In this thesis, I have developed a range of theoretical and numerical techniques for modelling the behaviour of partially coherent optical systems and multi-mode detectors. The numerical simulations were carried out for the ultra-low-noise Transition Edge Sensors (TESs) being proposed for use on the SAFARI instrument on the cooled aperture infrared space telescope SPICA (34 - 210 μm). The optical behaviour of the SAFARI system is described in terms of the optical modes of the telescope, as distinct from the optical modes of the detector. The performance of the TESs were assessed in terms of signal power, background power and photon noise. To establish a method for precisely characterising and calibrating ultra-low-noise TESs, a cryogenic test system was designed and engineered to measure the optical efficiencies of the SAFARI TESs. The multi-mode, partially coherent illumination conditions of the measurement system were engineered to be precisely the same as those of the telescope. A major difference between the test system and the telescope’s optics is that the telescope will have focusing elements, but the test system was designed to avoid focusing elements in order to keep the optical path as clean as possible. The theoretical formalism and numerical models were adapted accordingly to address this difference. The numerical simulations show that the test system could provide near identical optical performance as that of the telescope system even though the focusing elements were absent. I also performed experimental measurements to investigate the optical efficiencies of the multi-mode TESs. The detectors worked exceedingly well in all respects with satisfactory optical efficiencies. In addition, it has been shown that the optical model provides a good description of the optical behaviour of the test system and detectors. Further modal analysis was developed to study losses in the multi-mode horns. The optical behaviour of the waveguide-mounted thin absorbing films in the far-infrared was modelled using a mode-matching method.

In the recent years, the exponential Internet traffic growth projections place enormous transmission rate demand on the underlying information infrastructure at every level, from the long haul submarine transmission to optical metro networks. In recent years, optical transmission at 100 Gb/s Ethernet date rate has been standardized by ITU-T and IEEE forums and 400Gb/s and 1Tb/s rates per DWDM channel systems has been under intensive investigation which are expected to be standardized within next couple of years.To facilitate the implementation of 400GbE and 1TbE technologies, the new advanced modulation scheme combined with advanced forward error correction code should be proposed. Instead of using traditional QAM, we prefer to use some other modulation techniques, which are more suitable for current coherent optical transmission systems and can also deal with the channel impairments. In this dissertation, we target at improving the channel capacity by designing the new modulation formats. For the first part of the dissertation, we first describe the optimal signal constellation design algorithm (OSCD), which is designed by placing constellation points onto a two dimensional space. Then, we expand the OSCD onto multidimensional space and design its corresponding mapping rule. At last, we also develop the OSCD algorithm for different channel scenario in order to make the constellation more tolerant to different channel impairments. We propose the LLR-OSCD for linear phase noise dominated channel and NL-OSCD for nonlinear phase noise dominated channel including both self-phase modulation (SPM) and cross-phase modulation (XPM) cases. For the second part of the dissertation, we target at probability shaping of the constellation sets (non-uniform signaling). In the conventional data transmission schemes, the probability of each point in a given constellation is transmitted equally likely and the number of constellation sets is set to 2!. If the points with low energy are transmitted with larger probability then the others with large energy, the non- uniform scheme can achieve higher energy efficiency. Meanwhile, this scheme may be more suitable for optical communication because the transmitted points with large probabilities, which have small energy, suffer less nonlinearity. Both the Monte Carlo simulations and experiment demonstration of both OSCD and non-uniform signaling schemes indicate that our proposed signal constellation significantly outperforms QAM, IPQ, and sphere-packing based signal constellations.