COL 10(9), 092301(2012) CHINESE OPTICS LETTERS September 10, 2012
Design of all-optical temporal differentiator using a Moir´e
fiber grating
Qiong Liu (
444
), Qing Ye (
)
∗
, Zhengqing Pan (
),
Haiwen Cai (
ééé
°°°
©©©
), Ronghui Qu (
YYY
JJJ
)
∗∗
, and Zujie Fang (
yyy
$$$
)
Shanghai Key Laboratory of All Solid-State Laser and Applied Techniques
§
Shanghai Institute of Optics and Fine Mechanics,
Chinese Academy of Sciences, Shanghai 201800, China
∗
Corresponding author: yeqing@siom.ac.cn;
∗∗
corresponding author: rhqu@siom.ac.cn
Received March 19, 2012; accepted April 13, 2012; posted online July 5, 2012
We design and demonstrate an all-optical temporal differentiator based on a simple Moir´e fiber grating
operated in reflection. The simulation results prove that a single Moir´e fiber grating with only one π-phase
shifted point can act as the first-order temporal differentiator and that a Moir´e fiber grating incorporating
two symmetrical π-phase shifted points can act as the second-order temporal differentiator. A practical
Moir´e fiber grating is fabricated, thereby proving that such a grating can act as the first-order t emporal
differentiator. Our results verify the feasibility, flex ibility, and accuracy of the proposed method.
OCIS codes: 230.1150, 060.3735, 320.7085.
doi: 10.3788/COL201210.092301.
Recently, all-optical circuits implemented for all-optical
computing and signal processing have attracted sig-
nificant attention due to the exponentia l development
of photonics technologies. Such devices operated in
the optical domain can provide a wider bandwidth and
higher oper ating speed than devices operated in the
conventional-electronics-based system. One of the fun-
damental devices, the temporal differ e ntiator, has been
designed and researched by several groups. A temporal
differentiator can transform the field complex profile of
an optical signal to its differ ential signal immediately.
Aside from applications in the all- optical computing and
signal processing fields, a temporal differentiator has a
wide variety of applications in other areas, such as pulse
characterization
[1,2]
, femtosecond pulse shaping
[3,4]
, ul-
trashort pulse train genera tio n
[5]
, and high-speed optical
communication
[6]
.
Currently, several technologies have been proposed
to r e alize a temporal differentiator theoretically and
exp erimentally. In general, these reported temporal
differentiators can be classified into two categories: inco-
herent and coherent
[7]
. Inco herent optical differentiators
based on cross- gain modulation in a semiconductor opti-
cal amplifier have been reported since 2007
[8,9]
. The inco-
herent o ptical differentiator operates on the optical inten-
sity, instea d of the field complex profile, of an initial op-
tical signa l. Many methods have be e n proposed to realize
the coherent optica l differentiator, including the use of
silicon micro ring resonato r
[10]
, long-perio d fiber grating
(LPFG)
[11,12]
, and optical interferometer
[13]
. The silicon
micro ring resonator can offer an operational bandwidth
in the tens of gigahertzs
[10]
, whereas the experimentally
proven differentiator based on LPFG offers operational
bandwidth up to many terahertzs. However, the lo ng-
period fib e r grating is extremely sensitive to environ-
mental changes
[7,14]
. In addition integral differentiator
(the differentiation order is a n integer) and fractional
differentiators have been proposed s ince 2008, including
the use of a Mach-Zehnder interferometer
[15]
, LPFG
[16]
,
and tilted fiber gr ating
[17]
. The differentiation order can
be continuously adjusted when the tilted fiber grating
acts as a fractional differentiator
[17]
. High-order tem-
poral differentiator can be obtained by concatenating a
linearly chirpe d fiber Bragg grating with the first-order
temporal differentiator
[18]
or by using a long-period fiber
Bragg grating that provides full energy recoupling from
the cladding mode back into the core mode
[11]
.
In this letter, we des ign and demonstrate a single
Moir´e fiber grating to realize an all-fibe r temporal
differentiator that utilizes the mathematical existence of
exact π-phase shifted points when the refrac tive modula-
tion profile of the Moir´e fiber grating passes through the
zero point. The operational bandwidth of the propos ed
method is from many giga hertzs to ma ny tens of giga-
hertzs. In addition, the Moir´e fiber grating has a higher
tolerance to the environmental changes than the LPFG.
Therefore, our proposed differentiator can be widely used
in all-optical communications. The first- and second-
order temporal differentiators are designed as examples
in this letter. The simulation results prove that a sin-
gle Moir´e fiber grating with only one π-phase shifted
point can act as the first-order temporal differentiator.
The second-order tempora l differentiator is achieved by
a Moir´e fiber grating incorporating two symmetrical π-
phase shifted points. Good waveform matches between
the ideal differential signal and the output temporal
waveform are recorded for both of the first- and second-
order temporal differentiators. Thus, practical Moir´e
fiber grating is fabricated, thereby proving that such a
grating can act as the first-order temporal differentiator.
We suppos e that the temporal waveform of the initial
input signal is described as u(t), and that the frequency
waveform is described as U(ω). In addition, the tem-
poral waveform of derivative signal ca n be written as
v(t) = d
N
u(t)/dt
N
, a nd V (ω) is the frequency domain
expression of v(t). The basic relationship in the fre-
1671-7694/2012/092301(4) 092301-1
c
2012 Chinese Optics Letters