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LosslessOperationinInPMach-ZehnderModulator MonolithicallyIntegratedwithSemiconductorOpticalAmplier 413 broadening as a result of the instantaneous frequency change of the signal light, a phenomenon normally designated as ‘chirp’. Therefore, frequency chirping is an important issue in any discussion of the dynamic modulation characteristics of a modulator. The amount of chirp is expressed by using a chirp parameter cp , and the parameter is defined by [Kawanishi et al. (2001)] ' cp nn (1) where n and n’ are the relative changes in the real and imaginary parts of the complex refractive index, respectively. It is well known that a negative chirp parameter of around -0.7 provides the best transmission distance results when using an NRZ intensity modulation format through an SMF fiber, while zero chirp is required for an advanced modulation format that utilizes phase information as well as intensity information such as the optical duobinary format. Therefore, we examined the dynamic modulation characteristics under two different driving conditions, namely a negative chirp condition and a zero chirp condition. A. Negative chirp condition We investigated the dynamic modulation characteristics when we applied a 2 31 -1 pseudorandom binary sequence (PRBS) NRZ pattern at a bit rate of 9.953 Gbit/s to the MZM across the C-band. For the negative chirp driving condition, phase modulator 1 in the upper arm was dc biased and modulated with an NRZ signal of 3.0 V pp , while phase modulator 2 in the lower arm was only dc biased to adjust the operation condition. The chirp parameter of the Mach-Zehnder modulator can be represented by 12 12 cp VV VV (2) where V 1 and V 2 are the modulation (RF) voltages applied to electrode1 of phase modulator 1 in the upper arm and to electrode2 of phase modulator 2 in the lower arm, respectively. Under this driving condition, since phase modulator 2 in the lower arm was only dc biased, V 2 = 0. Therefore, according to equation (2), the calculated chirp parameter cp was -1. The fiber input optical power was -4.6 dBm, and the bias current to the SOA was 100 mA. Under this condition, the monolithic device had a signal gain of over 10 dB. Figure 6(a) shows electrically filtered back-to-back eye diagrams for the measured wavelength region of 1530 to 1560 nm. The waveforms were almost the same for the entire C-band region and the dynamic ER exceeded 9.6 dB for all wavelengths. The bit error rate (BER) performance is shown in Fig. 7. Error free operation was confirmed for every wavelength. The wavelength dependence of the variation in received power sensitivity at a BER of 10 -12 was less than 0.5 dB for the measured wavelength region. The transmission characteristics were then investigated using a 100-km long SMF. Electrically filtered eye diagrams after a 100-km transmission are shown in Fig. 6(b). Clear eye opening was obtained even after 100-km transmission. The BER characteristics of the transmitted signal are also shown in Fig. 7. As shown in the figure, no floor was observed in the BER curve for any of the wavelengths, and error free operation after transmission was confirmed for every wavelength. The power penalty defined by the sensitivity degradation at a BER of 10 -12 after a 100-km transmission was less than 1.5 dB across the C-band. Fig. 6. Eye diagrams of back-to-back(a), and after 100-km transmission. Fig. 7. Bit-error-rate characteristics for NRZ modulation. SemiconductorTechnologies414 B. Zero chirp condition We examined the optical duobinary format for a zero-chirp driving condition [Yonenaga et al. (1997)]. The feature of an optical duobinary signal is its narrow spectral broadening compared with that of conventional non-return-to-zero (NRZ) modulation. An optical duobinary signal enables us to realize high-speed transmission with a large chromatic dispersion tolerance and a dense wavelength-division-multiplexing (DWDM) transmission with low adjacent channel crosstalk. Figure 8(a) is a diagram showing a method for generating an optical duobinary signal from a three-level electrical duobinary signal using an MZ modulator. A three-level electrical duobinary encoded signal ("-1", "0" and "1") is converted into a two-level optical duobinary signal ("1" and "0"), which is identical to the original binary signal inverted. The experimental setup is shown in Fig. 8(b). A TE polarized continuous-wave (CW) light is input into the dual-drive SOA-MZM using a lensed polarization maintaining fiber (PMF) with a coupling loss of 4 dB/facet. The optical duobinary signal is generated by differentially driving the MZM using three-level electrical signals with an amplitude of V while the MZM was dc biased at the null point where the optical output exhibits its minimum value without the RF modulation. As the modulation voltages were applied differentially, namely in a push-pull manner, V 1 = V 2 , and therefore, according to equation (2), the calculated chirp parameter cp was 0. The three-level electrical signals were generated by low-pass filtering the 2 31 -1 pseudorandom binary sequence (PRBS) NRZ signals at a bit rate of 9.953 Gbit/s with a cut-off frequency of 3 GHz. The output optical duobinary signals from the SOA-MZM were also coupled with the lensed SMF with a coupling loss of 4 dB. Following the 100-km SMF transmission, an erbium- doped fiber amplifier (EDFA) was employed to compensate for the fiber loss. The receiver consisted of an EDFA, an optical band-pass filter, a photodiode, and a clock and data recovery (CDR) circuit. The BER was measured using an error detector with the change of the input power into the receiver by a variable optical attenuator. The wavelengths of the CW light were 1550 nm. The temperature of the device was controlled at 25 ºC. The transmission characteristics were investigated for SMF lengths of 0 (back-to-back), 60, 100, 160, and 200 km. Figure 9(a) shows a back-to-back eye diagram of 10 Gbit/s optical duobinary signals using the SOA-MZM under the null condition shown in Fig. 3. Considering the electrical high- frequency loss at bias-T, and the connecting cables, the driving voltage was set at 2.8 peak- to-peak voltage (V pp ), which is slightly larger than the V value of 2.6 V shown in Fig. 3. The optical spectrum of the duobinary signal is shown in Fig. 9(b). We observed a narrow bandwidth with a 20-dB bandwidth of 13.6 GHz and no carrier frequency component, which is evidence that optical duobinary modulation was successfully realized with the fabricated MZ-SOA. Figure 10(a) shows the measured eye diagrams for 10 Gbit/s optical duobinary signals after 60-, 100-, 160-, and 200-km SMF transmissions. Although chromatic dispersion degraded the eye opening as the transmission distance increased, clear eye opening was still obtained after a 200-km transmission. Figure 10(b) shows simulated results assuming a fiber dispersion of 16 ps/nm/km. Fig. 8. Principle of generating optical duobinary signal (a), and experimental set-up (b). Fig. 9. Eye diagram (a) and optical spectrum (b) of the optical duobinary signal. As can be seen, the experimental and simulation results are very similar for all distances, indicating the good quality of the modulator. Figure 11 shows the BER characteristics for all transmissions at a wavelength of 1550 nm. No floors were observed in the BER curves and error free operation was confirmed for all transmission distances. The power penalties defined by the sensitivity degradation at a BER of 10 -12 were -0.7, -1.5, 0.4, 1.4 dB for 60-, 100-, 160-, and 200-km transmissions, respectively. These results are very similar to those obtained with a conventional (or non-integrated) MZ module [Kurosaki et al. (2007)], and therefore we can conclude that the monolithic integration process used in this work does not degrade the modulator quality. Figure 12 shows the wavelength dependence of the power penalty. The power penalty is less than -0.4, -1.4, 0.7, 2.3 dB for 60-, 100-, 160-, and 200-km transmissions, respectively, for the entire C-band region. These results prove that this LosslessOperationinInPMach-ZehnderModulator MonolithicallyIntegratedwithSemiconductorOpticalAmplier 415 B. Zero chirp condition We examined the optical duobinary format for a zero-chirp driving condition [Yonenaga et al. (1997)]. The feature of an optical duobinary signal is its narrow spectral broadening compared with that of conventional non-return-to-zero (NRZ) modulation. An optical duobinary signal enables us to realize high-speed transmission with a large chromatic dispersion tolerance and a dense wavelength-division-multiplexing (DWDM) transmission with low adjacent channel crosstalk. Figure 8(a) is a diagram showing a method for generating an optical duobinary signal from a three-level electrical duobinary signal using an MZ modulator. A three-level electrical duobinary encoded signal ("-1", "0" and "1") is converted into a two-level optical duobinary signal ("1" and "0"), which is identical to the original binary signal inverted. The experimental setup is shown in Fig. 8(b). A TE polarized continuous-wave (CW) light is input into the dual-drive SOA-MZM using a lensed polarization maintaining fiber (PMF) with a coupling loss of 4 dB/facet. The optical duobinary signal is generated by differentially driving the MZM using three-level electrical signals with an amplitude of V while the MZM was dc biased at the null point where the optical output exhibits its minimum value without the RF modulation. As the modulation voltages were applied differentially, namely in a push-pull manner, V 1 = V 2 , and therefore, according to equation (2), the calculated chirp parameter cp was 0. The three-level electrical signals were generated by low-pass filtering the 2 31 -1 pseudorandom binary sequence (PRBS) NRZ signals at a bit rate of 9.953 Gbit/s with a cut-off frequency of 3 GHz. The output optical duobinary signals from the SOA-MZM were also coupled with the lensed SMF with a coupling loss of 4 dB. Following the 100-km SMF transmission, an erbium- doped fiber amplifier (EDFA) was employed to compensate for the fiber loss. The receiver consisted of an EDFA, an optical band-pass filter, a photodiode, and a clock and data recovery (CDR) circuit. The BER was measured using an error detector with the change of the input power into the receiver by a variable optical attenuator. The wavelengths of the CW light were 1550 nm. The temperature of the device was controlled at 25 ºC. The transmission characteristics were investigated for SMF lengths of 0 (back-to-back), 60, 100, 160, and 200 km. Figure 9(a) shows a back-to-back eye diagram of 10 Gbit/s optical duobinary signals using the SOA-MZM under the null condition shown in Fig. 3. Considering the electrical high- frequency loss at bias-T, and the connecting cables, the driving voltage was set at 2.8 peak- to-peak voltage (V pp ), which is slightly larger than the V value of 2.6 V shown in Fig. 3. The optical spectrum of the duobinary signal is shown in Fig. 9(b). We observed a narrow bandwidth with a 20-dB bandwidth of 13.6 GHz and no carrier frequency component, which is evidence that optical duobinary modulation was successfully realized with the fabricated MZ-SOA. Figure 10(a) shows the measured eye diagrams for 10 Gbit/s optical duobinary signals after 60-, 100-, 160-, and 200-km SMF transmissions. Although chromatic dispersion degraded the eye opening as the transmission distance increased, clear eye opening was still obtained after a 200-km transmission. Figure 10(b) shows simulated results assuming a fiber dispersion of 16 ps/nm/km. Fig. 8. Principle of generating optical duobinary signal (a), and experimental set-up (b). Fig. 9. Eye diagram (a) and optical spectrum (b) of the optical duobinary signal. As can be seen, the experimental and simulation results are very similar for all distances, indicating the good quality of the modulator. Figure 11 shows the BER characteristics for all transmissions at a wavelength of 1550 nm. No floors were observed in the BER curves and error free operation was confirmed for all transmission distances. The power penalties defined by the sensitivity degradation at a BER of 10 -12 were -0.7, -1.5, 0.4, 1.4 dB for 60-, 100-, 160-, and 200-km transmissions, respectively. These results are very similar to those obtained with a conventional (or non-integrated) MZ module [Kurosaki et al. (2007)], and therefore we can conclude that the monolithic integration process used in this work does not degrade the modulator quality. Figure 12 shows the wavelength dependence of the power penalty. The power penalty is less than -0.4, -1.4, 0.7, 2.3 dB for 60-, 100-, 160-, and 200-km transmissions, respectively, for the entire C-band region. These results prove that this SemiconductorTechnologies416 compact lossless MZM performs sufficiently well for application to optical duobinary transmission systems. Fig. 10 Experimentally measured (a) and simulated (b) eye diagrams of optical duobinary signal after SMF transmission. Fig. 11. Bit-error-rate characteristics for optical duobinary modulation. Fig. 12. Wavelength dependence of the power penalty. 5. Conclusion An InP n-p-i-n MZM and an SOA were monolithically integrated to compensate for insertion loss. The device gain exceeded 10 dB, and fiber-to-fiber lossless operation was demonstrated for the entire C-band region. By using a lossless MZM, error free 100-km SMF transmissions were also demonstrated using an NRZ format at a bit rate of 10 Gbit/s for the entire C-band wavelength region. The measured power penalty after a 100-km transmission was only 1.5 dB. 10-Gbit/s optical duobinary transmissions were also demonstrated using the fabricated device. Lossless and error free operation was achieved with power penalties of less than - 0.4, -1.4, 0.7, 2.3 dB for 0- (back-to-back), 60-, 100-, 160-, and 200-km SMF transmissions, respectively, at a low driving voltage of 2.8 V pp for push-pull operation. By comparing the experimental and simulation results, we confirmed that the modulation characteristics of this SOA-integrated lossless modulator are comparable to those of a discrete modulator. These results prove that this compact lossless MZM performs sufficiently well for application to optical duobinary transmission systems, and the integration process does not degrade modulator performance. These results constitute an important step towards achieving compact tunable light sources, realized by integrating a tunable laser and an MZM. 6. References Barton, J. S.; Skogen, E. J.; Masanovic, M. L.; Denbaars, S. P. &Coldren, L. A. (2003). A widely tunable high-speed transmitter using an integrated SGDBR laser- semiconductor optical amplifier and Mach-Zehnder modulator. IEEE J. Sel. Topics Quantum Electron., 9, 1113-1117 LosslessOperationinInPMach-ZehnderModulator MonolithicallyIntegratedwithSemiconductorOpticalAmplier 417 compact lossless MZM performs sufficiently well for application to optical duobinary transmission systems. Fig. 10 Experimentally measured (a) and simulated (b) eye diagrams of optical duobinary signal after SMF transmission. Fig. 11. Bit-error-rate characteristics for optical duobinary modulation. Fig. 12. Wavelength dependence of the power penalty. 5. Conclusion An InP n-p-i-n MZM and an SOA were monolithically integrated to compensate for insertion loss. The device gain exceeded 10 dB, and fiber-to-fiber lossless operation was demonstrated for the entire C-band region. By using a lossless MZM, error free 100-km SMF transmissions were also demonstrated using an NRZ format at a bit rate of 10 Gbit/s for the entire C-band wavelength region. The measured power penalty after a 100-km transmission was only 1.5 dB. 10-Gbit/s optical duobinary transmissions were also demonstrated using the fabricated device. Lossless and error free operation was achieved with power penalties of less than - 0.4, -1.4, 0.7, 2.3 dB for 0- (back-to-back), 60-, 100-, 160-, and 200-km SMF transmissions, respectively, at a low driving voltage of 2.8 V pp for push-pull operation. By comparing the experimental and simulation results, we confirmed that the modulation characteristics of this SOA-integrated lossless modulator are comparable to those of a discrete modulator. These results prove that this compact lossless MZM performs sufficiently well for application to optical duobinary transmission systems, and the integration process does not degrade modulator performance. These results constitute an important step towards achieving compact tunable light sources, realized by integrating a tunable laser and an MZM. 6. References Barton, J. S.; Skogen, E. J.; Masanovic, M. L.; Denbaars, S. P. &Coldren, L. A. (2003). A widely tunable high-speed transmitter using an integrated SGDBR laser- semiconductor optical amplifier and Mach-Zehnder modulator. IEEE J. Sel. Topics Quantum Electron., 9, 1113-1117 SemiconductorTechnologies418 Kawanishi, T.; Kogo, K.; Okikawa, S. &Izutsu, M. (2001). Direct measurement of chirp parameters of high-speed Mach-Zehnder-type optical modulators. Optics Communications, 195, 399-404 Kikuchi, N.; Shibata, Y.; Okamoto, H.; Kawaguchi, Y.; Oku, S.; Ishii, H.; Yoshikuni, Y. & Tohmori, Y. (2002). Error-free signal selection and high-speed channel switching by monolithically integrated 64-channel WDM channel selector. Electron. Lett., 38, 823-824 Kikuchi, N.; Sanjho, H.; Shibata, Y.; Tsuzuki, K.; Sato, T.; Yamada, E.; Ishibashi, T. & Yasaka, H. (2007). 80-Gbit/s InP DQPSK modulator with an n-p-i-n structure. 32nd European Conference on Optical Communication, Th10.3.1 Kurosaki, T.; Shibata, Y.; Kikuchi, N.; Tsuzuki, K.; Kobayashi, W.; Yasaka, H. & Kato, K. (2007). 200-km 10-Gbit/s optical duobinary transmission using an n-i-n InP Mach- Zehnder modulator. Proc. 19th IPRM, Matsue, Japan, May 14-18, WeB1-3 Rolland, C; Moore, R. S.; Shepherd, F. & Hillier, G. (1993). 10 Gbit/s, 1.56 µm multiquantum well InP/InGaAsP Mach-Zehnder optical modulator. Electronics Lett., 29, 471-472 Tsuzuki, K.; Kikuchi, N.; Sanjho, H.; Shibata, Y.; Kasaya, K.; Oohashi, H.; Ishii, H.; Kato, K.; Tohmori, Y. & Yasaka, H. (2006). Compact wavelength tunable laser module integrated with n-i-n structure Mach-Zehnder modulator. 31st European Conference on Optical Communication, Tu3.4.3 Yonenaga, K. & Kuwano, S. (1997). Dispersion-tolerant optical transmission system using duobinary transmitter and binary receiver. IEEE J. Lightwave Technol., 15, 1530- 1537 Yoshimoto, N.; Shibata, Y.; Oku, S.; Kondo, S. & Noguchi, Y. (1999). Design and demonstration of polarization-insensitive Mach–Zehnder switch using a lattice- matched InGaAlAs/InAlAs MQW and deep-etched high-mesa waveguide structure. J.L.T, 17, 1662-1669 NewApproachtoUltra-FastAll-OpticalSignalProcessingBasedonQuantumDotDevices 419 New Approach to Ultra-Fast All-Optical Signal Processing Based on QuantumDotDevices Y.BenEzra,B.I.Lembrikov 0 New Approach to Ultra-Fast All-Optical Signal Processing Based on Quantum Dot Devices Y. Ben Ezra, B.I. Lembrikov Holon Institute of Technology (HIT),P.O.Box 305, 58102, 52 Golomb Str., Holon Israel 1. Introduction Fiber-optic technology is characterized by enormous potential capabilities: huge bandwidth up to nearly 50Tb/s due to a high frequency of an optical carrier, low signal attenuation of about 0.2dB/ km, low signal distortion, low power requirement, low material usage, small space requirement, and low cost Agrawal (2002), Mukherjee (2001). However, the realization of these capabilities requires very high-bandwidth transport network facilities which cannot be provided by existing networks consisting of electronic components of the transmitters and receivers, electronic switches and routers Agrawal (2002). Most current networks employ electronic signal processing and use optical fiber as a transmission medium. Switching and signal processing are realized by an optical signal down-conversion to an elec- tronic signal, and the speed of electronics cannot match the optical fiber bandwidth Rama- murthy (2001). For instance, a single-mode fiber (SMF) bandwidth is nearly 50Tb/s, which is nearly four orders of magnitude higher than electronic data rates of a few Gb/s Mukherjee (2001). Typically, the maximum rate at which a gateway that interfaces with lower-speed sub- networks can access the network is limited by an electronic component speed up to a few tens of Gb/s. These limitations may be overcome by the replacement of electronic components with ultra-fast all-optical signal processing components such as fiber gratings, fiber couplers, fiber interferometers Agrawal (2001), semiconductor optical amplifiers (SOAs) Dong (2008), Hamié (2002), SOA and quantum dot SOA (QD-SOA) based monolithic Mach-Zehnder inter- ferometers (MZIs) Joergensen (1996), Wang (2004), Sun (2005), Kanellos (2007), Wada (2007), Ben-Ezra (2008), Ben-Ezra (2009), all-optical switches based on multilayer system with en- hanced nonlinearity and carbon nanotubes Wada (2007). SOAs are among the most promising candidates for all-optical processing devices due to their high-speed capability up to 160Gb/s , low switching energy, compactness, and optical integra- tion compatibility Dong (2008). Their performance may be substantially improved by using QD-SOAs characterized by a low threshold current density, high saturation power, broad gain bandwidth, and a weak temperature dependence as compared to bulk and multi-quantum well (MQW) devices Bimberg (1999), Sugawara (2004), Ustinov (2003). High-speed wavelength conversion, logic gate operations, and signal regeneration are im- portant operations of the all-optical signal processing where SOAs are widely used Agrawal (2002), Ramamurthy (2001), Dong (2008). A wavelength converter (WC) changes the input wavelength to a new wavelength without modifying the data content of a signal Agrawal (2002). Wavelength conversion is essential for optical wavelength division multiplexing (WDM) network operation Ramamurthy (2001). 18 SemiconductorTechnologies420 There exist several all-optical techniques for wavelength conversion based on SOAs using the cross gain modulation (XGM) and cross phase modulation (XPM) effects between the pulsed signal and the continuous wave (CW) beam at the wavelength at which the converted signal is desired Agrawal (2002). In particular, MZI with a SOA inserted in each arm is characterized by a high on-off contrast and the output converted signal consisting of the exact replica of the incident signal Agrawal (2002). All-optical logic operations are important for all-optical signal processing Sun (2005). All- optical logic gates operation is based on nonlinearities of optical fibers and SOAs. However, the disadvantages of optical fibers are weak nonlinearity, long interaction length, and/or high control energy required in order to achieve a reasonable switching efficiency Sun (2005). On the contrary, SOAs, and especially QD-SOAs, possess high nonlinearity, small dimensions, low energy consumption, high operation speed, and can be easily integrated into photonic and electronic systems Sun (2005), Hamié (2002), Kanellos (2007), Dong (2008). The major problems of the improving transmission optical systems emerge from the signal-to- noise ratio (SNR) degradation, chromatic dispersion, and other impairment mechanisms Zhu (2007). For this reason, the optical signal reamplification, reshaping, and retiming (3R), or the so-called 3R regeneration, is necessary in order to avoid the accumulation of noise, crosstalk and nonlinear distortions and to provide a good signal quality for transmission over any path in all-optical networks Sartorius (2001), Zhu (2007), Leem (2006), Kanellos (2007). Optical re- generation technology can work with lower power, much more compact size, and can provide transparency in the needed region of spectrum Zhu (2007). All-optical 3R regeneration should be also less complex, and use fewer optoelectronics/electronics components than electrical re- generation providing better performance Leem (2006). All-optical 3R regenerator for different length packets at 40Gb/s based on SOA-MZI has been recently demonstrated Kanellos (2007). We developed for the first time a theoretical model of an ultra-fast all-optical signal proces- sor based on the QD SOA-MZI where XOR operation, WC, and 3R signal regeneration can be simultaneously carried out by AO-XOR logic gates for bit rate up to ( 100 − 200 ) Gb/s de- pending on the value of the bias current I ∼ ( 30 − 50 ) mA Ben-Ezra (2009). We investigated theoretically different regimes of RZ optical signal operation for such a processor and carried out numerical simulations. We developed a realistic model of QD-SOA taking into account two energy levels in the conduction band of each QD and a Gaussian distribution for the de- scription of the different QD size Ben-Ezra (2007), Ben-Ezra (2009), unlike the one-level model of the identical QDs recently used Berg (2004a), Sun (2005). We have shown that the accu- rate description of the QD-SOA dynamics predicts the high quality output signals of the QD SOA-MZI based logic gate without significant amplitude distortions up to a bit rate of about 100Gb/s for the bias current I = 30mA and 200Gb/s for the bias current I = 50mA being limited by the relaxation time of the electron transitions between the wetting layer (WL), the excited state (ES) and the ground state (GS) in a QD conduction band Ben-Ezra (2009). The chapter is constructed as follows. The QD structure, electronic and optical properties are discussed in Section 2. The dynamics of QD SOA, XGM and XPM phenomena in QD SOA are described in Section 3. The theory of ultra-fast all-optical processor based on MZI with QD SOA is developed in Section 4. The simulation results are discussed in Section 5. Conclusions are presented in Section 6. 2. Structure, Electronic and Optical Properties of Quantum Dots (QDs) Quantization of electron states in all three dimensions results in a creation of a novel physical object - a macroatom, or quantum dot (QD) containing a zero dimensional electron gas. Size quantization is effective when the quantum dot three dimensions are of the order of magni- tude of the electron de Broglie wavelength which is about several nanometers Ustinov (2003). An electron-hole pair created by light in a QD has discrete energy eigenvalues caused by the electron-hole confinement in the material. As a result, QD has unique electronic and optical properties that do not exist in bulk semiconductor material Ohtsu (2008). QDs based on different technologies and operating in different parts of spectrum are known such as In(Ga)As QDs grown on GaAs substrates, InAs QDs grown on InP substrates, and col- loidal free-standing InAs QDs. QD structures are commonly realized by a self-organized epi- taxial growth where QDs are statistically distributed in size and area. A widely used QDs fab- rication method is a direct synthesis of semiconductor nanostructures based on the island for- mation during strained-layer heteroepitaxy called the Stranski-Krastanow (SK) growth mode Ustinov (2003). The spontaneously growing QDs are said to be self-assembling. The energy shift of the emitted light is determined by size of QDs that can be adjusted within a certain range by changing the amount of deposited QD material. Smaller QDs emit photons of shorter wavelengths Ustinov (2003). The main advantages of the SK growth are following Ustinov (2003). 1. SK growth permits the preparation of extremely small QDs in a maskless process with- out lithography and etching which makes it a promising technique to realize QD lasers. 2. A great number of QDs is formed in one simple deposition step. 3. The synthesized QDs have a high uniformity in size and composition. 4. QDs can be covered epitaxially by host material without any crystal or interface defects. The simplest QD models are a spherical QD with a radius R, and a parallelepiped QD with a side length L x,y,z . The spherical QD is described by the spherical boundary conditions for an electron or a hole confinement which results in the electron and hole energy spectra E e,nlm and E h,nlm given by, respectively Ohtsu (2008) E e,nlm = E g + ¯h 2 2m e α nl R 2 ; E h,nlm = ¯h 2 2m h α nl R 2 (1) where n = 1, 2, 3, ; l = 0, 1, 2, n − 1; m = 0, ±1, ±2, ± l (2) E g is the QD semiconductor material band gap, m e,h are the electron and hole effective mass, respectively, ¯h = h/2π, h is the Planck constant, and α nl is the n-th root of the spherical Bessel function. The parallelepiped QD is described by the boundary conditions at its corresponding surfaces, which yield the energy eigenvalues E e,nlm and E h,nlm given by, respectively Ohtsu (2008) E e,nlm = E g + ¯h 2 π 2 2m e n L x 2 + l L y 2 + m L z 2 (3) E h,nlm = ¯h 2 π 2 2m h n L x 2 + l L y 2 + m L z 2 , n, l, m = 1, 2, 3, (4) The density of states ρ QD ( E ) for an array of QDs has the form Ustinov (2003) ρ QD ( E ) = ∑ n ∑ m ∑ l 2n QD δ E − E e,nlm (5) NewApproachtoUltra-FastAll-OpticalSignalProcessingBasedonQuantumDotDevices 421 There exist several all-optical techniques for wavelength conversion based on SOAs using the cross gain modulation (XGM) and cross phase modulation (XPM) effects between the pulsed signal and the continuous wave (CW) beam at the wavelength at which the converted signal is desired Agrawal (2002). In particular, MZI with a SOA inserted in each arm is characterized by a high on-off contrast and the output converted signal consisting of the exact replica of the incident signal Agrawal (2002). All-optical logic operations are important for all-optical signal processing Sun (2005). All- optical logic gates operation is based on nonlinearities of optical fibers and SOAs. However, the disadvantages of optical fibers are weak nonlinearity, long interaction length, and/or high control energy required in order to achieve a reasonable switching efficiency Sun (2005). On the contrary, SOAs, and especially QD-SOAs, possess high nonlinearity, small dimensions, low energy consumption, high operation speed, and can be easily integrated into photonic and electronic systems Sun (2005), Hamié (2002), Kanellos (2007), Dong (2008). The major problems of the improving transmission optical systems emerge from the signal-to- noise ratio (SNR) degradation, chromatic dispersion, and other impairment mechanisms Zhu (2007). For this reason, the optical signal reamplification, reshaping, and retiming (3R), or the so-called 3R regeneration, is necessary in order to avoid the accumulation of noise, crosstalk and nonlinear distortions and to provide a good signal quality for transmission over any path in all-optical networks Sartorius (2001), Zhu (2007), Leem (2006), Kanellos (2007). Optical re- generation technology can work with lower power, much more compact size, and can provide transparency in the needed region of spectrum Zhu (2007). All-optical 3R regeneration should be also less complex, and use fewer optoelectronics/electronics components than electrical re- generation providing better performance Leem (2006). All-optical 3R regenerator for different length packets at 40Gb/s based on SOA-MZI has been recently demonstrated Kanellos (2007). We developed for the first time a theoretical model of an ultra-fast all-optical signal proces- sor based on the QD SOA-MZI where XOR operation, WC, and 3R signal regeneration can be simultaneously carried out by AO-XOR logic gates for bit rate up to ( 100 − 200 ) Gb/s de- pending on the value of the bias current I ∼ ( 30 − 50 ) mA Ben-Ezra (2009). We investigated theoretically different regimes of RZ optical signal operation for such a processor and carried out numerical simulations. We developed a realistic model of QD-SOA taking into account two energy levels in the conduction band of each QD and a Gaussian distribution for the de- scription of the different QD size Ben-Ezra (2007), Ben-Ezra (2009), unlike the one-level model of the identical QDs recently used Berg (2004a), Sun (2005). We have shown that the accu- rate description of the QD-SOA dynamics predicts the high quality output signals of the QD SOA-MZI based logic gate without significant amplitude distortions up to a bit rate of about 100Gb/s for the bias current I = 30mA and 200Gb/s for the bias current I = 50mA being limited by the relaxation time of the electron transitions between the wetting layer (WL), the excited state (ES) and the ground state (GS) in a QD conduction band Ben-Ezra (2009). The chapter is constructed as follows. The QD structure, electronic and optical properties are discussed in Section 2. The dynamics of QD SOA, XGM and XPM phenomena in QD SOA are described in Section 3. The theory of ultra-fast all-optical processor based on MZI with QD SOA is developed in Section 4. The simulation results are discussed in Section 5. Conclusions are presented in Section 6. 2. Structure, Electronic and Optical Properties of Quantum Dots (QDs) Quantization of electron states in all three dimensions results in a creation of a novel physical object - a macroatom, or quantum dot (QD) containing a zero dimensional electron gas. Size quantization is effective when the quantum dot three dimensions are of the order of magni- tude of the electron de Broglie wavelength which is about several nanometers Ustinov (2003). An electron-hole pair created by light in a QD has discrete energy eigenvalues caused by the electron-hole confinement in the material. As a result, QD has unique electronic and optical properties that do not exist in bulk semiconductor material Ohtsu (2008). QDs based on different technologies and operating in different parts of spectrum are known such as In(Ga)As QDs grown on GaAs substrates, InAs QDs grown on InP substrates, and col- loidal free-standing InAs QDs. QD structures are commonly realized by a self-organized epi- taxial growth where QDs are statistically distributed in size and area. A widely used QDs fab- rication method is a direct synthesis of semiconductor nanostructures based on the island for- mation during strained-layer heteroepitaxy called the Stranski-Krastanow (SK) growth mode Ustinov (2003). The spontaneously growing QDs are said to be self-assembling. The energy shift of the emitted light is determined by size of QDs that can be adjusted within a certain range by changing the amount of deposited QD material. Smaller QDs emit photons of shorter wavelengths Ustinov (2003). The main advantages of the SK growth are following Ustinov (2003). 1. SK growth permits the preparation of extremely small QDs in a maskless process with- out lithography and etching which makes it a promising technique to realize QD lasers. 2. A great number of QDs is formed in one simple deposition step. 3. The synthesized QDs have a high uniformity in size and composition. 4. QDs can be covered epitaxially by host material without any crystal or interface defects. The simplest QD models are a spherical QD with a radius R, and a parallelepiped QD with a side length L x,y,z . The spherical QD is described by the spherical boundary conditions for an electron or a hole confinement which results in the electron and hole energy spectra E e,nlm and E h,nlm given by, respectively Ohtsu (2008) E e,nlm = E g + ¯h 2 2m e α nl R 2 ; E h,nlm = ¯h 2 2m h α nl R 2 (1) where n = 1, 2, 3, ; l = 0, 1, 2, n − 1; m = 0, ±1, ±2, ± l (2) E g is the QD semiconductor material band gap, m e,h are the electron and hole effective mass, respectively, ¯h = h/2π, h is the Planck constant, and α nl is the n-th root of the spherical Bessel function. The parallelepiped QD is described by the boundary conditions at its corresponding surfaces, which yield the energy eigenvalues E e,nlm and E h,nlm given by, respectively Ohtsu (2008) E e,nlm = E g + ¯h 2 π 2 2m e n L x 2 + l L y 2 + m L z 2 (3) E h,nlm = ¯h 2 π 2 2m h n L x 2 + l L y 2 + m L z 2 , n, l, m = 1, 2, 3, (4) The density of states ρ QD ( E ) for an array of QDs has the form Ustinov (2003) ρ QD ( E ) = ∑ n ∑ m ∑ l 2n QD δ E − E e,nlm (5) SemiconductorTechnologies422 where δ E − E e,nlm is the δ-function, and n QD is the surface density of QDs. The optical spectrum of QDs consists of a series of transitions between the zero-dimensional electron gas energy states where the selections rules are determined by the form and sym- metry of QDs Ustinov (2003). The finite carrier lifetime results in Lorentzian broadening of a finite width Ustinov (2003). Detailed theoretical and experimental investigations of InAs/GaAs and InAs QDs electronic structure taking into account their more realistic lens or pyramidal shape, size, composition profile, and production technique have been carried out Bimberg (1999), Bányai (2005), Usti- nov (2003). A system of QDs can be approximated with a three energy level model in the conduction band containing a spin degenerate ground state GS, fourfold degenerate excited state (ES) with comparatively large energy separations of about 50 − 70meV, and a narrow continuum wetting layer (WL). The electron WL is situated 150meV above the lowest electron energy level in the conduction band, i.e. GS and has a width of approximately 120meV. In real cases, the QDs vary in size, shape, and local strain which leads to the fluctuations in the quantized energy levels and the inhomogeneous broadening in the optical transition energy. A Gaussian distribution may be used for the description of the QD sizes, and it shows that the discrete resonances merge into a continuous structure with widths around 10% Bányai (2005). The QDs and WL are surrounded by a barrier material which prevents direct coupling between QD layers. The absolute number of states in the WL is much larger than in the QDs. GS and ES in QDs are characterized by homogeneous and inhomogeneous broadening Bányai (2005). The homogeneous broadening caused by the scattering of the optically generated elec- trons and holes with imperfections, impurities, phonons, or through the radiative electron- hole pair recombination Bányai (2005) is about 15meV at room temperature Sugawara (2002). The inhomogeneous broadening in the optical transition energy is due to the QDs variations in size, shape, and local strain Bányai (2005), Sugawara (2004), Ustinov (2003). In(Ga)As/GaAs QDs are characterized by emission at wavelengths no longer than λ = 1.35µm, while the InAs/InP QDs have been proposed for emission at the usual telecommuni- cation wavelength λ = 1.55µm Ustinov (2003). 3. Structure and Operation Mode of QD SOA In this section, we will discuss the theory of QD SOA operation based on the electron rate equations and photon propagation equation Qasaimeh (2003), Qasaimeh (2004), Ben-Ezra (2005a), Ben-Ezra (2005b), Ben-Ezra (2007). 3.1 Basic Equations of QD SOA Dynamics The active region of a QD SOA is a layer including self-assembled InGaAs QDs on a GaAs sub- strate Sugawara (2004). Typically, the QD density per unit area is about 10 10 − 10 11 cm −2 . The bias current is injected into the active layer including QDs, and the input optical sig- nals are amplified via the stimulated emission or processed via the optical nonlinearity by QDs Sugawara (2004). The stimulated radiative transitions occur between GS and the valence band of QDs. A detailed theory of QD SOAs based on the density matrix approach has been developed in the pioneering work Sugawara (2004) where the linear and nonlinear optical responses of QD SOAs with arbitrary spectral and spatial distribution of quantum dots in ac- tive region under the multimode light propagation have been considered. It has been shown theoretically that XGM takes place due to the coherent terms under the condition that the mode separation is comparable to or less than the polarization relaxation rate | ω m − ω n | ≤ Γ g where ω m,n are the mode frequencies and the relaxation time τ = Γ −1 g = 130 f s Sugawara (2004). XGM is also possible in the case of the incoherent nonlinear polarization, or the so- called incoherent spectral hole burning Sugawara (2004). XGM occurs only for signals with a detuning limited by the comparatively small homogeneous broadening, and for this reason the ensemble of QDs should be divided into groups by their resonant frequency of the GS transition between the conduction and valence bands Sugawara (2004). The phenomenological approach to the QD SOA dynamics is based on the rate equations for the electron densities of GS, ES and for combined WL and barrier serving as a reservoir. It is determined by electrons, because of the much larger effective mass of holes and their smaller state spacing Berg (2004a). Recently, an attempt has been carried out to take into account the hole dynamics for small-signal XGM case Kim (2009). In the QD SOA-MZI, optical signals propagate in an active medium with the gain determined by the rate equations for the electron transitions in QD-SOA between WL, GS and ES Qa- saimeh (2003), Qasaimeh (2004), Ben-Ezra (2005a), Ben-Ezra (2008). Unlike the model with the one energy level in the conduction band Berg (2004a), Sun (2005), we have taken into ac- count the two energy levels in the conduction band: GS and ES Ben-Ezra (2007), Ben-Ezra (2009). The diagram of the energy levels and electron transitions in the QD conduction band is shown in Fig. 1. Fig. 1. Energy levels and electron transitions in a QD conduction band The stimulated and spontaneous radiative transitions occur from GS to the QD valence band level. The system of the rate equations accounts for the following transitions: 1. the fast electron transitions from WL to ES with the relaxation time τ w2 ∼ 3p s ; 2. the fast electron transitions between ES and GS with the relaxation time from ES to GS τ 21 = 0.16p s and the relaxation time from GS to ES τ 12 ∼ 1.2p s; 3. the slow electron escape transitions from ES back to WL with the electron escape time τ 2w ∼ 1ns. The balance between the WL and ES is determined by the shorter time τ w2 of QDs filling. Carriers relax quickly from the ES level to the GS level, while the former serves as a carrier reservoir for the latter Berg (2001). In general case, the radiative relaxation times depend on the bias current. However, it can be shown that for moderate values of the WL carrier density N w ∼ 10 14 − 10 15 cm −3 this dependence can be neglected Berg (2001), Berg (2004b). The spontaneous radiative time in QDs τ 1R ( 0.4 − 0.5 ) ns remains large enough Sakamoto (2000), Qasaimeh (2003), Qasaimeh (2004), Sugawara (2004), Matthews (2005). The carrier dynamics is characterized by slow relaxation processes between WL and ES. The rapidly varying coherent nonlinear population terms vanish after the averaging over the com- paratively large relaxation time τ w2 ∼several ps from the two-dimensional WL to the ES. We [...]... gate is summarized in Fig 2 (a) and (b) The logic gate is tested with 10 Gb/s signals at A =155 0.9 nm, B =155 2.5 nm, and All-optical digital processing through semiconductor optical amplifiers: state of the art and perspectives 441 probe=FWM =154 9.3 nm or probe≠FWM =154 6.1 nm The wavelength of the CW signal is 154 4 nm The SOA is a commercial polarization independent bulk SOA The input average power... conversion realization by XGM between the data signal B with λ B = 156 0nm and the clock stream signal with λ p = 153 0nm for the signal bit rate 2.5Gb/s In such a case, wavelength conversion occurs between the optical signal B at the wavelength λ B = 156 0nm propagating through the lower arm of QD SOA-MZI and the clock stream signal with λ p = 153 0nm Pattern-effect free wavelength conversion can be realized... regular structure with the equal amplitudes and a shape defined by the clock 430 Semiconductor Technologies Fig 4 Optical signal 3R regeneration process The simultaneous XOR logic operation, wavelength conversion and 3R regeneration for the distorted at the input RZ signals A and B with the wavelengths λ A = 155 0nm and λ B = 156 0nm for the bit rate of 100Gb/s are shown in Fig 5 Here the RZ clock stream... large relaxation time τw2 ∼several ps from the two-dimensional WL to the ES We 424 Semiconductor Technologies have taken into account only incoherent population terms because for XGM between modes with the maximum detuning ∆λmax = 30nm within the especially important in optical communications conventional band of λ = (153 0 ÷ 156 5) nm the condition ω1 − ω2 > Γ−1 is valid g even for the lowest relaxation... Berg, T.W.; Mørk, J & Hvam, J.M (2004) Gain dynamics and saturation in semiconductor quantum dot amplifiers New Journal of Physics, Vol 6, No 178, (2004) 1-23, ISSN 1367-2630 Berg, T.W & Mørk, J (2004) Saturation and Noise Properties of Quantum-Dot Optical Amplifiers IEEE J of Quantum Electronics, Vol 40, No 11, (November 2004) 152 7 -153 9, ISSN 0018-9197 Bimberg, D.; Grundmann, M & Ledentsov, N N (1999)... quantum-dot laser diodes, IEEE Photonics Technology Letters, Vol 11, (November 1999), 152 7 -152 9, ISSN 1041-1135 Ohtsu, N.; Kobayashi, K.; Kawazoe, T.; Yatsui, T & Naruse, N (2008) Principles of Nanophotonics, CRC Press, ISBN-13 978-1-58488-972-4, London Qasaimeh, O (2003) Optical gain and saturation characteristics quantum-dot semiconductor optical amplifiers IEEE J of Quantum Electronics, Vol 39, No 6, (June... conversion in quantum dot semiconductor optical amplifiers IEEE Photonics Technology Letters, Vol 16, No 2, (February 2004) 542-544, ISSN 1041-1135 Ramamurthy, B (2001) Swithches, wavelength routers, and wavelength converters In: Optical WDM Networks Principles and Practice, Sivalingam, K.M & Subramaniam, S (Ed.), 51-75, Kluwer, ISBN 0-7923-7825-3, Boston 436 Semiconductor Technologies Sakamoto, A &... 2005; Chbat et al., 1992), in semiconductor devices (Ibrahim et al., 2003; Dorren et al., 2004) or in waveguides (Collecutt & Drummond, 2000) Moreover several efforts have been done to demonstrate the suitability of new structures for the realization of optical logic gates (Wu, 2005; Brzozowski & Sargent, 2001) In particular SOAs are very All-optical digital processing through semiconductor optical amplifiers:... increase 434 Semiconductor Technologies of repetition rates The limiting bit rate also depends on the bias current value Analysis shows that for I = 30mA and I = 50mA the highest bit rates corresponding to the processor successful performance are 100Gb/s and 200Gb/s, respectively 7 References Agrawal, G.P & Olsson, N.A (1989) Self-phase modulation and spectral broadening of optical pulses in semiconductor. .. 0018-9197 Agrawal, G.P (2001) Applications of Nonlinear Fiber Optics Academic Press, ISBN 0-12-0451441, New York Agrawal, G.P (2002) Fiber-Optic Communication Systems Wiley, ISBN 0-471- 2157 1-6, New York Bányai, L & Koch, S W (2005) Semiconductor Quantum Dots (Second Edition) World Scientific, ISBN 9810213905, London, Ben-Ezra, Y.; Haridim, M & Lembrikov, B I (2005) Theoretical analysis of gain-recovery time . using an integrated SGDBR laser- semiconductor optical amplifier and Mach-Zehnder modulator. IEEE J. Sel. Topics Quantum Electron., 9, 1113-1117 Semiconductor Technologies4 18 Kawanishi, T.;. transmission system using duobinary transmitter and binary receiver. IEEE J. Lightwave Technol., 15, 153 0- 153 7 Yoshimoto, N.; Shibata, Y.; Oku, S.; Kondo, S. & Noguchi, Y. (1999). Design and demonstration. optical properties that do not exist in bulk semiconductor material Ohtsu (2008). QDs based on different technologies and operating in different parts of spectrum are known such as In(Ga)As QDs
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