Abstract

A bidirectional fiber optical CATV transport system employing phase modulation (PM) scheme and frequency up-conversion technique to deal with downstream CATV signals, and using light injection-locked distributed feedback laser diode (DFB LD) as a duplex transceiver at the receiving site is proposed and experimentally demonstrated. With optimum injection wavelength and power level, a DFB LD is efficiently employed for both the transmitter and receiver operations. Such DFB LD is used to replace the functions of delay interferometer (DI) and CATV receiver, and also to be as the upstream light source. To the best of our knowledge, it is the first time to successfully utilize a DFB LD to detect the phase-modulated CATV signals. Impressive experimental results prove that our proposed systems not only can employ the PM scheme and the frequency up-conversion technique to optimize the overall performances of systems, but also can use an injection-locked DFB LD to detect the downstream phase-modulated CATV signals as well as to transmit the upstream CATV ones simultaneously.

© 2011 OSA

1. Introduction

High video quality requirement in CATV services has significantly transformed the CATV industry recently, and the development of fiber optical CATV access networks has greatly speeded up this tendency worldwide. In order to efficiently transmit high quality CATV programs over fiber optics networks, various novel architectures have been developed based on intensity-modulated CATV signals in the CATV frequency bands. However, the optical CATV signal with its high power requirement (>10 dBm/channel) in nature will induce various non-linear distortions during transmission. So various compensation ways such as sophisticated sideband filtering, external light injection locking, or differential detection techniques are employed widely to promote the overall transmission performances [13]. Even though, their transmission performances are still limited by the composite second-order (CSO) and composite triple beat (CTB) distortions which always occur in a multi-carrier transport system [4]. In order to reduce the CSO and CTB distortions, a bidirectional fiber optical CATV transport system with frequency up-conversion and phase modulation (PM) schemes is proposed [5]. In the previous literatures, the PM scheme is mainly employed in digital communication or radio-over-fiber systems. This is the first time to employ the PM scheme in multi-carrier CATV transport systems. Different from a conventional intensity modulation (IM) scheme, the CATV signals in the published architecture are presented by phase shifting which provides high robustness against noise and distortion. In addition, by up-conversion the CATV frequency band, parts of the CSO and CTB distortions will be located at different frequency band, in which resulting in better CSO and CTB performances. Similar with other PM schemes, the phase-modulated CATV transport system also needs a delay interferometer (DI) to transfer the phase-modulated signal into intensity-modulated one before fed into a CATV receiver. This scheme can greatly promote the overall transmission performances. However, the sophisticated and expensive DI will be a serious limitation in promoting such novel transport systems. To face this situation, an optical PM-to-IM conversion scheme is developed based on a dedicated dispersive devices in which is employed to introduce a dispersion-induced PM-to-IM conversion [6]. However, such PM-to-IM conversion scheme requires a high wavelength stability and a dedicated dispersion value to maximum PM-to-IM conversion. It is not flexible in a WDM transport system. Fortunately, employing an injection-locked semiconductor laser to detect a phase-modulated optical signal directly was theoretically analyzed by O. Lidoyne and P. Gallion in [7] and was successfully adopted in some systems [8-9]. It is proved that a phase-modulated optical signal can be converted into voltage modulated one when a semiconductor laser is locked by the signal and the modulation frequency is within the laser’s locking range and frequency response. Under this condition, a phase-modulated lightwave can be coupled into the laser cavity and the external field will increase the rate of stimulated emission which will deplete the carrier density in the laser [10]. As a result, the phase-modulated optical signal can be detected and a measureable electrical signal can be obtained from the RF port of the semiconductor laser. Nevertheless, those systems just utilized vertical-cavity surface-mitting lasers (VCSELs) to detect phase-modulated baseband signals or radio-frequency (RF) signals only. Its application in fiber optical CATV transport systems has not reported because its low power characteristic is not suitable to detect the CATV signals. Similarly, a Fabry-Perot laser diode (FP-LD) with multi-mode characteristic will cause serious dispersion, so it is also not a suitable candidate. Comparing with transmitting the baseband and RF signals, delivering multi-carrier CATV signals requires much more restricted transmission performances to provide high quality services and to reduce non-linear distortions, such as second-order harmonic distortion (HD2) and third-order intermodulation distortion (IMD3). In order to integrate this technique into the CATV transport systems, a novel fiber optical CATV transport system employing PM scheme and frequency up-conversion technique to deal with downstream CATV signals, as well as using light injection-locked distributed feedback laser diode (DFB LD) as a duplex transceiver is proposed and experimentally demonstrated. With optimum injection wavelength and power level, a DFB LD is efficiently employed for both the transmitter and receiver operations. Such DFB LD is used to replace the functions of DI and CATV receiver, and also to be as the upstream light source. To the best of our knowledge, it is the first time to successfully utilize a DFB LD to detect phase-modulated CATV signals. Brilliant experimental results prove that the proposed systems not only can employ the PM scheme and the frequency up-conversion technique to optimize the transmission performances, but also can use an injection-locked DFB LD to detect the downstream phase-modulated CATV signals as well as to transmit the upstream CATV ones simultaneously.

2. Experimental setup

Figure 1 shows two bidirectional optically amplified CATV transport systems with PM scheme and frequency up-conversion technique. Figure 1(a) (referred to as system I) shows a fiber optical CATV transport system using traditional DI and CATV receiver at the receiving site. Figure 1(b) (referred to as system II) shows the experimental configuration of our proposed fiber optical CATV transport systems employing an injection-locked DFB LD as a duplex transceiver (transmitter and receiver) at the receiving site. The output power and noise figure of erbium-doped fiber amplifiers (EDFAs) used in the systems I and II are ~17 dBm and ~4.5 dB, at an input power of 0 dBm, respectively. In system I, RF subcarriers generated from a 77-channel (CH2-78, 55.25-547.25 MHz) NTSC Matrix SX-16 signal generator were fed into a phase modulator. The DFB LD1, with a central wavelength of 1549.53 nm (λ1), provided an optical carrier to the phase modulator to transfer the intensity modulated signal into phase modulated one. The polarization controller (PC), at the transmitter output, was used to adjust the polarization state of the transmitter signal. The CATV frequency band (55.25-547.25 MHz) is up-converted to the microwave frequency band (9.508-10 GHz), and then fed into the phase modulator. When the lightwave is modulated by a phase modulator, some sidebands will be generated depending on the amplitude of the driven RF subcarriers. Here, we drive the phase modulator with 3.4% optical modulation index (OMI), in which resulting in small second-order sidebands after PM. Only the first-order sidebands are generated, and the peak of the first-order sidebands is roughly about 10 GHz away from the optical carrier of the lightwave. The optical signal is amplified by an EDFA firstly; next to the EDFA, two optical circulators (OC1 and OC2) are placed to bridge both downstream and upstream optical signals. Over a 40-km single-mode fiber (SMF) transportation, the downstream optical signal is firstly passed through a delay interferometer (DI) with a 10 GHz free spectral range (FSR) to transfer the phase modulated signal into intensity modulated one. Following with the DI, the optical signal is detected by a 10 GHz broadband photodiode (PD), down-converted from the microwave frequency band to the CATV frequency band, and then filtered by a RF band-pass filter (BPF) (50-550 MHz) to remove the spurious. Carrier-to-noise ratio (CNR), CSO, and CTB values are measured by using an HP-8591C CATV analyzer. For up-link transmission, a 1544.73 nm (λ2) lightwave generated from a DFB LD2 is directly intensity-modulated with CATV signal and is circulated by the OC2 before coupled into the same 40 km SMF link. Over a 40-km SMF transport, the upstream optical signal is circulated by the OC1, amplified by an EDFA, attenuated by a variable optical attenuator (VOA), filtered by an OBPF, and received by a CATV receiver. All CATV RF parameters are also measured by using an HP-8591C CATV analyzer.

 

Fig. 1 (a) System I: A fiber optical CATV transport system using traditional DI and CATV receiver at the receiving site. (b) System II: The experimental configuration of our proposed fiber optical CATV transport systems employing an injection-locked DFB LD for the transceiver operations at the receiving site.

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In system II, 77 standard NTSC channels (CH2-78) generated from Matrix SX-16 were also up-converted to microwave frequency band (9.508-10 GHz), and then fed into a phase modulator to modulate with a 1549.53 (λ1) nm lightwave. A PC was used at the transmitter output to adjust the polarization state of the output lightwave. Subsequently, the downstream signal was amplified by an EDFA before fed into a 40-km SMF link. At the receiving site, the downstream lightwave is routed by an OC, injected into another DFB LD (DFB LD3, λ3 = 1549.41 nm) to obtain the microwave signals, and then frequency down-converted into the CATV frequency band. Subsequently, the signal is purified by passing through a RF BPF (50-550 MHz) and analyzed by a CATV analyzer (HP-8591C). In parallel with the down-link transmission, another 77 standard NTSC channels are also coupled into the RF port of the DFB LD3 for uplink transmission. Since the downstream (microwave frequency band) and upstream (CATV frequency band) signals are located at different frequency bands, the DFB LD3 can be shared using a frequency-division-multiplexing scheme. The directly modulated upstream signal is then routed by the OC, amplified by another EDFA, attenuated by a VOA, and fed into another 40 km SMF for uplink transmission. At the receiving site, the upstream signal is filtered by an OBPF, received by a CATV receiver, and analyzed by an HP-8591C.

To verify the implementation of frequency up-conversion, two microwave signal generators are used to simulate two up-converted CATV channels. The experimental configuration of the simulated up-conversion CATV transport system is shown in Fig. 2 . Two microwave carriers (f1 = 9.994 GHz, f2 = 10 GHz) are provided for two-tone signal measurement. Over a 40-km SMF link, the optical signal is injected into another DFB LD to obtain the microwave signals, and then frequency down-converted into the CATV frequency band (CH77 and CH78). Subsequently, the signal is purified by passing through a RF BPF (50-550 MHz), and finally the third-order intermodulation distortion to carrier ratio (IMD3/C) parameter is analyzed by a spectrum analyzer.

 

Fig. 2 The experimental configuration of the simulated up-conversion CATV transport systems.

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3. Experimental results and discussions

Electrical spectrum of the received two carriers (CH77 and CH78, down-converted from f1 and f2) is shown in Fig. 3 . It is obvious that the residue IMD3/C level of −69 dBc is obtained. In PM scheme, noise and distortion will be reduced dramatically resulting in a large improvement of IMD3/C value. There are many advantages to PM and one of them is a great reduction in noise and distortion which will affect the signals amplitude. If the changes in amplitude can be reduced, then systems will have good transmission performances. For PM scheme, the amplitude limitation removes the effect of noise and distortion but does not disturb the original modulating information. In addition, it has been experimentally shown that a DFB LD injection-locked to a phase-modulated optical signal can convert the PM signal into the IM one. It should be noted that no RF signal is obtained as the DFB LD is not injection-locked to the phase-modulated signal. However, as the DFB LD is locked to the phase-modulated signal, two carriers at frequencies of 9.994 and 10 GHz are detected. The outer boundary of the locking range for laser under light injection is given by [11]

d<±kc2πSiS(1+α2)
where the frequency detuning d = finjffree (finj is the frequency of master laser, ffree is the frequency of free running slave laser), kc is the coupling coefficient, Si/S is the injection ratio, and αis the linewidth enhancement factor. An optimum injection locking can be achieved if the frequency of the master laser (DFB LD1) is lower than that of the slave laser (DFB LD3), i.e., negative detuning [11-12]. Within the injection locking range, the frequency of the slave laser is locked nearly to the frequency of the master laser. However, outside the locking range, severe oscillation occurs. When DFB LD3 is injection-locked, its optical spectrum shifts a slightly longer wavelength (0.12 nm), matching to that of λ1. The injection locking behavior happens when an injection source laser is slightly detuned to wavelength slightly longer than that of the injection-locked laser. The optimal injection locking condition is found when the detuning between λ1 and the λ3 is + 0.12 nm (1549.53nm - 1549.41nm = 0.12nm) where the best CSO and CTB performances are found.

 

Fig. 3 Electrical spectrum of the received two carriers (CH77 and CH78, down-converted from f1 and f2).

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In system I, the wavelength spacing between the DFB LD1 and DFB LD2 is 4.8 nm (1549.53nm - 1544.73nm = 4.8nm). In system II, however, the wavelength spacing between the DFB LD1 and DFB LD3 is 0.12 nm only (1549.53nm - 1549.41nm = 0.12nm). Crosstalk for the systems with wavelength spacing <4 nm is dominated by the cross-phase modulation (XPM) interaction. As a result of FM-AM conversion due to fiber dispersion, XPM interaction between two wavelengths (downstream and upstream wavelengths) will introduce large crosstalk in lightwave transport systems [13-14]. In system I, no XPM-induced crosstalk is observed due to large wavelength spacing. In system II, XPM-induced crosstalk is observed due to small wavelength spacing. In order to reduce the XPM-induced crosstalk between the downstream and upstream signals, the uplink signal is communicated through another SMF.

Figure 4 (a), (b) and (c) illustrate the measured downstream CNR, CSO and CTB values of system II; as the DFB LD3 under 3, 0, and −3 dBm injection power levels, respectively. Employing an injection-locked semiconductor laser to detect phase-modulated optical signal was firstly proposed by Lidoyne and Gallion in [7], but this is the first time to employ this technique in a multi-carrier transport system. From these three figures, it is clear that the measured CNR, CSO and CTB values will be affected by the DFB LD3 injection power level. When the injection power is −3 dBm, the CNR, CSO and CTB values are limited at around 49, 66, and 65 dB, respectively. Nevertheless, when the injection power is increased up to 3 dBm, the CNR, CSO and CTB values are increased by 2.5, 5, and 5 dB, respectively. These results prove that the DFB LD3 is successfully employed to replace a DI and a CATV receiver, as well as its detection efficiency is in proportion to the injection power level.

 

Fig. 4 The measured downstream (a) CNR, (b) CSO, and (c) CTB values of system II; as DFB LD3 under 3, 0, and −3 dBm injection power levels, respectively.

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Figure 5(a), (b) and (c) show the measured downstream CNR, CSO and CTB values for back-to-back (BTB), system I (40km IM), and system II (40km PM, DFB LD3 under 3 dBm injection power level), respectively. For CNR performance (Fig. 5(a)), there exists a power penalty of about 1.5 dB between the BTB case (≥53 dB) and systems I and II (≥51.5 dB). It also indicates that the CNR values of systems I and II are almost identical. The CNR value can be improved by higher EDFA input power. Higher EDFA input power increases EDFAs’ CNRsig-sp (due to signal-spontaneous beat noise) and CNRsp-sp (due to spontaneous-spontaneous beat noise) values, in which leading to an improvement of CNR value. Similarly, good performances of CSO/CTB are achieved for systems I (≥73/72 dB) and II (≥71/70 dB), due to the use of up-converted technique to reduce the CSO/CTB distortions and the constant power operation characteristic of PM scheme [5]. There exists a power penalty of about 3 dB between the BTB case (≥76/75 dB) and system I. This CSO/CTB degradations can be attributed to the fiber dispersion-induced distortion. And further, there exists a power penalty of about 2 dB between the system I and system II. The dynamic nonlinearity of the laser is very large at the resonance frequency when light injection is employed. As RF band around the resonance frequency is being used for the CATV transmission, this large dynamic laser nonlinearity degrades the transmission performance of systems. Nevertheless, the CSO/CTB performances of system II still satisfy the requirements of fiber optical CATV systems at the optical node (≥60/60 dB). Furthermore, to achieve acceptable quality of service (QoS) for clients, the received optical power level at the clients’ premises needs to be kept at −3 ~ + 3 dBm. Since the CATV signal is broadcast to all subscribers after received by the CATV receiver. To meet the CNR/CSO/CTB demands at the subscriber (43/53/53 dB), the maximum subscriber numbers for each CATV receiver are 200. Light injection-locked DFB LD as a duplex transceiver is worth employing owing to sophisticated and expensive DI as well as CATV receiver are not required at the receiving site. Furthermore, in order to know how much CSO and CTB performances improvements are based on each of the schemes, systems II with up-converted technique alone has been employed to measure the CSO and CTB values (>66/65 dB). Also, system II with PM scheme alone has been used to measure the CSO and CTB values (>67/66 dB). It means that when system II employs the up-converted technique or the PM scheme alone to compensate the CSO and CTB distortions, the compensation results are limited. The large improvements in CSO and CTB performances (>71/70 dB) are the results of employing up-converted and PM schemes simultaneously.

 

Fig. 5 The measured downstream (a) CNR, (b) CSO, and (c) CTB values for BTB, system I, and system II (DFB LD3 with 3 dBm injection).

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Figure 6(a), (b) and (c) illustrate the measured upstream CNR, CSO and CTB values under NTSC channel number for systems I and II, respectively. With the operation characteristic of the PM scheme, the amplitude fluctuation effect caused by downstream noise and distortion can be reduced dramatically. Although the amplitude of the downstream carrier is still affected by the PM-to-IM conversion during the 40-km transmission, such injection power variation will not seriously impact the DFB output steady. Thereby, the measured upstream CNR/CSO/CTB values are not much worse than those of the downstream ones. Furthermore, since the DFB chirp is related to deviations of the phase of the optical field, a reduction of chirp can be obtained by an injection locking, the upstream CNR/CSO/CTB performances of our proposed systems (system II) (≥50.5/65/64 dB) still meet the demands of fiber optical CATV systems at the optical node (≥50/60/60 dB). From Fig. 6(a), (b) and (c), we also can see that the CNR/CSO/CTB performances of system II are better than those of the system I. In system II, the VOA is introduced at the start of the optical link, in which resulting in less noise and distortion. In system I, however, the VOA is introduced at the end of the optical link, in which leading to more noise and distortion.

 

Fig. 6 The measured upstream (a) CNR, (b) CSO, and (c) CTB values for systems I and II.

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4. Conclusions

A novel and bidirectional fiber optical CATV transport system is proposed and experimentally demonstrated. By employing a frequency up-conversion technique and a PM scheme to optimized the downstream transmission performances, some unwanted noise and distortion are reduced dramatically. And further, by using an injection-locked DFB LD to detect the downstream phase modulated CATV signals and to transmit the upstream CATV ones simultaneously, sophisticated and expensive DI as well as CATV receiver are not required at the receiveing site. Our proposed systems present brilliant performances and cost-effective characteristic in transmitting CATV signals over fiber links.

References and links

1. S. J. Tzeng, H. H. Lu, C. Y. Li, K. H. Chang, and C. H. Lee, “CSO/CTB performance improvement by using Fabry-Perot etalon at the receiving site,” Prog. Electromagn Res Lett. 6(14), 107–113 (2009). [CrossRef]  

2. H. H. Lu, A. S. Patra, S. J. Tzeng, H. C. Peng, and W. I. Lin, “Improvement of fiber optical CATV transport systems performance based on lower-frequency side mode injection-locked technique,” IEEE Photon. Technol. Lett. 20(5), 351–353 (2008). [CrossRef]  

3. D. Piehler, X. Zou, C. Y. Kuo, A. Nilsson, J. Kleefeld, G. Garcia, J. D. Ralston, and A. Mathur, “55dB CNR over 50km of fiber in an 80-channel externally-modulated AM-CATV system without optical amplification,” Electron. Lett. 33(3), 226–227 (1997). [CrossRef]  

4. H. Kim, S. B. Jun, and Y. C. Chung, “Raman crosstalk suppression in CATV overlay passive optical network,” IEEE Photon. Technol. Lett. 19 (9), 695–697 (2007). [CrossRef]  

5. P. Y. Wu, H. H. Lu, C. L. Ying, C. Y. Li, and H. S. Su, “An up-converted phase modulated fiber optical CATV transport system,” IEEE/OSA, J. Lightwave Technol. 29(16), 2422–2427 (2011). [CrossRef]  

6. X. Xue, X. Zheng, H. Zhang, and B. Zhou, “Optical beamforming networks employing phase modulation and direct detection,” Opt. Commun. 284(12), 2695–2699 (2011). [CrossRef]  

7. O. Lidoyne and P. Gallion, “Analysis of receiver using injection-locked semiconductor laser for direct demodulation of PSK optical signals,” Electron. Lett. 27(11), 995–997 (1991). [CrossRef]  

8. N. Hoghooghi, I. Ozdur, S. Bhooplapur, and P. J. Delfyett, “Direct modulation and channel filtering of phase-modulated signals using an injection-locked VCSEL,” IEEE Photon. Technol. Lett. 22(20), 1509–1511 (2010). [CrossRef]  

9. Q. Gu, W. Hofmann, M. C. Amann, and L. Chrostowski, “Optically injection-locked VCSEL as a duplex transmitter/receiver,” IEEE Photon. Technol. Lett. 20(7), 463–465 (2008). [CrossRef]  

10. S. Wieczorek, W. W. Chow, L. Chrostowski, and C. J. Chang-Hasnain, “Improved semiconductor-laser dynamics from induced population pulsation,” IEEE J. Sel. Top. Quantum Electron. 42(6), 552–562 (2006). [CrossRef]  

11. S. Mohrdiek, H. Burkhard, and H. Walter, “Chirp reduction of directly modulated semiconductor lasers at 10 Gb/s by strong CW light injection,” IEEE/OSA, J. Lightwave Technol. 12(3), 418–424 (1994). [CrossRef]  

12. G. Yabre, “Effect of relatively strong light injection on the chirp-to-power ratio and the 3 dB bandwidth of directly modulated semiconductor lasers,” IEEE/OSA, J. Lightwave Technol. 14(10), 2367–2373 (1996). [CrossRef]  

13. H. H. Lu, H. C. Peng, W. S. Tsai, C. C. Lin, S. J. Tzeng, and Y. Z. Lin, “Bidirectional hybrid CATV/radio-over-fiber WDM transport system,” Opt. Lett. 35(3), 279–281 (2010). [CrossRef]   [PubMed]  

14. M. R. Phillips and D. M. Ott, “Crosstalk due to optical fiber nonlinearities in WDM CATV lightwave systems,” IEEE/OSA, J. Lightwave Technol. 17(10), 1782–1792 (1999). [CrossRef]  

References

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  1. S. J. Tzeng, H. H. Lu, C. Y. Li, K. H. Chang, and C. H. Lee, “CSO/CTB performance improvement by using Fabry-Perot etalon at the receiving site,” Prog. Electromagn Res Lett. 6(14), 107–113 (2009).
    [CrossRef]
  2. H. H. Lu, A. S. Patra, S. J. Tzeng, H. C. Peng, and W. I. Lin, “Improvement of fiber optical CATV transport systems performance based on lower-frequency side mode injection-locked technique,” IEEE Photon. Technol. Lett. 20(5), 351–353 (2008).
    [CrossRef]
  3. D. Piehler, X. Zou, C. Y. Kuo, A. Nilsson, J. Kleefeld, G. Garcia, J. D. Ralston, and A. Mathur, “55dB CNR over 50km of fiber in an 80-channel externally-modulated AM-CATV system without optical amplification,” Electron. Lett. 33(3), 226–227 (1997).
    [CrossRef]
  4. H. Kim, S. B. Jun, and Y. C. Chung, “Raman crosstalk suppression in CATV overlay passive optical network,” IEEE Photon. Technol. Lett. 19 (9), 695–697 (2007).
    [CrossRef]
  5. P. Y. Wu, H. H. Lu, C. L. Ying, C. Y. Li, and H. S. Su, “An up-converted phase modulated fiber optical CATV transport system,” IEEE/OSA, J. Lightwave Technol. 29(16), 2422–2427 (2011).
    [CrossRef]
  6. X. Xue, X. Zheng, H. Zhang, and B. Zhou, “Optical beamforming networks employing phase modulation and direct detection,” Opt. Commun. 284(12), 2695–2699 (2011).
    [CrossRef]
  7. O. Lidoyne and P. Gallion, “Analysis of receiver using injection-locked semiconductor laser for direct demodulation of PSK optical signals,” Electron. Lett. 27(11), 995–997 (1991).
    [CrossRef]
  8. N. Hoghooghi, I. Ozdur, S. Bhooplapur, and P. J. Delfyett, “Direct modulation and channel filtering of phase-modulated signals using an injection-locked VCSEL,” IEEE Photon. Technol. Lett. 22(20), 1509–1511 (2010).
    [CrossRef]
  9. Q. Gu, W. Hofmann, M. C. Amann, and L. Chrostowski, “Optically injection-locked VCSEL as a duplex transmitter/receiver,” IEEE Photon. Technol. Lett. 20(7), 463–465 (2008).
    [CrossRef]
  10. S. Wieczorek, W. W. Chow, L. Chrostowski, and C. J. Chang-Hasnain, “Improved semiconductor-laser dynamics from induced population pulsation,” IEEE J. Sel. Top. Quantum Electron. 42(6), 552–562 (2006).
    [CrossRef]
  11. S. Mohrdiek, H. Burkhard, and H. Walter, “Chirp reduction of directly modulated semiconductor lasers at 10 Gb/s by strong CW light injection,” IEEE/OSA, J. Lightwave Technol. 12(3), 418–424 (1994).
    [CrossRef]
  12. G. Yabre, “Effect of relatively strong light injection on the chirp-to-power ratio and the 3 dB bandwidth of directly modulated semiconductor lasers,” IEEE/OSA, J. Lightwave Technol. 14(10), 2367–2373 (1996).
    [CrossRef]
  13. H. H. Lu, H. C. Peng, W. S. Tsai, C. C. Lin, S. J. Tzeng, and Y. Z. Lin, “Bidirectional hybrid CATV/radio-over-fiber WDM transport system,” Opt. Lett. 35(3), 279–281 (2010).
    [CrossRef] [PubMed]
  14. M. R. Phillips and D. M. Ott, “Crosstalk due to optical fiber nonlinearities in WDM CATV lightwave systems,” IEEE/OSA, J. Lightwave Technol. 17(10), 1782–1792 (1999).
    [CrossRef]

2011 (2)

P. Y. Wu, H. H. Lu, C. L. Ying, C. Y. Li, and H. S. Su, “An up-converted phase modulated fiber optical CATV transport system,” IEEE/OSA, J. Lightwave Technol. 29(16), 2422–2427 (2011).
[CrossRef]

X. Xue, X. Zheng, H. Zhang, and B. Zhou, “Optical beamforming networks employing phase modulation and direct detection,” Opt. Commun. 284(12), 2695–2699 (2011).
[CrossRef]

2010 (2)

N. Hoghooghi, I. Ozdur, S. Bhooplapur, and P. J. Delfyett, “Direct modulation and channel filtering of phase-modulated signals using an injection-locked VCSEL,” IEEE Photon. Technol. Lett. 22(20), 1509–1511 (2010).
[CrossRef]

H. H. Lu, H. C. Peng, W. S. Tsai, C. C. Lin, S. J. Tzeng, and Y. Z. Lin, “Bidirectional hybrid CATV/radio-over-fiber WDM transport system,” Opt. Lett. 35(3), 279–281 (2010).
[CrossRef] [PubMed]

2009 (1)

S. J. Tzeng, H. H. Lu, C. Y. Li, K. H. Chang, and C. H. Lee, “CSO/CTB performance improvement by using Fabry-Perot etalon at the receiving site,” Prog. Electromagn Res Lett. 6(14), 107–113 (2009).
[CrossRef]

2008 (2)

H. H. Lu, A. S. Patra, S. J. Tzeng, H. C. Peng, and W. I. Lin, “Improvement of fiber optical CATV transport systems performance based on lower-frequency side mode injection-locked technique,” IEEE Photon. Technol. Lett. 20(5), 351–353 (2008).
[CrossRef]

Q. Gu, W. Hofmann, M. C. Amann, and L. Chrostowski, “Optically injection-locked VCSEL as a duplex transmitter/receiver,” IEEE Photon. Technol. Lett. 20(7), 463–465 (2008).
[CrossRef]

2007 (1)

H. Kim, S. B. Jun, and Y. C. Chung, “Raman crosstalk suppression in CATV overlay passive optical network,” IEEE Photon. Technol. Lett. 19 (9), 695–697 (2007).
[CrossRef]

2006 (1)

S. Wieczorek, W. W. Chow, L. Chrostowski, and C. J. Chang-Hasnain, “Improved semiconductor-laser dynamics from induced population pulsation,” IEEE J. Sel. Top. Quantum Electron. 42(6), 552–562 (2006).
[CrossRef]

1999 (1)

M. R. Phillips and D. M. Ott, “Crosstalk due to optical fiber nonlinearities in WDM CATV lightwave systems,” IEEE/OSA, J. Lightwave Technol. 17(10), 1782–1792 (1999).
[CrossRef]

1997 (1)

D. Piehler, X. Zou, C. Y. Kuo, A. Nilsson, J. Kleefeld, G. Garcia, J. D. Ralston, and A. Mathur, “55dB CNR over 50km of fiber in an 80-channel externally-modulated AM-CATV system without optical amplification,” Electron. Lett. 33(3), 226–227 (1997).
[CrossRef]

1996 (1)

G. Yabre, “Effect of relatively strong light injection on the chirp-to-power ratio and the 3 dB bandwidth of directly modulated semiconductor lasers,” IEEE/OSA, J. Lightwave Technol. 14(10), 2367–2373 (1996).
[CrossRef]

1994 (1)

S. Mohrdiek, H. Burkhard, and H. Walter, “Chirp reduction of directly modulated semiconductor lasers at 10 Gb/s by strong CW light injection,” IEEE/OSA, J. Lightwave Technol. 12(3), 418–424 (1994).
[CrossRef]

1991 (1)

O. Lidoyne and P. Gallion, “Analysis of receiver using injection-locked semiconductor laser for direct demodulation of PSK optical signals,” Electron. Lett. 27(11), 995–997 (1991).
[CrossRef]

Amann, M. C.

Q. Gu, W. Hofmann, M. C. Amann, and L. Chrostowski, “Optically injection-locked VCSEL as a duplex transmitter/receiver,” IEEE Photon. Technol. Lett. 20(7), 463–465 (2008).
[CrossRef]

Bhooplapur, S.

N. Hoghooghi, I. Ozdur, S. Bhooplapur, and P. J. Delfyett, “Direct modulation and channel filtering of phase-modulated signals using an injection-locked VCSEL,” IEEE Photon. Technol. Lett. 22(20), 1509–1511 (2010).
[CrossRef]

Burkhard, H.

S. Mohrdiek, H. Burkhard, and H. Walter, “Chirp reduction of directly modulated semiconductor lasers at 10 Gb/s by strong CW light injection,” IEEE/OSA, J. Lightwave Technol. 12(3), 418–424 (1994).
[CrossRef]

Chang, K. H.

S. J. Tzeng, H. H. Lu, C. Y. Li, K. H. Chang, and C. H. Lee, “CSO/CTB performance improvement by using Fabry-Perot etalon at the receiving site,” Prog. Electromagn Res Lett. 6(14), 107–113 (2009).
[CrossRef]

Chang-Hasnain, C. J.

S. Wieczorek, W. W. Chow, L. Chrostowski, and C. J. Chang-Hasnain, “Improved semiconductor-laser dynamics from induced population pulsation,” IEEE J. Sel. Top. Quantum Electron. 42(6), 552–562 (2006).
[CrossRef]

Chow, W. W.

S. Wieczorek, W. W. Chow, L. Chrostowski, and C. J. Chang-Hasnain, “Improved semiconductor-laser dynamics from induced population pulsation,” IEEE J. Sel. Top. Quantum Electron. 42(6), 552–562 (2006).
[CrossRef]

Chrostowski, L.

Q. Gu, W. Hofmann, M. C. Amann, and L. Chrostowski, “Optically injection-locked VCSEL as a duplex transmitter/receiver,” IEEE Photon. Technol. Lett. 20(7), 463–465 (2008).
[CrossRef]

S. Wieczorek, W. W. Chow, L. Chrostowski, and C. J. Chang-Hasnain, “Improved semiconductor-laser dynamics from induced population pulsation,” IEEE J. Sel. Top. Quantum Electron. 42(6), 552–562 (2006).
[CrossRef]

Chung, Y. C.

H. Kim, S. B. Jun, and Y. C. Chung, “Raman crosstalk suppression in CATV overlay passive optical network,” IEEE Photon. Technol. Lett. 19 (9), 695–697 (2007).
[CrossRef]

Delfyett, P. J.

N. Hoghooghi, I. Ozdur, S. Bhooplapur, and P. J. Delfyett, “Direct modulation and channel filtering of phase-modulated signals using an injection-locked VCSEL,” IEEE Photon. Technol. Lett. 22(20), 1509–1511 (2010).
[CrossRef]

Gallion, P.

O. Lidoyne and P. Gallion, “Analysis of receiver using injection-locked semiconductor laser for direct demodulation of PSK optical signals,” Electron. Lett. 27(11), 995–997 (1991).
[CrossRef]

Garcia, G.

D. Piehler, X. Zou, C. Y. Kuo, A. Nilsson, J. Kleefeld, G. Garcia, J. D. Ralston, and A. Mathur, “55dB CNR over 50km of fiber in an 80-channel externally-modulated AM-CATV system without optical amplification,” Electron. Lett. 33(3), 226–227 (1997).
[CrossRef]

Gu, Q.

Q. Gu, W. Hofmann, M. C. Amann, and L. Chrostowski, “Optically injection-locked VCSEL as a duplex transmitter/receiver,” IEEE Photon. Technol. Lett. 20(7), 463–465 (2008).
[CrossRef]

Hofmann, W.

Q. Gu, W. Hofmann, M. C. Amann, and L. Chrostowski, “Optically injection-locked VCSEL as a duplex transmitter/receiver,” IEEE Photon. Technol. Lett. 20(7), 463–465 (2008).
[CrossRef]

Hoghooghi, N.

N. Hoghooghi, I. Ozdur, S. Bhooplapur, and P. J. Delfyett, “Direct modulation and channel filtering of phase-modulated signals using an injection-locked VCSEL,” IEEE Photon. Technol. Lett. 22(20), 1509–1511 (2010).
[CrossRef]

Jun, S. B.

H. Kim, S. B. Jun, and Y. C. Chung, “Raman crosstalk suppression in CATV overlay passive optical network,” IEEE Photon. Technol. Lett. 19 (9), 695–697 (2007).
[CrossRef]

Kim, H.

H. Kim, S. B. Jun, and Y. C. Chung, “Raman crosstalk suppression in CATV overlay passive optical network,” IEEE Photon. Technol. Lett. 19 (9), 695–697 (2007).
[CrossRef]

Kleefeld, J.

D. Piehler, X. Zou, C. Y. Kuo, A. Nilsson, J. Kleefeld, G. Garcia, J. D. Ralston, and A. Mathur, “55dB CNR over 50km of fiber in an 80-channel externally-modulated AM-CATV system without optical amplification,” Electron. Lett. 33(3), 226–227 (1997).
[CrossRef]

Kuo, C. Y.

D. Piehler, X. Zou, C. Y. Kuo, A. Nilsson, J. Kleefeld, G. Garcia, J. D. Ralston, and A. Mathur, “55dB CNR over 50km of fiber in an 80-channel externally-modulated AM-CATV system without optical amplification,” Electron. Lett. 33(3), 226–227 (1997).
[CrossRef]

Lee, C. H.

S. J. Tzeng, H. H. Lu, C. Y. Li, K. H. Chang, and C. H. Lee, “CSO/CTB performance improvement by using Fabry-Perot etalon at the receiving site,” Prog. Electromagn Res Lett. 6(14), 107–113 (2009).
[CrossRef]

Li, C. Y.

P. Y. Wu, H. H. Lu, C. L. Ying, C. Y. Li, and H. S. Su, “An up-converted phase modulated fiber optical CATV transport system,” IEEE/OSA, J. Lightwave Technol. 29(16), 2422–2427 (2011).
[CrossRef]

S. J. Tzeng, H. H. Lu, C. Y. Li, K. H. Chang, and C. H. Lee, “CSO/CTB performance improvement by using Fabry-Perot etalon at the receiving site,” Prog. Electromagn Res Lett. 6(14), 107–113 (2009).
[CrossRef]

Lidoyne, O.

O. Lidoyne and P. Gallion, “Analysis of receiver using injection-locked semiconductor laser for direct demodulation of PSK optical signals,” Electron. Lett. 27(11), 995–997 (1991).
[CrossRef]

Lin, C. C.

Lin, W. I.

H. H. Lu, A. S. Patra, S. J. Tzeng, H. C. Peng, and W. I. Lin, “Improvement of fiber optical CATV transport systems performance based on lower-frequency side mode injection-locked technique,” IEEE Photon. Technol. Lett. 20(5), 351–353 (2008).
[CrossRef]

Lin, Y. Z.

Lu, H. H.

P. Y. Wu, H. H. Lu, C. L. Ying, C. Y. Li, and H. S. Su, “An up-converted phase modulated fiber optical CATV transport system,” IEEE/OSA, J. Lightwave Technol. 29(16), 2422–2427 (2011).
[CrossRef]

H. H. Lu, H. C. Peng, W. S. Tsai, C. C. Lin, S. J. Tzeng, and Y. Z. Lin, “Bidirectional hybrid CATV/radio-over-fiber WDM transport system,” Opt. Lett. 35(3), 279–281 (2010).
[CrossRef] [PubMed]

S. J. Tzeng, H. H. Lu, C. Y. Li, K. H. Chang, and C. H. Lee, “CSO/CTB performance improvement by using Fabry-Perot etalon at the receiving site,” Prog. Electromagn Res Lett. 6(14), 107–113 (2009).
[CrossRef]

H. H. Lu, A. S. Patra, S. J. Tzeng, H. C. Peng, and W. I. Lin, “Improvement of fiber optical CATV transport systems performance based on lower-frequency side mode injection-locked technique,” IEEE Photon. Technol. Lett. 20(5), 351–353 (2008).
[CrossRef]

Mathur, A.

D. Piehler, X. Zou, C. Y. Kuo, A. Nilsson, J. Kleefeld, G. Garcia, J. D. Ralston, and A. Mathur, “55dB CNR over 50km of fiber in an 80-channel externally-modulated AM-CATV system without optical amplification,” Electron. Lett. 33(3), 226–227 (1997).
[CrossRef]

Mohrdiek, S.

S. Mohrdiek, H. Burkhard, and H. Walter, “Chirp reduction of directly modulated semiconductor lasers at 10 Gb/s by strong CW light injection,” IEEE/OSA, J. Lightwave Technol. 12(3), 418–424 (1994).
[CrossRef]

Nilsson, A.

D. Piehler, X. Zou, C. Y. Kuo, A. Nilsson, J. Kleefeld, G. Garcia, J. D. Ralston, and A. Mathur, “55dB CNR over 50km of fiber in an 80-channel externally-modulated AM-CATV system without optical amplification,” Electron. Lett. 33(3), 226–227 (1997).
[CrossRef]

Ott, D. M.

M. R. Phillips and D. M. Ott, “Crosstalk due to optical fiber nonlinearities in WDM CATV lightwave systems,” IEEE/OSA, J. Lightwave Technol. 17(10), 1782–1792 (1999).
[CrossRef]

Ozdur, I.

N. Hoghooghi, I. Ozdur, S. Bhooplapur, and P. J. Delfyett, “Direct modulation and channel filtering of phase-modulated signals using an injection-locked VCSEL,” IEEE Photon. Technol. Lett. 22(20), 1509–1511 (2010).
[CrossRef]

Patra, A. S.

H. H. Lu, A. S. Patra, S. J. Tzeng, H. C. Peng, and W. I. Lin, “Improvement of fiber optical CATV transport systems performance based on lower-frequency side mode injection-locked technique,” IEEE Photon. Technol. Lett. 20(5), 351–353 (2008).
[CrossRef]

Peng, H. C.

H. H. Lu, H. C. Peng, W. S. Tsai, C. C. Lin, S. J. Tzeng, and Y. Z. Lin, “Bidirectional hybrid CATV/radio-over-fiber WDM transport system,” Opt. Lett. 35(3), 279–281 (2010).
[CrossRef] [PubMed]

H. H. Lu, A. S. Patra, S. J. Tzeng, H. C. Peng, and W. I. Lin, “Improvement of fiber optical CATV transport systems performance based on lower-frequency side mode injection-locked technique,” IEEE Photon. Technol. Lett. 20(5), 351–353 (2008).
[CrossRef]

Phillips, M. R.

M. R. Phillips and D. M. Ott, “Crosstalk due to optical fiber nonlinearities in WDM CATV lightwave systems,” IEEE/OSA, J. Lightwave Technol. 17(10), 1782–1792 (1999).
[CrossRef]

Piehler, D.

D. Piehler, X. Zou, C. Y. Kuo, A. Nilsson, J. Kleefeld, G. Garcia, J. D. Ralston, and A. Mathur, “55dB CNR over 50km of fiber in an 80-channel externally-modulated AM-CATV system without optical amplification,” Electron. Lett. 33(3), 226–227 (1997).
[CrossRef]

Ralston, J. D.

D. Piehler, X. Zou, C. Y. Kuo, A. Nilsson, J. Kleefeld, G. Garcia, J. D. Ralston, and A. Mathur, “55dB CNR over 50km of fiber in an 80-channel externally-modulated AM-CATV system without optical amplification,” Electron. Lett. 33(3), 226–227 (1997).
[CrossRef]

Su, H. S.

P. Y. Wu, H. H. Lu, C. L. Ying, C. Y. Li, and H. S. Su, “An up-converted phase modulated fiber optical CATV transport system,” IEEE/OSA, J. Lightwave Technol. 29(16), 2422–2427 (2011).
[CrossRef]

Tsai, W. S.

Tzeng, S. J.

H. H. Lu, H. C. Peng, W. S. Tsai, C. C. Lin, S. J. Tzeng, and Y. Z. Lin, “Bidirectional hybrid CATV/radio-over-fiber WDM transport system,” Opt. Lett. 35(3), 279–281 (2010).
[CrossRef] [PubMed]

S. J. Tzeng, H. H. Lu, C. Y. Li, K. H. Chang, and C. H. Lee, “CSO/CTB performance improvement by using Fabry-Perot etalon at the receiving site,” Prog. Electromagn Res Lett. 6(14), 107–113 (2009).
[CrossRef]

H. H. Lu, A. S. Patra, S. J. Tzeng, H. C. Peng, and W. I. Lin, “Improvement of fiber optical CATV transport systems performance based on lower-frequency side mode injection-locked technique,” IEEE Photon. Technol. Lett. 20(5), 351–353 (2008).
[CrossRef]

Walter, H.

S. Mohrdiek, H. Burkhard, and H. Walter, “Chirp reduction of directly modulated semiconductor lasers at 10 Gb/s by strong CW light injection,” IEEE/OSA, J. Lightwave Technol. 12(3), 418–424 (1994).
[CrossRef]

Wieczorek, S.

S. Wieczorek, W. W. Chow, L. Chrostowski, and C. J. Chang-Hasnain, “Improved semiconductor-laser dynamics from induced population pulsation,” IEEE J. Sel. Top. Quantum Electron. 42(6), 552–562 (2006).
[CrossRef]

Wu, P. Y.

P. Y. Wu, H. H. Lu, C. L. Ying, C. Y. Li, and H. S. Su, “An up-converted phase modulated fiber optical CATV transport system,” IEEE/OSA, J. Lightwave Technol. 29(16), 2422–2427 (2011).
[CrossRef]

Xue, X.

X. Xue, X. Zheng, H. Zhang, and B. Zhou, “Optical beamforming networks employing phase modulation and direct detection,” Opt. Commun. 284(12), 2695–2699 (2011).
[CrossRef]

Yabre, G.

G. Yabre, “Effect of relatively strong light injection on the chirp-to-power ratio and the 3 dB bandwidth of directly modulated semiconductor lasers,” IEEE/OSA, J. Lightwave Technol. 14(10), 2367–2373 (1996).
[CrossRef]

Ying, C. L.

P. Y. Wu, H. H. Lu, C. L. Ying, C. Y. Li, and H. S. Su, “An up-converted phase modulated fiber optical CATV transport system,” IEEE/OSA, J. Lightwave Technol. 29(16), 2422–2427 (2011).
[CrossRef]

Zhang, H.

X. Xue, X. Zheng, H. Zhang, and B. Zhou, “Optical beamforming networks employing phase modulation and direct detection,” Opt. Commun. 284(12), 2695–2699 (2011).
[CrossRef]

Zheng, X.

X. Xue, X. Zheng, H. Zhang, and B. Zhou, “Optical beamforming networks employing phase modulation and direct detection,” Opt. Commun. 284(12), 2695–2699 (2011).
[CrossRef]

Zhou, B.

X. Xue, X. Zheng, H. Zhang, and B. Zhou, “Optical beamforming networks employing phase modulation and direct detection,” Opt. Commun. 284(12), 2695–2699 (2011).
[CrossRef]

Zou, X.

D. Piehler, X. Zou, C. Y. Kuo, A. Nilsson, J. Kleefeld, G. Garcia, J. D. Ralston, and A. Mathur, “55dB CNR over 50km of fiber in an 80-channel externally-modulated AM-CATV system without optical amplification,” Electron. Lett. 33(3), 226–227 (1997).
[CrossRef]

Electron. Lett. (2)

D. Piehler, X. Zou, C. Y. Kuo, A. Nilsson, J. Kleefeld, G. Garcia, J. D. Ralston, and A. Mathur, “55dB CNR over 50km of fiber in an 80-channel externally-modulated AM-CATV system without optical amplification,” Electron. Lett. 33(3), 226–227 (1997).
[CrossRef]

O. Lidoyne and P. Gallion, “Analysis of receiver using injection-locked semiconductor laser for direct demodulation of PSK optical signals,” Electron. Lett. 27(11), 995–997 (1991).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (1)

S. Wieczorek, W. W. Chow, L. Chrostowski, and C. J. Chang-Hasnain, “Improved semiconductor-laser dynamics from induced population pulsation,” IEEE J. Sel. Top. Quantum Electron. 42(6), 552–562 (2006).
[CrossRef]

IEEE Photon. Technol. Lett. (4)

N. Hoghooghi, I. Ozdur, S. Bhooplapur, and P. J. Delfyett, “Direct modulation and channel filtering of phase-modulated signals using an injection-locked VCSEL,” IEEE Photon. Technol. Lett. 22(20), 1509–1511 (2010).
[CrossRef]

Q. Gu, W. Hofmann, M. C. Amann, and L. Chrostowski, “Optically injection-locked VCSEL as a duplex transmitter/receiver,” IEEE Photon. Technol. Lett. 20(7), 463–465 (2008).
[CrossRef]

H. H. Lu, A. S. Patra, S. J. Tzeng, H. C. Peng, and W. I. Lin, “Improvement of fiber optical CATV transport systems performance based on lower-frequency side mode injection-locked technique,” IEEE Photon. Technol. Lett. 20(5), 351–353 (2008).
[CrossRef]

H. Kim, S. B. Jun, and Y. C. Chung, “Raman crosstalk suppression in CATV overlay passive optical network,” IEEE Photon. Technol. Lett. 19 (9), 695–697 (2007).
[CrossRef]

IEEE/OSA, J. Lightwave Technol. (4)

P. Y. Wu, H. H. Lu, C. L. Ying, C. Y. Li, and H. S. Su, “An up-converted phase modulated fiber optical CATV transport system,” IEEE/OSA, J. Lightwave Technol. 29(16), 2422–2427 (2011).
[CrossRef]

S. Mohrdiek, H. Burkhard, and H. Walter, “Chirp reduction of directly modulated semiconductor lasers at 10 Gb/s by strong CW light injection,” IEEE/OSA, J. Lightwave Technol. 12(3), 418–424 (1994).
[CrossRef]

G. Yabre, “Effect of relatively strong light injection on the chirp-to-power ratio and the 3 dB bandwidth of directly modulated semiconductor lasers,” IEEE/OSA, J. Lightwave Technol. 14(10), 2367–2373 (1996).
[CrossRef]

M. R. Phillips and D. M. Ott, “Crosstalk due to optical fiber nonlinearities in WDM CATV lightwave systems,” IEEE/OSA, J. Lightwave Technol. 17(10), 1782–1792 (1999).
[CrossRef]

Opt. Commun. (1)

X. Xue, X. Zheng, H. Zhang, and B. Zhou, “Optical beamforming networks employing phase modulation and direct detection,” Opt. Commun. 284(12), 2695–2699 (2011).
[CrossRef]

Opt. Lett. (1)

Prog. Electromagn Res Lett. (1)

S. J. Tzeng, H. H. Lu, C. Y. Li, K. H. Chang, and C. H. Lee, “CSO/CTB performance improvement by using Fabry-Perot etalon at the receiving site,” Prog. Electromagn Res Lett. 6(14), 107–113 (2009).
[CrossRef]

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Figures (6)

Fig. 1
Fig. 1

(a) System I: A fiber optical CATV transport system using traditional DI and CATV receiver at the receiving site. (b) System II: The experimental configuration of our proposed fiber optical CATV transport systems employing an injection-locked DFB LD for the transceiver operations at the receiving site.

Fig. 2
Fig. 2

The experimental configuration of the simulated up-conversion CATV transport systems.

Fig. 3
Fig. 3

Electrical spectrum of the received two carriers (CH77 and CH78, down-converted from f1 and f2).

Fig. 4
Fig. 4

The measured downstream (a) CNR, (b) CSO, and (c) CTB values of system II; as DFB LD3 under 3, 0, and −3 dBm injection power levels, respectively.

Fig. 5
Fig. 5

The measured downstream (a) CNR, (b) CSO, and (c) CTB values for BTB, system I, and system II (DFB LD3 with 3 dBm injection).

Fig. 6
Fig. 6

The measured upstream (a) CNR, (b) CSO, and (c) CTB values for systems I and II.

Equations (1)

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d<± k c 2π S i S (1+ α 2 )

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