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Abstract:

The purpose of this study is the investigation of heat transfer and fluid flow around a heated solid block inside a lid-driven cavity filled with hybrid TiO2-Cu/water nanofluid. The considered geometry is a two-dimensional cavity with an aspect ratio of 5. The upper wall translates with uniform velocity Ulid. The solid block attached to the bottom wall of the cavity is maintained at a high temperature compared to the temperature of the upper and lower walls, whereas the other walls are kept insulated. The hybrid nanofluid flow is assumed to be Newtonian, laminar, and incompressible. The effect of the Richardson number is considered by fixing the Reynolds number to 100, and by varying the Grashof number from 102 to 104. Volume fractions for both nanoparticles are varied from 0% to 8%. Results are shown in terms of streamlines, isotherms, and profiles of the average Nusselt number. Numerical results show that clockwise and counterclockwise cells are generated within the rectangular enclosure due to the combined effects of natural and forced convection. Furthermore, increasing the Richardson number from Ri = 0.01 to Ri = 1, which results from an increase in the buoyancy effect, leads to an increase in the Nusselt number of about 4.5%.  Moreover, for each Richardson number, an increase of 8% in nanoparticles volume fraction leads to an enhancement of the heat transfer rate by about 9.8%.

Keywords:

Nanoparticles,Richardson number,rectangular cavity,Nusselt number,

Refference:

I. Aljabair, S., Ekaid, A. L., Hasan ibrahim, S. and Alesbe, I : MIXED CONVECTION IN SINUSOIDAL LID- DRIVEN CAVITY WITH NON-UNIFORM TEMPERATURE DISTRIBUTION ON THE WALL UTILIZING NANOFLUID. Heliyon 7, e06907, 2021.
II. Bakar, N. A., Karimipour, A. and Roslan, R. : EFFECT OF MAGNETIC FIELD ON MIXED CONVECTION HEAT TRANSFER IN A LID-DRIVEN SQUARE CAVITY. Journal of Thermodynamics, Article ID 3487182, 2016. 10.1155/2016/3487182.
III. Bakar, N. A., Roslan, R., Karimipour, A. and Hashim, I. : MIXED CONVECTION IN LID-DRIVEN CAVITY WITH INCLINED MAGNETIC FIELD. Sains Malaysiana, 48(2), pp 451–471, 2019. 10.17576/jsm-2019-4802-24.

IV. Brinkman, H. C. : THE VISCOSITY OF CONCENTRATED SUSPENSIONS AND SOLUTIONS. Journal of Chemical Physics, 3, pp 571–581, 1952. 10.1063/1.1700493.
V. Dumon, A., Allery, C. and Ammar, A. : SIMULATION OF HEAT AND MASS TRANSPORT IN A SQUARE LID-DRIVEN CAVITY WITH PROPER GENERALIZED DECOMPOSITION (PGD). Numerical Heat Transfer, Part B: Fundamentals An International Journal of Computation and Methodology, 63(1), pp 18-43, 2013. 10.1080/10407790.2012.724991.
VI. Geridonmez, B. P. and Oztop, H. F. : ENTROPY GENERATION DUE TO MAGNETO-CONVECTION OF A HYBRID NANOFLUID IN THE PRESENCE OF A WAVY CONDUCTING WALL. Mathematics, 10(24), 4663, 2022. 10.3390/math10244663.
VII. Goodarzi, M., D’orazio, A., Keshavarzi, A., Mousavi, S. and Karimipour, A. : DEVELOP THE NANO-SCALE METHOD OF LATTICE BOLTZMANN TO PREDICT THE FLUID FLOW AND HEAT TRANSFER OF AIR IN THE INCLINED LID DRIVEN CAVITY WITH A LARGE HEAT SOURCE INSIDE, TWO CASE STUDIES: PURE NATURAL CONVECTION & MIXED CONVECTION. Physica A, 509, pp 210–233, 2018. 10.1016/j.physa.2018.06.013.
VIII. Incropera, F. P. and De witt, D. P. (2002), Introduction to Heat Transfer, Wiley 4th edition, New York.
IX. Karimipour, A., Hemmat esfe, M., Reza Safaei, M., Toghrai, D., Jafari, S. and Kazi, S. N. : MIXED CONVECTION OF COPPER–WATER NANOFLUID IN A SHALLOW INCLINED LID DRIVEN CAVITY USING THE LATTICE BOLTZMANN METHOD. Physica A, 402, pp 150–168, 2014. 10.1016/j.physa.2014.01.057.
X. Khanafer, K. and Vafai, K. : A CRITICAL SYNTHESIS OF THERMOPHYSICAL CHARACTERISTICS OF NANOFLUIDS, Int. J. Heat Mass Trans., 54, pp 4410-4442, 2012. 10.1016/j.ijheatmasstransfer.2011.04.048.
XI. Korei, Z. and Benissaad, S. : ENTROPY GENERATION OF A HYBRID NANOFLUID ON MHD MIXED CONVECTION IS A LID-DRIVEN CAVITY WITH PARTIAL HEATING HAVING TWO ROUNDED CORNERS. E3S Web of Conferences 321, 02004, 2021. 10.1051/e3sconf/202132102004
XII. Kosti, S. and Rathore, V. S. : NUMERICAL STUDY OF LID DRIVEN CAVITY AT DIFFERENT REYNOLDS NUMBER. Trends in Mechanical Engineering and Technology, 5(3), pp 1-5, 2015.
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XIV. Nahak, P., Triveni, M. K. and Panua, R. : NUMERICAL INVESTIGATION OF MIXED CONVECTION IN A LID-DRIVEN TRIANGULAR CAVITY WITH A CIRCULAR CYLINDER USING ANN MODELING. International Journal of Heat and Technology, 35(4), pp 903-918, 2017. 10.18280/ijht.350427.
XV. Pashaie, P., Jafari, M., Baseri, H. and Farhadi, M. : NUSSELT NUMBER ESTIMATION ALONG A WAVY WALL IN AN INCLINED LID-DRIVEN CAVITY USING ADAPTIVE NEURO-FUZZY INFERENCE SYSTEM (ANFIS). IJE TRANSACTIONS A: Basics, 26(4), pp 383-392, 2013.
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XVII. Rashidi, M. M., Sadri, M. and Sheremet, M. A. : NUMERICAL SIMULATION OF HYBRID NANOFLUID MIXED CONVECTION IN A LID-DRIVEN SQUARE CAVITY WITH MAGNETIC FIELD USING HIGH-ORDER COMPACT SCHEME. Nanomaterials, 11(9), 2250, 2021.
XVIII. Saha, L. K., Somadder, M. C. and Salah uddin, K. M. : MIXED CONVECTION HEAT TRANSFER IN A LID DRIVEN CAVITY WITH WAVY BOTTOM SURFACE. American Journal of Applied Mathematics, 1(5), pp 92-101, 2013.
XIX. Saidur, R., Leong, K. Y. and Mohammad, H. A. : A REVIEW ON APPLICATIONS AND CHALLENGES OF NANOFLUIDS. Renew. Sustain. Energy. Rev.,15, pp 1646-1668, 2011.
XX. Sarlak, R., Yousefzadeh, S., Akbari, O. A., Toghraie, D., Sarlak, S. and Assadi, F. : THE INVESTIGATION OF SIMULTANEOUS HEAT TRANSFER OF WATER/AL2O3 NANOFLUID IN A CLOSE ENCLOSURE BY APPLYING HOMOGENEOUS MAGNETIC FIELD. International Journal of Mechanical Sciences, 133, pp 674-688, 2017. 10.1016/j.ijmecsci.2017.09.035.
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XXII. Zahan, I., Nasrin, R. and Alim, M. A. : MIXED CONVECTIVE HYBRID NANOFLUID FLOW IN LID-DRIVEN UNDULATED CAVITY: EFFECT OF MHD AND JOULE HEATING. Journal of Naval Architecture and Marine Engineering, 16, pp 109-126, 2019. 10.3329/jname.v16i2.40585.

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Abstract:

This paper presents the design and implementation of an Optical 4:1 Multiplexer using Sagnac Switches as Terahertz Optical Asymmetric Demultiplexers (TOADs). Optical multiplexers play a crucial role in modern communication systems by combining multiple signals onto a single optical channel. The proposed multiplexer architecture leverages the benefits of Sagnac Switches, such as low insertion loss, high extinction ratio, and low crosstalk, along with TOADs to achieve efficient signal routing and demultiplexing. The design is evaluated through simulations, demonstrating its performance in terms of insertion loss, extinction ratio, and crosstalk. The experimental validation of the multiplexer verifies its effectiveness in real-world scenarios. The Optical 4:1 Multiplexer using Sagnac Switches as TOADs offers a promising solution for optical communication networks, enabling efficient signal multiplexing and demultiplexing while maintaining high data integrity and low signal degradation.

Keywords:

Optical communication,multiplexer,Sagnac Switches,Terahertz Optical Asymmetric Demultiplexers (TOADs),signal routing,signal demultiplexing,insertion loss,extinction ratio,crosstalk,optical networks,

Refference:

I. C. S. Pittala, V. Vijay and Reddy, B.N.K. : “1-Bit FinFET Carry Cells for Low Voltage High-Speed Digital Signal Processing Applications”, Silicon 15, 713–724, 2023. 10.1007/s12633-022-02016-8.
II. D. K. Gayen. “Optical Multiplexer”. J. Mech. Cont. & Math. Sci., Vol.-18, No.-03, March (2023) pp 32-42. 10.26782/jmcms.2023.03.00003
III. El-Hageen, Hazem M., Alatwi, Aadel M. and Zaki Rashed, Ahmed Nabih. : “High-speed signal processing and wideband optical semiconductor amplifier in the optical communication systems”, Journal of Optical Communications, pp. 000010151520200070, 2020. 10.1515/joc-2020-0070.
IV. H. Furukawa et al., : “Demonstration of 10 Gbit Ethernet/Optical-Packet Converter for IP Over Optical Packet Switching Network.” Journal of Lightwave Technology, vol. 27, no. 13, pp. 2379-2380, July 1, 2009. 10.1109/JLT.2008.2010063.
V. I. S. Choi, Jongseon Park, Hoon Jeong, Ji Won Kim, Min Yong Jeon, and Hong-Seok Seo. : “Fabrication of 4 × 1 signal combiner for high-power lasers using hydrofluoric acid,” Opt. Express 26, 30667-30677, 2018. 10.1364/OE.26.030667
VI. J. H. Huh, H. Homma, H. Nakayama and Y. Maeda. : “All optical switching triode based on cross-gain modulation in semiconductor optical amplifier,” Photonics in Switching, San Francisco, CA, USA, pp. 73-74, 2007.
VII. J. M. Tang, P. S. Spencer, P. Rees and K. A. Shore. : “Pump-power dependence of transparency characteristics in semiconductor optical amplifiers,” IEEE Journal of Quantum Electronics, vol. 36, no. 12, pp. 1462-1467, Dec. 2000.
VIII. J. P. Sokoloff, P. R. Prucnal, I. Glesk and M. Kane. : “A terahertz optical asymmetric demultiplexer (TOAD),” IEEE Photonics Technology Letters, vol. 5, no. 7, pp. 787-790, July 1993.
IX. K. Christodoulopoulos, I. Tomkos and E. Varvarigos. : “Dynamic bandwidth allocation in flexible OFDM-based networks,” Optical Fiber Communication Conference and Exposition and the National Fiber Optic Engineers Conference, Los Angeles, CA, USA, 2011, pp. 1-3 2011.
X. Lei Xu, I. Glesk, V. Baby and P. R. Prucnal. : “All-optical wavelength conversion using SOA at nearly symmetric position in a fiber-based sagnac interferometric loop,” IEEE Photonics Technology Letters, vol. 16, no. 2, pp. 539-541, Feb. 2004.
XI. M. F. C. Stephens, M. Asghari, R. V. Penty and I. H. White. : “Demonstration of ultrafast all-optical wavelength conversion utilizing birefringence in semiconductor optical amplifiers,” IEEE Photonics Technology Letters, vol. 9, no. 4, pp. 449-451, April 1997.

XII. N. Bai, Ezra Ip, Yue-Kai Huang, Eduardo Mateo, Fatih Yaman, Ming-Jun Li, Scott Bickham, Sergey Ten, Jesús Liñares, Carlos Montero, Vicente Moreno, Xesús Prieto, Vincent Tse, Kit Man Chung, Alan Pak Tao Lau, Hwa-Yaw Tam, Chao Lu, Yanhua Luo, Gang-Ding Peng, Guifang Li, and Ting Wang. : “Mode-division multiplexed transmission with inline few-mode fiber amplifier,” Opt. Express 20, 2668-2680, 2012.
XIII. S. Soysouvanh, Phongsanam, P., Mitatha, S. et al. : “Ultrafast all-optical ALU operation using a soliton control within the cascaded InGaAsP/InP microring circuits.” Microsyst Technol 25, 431–440, 2019.
XIV. V. M. Menon et al. : “All-optical wavelength conversion using a regrowth-free monolithically integrated Sagnac interferometer,” IEEE Photonics Technology Letters, vol. 15, no. 2, pp. 254-256, Feb. 2003.
XV. V. Sasikala, Chitra, K. : “All optical switching and associated technologies: a review.” J Opt 47, 307–317, 2018.
XVI. Y. Liu, E. Tangdiongga, Z. Li, Shaoxian Zhang, Huug de Waardt, G. D. Khoe, and H. J. S. Dorren. : “Error-Free All-Optical Wavelength Conversion at 160 Gb/s Using a Semiconductor Optical Amplifier and an Optical Bandpass Filter,” J. Lightwave Technol. 24, 230-,2006.
XVII. Y. Xiao, F. Brunet, M. Kanskar, M. Faucher, A. Wetter, and N. Holehouse. : “1-kilowatt CW all-fiber laser oscillator pumped with wavelength-beam-combined diode stacks,” Opt. Express 20, 3296-3301, 2012.

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Abstract:

In this research paper, we solve the Euler-Bernoulli beam (EBB) differential equations by taking the general boundary conditions. Instead of finding a solution for the EBB model for a particular load and its particular boundary conditions, we derive the general analytical solution with general boundary conditions by using techniques of integration. The proposed general analytical solutions are neither load specific nor dependent on specific boundary conditions but can be used for any load and any boundary condition without having to integrate again and again. We have taken a general polynomial load function with general boundary conditions, and get the general analytical solution for the deflection and slope parameters of EBB. We find the direct solution for uniform distributed load and linearly varying load for a fixed beam.

Keywords:

Euler Bernoulli Beam,General analytical solution,Deflection,Slope,

Refference:

I. Barari, A., Kaliji, H. D., Ghadimi, M., & Domairry, G. (2011). : “Non-linear vibration of Euler-Bernoulli beams.” Latin American Journal of Solids and Structures, 8, 139-148. 10.1590/S1679-78252011000200002.
II. Beck, A. T., & da Silva Jr, C. R. (2011). “Timoshenko versus Euler beam theory: Pitfalls of a deterministic approach.” Structural Safety, 33(1), 19-25. 10.1016/j.strusafe.2010.04.006.
III. Bokhari, A. H., Mahomed, F. M., & Zaman, F. D. (2010). “Symmetries and integrability of a fourth-order Euler–Bernoulli beam equation.” Journal of Mathematical Physics, 51(5), 053517. 10.1063/1.3377045.
IV. Di Paola, M., Heuer, R., & Pirrotta, A. (2013). “Fractional visco-elastic Euler–Bernoulli beam.” International Journal of Solids and Structures, 50(22-23), 3505-3510. 10.1016/j.ijsolstr.2013.06.010.

V. Hafeezullah Channa, Muhammad Mujtaba Shaikh, and Kamran Malik (2022). “GENERAL ANALYTICAL SOLUTION OF AN ELASTIC BEAM UNDER VARYING LOADS WITH VALIDATION”, Journal of Mechanics of Continua and Mathematical Sciences, 17 (11): 54-62. 10.26782/jmcms.2022.11.00004.
VI. Malik, K., Shaikh, A. W., & Shaikh, M. M. “AN EFFICIENT FINITE DIFFERENCE SCHEME FOR THE NUMERICAL SOLUTION OF TIMOSHENKO BEAM MODEL.” Journal of Mechanics of Continua and Mathematical Sciences, 16(5):76-88. 10.26782/jmcms.2021.05.00007.
VII. Malik, K., Shaikh, M. M., & Shaikh, A. W (2021). “ON EXACT ANALYTICAL SOLUTIONS OF THE TIMOSHENKO BEAM MODEL UNDER UNIFORM AND VARIABLE LOADS.” Journal of Mechanics of Continua and Mathematical Sciences, 16 (5): 66-75. 10.26782/jmcms.2021.05.00006
VIII. Manoli, C. K., Papatzani, S., & Mouzakis, D. E. (2022). “Exploring the Limits of Euler–Bernoulli Theory in Micromechanics.” Axioms, 11(3), 142. 10.3390/axioms11030142.
IX. Nguyen, N. T., Kim, N. I., & Lee, J. (2015). “Mixed finite element analysis of nonlocal Euler–Bernoulli nanobeams.” Finite Elements in Analysis and Design, 106, 65-72. 10.1016/j.finel.2015.07.012.
X. Park, S. K., & Gao, X. L. (2006). “Bernoulli–Euler beam model based on a modified couple stress theory.” Journal of Micromechanics and Microengineering, 16(11), 2355. 10.1088/0960-1317/16/11/015
XI. Pisano, A. A., Fuschi, P., & Polizzotto, C. (2021). “Euler–Bernoulli elastic beam models of Eringen’s differential nonlocal type revisited within a $$\mathbf {C}^{0}-$$ C 0-continuous displacement framework.” Meccanica, 56(9), 2323-2337. doi.org/10.1007/s11012-021-01361-z.
XII. Wang, C. M. (1995). “Timoshenko beam-bending solutions in terms of Euler-Bernoulli solutions.” Journal of engineering mechanics, 121(6), 763-765. 10.1061/(ASCE)0733-9399(1995)121:6(763)
XIII. Yavari, A., & Sarkani, S. (2001). “On applications of generalized functions to the analysis of Euler–Bernoulli beam–columns with jump discontinuities.” International Journal of Mechanical Sciences, 43(6), 1543-1562. 10.1016/S0020-7403(00)00041-2.
XIV. Yu, H., & Yuan, Y. (2014). “Analytical solution for an infinite Euler-Bernoulli beam on a viscoelastic foundation subjected to arbitrary dynamic loads.” Journal of Engineering Mechanics, 140(3), 542-551. 10.1061/(ASCE)EM.1943-7889.00006
XV. Zamorska, I. (2014). “Solution of differential equation for the Euler-Bernoulli beam.” Journal of Applied Mathematics and Computational Mechanics, 13(4), 157-162. 10.17512/jamcm.2014.4.21
XVI. Zhang, P., Qing, H., & Gao, C. (2019). “Theoretical analysis for static bending of circular Euler–Bernoulli beam using local and Eringen’s nonlocal integral mixed model.” ZAMM‐Journal of Applied Mathematics and Mechanics/Zeitschrift für Angewandte Mathematik and Mechanik, 99(8), e201800329. doi.org/10.1002/zamm.201800329.

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Abstract:

The terahertz optical asymmetric demultiplexer (TOAD) or semiconductor optical amplifier (SOA)-assisted Sagnac switches have been used to construct an all-optical 4-bit carry skip adder. This design aims to satisfy the high speed and accuracy requirements of modern ultrafast digital transmission. Using a combination of an all-optical multiplexer and an all-optical full adder, we describe an all-optical carry skip adder. When compared to ripple carry adder and carry look-ahead adder, carry skip adder may be employed to create a fast arithmetical processing unit. Numerical simulation is used to develop and validate this theoretical model.

Keywords:

Terahertz optical asymmetric demultiplexer,semiconductor optical amplifier,carry skip adder,optical logic,

Refference:

I. A. Bhattachryya, D. K. Gayen. ALL-OPTICAL N-BIT BINARY TO TWO’S COMPLEMENT CONVERTER WITH THE HELP OF SEMICONDUCTOR OPTICAL AMPLIFIER-ASSISTED SAGNAC SWITCH. J. Mech. Cont. & Math. Sci., Vol.-17, No.-1, January (2022) pp 117-125. 10.26782/jmcms.2022.01.00009.
II. D. Cotter, R.J. Manning, K.J. Blow, A.D. Ellis, A.E. Kelly, D. Nesset, I.D. Phillips, A.J. Poustie, D.C. Rogers, “Nonlinear optics for high-speed digital information processing,” Science 286, 1523-1528 (1999).
III. D. K. Gayen and J. N. Roy, “All-optical arithmetic unit with the help of terahertz optical asymmetric demultiplexer-based tree architecture”, Applied Optics, Optical Society of America, 47(7), 933-943 (2008).
IV. D. K. Gayen, T. Chattopadhyay, M. K. Das, J. N. Roy, and R. K. Pal, “All-optical binary to gray code and gray to binary code conversion scheme with the help of semiconductor optical amplifier -assisted sagnac switch”, IET Circuits, Devices & Systems, 5(2), 123-131 (2011).
V. D. K. Gayen, A. Bhattacharyya, T. Chattopadhyay, and J. N. Roy, “Ultrafast all-optical half adder using quantum-dot semiconductor optical amplifier-based Mach-Zehnder Interferometer”, IEEE/OSA Journal of Lightwave Technology, 30 (21), 3387-93 (2012).
VI. G. Li, F. Qian, H. Ruan, and L. Liu, “Compact parallel optical modified-signed-digit arithmetic-logic array processor with electron-trapping device,” Applied Optics 38, 5039–5045 (1999).
VII. G. Li, “Recent advances in coherent optical communication”, Advances in Optics and Photonics, 1(2), 279-307 (2009).
VIII. H. J. S. Dorren, M.T. Hill, Y. Liu, E. Tangdiongga, M.K. Smit, G.D. Khoe, “Optical signal processing and telecommunication applications,” Proceedings of the Conference on Optical Amplifiers and their Applications (WD1), on CD-ROM (2005).
IX. J. P. Sokoloff, P. R. Prucnal, I. Glesk, and M. Kane, “A terahertz optical asymmetric demultiplexer (TOAD)”, IEEE Photonic Technology Letters, 5(7), 787-789 (1993).
X. J. P. Sokoloff, I. Glesk, P. R. Prucnal, and R. K. Boneck, “Performance of a 50 Gbit/s optical time domain multiplexed system using a terahertz optical asymmetric demultiplexer”, IEEE Photonics Technology Letters, 6(1), 98-100 (1994).
XI. J. H. Kim, Y. T. Byun, Y. M. Jhon, S. Lee, D. H. Woo, S. H. Kim, “All-optical half adder using semiconductor optical amplifier based devices,” Optics Communications, 218, 345–349 (2003).
XII. K. E. Zoiros, C. S. Koukourlis, and T. Houbavlis, “Analysis and design of ultrahigh-speed all-optical semiconductor-optical-amplifier-assisted Sagnac recirculating shift register with an inverter”, Optical Engineering, 44(6), 065001-12 (2005).
XIII. K. E. Zoiros, A. Kalaitzi, and C. S. Koukourlis, “Study on the cascadability of a SOA-assisted Sagnac switch pair”, International Journal for Light and Electron Optics, 121(13), 1180-1193 (2010).
XIV. K. E. Zoiros, M. Kalyvas, and T. Houbavlis, ‘‘The path towards all-optical packet switching in future broadband networks,’’ Journal of Communication Networking, 2(3), 124–129 (2003).
XV. M. Eiselt, W. Pieper, and H. G. Weber, “SLALOM: Semiconductor laser amplifier in a loop mirror”, Journal of lightwave Technology, 13(10), 2099-2112 (1995).
XVI. P. Phongsanam, S. Mitatha, C. Teeka, and P. P. Yupapin, “All-optical half-adder / half-subtractor using dark bright soliton conversion control”, Microwave and Optical Technology Letters, 53(7), 1541-1544 (2011).
XVII. R. P. Webb, R.J. Manning, X. Yang, R. Giller, “All-optical 40Gb/s XOR gate with dual ultrafast nonlinear interferometers,” Electronics Letters, 41, 1396-1397 (2005).
XVIII. S. K. Garai, ‘A novel all-optical frequency encoded method to develop Arithmetic and Logic Unit (ALU) using semiconductor optical amplifiers’, Journal Of Light wave Technology, 29(23), 3506-3514, (2011).
XIX. Y. Liu, E. Tangdiongga, Z. Li, S. Zhang, H. de Waardt, G.D. Khoe, H.J.S. Dorren, “Error-free all-optical wavelength conversion at 160Gbit/s using a semiconductor optical amplifier and an optical bandpass filter,” Jounal of Lightwave Technology 24, 230-236 (2006).

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