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

Abstract

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).

Investigation of coupling of a laser diode to photonic crystal fiber via hyperbolic microlens on the fiber tip by ABCD matrix formalism

“…The input and output parameters (q 1 , q 2 ) of the light beam are given by [7][8][9] E Q -T A R G E T ; t e m p : i n t r a l i n k -; e 0 1 4 ; 3 2 6 ; 4 4 8…”

“…For a highly efficient LD, the use of microlensed fibers is very common in practical semiconductor laser packages. [3][4][5][6][7][8][9][10][11][12][13][14] These microlenses may have hyperbolic, hemispherical, parabolic, and upside-down tapered surfaces to modulate the spot size of LD light incident on them and properly match and couple with SMF spot size. Also, for a more compact design of optical components and modules, the fabrication and design of fiber microlens have emerged as the extremely attractive state of the art.…”

“…In this regard, a hyperbolic microlens (HML) on the tip of an SMF has been shown to be most effective in comparison with other types of conventional microlenses with respect to large light gathering efficiency, absence of spherical aberration, [3][4][5][6][7][8][9][10][11][12][13][14] and other factors. According to geometrical optics, transformation of the incident spherical wave into a plane wave via HML is possible by avoiding spherical aberrations.…”

“…According to geometrical optics, transformation of the incident spherical wave into a plane wave via HML is possible by avoiding spherical aberrations. 5,[7][8][9] In this context, it is worth mentioning that the photonic crystal fiber (PCF) [15][16][17][18][19][20][21] is drawing tremendous attention as an emerging medium in device applications for its many significant characteristics, including large or ultrasmall mode field diameters (MFDs), endlessly single moded merit, highly tailorable group velocity dispersion, birefringence, high nonlinearity. 9 In this connection, the involved numerical integration generally used earlier to compute coupling efficiency is now replaced through the use of a simple ABCD matrix technique.…”

“…[7][8][9] The calculations herein are easily executable with very little computation. The λ ¼ 1.5 μm wavelength corresponds to the lowest loss window of glass and that of λ ¼ 1.3 μm for minimum dispersion.…”