316 CHINESE OPTICS LETTERS / Vol. 8, No. 3 / March 10, 2010
Equal-amplitude optical comb generation using
multi-frequency phase modulation in optical fibers
Yuelan Lu (½½½===)
1∗
, Yongwei Xing (111[[[)
1
, and Yongkang Dong (ÂÂÂ[[[xxx)
2
1
College of Science, Harbin Engineering University, Harbin 150001, China
2
Institute of Opto-Electronics, Harbin Institute of Technology, Harbin 150001, China
∗
E-mail: luyuelan1968@163.com
Received May 12, 2009
We theoretically analyze and experimentally demonstrate a method of generating equal-amplitude opti-
cal comb exploiting multi-frequency phase modulation. The theoretical analysis shows that 4n–1 equal-
amplitude spectral lines can be obtained when the modulation signal comprises n frequency components
including the fundamental frequency and the odd harmonic frequencies, and 2n+1 equal-amplitude spec-
tral lines can be obtained when the modulation signal comprises n frequency components including the
fundamental frequency and the even harmonic frequencies. Then, we numerically simulate the spectra of
5, 7, 9, and 11 equal-amplitude spectral lines, respectively, which are also obtained in experiments with
frequency separation of 30 MHz and flatness of better than 0.3 dB.
OCIS co des: 190.0190, 260.0260.
doi: 10.3788/COL20100803.0316.
In recent years, optical comb generation has gathered
great interests in a number of areas in photonics tech-
nology. For example, in microwave photonics technology,
optical comb has been used for optical frequency stan-
dards in absolute frequency measurement systems, local-
oscillator remoting in radio-on-fiber systems, and control
of phased array antennas in radio astronomy systems
[1]
;
in optical communications, superdense wavelength divi-
sion multiplexing (SD-WDM) uses tightly spaced optical
channels (<50 GHz spacing) generated from optical comb
to transmit data in both access and long-haul networks
[2]
.
Recently, a novel optical transmission format known as
coherent wavelength division multiplexing (CoWDM) has
been proposed, which relies on a stable phase relationship
between adjacent spectral lines
[3]
. Of all the applications
mentioned above, a flattened spectrum profile of optical
comb is an important essential.
Conventionally, mode-locked laser
[4]
and supercontin-
uum
[2]
based on optical pulse compression through a non-
linear fiber are popular candidates for such optical comb
generation. However, the mode-locked laser has difficul-
ties in starting and maintaining mode locking, and su-
percontinuum needs a complicated design and an adjust-
ment to obtain flattened profile of the output spectrum.
With the development of waveguide electro-optic mod-
ulators (EDMs), optical comb generated with a waveg-
uide EDM has gathered great attentions, which provides
phase-locked optical comb with compact devices. In Ref.
[5] tandem Mach-Zehnder (MZ) amplitude modulator
and phase modulator are used to generate 9 spectral lines
with flatness of 2 dB, where the mo dulated voltages of
amplitude modulator and phase modulator are set to π V
and 2.4π V, respectively. In Ref. [3], two MZ amplitude
modulators are used to generate 11 spectral lines with
flatness of 1.97 dB, where the modulated voltage is set
to 3.5π V. A phase modulator is also used in optoelec-
tronic oscillator to generate optical comb with a larger
modulated voltage
[6]
. These technologies, however, can-
not obtain equal-amplitude optical comb. Previously it
was considered that equal-amplitude optical comb could
not be achieved by only phase modulation
[5,7]
, since just
single frequency modulation signal was considered. More
recently, Ozharar et al. has demonstrated dual-sine-wave
phase modulation, and obtained 9 and 11 comb lines with
flatness of 0.8 and 1.9 dB, respectively
[8]
.
In this letter, we propose a method to generate equal-
amplitude optical comb by multi-frequency phase modu-
lation, which features several advantages. Firstly, just
a single phase modulator is needed, so that the sys-
tem is simple and cheap. Secondly, the driving volt-
ages are relatively low (i.e., about one half-wave volt-
age), so the needed radio-frequency (RF) power level
is small. Thirdly, compared with amplitude modulator,
phase modulator needs no precise adjustment on direct
current (DC) bias. In experiment, we obtained 5, 7, 9,
and 11 spectral lines with very goo d flatness of 0.13, 0.17,
0.24, 0.29, and 0.29 dB, respectively (the case of 7 spec-
tral lines corresponds to two values of 0.17 and 0.24 dB).
In the case of single-frequency phase modulation, 3
equal-amplitude spectral lines can be obtained at most
[9]
.
In order to obtain more equal-amplitude spectral lines,
multi-frequency phase modulation should be applied to
the incident lightwave. As for an arbitrary modulation
signal m (t) with a period of f
m
, its Fourier expansion is
given by
m (t) =
X
+∞
k=0
γ
k
sin (2πkf
m
t + φ
k
) . (1)
With this multi-frequency modulation signal, the modu-
lated field E
m
is given by
E
m
(t) = cos
h
2πf
c
t +
X
+∞
k=1
γ
k
sin (2πkf
m
t + φ
k
)
i
,
(2)
where f
c
is the carrier wave, f
m
is the fundamental fre-
quency of modulation signal, γ
k
= π · V
k
/V
π
represents
the modulated indices, V
k
and V
π
are the amplitudes
of the modulated voltage and the half-wave voltage of
phase modulator, respectively, φ
k
is the initial phase
1671-7694/2010/030316-04
c
° 2010 Chinese Optics Letters