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444    Fi b er   L a s er s                                                                                      Intr oduction to Optical Fiber Lasers    445


                    900                                         20
                                                                10
                    800
                                                                 0
                    700
                                   44-µm core diameter         −10
                   A eff  (µm 2 )  600                         −20  −20  0   20
                    500
                    400                                         20
                                   27-µm core diameter
                    300                                         10
                                                                 0
                    200
                       0   5   10  15   20  25  30  35  40     −10
                                   Bend radius (cm)
                                                               −20
                                        (a)
                                                                  −20    0   20
                                                                        (b)
                 Figure 15.25   (a) Effective mode area compression in bent fibers. (b) Top: Mode in
                 straight fiber with A = 862 µm ; Bottom: Mode in bent fiber with a bend radius of
                                        2
                               eff
                                   2
                 10 cm and A = 627 µm  (core diameter is 44 µm). (Courtesy of John Fini)
                          eff
                           10000
                          Effective mode area (µm 2 )  1000











                             100


                                  1996   1998  2000  2002   2004  2006   2008
                                                      Year

                      Figure 15.26  Development of fiber mode areas of a variety of diffraction-
                      limited single-core optical fibers as a function of time. Circles: single-mode
                      step-index fibers; squares: multimode step-index fibers; triangles: photonic
                      crystal fibers and rods; diamonds: higher-order mode fiber; stars: leakage
                      channel fibers.


                      greater than 50 W, it is typically advisable to use silica optics to mini-
                      mize thermal beam distortions. In addition, water-cooled fiber hold-
                      ers and isolators may also be required at high powers.
                         Beam quality is usually measured by the M parameter, which
                                                               2
                      characterizes  how  much  a  beam’s  diffraction  angle  is  increased
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