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8  Tunable External-Cavity Semiconductor lasers   37
                     Placing the laser diode in an external cavity with wavelength-selective feedback
                     narrows the spectral width by replacing the solitary diode spectrum with a small
                     number of closely spaced external-cavity modes (ideally a single mode).
                         The width of each individual mode is also narrowed by the external cavity.
                     The ratio of external-cavity to solitary diode linewidth is given by [39]
                                                     (1 + k)
                                                             -2
                                            6ve,, =


                     where T~~~ and T~~~ are, respectively. the round-trip times of the solitary and exter-
                     nal cavities. The external-cavity linewidth is proportional to P;:,  (Fig.  12) and
                     L;;t  (Fig.  113). The power and cavity length dependencies of the linewidth have
                     been experimentally confirmed, respectively. by workers at British Telecom [40]
                     and at AT&rT Bell Laboratories [41].


                     4.4 Multimoding
                         ECLs sometimes have a tendency to exhibit a state of multimode oscillation
                     in which rapid hopping between several neighboring external-cavity longitudinal
                     modes occurs. One estimate of the average mode-hopping frequency for a  1.3-
                     pm InGaAsP laser diode in a 7.5-cm external cavity is [42]







                     where T~ is the photon lifetime. Even though a complete theory is not available,
                     multimodhg behavior  has  been  found  to  depend  on  a  number  of  additional











                                          .-
                                          5  4
                                          c
                                          ._
                                                 1  2  3  4  5
                                          -1 il:. 2 0 0

                                            Reciprocal output power, mW-'
                     FIGURE  1 2  ECL 1ineu.idth versus reciprocal power dependence. (Reproduced with permission
                     from Wyatt et al. [30] and Chapman and Hall Pub1ishers.j
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