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A simple and accurate theoretical investigation is presented, based on a novel, effective, and straightforward ABCD matrix technique, in relation to estimation of optimum coupling efficiency between the laser diode and the photonic crystal fiber (PCF) with a hyperbolic microlens (HML) on its tip. By tailoring different parameters, such as the air-filling factor and lattice constant of the PCF, the criteria for achieving maximum coupling are predicted and reported for two different light wavelengths of practical interest. It is observed that such fiber parameters play a crucial role in predicting the optimum focal length of HML for a particular wavelength. The formulation should find application in the design of HML, for achieving a long working distance between the laser source facet and the fiber tip. Downloaded From: http://opticalengineering.spiedigitallibrary.org/ on 08/19/2015 Terms of Use: http://spiedigitallibrary.org/ss/TermsOfUse.aspx Somenath Sarkar is currently a professor of the Department of Electronic Science, CU, where he has rendered services since September 1989. He received his MSc degree (physics) from Delhi University and his PhD (physics) from IIT, Delhi, in fiber optics. He carried out investigations successfully through two R&D projects of CSIR and AICTE and one DST-FIST and AICTE MODROB project with colleagues to upgrade teaching and laboratories. He is an associate editor of Advances in Optoelectronics. Optical Engineering 086102-7 August 2015 • Vol. 54(8) Karak et al.: Investigation of coupling of a laser diode to photonic crystal fiber via hyperbolic microlens. . . Downloaded From: http://opticalengineering.spiedigitallibrary.org/ on 08/19/2015 Terms of Use: http://spiedigitallibrary.org/ss/TermsOfUse.aspx

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With an aim to explore the suitable refractive index profile for maximum coupling, we present a theoretical investigation of coupling optics involving a laser diode and single mode circular core graded index fiber via a hyperbolic microlens on the fiber tip in absence and presence of any possible transverse and angular misalignments. By employing Gaussian field distributions for both the source and the fiber and also ABCD matrix for hyperbolic microlens under paraxial approximation, we formulate analytical expressions for the concerned coupling efficiencies. The investigations are performed for two different light-emitting wavelengths of 1.3 and 1.5 μm for such fibers with different profile exponents in refractive index profile. Further, it is observed that out of the studied refractive index profiles, the triangular index profile having the dispersionshifted merit comes out to be the most suitable profile to couple laser diode to single mode circular core graded index fiber for two wavelengths of practical interest. The analysis should find use in ongoing investigations for optimum launch optics for the design of hyperbolic microlens either directly on the graded index circular core single mode fiber tip or such fiber attached to single mode fiber to achieve a long working distance. C 2011 Society of Photo-Optical Instrumentation Engineers (SPIE).