Femtosecond harmonically mode-locked fiber laser with time jitter by fdjerue7eeu


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									January 15, 1995 / Vol. 20, No. 2 / OPTICS LETTERS
Femtosecond harmonically mode-locked fiber laser
with time jitter below 1 ps
S. Gray, A. B. Grudinin, W. H. Loh, and D. N. Payne
Optoelectronics Research Centre, Southampton University, Southampton SOl7 1BJ, UK
Received May 24, 1994
We have made an experimental study of the time jitter in a harmonic passively mode-locked fiber soliton ring
laser. We demonstrate that jitter as low as 600 fs (100-550 Hz), which is less than the soliton pulse width, can
be achieved at a repetition frequency of 463 MHz. The results support the suggestion that the stability of the
laser is dependent on the long-range soliton interaction through the excitation of acoustic waves that is induced
by the propagating pulses.
The time jitter was measured by analysis of the rf
spectrum of the laser output intensity.7 Generally
this spectrum consists of a main peak sitting on
a broadband pedestal. Knowing the intensity and
bandwidth of the pedestal, one can deduce the
time jitter of the laser.7 Figure 2 shows the jitter
measured as a function of the pulse repetition
rate for a laser cavity fundamental frequency of
Passively mode-locked fiber soliton lasers are attrac¬
tive optical short-pulse sources for laboratory and
telecommunications applications by virtue of various
appealing properties such as their simplicity of con¬
struction, tunability, and subpicosecond operation.
The energy quantization effect1 caused by the soliton
regime of operation of fiber soliton lasers results in
excellent stability of the duration and energy of the
individual pulses, but it also leads to pulse-repetition-
rate instabilities that for many applications are un¬
acceptable. One solution is to operate the laser
with just a single pulse circulating inside the cav¬
ity, but this generally leads to low repetition rates
(—5 MHz) and correspondingly low average output
powers, unless short cavities of a few meters are used.
Other techniques involving additional subcavities,2
extracavity feedback,3 or intracavity modulation4
have been demonstrated, permitting higher-harmonic
mode locking, but these techniques would appear to
be difficult to implement in a practical system.
Recently we experimentally demonstrated that, un¬
der certain conditions, stable passive harmonic mode
locking occurs in a ring laser configuration,5 and
it was postulated that the so-called long-range soli¬
ton interaction effect6 is responsible for such passive
repetition-rate self-stabilization.
In this Letter we present an investigation of this
effect and demonstrate that time jitter as low as
600 fs (over the 100-500-Hz range) can be obtained
at a repetition rate as high as 463 MHz in a fully
passive mode-locked ring configuration.
The laser configuration used in our experiments
is shown in Fig. 1 and is similar to that de¬
scribed elsewhere.5 It consists of 4 m of Er/Yb
codoped fiber, a length of standard telecom fiber,
a polarization-sensitive isolator, and two sets of po¬
larization controllers. The laser was pumped by a
conventional Nd:YAG laser at 1064 nm. To reduce
pump power amplitude noise, we used an external
feedback loop that permitted us to keep pump power
fluctuations to below 1%. Mode locking of the laser
was achieved by adjustment of the polarization con¬
trollers, and at certain positions of the polarization
controllers a harmonic passively mode-locked regime
was observed. By changing the pump power we were
able to change the repetition rate of the laser.5
5.78 MHz and pulse width of 0.8 ps (FWHM). The
figure shows a strong oscillatory behavior and
a general tendency for the jitter to decrease at
frequencies near 500 MHz. The lowest jitter of
1.1 ps (100-550 Hz) was observed at the frequency
of 526 MHz. A similar oscillatory dependence (with
maxima at the same frequencies) was observed when
the pump power feedback loop was switched off,
but the lowest time jitter was then —10 ps. Note
also that we obtained the same general behavior
for several different cavity lengths as well.
By changing the length of the laser cavity we were
able to study the jitter for different pulse widths and '
observed that the shorter the pulses, the lower the
time jitter. The lowest jitter of 600 fs (100-550 Hz)
was obtained for 0.7-ps pulses at a repetition rate of
463 MHz in a laser cavity with a fundamental fre¬
quency of 11.0 MHz (zc = 18 m). The third-order rf
spectrum at 1388 MHz is shown in Fig. 3. The ra¬
tio of jitter to pulse separation is 3 X 10~4. Further
reduction of the cavity length did not result in an im¬
provement of the time jitter, but at a rather short
cavity length (zc = 8.6 m) we found that the laser
tends to operate at the same harmonic frequency
of 139 MHz in a very broad range of pump power;
i.e., the change of pump power level simply caused
_ Pump
Fig. 1. Experimental configuration. WDM, wavelength-
division multiplexer; PC's, polarization controllers.
0146-9592/95/020189-03$6.00/0 © 1995 Optical Society of America
OPTICS LETTERS / Vol. 20, No. 2 / January 15, 1995
ation. As was shown recently,6 each soliton excites
a weak transverse acoustic wave, which causes a
change of the refractive index. In accordance with
the theory, each 0.7 soliton in the standard tele¬
com fiber directly perturbs the refractive index by
Sraac — 10-11. In addition, however, the cylindri¬
cal structure of the fiber can act as a resonator for
acoustic waves excited at the appropriate eigenfre-
quencies. The relevant eigenfrequencies show up as
a series of peaks in the acoustic response spectrum
that are separated by ~50 MHz, with a maximum
near 500 MHz.6 The refractive-index perturbation
is thus considerably enhanced when the waves are
periodically excited at these frequencies. The en¬
hancement factor can be estimated from a simple
model of a resonantly driven damped harmonic os¬
cillator and is of the order of tJT, where rd is the
damping constant of the oscillator and T is the reso¬
nant (driving) period. Since rd and T are of the order
of microseconds13 and nanoseconds, respectively, the
index change is thus increased by a factor of 103 at
resonant frequencies near 500 MHz. (Our recent
measurements of the acoustic phase indicate that
the refractive-index change at these resonant acous¬
tic frequencies is in the range of 10-8-10"7.) Thus
the soliton stream imposes a significant phase mod¬
ulation on itself, and in the steady-state regime
each soliton is trapped by the acoustic field of its
The oscillatory nature of the measured time jit¬
ter in Fig. 2 fits well with the above picture. Note
that the frequency separation between minima in the
time-jitter dependence is also close to 50 MHz and
that the jitter is lowest near 500 MHz, indicating
that the mode-locked laser is most strongly stabilized
when the mode-locking frequency coincides with one
of the acoustic resonant frequencies, and thus the in¬
duced phase modulation is enhanced. Variations in
the 50-MHz separation may be accounted for by the
excitation of different types of acoustic wave, and the
decrease of jitter with pulse width, as observed previ¬
ously, is the result of stronger refractive-index pertur¬
bation, which is proportional to the soliton energy.6
Knowing the change of the refractive index induced
by the acoustic waves, we can estimate the time jit¬
ter by using perturbation theory for the distributed
model, based on solution of the nonlinear Schrodinger
15 -
Jjio .
5 - *
100 200 300 400 500 600 700
Frequency (MHz)
Fig. 2. Time jitter as a function of repetition frequency
for a total cavity length of 35 m.
a change in the fraction of the nonsoliton compo¬
nent without breaking up the harmonic mode lock¬
ing. Note, however, that for such a short cavity the
. length of the codoped fiber, which has a low disper¬
sion, is now comparable with the length of standard
telecom fiber. This results in a reduction of the net
intracavity dispersion and consequently in a decrease
of the pulse energy, which, as will be mentioned be¬
low, is a key parameter for the self-stabilization.
There are several sources of time jitter in mode-
locked lasers: pump power fluctuations, various
thermal effects, and noise of the laser gain medium.8
However, a harmonically mode-locked fiber laser has
an additional source of time jitter owing to uncon¬
trolled changes of adjacent pulse temporal positions,
and hence the jitter is significantly stronger than that
which occurs in lasers operating at the fundamental
frequency. In this sense a fiber soliton laser operat¬
ing in the harmonically mode-locked regime is similar
to a soliton transmission system; i.e., a soliton stream
in a fiber laser experiences periodic gain and loss and
suffers from the same sources of time jitter, including
the Gordon-Haus effect9 and soliton-soliton inter¬
action. Extensive studies of soliton transmission
systems that have been performed in the past sev¬
eral years (see, for example, Ref. 10 and references
therein) revealed that in order to maintain the soli¬
ton stream intact over unlimited distances one has
to incorporate into the transmission line spectral fil¬
tering and synchronous modulation. The existence
of just one component (either filter or modulator)
results in only a partial reduction of instability,10
whereas phase modulators have been shown to be
able to suppress Gordon-Haus jitter with minimal
generation of dispersive wave components.11 There¬
fore a stable steady-state regime of operation for a
harmonically mode-locked fiber soliton laser needs
spectral filtering and synchronous modulation.
In the present laser configuration (see Fig. 1) it is
easy to find a spectral filter; the laser gain curve
acts as a natural spectral filter with a bandwidth of
—35 nm.12
The synchronous modulation action is provided by
the solitons themselves through acoustic wave gener-
£ "40
| -60
t -80
-100 -
Frequency (GHz)
Fig. 3. Third-order rf spectrum for a repetition fre¬
quency of 463 MHz and a cavity length of 18 m, indicating
600-fs (100-550-Hz) jitter.
January 15, 1995 / Vol. 20, No. 2 / OPTICS LETTERS
For our case 0ac = 0.33 rad, = 2.3, T = 3 x 103,
Clf = 10, G2 = 5, and N0 = 3 X 108, which gives us
or = 0.4, or 160 fs in physical units, in reasonably
good agreement with the experimental results.
In conclusion, we have experimentally studied a
harmonically mode-locked fiber soliton laser and
demonstrated that time jitter as low as 600 fs, which
is less than the pulse width, can be obtained at a repe¬
tition rate of 463 MHz. Time-jitter dependence with
the laser repetition rate has revealed oscillatory be¬
havior with a characteristic period of ~50 MHz and a
tendency for the time jitter to decrease with the pulse
width. The experimental results are consistent with
the suggestion of a passive self-stabilization effect
driven by transverse acoustic wave excitation owing
to electrostriction. Theoretical estimates are in good
agreement with experimental results.
The authors gratefully acknowledge the useful re¬
marks of the anonymous referees regarding the fre¬
quency response of the self-induced acoustic phase
equation (NSE). In the case of a passively mode-
locked fiber laser the NSE can be written in the form
+ (</>ac - yr2)i/> + ia\<I)\24> + S(z)
where the left-hand side is the unperturbed NSE;
the first term in the right-hand side describes the
laser gain, the second term stands for the intracav-
ity laser filter, and the third term describes the ac¬
tion of the acoustic phase modulation, where <f>M =
2tt/ ASnaczd, y = 4>ac$c2/T2, <fc = zjzd, zd is the dis¬
persion length, and T is the time interval between
pulses normalized to the soliton pulse width. The
fourth term represents mode locking by means of a
fast saturable absorber, and S(z) is the noise source
from the laser amplifier. In the model, we have
made an assumption that the time jitter is much less
than the pulse period, and therefore we consider T as
a constant parameter. Note also that, in our case,
the dimensionless cavity length £c = 2.3, and there¬
fore a distributed model simply gives us an estimate
of the time jitter.
Applying perturbation theory for the NSE14 and
taking the solution of the unperturbed NSE as
1. A. B. Grudinin, D. J. Richardson, and D. N. Payne,
Electron. Lett. 28, 67 (1992).
2.	E. Youshida, Y. Kimura, and M. Nakazawa, Appl.
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28, 1894 (1992).
i/f(z,r) = rj sech rj(r — rJexpftQr — </>], (2)
we can obtain the equation for the soliton temporal
position rc in the steady-state regime (17 — 1):
4.	I. Y. Khrushchev, D. J. Richardson, and E. M. Dianov,
in Proceedings of the Nineteenth European Conference
on Optical Communications (Convention of National
Societies of Electrical Engineers of Western Europe,
Montreux, Switzerland, 1993), p. 33.
5.	A. B. Grudinin, D. J. Richardson, and D. N. Payne,
d2rc(z) 4/3 drc(z)
dz2 3 dz
+ 2yrc(z) = Sn(z). (3)
Here we assume that the noise impact on the soliton
temporal position is driven by the soliton frequency
fluctuations. The noise correlation function is9
Electron. Lett. 29, 1860 (1993).
6. A. N. Pilipetskii, A. V. Luchnikov, and A. M.
Prokhorov, Sov. Lightwave Commun. 3, 29 (1993).
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8. H. A. Haus and A. Mecozzi, IEEE J. Quantum Elec-
(G2 - 1)
(Sn(z)Sn(z')> = S(z ~ z')
= S(z - z')No
tron. 29, 983 (1993).
9. J. P. Gordon and H. A. Haus, Opt. Lett. 11, (1986).
10.	A. Mecozzi, J. D. Moores, H. A. Haus, and Y. Lai, J.
Opt. Soc. Am. B 9, 1350 (1992).
11.	N. J. Smith, K. J. Blow, W. J. Firth, and K. Smith, in
where N0 — WJhu is the number of photons per unit
energy and Ws is the soliton energy.
Taking the Fourier transform of Eq. (3) and solving
the equation in the spatial frequency domain k, we
arrive at the expression for the rms time jitter (z —»
Nonlinear Guided-Wave Phenomena, Vol. 15 of 1993
OSA Technical Digest Series (Optical Society of Amer¬
ica, Washington, D.C., 1993), p. 363.
12. J. E. Townsend, W. L. Barnes, K. P. Jedrzeijewski,
and S. G. Grubb, Electron. Lett. 27, 1958 (1991).
13. R. M. Shelby, M. D. Levenson, and P. W. Bayer, Phys.
Rev. B 31, 5244 (1985).
3Nn _ (G2 - i)r2iy
r +90
= <|rc(,fe)|2>d& =
J —x
14. A. Bondeson, M. Lisak, and D. Anderson, Phys. Scr.
20, 479 (1979).
32/V0</>ac£c2 '
where /3 = 2/(Cl2^c) and is the dimensionless
filter bandwidth.

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