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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

  • Bishuddhananda Das , Tapas Ranjan Middya and Sankar Gangopadhyay EMAIL logo
Published/Copyright: November 21, 2017
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Journal of Optical Communications
From the journal Journal of Optical Communications Volume 38 Issue 4

Abstract

We report the theoretical investigation of the coupling optics involving laser diode to single-mode circular core parabolic index fiber via upside down tapered hemispherical microlens on the tip of the fiber in the presence of possible transverse and angular mismatches. Using the relevant ABCD matrix for such tapered hemispherical microlens, we formulate analytical expressions for the coupling efficiencies in the presence of the said two mismatches. Further, the transmitted spot size of the source via the hemispherical lens and the tapered region should match with the spot size of the fiber for obtaining maximum coupling. The investigations have been made for two practical wavelengths, namely 1.3 and 1.5 μm in order to find the tolerance of this coupling device with respect to the said kinds of mismatches at the concerned wavelengths. Although our simple method predicts the concerned coupling optics excellently, the evaluation of the concerned efficiencies and associated losses involve little computations. Thus this user-friendly technique and also the results found thereof will benefit the designers and packagers who are working in the field of optical technology.

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

Appendix

The light beam input and output parameters of laser beam, namely q1 and q2, respectively, are mutually related as follows:

(18)q2=Aq1+BCq1+D

where

(19)1q1,2=1R1,2−jλ0πw1,22n1,2

with R, n, w and λ0 representing the radius of curvature of wavefront, refractive index, spot size and the wavelength in free space, respectively.

The ray matrix M for the upside down tapered hemispherical microlens on the fiber tip can be given as [6, 20]

(20)M=A1B1C1D11u01=ABCD

where

(21)A1=R2(z)−(nco−1)ncoR0R1(z),B1=1ncoR1(z),C1=ncodR2(z)dz−(nco−1)R0dR1(z)dz,D1=dR1(z)dz,

Further, R1z,dR1zdz,R2zanddR2zdz are given by

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

where z represents the axial length in the tapered region, L stands for the axial length from the end face of the fiber to the geometrical vertex of the tapered profile and d is the aperture radius.

Again, the parameters G(z), η, A0, z have been found as [6]

(23)Gz=1−zLη=A02a02L2d2−14A0=d1−zL1−n2cln2co12a02z=Ld−a0d

Using eq. (20), one gets

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

The upside down tapered hemispherical microlens transformed spot sizes w2x, 2y and radii of curvature R2x, 2yr can be found by using eqs (18), (19) and the ABCD matrix given by eq. (20) and those are as follows:

(25)w2x,2y2=A22w1x,1y2+(λ12B2)/(π2w1x,1y2)nA2D−BC2
(26)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.

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Received: 2016-4-16
Accepted: 2016-6-10
Published Online: 2017-11-21
Published in Print: 2017-12-20

© 2017 Walter de Gruyter GmbH, Berlin/Boston

Articles in the same Issue

  1. Frontmatter
  2. Amplifiers
  3. Analysis of DWDM System Using DPSK Modulation Technique with Raman–EDFA Hybrid Optical Amplifier
  4. Devices
  5. Comprehensive Study of Z-Cut Highly Integrated LiNbO3 Optical Modulator with Adjustable Chirp Parameters
  6. 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
  7. Review on Photonic Generation of Chirp Arbitrary Microwave Waveforms for Remote Sensing Application
  8. Networks
  9. Multi-granularity Bandwidth Allocation for Large-Scale WDM/TDM PON
  10. New Scheduling Algorithms for Agile All-Photonic Networks
  11. Energy-Efficient Routing and Spectrum Assignment Algorithm with Physical-Layer Impairments Constraint in Flexible Optical Networks
  12. Multipath Routing and Wavelength Assignment Technique in Optical WDM Mesh Networks
  13. Secured Hash Based Burst Header Authentication Design for Optical Burst Switched Networks
  14. A Dynamic Resilience Approach for WDM Optical Networks
  15. Receiver
  16. Effect of Pointing Error on the BER Performance of an Optical CDMA FSO Link with SIK Receiver
  17. 2.5 Gbit/s Optical Receiver Front-End Circuit with High Sensitivity and Wide Dynamic Range
  18. Systems
  19. Performance Analysis of Long-Reach Coherent Detection OFDM-PON Downstream Transmission Using m-QAM-Mapped OFDM Signal
  20. Capacity Improvement of a Free Space Optical Satellite Uplink using Transmitter Power and Rate Adaptation
https://doi.org/10.1515/joc-2016-0043
Keywords for this article
laser diode; upside down tapered hemispherical microlens; single-mode circular core parabolic index fiber; optical coupling; coupling losses

Articles in the same Issue

  1. Frontmatter
  2. Amplifiers
  3. Analysis of DWDM System Using DPSK Modulation Technique with Raman–EDFA Hybrid Optical Amplifier
  4. Devices
  5. Comprehensive Study of Z-Cut Highly Integrated LiNbO3 Optical Modulator with Adjustable Chirp Parameters
  6. 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
  7. Review on Photonic Generation of Chirp Arbitrary Microwave Waveforms for Remote Sensing Application
  8. Networks
  9. Multi-granularity Bandwidth Allocation for Large-Scale WDM/TDM PON
  10. New Scheduling Algorithms for Agile All-Photonic Networks
  11. Energy-Efficient Routing and Spectrum Assignment Algorithm with Physical-Layer Impairments Constraint in Flexible Optical Networks
  12. Multipath Routing and Wavelength Assignment Technique in Optical WDM Mesh Networks
  13. Secured Hash Based Burst Header Authentication Design for Optical Burst Switched Networks
  14. A Dynamic Resilience Approach for WDM Optical Networks
  15. Receiver
  16. Effect of Pointing Error on the BER Performance of an Optical CDMA FSO Link with SIK Receiver
  17. 2.5 Gbit/s Optical Receiver Front-End Circuit with High Sensitivity and Wide Dynamic Range
  18. Systems
  19. Performance Analysis of Long-Reach Coherent Detection OFDM-PON Downstream Transmission Using m-QAM-Mapped OFDM Signal
  20. Capacity Improvement of a Free Space Optical Satellite Uplink using Transmitter Power and Rate Adaptation
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