Page 449 - Tunable Lasers Handbook
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8  Tunable External-Cavity Semiconductor  Lasers   409

                    to result in a1  fairly short cavity. If a longer cavity is needed in order to obtain a nar-
                    rower linewidth, the requisite path length can be filled with prisms to expand the
                    filled depth in proportion to the total length.  A 1300-nm external cavity containing
                    a GRIN rod collimator followed by two silicon prisms resulted in a 7-cm-long cav-
                    ity with  about three modes in the grating passband  [61]. Single-mode operation
                     was achieved over a 50-nm tuning range with a linewidth of 100 kHz or less.



                     10.  PHASE-CONTINUOUS TUNING

                        Phase-continuous tuning [ 1061 means tuning without mode hopping or other-
                     wise intempting the phase of the oscillation. A prerequisite for phase-continuous
                     tuning is  thlat  the mode number-the   number of  half-wavelengths between the
                    laser  mirrors-remains   constant as the  wavelength is varied.  Phase-continuous
                    tuning is required for locking the oscillation to a wavelength reference. It is also
                    useful  for  interferometric measurements, optical frequency  synthesis schemes,
                     and in general whenever fine control of the laser wavelength is needed.
                        Two  regimes  of  phase-continuous tuning can be  distinguished: short range
                     and long range. Short-range phase-continuous tuning over several euternal-cal,,ity
                    mode spacings (Le., up to a €ew tens of gigahertz) can be accomplished by chang-
                    ing  the  cavity  length  while  keeping  the  position  of  the  filter peak  fixed  [MI.
                    Eventually the lasing mode moves too far from the filter peak and a mode hop
                    occurs to a new mode with lower loss. Long-range phase-continuous tuning over
                    many  nanometers  requires  precisely  coordinated  simultaneous  shewing  of  the
                    axial-mode frequencies in synchronism with the filter peak. The requirements for
                    this type of tuning are considered next,


                     1 0.1  General Requirements for Long-Range PhaseContinuous Tuning
                        In  phase-continuous  tuning.  the  longitudinal  modes  must  be  shifted  at
                    exactly the same rate as the filter peak so that the same mode maintains its status
                    as the lowest loss mode and thus continues to oscillate. Assume that the u’th lon-
                    gitudinal mode of  the ECL starts out exactly at the peak of  the filter passband.
                    The frequency of the q’th mode is given by

                                                                                  ;70j


                    where q is an integer, c is the speed of light, and
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