A Novel and Simple Formalism for Study of Effect of Kerr Nonlinearity on Petermann I and II Spot Sizes of Single-Mode-Graded Index Fiber
Abstract
We present investigation of Petermann I and II spot sizes in the presence of Kerr nonlinearity. Our study is based on the simple power series formulation for fundamental modal field of single-mode-graded index fiber developed by Chebyshev formalism. Based on the said power series expression in the absence of nonlinearity, analytical expressions of the said spot sizes can be prescribed. Using the analytical expressions of the said spot sizes in the absence of nonlinearity, we apply iterative technique in order to predict the said propagation characteristics in presence of Kerr nonlinearity. In this context, we choose some typical single-mode step and parabolic index fibers. We show that the our results agree excellently with the exact results which can be obtained by using rigorous finite-element technique. This leads to verification of accuracy of our simple technique. Moreover, evaluation of the concerned parameters by our formalism involves little computation. Thus, our method provides an accurate but simple alternative to the existing rigorous methods in this context. Accordingly, this novel and simple formalism will prove user friendly to the system engineers in the field non linear optics.
Acknowledgements
The authors are grateful to the anonymous reviewers for constructive suggestions
References
1. Agrawal GP. Nonlinear fiber optics. Cambridge, Massachusetts: Academic Press; 2013.10.1016/B978-0-12-397023-7.00011-5Suche in Google Scholar
2. Tomlinson WJ, Stolen RH, Chank CV. Compression of optical pulses chirped by self-phase modulation in fibers. J Opt Soc. 1984;1:139–49.10.1364/JOSAB.1.000139Suche in Google Scholar
3. Tai K, Tomita A, Jewell JL, Hasegawa A. Generation of subpicosecondsolitonlike optical pulses 0.3 THz repetition rate by induced modulational instability. Appl Phys Lett. 1986;49:236–8.10.1063/1.97181Suche in Google Scholar
4. Snyder AW, Chen Y, Poladian L, Mitchel DJ. Fundamental mode of highly nonlinear fibres. Electron Lett. 1990;26:643–4.10.1049/el:19900421Suche in Google Scholar
5. Goncharenko IA. Influence of nonlinearity on mode parameters of anisotropic optical fibres. J Mod Opt. 1990;37:1673–84.10.1080/09500349014551831Suche in Google Scholar
6. Sammut RA, Pask C. Variational approach to nonlinear waveguides-gaussian approximations. Electron Lett. 1990;26:1131–2.10.1049/el:19900731Suche in Google Scholar
7. Agrawal GP, Boyd RW. Contemporary Nonlinear Optics. Boston: Academic Press, 1992.Suche in Google Scholar
8. Antonelli C, Golani O, Shtaif M, Mecozzi A. Nonlinear interference noise in space-division multiplexed transmission through optical fibers. Opt Express. 2017;25:13055–78.10.1364/OE.25.013055Suche in Google Scholar PubMed
9. Lu X, Lee JY, Rogers S, Lin Q. Optical Kerr nonlinearity in a high-Q silicon carbide microresonator. Opt Express. 2014;22:30826–32.10.1364/OE.22.030826Suche in Google Scholar PubMed
10. Yu YF, Ren M, Zhang JB, Bourouina T, Tan CS, Tsai JM, et al. Force-induced optical nonlinearity and Kerr-like coefficient in opto-mechanical ring resonators. Opt Express. 2012;20:18005–15.10.1364/OE.20.018005Suche in Google Scholar PubMed
11. Neumann EG. Single mode fibers fundamentals, Vol. 57. Berlin, Heidelberg: Springer-Verlag, 1988.10.1007/978-3-540-48173-7Suche in Google Scholar
12. Sansonetti P. Prediction of modal dispersion in single-mode fibres from spectral behaviour of mode spot size. Electron Lett. 1982;18:136–8.10.1049/el:19820091Suche in Google Scholar
13. Sansonetti P. Modal dispersion in single-mode fibres: Simple approximation issued from mode spot size spectral behaviour. Electron Lett. 1982;18:647–8.10.1049/el:19820441Suche in Google Scholar
14. Ankiewicz A, Peng GD. Generalised Gaussian approximation for single mode fibers. IEEE J Lightwave Technol. 1992;10:22–7.10.1109/50.108731Suche in Google Scholar
15. Mishra PK, Hosain SI, Goyal IC, Sharma A. Scalar variational analysis of single mode graded core W-type fibers. Opt Quant Electron. 1984;16:287–96.10.1007/BF00620069Suche in Google Scholar
16. Hosain SI, Sharma A, Ghatak AK. Splice loss evaluation for single-mode graded index fibers. Appl Opt. 1982;21:2716–21.10.1364/AO.21.002716Suche in Google Scholar PubMed
17. Roy D, Sarkar SN. Simple but accurate method to compute LP11 mode cut off frequency of nonlinear optical fibers by Chebyshev technique. Optl Eng. 2016;55:0841051–4.10.1117/1.OE.55.8.084105Suche in Google Scholar
18. Sadhu A, Karak A, Sarkar S. A simple and effective method to analyze the propagation characteristics of nonlinear single mode fiber using Chebyshev method. Micro Opt Technol Lett. 2014;56:787–90.10.1002/mop.28227Suche in Google Scholar
19. Chakraborty S, Mandal CK, Gangopadhyay S. Prediction of fundamental modal field for graded index fiber in the presence of Kerr nonlinearity. J Opt Commun. 2017;1–6. DOI: 10.1515/joc-2017-0126.Suche in Google Scholar
20. Hayata K, Koshiba M, Suzuki M. Finite-element solution of arbitrarily nonlinear, graded-index slab waveguides. Electron Lett. 1987;23:429–31.10.1049/el:19870311Suche in Google Scholar
21. Mondal SK, Sarkar SN. Effect of optical Kerr effect nonlinearity on LP11 mode cutoff frequency of single-mode dispersion shifted and dispersion flattened fibers. Opt Commun. 1996;127:25–30.10.1016/0030-4018(95)00706-7Suche in Google Scholar
22. Ghatak A, Thyagarajan K. Introduction to fiber optics. Cambridge, UK: Cambridge University Press, 1998.10.1017/CBO9781139174770Suche in Google Scholar
23. Ghatak A, Thyagarajan K. Optical electronics. Cambridge, UK: Cambridge University Press, 1993.Suche in Google Scholar
24. Gradshteyn IS, Ryzhik IM. Table of integrals, series, and products. London: Academic Press, 2014.Suche in Google Scholar
25. Watson GN. A treatise on the theory of Bessel functions. Cambridge, UK: Cambridge University Press, 1995.Suche in Google Scholar
26. Abramowitz M, Stegun IA. Handbook of mathematical functions: with formulas, graphs, and mathematical tables, Dover books on mathematics, 2012.Suche in Google Scholar
27. Shijun J. Simple explicit formula for calculating LP11 mode cut-off frequency. Electron Lett. 1987;23:534–6.10.1049/el:19870385Suche in Google Scholar
28. Chen PY. Fast method for calculating cut-off frequencies in single-mode fibers with arbitrary index profile. Electron Lett. 1982;18:1048–9.10.1049/el:19820716Suche in Google Scholar
29. Gangopadhyay S, Sengupta M, Mondal SK, Das G, Sarkar SN. Novel method for studying single-mode fibers involving Chebyshev technique. J Opt Commun. 1997;18:75–8.10.1515/JOC.1997.18.2.75Suche in Google Scholar
30. Patra P, Gangopadhyay S, Sarkar SN. A simple method for studying single-mode graded index fibers in the low V region. J Opt Commun. 2000;21:225–8.10.1515/JOC.2000.21.6.225Suche in Google Scholar
31. Gangopadhyay S, Sarkar SN. Evaluation of modal spot size in single-mode graded index fibers by a simple technique. J Opt Commun. 1998;19:173–5.10.1515/JOC.1998.19.5.173Suche in Google Scholar
32. Patra P, Gangopadhyay S, Sarkar SN. Evaluation of Petermann I and II spot sizes and dispersion parameters in the single-mode graded index fiber in the low V region by simple technique. J Opt Commun. 2001;22:19–23.10.1515/JOC.2001.22.1.19Suche in Google Scholar
33. Chakraborty S, Mandal CK, Gangopadhyay S. Prediction of first higher order modal field for graded index fiber in presence of Kerr nonlinearity. J Opt Commun. DOI: 10.1515/joc-2017-0206.Suche in Google Scholar
34. Burdin VA, Bourdine AV, Volkov KA. Spectral characteristics of LP11 mode of step index optical fiber with Kerr nonlinearity. SPIE10774 Opt Technol Telecommun. 2018;10774:107740N. DOI: 10.1117/12.2318982.Suche in Google Scholar
35. Brehler M, Schirwon M, Göddeke D, Krummrich PM. Modeling the Kerr-nonlinearity in mode-division multiplexing fiber transmission systems on GPUs. Adv Photonics. 2018;JTu5A–27. DOI: 10.1364/BGPPM.2018.JTu5A.27.Suche in Google Scholar
36. Nesrallah M, Hakami A, Bart G, McDonald CR, Varin C, Brabec T. Measuring the Kerr nonlinearity via seeded Kerr instability amplification: conceptual analysis. Opt Express. 2018;25:7646–54.10.1364/OE.26.007646Suche in Google Scholar PubMed
37. Le ST, Aref V, Buelow H. Nonlinear signal multiplexing for communication beyond the Kerr nonlinearity limit. Nat Photonics. 2017;11:570.10.1038/nphoton.2017.118Suche in Google Scholar
38. Derevyanko SA, Prilepsky JE, Turitsyn SK. Capacity estimates for optical transmission based on the nonlinear Fourier transform. Nat Commun. 2016;7:12710.10.1038/ncomms12710Suche in Google Scholar PubMed PubMed Central
39. Manafian J, Lakestani M. Application of tan (ϕ/2)-expansion method for solving the Biswas–Milovic equation for Kerr law nonlinearity. Optik-Int J Light Electron Opt. 2016;127:2040–54.10.1016/j.ijleo.2015.11.078Suche in Google Scholar
40. Liu Z, Wright LG, Christodoulides DN, Wise FW. Kerr self-cleaning of femtosecond-pulsed beams in graded-index multimode fiber. Opt Lett. 2016;41:3675–8.10.1364/OL.41.003675Suche in Google Scholar PubMed
41. Ekici M, Mirzazadeh M, Sonmezoglu A, Zhou Q, Triki H, Ullah MZ, et al. Optical solitons in birefringent fibers with Kerr nonlinearity by exp-function method. Optik. 2017;131:964–76.10.1016/j.ijleo.2016.12.015Suche in Google Scholar
42. John J, Maclean TS, Ghafouri-Shiraz H, Niblett J. Matching of single-mode fibre to laser diode by microlenses at 1.5–1.3 μm wavelength. IEE Proc: Optoelectron. 1994;141:178–84.10.1049/ip-opt:19941052Suche in Google Scholar
43. Presby HM, Edwards CA. Near 100% efficient fibre microlenses. Electron Lett. 1992;28:582–4.10.1049/el:19920367Suche in Google Scholar
44. Edwards CA, Presby HM, Dragone C. Ideal microlenses for laser to fiber coupling. J Lightwave Technol. 1993;11:252–7.10.1109/50.212535Suche in Google Scholar
45. Magni V, Cerullo G, De Silvestri S, Monguzzi A. Astigmatism in Gaussian-beam self-focusing and in resonators for Kerr-lens mode locking. J Opt Soc Am B. 1995;12:476–85.10.1364/JOSAB.12.000476Suche in Google Scholar
46. Sadhu A, Sarkar S. Effect of grading in refractive index profile on Kerr nonlinear optical processes in single-mode sub-wavelength diameter optical fibre using a straightforward method. J Mod Opt. 2016;64:156–63.10.1080/09500340.2016.1216193Suche in Google Scholar
47. Towers I, Malomed BA. Stable (2+1)-dimensional solitons in a layered medium with sign-alternating Kerr nonlinearity. J Opt Soc Am B. 2002;19:537–43.10.1364/JOSAB.19.000537Suche in Google Scholar
© 2019 Walter de Gruyter GmbH, Berlin/Boston
Artikel in diesem Heft
- Frontmatter
- Amplifiers
- A Multistage High Performance Amplification Approach for Improving WDM Communication System
- Devices
- Design and performance analysis of all optical 4-bit parity generator and checker using dual-control dual SOA terahertz optical asymmetric demultiplexer (DCDS-TOAD)
- Micro-Ring Resonator-Based Sensors for Detection of Different Chemicals
- Quaternary Bit-Swap Logic with QPSK Signal Using Four Wave Mixing
- Fibers
- Comparative crosstalk performance analysis of different configurations of heterogeneous multicore fiber
- A Novel and Simple Formalism for Study of Effect of Kerr Nonlinearity on Petermann I and II Spot Sizes of Single-Mode-Graded Index Fiber
- Networks
- A controlled deflection routing and wavelength assignment based scheme in Optical Burst Switched (OBS) networks
- Experiment Study of Downstream Traffic Balancing Strategy on 40G Long Reach Coherent PON
- Reduction of Blocking Probability in Generalized Multi-Protocol Label Switched Optical Networks
- Performance Evaluation of Bidirectional Wavelength Division Multiple Access Broadband Optical Passive Elastic Networks Operation Efficiency
- Systems
- Evaluation of Atmospheric Detrimental Effects on Free Space Optical Communication System for Delhi Weather
- Design and Performance Investigations with Ultra High Speed Optical ALU
- Enhancement of Signals Characteristics with Least Effect of Optical Communication Losses for Dense Optical Communication Systems
- Performance comparison of code division multiple access and orthogonal frequency division multiplexing over turbulent effected free space optics link under the impact of advance coding formats
- Wavelength division multiplexing techniques based on multi transceiver in low earth orbit intersatellite systems
- Selection of suitable wavelengths for the dual-wavelength model of free space optics (FSO) systems for high-speed trains
- Effects of Laser Linewidth on the Performance of DP-QPSK DWDM System
Artikel in diesem Heft
- Frontmatter
- Amplifiers
- A Multistage High Performance Amplification Approach for Improving WDM Communication System
- Devices
- Design and performance analysis of all optical 4-bit parity generator and checker using dual-control dual SOA terahertz optical asymmetric demultiplexer (DCDS-TOAD)
- Micro-Ring Resonator-Based Sensors for Detection of Different Chemicals
- Quaternary Bit-Swap Logic with QPSK Signal Using Four Wave Mixing
- Fibers
- Comparative crosstalk performance analysis of different configurations of heterogeneous multicore fiber
- A Novel and Simple Formalism for Study of Effect of Kerr Nonlinearity on Petermann I and II Spot Sizes of Single-Mode-Graded Index Fiber
- Networks
- A controlled deflection routing and wavelength assignment based scheme in Optical Burst Switched (OBS) networks
- Experiment Study of Downstream Traffic Balancing Strategy on 40G Long Reach Coherent PON
- Reduction of Blocking Probability in Generalized Multi-Protocol Label Switched Optical Networks
- Performance Evaluation of Bidirectional Wavelength Division Multiple Access Broadband Optical Passive Elastic Networks Operation Efficiency
- Systems
- Evaluation of Atmospheric Detrimental Effects on Free Space Optical Communication System for Delhi Weather
- Design and Performance Investigations with Ultra High Speed Optical ALU
- Enhancement of Signals Characteristics with Least Effect of Optical Communication Losses for Dense Optical Communication Systems
- Performance comparison of code division multiple access and orthogonal frequency division multiplexing over turbulent effected free space optics link under the impact of advance coding formats
- Wavelength division multiplexing techniques based on multi transceiver in low earth orbit intersatellite systems
- Selection of suitable wavelengths for the dual-wavelength model of free space optics (FSO) systems for high-speed trains
- Effects of Laser Linewidth on the Performance of DP-QPSK DWDM System