April 15, 1996 / Vol. 21, No. 8 / OPTICS LETTERS
Broadband fiber optical parametric amplifiers
M.E. Marhic,* N. Kagi,†T.-K. Chiang, and L.G. Kazovsky
Department of Electrical Engineering, Stanford University, Stanford, California 94305
Received November 9, 1995
The bandwidth of a single-pump fiber optical parametric amplifier is governed by the even orders of fiber
dispersion at the pump wavelength.The amplifier can exhibit gain over a wide wavelength range when
operated near the fiber’s zero-dispersion wavelength.It can also be used for broadband wavelength conversion,
with gain.We have experimentally obtained gain of 10–18 dB as the signal wavelength was tuned over a
35-nm bandwidth near 1560 nm.
1996 Optical Society of America
The recent development of doped-fiber optical am-
plifiers (DFA’s) has provided optical network de-
signers with a useful tool for overcoming fiber and
interconnection losses.However, because these am-
plifiers are based on stimulated emission by doping
ions, a typical DFA operates in a wavelength range
determined by the type of ion used.
the erbium DFA (EDFA) operates near l ? 1550 nm,
with a 35-nm bandwidth.
being developed for amplification near 1.3 mm have
The bandwidth available for
transmission through optical fibers is of the order of
300 nm, and thus DFA’s may not be adequate to han-
dle the broad spectrum that might be used in future
optical communication systems.
important to seek other means for making broadband
Fiber optical parametric amplifiers (OPA’s) rely not
on properties of doping ions but on the third-order non-
linearity of the fiber material.
ciple be operated at an arbitrary center wavelength,
corresponding to the zero-dispersion wavelength ?l0? of
the fiber used in the OPA. Their bandwidths depend
on pump power, fiber nonlinearity, and fiber disper-
sion; hence there are opportunities for increasing OPA
bandwidth that are not available with DFA’s or Raman
In addition, the presence of a frequency-shifted
idler indicates that such devices can also be used as
broadband wavelength converters, possibly exhibiting
conversion efficiency greater than 1.
In early experiments with fiber OPA’s the empha-
sis was on achieving frequency conversion with a
wide but fixed spacing.2–4
was studied in communication fibers, as it can arise
near l0 and introduce noise by amplifying the am-
plified stimulated emission generated by EDFA’s:
gain of 3.5 dB was measured in an experiment
designed to study this aspect.5
conversion by parametric amplification has been
investigated, yielding a maximum gain of 5 dB and
a 25-nm bandwidth.6
Cw wavelength conversion by
parametric amplification has been demonstrated,
with a conversion efficiency of 24.6 dB (Ref. 7); the
bandwidth was not reported.
gain of as much as 12 dB with a pump power of
180 mW over a 20-nm bandwidth near l0.8
Raman amplifiers that are
For this reason it is
Thus they can in prin-
Recently parametric gain
Recently we obtained
In this Letter we explore the potential of single-pump
fiber OPA’s to provide broadband optical amplification
and wavelength conversion.
width depends only on the even orders of fiber disper-
sion at the pump wavelength and can reach tens of
nanometers for operation near l0.
Consider a strong pump field Ep?z? and a small-
signal field Es?z?, with respective radian frequencies
vp and vs, copropagating in the z direction in a
lossless fiber with nonlinear coefficient g (we assume
that g . 0, as is the case for silica fibers).
signal theory reveals the existence of parametric gain,
which amplifies the signal, as well as an idler field
Ei?z? arising at vi? 2vp2 vs.9
be studied by means of the signal power gain, given by
jEs?0?j2? 1 1
The parametric gain g is given by9
g2? 2Db?Db?4 1 gP0?,
and P0 is the pump power.
vector mismatch determined by the waveguide char-
acteristics, i.e., Db ? bs 1 bi 2 2bp, where bs, bi,
and bpare the respective propagation constants of the
signal, the idler, and the pump.
(2) are valid when the pump is not depleted by the
nonlinear process, i.e., when the signal is small com-
pared with the pump.The idler conversion efficiency
is Gi?L? ? Gs?L? 2 1. When gL ¿ 1, Gs?L? and Gi?L?
are both large and are nearly equal.
As a first approximation the gain bandwidth corre-
sponds to g real, which implies that 24gP0# Db # 0.
The gain bandwidth measured in terms of Db is thus of
the order of 4gP0. This shows that the larger P0, g, or
both, the larger is the range of tolerable values of Db,
which in turn indicates that a larger frequency differ-
ence between the pump and the signal can be tolerated.
What the bandwidth is in terms of frequency is deter-
mined by the fiber dispersion characteristics.
By expanding b in power series near vp, we can put
Db in the form
where b2m denotes the ?2m?th derivative of b at
vp. This shows that Db is only a function of u ?
We show that the band-
Db is the linear wave-
Equations (1) and
Db ? 2
1996 Optical Society of America
OPTICS LETTERS / Vol. 21, No. 8 / April 15, 1996
?vs 2 vp?2; together with Eq. (1) this implies that
the gain spectrum ?g versus vs? is always symmetric
with respect to vp.Also, Eq. (3) shows that the odd
dispersion orders play no role in determining the
gain spectrum; only the even dispersion orders affect
the gain spectrum. This implies that the type of
fiber needed to optimize fiber OPA bandwidth is not
necessarily the same as the type of fiber needed to
reduce linear pulse spreading that is due to dispersion:
that is because odd orders of dispersion affect pulse
spreading but not fiber OPA bandwidth.
One could in principle obtain linear phase matching
?Db ? 0? for all vsif b?vs? had only odd derivatives at
vp, i.e., if its graph were symmetric about the point
?vp,b?vp??.This is probably impossible to realize
in practice, and thus other ways must be sought to
First we consider what happens if Db is dominated
in the gain region by the 2mth-order term in Eq. (3).
If b2m, 0, gain ?g2. 0? will be available for vswithin
Dv2mof vp, with
We define Dv2m as the bandwidth of the OPA for
A natural choice for achieving large bandwidth is to
place vpat or near v0, for which b2? 0.
distinguish three possibilities:
We can then
(i) vp precisely at v0.
in Eq. (3) is proportional to b4.
dominates Db, the bandwidth is Dv4 obtained from
(ii) vp close enough to v0 that both second- and
fourth-order dispersion must be considered.
does not vanish, but its sign and magnitude can
be chosen to add to or substract from the fourth-
order term, thereby possibly allowing for bandwidth
optimization. Keeping now only the m ? 1 and m ? 2
terms in Eq. (3), we see that Db has a quadratic
dependence on u. For b4 , 0, no improvement is
possible over Dv4, because if b2, 0 the magnitude of
Db is larger, and thus g ? 0 is reached for a smaller
u than in possibility (i); if b2. 0, Db . 0 for small
u, which we want to avoid.
situation is different: If b2, 0, Db vanishes not only
at u ? 0 but also at umax ? 212b2?b4, and Db is
minimum at umax?2.If we require that this minimum
be equal to 24gP0(to have g ? 0), we can solve for
b2and umax.The bandwidth, which we denote in this
case by Dv2,4, is given by
Then the leading term
Assuming that it
For b4. 0, however, the
In this particular case g2can be expressed in terms of
an eighth-order Chebyshev polynomial in ?vs2 vp?.
(iii) vp far enough from v0 that bandwidth is de-
termined primarily by second-order dispersion.
bandwidth is then given by Dv2obtained from Eq. (4).
We can obtain cases (i)–(iii) in the same fiber by
tuning vpnear v0.
As an example of case (i), consider a fiber op-
erated near the zero-dispersion wavelength, l0 ?
2pc?v0? 1.55 mm, with b4? 24.93 3 10255m21s4
(the value for bulk silica at this wavelength, ob-
tained from Sellmeier’s equation9).
gP0 ? 3 3 1022m21, which can be achieved with a
power of ?15 W in typical silica fibers.
Dv4, and translating it into wavelength units, we
obtain a bandwidth of the order of 52 nm.
with the opposite value for b4 [case (ii)] one could in
principle boost this to 73 nm by optimizing b2.
numbers are quite respectable and indicate that fiber
OPA’s indeed offer good prospects for making wideband
optical amplifiers.Figure 1 shows theoretical gain
spectra corresponding to different values of lp2 l0.
We have performed experiments to test the prac-
tical feasibility of obtaining such large bandwidths
(Fig. 2). Inasmuch as the parametric amplifier needs
high pump power, a pulsed power source was used in
our experiments.A DFB laser diode was driven with
a train of 20-ns square pulses with a duty cycle of
1?1024.The laser output was amplified by an EDFA
and used as a pump.A tunable external-cavity laser
diode (ECL; Fig. 2) was used as a signal light source.
Pump and signal were combined by a fiber coupler and
amplified together by a second EDFA. The pump and
signal wavelengths were monitored by an optical spec-
trum analyzer (OSA).The intensity of the signal
light was modulated at 400 MHz to permit measure-
ments.A variable optical attenuator (ATT) was used
to adjust the signal power.
nal were launched into the OPA medium, a dispersion-
shifted fiber (DSF) of length L ? 200 m.
l0? 1539.3 nm, attenuation constant a ? 0.23 dB?km,
We assume that
For a fiber
The pump and the sig-
The DSF had
lowing values: g ? 2 3 1023m21W21, P0? 7 W, L? 200 m,
b3 ? 1.2 3 10240s3m21, b4 ? 2.5 3 10255s4m21.
labels on the curves are the values of lp2 l0.
Theoretical gain spectra corresponding to the fol-
back laser diode.
Experimental setup.DFB LD, distributed-feed-
April 15, 1996 / Vol. 21, No. 8 / OPTICS LETTERS Download full-text
experimental results; curves correspond to theoretically
predicted spectra.The input signal power is 212 dBm in
Experimental gain spectra.Symbols represent
b4? 2.5 3 10255s4m21, and b3? 1.2 3 10240s3m21
[b3is used to calculate b2? b3?vp2 v0?].
pump power launched into the DSF was 7 W.
confirmed that stimulated Brillouin scattering in the
DSF was negligible by measuring the transmitted and
reflected pump powers. At the end of the DSF a
tunable optical bandpass filter (OBPF) was used to
select the signal frequency and reject the pump.
output from the filter was detected by an optic-to-
electronic converter ?O?E? and sent to an oscilloscope.
No optical isolator was needed because the paramet-
ric gain is unidirectional.
metric gain in the DSF by monitoring the 400-MHz
component of the output signal.
the signal was adjusted with a polarization controller
(PC) to yield the maximum gain.
our experimental results; the corresponding theoreti-
cal gain curves are also shown.
The measurements were performed over a wave-
length range of the order of 35 nm, limited by the gain
bandwidth of the EDFA’s used in the experimental
setup.Thus, even in this preliminary experiment, the
fiber OPA exhibits a bandwidth greater than that of
EDFA’s.The experimental results are in good agree-
ment with theoretical predictions.
We measured the para-
The polarization of
Figure 3 shows
In summary, we have shown that the bandwidths of
fiber optic parametric optical amplifiers depend only
on the even orders of fiber dispersion and that band-
widths of tens of nanometers can readily be obtained by
operation near the zero-dispersion wavelength, and we
have verified these predictions experimentally.
devices could find applications as broadband amplifiers
or alternatively as broadband wavelength converters
with high conversion efficiency.
This research was supported in part by the U.S.
Office of Naval Research through grant 4148130-01
and by the National Science Foundation through grant
ECS-94175 95. That of T.-K. Chiang was partially
supported by a graduate fellowship from Hitachi Ltd.
*Permanent address, Department of Electrical En-
gineering and Computer Science, Northwestern Uni-
versity, Evanston, Illinois 60208, the address for any
†Permanent address, General Planning Depart-
ment, Research & Development Division, Furukawa
Electric Ltd., 2-6-1 Marunouchi, Chiyoda-ku, Tokyo,
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