GENERATION OF DARK SOLITONS
In our earlier work[#!ZBD!#,#!ZBE!#] we discussed the possibility of using an
integrated Mach–Zehnder interferometer (MZI) to generate dark solitons
with constant background. The idea is to drive a broad bandwidth MZI with
a square-shape electric voltage with picosecond rise time. The applied
electric voltage signal introduces a relative phase shift, proportional to
the voltage, between the two arms of the interferometer by means of the
electro-optic effect of the waveguide material. At the output, the two
components of light are recombined, and the resultant optical field is
proportional to the cosine of half of the total phase difference, the
induced relative phase shift plus any other static (residual) phase
differences. Therefore the pulse after the MZI, when properly biased, can
have the form
| u(0, t) = a sin[δπ/2 tanh(t)], |
|
|
(1) |
where a is the field amplitude of the input cw laser beam and δ
the ratio of the applied voltage, approximated by a hyperbolic tangent
function of time, to the half-wave voltage of the MZI.
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The bandwidth requirement of the MZI is determined by the desired pulse
duration, which is approximately half of the reciprocal of pulse duration.
For a 50 ps dark soliton, 10 GHz is required, and this is achievable by
current technology.