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Laser Diode to Single-Mode Circular Core Parabolic Index Fiber Coupling via Upside-Down Tapered Hyperbolic Microlens on the Tip of the Fiber: Prediction of Coupling Optics by ABCD Matrix Formalism

  • Angshuman Majumdar , Chintan Kumar Mandal and Sankar Gangopadhyay EMAIL logo
Published/Copyright: August 12, 2017
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Journal of Optical Communications
From the journal Journal of Optical Communications Volume 40 Issue 3

Abstract

We employ ABCD matrix formalism in order to investigate the coupling optics involving laser diode to single-mode circular core parabolic index fiber excitation via upside-down tapered hyperbolic microlens on the fiber tip. Analytic expressions for coupling efficiencies both in absence and in presence of transverse and angular mismatches are formulated. The concerned investigations are made for two practical wavelengths namely 1.3 µm and 1.5 µm. The execution of the prescribed formulations involves little computation. It has been found that the wavelength 1.5 µm is more efficient in respect of coupling. It is also seen that the present coupling device at both the wavelengths shows more tolerance with respect to angular mismatch. As regards tolerance with respect to transverse mismatch, the result is poor at both the wavelengths used. Consequently, it is desirable that designers should not to exceed transverse mismatch beyond 1 μm.

Keywords: laser diode; upside-down tapered hyperbolic microlens; single-mode circular core parabolic index fiber; optical coupling; coupling losses

Acknowledgments

The authors are grateful to the anonymous reviewer for the constructive suggestion.

Appendix

The laser beam input and output parameters(q1,q2) are connected by the relation given below

(19)q2=Aq1+BCq1+D

where,

(20)1q1,2=1R1,2−jλ0πw1,22n1,2

Here, R, n, w and λ0represent the radius of curvature of wavefront, refractive index, spot size and the wavelength in free space respectively.

The transformation matrix T1 of the graded-index taper lens with parallel ends is given by [8, 9]

(21)T1=R2zR1z/nconcodR2zdzdR1zdz

Further, the transformation matrix T2 of the hyperbolic end face has been found as [16, 17]

(22)T2= (101−nconco(b2/a)1nco) 

Accordingly, the transformation matrix T=(T1T2) of the system can be expressed as [8, 9]

(23)T=[R2(z)R1(z)/nconcodR2(z)dzdR1(z)dz]  (101−nconco(b2/a)1nco) 
=A1B1C1D1    

The ray matrix M for the upside down tapered hyperbolic microlens on the fiber tip is given by [9, 16, 17]

(24)M=A1B1C1D11u01=ABCD

Here,

(25)A1=R2(z)−(nco−1)nco(b2/a)R1(z),B1=1ncoR1(z),C1=ncodR2(z)dz−(nco−1)(b2/a)dR1(z)dz,D1=dR1(z)dz,

Here, b and a denote lengths of semi-axes of the hyperbolic interface in the plane of the paper

Further,

(26)R1z=−LηGz12SinηlnGzdR1zdz=1Gz12CosηlnGz+12ηSinηlnGzR2z=Gz12CosηlnGz−12ηSinηlnGzdR2zdz=A02a02Ld2Gz12SinηlnGz

where z is the axial length along the tapered region, L is axial length from the end face of the fiber to the geometrical vertex of the tapered profile, d is the radius of the aperture.

Further, the used parameters G (z), η, A0, z are given by

(27)G(z) = 1 − zLη = A02 a02 L2d2 − 14A0 =d (1 − zL) (1 − n2cln2co)12a02z = L (d − a0)d}

Further, from eq. (21)

A=A1;B=A1u+B1;C=C1;D=C1u+D1

The lens transformed spot sizes w2x,2y and radii of curvature R2x,2y are obtained by using eqs (19), (20) and the ABCD matrix given by (21) and those are given below

(28)w2x,2y2=A22w1x,1y2+(λ12B2)/(π2w1x,1y2)nA2D−BC2
(29)1R2x,2y=A2C2w1x,1y2+λ12BD/(π2w1x,1y2)A22w1x,1y2+λ12B2/(π2w1x,1y2)

where λ1=λ0/n1,A2=A+B/R1;C2=C+D/R1andn=n2n1

References

1. John J, Maclean TSM, 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;141:178–184.Search in Google Scholar

2. Neumann EG. Single-mode fibers fundamentals. Berlin: Springer-Verlag, 1988.10.1007/978-3-540-48173-7Search in Google Scholar

3. Presby HM, Edwards CA. Near 100  % efficient fibre microlenses. Electron Lett 1992;28:582–584.10.1049/el:19920367Search in Google Scholar

4. Edwards CA, Presby HM, Dragone C. Ideal microlenses for laser to fiber coupling. J Lightwave Technol 1993;11:252–257.10.1109/50.212535Search in Google Scholar

5. Presby HM, Edwards CA. Efficient coupling of polarization maintaining fiber to laser diodes. IEEE Photonics Techn Lett 1992;4:897–899.10.1109/68.149901Search in Google Scholar

6. Edwards CA, Presby HM. Coupling-sensitivity comparison of hemispheric and hyperbolic microlens. App Opt 1993;32:1573–1577.10.1364/AO.32.001573Search in Google Scholar

7. Kurokawa K, Becker EE. Laser fiber coupling with a hyperbolic lens. IEEE Trans Microwave Theory Technique 1975;23:309–311.10.1109/TMTT.1975.1128553Search in Google Scholar

8. Mondal SK, Gangopadhyay S, Sarkar SN. Analysis of an upside- down taper lens end from a single-mode step-index fiber. Appl Opt 1998;37:1006–1009.10.1364/AO.37.001006Search in Google Scholar

9. Yuan L, Qui A. Analysis of a single-mode fiber with taper lens end. J Opt Soc Am 1992;A9:950–952.10.1364/JOSAA.9.000950Search in Google Scholar

10. Mondal SK, Sarkar SN. Coupling of a laser diode to single-mode fiber with an upside-down tapered lens end. Appl Opt 1999;38:6272–6277.10.1364/AO.38.006272Search in Google Scholar

11. Yuan LB, Shou RL. Formation and power distribution properties of an upside-down tapered lens at the end of an optical fiber. Sens Actuators 1990;A23:1158–1161.10.1016/0924-4247(90)87108-USearch in Google Scholar

12. Lie Y. Theoretical analysis of tapered fiber microlens parameter and its new fabricating technique. IEEE Int Conf Comput Appl Syst Modeling 2010;13:448–451.Search in Google Scholar

13. Sankar SP, Hariharan N, Varatharajan R. A novel method to increase the coupling efficiency of laser to single mode fiber. Wireless Personal Commun 2016;87:419–430.10.1007/s11277-015-3028-4Search in Google Scholar

14. Das B, Maiti AK, Gangopadhyay S. Laser diode to single-mode circular core dispersion-shifted/dispersion- flattened fiber excitation via hyperbolic microlens on the fiber tip: Prediction of coupling efficiency by ABCD matrix formalism. Optik 2014;125:3277–3282.10.1016/j.ijleo.2013.12.043Search in Google Scholar

15. Das B, Middya TR, Gangopadhyay S. Mismatch considerations in excitation of single-mode circular core parabolic index fiber by laser diode via upside down tapered hemispherical microlens on the tip of the fiber. J Opt Commun 2016. DOI: 10.1515/joc-2016-0043.Search in Google Scholar

16. Gangopadhyay S, Sarkar SN. Laser diode to single-mode fibre excited via hyperbolic lens on the fibre tip: Formulation of ABCD matrix and efficiency computation. Opt Commun 1996;132:55–60.10.1016/0030-4018(96)00328-8Search in Google Scholar

17. Gangopadhyay S, Sarkar SN. ABCD matrix for reflection and refraction of Gaussian light beams at surfaces of hyperboloid of revolution and efficiency computation for laser diode to single-mode fiber coupling by way of a hyperbolic lens on the fiber tip. Appl Opt 1997;36:8582–8586.10.1364/AO.36.008582Search in Google Scholar

18. Mukhopadhyay S, Sarkar SN. Coupling of a laser diode to single mode circular core graded index fiber via hyperbolic microlens on the fiber tip and identification of the suitable refractive index profile with consideration for possible misalignments. Opt Engg 2011;50:1–9.Search in Google Scholar

19. Gangopadhyay S, Sarkar SN. Misalignment considerations in laser diode to single-mode fibre excitation via hyperbolic lens on the fibre tip. Opt Commun 1998;146:104–108.10.1016/S0030-4018(97)00487-2Search in Google Scholar

20. Sarkar S, Thyagrajan K, Kumar A. Gaussian approximation of the fundamental mode in single mode elliptic core fibers. Opt Commun 1984;49:178–183.10.1016/0030-4018(84)90259-1Search in Google Scholar

21. Marcuse D. Gaussian approximation of the fundamental modes of graded index fibers. J Opt Soc Am 1978;68:103–109.10.1364/JOSA.68.000103Search in Google Scholar

22. Ghatak AK, Thygarajan K. Introduction of fiber optics. Cambridge, NY: Cambridge University Press, 1998.10.1017/CBO9781139174770Search in Google Scholar

23. Yang H-M, Huang S-Y, Lee C-W, Lay T-S, Cheng W-H. High-coupling tapered hyperbolic fiber microlens and taper asymmetry effect. J Lightwave Tech 2004;22:1395–1401.10.1109/JLT.2004.827664Search in Google Scholar

24. Presby HM, Benner AF, Edwards CA. Laser microlensing of efficient fiber microlenses. Appl Opt 1990;29:2692–2695.10.1364/AO.29.002692Search in Google Scholar PubMed

25. Thyagarajan K, Kakkar C. S-band single-stage EDFA with 25-dB gain using distributed ASE suppression. IEEE Photonics Technol Lett 2004;16:2448–2450.10.1109/LPT.2004.835196Search in Google Scholar

26. Pramanik S, Das G, Sarkar S. Comparative study of the influence of the aspect ratio of trapezoidal index profiles on the performance of a fiber Raman amplifier. Opt Eng 2010;49:055001(1–3).10.1117/1.3421554Search in Google Scholar

Received: 2017-03-11
Accepted: 2017-07-20
Published Online: 2017-08-12
Published in Print: 2019-07-26

© 2019 Walter de Gruyter GmbH, Berlin/Boston

Articles in the same Issue

  1. Frontmatter
  2. Amplifiers
  3. Flattened gain S + C + L Band RAMAN–Thulium-Doped Tellurite Fiber Amplifier Hybrid Optical Amplifier for Super Dense Wavelength Division Multiplexing System
  4. Devices
  5. Laser Diode to Single-Mode Circular Core Parabolic Index Fiber Coupling via Upside-Down Tapered Hyperbolic Microlens on the Tip of the Fiber: Prediction of Coupling Optics by ABCD Matrix Formalism
  6. Impact of Various Parameters on the Performance of Optical Directional Coupler
  7. Perfect Tunable All-Optical Diode based on Periodic Photonic Crystal Grand Graded Structures
  8. Design of All-optical Half-subtractor Circuit Device using 2-D Principle of Photonic Crystal Waveguides
  9. Networks
  10. Minimization Number of Network-Coded Links Based on Improved Adaptive Genetic Algorithm for Multi-source Optical Networks
  11. Design and Investigations with all Optical Multilogic Network
  12. Comparative Study of Optical Interconnection Architectures in Data Center Networks
  13. Fallacious Node Algorithm for Performance Enhancement in Optical-Burst-Switching Networks
  14. Receiver
  15. Effect of Pointing Error on BER Performance of a Multi-wavelength OCDMA FSO System with SIK Dual Detector Receiver
  16. Systems
  17. 40 Gbps Downstream Transmission Using DQPSK and 20 Gbps Upstream Transmission Using IRZ Modulation in Full-Duplex WDM-PON
  18. Performance Evaluation of Wavelet-Based Optical Wireless System using On-Off Keying Modulation
  19. Construction and Analysis of a Novel SAC-OCDMA System with EDW Coding using Direct Detection Technique
  20. Effects of Diverse Dispersion Compensation Formats at Different Data Rates in Light-Wave System
  21. 10 Gbps-60 GHz RoF Transmission System for 5 G Applications
  22. High Speed 4 × 2.5 Gbps-5 GHz AMI-WDM-RoF Transmission System for WLANs
  23. Theory
  24. Optical Buffer Design based on SOA and DCFBG
  25. Statistical Analysis of FSO Links Employing Multiple Transmitter/Receiver Strategy over Double-Generalized and Gamma–Gamma Fading Channel Using Different Modulation Techniques
  26. Bit Error Rate Performance Analysis of Hybrid Subcarrier Intensity Modulation-Based FSO with Spatial Diversity in Various Weather Conditions
  27. Analyzing DWDM System with Different Modulation Formats and Channel Spacing
  28. On the End-to-End Performance of a Mixed RF-FSO link with a Decode-and-Forward Relay
  29. Retraction
  30. Retraction
https://doi.org/10.1515/joc-2017-0040
Keywords for this article
laser diode; upside-down tapered hyperbolic microlens; single-mode circular core parabolic index fiber; optical coupling; coupling losses

Articles in the same Issue

  1. Frontmatter
  2. Amplifiers
  3. Flattened gain S + C + L Band RAMAN–Thulium-Doped Tellurite Fiber Amplifier Hybrid Optical Amplifier for Super Dense Wavelength Division Multiplexing System
  4. Devices
  5. Laser Diode to Single-Mode Circular Core Parabolic Index Fiber Coupling via Upside-Down Tapered Hyperbolic Microlens on the Tip of the Fiber: Prediction of Coupling Optics by ABCD Matrix Formalism
  6. Impact of Various Parameters on the Performance of Optical Directional Coupler
  7. Perfect Tunable All-Optical Diode based on Periodic Photonic Crystal Grand Graded Structures
  8. Design of All-optical Half-subtractor Circuit Device using 2-D Principle of Photonic Crystal Waveguides
  9. Networks
  10. Minimization Number of Network-Coded Links Based on Improved Adaptive Genetic Algorithm for Multi-source Optical Networks
  11. Design and Investigations with all Optical Multilogic Network
  12. Comparative Study of Optical Interconnection Architectures in Data Center Networks
  13. Fallacious Node Algorithm for Performance Enhancement in Optical-Burst-Switching Networks
  14. Receiver
  15. Effect of Pointing Error on BER Performance of a Multi-wavelength OCDMA FSO System with SIK Dual Detector Receiver
  16. Systems
  17. 40 Gbps Downstream Transmission Using DQPSK and 20 Gbps Upstream Transmission Using IRZ Modulation in Full-Duplex WDM-PON
  18. Performance Evaluation of Wavelet-Based Optical Wireless System using On-Off Keying Modulation
  19. Construction and Analysis of a Novel SAC-OCDMA System with EDW Coding using Direct Detection Technique
  20. Effects of Diverse Dispersion Compensation Formats at Different Data Rates in Light-Wave System
  21. 10 Gbps-60 GHz RoF Transmission System for 5 G Applications
  22. High Speed 4 × 2.5 Gbps-5 GHz AMI-WDM-RoF Transmission System for WLANs
  23. Theory
  24. Optical Buffer Design based on SOA and DCFBG
  25. Statistical Analysis of FSO Links Employing Multiple Transmitter/Receiver Strategy over Double-Generalized and Gamma–Gamma Fading Channel Using Different Modulation Techniques
  26. Bit Error Rate Performance Analysis of Hybrid Subcarrier Intensity Modulation-Based FSO with Spatial Diversity in Various Weather Conditions
  27. Analyzing DWDM System with Different Modulation Formats and Channel Spacing
  28. On the End-to-End Performance of a Mixed RF-FSO link with a Decode-and-Forward Relay
  29. Retraction
  30. Retraction
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