An Introduction to Fiber Optics by Ajoy Ghatak

By Ajoy Ghatak

Fresh advances within the improvement of low-loss optical fibers have revolutionized the sector of telecommunications, and fiber-based networks shape a key a part of overseas communications structures. This ebook introduces the actual rules of optical fibers, and info their use in sensor expertise and smooth optical communique structures. The authors commence by way of starting off the fundamental propagation features of unmarried mode and multimode optical fibers. In later chapters they conceal optical assets, optical detectors, and fiber-optic conversation approach layout. in addition they deal with a wide selection of similar subject matters akin to doped fiber amplifiers, dispersion reimbursement, fiber sensors, and size strategies for the characterization of optical fibers. during the e-book, actual and engineering points of the topic are interwoven, and lots of labored examples and workouts are incorporated. will probably be an incredible textbook for undergraduate or graduate scholars taking classes in optical fiber communications, photonics, or optoelectronics.

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1 33 Algebraic order at low T As we have seen from BdG theory, the condensate survives in two dimensions at T = 0. We will now see that phase fluctuations destroy it at any T > 0. To this end we use the BdG theory for the density and phase fluctuations. e. taken in the low-energy phonon regime. We have assumed n ˆ (x) = n ¯ (x) + δˆ n(x). 59) where n ¯= n ˆ is the mean density, which includes the thermal excitations. Similarly to the 1D section we employ: 1 ˆ 0) − θ(0, ˆ 0))2 ˆ 0) = n ¯ exp − T (θ(x, φˆ† (x, 0)φ(0, 2 .

Du/dl = u − t2 − 16tu − 72u2 + . . 17) where l = ln b for b 1, and = 4 − d. Here we have done some of the work already: we used perturbation theory in u in order to treat the coupling between the high momentum modes that were integrated out and the low momentum ones. The Gaussian part of the theory was treated exactly. As can readily be seen, apart from the Gaussian fixed point there is another one for h = 0, u = /72 + O( 2 ), t = O( 2 ). This is the celebrated Wilson–Fisher fixed point, which gives yt = 2 − (24/27) + O( 2 ) and ν = 1/2 + /12 + O( 2 ).

This will be discussed in the sections below. • d = 2. In harmonic traps there is condensation in two dimensions. For weakly interacting gases the BEC transition is preceded at higher T , or even substituted by a BKT transition. Again, there is a crossover to a ‘true’ BEC when the phase correlation length becomes larger than the size of the cloud. • d = 3. Similarly to the situation in the box, the BEC takes place in harmonic traps in three dimensions and obviously persists in the case of a weakly interacting gas.

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