Lasers, Fiber Optics, and Communications

Nonlinear distortion evaluation in a directly modulated distributed feedback laser diode-based fiber-optic cable television transport system

[+] Author Affiliations
Chung-Yi Li, Chun-Yu Lin, Chien-An Chu

National Taipei University of Technology, Institute of Electro-Optical Engineering, 1, Sec. 3, Zhongxiao East Road, Taipei 10608, Taiwan

Cheng-Ling Ying

Jinwen University of Science and Technology, Department of Electronic Engineering, 99, Anzhong Road, Xindian District, New Taipei City 23154, Taiwan

Opt. Eng. 54(12), 126112 (Dec 23, 2015). doi:10.1117/1.OE.54.12.126112
History: Received September 8, 2015; Accepted December 4, 2015
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Abstract.  This study evaluated a directly modulated distributed feedback (DFB) laser diode (LD) for cable TV systems with respect to carrier-to-nonlinear distortion of LDs. The second-order distortion-to-carrier ratio is found to be proportional to that of the second-order coefficient-to-first-order coefficient of the DFB laser diode driving current and to the optical modulation index (OMI). Furthermore, the third-order distortion-to-carrier ratio is proportional to that of the third-order coefficient-to-first-order coefficient of the DFB laser diode driving current, and to the OMI2.

Figures in this Article

With the popularity of optical fiber networks and the demand for high-quality videos, the development of changing TV signals from traditional cables to optic fibers has been promoted globally; thus, fiber-optic cable television (CATV) has been widely discussed.15 Therefore, the transmission quality of such a system has been defined and regulated, which basically determines the signal-receiving quality of the system based on the following three parameters: carrier-to-noise ratio (CNR), composite second order (CSO), and composite triple beat (CTB).6 Both noise and nonlinear effects in the fiber-optic CATV transmission system are mostly caused by active components but rarely by passive components. Such noise severely affects both system performance and transmission distance; thus, CNR is usually adopted in the parameter measurement of CATV systems to analyze the characteristics of the transmission signal quality of the system. Given that CNR is proportional to the optical modulation index (OMI), a higher CNR could be obtained by increasing the OMI. However, an extremely high OMI could worsen the nonlinear distortion of the system, causing the system to generate second and third harmonic distortions, as well as second and third intermodulation distortions. These nonlinear distortions result from the accumulation of signals that fall on other channels, which decreases both CSO and CTB of the system. Under ordinary conditions, designing a CATV system to obtain high CNR, CSO, and CTB values altogether is impossible, but an optimum balance range between noise and the systematic nonlinear effect could be determined. Such a nonlinear effect has become an important research topic to directly modulate distributed feedback (DFB) laser diode (LD) in fiber-optic CATV systems.710 The present study theoretically deduces the relationship among the direct modulation, driving current, OMI, harmonic distortion, and intermodulation distortion of DFB LD, as proven through experiments.

Figures 1(a) and 1(b) show the fiber-optic CATV transmission system by directly modulating DFB LDs 1 and 2, respectively. In Fig. 1(a), a multiple carrier generator (Matrix SX-16) is used to generate signals from channels 2 to 78 (55.25 to 547.25 MHz), which are directly modulated on DFB LD 1, whose driving current is set to 90 mA and output optical power to 10 mW (10 dBm). The signals are expected to reach an optical receiver after a certain fiber transmission distance. In this case, the optical power received by the optical receiver is expected to be 0 dBm, which generates a 10-dB fiber link loss with 25 km total transmission distance. Concurrently, the OMI of each channel changes from 8.5% to 13%, and an HP-8591C CATV analyzer is used to record variations in the CSO and CTB values. Similarly, Fig. 1(b) uses a multiple carrier generator (Matrix SX-16) to generate signals from channels 2 to 78 (55.25 to 547.25 MHz), which are directly modulated on DFB LD 2, whose driving current is set to 275 mA and output optical power to 40 mW (16 dBm). The optical link loss was expected to be 16 dB with 40  km total transmission distance. Additionally, the OMI of each channel changes from 8.5% to 13%, and an HP-8591C CATV analyzer is used to record variations in the CNR, CSO, and CTB values.

Graphic Jump Location
Fig. 1
F1 :

Experimental setup of proposed directly modulated fiber optic cable television system using (a) distributed feedback laser diode (DFB LD) 1 and (b) DFB LD 2.

In a fiber CATV system, CNR, CSO, and CTB exhibit a complementary relationship. CNR and OMI are positively correlated, whereas CSO, CTB, and OMI are negatively correlated. A higher OMI means a higher CNR value of signal reception, which would distort transmission signals and worsen both CSO and CTB values. By contrast, a lower OMI generates higher CSO and CTB values, and a lower CNR value. A compromise is required between these two conditions. Therefore, harmonic and intermodulation distortions in a fiber CATV system are evaluated through a Taylor series expansion of optical power Po in terms of DC bias current Iop and modulating driving current i(t) within the source bias point.11 Under general conditions, optical output power Po(t) of DFB LD could be represented as Display Formula

Po(t)=a·Iop+b·i(t)+c·i2(t)+d·i3(t),(1)
where the series higher than the third term is truncated. As a modulation driving current, i(t)=i=1nAicos(ωit+ϕi) flows through the DFB LD, where n denotes the total number of transmission channels, and the system reaches 550 and 750 MHz if n=80 or 110. In addition,   Ai, ωi, and ϕ represent the amplitude, angular frequency, and phase of the ith channel, respectively. By introducing i(t) into Eq. (1), we can derive all types of nonlinear effects and outputs of the optical power of DFB LD as follows:

  • Second-order harmonic-to-carrier ratio (2HD/C): Display Formula
    2HD/C=Po(2ωx)Po(ωx)=c·Ax2b,(2)
  • Second-order intermodulation distortion-to-carrier ratio (IMD2/C): Display Formula
    IMD2/C=Po(ωx+ωi)Po(ωi)=c·Axb,(3)
  • Third-order harmonic-to-carrier ratio (3HD/C): Display Formula
    3HD/C=Po(3ωx)Po(ωx)=d·Ax24b,(4)
  • Third-order intermodulation distortion-to-carrier ratio (IMD3/C): Display Formula
    IMD3/C=Po(2ωx+ωi)Po(ωx)=3d·Ax·Ai4b,(5)
    or Display Formula
    IMD3/C=Po(ωx+ωi+ωk)Po(ωx)=3d·Ai·Ak2b,(6)
    where ωx and Ax are the angular frequency and amplitude of the x’th channel, respectively.

Given that amplitude Ax is a function of the OMI, Ax=OMI+K, where K is a constant. By introducing Ax into Eqs. (2)–(6), we can derive the following results: Display Formula

CSO=K1·(c/b)(OMI)+K2,(7)
Display Formula
CTB=K3·(d/b)(OMI)2K4(d/b)(OMI)K5,(8)
where Km (m=1, 2, 3, 4, 5) is a constant.

The experimental structure is shown in Fig. 1. Two DFB LDs available in the market with different driving currents and output optical powers are utilized. The DFB LD 1 used is manufactured by Mitsubishi with model number FU-68SDF-22, which outputs an optical power of 6 to 10 mW, according to a driving current of 55 to 90 mA. The DFB LD 2 used is manufactured by JDS Uniphase with model number CQF938/400, which outputs an optical power of 30 to 40 mW, according to a driving current of 200 to 275 mA. The relative intensity noises are 155  dB/Hz and 160  dB/Hz for DFB LDs 1 and 2, respectively. The characteristic of the driving current of DFB LD to the corresponding output optical power of this laser diode is shown in Fig. 2. Through curve fitting, the characteristic Po-i(t) of DFB LD1 and DFB LD2 could be represented as Display Formula

Po(DFB  LD1)=86960.5·i(t)+1.63·i2(t)0.0207·i3(t)+0.000108·i4(t)1.35e9·i6(t),(9)
Display Formula
Po(DFB  LD2)=5729.38·i(t)+0.0593·i2(t)0.000164·i3(t)+1.68e7·i4(t).(10)

Graphic Jump Location
Fig. 2
F2 :

Optical output power versus driving current characteristic for (a) DFB LD 1 and (b) DFB LD 2.

According to the Po-i(t) characteristic of DFB LD 1 in Eq. (7), c/b=1.63/60.5=0.027 and d/b=0.0207/60.5=0.00034 can be obtained. Similarly, based on the Po-i(t) characteristic of DFB LD 2, c/b=0.0593/9.38=0.0063 and d/b=0.000164/9.38=0.0000175 can be obtained. Given that both c/b and d/b for DFB LD 1 are larger than those of DFB LD 2, the latter linearly performs better than the former.

Figure 3 shows the measured CNR values using DFB LDs 1 and 2, respectively, to directly modulate channels 2 to 78. The simultaneous change of OMI corresponds to the x-axis in the chart while the y-axis shows the CNR value of different OMI reacting on the CATV parameter. Such CNR value is the mean of all CNR values measured by the HP-8591C CATV analyzer at the system’s reception side regarding all 2 to 78 channels. The theoretical expression for CNR is Display Formula

CNR=OMI2I22BN,(11)
where I is the optical power incident on the receiver that generates photocurrent. OMI and I indicate the carrier level while B corresponds to the bandwidth in which the noise is measured. N is the grand total of all noise, which includes thermal and shot noise that are associated with the receiver, laser noise results from the intrinsic laser RIN, and phase noise and multipath interference noise result from interactions between the light and the fiber. From Eq. (11), we derive the relationship of CNR and OMI as CNROMI2, that is, CNR is proportional to OMI squared.

Graphic Jump Location
Fig. 3
F3 :

Measured carrier-to-noise ratio values for distributed feedback laser diodes 1 and 2 for different optical modulation indices (OMIs) per channel.

Figures 4 and 5 show the measured CSO and CTB values using DFB LDs 1 and 2, respectively, to directly modulate channels 2 to 78. Similar to the CNR measurement method, we used the HP-8591C CATV analyzer to measure the CSO/CTB values from channels 2 to 78 and by averaging the CSO/CTB values of all channels, we derived the CSO/CTB value corresponding to the concerned OMI. By altering OMI and repeating the above measurement, the changes of CSO/CTB were recorded. The result clearly shows that the measured CSO and CTB values have differences of 2–3.8 dB and 0–7 dB in the system when DFB LD 1 is used compared with using DFB LD 2. Evidently, the ratio of the second- and third-order coefficients generates such a result, and the first-order coefficient of the DFB LD 1 driving current is larger than that of DFB LD 2. According to the measurement results in Figs. 4 and 5, both CSO and CTB can be degraded in proportion to OMI and OMI2, respectively, regardless of whether the degradation is for DFB LD 1 or 2. When the OMI of each channel increases from 8.5% to 13%, the measured CSO and CTB values of DFB LDs 1 and 2 could be represented as follows via curve fitting: Display Formula

CSO(DFB  LD1)=1.86(OMI)81.5(dBc),(12)
Display Formula
CTB(DFB  LD1)=0.261(OMI)24.28(OMI)48.6(dBc),(13)
Display Formula
CSO(DFB  LD2)=2.41(OMI)90.2(dBc),and(14)
Display Formula
CTB(DFB  LD2)=0.99(OMI)217.7(OMI)+6.04(dBc).(15)

Graphic Jump Location
Fig. 4
F4 :

Measured composite second-order values for distributed feedback laser diodes 1 and 2 for different OMIs per channel.

Graphic Jump Location
Fig. 5
F5 :

Measured composite triple-beat values for distributed feedback laser diodes 1 and 2 for different OMIs per channel.

According to Eqs. (11)–(14), different nonlinear distortion degradations of CSO and CTB values occur in various laser diodes. The results of Eqs. (12)–(15) are obviously derived from Eqs. (7) and (8). When the strength of the light signal becomes 0 dBm (1 mW) at the light receiver, the CNR/CSO/CTB values at the optical node should be 50  dB/60  dBc/60  dBc. According to the measurement result of OMI to CNR, CSO, and CTB parameters (as shown in Figs. 35), the OMI of DFB LD1 shall be within 9.5% to 11.7% and the OMI of DFB LD2 shall be within 10.5% to 12.6% for the system to satisfy the required CNR/CSO/CTB performance, which would verify the positive relationship between OMI and CNR as well as the negative relationship between CSO/CTB. Therefore, the system shall attain a balance in between in order to satisfy the CNR/CSO/CTB values simultaneously.

Based on deduction theory and experimental measurements, the second-order distortion-to-carrier ratio is proportional to that of the second-order coefficient-to-first-order coefficient of the DFB LD driving current and to the OMI. Additionally, the third-order distortion-to-carrier ratio is proportional to that of the third-order coefficient-to-first-order coefficient of the DFB LD driving current, and to the OMI2. By introducing the derived CSO and CTB degradation equations, we can deduce the transmission characteristics of the system from the optical receiver node of an optical CATV transmission system.

This study was supported by the Ministry of Science and Technology of the Republic of China, Taiwan, under contract MOST 103-2218-E-027-001 and MOST 104-2633-E-228-001.

Tsai  W. S.  et al., “Bidirectional direct modulation CATV and phase remodulation radio-over-fiber transport systems,” Opt. Express. 18, (25 ), 26077 –26083 (2010). 1094-4087 CrossRef
Lin  W. Y.  et al., “Direct CATV modulation and phase remodulated radio-over-fiber transport system,” Opt. Express. 18, (10 ), 10301 –10307 (2010). 1094-4087 CrossRef
Su  H. S.  et al., “Fiber optical CATV transport systems based on PM and light injection-locked DFB LD as a duplex transceiver,” Opt. Express. 19, (27 ), 26928 –26935 (2011). 1094-4087 CrossRef
Lu  H. H.  et al., “Improvement of fiber-optical CATV transport systems performance based on lower-frequency sidemode injection-locked technique,” IEEE Photonics Technol. Lett.. 20, (5 ), 351 –353 (2008). 1041-1135 CrossRef
Li  C. Y.  et al., “Full-duplex lightwave transport systems employing phase-modulated RoF and intensity-remodulated CATV signals,” Opt. Express. 19, (15 ), 14000 –14007 (2011). 1094-4087 CrossRef
Rainal  A. J., “Distortion spectrum of laser intensity modulation,” IEEE Trans. Commun.. 43, (234 ), 1644 –1652 (1995).
Mazo  J. E., “Asymptotic distortion spectrum of clipped, dc-biased, Gaussian noise,” IEEE Trans. Commun.. 40, (8 ), 1339 –1344 (1992). 0090-6778 CrossRef
Rainal  A. J., “Laser intensity modulation as a clipped Gaussian process,” IEEE Trans. Commun.. 43, (2/3/4 ), 490 –494 (1995).
Pucel  B., “Comparison between static and dynamic clipping distortion in semiconductor laser,” IEEE Photonics Technol. Lett.. 9, (11 ), 1532 –1534 (1997).CrossRef
Lu  H. H., “CSO/CTB performances improvement by using optical VSB modulation technique,” IEEE Photonics Technol. Lett.. 14, (10 ), 1478 –1480 (2002). 1041-1135 CrossRef
Frigo  N. J., “A model of intermodulation distortion in nonlinear lightwave multicarrier systems,” IEEE Trans. Commun.. 42, (234 ), 1216 –1222 (1994). 0090-6778 CrossRef

Chung-Yi Li received his MS and PhD degrees from the Institute of Electro-Optical Engineering, National Taipei University of Technology, Taiwan, in 2008 and 2012, respectively. From 2013 to 2014, he worked as an engineer at the Innovation and Product Development Department, Fiber Optic Communications Inc. in Hsinchu, Taiwan. In 2014, he joined the Department of Electro-Optical Engineering, National Taipei University of Technology, as a research assistant professor.

Cheng-Ling Ying received his MS and PhD degrees from the Institute of Electrical Engineering, Yuan-Ze University, Chungli, Taiwan, in 1995 and 2002, respectively. From 2002 to 2005, he worked as an assistant professor at the Department of Electrical Engineering, China Institute of Technology, Taipei, Taiwan. In 2005, he joined the Department of Electronic Engineering, Jinwen University of Science and Technology, New Taipei City, Taiwan, where he became an associate professor in 2011.

Chun-Yu Lin received his MS degree from the National Taiwan Normal University, Taipei, in 2005. He has been pursuing his PhD degree at the Department of Electro-Optical Engineering, National Taipei University of Technology, since 2008. His current research interests include CATV applications and ROF transport systems.

Chien-An Chu has graduated from the Yuan Ze University, Taoyuan, in 2014. He has been pursuing his master degree at the Department of Electro-Optical Engineering, National Taipei University of Technology, since 2014. His current research interests include visible light communication and CATV/ROF transport systems.

© The Authors. Published by SPIE under a Creative Commons Attribution 3.0 Unported License. Distribution or reproduction of this work in whole or in part requires full attribution of the original publication, including its DOI.

Citation

Chung-Yi Li ; Cheng-Ling Ying ; Chun-Yu Lin and Chien-An Chu
"Nonlinear distortion evaluation in a directly modulated distributed feedback laser diode-based fiber-optic cable television transport system", Opt. Eng. 54(12), 126112 (Dec 23, 2015). ; http://dx.doi.org/10.1117/1.OE.54.12.126112


Figures

Graphic Jump Location
Fig. 1
F1 :

Experimental setup of proposed directly modulated fiber optic cable television system using (a) distributed feedback laser diode (DFB LD) 1 and (b) DFB LD 2.

Graphic Jump Location
Fig. 2
F2 :

Optical output power versus driving current characteristic for (a) DFB LD 1 and (b) DFB LD 2.

Graphic Jump Location
Fig. 3
F3 :

Measured carrier-to-noise ratio values for distributed feedback laser diodes 1 and 2 for different optical modulation indices (OMIs) per channel.

Graphic Jump Location
Fig. 4
F4 :

Measured composite second-order values for distributed feedback laser diodes 1 and 2 for different OMIs per channel.

Graphic Jump Location
Fig. 5
F5 :

Measured composite triple-beat values for distributed feedback laser diodes 1 and 2 for different OMIs per channel.

Tables

References

Tsai  W. S.  et al., “Bidirectional direct modulation CATV and phase remodulation radio-over-fiber transport systems,” Opt. Express. 18, (25 ), 26077 –26083 (2010). 1094-4087 CrossRef
Lin  W. Y.  et al., “Direct CATV modulation and phase remodulated radio-over-fiber transport system,” Opt. Express. 18, (10 ), 10301 –10307 (2010). 1094-4087 CrossRef
Su  H. S.  et al., “Fiber optical CATV transport systems based on PM and light injection-locked DFB LD as a duplex transceiver,” Opt. Express. 19, (27 ), 26928 –26935 (2011). 1094-4087 CrossRef
Lu  H. H.  et al., “Improvement of fiber-optical CATV transport systems performance based on lower-frequency sidemode injection-locked technique,” IEEE Photonics Technol. Lett.. 20, (5 ), 351 –353 (2008). 1041-1135 CrossRef
Li  C. Y.  et al., “Full-duplex lightwave transport systems employing phase-modulated RoF and intensity-remodulated CATV signals,” Opt. Express. 19, (15 ), 14000 –14007 (2011). 1094-4087 CrossRef
Rainal  A. J., “Distortion spectrum of laser intensity modulation,” IEEE Trans. Commun.. 43, (234 ), 1644 –1652 (1995).
Mazo  J. E., “Asymptotic distortion spectrum of clipped, dc-biased, Gaussian noise,” IEEE Trans. Commun.. 40, (8 ), 1339 –1344 (1992). 0090-6778 CrossRef
Rainal  A. J., “Laser intensity modulation as a clipped Gaussian process,” IEEE Trans. Commun.. 43, (2/3/4 ), 490 –494 (1995).
Pucel  B., “Comparison between static and dynamic clipping distortion in semiconductor laser,” IEEE Photonics Technol. Lett.. 9, (11 ), 1532 –1534 (1997).CrossRef
Lu  H. H., “CSO/CTB performances improvement by using optical VSB modulation technique,” IEEE Photonics Technol. Lett.. 14, (10 ), 1478 –1480 (2002). 1041-1135 CrossRef
Frigo  N. J., “A model of intermodulation distortion in nonlinear lightwave multicarrier systems,” IEEE Trans. Commun.. 42, (234 ), 1216 –1222 (1994). 0090-6778 CrossRef

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