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Most of this thesis describes experiments conducted in order to generate soft x-rays of energy >67 eV from a laser-generated plasma, in order to pump the Xe III Auger laser at 109 nm. In attempts to obtain the optimal sub-nanosecond laser pulses for amplification in a very simple KrF (248 nm) laser a compact KrF oscillator was used to obtain 1 ml pulses of FWHM duration 2 ns, and plasma-truncated reflection of a focused KrF beam from metal targets gave 1.8 ns pulses. Longer pulses were obtained by truncated stimulated Brillouin scattering (TRUBS), and by plasma-truncated spatial-filtering. Experiments were conducted to pump the Xe III laser using the leading edge of a 20 ns KrF laser pulse. An off-axis spherical mirror produced a 3 cm line plasma on a tantalum target. A poor conversion efficiency to soft x-rays was observed. Unexpectedly poor KrF beam quality was shown to have been a potential cause, a fault in the detection system having been ruled out. A repeat experiment was started, employing tighter focusing and better KrF beam quality. A 7 ps KrF laser system was also investigated for the generation of the necessary plasmas. No 109 nm lasing was observed, and a low conversion efficiency into soft x-rays was measured. The short duration of the KrF pulse was suspected as the cause, and some attempts were made to compensate for this by means of preformed plasmas. Over the course of the work, several aspects of KrF laser technology were improved, including: the characterisation of a novel, safe, solid-state source of fluorine (F₂); the quantitative characterisation of nitrogen dioxide (NO₂) as a variable attenuator for KrF radiation; and the manufacture of uniform, transparent, electrodes led to the laser system having the highest single pulse energy (2.55 J) of any UV-preionised, discharge-excited, conventional-aperture KrF laser. Finally, separate work led to the development and absolute characterisation of a laser-plasma source of tunable VUV/EUV/XUV radiation (30 nm to 200 nm; 6 eV to 41 eV), as well as a sodium salicylate scintillator-based detection system. After optimisation of the target material, laser focusing, and micro-channel-plate (MCP) focusing of the plasma emission, an output of between 10⁶ and 10⁷ photons per shot in a 4 nm bandwidth could be delivered on target.

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Grazing incidence pumping (GRIP) is a scheme to produce x-ray lasers and extreme ultraviolet lithography is a means of lithographic production which requires soft x-rays with a bandwidth of 2% centred at 13,5 nm. In this work firstly a grazing incidence pumping of Ni-like Mo and Ne-like Ti x-ray laser media were simulated by using EHYBRID and a post-processor code coupled to it. The required atomic data were obtained from the Cowan code. Besides, the timing issue needed for amplification purpose in a Ti:Sapphire laser system has been described theoretically. Afterwards, in order to produce soft x-ray lasers for extreme ultraviolet lithographic applications, emission of soft x-rays in the 2% bandwidth centred at 13.5 nm emitted from Sn XII and Sn XIII ions were simulated by using the EHYBRID code for a laser operating at 1064 nm with 1 J of pulse energy and 6 ns of pulse duration. The intensity range that has been investigated is between 1-5 x 1012 W/cm2. Ion fractions of tin ions and line intensities corresponding to different electron temperatures were calculated by using the collisional radiative code NeF.

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It is well known that the optical properties of multi-level atomic and molecular system can be controlled and manipulated efficiently using quantum coherence and interference, which has led to many new effects in quantum optics for e.g. lasing action without population inversion, ultraslow light, high resolution nonlinear spectroscopy etc. Recent experimental and theoretical studies have also provided support for the hypothesis that biological systems uses quantum coherence. Nearly perfect excitation energy transfer in photosynthesis is an excellent example of this. In this dissertation we studied quantum coherence and interference effects in the transient and the continuous-wave regimes. This study led to (i) the first experimental demonstration of carrier-envelope phase effects on bound-bound atomic excitation in multi-cycle regime (~15 cycles), (ii) a unique possibility for standoff detection of trace gases using their rotational and vibrational spectroscopic signals and from herein called Coherent Raman Umklappscattering, (iii) several possibilities for frequency up-conversion and generation of short-wavelength radiation using quantum coherence (iv) the measurement of spontaneous emission noise intensity in Yoked-superfluorescence scheme. Applications of the obtained results are development of XUV (X-Ray) lasers, con- trolled superfluorescent (superradiant) emission, carrier-envelope phase effects, coherent Raman scattering in the backward direction, enhancement of efficiency for generating radiation in XUV and X-Ray regime using quantum coherence with and without population inversion and to extend XUV and X-Ray lasing to ~4.023 nm in Helium-like carbon.

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Optical response of an active medium can substantially be modified when coherent superpositions of states are excited, that is, when systems display quantum coherence and interference. This has led to fascinating applications in atomic and molecular systems. Examples include coherent population trapping, lasing without inversion, electromagnetically induced transparency, cooperative spontaneous emission, and quantum entanglement. We study quantum coherence effects in several quantum optical systems and find interesting applications. We show that quantum coherence can lead to transient Raman lasing and lasing without inversion in short wavelength spectral regions--extreme ultraviolet and x-ray--without the requirement of incoherent pumping. For example, we demonstrate transient Raman lasing at 58.4 nm in Helium atom and transient lasing without inversion at 6.1 nm in Helium-like Boron (triply-ionized Boron). We also investigate dynamical properties of a collective superradiant state prepared by absorption of a single photon when the size of the sample is larger than the radiation wavelength. We show that for large number of atoms such a state, to a good approximation, decays exponentially with a rate proportional to the number of atoms. We also find that the collective frequency shift resulting from repeated emission and reabsorption of short-lived virtual photons is proportional to the number of species in the sample. Furthermore, we examine how a position-dependent excitation phase affects the evolution of entanglement between two dipole-coupled qubits. It turns out that the coherence induced by position-dependent excitation phase slows down the otherwise fast decay of the two-qubit entanglement. We also show that it is possible to entangle two spatially separated and uncoupled qubits via interaction with correlated photons in a cavity quantum electrodynamics setup. Finally, we analyze how quantum coherence can be used to generate continuous-variable entanglement in quantum-beat lasers in steady state and propose possible implementation in quantum lithography.