- Email: [email protected]
Experimental demonstration of impact of optical nonlinearity on photonic time stretched analog-to-digital converter based on photonic crystal fiber
Accepted Manuscript Title: Experimental demonstration of impact of optical nonlinearity on photonic time stretched analog-to-digital converter based on photonic crystal fiber Author: Sha Li Chongxiu Yu Zhe Kang Shuai Wei Gerald Farrell Qiang Wu PII: DOI: Reference:
S0030-4026(15)01229-2 http://dx.doi.org/doi:10.1016/j.ijleo.2015.09.160 IJLEO 56365
To appear in: Received date: Accepted date:
23-10-2014 9-9-2015
Please cite this article as: S. Li, C. Yu, Z. Kang, S. Wei, G. Farrell, Q. Wu, Experimental demonstration of impact of optical nonlinearity on photonic time stretched analog-todigital converter based on photonic crystal fiber, Optik - International Journal for Light and Electron Optics (2015), http://dx.doi.org/10.1016/j.ijleo.2015.09.160 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Experimental demonstration of impact of optical nonlinearity on photonic time stretched analog-to-digital converter based on photonic crystal fiber
Sha Li1)*, Chongxiu Yu2), Zhe Kang2), Shuai Wei2), Gerald Farrell3), Qiang Wu3)
ip t
1) School of Computer & Communication Engineering, University of Science & Technology Beijing, Beijing, China
cr
2) State key laboratory of Information Photonics and Optical communications, Beijing University of Posts and Telecommunications, Beijing, China
us
3) Photonic Research Centre, Dublin Institute of Technology, Dublin, Ireland
an
*Corresponding author:[email protected]
ce pt
ed
M
Abstract: photonic time stretched analog-to-digital converter (PTS-ADC) utilizes a broadband optical source and dispersion medium to expand the capabilities of electrical digitizers, achieving real-time sampling with high resolution. In order to minimize used fiber length and simplify PTS-ADC equipment, large dispersion photonic crystal fiber (PCF) is used as dispersion medium. In this letter we demonstrated the impact of optical nonlinearity on PTS-ADC based on large dispersion PCF performance as compared with single mode fiber (SMF) and dispersion compensation fiber (DCF). It is stimulated that dispersion penalty null frequency of fundamental tone will shift using three fibers when nonlinearity is added. In comparison, SMF is most insensitivity by changing input optical power, then PCF. However PCF is most insensitive by changing pulse width. Meanwhile, PCF is best to suppress 3rd-order harmonic distortion according to carrier-to-interference ratio (CIR) in three fibers. PCF is the most suitable as broadening medium in PTS-ADC. Keywords: photonic time-stretch analog-to-digital converter (PTS-ADC), photonic crystal fiber (PCF), optical Kerr nonlinearity, large dispersion, optical fiber communication, optical signal processing
Ac
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65
I. Introduction Analog-to-digital converter (ADC) plays a vital role in digital signal processing (DSP). Internet communication needs ADC that has high-resolution, high-bandwidth and high-capacity recently. High-quality ADC is used in military systems, biomedical imaging and industrial applications[1-5]. In military, the United States of America’s Defense Advanced Research Projects Agency has made a project about high-speed photoelectric ADC technology recently.
Page 1 of 11
As one of primary ADC schemes in international, Prof. Jalali group researches photonic time-stretch analog-to-digital converter (PTS-ADC) that can provide continuous digitization of ultrahigh-bandwidth electrical signals with high resolution, which cannot be achieved by electronic ADC[6-9]. The signal is modulated on time stretched optical pulses by Mach-Zehnder modulator, and then the modulated optical pulses are further stretched in another fiber. In their schemes, dispersion
ip t
compensation fiber (DCF) is used to provide a large dispersion-to-loss ratio with minimal phase distortion over a wide optical bandwidth in PTS-ADC. However,
cr
photonic crystal fiber (PCF) is a highlight in photoelectron field because of nearly
ideal controllable dispersion and high nonlinear, strong birefringence effect, ultra-long
us
distance transmission[10-18]. PCF gets different effect through devising its structure. For example, designed PCF with large dispersion shows high negative dispersion
an
coefficient, providing about 10 times dispersion compensation than DCF[19-27]. When multiple wavelength channels PTS-ADC is employed, intensity modulated optical pulses with high peak power are required. However, when high power pulses
and spectrum of optical pulses.
M
propagate inside fiber, both optical nonlinearity and dispersion influence the shape
ed
In this paper, we discuss the impact of optical Kerr nonlinearity on the performance of the PTS-ADC. The nonlinear interaction of the optical field is numerically simulated by the split-step Fourier method. In the system, SMF, DCF and
ce pt
PCF are used as dispersion medium respectively. We stimulate dispersion penalty of fundamental tone and 3rd-order harmonic distortion versus the frequency of the radio frequency (RF) signal for SMF, DCF and PCF. Moreover, dispersion null frequency versus optical power and optical pulse width for different fibers are stimulated. We show that carrier-to-interference ratio (CIR) of the PTS-ADC versus the frequency of
Ac
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65
the RF signal for the three fibers, PCF is best to suppress 3rd-order harmonic distortion.
II. Photonic time-stretch analog-to-digital converter based on large dispersion PCF The PTS-ADC stretches the RF signal in time by employing a broadband optical source, the PTS-ADC scheme is illustrated in figure 1. A mode-locked laser as a broadband optical source follows a segment of PCF as dispersion medium. The RF signal is modulated on the stretched optical pulses using Mach-Zehnder modulator. The modulated optical pulses are further stretched in another segment of PCF in time.
Page 2 of 11
In order to minimize used fiber and simplify device, large dispersion PCF is used as dispersion medium with minimal phase distortion. In the scheme, the PCF constitutes of three different air-hole diameters, as shown in figure 1,
d1 0.609 m
is shown
by white color, d2 0.407 m is shown by red color and d3 0.825 m is yellow color. The air-holes are regularly spaced in a hexagonal array with a lattice constant
ip t
1.375 m . The PCF has a very high negative dispersion coefficient -1400
ps/nm/km at 1520 nm. Simulation results show the PCF with 1.14 km can compensate
cr
for the dispersion accumulated in a span 80 km of SMF and accumulate negative
PCF is only 2.21 /W/km at 1520 nm[23,24].
PCF
Mach-Zehnder Modulator
PCF
PD
an
Mode-Locked Laser
us
dispersion which DCF with 16 km achieves. Meanwhile, nonlinear coefficient of the
M
RF Source
ed
Figure 1. block diagram of the PTS-ADC based on large dispersion PCF. Insert diagram is transverse cross-section of the large dispersion PCF. In order to operate multiple wavelength channels, it is desirable to utilize high
ce pt
optical power in the PTS-ADC system. However, high intensity causes the pulse propagation to deviate from the linear regime. Therefore, it is imperative to consider the effect of fiber nonlinearity (Kerr effect) on the performance of the PTS-ADC. The basic equation that governs the propagation of optical pulses in the presence of dispersion and optical nonlinearity is the nonlinear Schrodinger equation (NLSE)[28]
Ac
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65
A i 2 2 A 2 A i A A (1) 2 z 2 z 2
where is the attenuation constant, 2 is the second derivative with respect to angular frequency of the modal wave number, is the nonlinear coefficient related to the nonlinear index, A is the slowly varying envelope proportional to the optical field. Equation has been successful in explaining a large number of nonlinear effects, self-phase modulation and four-wave mixing, which are the main causes of nonlinear optical distortions in the PTS-ADC.
Page 3 of 11
To suppose that optical pulse is Gaussian with pulse width T0 and power P0 at beginning. After the first segment of PCF with length L1 and group velocity dispersion (GVD) parameter 2 . The envelope is given by in time
2
and z, t L z, t
zt 2 / LD 1 tan 1 z / LD , 2T 2 z 2
cr
where T z T0 1 z / LD
ip t
t2
P0T0 i z ,t T 2 z (2) Ac z, t e e T z
us
LD is dispersion length, t is time and z is propagation distance. After the first PCF, the optical pulse envelope maintains Gaussian profile because of weak
equation[29,30]
z L1
NL z, t Ac z , t dz z
2
L1
(3).
M
z, t L z, t NL z, t
an
nonlinearity. In the second PCF, nonlinear phase is added that effect on RF signal in
ed
III. Simulations and results The PTS-ADC configuration is shown as figure 1. The first fiber is used to
ce pt
stretch optical pulses to suitable time aperture and the second fiber is adopted to stretch modulated optical pulses in time, respectively. Through designing the length of two fibers, a stretched factor of 10 is easily provided. The sinusoidal transfer function of the Mach-Zehnder modulator followed by GVD generates the RF signal sidebands and their harmonics. Many techniques have been developed to mitigate or cancel out
Ac
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65
these harmonic distortions. If a dual-output push-pull Mach-Zehnder modulator is adopted, the even-order distortions will be cancel out, however, the odd-order distortions cannot be fully eliminated due to frequency dependent phase shift. In particular, the 3rd-order distortion limits the performance of the PTS-ADC. The dispersion penalty for the fundamental tone and 3rd-order harmonic distortion by SMF, DCF and PCF as dispersion medium is illustrated in figure 2 and figure 3 with constant transmitted optical power (300 mW), respectively. The dispersion penalty exists in the linear-optical regime, however, nonlinearity causes a
Page 4 of 11
shift in the dispersion penalty null frequency using SMF, DCF or PCF as dispersion medium. This shift can be explained by introducing the nonlinear phase term in equation (3). In figure 2 and figure 3, the curves with no nonlinearity almost overlap using three fibers. So linearity dispersion penalty of fundamental tone or 3rd-order harmonic distortion is almost same regardless of what kind of fiber. While the
ip t
nonlinear phase is added in the second fiber, nonlinearity causes different shifts in the dispersion penalty null frequency by different dispersion medium. On the transmitted
cr
optical power and the input optical pulse width, the null frequency using SMF and
us
DCF as dispersion medium shifts ~15 GHz and 27 GHz, respectively. However, the one using PCF only shifts ~1 GHz. As we know, the linearity dispersion penalty of the fundamental tone is periodic, nonlinearity dispersion penalty of the one will overlap
an
with linearity curve using any fiber as dispersion medium. So we can choose suitable transmitted optical power and input pulse width to close the linearity dispersion
M
penalty curve and restrain nonlinearity possibly. As shown in figure 3, nonlinearity dispersion penalty curves of 3rd-order harmonic distortion become irregular jitters
ed
compared with linearity ones. While nonlinearity phase is considered, 3rd-order harmonic distortion cannot be suppressed preferably. he he linear-optical regime,
ce pt
however, nonlinearity causes a shift in the dispersion penalty null freq
Ac
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65
Figure 2 dispersion penalty of the fundamental tone for SMF, DCF and PCF as dispersion medium.
Page 5 of 11
ip t cr
us
Figure 3 dispersion penalty of the 3rd-order harmonic distortion for SMF, DCF and PCF as dispersion medium. A set of simulations was performed to understand the behavior of the dispersion
an
null frequency versus optical power and input optical pulse width using three fibers as dispersion medium. As illustrated in figure 4, the null frequency goes to lower
M
frequencies for higher optical powers whatever fibers. Because of periodicity of dispersion penalty, a new nonlinearity null frequency will draw near the linearity one when the original one's gone. As shown in figure 4, the slope of curve using SMF as
ed
dispersion medium is minimum, second is one using PCF, the largest is one using DCF. The null frequency by DCF shifts sensitively changing optical power and
ce pt
fluctuates once every 10 mW, so the curve is only recorded between 50~70 mW. The one by SMF is not sensitive increasing optical power. The sensitivity of PCF is between SMF and DCF.
Ac
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65
Figure 4 dispersion null frequency versus transmitted optical power for different fibers with constant input optical pulse width (100 ps).
Page 6 of 11
(b)
cr
ip t
(a)
an
us
(c)
M
Figure 5 dispersion null frequency versus optical pulse width for (a) SMF, (b) DCF and (c) PCF with constant transmitted optical power (300 mW).
ed
As shown in figure 5(a), the null frequency goes to higher frequencies for larger optical pulse width using SMF as dispersion medium, and the null frequency goes to
ce pt
lower frequencies for larger optical pulse width using DCF and PCF as dispersion medium in figure 5(b) and 5(c), which is due to the dependence of nonlinear phase shift on positive or negative of group velocity dispersion constant. The null frequency by SMF shifts sensitively changing optical pulse width, the one by PCF is not sensitive increasing optical pulse width, and the sensitivity of DCF is between SMF
Ac
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65
and PCF.
As we know, fiber is used as dispersion medium to stretch pulses in the
PTS-ADC. However, the performance that PCF resists change of optical power is between one of SMF and DCF, PCF is the most insensitive by changing optical pulse width.
Page 7 of 11
ip t cr us
Figure 6 carrier-to-interference ratio (CIR) of the PTS-ADC versus the frequency of the RF signal for different fibers with constant optical power (300 mW).
an
Because 3rd-order distortion limits the performance of the whole system, the CIR in the PTS-ADC is defined as the ratio of the fundamental tone to the 3rd-order
M
harmonic. The figure 6 shows the CIR versus the frequency of the RF signal for SMF, DCF and PCF as dispersion medium while the optical power of the optical source is
ed
constant (300 mW). Optical nonlinearity can greatly degrade the CIR whatever any fiber is used as dispersion medium. The CIR of PCF improves the most area in
ce pt
comparison with the ones of SMF and DCF. IV Conclusion
In this paper, we have researched the impact of PCF nonlinearity on PTS-ADC as compared with SMF and DCF. We showed dispersion penalty of fundamental tone and 3rd-order harmonic distortion versus the frequency of the RF signal for SMF,
Ac
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65
DCF and PCF as dispersion medium. Moreover, dispersion null frequency versus optical power and optical pulse width for three fibers are stimulated. We show the CIR of the PTS-ADC versus the frequency of the RF signal for the three fibers. PCF has highest dispersion coefficient and smallest nonlinear coefficient, it is most insensitive by changing pulse width in the PTS-ADC. According to CIR, PCF is best to suppress 3rd-order harmonic distortion with considering fiber nonlinearity. In the PTS-ADC, PCF is the most suitable as dispersion medium.
Page 8 of 11
Reference [1] H.F. Taylor, “An optical analog-to-digital converter degian and analysis”. IEEE J. Quantumn Electron., 1975, QE-15(4):210-216. [2] A. Yariv and R.G.M.P. Koumans. “Time interleaved optical sampling form untrahigh speed A/D conversion”, IEE Electron. Lett.1998, 34(21):2012-2013. [3] M.Y. Frankel, J.U. Kang and R.D. Esman.“High performance photonic
ip t
analogue-digitalconverter”. IEE Electron. Lett.1997, 33(25):2096-2097.
[4] J. Chou, O. Boyraz, D. Solli and B. Jalali. “Femtosecond real-time single-shot
cr
digitizer”. Appl. Phys. Lett., 2007, 91(161105):1-3.
[5] J. Stigwall and S. Galt. “Demonstration and analysis of a 40-Gigasample/s
us
interferometric analog-to-digital converter”. J. Lightwave Technol. 2006, 24(3):1247-1256.
[6] Y. Han and B. Jalali, “Photonic time-stretched analog-to-digital converter:
an
Fundamental concepts and practical considerations,”J. Lightw. Technol, vol.21, no.12, pp. 3085-3103, Dec.2003.
M
[7] Y. Han and B. Jalali, Ultra-wideband signal detection using photonic signal preprocessing, 2005, LEOS summer topical meetings. [8] Y. Han and B. Jalali, “Ultrawide-band photonic time-stretch A/D converter
ed
employing phase diversity,”IEEE Transactions on microwave theory and techniques, vol.53, no.4, April 2005.
ce pt
[9] Y. Han and Bahram Jalali, “One Tera-Sample/sec Real-Time Transient Digitizer”, IMTC 2005-Instrumentation and Measurement Technology Conference Ottawa, Canada, 17-19 May 2005.
[10] Wang Jian, Lei Nai-Guang and Yu Chong-xiu. "Design of Micrstructrued Optical Fibres with Elliptical Air Holes for Properties: Single-Polarization Single-Mode and Nearly Zero Ultra-Flattened Dispersion". Chin. Phys. Lett., 2007,
Ac
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65
24(8):2255-2258.
[11] Knight J C, Birks B A, Russell P St J, et al., "All-silica single-mode optical fiber with photonic crystal cladding". Opt. Lett., 1996, 21:1547-1549. [12] Birks T. A., Roberts P. J., Russell P. S. J., Atkin D. M., and Shepherd T. J., "Full 2-D Photonic Bandgaps in Silica/Air Structures". Electronics Letters, 1995, 31:1941-1943. [13] P. Petropoulos, H. Ebendorff-Heidepriem, V. Finazzi, R.C. Moore, K. Frampton, D.J. Richardson, T. M. Monro, "Highly nonlinear and anomalously dispersive lead silicate glass holey fibers". Optics Express, 2003, 11:3568-3573.
Page 9 of 11
[14] Monro T. M., Richardson D. J., Broerick N. G. R, et al., "Modeling large air freaction holey optical fiber". J. Lightwave Technol., 2003, 21(2):138-142. [15] Q.Y.Wang, M.L.Hu and L.Chai. Progress in Nonlinear Optics with Photonic Crystal Fibers. Chin.J.Laser, 33(1), 2006, pp.57-66. [16] M.P.Hiscocks, M.A. van Eijkelenborg, A.Argyros, et al., Stable inpringting of long-period gratings in microstructured polymer Optical Fibre, Opt. Express,
ip t
14(11), 2006, pp.4644-4649.
[17] M.A.van Eijkelenborg, A.Argyros, G.Batron, et al., Recent progress in
cr
microstructured polymer optical fibre fabrication and characterisation, Opt.Fiber Technol., 9(4), 2003, pp.199-209.
us
[18] P.G.Yan, Y.Q.Jia, H.X.Su, et al., Broadband Continuum Generation in an Irregularly Multicore Micrstructured Optical Fiber, Chin. Opt. Lett., 3(6), 2005,
an
pp.355-357.
[19] Z. Yusoff, J.H. Lee, W. Belardi, T.M.Monro, P.C. Teh, and D. J. Richardson, Opt. Lett. 27, 424-426 (2002).
M
“Raman effects in a highly nonlinear holey fiber: amplification and modulation,” [20] C.J.S. de Matos, K. P. Hansen, and J. R. Taylor, “Experimental characterization of Raman gain efficiency of holey fiber,” Electron. Lett. 39, 424-425 (2003).
ed
[21] M. Bottacini, F. Poli, A. Cucinotta, and S. Selleri, “Modeling of photonic crystal fiber Raman amplifiers,” J. Lightwave Technol. 22, 1707-1713 (2004).
ce pt
[22] S.K. Varshney, K. Saitoh, and M. Koshiba, “Raman performances of ultralow loss photonic crystal fiber amplifiers,” in Proc. Lasers and Electro-Optics (IQEC/CLEO-PR 2005), paper no. CWE2-3, (2005). [23] S.K. Varshney, K. Saitoh, and M. Koshiba, “A novel design of dispersion compensating photonic crystal fiber Raman amplifier,” IEEE Photon. Technol.
Ac
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65
Lett. 17, 2062-2064 (2005).
[24] S.K. Varshney, T. Fujisawa, K. Saitoh, and M. Koshiba, “Novel design of inherently gain-flattened discrete highly nonlinear photonic crystal fiber Raman amplifier and dispersion compensation using a single pump in C-band,” Opt. Express 13, 9516-9526 (2005). [25] S.K. Varshney, K. Saitoh, T. Fujisawa, and M. Koshiba, “Design of gain-flattened highly nonlinear photonic crystal fiber Raman amplifier using a single pump: a leakage approach,” in Proc. Optical Fiber Communication (OFC/NFOEC), paper no. OWD4, (2006).
Page 10 of 11
[26] T.A. Birks, J.C. Knight, and P.St.J. Russell, “Endlessly single-mode photonic crystal fiber,” Opt. Lett. 22, 961-963 (1997). [27] A. Bjarklev, J. Broeng, and A.S. Bjarklev, Photonic Crystal Fibres (Kulwer Academic Publishers 2003). [28] G.P. Agrawal, Nonlinear Fiber Optics, 3rded. New York: Academic, 2001,ch.3. fibers,” Phys. Rev. A, vol. 27, pp. 3135–3145, Jun. 1983.
ip t
[29] D. Anderson, “Variational approach to nonlinear pulse propagation in optical [30] S. Gupta, B. Jalali, J. Stigwall, and S. Gait, “Demonstration of distortion
cr
suppression in photonic time-stretch ADC using back propagation method,” in
ce pt
ed
M
an
us
Proc. IEEE Int. Topical Meeting Microw. Photon., 2007, pp. 141–144.
Ac
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65
Page 11 of 11
S0030-4026(15)01229-2 http://dx.doi.org/doi:10.1016/j.ijleo.2015.09.160 IJLEO 56365
To appear in: Received date: Accepted date:
23-10-2014 9-9-2015
Please cite this article as: S. Li, C. Yu, Z. Kang, S. Wei, G. Farrell, Q. Wu, Experimental demonstration of impact of optical nonlinearity on photonic time stretched analog-todigital converter based on photonic crystal fiber, Optik - International Journal for Light and Electron Optics (2015), http://dx.doi.org/10.1016/j.ijleo.2015.09.160 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Experimental demonstration of impact of optical nonlinearity on photonic time stretched analog-to-digital converter based on photonic crystal fiber
Sha Li1)*, Chongxiu Yu2), Zhe Kang2), Shuai Wei2), Gerald Farrell3), Qiang Wu3)
ip t
1) School of Computer & Communication Engineering, University of Science & Technology Beijing, Beijing, China
cr
2) State key laboratory of Information Photonics and Optical communications, Beijing University of Posts and Telecommunications, Beijing, China
us
3) Photonic Research Centre, Dublin Institute of Technology, Dublin, Ireland
an
*Corresponding author:[email protected]
ce pt
ed
M
Abstract: photonic time stretched analog-to-digital converter (PTS-ADC) utilizes a broadband optical source and dispersion medium to expand the capabilities of electrical digitizers, achieving real-time sampling with high resolution. In order to minimize used fiber length and simplify PTS-ADC equipment, large dispersion photonic crystal fiber (PCF) is used as dispersion medium. In this letter we demonstrated the impact of optical nonlinearity on PTS-ADC based on large dispersion PCF performance as compared with single mode fiber (SMF) and dispersion compensation fiber (DCF). It is stimulated that dispersion penalty null frequency of fundamental tone will shift using three fibers when nonlinearity is added. In comparison, SMF is most insensitivity by changing input optical power, then PCF. However PCF is most insensitive by changing pulse width. Meanwhile, PCF is best to suppress 3rd-order harmonic distortion according to carrier-to-interference ratio (CIR) in three fibers. PCF is the most suitable as broadening medium in PTS-ADC. Keywords: photonic time-stretch analog-to-digital converter (PTS-ADC), photonic crystal fiber (PCF), optical Kerr nonlinearity, large dispersion, optical fiber communication, optical signal processing
Ac
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65
I. Introduction Analog-to-digital converter (ADC) plays a vital role in digital signal processing (DSP). Internet communication needs ADC that has high-resolution, high-bandwidth and high-capacity recently. High-quality ADC is used in military systems, biomedical imaging and industrial applications[1-5]. In military, the United States of America’s Defense Advanced Research Projects Agency has made a project about high-speed photoelectric ADC technology recently.
Page 1 of 11
As one of primary ADC schemes in international, Prof. Jalali group researches photonic time-stretch analog-to-digital converter (PTS-ADC) that can provide continuous digitization of ultrahigh-bandwidth electrical signals with high resolution, which cannot be achieved by electronic ADC[6-9]. The signal is modulated on time stretched optical pulses by Mach-Zehnder modulator, and then the modulated optical pulses are further stretched in another fiber. In their schemes, dispersion
ip t
compensation fiber (DCF) is used to provide a large dispersion-to-loss ratio with minimal phase distortion over a wide optical bandwidth in PTS-ADC. However,
cr
photonic crystal fiber (PCF) is a highlight in photoelectron field because of nearly
ideal controllable dispersion and high nonlinear, strong birefringence effect, ultra-long
us
distance transmission[10-18]. PCF gets different effect through devising its structure. For example, designed PCF with large dispersion shows high negative dispersion
an
coefficient, providing about 10 times dispersion compensation than DCF[19-27]. When multiple wavelength channels PTS-ADC is employed, intensity modulated optical pulses with high peak power are required. However, when high power pulses
and spectrum of optical pulses.
M
propagate inside fiber, both optical nonlinearity and dispersion influence the shape
ed
In this paper, we discuss the impact of optical Kerr nonlinearity on the performance of the PTS-ADC. The nonlinear interaction of the optical field is numerically simulated by the split-step Fourier method. In the system, SMF, DCF and
ce pt
PCF are used as dispersion medium respectively. We stimulate dispersion penalty of fundamental tone and 3rd-order harmonic distortion versus the frequency of the radio frequency (RF) signal for SMF, DCF and PCF. Moreover, dispersion null frequency versus optical power and optical pulse width for different fibers are stimulated. We show that carrier-to-interference ratio (CIR) of the PTS-ADC versus the frequency of
Ac
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65
the RF signal for the three fibers, PCF is best to suppress 3rd-order harmonic distortion.
II. Photonic time-stretch analog-to-digital converter based on large dispersion PCF The PTS-ADC stretches the RF signal in time by employing a broadband optical source, the PTS-ADC scheme is illustrated in figure 1. A mode-locked laser as a broadband optical source follows a segment of PCF as dispersion medium. The RF signal is modulated on the stretched optical pulses using Mach-Zehnder modulator. The modulated optical pulses are further stretched in another segment of PCF in time.
Page 2 of 11
In order to minimize used fiber and simplify device, large dispersion PCF is used as dispersion medium with minimal phase distortion. In the scheme, the PCF constitutes of three different air-hole diameters, as shown in figure 1,
d1 0.609 m
is shown
by white color, d2 0.407 m is shown by red color and d3 0.825 m is yellow color. The air-holes are regularly spaced in a hexagonal array with a lattice constant
ip t
1.375 m . The PCF has a very high negative dispersion coefficient -1400
ps/nm/km at 1520 nm. Simulation results show the PCF with 1.14 km can compensate
cr
for the dispersion accumulated in a span 80 km of SMF and accumulate negative
PCF is only 2.21 /W/km at 1520 nm[23,24].
PCF
Mach-Zehnder Modulator
PCF
PD
an
Mode-Locked Laser
us
dispersion which DCF with 16 km achieves. Meanwhile, nonlinear coefficient of the
M
RF Source
ed
Figure 1. block diagram of the PTS-ADC based on large dispersion PCF. Insert diagram is transverse cross-section of the large dispersion PCF. In order to operate multiple wavelength channels, it is desirable to utilize high
ce pt
optical power in the PTS-ADC system. However, high intensity causes the pulse propagation to deviate from the linear regime. Therefore, it is imperative to consider the effect of fiber nonlinearity (Kerr effect) on the performance of the PTS-ADC. The basic equation that governs the propagation of optical pulses in the presence of dispersion and optical nonlinearity is the nonlinear Schrodinger equation (NLSE)[28]
Ac
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65
A i 2 2 A 2 A i A A (1) 2 z 2 z 2
where is the attenuation constant, 2 is the second derivative with respect to angular frequency of the modal wave number, is the nonlinear coefficient related to the nonlinear index, A is the slowly varying envelope proportional to the optical field. Equation has been successful in explaining a large number of nonlinear effects, self-phase modulation and four-wave mixing, which are the main causes of nonlinear optical distortions in the PTS-ADC.
Page 3 of 11
To suppose that optical pulse is Gaussian with pulse width T0 and power P0 at beginning. After the first segment of PCF with length L1 and group velocity dispersion (GVD) parameter 2 . The envelope is given by in time
2
and z, t L z, t
zt 2 / LD 1 tan 1 z / LD , 2T 2 z 2
cr
where T z T0 1 z / LD
ip t
t2
P0T0 i z ,t T 2 z (2) Ac z, t e e T z
us
LD is dispersion length, t is time and z is propagation distance. After the first PCF, the optical pulse envelope maintains Gaussian profile because of weak
equation[29,30]
z L1
NL z, t Ac z , t dz z
2
L1
(3).
M
z, t L z, t NL z, t
an
nonlinearity. In the second PCF, nonlinear phase is added that effect on RF signal in
ed
III. Simulations and results The PTS-ADC configuration is shown as figure 1. The first fiber is used to
ce pt
stretch optical pulses to suitable time aperture and the second fiber is adopted to stretch modulated optical pulses in time, respectively. Through designing the length of two fibers, a stretched factor of 10 is easily provided. The sinusoidal transfer function of the Mach-Zehnder modulator followed by GVD generates the RF signal sidebands and their harmonics. Many techniques have been developed to mitigate or cancel out
Ac
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65
these harmonic distortions. If a dual-output push-pull Mach-Zehnder modulator is adopted, the even-order distortions will be cancel out, however, the odd-order distortions cannot be fully eliminated due to frequency dependent phase shift. In particular, the 3rd-order distortion limits the performance of the PTS-ADC. The dispersion penalty for the fundamental tone and 3rd-order harmonic distortion by SMF, DCF and PCF as dispersion medium is illustrated in figure 2 and figure 3 with constant transmitted optical power (300 mW), respectively. The dispersion penalty exists in the linear-optical regime, however, nonlinearity causes a
Page 4 of 11
shift in the dispersion penalty null frequency using SMF, DCF or PCF as dispersion medium. This shift can be explained by introducing the nonlinear phase term in equation (3). In figure 2 and figure 3, the curves with no nonlinearity almost overlap using three fibers. So linearity dispersion penalty of fundamental tone or 3rd-order harmonic distortion is almost same regardless of what kind of fiber. While the
ip t
nonlinear phase is added in the second fiber, nonlinearity causes different shifts in the dispersion penalty null frequency by different dispersion medium. On the transmitted
cr
optical power and the input optical pulse width, the null frequency using SMF and
us
DCF as dispersion medium shifts ~15 GHz and 27 GHz, respectively. However, the one using PCF only shifts ~1 GHz. As we know, the linearity dispersion penalty of the fundamental tone is periodic, nonlinearity dispersion penalty of the one will overlap
an
with linearity curve using any fiber as dispersion medium. So we can choose suitable transmitted optical power and input pulse width to close the linearity dispersion
M
penalty curve and restrain nonlinearity possibly. As shown in figure 3, nonlinearity dispersion penalty curves of 3rd-order harmonic distortion become irregular jitters
ed
compared with linearity ones. While nonlinearity phase is considered, 3rd-order harmonic distortion cannot be suppressed preferably. he he linear-optical regime,
ce pt
however, nonlinearity causes a shift in the dispersion penalty null freq
Ac
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65
Figure 2 dispersion penalty of the fundamental tone for SMF, DCF and PCF as dispersion medium.
Page 5 of 11
ip t cr
us
Figure 3 dispersion penalty of the 3rd-order harmonic distortion for SMF, DCF and PCF as dispersion medium. A set of simulations was performed to understand the behavior of the dispersion
an
null frequency versus optical power and input optical pulse width using three fibers as dispersion medium. As illustrated in figure 4, the null frequency goes to lower
M
frequencies for higher optical powers whatever fibers. Because of periodicity of dispersion penalty, a new nonlinearity null frequency will draw near the linearity one when the original one's gone. As shown in figure 4, the slope of curve using SMF as
ed
dispersion medium is minimum, second is one using PCF, the largest is one using DCF. The null frequency by DCF shifts sensitively changing optical power and
ce pt
fluctuates once every 10 mW, so the curve is only recorded between 50~70 mW. The one by SMF is not sensitive increasing optical power. The sensitivity of PCF is between SMF and DCF.
Ac
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65
Figure 4 dispersion null frequency versus transmitted optical power for different fibers with constant input optical pulse width (100 ps).
Page 6 of 11
(b)
cr
ip t
(a)
an
us
(c)
M
Figure 5 dispersion null frequency versus optical pulse width for (a) SMF, (b) DCF and (c) PCF with constant transmitted optical power (300 mW).
ed
As shown in figure 5(a), the null frequency goes to higher frequencies for larger optical pulse width using SMF as dispersion medium, and the null frequency goes to
ce pt
lower frequencies for larger optical pulse width using DCF and PCF as dispersion medium in figure 5(b) and 5(c), which is due to the dependence of nonlinear phase shift on positive or negative of group velocity dispersion constant. The null frequency by SMF shifts sensitively changing optical pulse width, the one by PCF is not sensitive increasing optical pulse width, and the sensitivity of DCF is between SMF
Ac
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65
and PCF.
As we know, fiber is used as dispersion medium to stretch pulses in the
PTS-ADC. However, the performance that PCF resists change of optical power is between one of SMF and DCF, PCF is the most insensitive by changing optical pulse width.
Page 7 of 11
ip t cr us
Figure 6 carrier-to-interference ratio (CIR) of the PTS-ADC versus the frequency of the RF signal for different fibers with constant optical power (300 mW).
an
Because 3rd-order distortion limits the performance of the whole system, the CIR in the PTS-ADC is defined as the ratio of the fundamental tone to the 3rd-order
M
harmonic. The figure 6 shows the CIR versus the frequency of the RF signal for SMF, DCF and PCF as dispersion medium while the optical power of the optical source is
ed
constant (300 mW). Optical nonlinearity can greatly degrade the CIR whatever any fiber is used as dispersion medium. The CIR of PCF improves the most area in
ce pt
comparison with the ones of SMF and DCF. IV Conclusion
In this paper, we have researched the impact of PCF nonlinearity on PTS-ADC as compared with SMF and DCF. We showed dispersion penalty of fundamental tone and 3rd-order harmonic distortion versus the frequency of the RF signal for SMF,
Ac
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65
DCF and PCF as dispersion medium. Moreover, dispersion null frequency versus optical power and optical pulse width for three fibers are stimulated. We show the CIR of the PTS-ADC versus the frequency of the RF signal for the three fibers. PCF has highest dispersion coefficient and smallest nonlinear coefficient, it is most insensitive by changing pulse width in the PTS-ADC. According to CIR, PCF is best to suppress 3rd-order harmonic distortion with considering fiber nonlinearity. In the PTS-ADC, PCF is the most suitable as dispersion medium.
Page 8 of 11
Reference [1] H.F. Taylor, “An optical analog-to-digital converter degian and analysis”. IEEE J. Quantumn Electron., 1975, QE-15(4):210-216. [2] A. Yariv and R.G.M.P. Koumans. “Time interleaved optical sampling form untrahigh speed A/D conversion”, IEE Electron. Lett.1998, 34(21):2012-2013. [3] M.Y. Frankel, J.U. Kang and R.D. Esman.“High performance photonic
ip t
analogue-digitalconverter”. IEE Electron. Lett.1997, 33(25):2096-2097.
[4] J. Chou, O. Boyraz, D. Solli and B. Jalali. “Femtosecond real-time single-shot
cr
digitizer”. Appl. Phys. Lett., 2007, 91(161105):1-3.
[5] J. Stigwall and S. Galt. “Demonstration and analysis of a 40-Gigasample/s
us
interferometric analog-to-digital converter”. J. Lightwave Technol. 2006, 24(3):1247-1256.
[6] Y. Han and B. Jalali, “Photonic time-stretched analog-to-digital converter:
an
Fundamental concepts and practical considerations,”J. Lightw. Technol, vol.21, no.12, pp. 3085-3103, Dec.2003.
M
[7] Y. Han and B. Jalali, Ultra-wideband signal detection using photonic signal preprocessing, 2005, LEOS summer topical meetings. [8] Y. Han and B. Jalali, “Ultrawide-band photonic time-stretch A/D converter
ed
employing phase diversity,”IEEE Transactions on microwave theory and techniques, vol.53, no.4, April 2005.
ce pt
[9] Y. Han and Bahram Jalali, “One Tera-Sample/sec Real-Time Transient Digitizer”, IMTC 2005-Instrumentation and Measurement Technology Conference Ottawa, Canada, 17-19 May 2005.
[10] Wang Jian, Lei Nai-Guang and Yu Chong-xiu. "Design of Micrstructrued Optical Fibres with Elliptical Air Holes for Properties: Single-Polarization Single-Mode and Nearly Zero Ultra-Flattened Dispersion". Chin. Phys. Lett., 2007,
Ac
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65
24(8):2255-2258.
[11] Knight J C, Birks B A, Russell P St J, et al., "All-silica single-mode optical fiber with photonic crystal cladding". Opt. Lett., 1996, 21:1547-1549. [12] Birks T. A., Roberts P. J., Russell P. S. J., Atkin D. M., and Shepherd T. J., "Full 2-D Photonic Bandgaps in Silica/Air Structures". Electronics Letters, 1995, 31:1941-1943. [13] P. Petropoulos, H. Ebendorff-Heidepriem, V. Finazzi, R.C. Moore, K. Frampton, D.J. Richardson, T. M. Monro, "Highly nonlinear and anomalously dispersive lead silicate glass holey fibers". Optics Express, 2003, 11:3568-3573.
Page 9 of 11
[14] Monro T. M., Richardson D. J., Broerick N. G. R, et al., "Modeling large air freaction holey optical fiber". J. Lightwave Technol., 2003, 21(2):138-142. [15] Q.Y.Wang, M.L.Hu and L.Chai. Progress in Nonlinear Optics with Photonic Crystal Fibers. Chin.J.Laser, 33(1), 2006, pp.57-66. [16] M.P.Hiscocks, M.A. van Eijkelenborg, A.Argyros, et al., Stable inpringting of long-period gratings in microstructured polymer Optical Fibre, Opt. Express,
ip t
14(11), 2006, pp.4644-4649.
[17] M.A.van Eijkelenborg, A.Argyros, G.Batron, et al., Recent progress in
cr
microstructured polymer optical fibre fabrication and characterisation, Opt.Fiber Technol., 9(4), 2003, pp.199-209.
us
[18] P.G.Yan, Y.Q.Jia, H.X.Su, et al., Broadband Continuum Generation in an Irregularly Multicore Micrstructured Optical Fiber, Chin. Opt. Lett., 3(6), 2005,
an
pp.355-357.
[19] Z. Yusoff, J.H. Lee, W. Belardi, T.M.Monro, P.C. Teh, and D. J. Richardson, Opt. Lett. 27, 424-426 (2002).
M
“Raman effects in a highly nonlinear holey fiber: amplification and modulation,” [20] C.J.S. de Matos, K. P. Hansen, and J. R. Taylor, “Experimental characterization of Raman gain efficiency of holey fiber,” Electron. Lett. 39, 424-425 (2003).
ed
[21] M. Bottacini, F. Poli, A. Cucinotta, and S. Selleri, “Modeling of photonic crystal fiber Raman amplifiers,” J. Lightwave Technol. 22, 1707-1713 (2004).
ce pt
[22] S.K. Varshney, K. Saitoh, and M. Koshiba, “Raman performances of ultralow loss photonic crystal fiber amplifiers,” in Proc. Lasers and Electro-Optics (IQEC/CLEO-PR 2005), paper no. CWE2-3, (2005). [23] S.K. Varshney, K. Saitoh, and M. Koshiba, “A novel design of dispersion compensating photonic crystal fiber Raman amplifier,” IEEE Photon. Technol.
Ac
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65
Lett. 17, 2062-2064 (2005).
[24] S.K. Varshney, T. Fujisawa, K. Saitoh, and M. Koshiba, “Novel design of inherently gain-flattened discrete highly nonlinear photonic crystal fiber Raman amplifier and dispersion compensation using a single pump in C-band,” Opt. Express 13, 9516-9526 (2005). [25] S.K. Varshney, K. Saitoh, T. Fujisawa, and M. Koshiba, “Design of gain-flattened highly nonlinear photonic crystal fiber Raman amplifier using a single pump: a leakage approach,” in Proc. Optical Fiber Communication (OFC/NFOEC), paper no. OWD4, (2006).
Page 10 of 11
[26] T.A. Birks, J.C. Knight, and P.St.J. Russell, “Endlessly single-mode photonic crystal fiber,” Opt. Lett. 22, 961-963 (1997). [27] A. Bjarklev, J. Broeng, and A.S. Bjarklev, Photonic Crystal Fibres (Kulwer Academic Publishers 2003). [28] G.P. Agrawal, Nonlinear Fiber Optics, 3rded. New York: Academic, 2001,ch.3. fibers,” Phys. Rev. A, vol. 27, pp. 3135–3145, Jun. 1983.
ip t
[29] D. Anderson, “Variational approach to nonlinear pulse propagation in optical [30] S. Gupta, B. Jalali, J. Stigwall, and S. Gait, “Demonstration of distortion
cr
suppression in photonic time-stretch ADC using back propagation method,” in
ce pt
ed
M
an
us
Proc. IEEE Int. Topical Meeting Microw. Photon., 2007, pp. 141–144.
Ac
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65
Page 11 of 11