using a telescope with D less than a few times r 0 as it is the case in a typical satellite-to-HAP communication scenario, will, after tip-tilt correction, lead to a residual phase variance which is small compared to unity and therefore results in close-to-diffraction-limited performance.

SUMMARY
We have analyzed the effect of atmospheric turbulence on a free-space optical communication system employing fiberoptic components for different link scenarios including a geostationary satellite, a high-altitude platform, and an optical ground station. We show that single-mode coupled optically preamplified receivers allow for efficient suppression of background noise and highly sensitive detection. While the phase perturbations in a downlink from GEO-to-OGS prevent the use of optically preamplified receivers because of the low achievable coupling efficiency, the perturbations are small in typical GEO-to-HAP links, thus allowing for efficient single-mode fiber coupling. Active tip-tilt correction reduces phasefront perturbations and allows for achieving close to diffraction limited performance. We showed that the Strehl ratio is a good approximation for the coupling efficiency into a single-mode coupled receiver.

Call for Papers
Computing platforms that are embedded within larger systems they control, called embedded systems, are inherently very complex as they are responsible for controlling and regulating multiple system functionalities. Often embedded systems are also safety-critical requiring high degree of reliability and fault tolerance. Examples include distributed microprocessors controlling the modern cars or aircrafts and airport baggage handling system that track and trace unsafe baggage. To address this growing need for safety and reliability, formal techniques are increasingly being adapted to suit embedded platforms. There has been widespread use of synchronous languages such as Esterel for the design of automotive and flight control software that requires stronger guarantees. Languages like Esterel not only provide nice features for high-level specification but also enable model checkingbased verification due to their formal semantics. Other semiformal notations are also being proposed as standards to specify industrial embedded systems using, for example, the newly developed IEC61499 standard for process control. This standard primarily focuses on component-oriented description of embedded control systems. The goal of this special issue is to bring together a set of high-quality research articles looking at different applications of formal or semiformal techniques in specification, verification, and synthesis of embedded systems. Topics of interest are (but not limited to):

Call for Papers
Over the last years, many journal articles appeared on the principles, analysis, and design of active and active integrated antennas (AAs and AIAs). An AA is a single system comprising both a radiating element and one or more active components which are tightly integrated. This gives clear advantages in terms of costs, dimensions, and efficiency. In the case of an AIA, both the active device and the radiator are integrated on the same substrate. Both options lead to very compact, lowloss, flexible antennas, and this is very important especially at high frequencies, such as those typical of a satellite link. As microwave integrated-circuit and the microwave monolithic integrated-circuit technologies have ripened, AA and AIA applications have become more and more interesting, not only at a scientific level but also from a commercial point of view, up to the point that they have recently been applied to phased array antennas on board moving vehicles for satellite broadband communication systems. The goal of this special issue it to present the most recent developments and researches in this field, with particular attention to space-borne applications, as well as to enhance the state of the art and show how AAs and AIAs can meet the challenge of the XXI century telecommunications applications.
Topics of interest include, but are not limited to: • Active (integrated) antenna design, analysis, and simulation techniques • Active (integrated) antenna applications in arrays, retrodirective arrays and discrete lenses • Millimeter-wave active (integrated) antennas Authors should follow International Journal of Antennas and Propagation manuscript format described at the journal site http://www.hindawi.com/journals/ijap/. Prospective authors should submit an electronic copy of their complete manuscript through th journal Manuscript Tracking System at http://mts.hindawi.com/, according to the following timetable: Manuscript Due September 1, 2008 First Round of Reviews December 1, 2008