OPTICS LETTERS / Vol. 28, No. 15 / August 1, 2003
Tunable all-optical negative multitap microwave filters based
on uniform fiber Bragg gratings
J. Mora, M. V. Andrés, and J. L. Cruz
Instituto de Ciencia de los Materials, Universidad de Valencia, Dr. Moliner 50, 46100 Burjassort (Valencia), Spain
B. Ortega, J. Capmany, D. Pastor, and S. Sales
Instituto de Informatica, Multimedia, Communicacion y Computadors, Departamento de Comunicaciones,
Universidad Politécnica de Valencia, Camino de Vera, s/n 46022 Valencia, Spain
Received January 27, 2003
We present a novel and simple technique for obtaining transversal filters with negative coefficients by using
uniform fiber Bragg gratings.We demonstrate a wide tuning range, good performance, low cost, and easy
implementation of multitap filters in an all-optical passive configuration in which negative taps are obtained
by use of the transmission of a broadband source through uniform Bragg gratings.
060.0060, 060.4510, 230.1480.
© 2003 Optical Society
Fiber-optic transversal filters have attracted the
interest of many research groups during the past
several years because of their applications in the
processing and switching of wideband rf, microwave,
and millimetric signals directly in the optical domain.
Various kinds of coherent and incoherent optical
processing to obtain a large degree of flexibility
in the shaping of the filter transfer function have
been proposed. Coherent optical processing gives
precise control of the optical phase that can be used
to generate negative tap weights, which are neces-
sary for obtaining negative-tap transversal filters,
whereas incoherent optical processing is insensitive
to any phase variation.
to overcome this limitation have been reported.
The first one was an optoelectronic approach that
uses differential detection1; other proposals for all-
optical configurations with active elements to generate
modulation in the homogeneously broadened medium
of a semiconductor optical amplifier to obtain a nega-
tive tap2; distortion inside the semiconductor optical
amplifier and elevated costs are the main drawbacks
of this method. Other configurations have been used
to demonstrate incoherent negative-tap transversal
filters, such as those that use a carrier depletion effect
in a distributed-feedback laser diode,3cross-intensity
modulation of the longitudinal modes of an injection-
locked Fabry–Perot laser diode,4
wavelength converter based on cross-gain modulation
of the amplified spontaneous emission spectrum of a
semiconductor optical amplifier.5
In previous optical configurations the experimental
scheme became complicated and required active com-
ponents, showing a limited tuning range and permit-
ting implementation of only a two-tap negative filter.
Here we propose a new passive and incoherent method
for obtaining transversal filters with various negative
coefficients.We generate negative taps by using the
output signal of a broadband optical source when it
Therefore several means
One can use cross-gain
and a low-cost
has been transmitted by uniform fiber Bragg gratings
(UFBGs). The positive taps are independently pro-
vided by a laser array, and therefore a high tuning
range can be demonstrated in these novel filters.
In our proposal the ideal arrangement of a two-tap
filter with one negative coefficient is based on the use
of a narrow source with emission frequency at v1and
a signal transmitted by a notched optical filter that
suppresses frequency v2, illuminated by a uniform
broadband optical source.
combined in a directional coupler (see the inset of
Fig. 2 below).Ideally, spectral distribution S?v? can
be represented by
The two optical signals are
S?v? ? P0d?v 2 v1? 1 P0?Q?v? 2 d?v 2 v2??,
where P0 is a constant, d?v? is the Dirac function,
and Q?v? is the spectral distribution of the broadband
source, which is Q?v? ? 1 in the ideal case.
The resultant signal of Eq. (1) is modulated in an
external electro-optic modulator at radio frequency
f ?V ? 2pf? and driven to a linear dispersive ele-
ment. The rf signal is generated and measured by a
light-wave component analyzer (LCA).
the filter transfer function by substituting Eq. (1) into
Eq. (4) of Ref. 6 to obtain
jH?V?j ? ?
where ? is the photodiode’s responsivity.
delay value that corresponds to the signal is Dt ?
DDv, where D is the delay slope of the dispersive ele-
ment and Dv is the separation frequency between taps.
We can identify the first term in Eq. (2) as the
negative two-tap filter.In Fig. 1 we show the theo-
retical transfer function versus rf normalized to
f0 ? 1??DDv?, where f0 is the free spectral range
(FSR).A phase shift of p?2 is observed between the
two-tap filter with positive coefficients and function
0146-9592/03/151308-03$15.00/0© 2003 Optical Society of America
August 1, 2003 / Vol. 28, No. 15 / OPTICS LETTERS
with no negative taps (dotted–dashed curves).
Theoretical transfer function for a two-tap fil-
filter with one negative tap (solid curves) and filter
jH?V?j, which corresponds to a filter with one negative
coefficient.The second term in Eq. (2) introduces a
dc signal. That signal comes from the total optical
power of the spectral distribution that is driven to the
LCA and is proportional to the total optical power PT
of the broadband source.
finite bandwidth, dv, for example, with a Gaussian
shape, then the additional term PTd?V? broadens
up to a frequency fc, given by fc ? 1??Ddv?, which
we can reduce by using higher dispersion values D
and broader-band sources.
introduces a spurious signal at low frequencies, which
can be filtered by use of an electric filter in the system
To demonstrate our proposal we implemented three
filters. The first is a filter formed by a tunable laser
(TL) and a signal transmitted by a UFBG, which is
illuminated with the amplified spontaneous emission
of an erbium-doped fiber amplifier.
optical source has a 3-dB bandwidth of 5 nm near
1530 nm when the injected current is 150 mA.
UFBG is 1 cm long and is written on photosensi-
tive fiber; its Bragg wavelength is 1530.96 nm, its
3-dB bandwidth is 0.15 nm, and it has maximum
reflectivity of 8 dB. The use of UFBGs as selective
filtering elements in fiber-optic transversal filters
was demonstrated and analyzed previously.6
light transmitted through the UFBG and the emission
of the TL are driven to a 90?10 optical coupler.
combined signal can be monitored by an optical spec-
trum analyzer by use of the 10% arm.
signal is amplitude modulated in the electro-optic
modulator.A fiber length of 23 km will be the disper-
sive element in the filter, so D ? bLF, where b is the
linear dispersion ?15.5 ps??nm 3 km? at 1530 nm? and
LF is the fiber length.Finally, the transfer function
of the filter is measured in the LCA (see Fig. 2).
To show the tunability of the system, we plot the
experimental transfer functions of two rf filters with
different free spectral ranges (FSRs) (Fig. 3).
see that the negative filter response appears above
fc? 0.58 GHz, i.e., when the spurious low-frequency
term is negligible. The separation wavelengths be-
tween the TL and the UFBG are 2.56 and 0.54 nm,
corresponding to FSRs of 1.09 and 5.15 GHz, respec-
tively.We must point out that the spectrum shown in
the inset of Fig. 2 was measured with a resolution of
0.1 nm and is indicative only of tap positions; in the
experiment, the power level of the laser was adjusted
to the total power reflected by the grating and to com-
pensate for possible wavelength and polarization de-
If the optical source has a
Therefore the system
The 90% arm’s
pendent loss in the system, so the peak powers of grat-
ings and laser are not identical.
Figure 4 gives the FSR of the negative transversal
filter versus several wavelength spacings between
the central Bragg wavelength of the UFBG and the
TL output signal.The filled squares correspond
to the measured FSR of the filter, and the solid
line is the theoretical prediction.
previous findings,6this frequency range can be in-
2.80 6 0.04 GHz 3 nm, according to the delay slope,
357 ps?nm at 1530 nm, of the dispersive element.
In a second experiment and to show the good perfor-
mance of these filters when several taps are added, we
According to our
cal spectrum analyzer; other abbreviations defined in text.
Inset (a), output power of the broadband optical source, an
erbium-doped fiber amplifier (EDFA).
nal launched into the electro-optic modulator relative to the
EDFA power level.
Schematic of the rf negative-tap filter:OSA, opti-
Inset (b), input sig-
calculation (dotted curves) and experimental results (solid
Filter response versus rf signal frequency for two
(a) 1.09 GHz, (b) 5.15 GHz.Theoretical
wavelength spacing between taps.
(solid line) and experimental results (filled squares).
FSRs of the rf filters versus the reciprocal of the
OPTICS LETTERS / Vol. 28, No. 15 / August 1, 2003
equispaced taps near 1530 nm.
(dotted curves) and experimental results (solid curves).
Inset, spectral positions of the five taps.
Filter response versus signal’s rf with 1.16-nm
equispaced taps near 1550 nm.
(dotted curves) and experimental results (solid curves).
Inset, spectral positions of the four taps.
Filter response versus signal’s rf with 1.56-nm
implemented a five-tap rf filter, using two UFBGs and
three lasers with a wavelength separation of 1.16 nm
(Fig. 5).The FSR is 2.40 GHz, and the 3-dB band-
width is 0.437 GHz.
The third experiment that we report has the ob-
jective of showing how the bandwidth of the spurious
term, fc, can be reduced. For this purpose the experi-
mental arrangement includes an optical source with
larger bandwidth, 28 nm, and a dispersive element
that shows higher dispersion, a fiber of 46-km length.
We implemented a four-tap negative filter by using
two lasers and two 1-cm-long UFBGs, with maximum
reflectivity of 16 dB.The second term of Eq. (2)
does not appear in Fig. 6 because fc is less than
0.130 GHz (minimum frequency of the LCA).
FSR is 0.815 GHz, and the 3-dB bandwidth of the
filter is 0.176 GHz, with a wavelength separation
between taps of 1.56 nm, according to a fiber with
a linear dispersion of 17 ps??nm 3 km? at 1550 nm.
Therefore, for larger frequencies than fc, the filter
exhibits perfect agreement between the experimental
results (solid curves) and the theoretical response of
an ideal four-tap filter with two negative coefficients.
In summary, we have demonstrated a novel ap-
proach to setting up transversal filters with positive
and negative taps. Our approach facilitates the flex-
ible design of transfer functions by using a laser array
and a broadband optical source filtered by UFBGs.
Unlike previous configurations, our simple method is
based on all-optical and passive elements and exhibits
higher tunability and lower cost than previously
reported systems.The spurious term that our filters
generate is limited to a low-frequency bandwidth and
can be electrically filtered in the system’s receiver.
The authors acknowledge financial support from
TIC2001-2895-C02-01 and European projects NEFER-
TITI IST-2001-32786 and LABELS IST-2001-37435.
J. L. Cruz’s e-mail address is firstname.lastname@example.org.
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