Optical Communication Through the Turbulent Atmosphere with Transmitter and Receiver Diversity, Wavefront Control, and Coherent Detection

Thesis Supervisor: Vincent W. S. Chan Title: Joan and Irwin M. Jacobs Professor of Electrical Engineering and Computer ScienceFree space optical communication through the atmosphere has the potential to provide secure, low-cost, rapidly deployable, dynamic, data transmission at very high rates. However, the deleterious e ects of turbulence can severely limit the utility of such a system, causing outages of up to 100 ms. For this thesis, we investigate an architecture that uses multiple transmitters and multiple coherent receivers to overcome these turbulence-induced outages. By controlling the amplitude and phase of the optical eld at each transmitter, based on turbulence state information fed back from the receiver, we show that the system performance is greatly increased by exploiting the instantaneous structure of the turbulence. This architecture provides a robust highcapacity free-space optical communication link over multiple spectral bands, from visible to infrared. We aim to answer questions germane to the design and implementation of the diversity optical communication architecture in a turbulent environment. We analyze several di erent optical eld spatial modulation techniques, each of which is based on a di erent assumption about the quality of turbulence state information at the transmitter. For example, we explore a diversity optical system with perfect turbulence state information at the transmitter and receiver that allocates transmit power into the spatial modes with the smallest propagation losses in order to decrease bit errors and mitigate turbulence-induced outages. Another example of a diversity optical system that we examine is a diversity optical system with only a subset of the turbulence state information: this system could allocate all power to the transmitter with the smallest attenuation. We characterize the system performance for the various spatial modulation techniques in terms of average bit error rate (BER), outage probability, and power gain due to diversity. We rst characterize the performance of these techniques in the idealized case, where the instantaneous channel state is perfectly known at both the receiver and transmitter. The time evolution of the atmosphere, as wind moves tur- 3 bules across the propagation path, can limit the ability to have perfect turbulence state knowledge at the transmitter and, thus can limit any improvement realized by optical eld spatial modulation techniques. The improvement is especially limited if the latency is large or the feedback rate is short compared to the time it takes for turbules to move across the link. As a result, we make successive generalizations, until we describe the optimal system design and communication techniques for sparse aperture systems for the most general realistic case, one with inhomogeneous turbulence and imperfect (delayed, noisy, and distorted) knowledge of the atmospheric state

Reliable Communication over Optical Fading Channels

In free space optical communication links,atmospheric turbulence causes random fluctuations in the refractive index of air at optical wavelengths, which in turn cause random fluctuations in the intensity and phase of a propagating optical signal. These intensity fluctuations, termed ``fading,'' can lead to an increase in link error probability, thereby degrading communication performance. Two techniques are suggested to combat the detrimental effects of fading, viz., (a) estimation of channel fade and use of these estimates at the transmitter or receiver; and (b) use of multiple transmitter and receiver elements. In this thesis, we consider several key issues concerning reliable transmission over multiple input multiple output (MIMO) optical fading channels. These include the formulation of a block fading channel model that takes into account the slowly varying nature of optical fade; the determination of channel capacity, viz., the maximum achievable rate of reliable communication, when the receiver has perfect fade information while the transmitter is provided with varying degrees of fade information; characterization of good transmitter power control strategies that achieve capacity; and the capacity in the low and high signal-to-noise ratio (SNR) regimes. We consider a shot-noise limited, intensity modulated direct detection optical fading channel model in which the transmitted signals are subject to peak and average power constraints. The fading occurs in blocks of duration $T_{c}$ (seconds) during each of which the channel fade (or channel state) remains constant, and changes across successive such intervals in an independent and identically distributed (i.i.d.) manner. A single-letter characterization of the capacity of this channel is obtained when the receiver is provided with perfect channel state information (CSI) while the transmitter CSI can be imperfect. A two-level signaling scheme (``ON-OFF keying'') with arbitrarily fast intertransition times through each of the transmit apertures is shown to achieve channel capacity. Several interesting properties of the optimum transmission strategies for the transmit apertures are discussed. For the special case of a single input single output (SISO) optical fading channel, the behavior of channel capacity in the high and low signal-to-noise ratio (SNR) regimes is explicitly characterized, and the effects of transmitter CSI on capacity are studied

Long-Distance Quantum Communication with Entangled Photons using Satellites

The use of satellites to distribute entangled photon pairs (and single photons) provides a unique solution for long-distance quantum communication networks. This overcomes the principle limitations of Earth-bound technology, i.e. the narrow range of some 100 km provided by optical fiber and terrestrial free-space links.Comment: 12 pages, 7 figures; submitted to IEEE Journal of Selected Topics in Quantum Electronics, special issue on "Quantum Internet Technologies

Free-space propagation of high dimensional structured optical fields in an urban environment

Spatially structured optical fields have been used to enhance the functionality of a wide variety of systems that use light for sensing or information transfer. As higher-dimensional modes become a solution of choice in optical systems, it is important to develop channel models that suitably predict the effect of atmospheric turbulence on these modes. We investigate the propagation of a set of orthogonal spatial modes across a free-space channel between two buildings separated by 1.6 km. Given the circular geometry of a common optical lens, the orthogonal mode set we choose to implement is that described by the Laguerre-Gaussian (LG) field equations. Our study focuses on the preservation of phase purity, which is vital for spatial multiplexing and any system requiring full quantumstate tomography. We present experimental data for the modal degradation in a real urban environment and draw a comparison to recognized theoretical predictions of the link. Our findings indicate that adaptations to channel models are required to simulate the effects of atmospheric turbulence placed on high-dimensional structured modes that propagate over a long distance. Our study indicates that with mitigation of vortex splitting, potentially through precorrection techniques, one could overcome the challenges in a real point-to-point free-space channel in an urban environment