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454    Fi b er   L a s er s                                                                                      Intr oduction to Optical Fiber Lasers    455


                               Dichroic mirror                              HR
                   MM pump                Doped double-clad fiber  AOM
                    diodes                                         Q
                                                                  switch

                                  Output

                 Figure 15.34  A typical scheme for a Q-switched fiber laser. AOM: acousto-optic
                 modulator.

                      thresholds. Large core optical fibers also help minimize optical dam-
                      age at the end faces. Although high interpulse gain is clearly desirable
                      for high pulse energy, it is limited by potential interpulse lasing from
                      spurious reflections, such as from Rayleigh scattering. 66,67  In general,
                      the  maximum  extractable  energy  is  limited  to  ten  times  saturation
                      energy F A, which is A*10 µJ/µm  for ytterbium-doped fibers. The
                                                   2
                             sat
                      pulse energy does not critically depend on fiber length. Longer pulses
                      are typically generated in longer fibers in Q-switched lasers, while
                      pulse breakup can happen if the pulse duration becomes much longer
                      than the round-trip cavity time. Typically, the pulse buildup time is
                      much shorter than the decay time in a high-gain system, leading to a
                      steeper leading edge and a slower trailing edge. A typical Q-switched
                      fiber laser is illustrated in Fig. 15.34.

                      15.3.3  Mode-Locked Fiber Lasers
                      The large bandwidth of optical fiber amplifiers, as well as their ease of
                      construction, has created a considerable interest in the generation of
                      ultrashort pulses, which remains an ongoing research area. Ytterbium,
                      erbium and thulium optical fiber lasers support bandwidths of the
                      order of 50, 45, and 200 nm, respectively, allowing for the generation
                      of pulses of the order of 30 fs. Even shorter pulses can be obtained by
                      pulse-compression techniques. The ultimate limit for the generation
                      of the highest peak power inside an optical fiber is governed by self-
                      focusing (as explained in Sec. 15.2.3) and is in the range of 4–6 MW.
                         To use optical fibers in ultrashort pulse generation, many differ-
                      ent techniques have been tested over the years. An early review can
                      be found in Fermann.  Here we limit our discussion to short-pulse
                                         68
                      generation via mode locking, which optimally utilizes the intrinsic
                      cavity mode structure in an optical fiber oscillator. It is customary to
                      distinguish active and passive mode-locking techniques.

                      Active Mode Locking
                      A fiber oscillator supports a range of cavity modes with frequencies f
                                                                               k
                      given by
                                                   c
                                              f =  k  nL                  (15.43)
                                              k
                                                   p
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