Bandwidth-adjustable dynamic grating in
erbium-doped fiber by synthesis of opticalcoherence function
Xinyu Fan, Zuyuan He, Yosuke Mizuno, and Kazuo Hotate
Department of Electronic Engineering, The University of Tokyo
7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan
fan@sagnac.t.u-tokyo.ac.jp

Abstract: We present an approach for bandwidth-adjustable optical filter
with the dynamic grating in erbium-doped fiber (EDF). The dynamicgrating is introduced by the interference of two coherent light beams
counter-propagating in the pumped EDF per the phenomenon of gainsaturation. The bandwidth of the grating is determined by the length of thegrating, i.e., the length of the interference region. With the technique ofsynthesis of optical coherence function (SOCF), we localize the interference
into a range at an arbitrary position along the fiber by modulating thefrequency of the two interfering light beams. The length of the range iscontrolled by adjusting the frequency modulation parameter. In this way,
the length of the dynamic grating is controlled and its reflection bandwidththen adjusted. The experimental demonstration is given.
©2005 Optical Society of America
OCIS codes: (050.2770) Gratings; (060.2340) Fiber optics components; (060.2410) Fibers,erbium

References and links
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S. A. Havstad, B. Fischer, A. E. Willner, and M. G. Wickham, “Loop-mirror filters based on saturable-gain
or -absorber gratings,” Opt. Lett. 24, 1466-1468 (1999).
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spatial-hole burning,” IEEE Photonics Technol. Lett. 11, 182-184 (1999).
Z. He and K. Hotate, “Distributed fiber optic stress location measurement by arbitrary shaping of opticalcoherence function,” J. of Lightwave Technol. 20, 1715-1723 (2002).
B. Zhu, T. Saida, and K. Hotate, “Variable optical filter using dynamic grating in Er doped fiber controlled
by synthesis of optical coherence function: Proposal and experiment verification,” IEICE Trans. Electron.
E86-C, 97-99 (2003).
X. Fan, Z. He, and K. Hotate, “Novel distributed fiber-optic strain sensor by localizing dynamic grating inpolarization-maintaining erbium-doped fiber: proposal and theoretical analysis,” Jpn. J. App. Phys. 44,
1101-1106 (2005).
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Photonics Technol. Lett. 1, 196-199 (1989).

1. Introduction
The dynamic grating received considerable attention because of its real-time formation and its
potential for applications as tunable optical filters and other functional optical devices [1-5].
When two counter-propagating coherent light beams (referred to as writing beams hereafter)#7517 - $15.00 US

Received 19 May 2005; revised 12 July 2005; accepted 17 July 2005(C) 2005 OSA

25 July 2005 / Vol. 13, No. 15 / OPTICS EXPRESS 5756

are launched into a pumped erbium-doped fiber (EDF), they will interfere to each other andform stationary interference fringes in the EDF. The interference fringes then create aperiodical gain structure per the phenomenon of gain saturation and hence produce a dynamicgrating in the EDF [1-3]. A third beam launched into the fiber (referred to as reading beam
hereafter) will be reflected by the dynamic grating when its wavelength is the same as thewriting beams’. Simply by changing the wavelength of the writing beams, a tunable filter
with the dynamic grating was realized, and its center wavelength of the reflection band can betuned in a few milliseconds [1].
In this paper, we present a method to adjust the bandwidth of the dynamic grating in realtime. The reflection bandwidth of the grating is inversely proportional to the length of thegrating. By making use of the technique of synthesis of optical coherence function (SOCF)[6], we realized the control on the length of the dynamic grating, and then demonstrated thebandwidth-adjustable filter with the dynamic grating for the first time to the best of ourknowledge.
2. Principle
The reflectivity of the dynamic grating can be given as [2]r=

κ sinh( SL ),{ g~ − i ( kw − kr )} sinh( SL ) − S cosh( SL )(1)

where kw and kr are the wave-numbers of the writing and reading beams, g~ the saturated gainfactor, κ the coupling factor, L the length of the dynamic grating, andS 2 = κ + [ g~ − i (kw − kr )]2 .
2(2)The reflection bandwidth of the dynamic grating is obtained as [2]

δν =c
2π n

⎛π ⎞⎜⎟⎝L ⎠2+κ21 + ( g~ L π ) 2,

(3)

where n is the refractive index, and c the light velocity in free space. It is obvious that thebandwidth is inversely proportional to the length of the dynamic grating since the right side ofEq. (3) can be approximated as c/(2nL). Therefore, the reflection bandwidth can be adjusted
by controlling the length of the dynamic grating, i.e., the length of the region of theinterference between the two writing beams.
The contrast of the interference fringe as a function of the optical path difference in aninterferometer, referred to as the coherence degree or the optical coherence function, is given
with the Fourier transform of the spectral density of the light source. When we use a laser
diode (LD) as the light source of the interferometer, the frequency of the lightwave emitted
from the LD can easily be tuned by modulating directly the injection current to the LD. A
frequency modulation of the laser source produces a correspondent power spectrum in thepoint of view of time averaging, thus a particular shape of the coherence function can besynthesized. For example, the coherence function has been synthesized into various shapes,
such as delta-function-like peak, triangle, and rectangular, for applications in opticalreflectometry, optical tomography, optical information processing, and fiber optic sensors [6].
A notch-shaped filter with the dynamic grating in an EDF was also demonstrated withrectangular-pulse frequency modulation [7].
Among the various shapes of the synthesized coherence function, the delta-function-likepeak is especially significant for controlling the length of the dynamic grating. A narrow peakof coherence function means that the interference is localized into a region correspondent to
the width of the peak, which means, in the case of the dynamic grating, the grating is only
formed in correspondent region in the fiber [8].

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Fig.1. Coherence function synthesized by sinusoidal frequency modulation.

It has been demonstrated that the delta-function-like coherence function can besynthesized by stepwise- or sinusoidal-frequency modulation [6-8]. In this paper we adopt thesinusoidal-frequency modulation method. As given in Eq. (4), we denote the mean frequency,
the modulation amplitude, and the modulation frequency as f0, f1, and f2, respectively. Thenthe light frequency of the lightwave emitted from the LD is expressed as
f = f0 + f1 cos(2πf2t )(4)

By the modulation, the coherence function is synthesized into a series of periodical deltafunction-like peaks as shown in Fig. 1. The period and the FWHM (full width at halfmaximum) width of the peaks are in inverse proportion to f2 and f1, respectively. We can set
only one coherence-peak inside the EDF and to keep it at the middle of the fiber by selecting
suitable modulation frequency f2, which means, a dynamic grating is placed at the middle ofthe EDF. By changing the modulation amplitude f1, we can control the FWHM width of thecoherence peak. In this way, we can control the length of the dynamic grating, which
determines the reflective bandwidth of the grating.
3. Experiment
The experiment setup is shown in Fig. 2. The total length of the EDF (Nufern DD120 highdoped EDF) is 70 cm. Two 980-nm pump LDs are used to pump the EDF. The gain of thepumped EDF is 20 dB. Two light beams I1 and I2 from the distributed feedback laser diodeFig. 2. Experiment setup. VA: variable attenuator; PC: polarization controller; EDF: erbium-dopedfiber; IM: intensity modulator; PD: photodiode; LIA: lock-in amplifier; FG: function generator;
Ref: reference signal.

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DFB-LD1 are used to write the dynamic grating and their power are both set to –10 dBm byadjusting two variable attenuators (VAs). Two polarization controllers (PCs) are used to alignthe writing beams at the same polarization directions in order to obtain a maximum
interference pattern in the EDF. We use I3 from DFB-LD2 as the reading beam to read thegrating and its power is –20 dBm. I3 is chopped by using an intensity modulator (IM) for thepurpose of synchronous detection. The polarization direction of I3 need not be the same as
those of I1 and I2. The PC before the IM is used only for aligning the polarization direction of
I3 with the polarization axis of the IM. In experiment, we found that the chopping frequency
has to be fast enough to avoid the gain modulation, which is a phenomenon caused by thechopping of I3 here. The gain modulation results in a spurious signal in the frequency of thesynchronous detection. If the chopping is much faster than the sub-millisecond response timeof the EDF gain dynamics [9], the gain modulation induced spurious signal will disappear.
Here we set the chopping frequency at 10 MHz. The optical frequency of I3 is scanned bychanging the injection current and the I4, which is the reflection of I3 at the dynamic grating, ismonitored by using the lock-in amplifier (LIA) after the photodiode (PD).
We made sinusoidal frequency modulation for the writing beams as shown in Eq. (4). The
dynamic grating is localized at the middle of the fiber by selecting suitable modulation
frequency f2 to control the position of the coherence peak. In our experiment, we measured
the optical path difference between the two writing beams with optical method, then after
careful calculations, we decided the modulation frequency f2 to be 28.37MHz to put the firstorder coherence peak at the middle of the EDF. This frequency is also fast enough to avoid
the gain modulation.
The length of the dynamic grating is inversely proportional to the modulation amplitude f1.
We can change the f1 simply by adjusting the amplitude of AC injection current to DFB-LD1,i.e., by adjusting the peak-to-peak voltage Vpp supplied by the function generator (FG) in theexperiment. In our system, the FWHM of the coherence peak, i.e., the grating length LFWHM,
is pre-measured and is found to have a relationship with Vpp as
LFWHM [m] = 30 / Vpp [mV](5)

when the modulation amplitude f1 is ten times greater than the modulation speed f2. In ourexperiment, Vpp has been chosen as 40 mV and 100 mV, which correspond to grating lengthof 75 cm and 30 cm, respectively.
Figure 3 shows the reflectivity of the dynamic grating when no modulation for the DFBLD1 is performed. The raw data are fitted with a Gaussian function. We can see that a 10%
reflectivity at the Bragg frequency is obtained, and the –3-dB bandwidth of the reflection
spectrum is 175 MHz. The noise exhibiting in Fig. 3 includes following four components: 1)
amplified Rayleigh backscattering (RBS), 2) double-path amplified reflection of I3, i.e.,
amplified I3 reflected at the splicing point and then amplified again (RG2I3), 3) beating of
amplified I1 with RG2I3 (B13), and 4) beating of amplified I1 with amplified spontaneousemission (B1A). The noise of B13 not only contributes to the noise floor but also influences theFig. 3. Reflectivity from the dynamic grating without modulation on writing beams.

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Fig. 4. Reflectivity from the dynamic grating localized by using the technique of SOCF.
The length of the dynamic grating LFWHM = 75 cm.

peak while other three noises only contribute to the noise floor, which is around –30-dB
reflectivity in this experimental system.
When the optical frequency of the DFB-LD1 is modulated and the Vpp is set to be 40 mV,
which corresponds to LFWHM of 75 cm, the –3-dB bandwidth of the reflection spectrum isbroadened from 175 MHz to 200 MHz, as shown in Fig. 4.
In Fig. 5, the fitted reflection spectra of three different dynamic gratings are compared,
where Fig. 5(b) shows the normalized reflection spectra for comparison between theirbandwidths. From Fig. (5), we can see obviously that the bandwidth becomes wider and thereflectivity gets lower as the length of the dynamic grating decreases.
The bandwidth broadening can be seen clearly in Fig. 5(b). When the Vpp is set to be 40mV (LFWHM = 75 cm) and 100 mV (LFWHM = 30 cm), the –3-dB bandwidth of the reflection
spectrum is broadened from 175 MHz to 200 MHz and 475 MHz, respectively. This result isin good agreement with the theory that the bandwidth is in inverse proportion to the length ofthe dynamic grating. We also tried a peak-to-peak voltage Vpp larger than 100 mV (LFWHM <30 cm) in the experiment. In this case, the reflectivity is lower than the noise floor, which
prevents us from detecting any significant reflection signal.
Figure 5(a) shows that the bandwidth broadening is accompanied by significant decreaseof the reflectivity. This is an intrinsic limitation of the system because a shortened dynamic
grating for a broadened bandwidth will give a lower reflectivity. This problem can beimproved by adjusting the intensity of the pump light from the 980-nm LDs, that is, toincrease the pump level when the length of the dynamic grating is shortened, then thedecreased reflectivity can get compensated.

(a)

(b)

Fig. 5. (a) Fitted reflection spectra of three different dynamic gratings, (b) normalized graphs of (a).

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4. Conclusion
With sinusoidal-modulation on the optical frequency of the writing beams, we localized thedynamic grating in EDF in a region corresponding to the position of the coherence peak where
the interference of the writing beams takes place. By adjusting the modulation amplitude of
the frequency modulation to control the width of the coherence peak, the reflection bandwidthof the dynamic grating is adjusted. Our experiment results show that the reflection bandwidth
becomes wider when we use greater frequency modulation amplitude, which corresponds toshorter grating length. In this way, the manipulation on the dynamic grating in EDF with thetechnique of SOCF provides an approach to realize a bandwidth-adjustable optical filter.
Together with the tuning on the center frequency of the reflection band by changing thewavelength of the writing beams, and the adjustment of the reflectivity by controlling theintensity of the writing beams, we can synthesize arbitrary reflection characteristics with the
dynamic grating – arbitrary center frequency, arbitrary reflectivity and arbitrary bandwidth.
This kind of variable filter can provide us with great potential for applications in the fields of
optical communications and optical sensing.

#7517 - $15.00 US

Received 19 May 2005; revised 12 July 2005; accepted 17 July 2005

(C) 2005 OSA

25 July 2005 / Vol. 13, No. 15 / OPTICS EXPRESS 5761