Enhancement the Optical Transmission System by Using One Electrode Semiconductor Optical Amplifier for short distances

Насир Самах Аббас Хассан – аспирант факультета Электроники, радиотехники и систем связи Института сферы обслуживания и предпринимательства (филиала) Донского государственного технического университета в г.Шахты.

Аннотация: Целью настоящего исследования является изучение характеристики передачи адаптивно-модулированных оптических сигналов с ортогональным частотным разделением (AMOOFDM) с оптическим усилением и компенсацией хроматической дисперсии без помех в одномодовых волоконных системах модуляции интенсивности и прямого детектирования (IMDD) с использованием одноэлектродных полупроводниковых усилителей оптического диапазона (1Е-SOAs) в качестве модуляторов интенсивности. Разработана теоретическая модель, описывающая характеристики модуляторов интенсивности на основе SOA, на базе которой определены оптимальные режимы работы SOA. Показано, что оптимизированные модуляторы интенсивности на базе SOA поддерживают передачу сигнала AMOOFDM со скоростью 35,1563 Гбит / с на протяжении 20 км SMF. Вышеупомянутое повышение производительности в основном связано со значительным уменьшением эффекта частотного импульсного сигнала с ИМ, возникающего в результате мощного насыщения SOA-усиления индуцированного уменьшения эффективного срока службы SOA. Определено, что относительно низкий коэффициент затухания и амплитудное ограничение модулированных сигналов SOA являются ключевыми факторами ограничивающими максимально достижимую характеристику передачи AMOOFDM, также мы отмечаем, что более высокое значение фактора альфа (Linw_en) уменьшает скорость системы передачи, потому что фактор альфа представляет собой отрицательную хроматическую дисперсию. Мои исследования показали, что влияние коэффициента ширины полосы больше, чем влияние коэффициента отношения оптического сигнала к шуму (OSNR) (коэффициент затухания) (ER) только для расстояний до 100 км. Для более чем 100 км влияние фактора OSNR больше, чем влияние фактора ширины полосы, и это исследование доказывает, что основным фактором искажения сигнала является расстояние, потому что расстояние передачи значительно влияет на скорость системы, так как при увеличении расстояния передачи, положительная хроматическая дисперсия будет увеличиваться, потому что одномодовое волокно представляет собой положительную хроматическую дисперсию в дополнение к увеличенному затуханию, которое попадает на оптический сигнал, но коэффициент увеличения ширины линии (Альфа-фактор) оказывает незначительное влияние на искажение сигнала, поскольку Альфа-фактор представляет собой отрицательную хроматическую дисперсию, все эти факторы вызывают снижение скорости системы, также обнаружен еще один фактор: влияние фактора амплитудного ограничения на линейность полупроводниковых усилителей оптического диапазона.

Ключевые слова: Полупроводниковый усилитель оптического диапазона, мультиплексирование с ортогональным частотным разделением, отношение «оптический сигнал-шум», коэффициент битовой ошибки и I-смещение

Abstract: The purpose of this research is to investigate in the transmission performance of Adaptively Modulated Optical Orthogonal Frequency Division Multiplexed (AMOOFDM) signals, in optical amplification and chromatic dispersion compensation-free in Single Mode Fiber (SMF)-Based Intensity-Modulation and Direct Detection (IMDD) systems using one electrode Semi-Conductor Optical Amplifiers (1E-SOAs) as intensity modulators (IM). A theoretical model describing the characteristics of the SOA-based IM is developed, based on which optimum SOA operating conditions are identified. It is shown that the optimized SOA -based intensity modulators support a 35.1563 Gb/s AMOOFDM signal transmission over a 20 Km SMF. The aforementioned performance enhancement is mainly due to a considerable reduction in the frequency chirp effect, resulting from the strong SOA gain saturation-induced decrease in SOA effective carrier lifetime. Relatively low extinction ratio and clipping of the SOA modulated signals are identified to be the key factors limiting the maximum achievable AMOOFDM transmission performance, Also we note the higher value of alpha factor (Linw_en) reduces the speed of the transmission system because the alpha factor represents the negative chromatic dispersion.

Keyword: Semiconductor Optical Amplifier (SOA), OFDM, OSNR, bit error rate (BER) and I-Bias.

Chapter 1: Optical Amplifier

1.1: Introduction to Optical Amplifiers:

The transmission distance of a fiber-optic communication system has traditionally been limited by fiber attenuation and by fiber distortion. By using opto-electronic repeaters, these problems have been eliminated. These repeaters convert the signal into an electrical signal, and then use a transmitter to send the signal again at a higher intensity than it was before. Because of the high complexity with modern wavelength-division multiplexed signals (including the fact that they had to be installed about once every 20 km), the cost of these repeaters is very high. An alternative approach is to use an optical amplifier, which amplifies the optical signal directly without having to convert the signal into the electrical domain. It is made by doping a length of fiber with the rare-earth mineral erbium, and pumping it with light from a laser with a shorter wavelength than the communications signal (typically 980 nm). Amplifiers have largely replaced repeaters in new installations [4].

1.2: Semiconductor Optical Amplifiers (SOA)

1.2.1: SOA – Basic Description: An SOA is an optoelectronic device that under suitable operating conditions can amplify an input light signal. A schematic diagram of a basic SOA is shown in Figure (1.1) [35]. The active region in the device imparts gain to an input signal. An external electric current provides the energy source that enables gain to take place. An embedded waveguide is used to confine the propagating signal wave to the active region. However, the optical confinement is weak so some of the signal will leak into the surrounding lossy cladding regions. The output signal is accompanied by noise. This additive noise is produced by the amplification process itself and so cannot be entirely avoided. The amplifier facets are reflective causing ripples in the gain spectrum.

image001

Figure ‎1-1. Schematic Diagram of an SOA [2].

1.2.2: Gain: SOAs amplify incident light through stimulated emission; the same mechanism used by semiconductor lasers. An optical amplifier is essentially a laser without feedback. Its most useful feature is the optical gain realized when the amplifier is pumped to achieve population inversion. The optical gain depends not only on the frequency (or wavelength) of the incident signal but also on the local beam intensity at any point inside the amplifier [35]. The single pass optical gain (image002) below saturation is approximately determined by:

image003(1.1)

Where spectral effects and non-uniform distribution of the carrier density are not considered.

image004: is the optical confinement factor, image005: is the material gain, image006: is optical loss, image007: is the cavity length, image008: is the active width, image009: is the thickness of the active region in which the carriers are confined, image010: is the electronic charge, image011: is the gain coefficient, image012: is the current injection efficiency, image013: is the operating current, image014: is the carrier density at the operating current I, image015: is the carrier density at transparency, image016: is the spontaneous recombination lifetime of the carriers.

Equation (1.1) indicates that a high gain may be achieved with a high injection current, a large optical confinement, a long cavity, a multiple quantum well (MQW) structure, or a combination of them.

Chapter 2: Electrical to Optical Conversion of OFDM Signal

2.1: Transmission System Diagram Using 1E-SOA:

Based on Figure 2.2: Transmission system diagram together with block diagrams of the transmitter and the receiver using E/O converter, we extract an new transmission system (in Figure 2.3) considered in this research is illustrated, which includes a transmitter involving an 1E-SOA performing intensity modulation, a single-channel optical amplification- and dispersion compensation-free SMF intensity-modulation and direct-detection (IMDD) transmission link, a square-law photon detector and a receiver. The generation, transmission and detection of the Adaptively Modulation Optical Orthogonal Frequency Division Multiplexing (AMOOFDM) signals are modeled following procedures. These procedures are outlined as follows:

image017

Figure ‎2-1. Transmission system diagram using 1E-SOA with block diagrams of the transmitter and the receiver.

2.2: Simulation Parameters:

In simulating the AMOOFDM modems, the total number of subcarriers M is taken to be 64. In the positive frequency bins, 31 subcarriers are used to carry original data and the remaining one subcarrier close to the optical carrier frequency is dropped. The signal modulation formats taken on each subcarrier vary from differential binary phase shift keying (DBPSK), differential quadrature phase shift keying (DQPSK), and 8-quadrature amplitude modulation (QAM) to 256-QAM. It is worth addressing that, for BPSK, QPSK and QAM signal modulation formats, pilot tones are adopted to perform channel estimation for each subcarrier. However, the use of DQPSK and DBPSK can not only eliminate pilot bits required, but also reduce the susceptibility of the signal transmission performance to variations in system operating conditions. The sampling rates of the DAC/ADC are fixed at 12.5 GS/s in both the transmitter and the receiver. The above-mentioned parameters give a signal bandwidth in the positive frequency bins of 12.5 /2 = 6.25 GHz. The bandwidth for each subcarrier is 6.25 /32 ≈ 195.3MHz. The cyclic prefix parameter defined in [20] is taken to be 25%, which gives a cyclic prefix length of 1.28 ns within each OFDM symbol having a total time duration of 6.4 ns. The bits of quantization and the signal clipping ratio are set to be 7-bits and 13 dB, respectively, which are the optimum values identified in [30]. The parameters used in simulating SOA-based intensity modulators are representative for InGaAsP semiconductor materials operating at a wavelength of ~1550 nm, as listed in Table I, where both the SOA parameters and their corresponding references are shown. The SOA parameters without any references being listed are chosen within their typical variation ranges [13], [23]-[25], [30]. By attenuating/amplifying the modulated optical output signals from the SOAs, the optical power coupled into the SMF system is fixed at 6.3dBm. The simulation parameters for SMFs and PIN detectors are also listed in Table I, together with their corresponding references. It should be pointed out that, in numerical simulations, all the parameter values mentioned above and listed in Table I are treated as default ones, unless addressed explicitly in the corresponding text where necessary.

Table ‎2-1. 1E-SOA, SMF and PIN Parameters.

1E-SOA

Parameter

Value

Cavity length 300μm

Width of active region 1.5μm [24]

Depth of active region 0.27μm

Carrier lifetime SOA 0.3ns [26]

Confinement factor 0.35

Line width enhancement factor 5 [25]

Group velocity 8.43×107m/s [24]

Optical frequency 1550nm

Differential gain 3×10-20m2 [32]

Carrier density at transparency 1.05×1024m-3 [32]

Noise figure 8dB

SMF

Parameter

Value

Effective area 80μm2 [20]

Dispersion 17.0ps/nm/km [20]

Dispersion slope 0.07ps/nm/nm/km [20]

Dispersion wavelength 1550nm [20]

Loss 0.2dB/km [20]

Kerr coefficient 2.35×10-20m2/W [20]

PIN

Parameter

Value

Quantum efficiency 0.8 [20]

Noise current density 8pA/√Hz [33]

Chapter 3: Results of Simulation

3.1: Introduction:

In this section we will show the results of many simulations that we have done to find the optimum operating point to our system with respect to the line width enhancement (Linw-en) factor. The line width enhancement factor α is known to have an important impact on semiconductor laser frequency stability. We determine under what general circumstances the value of α for a semiconductor laser may depend upon the longitudinal laser structure. A longitudinal modulation of the modal refractive index is shown not to have any influence on α, while our results indicate that a longitudinal modulation of the modal gain such as would be used in a gain coupled laser will in general change the line width enhancement factor.

The usefulness and the limitations of the concept of the line width enhancement factor alpha in semiconductor lasers are examined by considering the laser dynamics without the rate-equation approximation. The rate equations with a constant value of alpha can be used for semiconductor lasers operating continuously or modulated directly such that the carrier density does not change significantly during each modulation cycle. A new set of generalized Bloch equations should be used whenever sub picosecond optical pulses are involved.

3.2: One Electrode-SOA

We find in simulations already done that the highest capacity point (35.1563Gb/s) and Bit Error Rate (BER=0.00071235), is the one that has the following parameters: section length L=300µm, the Input Bias Current=50mA, Power input (Pin=20dBm) and Driving Current=80mA.

According to those parameters, we do our simulations here by varying the input power and the I-Bias Current to check the difference when the line width enhancement (Linw_en)=5.

3.2.1: One Section SOA with I-Bias = 50mA

Table ‎3-1. Table of different input power on different SMF lengths using Linw_en=5 and I-Bias=50mA.

image018

image019

Figure ‎3-1. Curves and OSNR for different input power on different SMF lengths using Linw_en=5 and I-Bias=50mA.

The curves above shows the performance of 1 Electrode SOA taking the length section L = 300µm and input current (peak to peak current) (IP2P) = 80mA, but now we are trying to change the value of input power Pin in dbm (0, 5, 10, 20) using Linw_en=5 (figure 3-1)

Retrieve the system capacity using different P-in, SMF distance and the following parameter:

I-Bias=50mA, L=300µm, IP2P=80mA

We did the simulation with different single mode fiber (SMF) transmission distances of (20Km, 60Km, 100Km, 120Km and 140Km) to check which one will gives us the highest capacity in Gb/s using Linw_en=5.

The Results are: From 20Km to 100Km, the input of 20dBm will gives us the highest capacity which is 35.1563Gbps, 31.25Gbps, 23.75Gbps respectively. At 120Km, the input of 10dBm will gives us the highest capacity which is 16.7188Gbps. At 140Km, the input of 0dBm, 10dBm will gives us the highest capacity which is 9.0625Gbps.

3.2.2: One section SOA with I-Bias = 100mA

Table ‎3-2. Table of different input power on different SMF lengths using Linw_en=5 and I-Bias=100mA.

image020

The curves above shows the performance of 1 Electrode SOA taking the length section L=300 and input current (peak to peak current) (IP2P) = 80mA, but now we are trying to change the value of input power p-in in dbm (0, 5, 10, 20) using Linw_en=5 (figure 3-2). Retrieve the system capacity using different P-in, SMF distance and the following parameter: I-Bias = 100 mA.We did the simulation with different single mode fiber (SMF) transmission distances of (20Km, 60Km, 100Km, 120Km and 140Km) to check which one will gives us the highest capacity in Gb/s using Linw_en=5. The Results are:

From 20Km to 100Km, the input of 20dBm will gives us the highest capacity which is 34.0625Gbps, 31.0938Gbps, 23.75Gbps respectively.

At 120Km, the input of 5dBm will gives us the highest capacity which is 16.56Gbps.

At 140Km, the input of 5dBm will gives us the highest capacity which is 9.218Gbps.

3-3: Conclusion

In this work we have studied the potential of using a one electrodes SOA as an intensity modulator for an AMOOFDM system, the simulation results showed that the device can achieve high transmission capacities of 35.156 Gb/s even for high optical input powers of 20dBm, I-Bias=50mA and Linw_en=5. We have done a lot of simulations in order to find the optimum operating conditions of the device in terms of optical input power, bias current and distance of transmission. We have found a range of parameters in which it is possible to use the device for good transmission performance; moreover, we have done a simulation of the system under the optimum operating conditions with single mode fiber transmission distances from 20 up to 140Km. For the one section of the SOA with all values of bias current (50, 100mA), we have found that for short distances, we must have a high optical input power in order to have a high system capacity, while for long transmission distances we must decrease the optical input power to have a good transmission performance. The reason for the highest performance for the low optical input power of 5 and 10 dBm for long transmission distances compared with the 20dBm optical input power case is due to the fact that the more we increase the optical input power the more we are in the saturation mode of the SOA and thus the higher is the nonlinearity of the SOA, therefore we will have the RF signal clipped, the signal to noise ratio will be lower and we will have a degradation in performance for the long transmission distances because we will have attenuation. My research proved that the effect of the band width factor is greater than effect of optical signal to noise ratio factor (OSNR) (Extinction ratio) (ER) only for distances up to 100 Km. For more than 100Km the effect of the OSNR factor is greater than effect of band width factor. This research proved that the main factor for the signal distortion is the distance because the transmission distance significantly affect on the speed of the system because when we increase the transmission distance, the positive chromatic dispersion will increase because the single mode fiber represent the positive chromatic dispersion in addition to increased attenuation that get on the optical signal but Line width enhancement factor (alpha factor) have a minor effect on the signal distortion because the alpha factor represents the negative chromatic dispersion, all these factors cause a decrease system speed, also found another factor is clipping factor effects on the linearity of optical semiconductors amplifiers. The aforementioned performance enhancement is mainly due to a considerable reduction in the frequency chirp effect, resulting from the strong SOA gain saturation-induced decrease in SOA effective carrier lifetime. Relatively low extinction ratio and clipping of the SOA modulated signals are identified to be the key factors limiting the maximum achievable AMOOFDM transmission performance.

3.4: Future Works

As future work we can implement the simulation for I-Bias 150,200 mA

References

  1. J. L. Wei, A. Hamié, R. P. Giddings, and J. M. Tang, "Semiconductor Optical Amplifier-Enabled Intensity Modulation of Adaptively Modulated Optical OFDM Signals in SMF-Based IMDD Systems", IEEE, JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 27, NO. 16, AUGUST 15, 2009
  2. Moussa Kafal, “Intensity Modulation of Optical OFDM Signals Using Low-cost Semiconductor devices,” Doctoral School of The Lebanese University in Cooperation with the Engineering School in Berst-France, 2012.
  3. Harry J. R. Dutton, “Understanding Optical Communications,” International Technical Support Organization, September 1998.
  4. Ali Mokdad and Souad Mamo, “Comparison between one section Semiconductor Optical Amplifiers (1S-SOAs) and Two Electrode Semiconductor Optical Amplifiers (2S-SOAs),” Hamra - Lebanon, 2012.
  5. JOAN M. GENÉ BERNAUS, “FIBER-OPTIC COMMUNICATIONS,” UNIVERSITAT POLITÈCNICA DE CATALUNYA, 27 SEPTEMBER 2010.
  6. J. A. C. Bingham, “Multicarrier modulation for data transmission: An idea whose time has come,” IEEE Commun. Mag., vol. 28, pp. 5–14, 1990.
  7. J. H. Stott, “The how and why of COFDM,” EBUTech. Rev., pp. 43–50, 1998.
  8. H. Bülow, “Electronic dispersion compensation,” presented at the Proc. OFC/NFOEC 2007, Anaheim, CA, Mar. 25–29, 2007, Tutorial, OMG5.
  9. B. Spinnler, “Recent advances on polarization multiplexing,” presented at the Proc. IEEE Summer Topicals, 2008, TuD2.3.
  10. Jean Armstrong, Senior Member, IEEE, “OFDM for Optical Communications,” JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 27, NO. 3, FEBRUARY 1, 2009.
  11. John G. Proakis and Masoud Salehi, “COMMUNICATION SYSTEMS ENGINEERING,” New Jersey, August 9, 2001.
  12. David Tse, “A Brief History of Communication”.
  13. M. J. Connelly, “Semiconductor Optical Amplifiers,”. London, U.K. Kluwer, 2002.
  14. R. J. Manning, A. D. Ellis, A. J. Poustie, and K. J. Blow, “Semiconductor laser amplifiers for ultrafast all-optical signal processing,” J. Opt. Soc. Amer. B, vol. 14, no. 1, pp. 3204–3216, Nov. 1997.
  15. D. Nesset, T. Kelly, and D. Marcenac, “All-optical wavelength conversion using SOA nonlinearities,” IEEE Commun. Mag., vol. 36, no. 12, pp. 56–61, Dec. 1998.
  16. J. Dong, X. Zhang, Y. Wang, J. Xu, and D. Huang, “40 Gbit/s reconfigurable photonic logic gates based on various nonlinearities in single SOA,” Electron. Lett., vol. 43, no. 16, pp. 884 886, Aug. 2007.
  17. L. H. Spiekman, J. M. Wiesenfeld, A. H. Gnauck, L. D. Garrett, G. N. Van den Hoven, T. van Dongen, M. J. H. Sander-Jochem, and J. J. M. Binsma, “Transmission of 8 DWDM channels at 20 Gb/s over 160 km of standard fiber using a cascade of semiconductor optical amplifiers,” IEEE Photon. Tech. Lett., vol. 12, no. 6, pp. 717–719, Jun. 2000.
  18. J. M. Tang, P. M. Lane, and K. A. Shore, “High speed transmission of adaptively modulated optical OFDM signals over multimode fibers using directly modulated DFBs,” J. Lightw. Technol., vol. 24, no. , pp. 429–441, Jan. 2006.
  19. X. Q. Jin, J. M. Tang, P. S. Spencer, and K. A. Shore, “Optimization of adaptively modulated optical OFDM modems for multimode fiberbased local area networks,” J. Opt. Netw., vol. 7, no. 2, pp. 198–214, Feb. 2008.
  20. J. M. Tang and K. A. Shore, “30 Gb/s signal transmission over 40-km directly modulated DFB-laser-based single-mode-fibre links without optical amplification and dispersion compensation,” J. Lightw. Technol., vol. 24, no. 6, pp. 2318–232, Jun. 2006.
  21. X. Zheng, J. L. Wei, and J. M. Tang, “Transmission performance of adaptively modulated optical OFDM modems using subcarrier modulation over SMF IMDD links for access and metropolitan area networks,” Opt. Exp., vol. 16, no. 25, pp. 20427–20440, Dec. 2008.
  22. J. L. Wei, X. Q. Jin, and J. M. Tang, “The influence of directly modulated DFB lasers on the transmission performance of carrier suppressed single sideband optical OFDM signals over IMDD SMF systems,” J. Lightw. Technol., 2008, accepted for publication.
  23. A. J. Lowery, L. B. Du, and J. Armstrong, “Performance of optical OFDM in ultralong-haul WDM lightwave systems,” J. Lightw. Technol., vol. 25, no. 1, pp. 131–138, Jan. 2007.
  24. J. M. Tang and K. A. Shore, “Strong picosecond optical pulse propagation in semiconductor optical amplifiers at transparency,” IEEE J. Quantum Electron., vol. 34, no. 7, pp. 1263–1269, Jul. 1998.
  25. J. M. Tang and K. A. Shore, “Analysis of the characteristics of TOAD’s subject to frequency-detuned control and signal picosecond pulses,” IEEE J. Quantum Electron., vol. 35, no. 11, pp. 1704–1712, Nov. 1999.
  26. J. M. Tang and K. A. Shore, “Characteristics of optical phase conjugation of picosecond pulses in semiconductor optical amplifiers,” IEEE J. Quantum Electron., vol. 35, no. 7, pp. 1032–1040, Jul. 1999.
  27. J. M. Tang and K. A. Shore, “Active picoseconds optical pulse compression in semiconductor optical amplifiers,” IEEE J. Quantum Electron., vol. 35, no. 1, pp. 93–100, Jan. 1999.
  28. T. Duong, N. Genay, P. Chanclou, B. Charbonnier, A. Pizzinat, and R. Brenot, “Experimental demonstration of 10 Gbit/s for upstream transmission by remote modulation of 1 GHz RSOA using Adaptively Modulated Optical OFDM for WDM-PON single fiber architecture,” presented at the Eur. Conf. Opt. Commun. (ECOC), Brussels, Belgium, 2008, PD paper Th.3.F.1, unpublished.
  29. N. A. Olsson, “Lightwave systems with optical amplifiers,” J. Lightw. Technol., vol. 7, no. 7, pp. 1071–1082, Jul. 1989.
  30. G. P. Agrawal, Fibre-Optic Communication Systems, 2nd ed. Hoboken, NJ: Wiley, 1997.
  31. J. M. Tang and K. A. Shore, “Maximizing the transmission performance of adaptively modulated optical OFDM signals in multimode- fiber links by optimizing analog-to-digital converters,” J. Lightw. Technol., vol. 25, no. 3, pp. 787–798, Mar. 2007.
  32. J. Mørk, A. Mecozzi, and G. Eisenstein, “The modulation response of a semiconductor laser amplifier,” J. Sel. Topics. Quantum. Electron., vol. 5, no. 3, pp. 851–860, May/Jun. 1999.
  33. P. Fay, W. Wohlmuth, A. Mahajan, C. Caneau, S. Chandrasekhar, and I. Adesida, “Low noise performance of monolithically integrated 12-Gb/s p-i-n/HEMT photoreceiver for long wavelength transmission systems,” IEEE Photon. Tech. Lett., vol. 10, no. 5, pp. 713–715, May. 1998.
  34. R. Gutiérrez-Castrejón, L. Schares, L. Occhi, and G. Guekos, “Modeling and measurement of longitudinal gain dynamics in saturated semiconductor optical amplifiers of different length,” IEEE J. Quantum Electron., vol. 36, no. 12, pp. 1476–1484, Dec. 2000.
  35. 250 N. Mines Rd., Livermore CA 94551, “The Enhanced Functionalities of Semiconductor Optical Amplifiers and their Role in Advanced Optical Networking” InPhenix, Inc., 250 N. August, 2011.
  36. H. Khaleghi, P. Morel, A. Sharaiha, T. Rampone, and M. Guegan, “SOA modeling for advanced optical modulation formats,” in Numerical Simulation of Optoelectronic Devices (NUSOD), 2011 11th International Conference on, 2011, pp. 1997 –1998.
  37. G. P. Agrawal and N. A. Olsson, “Self-phase modulation and spectral broadening of optical pulses in semiconductor laser amplifiers,” Quantum Electronics, IEEE Journal of, vol. 25, no. 11, pp. 2297 –2306, Nov. 1989.
  38. Y. Boucher and A. Sharaiha, “Spectral properties of amplified spontaneous emission in semiconductor optical amplifiers,” Quantum Electronics, IEEE Journal of, vol. 36, no. 6, pp. 708 –720, Jun. 2000.
  39. W. Moench and J. Larikova, “Measuring the Optical Signal-to-Noise Ratio in Agile Optical Networks,” in Optical Fiber Communication and the National Fiber Optic Engineers Conference, 2007. OFC/NFOEC 2007. Conference on, 2007, pp. 1 –6.
  40. R. A. Shafik, S. Rahman, and A. R. Islam, “On the Extended Relationships Among EVM, BER and SNR as Performance Metrics,” in Electrical and Computer Engineering, 2006. ICECE ’06. International Conference on, 2006, pp. 408 –411.