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324                           Lasers

                                               3.5


                                               3.0



                                               2.5

                                             Wavelength (μm)  2.0



                                               1.5



                                               1.0
                                                      355 nm pump
                                                                        266 nm pump
                                               0.5
     Fig. 12.24
     Theoretical (solid lines) and
     experimental (  and  ) tuning
                                               0.0
     curves using BBO as the nonlinear           20          30          40           50
     medium.                                              Phase matching angle (degrees)


                                   served to amplify a signal. This idea was resurrected in the mid 1980s, using
                                   another rare earth element, erbium, as the dopant. Today, erbium-doped fibre
                                   amplifiers (acronym EDFA) pumped by diode lasers are standard components
                                   in an optical fibre communication system. Without them the World Wide Web
                                   could have hardly come into existence.


                                   12.11  Masers
                                   The acronym stands for ‘microwave amplification by stimulated emission of
                                   radiation’. It is like ‘laser’ but the word ‘light’ has been replaced by ‘mi-
                                   crowave’. In fact, the microwave application was there first, well before lasers.
                                   Masers represented the first two-state systems in which quantum-mechanical
                                   principles were used to achieve amplification. They were invented independ-
                                   ently by Townes in the United States and Basov and Prokhorov in the Soviet
                                   Union. All three received a Nobel Prize in 1964. For a while masers were used
                                   as low-noise amplifiers (e.g. in the first satellite communications across the
                                   Atlantic), but nowadays they are only of historical interest. It is worthwhile,
                                   though, to mention here one of their realizations as an example of magnetic
                                   tuning.
                                     When discussing paramagnetism in Section 11.7.2, we came across the
                                   splitting of energy levels in an applied magnetic field. The possible energies
                                   are given by eqn (11.41):

                                                 E =–M J gμ mB B,  M J = J, J –1, ... ,–J.  (12.52)
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