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Chromatic dispersion monitoring technique using optical asynchronous sampling and double sideband filtering
Optical Fiber Technology 16 (2010) 124–127
Contents lists available at ScienceDirect
Optical Fiber Technology www.elsevier.com/locate/yofte
Chromatic dispersion monitoring technique using optical asynchronous sampling and double sideband filtering Vítor Ribeiro a,*, António Teixeira a,b, Mário Lima a,b a b
Institute of Telecommunications, Campus Universitário de Santiago, University of Aveiro, Portugal Electronics, Telecommunications and Informatics Department, Campus Universitário de Santiago, University of Aveiro, Portugal
a r t i c l e
i n f o
Article history: Received 19 November 2009 Revised 28 January 2010 Available online 23 February 2010 Keywords: Chromatic dispersion Optical sampling
a b s t r a c t This paper introduces a new chromatic dispersion monitoring technique using optical asynchronous sampling and double sideband filtering. We present simulation results that relate chromatic dispersion with the ratio between the maximum amplitude of the signal and the average optical output power, yielding in a method which is power transparent. We also show theoretical investigation and theoretical results that prove the approach used in this paper. Ó 2010 Elsevier Inc. All rights reserved.
1. Introduction Chromatic dispersion is well known as one of the most limiting impairments in optical communications. Prior work in the field of chromatic dispersion monitoring, implemented various schemes, including asynchronous delay tap sampling [1,2], RF tone measurement [3,4], self phase modulation (SPM), four wave mixing (FWM) and cross phase modulation (XPM) [5–7], polarization scrambling [8], asynchronous chirp [9], two photon absorption (TPA) with semiconductor micro-cavity [10], and so on. The well known RF tone measurement techniques cannot isolate chromatic dispersion, because are known to be sensitive to a variety of distortion effects including PMD [11]. Although,is a technique with moderate dynamic range, cost, and acquisition time and also suitable to implement [12]. Monitoring chromatic dispersion by nonlinear effects (TPA, FWM, SPM, XPM) avoids high speed electrical domain signal processing, but requires normally high power, due to the low efficiency of the nonlinear process [5–7,10]. The technique here presented, collects samples of data at asynchronous intervals, and determines the maximum amplitude of the optical signal in an appropriate time window. Fig. 1 shows the simulation setup of the monitoring technique. The processor samples the signal asynchronously and determines the maximum amplitude of it. Then it divides this value by the average power calculated by the optical power meter of Fig. 1, yielding in a ratio (known in telecommunications engineering to be the Peak to Average Power Ratio (PAPR)) transparent to the average power of the laser. The optical filter selects the two sidebands of the signal, * Corresponding author. E-mail address: [email protected] (V. Ribeiro). 1068-5200/$ - see front matter Ó 2010 Elsevier Inc. All rights reserved. doi:10.1016/j.yofte.2010.01.006
rejecting all the others. The chromatic dispersion influence of the two sidebands, in the phase of the optical field, is isolated from the chromatic dispersion influence of the other sidebands. Without the filter, the phase shift produced by the chromatic dispersion in the other sidebands, will influence the phase and also the intensity of the optical field, in a manner, that the optical peak power versus chromatic dispersion is no longer a monotonic function. This implies that the optical filter is crucial for this method. The machzhender interferometer with s ¼ 1=ð2f p Þ, has the effect of reducing the optical power when there is no dispersion. The interferometer shifts the phase between the optical carrier and the two sidebands +p=2 and p=2, respectively, so that these two sidebands have a p phase difference, and therefore, they could cancel each other. Chromatic dispersion changes this phase difference, and the PAPR starts to increase when dispersion departs from 0 ps/nm. This method, relatively to the ones mentioned above, is very simple to implement. Also, by using optical sampling, has fast acquisition time and do not require high power, like the monitoring techniques using nonlinear effects. Relatively to the RF tone techniques and specifically to the one presented in [13], besides the most obvious differences, which is the fact that we do not measure the RF power, but measure the peak optical power (which is not correlated with the RF power, as stated further in this paper, by the final Eq. (14). This one relates chromatic dispersion with the optical peak power by a sine modulus, instead of a sine square or a cosine square as regular RF tone measurement techniques do), and the fact that the optical domain part of the setup is different, we do not use also an RF filter. This allows to use optical domain processing techniques, to measure the peak optical power, instead of using high speed electrical domain techniques, to measure the RF power. Optical sampling is
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V. Ribeiro et al. / Optical Fiber Technology 16 (2010) 124–127
Popt ¼ jrðtÞj2 ¼ ReðrðtÞÞ2 þ ImðrðtÞÞ2 pffiffiffiffiffi 2 ¼ 1=4 P0 mH2 cosð2ptf0 þ qf p þ /2 þ 2pfp tÞ pffiffiffiffiffi 2 þ1=4 P 0 mH3 cosð2ptf0 þ qf p 2pfp t þ /3 Þ 2 pffiffiffiffiffi pffiffiffiffiffi 2 þ P0 H1 cosð2ptf0 þ /1 Þ þ 1=4 P0 mH2 sinð2ptf0 þ qf p pffiffiffiffiffi 2 þ/2 þ 2pfp tÞ þ 1=4 P0 mH3 sinð2ptf0 þ qf p 2pfp t þ /3 Þ 2 pffiffiffiffiffi 1 P0 ðm2 H22 þ 2m2 H2 H3 cosð/2 þ P0 H1 sinð2ptf0 þ /1 Þ ¼ 16 2 þ4pfp t /3 Þ þ 8mH1 H2 cosðqf p þ /2 þ 2pfp t /1 Þ þ m2 H23 2
þ8mH3 H1 cosðqf p þ /3 2pfp t /1 Þ þ 16H21 Þ: Fig. 1. Simulation setup: BPF – band pass filter, BW – bandwidth, s – time delay of the intereferometer, EDFA – erbium doped fiber amplifier, SMF – single mode fiber, DCF – dispersion compensating fiber, and NF – noise figure.
Using (5) into (6) we obtain: 1 2 2 2 P opt ¼ P 0 H2 m þ 2m2 H2 H3 cosð4pfp tÞ 8mH2 H1 sin qf p þ 2pfp t 16 2
faster than electrical sampling. This implies that the acquisition time of this method is shorter than the monitoring technique of [13] or any other technique based in RF pilot tones. 2. Theory The electric field equation of a sinusoidal input modulation, after passing through a dispersive fiber, an ideal filter and an interferometer is given by (1) [13]: rðtÞ ¼
2 pffiffiffiffiffi mðH2 þ H3 Þeiðqf p /1 þ1=2/2 þ1=2/3 Þ P 0 H1 ei/1 þ2iptf0 1 þ 1=4 H1 2
cosð2pfp t þ 1=2/2 1=2/3 Þ mðH2 H3 Þeiðqf p /1 þ1=2/2 þ1=2/3 Þ þ 1=4i H1 H1 sinð2pfp t þ 1=2/2 1=2/3 Þ 1 F frectðf0 ; fBW Þg; ð1Þ H1
where fp is the frequency of the sinusoid, f0 is the carrier frequency, P0 is the average laser launch power, m is the modulation index, F1 frectðf0 ; f BW Þg is the inverse Fourier transform of an ideal filter centered at f0 , with frequency bandwidth equal to fBW and is the convolution operator. The H1 ; H2 ; H3 , /1 ; /2 ; /3 and q, parameters are defined as follows:
H1 ¼ j cosðpsf0 Þj;
/2 ¼ psf0 þ /3 ¼ psf0 þ q¼
pk20 DL c
p 2
p 2
p 2
þ \ cosðpsf0 Þ;
ð2Þ
þ \ cosðpsðf0 fp ÞÞ þ psfp ; ð3Þ
where k0 is the carrier central wavelength, D is the dispersion parameter, L is the fiber length, \ is the angle operator and s is the delay time of the delay line of Fig. 1 which is given by:
s¼
1 : 2f p
ð4Þ
In such conditions we can write:
H1 ¼ j cosðpsf0 Þj H3 ¼ H2
H2 ¼ j cosðpsðf0 þ fp ÞÞj /1 ¼ 2pn þ a
ð7Þ
To calculate the maximum amplitude of the signal we must derivate (7) in order to time and equalize it to zero:
dPopt 2 ¼ P0 mH3 H1 cos qf p 2pfp t fp p 1=2P0 m2 H3 H2 dt 2
sinð4pfp tÞfp p P0 H1 mH2 cos qf p þ 2pfp t fp p ¼ 0:
ð8Þ
Then we must find the solutions that fulfil this requirement. We conclude that the solutions are:
8 DL P 2nDTalbot > > > < ð2i þ 1Þ=ð2f p Þ if; DL < ð2n þ 1ÞD Talbot ; t¼ > DL P ð2n þ 1ÞDTalbot > > if; : ð2i þ 1Þ=ðfp Þ DL < ð2n þ 2ÞDTalbot
ð9Þ
where n ¼ . . . ; 2; 1; 0; 1; 2; . . . and i ¼ 0; 1; 2; . . . . The product DL is the total accumulated dispersion in the fiber. A more thorough study need to be done, because of the use of asynchronous sampling, but some clues can be found taking into account that:
1 Ts ¼ k f j p
k < j;
ð10Þ
k 1 P ; j 2m þ 1
ð11Þ
where m is the ith solution of (8), that represents the solution with highest value in an appropriate time window. DTalbot is defined as [14]:
þ \ cosðpsðf0 þ fp ÞÞ psfp ;
;
þm2 H23 8mH3 H1 sin qf p 2pfp t þ 16H21 :
where T s is the sampling period. Then the following condition must be met:
H2 ¼ j cosðpsðf0 þ fp ÞÞj; H3 ¼ j cosðpsðf0 fp ÞÞj; /1 ¼ psf0 þ
ð6Þ
ð5Þ
/2 ¼ 2pn þ a þ p2 /3 ¼ 2pn þ a þ p2 ; where a is an arbitrary angle dependent of f0 . The optical power is given by:
DTalbot ¼
c fp2 k20
:
ð12Þ
DTalbot is due to the Talbot effect, which describes the apparent re-emergence of a periodic sequence of pulses, propagating in the dispersive medium. Substituting the solutions given by (9) into (7), for instance for i ¼ 1, leads to (13a) and (13b), which is a novel relationship between the maximum amplitude of the signal and chromatic dispersion: 1 2 2 2 P opt ðqÞ ¼ P 0 m H2 þ 16mH2 H1 sinðqf p Þ2m2 H2 H3 þ m2 H23 þ 16H21 ; 16 ð13aÞ if 2nDTalbot 6 DL < ð2n þ 1ÞDTalbot and:
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V. Ribeiro et al. / Optical Fiber Technology 16 (2010) 124–127
P opt ðqÞ ¼
1 2 2 2 P 0 m H2 16mH2 H1 sinðqf p Þ2m2 H2 H3 þ m2 H23 þ 16H21 ; 16 ð13bÞ
if ð2n þ 1ÞDTalbot 6 DL < ð2n þ 2ÞDTalbot . The ratio between the optical power and the average power is given by:
ratio ¼
1 P 16 0
P opt ðqÞ H22 m2
þ m2 H23 þ 16H21
2m2 H2 H3 ¼1þ 2 2 H2 m þ m2 H23 þ 16H21 16mH2 H1 2 sinðqf p Þ þ H22 m2 þ m2 H23 þ 16H21
ð14Þ
which leads to an equation that is independent from the launch power P 0 . 3. Results and discussion Fig. 2 shows the theoretical plot versus the simulation data, in terms of the ratio value, for P 0 ¼ 1 mW, k0 ¼ 1550 nm, fp ¼ 10 GHz and m ¼ 1 using a sinusoidal format. We see a very close relationship
2.4
4. Conclusions We show a new chromatic dispersion monitoring technique based in asynchronous optical sampling, that eliminates ambiguity at 0 ps/nm, and also have high sensitivity at this region of the monitoring window. This technique has fast acquisition time (faster than the RF tone monitoring techniques), like the methods using nonlinear effects, although it does not require high power as this methods do. It also has an acceptable monitoring resolution and monitoring window. We also elaborate the theory that led to a new equation that relates the maximum optical power, with chromatic dispersion. Simulation results agree with the theoretical results.
* Simulation data ___Theoretical data
Acknowledgments
2.2
The Motion (PTDC/EEA-TEL/73529/2006) FCT project is acknowledged. The authors would like to thank to all the reviewers of this paper for their fruitful comments.
2
Ratio
between the theoretical curve obtained from (14) and simulation data, obtained using OptiSystem 7.0, indicating that the theoretical approach is correct. Some differences appear when chromatic dispersion departs from ±1240 ps=nm. We think that the cause of this is SPM and the fact that when dispersion length and nonlinear length become comparable to the fiber length, we must take into consideration the combined effects of chromatic dispersion and SPM [15]. We may also see a very distinct peak at 0 ps/nm, avoiding ambiguity at this dispersion value. Fig. 3 shows the simulation results for the RZ format. The curve is similar to the one of Fig. 2. This indicates that the theoretical approach is also similar to the one used in the sinusoidal format, indi 2 cating that the curve follows the form sin qf p .
1.8 1.6
References 1.4 1.2 −2500 −2000 −1500 −1000 −500
0
500
1000
1500
2000
2500
Chromatic dispersion(ps/nm) Fig. 2. Dispersion monitoring for a sinusoidal input modulation. Simulation and theoretical data are plotted. Theoretical data is plotted according to (14).
6
ratio
5
4
3
−500
0
500
Chromatic dispersion(ps/nm) Fig. 3. Dispersion monitoring for a return to zero modulation. Simulation data is plotted.
[1] B. Kozicki, A. Maruta, K.-i. Kitayama, Experimental investigation of delay-tap sampling technique for online monitoring of RZ-DQPSK signals, IEEE Photonic. Technol. Lett. 21 (3) (2009). [2] S.D. Dods, T.B. Anderson, Optical performance monitoring technique using delay tap asynchronous waveform sampling, in: Proc. OFC ’06, OThP5, 2006. [3] Y.K. Lize, L. Christen, J.-Y. Yang, P. Saghari, S. Nuccio, A.E. Willner, R. Kashyap, Independent and simultaneous monitoring of chromatic and polarizationmode dispersion in OOK and DPSK transmission, IEEE Photonic. Technol. Lett. 19 (1) (2007). [4] Z. Pan, Y. Xie, S.A. Havstad, Q. Yu, A.E. Willner, V. Grubsky, D.S. Starodubov, J. Feinberg, Real-time group-velocity dispersion monitoring and automated compensation without modifications of the transmitter, Opt. Commun. 230 (1-3) (2004) 145–149. [5] P.S. Westbrook, B.J. Eggleton, G. Raybon, S. Hunsche, Tsing Hua Her, Measurement of residual chromatic dispersion of a 40-Gb/s RZ signal via spectral broadening, IEEE Photonic. Technol. Lett. 14 (3) (2002). [6] Shenping Li, D.V. Kuksenkov, A novel dispersion monitoring technique based on four-wave mixing in optical fiber, IEEE Photonic. Technol. Lett. 16 (3) (2004). [7] T. Luo, C. Yu, Z. Pan, Y. Wang, J.E. Mcgeehan, M. Adler, A.E. Willner, All-optical chromatic dispersion monitoring of a 40-Gb/s RZ signal by measuring the XPM-generated optical tone power in a highly nonlinear fiber, IEEE Photonic. Technol. Lett. 18 (2) (2006). [8] K.J. Park, J.H. Lee, C.J. Youn, Y.C. Chung, A simultaneous monitoring technique for polarization-mode dispersion and group-velocity dispersion, WE4, OFC, 2002. [9] T. Inui, T. Komukai, K. Mori, T. Morioka, 160-gb/s adaptive dispersion equalization using an asynchronous dispersion-induced chirp monitor, J. Lightw. Technol. 23 (6) (2005). [10] K. Bondarczuk, P.J. Maguire, L.P. Barry, J. O’Dowd, W.H. Guo, M. Lynch, A.L. Bradley, J.F. Donegan, H. Folliot, H. Chromatic Dispersion Monitoring of 80-Gb/s OTDM Data Signal via Two-Photon Absorption in a Semiconductor Microcavity, vol. 19, No. 1, January 2007. [11] Zhongqi Pan, Changyuan Yu, Alan E. Willner, Optical performance monitoring for the next generation optical communication networks, Opt. Fiber Technol. 16 (1) (2010). [12] A. Teixeira, L. Costa, G. Frantzl, S. Azodolmolky, I. Tomkos, K. Vlachos, S. Zsigmond, T. Cinkler, G. Tosi Beleffi, P. Gravey, T. Loukina, J.A. Lázaro, C.
V. Ribeiro et al. / Optical Fiber Technology 16 (2010) 124–127 Vasquez, J. Montalvo, E. Le Rouzic, An integrated view on monitoring and compensation for dynamic optical networks from management to physical layer, Photon. Network Commun. (2009). [13] Kuen Ting Tsai, Winston I. Way, Chromatic dispersion monitoring using an optical delay-and-add filter, J. Lightw. Technol. 23 (11) (2005).
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[14] Stephan Wielandy, Michael Fishteyn, Benyuan Zhu, Optical performance monitoring using nonlinear detection, J. Lightw. Technol. 22 (3) (2004). [15] Govind P. Agrawal, Nonlinear Fiber Optics, fourth ed., Academic Press, Elsevier, 2007, pp. 89–102.
Contents lists available at ScienceDirect
Optical Fiber Technology www.elsevier.com/locate/yofte
Chromatic dispersion monitoring technique using optical asynchronous sampling and double sideband filtering Vítor Ribeiro a,*, António Teixeira a,b, Mário Lima a,b a b
Institute of Telecommunications, Campus Universitário de Santiago, University of Aveiro, Portugal Electronics, Telecommunications and Informatics Department, Campus Universitário de Santiago, University of Aveiro, Portugal
a r t i c l e
i n f o
Article history: Received 19 November 2009 Revised 28 January 2010 Available online 23 February 2010 Keywords: Chromatic dispersion Optical sampling
a b s t r a c t This paper introduces a new chromatic dispersion monitoring technique using optical asynchronous sampling and double sideband filtering. We present simulation results that relate chromatic dispersion with the ratio between the maximum amplitude of the signal and the average optical output power, yielding in a method which is power transparent. We also show theoretical investigation and theoretical results that prove the approach used in this paper. Ó 2010 Elsevier Inc. All rights reserved.
1. Introduction Chromatic dispersion is well known as one of the most limiting impairments in optical communications. Prior work in the field of chromatic dispersion monitoring, implemented various schemes, including asynchronous delay tap sampling [1,2], RF tone measurement [3,4], self phase modulation (SPM), four wave mixing (FWM) and cross phase modulation (XPM) [5–7], polarization scrambling [8], asynchronous chirp [9], two photon absorption (TPA) with semiconductor micro-cavity [10], and so on. The well known RF tone measurement techniques cannot isolate chromatic dispersion, because are known to be sensitive to a variety of distortion effects including PMD [11]. Although,is a technique with moderate dynamic range, cost, and acquisition time and also suitable to implement [12]. Monitoring chromatic dispersion by nonlinear effects (TPA, FWM, SPM, XPM) avoids high speed electrical domain signal processing, but requires normally high power, due to the low efficiency of the nonlinear process [5–7,10]. The technique here presented, collects samples of data at asynchronous intervals, and determines the maximum amplitude of the optical signal in an appropriate time window. Fig. 1 shows the simulation setup of the monitoring technique. The processor samples the signal asynchronously and determines the maximum amplitude of it. Then it divides this value by the average power calculated by the optical power meter of Fig. 1, yielding in a ratio (known in telecommunications engineering to be the Peak to Average Power Ratio (PAPR)) transparent to the average power of the laser. The optical filter selects the two sidebands of the signal, * Corresponding author. E-mail address: [email protected] (V. Ribeiro). 1068-5200/$ - see front matter Ó 2010 Elsevier Inc. All rights reserved. doi:10.1016/j.yofte.2010.01.006
rejecting all the others. The chromatic dispersion influence of the two sidebands, in the phase of the optical field, is isolated from the chromatic dispersion influence of the other sidebands. Without the filter, the phase shift produced by the chromatic dispersion in the other sidebands, will influence the phase and also the intensity of the optical field, in a manner, that the optical peak power versus chromatic dispersion is no longer a monotonic function. This implies that the optical filter is crucial for this method. The machzhender interferometer with s ¼ 1=ð2f p Þ, has the effect of reducing the optical power when there is no dispersion. The interferometer shifts the phase between the optical carrier and the two sidebands +p=2 and p=2, respectively, so that these two sidebands have a p phase difference, and therefore, they could cancel each other. Chromatic dispersion changes this phase difference, and the PAPR starts to increase when dispersion departs from 0 ps/nm. This method, relatively to the ones mentioned above, is very simple to implement. Also, by using optical sampling, has fast acquisition time and do not require high power, like the monitoring techniques using nonlinear effects. Relatively to the RF tone techniques and specifically to the one presented in [13], besides the most obvious differences, which is the fact that we do not measure the RF power, but measure the peak optical power (which is not correlated with the RF power, as stated further in this paper, by the final Eq. (14). This one relates chromatic dispersion with the optical peak power by a sine modulus, instead of a sine square or a cosine square as regular RF tone measurement techniques do), and the fact that the optical domain part of the setup is different, we do not use also an RF filter. This allows to use optical domain processing techniques, to measure the peak optical power, instead of using high speed electrical domain techniques, to measure the RF power. Optical sampling is
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V. Ribeiro et al. / Optical Fiber Technology 16 (2010) 124–127
Popt ¼ jrðtÞj2 ¼ ReðrðtÞÞ2 þ ImðrðtÞÞ2 pffiffiffiffiffi 2 ¼ 1=4 P0 mH2 cosð2ptf0 þ qf p þ /2 þ 2pfp tÞ pffiffiffiffiffi 2 þ1=4 P 0 mH3 cosð2ptf0 þ qf p 2pfp t þ /3 Þ 2 pffiffiffiffiffi pffiffiffiffiffi 2 þ P0 H1 cosð2ptf0 þ /1 Þ þ 1=4 P0 mH2 sinð2ptf0 þ qf p pffiffiffiffiffi 2 þ/2 þ 2pfp tÞ þ 1=4 P0 mH3 sinð2ptf0 þ qf p 2pfp t þ /3 Þ 2 pffiffiffiffiffi 1 P0 ðm2 H22 þ 2m2 H2 H3 cosð/2 þ P0 H1 sinð2ptf0 þ /1 Þ ¼ 16 2 þ4pfp t /3 Þ þ 8mH1 H2 cosðqf p þ /2 þ 2pfp t /1 Þ þ m2 H23 2
þ8mH3 H1 cosðqf p þ /3 2pfp t /1 Þ þ 16H21 Þ: Fig. 1. Simulation setup: BPF – band pass filter, BW – bandwidth, s – time delay of the intereferometer, EDFA – erbium doped fiber amplifier, SMF – single mode fiber, DCF – dispersion compensating fiber, and NF – noise figure.
Using (5) into (6) we obtain: 1 2 2 2 P opt ¼ P 0 H2 m þ 2m2 H2 H3 cosð4pfp tÞ 8mH2 H1 sin qf p þ 2pfp t 16 2
faster than electrical sampling. This implies that the acquisition time of this method is shorter than the monitoring technique of [13] or any other technique based in RF pilot tones. 2. Theory The electric field equation of a sinusoidal input modulation, after passing through a dispersive fiber, an ideal filter and an interferometer is given by (1) [13]: rðtÞ ¼
2 pffiffiffiffiffi mðH2 þ H3 Þeiðqf p /1 þ1=2/2 þ1=2/3 Þ P 0 H1 ei/1 þ2iptf0 1 þ 1=4 H1 2
cosð2pfp t þ 1=2/2 1=2/3 Þ mðH2 H3 Þeiðqf p /1 þ1=2/2 þ1=2/3 Þ þ 1=4i H1 H1 sinð2pfp t þ 1=2/2 1=2/3 Þ 1 F frectðf0 ; fBW Þg; ð1Þ H1
where fp is the frequency of the sinusoid, f0 is the carrier frequency, P0 is the average laser launch power, m is the modulation index, F1 frectðf0 ; f BW Þg is the inverse Fourier transform of an ideal filter centered at f0 , with frequency bandwidth equal to fBW and is the convolution operator. The H1 ; H2 ; H3 , /1 ; /2 ; /3 and q, parameters are defined as follows:
H1 ¼ j cosðpsf0 Þj;
/2 ¼ psf0 þ /3 ¼ psf0 þ q¼
pk20 DL c
p 2
p 2
p 2
þ \ cosðpsf0 Þ;
ð2Þ
þ \ cosðpsðf0 fp ÞÞ þ psfp ; ð3Þ
where k0 is the carrier central wavelength, D is the dispersion parameter, L is the fiber length, \ is the angle operator and s is the delay time of the delay line of Fig. 1 which is given by:
s¼
1 : 2f p
ð4Þ
In such conditions we can write:
H1 ¼ j cosðpsf0 Þj H3 ¼ H2
H2 ¼ j cosðpsðf0 þ fp ÞÞj /1 ¼ 2pn þ a
ð7Þ
To calculate the maximum amplitude of the signal we must derivate (7) in order to time and equalize it to zero:
dPopt 2 ¼ P0 mH3 H1 cos qf p 2pfp t fp p 1=2P0 m2 H3 H2 dt 2
sinð4pfp tÞfp p P0 H1 mH2 cos qf p þ 2pfp t fp p ¼ 0:
ð8Þ
Then we must find the solutions that fulfil this requirement. We conclude that the solutions are:
8 DL P 2nDTalbot > > > < ð2i þ 1Þ=ð2f p Þ if; DL < ð2n þ 1ÞD Talbot ; t¼ > DL P ð2n þ 1ÞDTalbot > > if; : ð2i þ 1Þ=ðfp Þ DL < ð2n þ 2ÞDTalbot
ð9Þ
where n ¼ . . . ; 2; 1; 0; 1; 2; . . . and i ¼ 0; 1; 2; . . . . The product DL is the total accumulated dispersion in the fiber. A more thorough study need to be done, because of the use of asynchronous sampling, but some clues can be found taking into account that:
1 Ts ¼ k f j p
k < j;
ð10Þ
k 1 P ; j 2m þ 1
ð11Þ
where m is the ith solution of (8), that represents the solution with highest value in an appropriate time window. DTalbot is defined as [14]:
þ \ cosðpsðf0 þ fp ÞÞ psfp ;
;
þm2 H23 8mH3 H1 sin qf p 2pfp t þ 16H21 :
where T s is the sampling period. Then the following condition must be met:
H2 ¼ j cosðpsðf0 þ fp ÞÞj; H3 ¼ j cosðpsðf0 fp ÞÞj; /1 ¼ psf0 þ
ð6Þ
ð5Þ
/2 ¼ 2pn þ a þ p2 /3 ¼ 2pn þ a þ p2 ; where a is an arbitrary angle dependent of f0 . The optical power is given by:
DTalbot ¼
c fp2 k20
:
ð12Þ
DTalbot is due to the Talbot effect, which describes the apparent re-emergence of a periodic sequence of pulses, propagating in the dispersive medium. Substituting the solutions given by (9) into (7), for instance for i ¼ 1, leads to (13a) and (13b), which is a novel relationship between the maximum amplitude of the signal and chromatic dispersion: 1 2 2 2 P opt ðqÞ ¼ P 0 m H2 þ 16mH2 H1 sinðqf p Þ2m2 H2 H3 þ m2 H23 þ 16H21 ; 16 ð13aÞ if 2nDTalbot 6 DL < ð2n þ 1ÞDTalbot and:
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P opt ðqÞ ¼
1 2 2 2 P 0 m H2 16mH2 H1 sinðqf p Þ2m2 H2 H3 þ m2 H23 þ 16H21 ; 16 ð13bÞ
if ð2n þ 1ÞDTalbot 6 DL < ð2n þ 2ÞDTalbot . The ratio between the optical power and the average power is given by:
ratio ¼
1 P 16 0
P opt ðqÞ H22 m2
þ m2 H23 þ 16H21
2m2 H2 H3 ¼1þ 2 2 H2 m þ m2 H23 þ 16H21 16mH2 H1 2 sinðqf p Þ þ H22 m2 þ m2 H23 þ 16H21
ð14Þ
which leads to an equation that is independent from the launch power P 0 . 3. Results and discussion Fig. 2 shows the theoretical plot versus the simulation data, in terms of the ratio value, for P 0 ¼ 1 mW, k0 ¼ 1550 nm, fp ¼ 10 GHz and m ¼ 1 using a sinusoidal format. We see a very close relationship
2.4
4. Conclusions We show a new chromatic dispersion monitoring technique based in asynchronous optical sampling, that eliminates ambiguity at 0 ps/nm, and also have high sensitivity at this region of the monitoring window. This technique has fast acquisition time (faster than the RF tone monitoring techniques), like the methods using nonlinear effects, although it does not require high power as this methods do. It also has an acceptable monitoring resolution and monitoring window. We also elaborate the theory that led to a new equation that relates the maximum optical power, with chromatic dispersion. Simulation results agree with the theoretical results.
* Simulation data ___Theoretical data
Acknowledgments
2.2
The Motion (PTDC/EEA-TEL/73529/2006) FCT project is acknowledged. The authors would like to thank to all the reviewers of this paper for their fruitful comments.
2
Ratio
between the theoretical curve obtained from (14) and simulation data, obtained using OptiSystem 7.0, indicating that the theoretical approach is correct. Some differences appear when chromatic dispersion departs from ±1240 ps=nm. We think that the cause of this is SPM and the fact that when dispersion length and nonlinear length become comparable to the fiber length, we must take into consideration the combined effects of chromatic dispersion and SPM [15]. We may also see a very distinct peak at 0 ps/nm, avoiding ambiguity at this dispersion value. Fig. 3 shows the simulation results for the RZ format. The curve is similar to the one of Fig. 2. This indicates that the theoretical approach is also similar to the one used in the sinusoidal format, indi 2 cating that the curve follows the form sin qf p .
1.8 1.6
References 1.4 1.2 −2500 −2000 −1500 −1000 −500
0
500
1000
1500
2000
2500
Chromatic dispersion(ps/nm) Fig. 2. Dispersion monitoring for a sinusoidal input modulation. Simulation and theoretical data are plotted. Theoretical data is plotted according to (14).
6
ratio
5
4
3
−500
0
500
Chromatic dispersion(ps/nm) Fig. 3. Dispersion monitoring for a return to zero modulation. Simulation data is plotted.
[1] B. Kozicki, A. Maruta, K.-i. Kitayama, Experimental investigation of delay-tap sampling technique for online monitoring of RZ-DQPSK signals, IEEE Photonic. Technol. Lett. 21 (3) (2009). [2] S.D. Dods, T.B. Anderson, Optical performance monitoring technique using delay tap asynchronous waveform sampling, in: Proc. OFC ’06, OThP5, 2006. [3] Y.K. Lize, L. Christen, J.-Y. Yang, P. Saghari, S. Nuccio, A.E. Willner, R. Kashyap, Independent and simultaneous monitoring of chromatic and polarizationmode dispersion in OOK and DPSK transmission, IEEE Photonic. Technol. Lett. 19 (1) (2007). [4] Z. Pan, Y. Xie, S.A. Havstad, Q. Yu, A.E. Willner, V. Grubsky, D.S. Starodubov, J. Feinberg, Real-time group-velocity dispersion monitoring and automated compensation without modifications of the transmitter, Opt. Commun. 230 (1-3) (2004) 145–149. [5] P.S. Westbrook, B.J. Eggleton, G. Raybon, S. Hunsche, Tsing Hua Her, Measurement of residual chromatic dispersion of a 40-Gb/s RZ signal via spectral broadening, IEEE Photonic. Technol. Lett. 14 (3) (2002). [6] Shenping Li, D.V. Kuksenkov, A novel dispersion monitoring technique based on four-wave mixing in optical fiber, IEEE Photonic. Technol. Lett. 16 (3) (2004). [7] T. Luo, C. Yu, Z. Pan, Y. Wang, J.E. Mcgeehan, M. Adler, A.E. Willner, All-optical chromatic dispersion monitoring of a 40-Gb/s RZ signal by measuring the XPM-generated optical tone power in a highly nonlinear fiber, IEEE Photonic. Technol. Lett. 18 (2) (2006). [8] K.J. Park, J.H. Lee, C.J. Youn, Y.C. Chung, A simultaneous monitoring technique for polarization-mode dispersion and group-velocity dispersion, WE4, OFC, 2002. [9] T. Inui, T. Komukai, K. Mori, T. Morioka, 160-gb/s adaptive dispersion equalization using an asynchronous dispersion-induced chirp monitor, J. Lightw. Technol. 23 (6) (2005). [10] K. Bondarczuk, P.J. Maguire, L.P. Barry, J. O’Dowd, W.H. Guo, M. Lynch, A.L. Bradley, J.F. Donegan, H. Folliot, H. Chromatic Dispersion Monitoring of 80-Gb/s OTDM Data Signal via Two-Photon Absorption in a Semiconductor Microcavity, vol. 19, No. 1, January 2007. [11] Zhongqi Pan, Changyuan Yu, Alan E. Willner, Optical performance monitoring for the next generation optical communication networks, Opt. Fiber Technol. 16 (1) (2010). [12] A. Teixeira, L. Costa, G. Frantzl, S. Azodolmolky, I. Tomkos, K. Vlachos, S. Zsigmond, T. Cinkler, G. Tosi Beleffi, P. Gravey, T. Loukina, J.A. Lázaro, C.
V. Ribeiro et al. / Optical Fiber Technology 16 (2010) 124–127 Vasquez, J. Montalvo, E. Le Rouzic, An integrated view on monitoring and compensation for dynamic optical networks from management to physical layer, Photon. Network Commun. (2009). [13] Kuen Ting Tsai, Winston I. Way, Chromatic dispersion monitoring using an optical delay-and-add filter, J. Lightw. Technol. 23 (11) (2005).
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[14] Stephan Wielandy, Michael Fishteyn, Benyuan Zhu, Optical performance monitoring using nonlinear detection, J. Lightw. Technol. 22 (3) (2004). [15] Govind P. Agrawal, Nonlinear Fiber Optics, fourth ed., Academic Press, Elsevier, 2007, pp. 89–102.