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April 15, 1996 / Vol. 21, No. 8 / OPTICS LETTERS

573

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

similar bandwidths.1

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

optical amplifiers.

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

amplifiers.

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

For example,

Raman amplifiers that are

For this reason it is

Thus they can in prin-

Recently parametric gain

a

Pulsed wavelength

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

Gs?L? ?jEs?L?j2

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

` X

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-

Small-

Amplification can

"

gP0

g

sinh?gL?

#2

.

(1)

(2)

Db is the linear wave-

Equations (1) and

Db ? 2

m?1

b2m

?2m?!?vs2 vp?2m,

(3)

0146-9592/96/080573-03$10.00/0

1996 Optical Society of America

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574

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

maximize bandwidth.

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

this case.

A natural choice for achieving large bandwidth is to

place vpat or near v0, for which b2? 0.

distinguish three possibilities:

Dv2m?

22?2m?!gP0

b2m

#1/2m

.

(4)

We can then

(i) vp precisely at v0.

in Eq. (3) is proportional to b4.

dominates Db, the bandwidth is Dv4 obtained from

Eq. (4).

(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

p

2

Then the leading term

Assuming that it

Then b2

For b4. 0, however, the

Dv2,4? 2

√

3gP0

b4

!1/4

.

(5)

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).

The

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

Calculating

For a fiber

These

The pump and the sig-

The DSF had

Fig. 1.

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-

The

Fig. 2.

back laser diode.

Experimental setup.DFB LD, distributed-feed-

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April 15, 1996 / Vol. 21, No. 8 / OPTICS LETTERS

575

Fig. 3.

experimental results; curves correspond to theoretically

predicted spectra.The input signal power is 212 dBm in

both cases.

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.

The peak

We

The

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.

Such

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

correspondence.

†Permanent address, General Planning Depart-

ment, Research & Development Division, Furukawa

Electric Ltd., 2-6-1 Marunouchi, Chiyoda-ku, Tokyo,

100, Japan.

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