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Traditionally, theoretical physicists develop and use powerful mathematics to describe nature. Most theoretical physicists not only do not use supercomputers but might also consider their use a weakness. Most great breakthroughs in theoretical physics have come from inspired thinking using paper and pencil. And this tradition is very much alive today as witnessed by the explosion of progress in string theory. This triumph of human ingenuity has, to date, absolutely no use for supercomputers. However, supercomputers are absolutely necessary to make progress in a branch of theoretical particle physics that attempts to simulate, from rst principles, the theory of the strong force. This theory describes how quarks and gluons interact to form protons, neutrons, pi-mesons, and the many resonances that make up the subnuclear world. The effort of designing, creating, and using powerful supercomputers to perform these simulations requires a focused, integrated approach. In





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line-center interaction of a simple resonance line pro le If operating off-line center, the gain coef cient is complex and a0 becomes a0/(1 id), where d is the detuning normalized to linewidth of the resonance The interference of two (or more) coherent beams I(x) in the laser ampli er can cause a spatial modulation of the population inversion N(x) This modulation of the inversion is commonly known as spatial hole burning in lasers and leads to formation of a gain grating a(x) 1sN(x), where s is the stimulated emission cross section The gain 2 grating can act as a very ef cient diffractive optical element exhibiting high diffraction ef ciency that may be even greater than unity [16] and also exhibiting very high phase conjugate re ectivity using four-wave mixing (FWM) geometries [5 7].

Figure 10.17. Protein arrays. There are two general types of protein arrays. (a) Analytical array for detection of antigens in serum. Multiple antibodies are attached at spots on array. These can bind speci c uorescently labelled antigens in biological uid (e.g. serum). In this example antigens a and d are detected. (b) Functional protein arrays are based on bioactivity of proteins such as receptor-ligand, enzyme-substrate recognition

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Phase conjugation by FWM has been performed in several types of gain media for example, dye lasers [5, 17], CO2 lasers [4], excimer lasers [18], ashlamppumped solid-state Nd:YAG [2, 5 7], diode-pumped solid-state Nd:YVO4 [19, 33, 34], and copper vapor lasers [20] There is a very signi cantly large body of work on phase conjugation in CO2 active media in the Russian and former Soviet literature In CO2 laser media, gain, refractive index, and thermal nonlinearities can be manifest and the precise physical process is generally more complex to describe than the pure gain process More recently, experiments have focused on development of solid-state lasers based on the gain-grating mechanism In this chapter, the theory developed applies broadly to most gain media, but we shall limit our illustration of experimental implementations to the solid-state laser systems Indeed, the highest phase conjugate re ectivities of .

250,000% have been demonstrated in ashlamp-pumped Nd:YAG by FWM geometries [6, 7]; in self-pumped phase conjugate geometries, re ectivities of 1,000,000% [21] have been achieved The simultaneous presence of refractive index and gain gratings can also occur, and this will be treated brie y The formation of thermally induced refractive index gratings will also be treated separately at the end of the chapter as an alternative to gain gratings for phase conjugation and adaptive laser operation The key to high phase conjugate re ectivity is to have a laser medium with high small-signal gain since this is a key nonlinearity of the gain medium, providing both ampli cation of the interacting beams and available magnitude of the gain modulation induced Table 11.

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