Abstract
A comprehensive and integrated exact analytical formalism is presented for erbium-doped fiber amplifiers and lasers (EDFALs) in one single configuration based on solutions of a system of rate and propagation equations represented by a homogenously broadened four band transition scheme while incorporating amplified spontaneous emission and excited state absorption effects. The formalism, under steady-state conditions, concurrently provides considerable insight into physical characteristics underlying phenomena pertinent to EDFALs and allows precise evaluation of behavior exhibited by EDFALs through a judicious selection of pump intensity and fiber length in standard eye-safe low-erbium concentration uniformly doped mono-mode silica glass fibers in co- and counter- propagating directions appropriate to signal, pump and ASE regimes.
References
1. Einstein A. Zur Quantentheorie der Strahlung. Physikalische Zeitschrift. 1917;18:121.10.1515/9783112596609-016Search in Google Scholar
2. Koester CJ, Snitzer E. Amplification in a fibre laser. Appl Opt. 1964;3:1182.10.1364/AO.3.001182Search in Google Scholar
3. Digonnet MJ, Gaeta CJ. Theoretical analysis of optical fibre laser amplifiers and oscillators. Appl Opt. 1985;24:333.10.1364/AO.24.000333Search in Google Scholar
4. Digonnet MJ. Theory of superfluorescent fibre lasers. J Lightwave Technol. 1986;4:1631.10.1109/JLT.1986.1074661Search in Google Scholar
5. Armitage JR. Three-level fibre laser amplifier: a theoretical model. Appl Opt. 1988;27:4831.10.1364/AO.27.004831Search in Google Scholar PubMed
6. Olshansky R. Noise figure for erbium-doped optical fibre amplifiers. Electron Lett. 1988;24:1363.10.1049/el:19880933Search in Google Scholar
7. Morkel PR, Laming RI. Theoretical modelling of erbium-doped fiber amplifiers with excited-state absorption. Opt Lett. 1989;14:1062.10.1364/OL.14.001062Search in Google Scholar
8. Deservire E, Simpson JR. Amplification of spontaneous emission in erbium doped single-mode fibres. J Lightwave Technol. 1989;7:835.10.1109/50.19124Search in Google Scholar
9. Desurvire E, Giles CR, Simpson JR. Gain saturation effects in high-speed, multichannel erbium-doped fibre amplifiers at k=1.53 lm. IEEE J Lightwave Technol. 1989;7:2095.10.1109/50.41635Search in Google Scholar
10. Desurvire E. Analysis of erbium-doped fibre amplifiers pumped in the 4I15/2-4I11/2. IEEE Photon Technol Lett. 1989;1:293.10.1109/68.43353Search in Google Scholar
11. Armitage R. Spectral dependence of the small-signal gain around 1.5 μm in erbium doped silica fiber amplifiers. IEEE J Quantum Electron. 1990;26:423.10.1109/3.52117Search in Google Scholar
12. Digonnet MJ. Closed form expressions for the gain in three- and four level laser fibres. IEEE J Quantum Electron. 1990;26:1788.10.1109/3.60903Search in Google Scholar
13. Peroni M, Tamburrini M. Gain in erbium-doped fibre amplifiers: a simple analytical solution for the rate equations. Opt Lett. 1990;15:843.10.1364/OL.15.000842Search in Google Scholar
14. Desurvire E, Zyskind JL, Giles CR. Design optimization for efficient erbium-doped fiber amplifiers. IEEE J Lightwave Technol. 1990;8:1730.10.1109/50.60573Search in Google Scholar
15. Desurvire E. Spectral noise figure of Er3+-doped fiber amplifiers. IEEE Photon Technol Lett. 1990;2:208.10.1109/68.50891Search in Google Scholar
16. Saleh AA, Jopson R, Evankow J, Aspell J. Modeling of gain in erbium-doped fibre amplifiers. IEEE Photon Technol Lett. 1990;2:714.10.1109/68.60769Search in Google Scholar
17. Giles CR, Giovanni DD. Spectral dependence of gain and noise in erbium-doped fiber amplifiers. IEEE Photon Technol Lett. 1990;2:797.10.1109/68.63225Search in Google Scholar
18. Pedersen B, Dybdal K, Hansen CD, Bjarklev A, Povlsen JH, Pommer HV, et al. Detailed theoretical and experimental investigation of high-gain erbium-doped fiber amplifier. IEEE Photon Technol Lett. 1990;2:863.10.1109/68.62011Search in Google Scholar
19. Ohashi M, Tsubokawa M. Optimum parameter design of Er3+-doped fiber for optical amplifiers. IEEE Photon Tech Lett. 1991;2:121.10.1109/68.76861Search in Google Scholar
20. Giles CR, Bums CA, DiGiovanni DJ, Dutta NK, Raybon G. Characterization of erbium-doped fibres and application to modeling 980-nm and 1480-nm pumped amplifiers. IEEE Photon Tech Lett. 1991;3:363.10.1109/68.82113Search in Google Scholar
21. Giles CR, Desurvire E. Propagation of signal and noise in concatenated erbium-doped fiber optical amplifiers. J Lightwave Technol. 1991;9:147.10.1109/50.65871Search in Google Scholar
22. Giles CR, Desurvire E. Modeling erbium-doped fiber amplifiers. J Lightwave Technol. 1991;9:271.10.1109/50.65886Search in Google Scholar
23. Desurvire E, Zirngibl M, Presby HM, DiGiovanni D. Characterization and modeling of amplified spontaneous emission in unsaturated erbium-doped fiber amplifiers. IEEE Photon Tech Lett. 1991;3:127.10.1364/OFC.1991.ThM1Search in Google Scholar
24. Pedersen B, Bjarklev A, Povlsen JH, Dybdal K, Larsen CC. The design of erbium-doped fiber amplifiers. J Lightwave Technol. 1991;9:1105.10.1109/50.85807Search in Google Scholar
25. Chen DN, Desurvire E. Noise performance evaluation of distributed erbium-doped fiber amplifiers with bidirectional pumping at 1.48 µm. IEEE Photon Technol Lett. 1992;4:52.10.1109/68.124874Search in Google Scholar
26. Chen J, Zhu X, Sibbett W. Derivation of the threshold pump power of erbium doped fiber lasers. Opt Lett. 1992;17:926.10.1364/OL.17.000926Search in Google Scholar PubMed
27. Chen J, Zhu X, Sibbett W. Rate-equation studies of erbium-doped fiber lasers with common pump and laser energy bands. J Opt Soc Am B. 1992;9:1876.10.1364/JOSAB.9.001876Search in Google Scholar
28. Pfeiffer T, Bulow H. Analytical gain equation for erbium-doped fiber including mode field profiles and dopant distribution. IEEE Photon Technol Lett. 1992;4:449.10.1109/68.136482Search in Google Scholar
29. Lin MC, Chi S. The gain and optimal length in the erbium-doped fiber amplifiers with 1480 nm pumping, IEEE photon. Technol Lett. 1992;4:354.10.1109/68.127211Search in Google Scholar
30. Mignonm M, Desurvire E. Analytical model for the determination of optimal output reflectivity and fiber length in erbium doped fiber lasers. IEEE Photon Technol Lett. 1992;4:850.10.1109/68.149884Search in Google Scholar
31. Georges T, Delevaque E. Analytical modelling of high-gain erbium doped fiber amplifiers. Opt Lett. 1992;17:1113.10.1364/OL.17.001113Search in Google Scholar
32. Ruhl FF. Implicit analytical solution for erbium doped fiber amplifier. Electron Lett. 1992;28:465.10.1049/el:19920293Search in Google Scholar
33. Barnard C, Myslinski P, Chrostowski J, Kavehard M. Analytical model for rare-earth-doped fiber amplifiers and lasers. IEEE J Quant Electron. 1994;30:1817.10.1109/3.301646Search in Google Scholar
34. Bertilsson K, Andrekson PA. Modeling of noise in erbium-doped fiber amplifiers in the saturated regime. J Lightwave Technol. 1994;12:1198.10.1109/50.301813Search in Google Scholar
35. Zech H. Theoretical investigation of the gain profile of erbium-doped fiber amplifiers. Opt Fiber Technol. 1995;1:327.10.1006/ofte.1995.1026Search in Google Scholar
36. Rebolledo MA, Jarabo S. Erbium-doped silica fiber modeling with overlapping factors. Appl Opt. 1994;33:5585.10.1364/AO.33.005585Search in Google Scholar PubMed
37. Jarabo S, Rebolledo MA. Analytic modeling of erbium-doped fiber amplifiers on the basis of intensity-dependent overlapping factors. Appl Opt. 1995;34:6158.10.1364/AO.34.006158Search in Google Scholar PubMed
38. Burger JP, Swart PL, Spammer SJ, Bulkin PV. Output power characteristics of a Fabry-Perrot Er+3- doped fiber laser. Opt Eng. 1997;36:593.10.1117/1.601232Search in Google Scholar
39. Sun Y, Zyskind JL, Srivastava AK. Average inversion level, modeling, and physics of erbium-doped fiber amplifiers. IEEE J Sel Topics Quant Electron. 1997;3:991.10.1109/2944.649527Search in Google Scholar
40. Hardy A, Oron R. Signal amplification in strongly pumped fiber amplifiers. IEEE J Quant Electron. 1997;33:307.10.1109/3.555997Search in Google Scholar
41. Oron R, Hardy A. Approximate analytical expressions for signal amplification in strongly pumped fiber amplifiers. Proc IEE-OptoElectron. 1998;145:138.10.1049/ip-opt:19981812Search in Google Scholar
42. Jarabo S. Analytical theoretical model of erbium-doped fiber amplifiers. Opt Commun. 2000;181:303.10.1016/S0030-4018(00)00771-9Search in Google Scholar
43. Escuer A, Jarabo S, Alvarez JM. Analysis of theoretical models for erbium-doped silica fiber lasers. Opt Commun. 2001;187:107.10.1016/S0030-4018(00)01076-2Search in Google Scholar
44. Nusinsky I, Hardy AA. Analysis of the effect of upconversion on signal amplification in erbium-doped fiber amplifiers (EDFAs). IEEE J Quantum Electronics. 2003;39:548.10.1109/JQE.2003.809339Search in Google Scholar
45. Nusinsky I, Hardy AA. Multichannel amplification in strongly pumped EDFAs. J Lightwave Technol. 2004;22:946.10.1109/JLT.2004.832428Search in Google Scholar
46. Bao PQ, Son LH. Gain and noise in erbium-doped fiber amplifier (EDFA) - A rate equation approach (REA). Commun Phys. 2004;14:1.10.15625/0868-3166/12Search in Google Scholar
47. Rieznik AA, Fragnito HL. Analytical solution for the dynamic behaviour of erbium-doped fiber amplifiers with constant population inversion along the fiber. J Opt Soc Am B. 2004;21:1732.10.1364/JOSAB.21.001732Search in Google Scholar
48. Xiao L, Yan P, Gong M, Wei W, Ou P. An approximate analytic solution of strongly pumped Yb-doped double-clad fiber lasers without neglecting the scattering loss. Opt Commun. 2004;230:401.10.1016/j.optcom.2003.11.017Search in Google Scholar
49. Dong X, Shum P, Ngo NQ, Tam HY, Dong X. Output power characteristics of tunable erbium-doped fiber ring lasers. J Lightwave Technol. 2005;23:1334.10.1109/JLT.2004.839986Search in Google Scholar
50. Drag PD. Analytical model for injection-seeded erbium-doped fiber ring lasers. IEEE Photon Technol Lett. 2005;17:1629.10.1109/LPT.2005.851883Search in Google Scholar
51. Barmenkov YO, Kiryanov AV, Chavez AD, Cruz JL, Andrés MV. Excited-state absorption in erbium-doped silica fibre with simultaneous excitation at 977 and 1531 nm. J Appl Phys. 2009;106:083108.10.1063/1.3248369Search in Google Scholar
52. Khan GR. Analytical method for gain in erbium doped fiber amplifier with pump excited state absorption. Opt Fiber Technol. 2012;18:421.10.1016/j.yofte.2012.06.005Search in Google Scholar
53. Khan GR. Exact analytical formulism for erbium doped fiber lasers. J Lightwave Technol. 2013;31:3158.10.1109/JLT.2013.2279848Search in Google Scholar
54. Digonnet MJ, editor. Rare earth doped glasses:optical properties. 2nd ed. New York: Marcel Dekker, 2001:83.Search in Google Scholar
55. Nakazawa M, Kimura Y, Suzuki K. High gain erbium fibre amplifier pumped by 800 nm band. Electron Lett. 1990;26:548.10.1049/el:19900357Search in Google Scholar
56. Kimura Y, Suzuki K, Nakazawa M. 46.5 dB gain in Er3+-doped fibre amplifier pumped by 1.48 µm GaLiAsP laser diodes. Electron Lett. 1989;25:1656.10.1049/el:19891110Search in Google Scholar
57. Hansen SL, Dybdal K, Larsen CC. Upper gain limit in Er-doped fiber amplifiers due to Rayleigh backscattering. OFC’92, San Jose, CA. OSA. 1992;5:68.10.1364/OFC.1992.TuL4Search in Google Scholar
58. Pedersen B. Small-signal erbium-doped fibre amplifiers pumped at 980 nm: a design study. Opt Quantum Electron. 1994;26:273.10.1007/BF00384679Search in Google Scholar
59. Zemon S, Pedersen B, Lambert G, Miniscalco WJ, Andrews LJ, Davies RW, et al. Excited-state absorption cross-sections in the 800-nm band for Er-doped, Al/P-silica fibers:measurements and amplifier modeling. IEEE Photon Technol Lett. 1991;3:621.10.1109/68.87933Search in Google Scholar
60. Kimura Y, Suzuki K, Nakazawa M. High gain erbium-doped fiber amplifier pumped in the 0.8 µm pump band. Ecoc-90. 1990;1:103.Search in Google Scholar
61. Pedersen B, Zemon S, Miniscalco WJ. Erbium-doped fibers pumped in 800 nm band. Electron Lett. 1991;27:1295.10.1049/el:19910810Search in Google Scholar
62. Millar CA, Miller ID, Ainslie BJ, Craig SP, Armitage JR Low-threshold cw operation of an erbium-doped fibre laser pumped at 807 nm wavelength. Electron Lett. 1987;23:865.10.1049/el:19870611Search in Google Scholar
63. Reekie LI, Jauncey M, Poole SB, Payne DN. Diode–laser-pumped operation of an Er3+-doped single-mode fibre laser. Electron Lett. 1987;23:1076.10.1049/el:19870752Search in Google Scholar
64. Myslinski P, Nguyen D, Chrostowski J. Effects of concentration on the performance of erbium-doped fiber amplifiers. IEEE J Lightwave Technol. 1997;15:112.10.1109/50.552118Search in Google Scholar
65. Kotov LV, Likhachev ME, Bubnov MM, Medvedkov OI, Yashkov MV, Guryanov AN, et al. 75 W 40 % efficiency single-mode all-fiber erbium-doped laser cladding pumped at 976. Opt Lett. 2013;38:2230.10.1364/OL.38.002230Search in Google Scholar PubMed
© 2019 Walter de Gruyter GmbH, Berlin/Boston
Articles in the same Issue
- Frontmatter
- Amplifiers
- Unified Formalism for Erbium-Doped Fiber Amplifiers and Lasers
- Nonlinear Effects with Semiconductor Optical Amplifiers
- Average Power Model of Optical Raman Amplifiers Based on Frequency Spacing and Amplifier Section Stage Optimization
- Devices
- An Optical Half Adder Using Nonlinear Ring Resonator Based on Photonic Crystal
- Implementation of Polarization-Encoded Quantum Fredkin Gate Using Kerr Effect
- Lasers
- Spatial Continuous Wave Laser and Spatiotemporal VCSEL for High-Speed Long Haul Optical Wireless Communication Channels
- Measurements
- Graphene Oxide Effect on Improvement of Silver Surface Plasmon Resonance D-Shaped Optical Fiber Sensor
- Networks
- High-Speed Light Sources in High-Speed Optical Passive Local Area Communication Networks
- RSVP-TE Bilateral-Recursive Region Re-Routing Crankback Mechanism for Large-Scale Optical Networks
- An Intelligent Vehicle Control System for Enhancing Road Safety Using Optimal Visible Light Communication Network
- Systems
- Design and Parameter Analysis of Underwater Wireless Optical Communication with Different Water Samples
- Free Space Optical Communication System under Different Weather Conditions
- Windowing Techniques for Reducing PAPR of OFDM in Li-Fi Systems
- Effects of Order Super Gaussian Pulses on the Performance of High Data Rate Optical Fiber Channel in the Presence of Self Phase Modulation
- Evaluation of Proposed Coherent Optical OFDM Link Using X-QAM with Polarization Division Multiplexing
- Theory
- Mathematical Model Analysis of Dispersion and Loss in Photonic Crystal Fibers
- Simulation of Optical ISL with 48 Transponders and Performance Analysis Using Ber and Q-Factor
Articles in the same Issue
- Frontmatter
- Amplifiers
- Unified Formalism for Erbium-Doped Fiber Amplifiers and Lasers
- Nonlinear Effects with Semiconductor Optical Amplifiers
- Average Power Model of Optical Raman Amplifiers Based on Frequency Spacing and Amplifier Section Stage Optimization
- Devices
- An Optical Half Adder Using Nonlinear Ring Resonator Based on Photonic Crystal
- Implementation of Polarization-Encoded Quantum Fredkin Gate Using Kerr Effect
- Lasers
- Spatial Continuous Wave Laser and Spatiotemporal VCSEL for High-Speed Long Haul Optical Wireless Communication Channels
- Measurements
- Graphene Oxide Effect on Improvement of Silver Surface Plasmon Resonance D-Shaped Optical Fiber Sensor
- Networks
- High-Speed Light Sources in High-Speed Optical Passive Local Area Communication Networks
- RSVP-TE Bilateral-Recursive Region Re-Routing Crankback Mechanism for Large-Scale Optical Networks
- An Intelligent Vehicle Control System for Enhancing Road Safety Using Optimal Visible Light Communication Network
- Systems
- Design and Parameter Analysis of Underwater Wireless Optical Communication with Different Water Samples
- Free Space Optical Communication System under Different Weather Conditions
- Windowing Techniques for Reducing PAPR of OFDM in Li-Fi Systems
- Effects of Order Super Gaussian Pulses on the Performance of High Data Rate Optical Fiber Channel in the Presence of Self Phase Modulation
- Evaluation of Proposed Coherent Optical OFDM Link Using X-QAM with Polarization Division Multiplexing
- Theory
- Mathematical Model Analysis of Dispersion and Loss in Photonic Crystal Fibers
- Simulation of Optical ISL with 48 Transponders and Performance Analysis Using Ber and Q-Factor