Abstract

To investigate the viability of a planar graded-index multimode waveguide fabricated using a new method (to our knowledge) employing polysilane with photobleaching properties, we designed a planar two-way multimode power splitter based on multimode interference, with a core possessing a vertically parabolic and horizontally uniform index profile. We carried out mode propagation analysis using the Marcatili model and optimization using a three-dimensional beam-propagation method. The prototype was fabricated by means of multiple dicing after UV exposure and heat treatment in air. Index profile measurements using a special end-face reflection method showed it to have a vertically graded-index profile with relative index difference of 0.0456. Output beam profile observation using a CCD camera showed that it successfully divided the beam planewise.

© 2006 Optical Society of America

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[CrossRef]

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L. B. Soldano and E. C. M. Pennings, "Optical multi-mode interference devices based on self-imaging: principles and applications," J. Lightwave Technol. 13, 615-627 (1995).
[CrossRef]

1994

1992

1989

R. D. Miller and J. Michel, "Polysilane high polymers," Chem. Rev. (Washington, D.C.) 89, 1359-1410 (1989).

1985

1980

1976

1975

M. Ikeda, M. Tateda, and H. Yoshikiyo, "Refractive index profile of a graded index fiber: measurement by a reflection method," Appl. Opt. 4, 814-815 (1975).
[CrossRef]

1973

1969

E. A. J. Marcatili, "Dielectric rectangular waveguide and directional coupler for integrated optics," Bell Syst. Tech. J. 48, 2071-2102 (1969).

Asada, K.

T. Yamamoto, S. Takahashi, T. Kaino, Y. Koike, K. Nakamura, M. Eto, T. Yamashita, A. Tanaka, H. Kobayashi, S. Taneichi, M. Nishiguchi, Y. Takezawa, S. Toyoshima, K. Naito, M. Ishiharada, S. Muto, N. Sakura, K. Kohayoshi, F. Miyasaka, H. Matagi, M. Kyozo, H. Yuuki, K. Asada, S. Takagi, K. Nakamura, T. Yamasaki, K. Senga, and S. Okamoto,Plastic Optical Fiber (Kyoritu, 1997).

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G. L. Tangonan, O. G. Ramer, H. R. Friedrich, C. K. Asawa, D. L. Persechini, and L. E. Gorre, "Planar multimode devices for fiber optics," in Proceedings of Fifth European Conference on Optical Communication ( ECOC, 1979), pp. 21.5-1.

Bachmann, M.

Beltrami, D. R.

D. R. Beltrami, J. D. Love, A. Durandet, A. Samoc, M. Samoc, B. Luther-Davies, and R. W. Boswell, "Planar graded-index (GRIN) PECVD lens," Electron. Lett. 32, 549-550 (1996).
[CrossRef]

Besse, P. A.

Boswell, R. W.

D. R. Beltrami, J. D. Love, A. Durandet, A. Samoc, M. Samoc, B. Luther-Davies, and R. W. Boswell, "Planar graded-index (GRIN) PECVD lens," Electron. Lett. 32, 549-550 (1996).
[CrossRef]

Bryngdahl, O.

Burke, J. J.

N. S. Kapany and J. J. Burke, Optical Waveguides (Academic, 1972).

Chartier, G.

Collier, P.

Deveraux, R. W.

Durandet, A.

D. R. Beltrami, J. D. Love, A. Durandet, A. Samoc, M. Samoc, B. Luther-Davies, and R. W. Boswell, "Planar graded-index (GRIN) PECVD lens," Electron. Lett. 32, 549-550 (1996).
[CrossRef]

Eto, M.

T. Yamamoto, S. Takahashi, T. Kaino, Y. Koike, K. Nakamura, M. Eto, T. Yamashita, A. Tanaka, H. Kobayashi, S. Taneichi, M. Nishiguchi, Y. Takezawa, S. Toyoshima, K. Naito, M. Ishiharada, S. Muto, N. Sakura, K. Kohayoshi, F. Miyasaka, H. Matagi, M. Kyozo, H. Yuuki, K. Asada, S. Takagi, K. Nakamura, T. Yamasaki, K. Senga, and S. Okamoto,Plastic Optical Fiber (Kyoritu, 1997).

Friedrich, H. R.

G. L. Tangonan, O. G. Ramer, H. R. Friedrich, C. K. Asawa, D. L. Persechini, and L. E. Gorre, "Planar multimode devices for fiber optics," in Proceedings of Fifth European Conference on Optical Communication ( ECOC, 1979), pp. 21.5-1.

Gorre, L. E.

G. L. Tangonan, O. G. Ramer, H. R. Friedrich, C. K. Asawa, D. L. Persechini, and L. E. Gorre, "Planar multimode devices for fiber optics," in Proceedings of Fifth European Conference on Optical Communication ( ECOC, 1979), pp. 21.5-1.

Guez, A.

Heaton, J. M.

Ikeda, M.

M. Ikeda, M. Tateda, and H. Yoshikiyo, "Refractive index profile of a graded index fiber: measurement by a reflection method," Appl. Opt. 4, 814-815 (1975).
[CrossRef]

Imoto, K.

K. Imoto, H. Tsushima, and E. Watanabe, "Photo-bleaching type waveguide and its fabrication method," Annual Meeting of IEICE of Japan (Institute of Electronics, Information, and Communications Engineers, 2002), p. 519.

Ishigure, T.

Ishiharada, M.

T. Yamamoto, S. Takahashi, T. Kaino, Y. Koike, K. Nakamura, M. Eto, T. Yamashita, A. Tanaka, H. Kobayashi, S. Taneichi, M. Nishiguchi, Y. Takezawa, S. Toyoshima, K. Naito, M. Ishiharada, S. Muto, N. Sakura, K. Kohayoshi, F. Miyasaka, H. Matagi, M. Kyozo, H. Yuuki, K. Asada, S. Takagi, K. Nakamura, T. Yamasaki, K. Senga, and S. Okamoto,Plastic Optical Fiber (Kyoritu, 1997).

Jaussaud, P.

Jenkins, R. M.

Kaino, T.

T. Yamamoto, S. Takahashi, T. Kaino, Y. Koike, K. Nakamura, M. Eto, T. Yamashita, A. Tanaka, H. Kobayashi, S. Taneichi, M. Nishiguchi, Y. Takezawa, S. Toyoshima, K. Naito, M. Ishiharada, S. Muto, N. Sakura, K. Kohayoshi, F. Miyasaka, H. Matagi, M. Kyozo, H. Yuuki, K. Asada, S. Takagi, K. Nakamura, T. Yamasaki, K. Senga, and S. Okamoto,Plastic Optical Fiber (Kyoritu, 1997).

Kapany, N. S.

N. S. Kapany and J. J. Burke, Optical Waveguides (Academic, 1972).

Kawakami, S.

S. Kawakami, Optical Waveguide (Asakura, 1978).

Kawano, K.

K. Kawano, Basis and Application of Optic Systems for Optical Devices (Gendaikougakusha, 1991).

Kobayash, H.

T. Yamamoto, S. Takahashi, T. Kaino, Y. Koike, K. Nakamura, M. Eto, T. Yamashita, A. Tanaka, H. Kobayashi, S. Taneichi, M. Nishiguchi, Y. Takezawa, S. Toyoshima, K. Naito, M. Ishiharada, S. Muto, N. Sakura, K. Kohayoshi, F. Miyasaka, H. Matagi, M. Kyozo, H. Yuuki, K. Asada, S. Takagi, K. Nakamura, T. Yamasaki, K. Senga, and S. Okamoto,Plastic Optical Fiber (Kyoritu, 1997).

Kohayoshi, K.

T. Yamamoto, S. Takahashi, T. Kaino, Y. Koike, K. Nakamura, M. Eto, T. Yamashita, A. Tanaka, H. Kobayashi, S. Taneichi, M. Nishiguchi, Y. Takezawa, S. Toyoshima, K. Naito, M. Ishiharada, S. Muto, N. Sakura, K. Kohayoshi, F. Miyasaka, H. Matagi, M. Kyozo, H. Yuuki, K. Asada, S. Takagi, K. Nakamura, T. Yamasaki, K. Senga, and S. Okamoto,Plastic Optical Fiber (Kyoritu, 1997).

Koike, Y.

T. Ishigure, E. Nihei, and Y. Koike, "Graded-index polymer optical fiber for high-speed data communication," Appl. Opt. 33, 4261-4266 (1994).
[CrossRef] [PubMed]

Y. Ohtsuka and Y. Koike, "Studies on the light-focusing plastic rod. 18: Control of refractive-index distribution of plastic radial gradient-index rod by photocopolymerization," Appl. Opt. 24, 4316-4320 (1985).
[CrossRef] [PubMed]

T. Yamamoto, S. Takahashi, T. Kaino, Y. Koike, K. Nakamura, M. Eto, T. Yamashita, A. Tanaka, H. Kobayashi, S. Taneichi, M. Nishiguchi, Y. Takezawa, S. Toyoshima, K. Naito, M. Ishiharada, S. Muto, N. Sakura, K. Kohayoshi, F. Miyasaka, H. Matagi, M. Kyozo, H. Yuuki, K. Asada, S. Takagi, K. Nakamura, T. Yamasaki, K. Senga, and S. Okamoto,Plastic Optical Fiber (Kyoritu, 1997).

Kyozo, M.

T. Yamamoto, S. Takahashi, T. Kaino, Y. Koike, K. Nakamura, M. Eto, T. Yamashita, A. Tanaka, H. Kobayashi, S. Taneichi, M. Nishiguchi, Y. Takezawa, S. Toyoshima, K. Naito, M. Ishiharada, S. Muto, N. Sakura, K. Kohayoshi, F. Miyasaka, H. Matagi, M. Kyozo, H. Yuuki, K. Asada, S. Takagi, K. Nakamura, T. Yamasaki, K. Senga, and S. Okamoto,Plastic Optical Fiber (Kyoritu, 1997).

Laakmann, K. D.

Love, J. D.

D. R. Beltrami, J. D. Love, A. Durandet, A. Samoc, M. Samoc, B. Luther-Davies, and R. W. Boswell, "Planar graded-index (GRIN) PECVD lens," Electron. Lett. 32, 549-550 (1996).
[CrossRef]

Luther-Davies, B.

D. R. Beltrami, J. D. Love, A. Durandet, A. Samoc, M. Samoc, B. Luther-Davies, and R. W. Boswell, "Planar graded-index (GRIN) PECVD lens," Electron. Lett. 32, 549-550 (1996).
[CrossRef]

Marcatili, E. A. J.

E. A. J. Marcatili, "Dielectric rectangular waveguide and directional coupler for integrated optics," Bell Syst. Tech. J. 48, 2071-2102 (1969).

Matagi, H.

T. Yamamoto, S. Takahashi, T. Kaino, Y. Koike, K. Nakamura, M. Eto, T. Yamashita, A. Tanaka, H. Kobayashi, S. Taneichi, M. Nishiguchi, Y. Takezawa, S. Toyoshima, K. Naito, M. Ishiharada, S. Muto, N. Sakura, K. Kohayoshi, F. Miyasaka, H. Matagi, M. Kyozo, H. Yuuki, K. Asada, S. Takagi, K. Nakamura, T. Yamasaki, K. Senga, and S. Okamoto,Plastic Optical Fiber (Kyoritu, 1997).

Melchior, H.

Michel, J.

R. D. Miller and J. Michel, "Polysilane high polymers," Chem. Rev. (Washington, D.C.) 89, 1359-1410 (1989).

Miller, R. D.

R. D. Miller and J. Michel, "Polysilane high polymers," Chem. Rev. (Washington, D.C.) 89, 1359-1410 (1989).

Miyasaka, F.

T. Yamamoto, S. Takahashi, T. Kaino, Y. Koike, K. Nakamura, M. Eto, T. Yamashita, A. Tanaka, H. Kobayashi, S. Taneichi, M. Nishiguchi, Y. Takezawa, S. Toyoshima, K. Naito, M. Ishiharada, S. Muto, N. Sakura, K. Kohayoshi, F. Miyasaka, H. Matagi, M. Kyozo, H. Yuuki, K. Asada, S. Takagi, K. Nakamura, T. Yamasaki, K. Senga, and S. Okamoto,Plastic Optical Fiber (Kyoritu, 1997).

Muto, S.

T. Yamamoto, S. Takahashi, T. Kaino, Y. Koike, K. Nakamura, M. Eto, T. Yamashita, A. Tanaka, H. Kobayashi, S. Taneichi, M. Nishiguchi, Y. Takezawa, S. Toyoshima, K. Naito, M. Ishiharada, S. Muto, N. Sakura, K. Kohayoshi, F. Miyasaka, H. Matagi, M. Kyozo, H. Yuuki, K. Asada, S. Takagi, K. Nakamura, T. Yamasaki, K. Senga, and S. Okamoto,Plastic Optical Fiber (Kyoritu, 1997).

Naito, K.

T. Yamamoto, S. Takahashi, T. Kaino, Y. Koike, K. Nakamura, M. Eto, T. Yamashita, A. Tanaka, H. Kobayashi, S. Taneichi, M. Nishiguchi, Y. Takezawa, S. Toyoshima, K. Naito, M. Ishiharada, S. Muto, N. Sakura, K. Kohayoshi, F. Miyasaka, H. Matagi, M. Kyozo, H. Yuuki, K. Asada, S. Takagi, K. Nakamura, T. Yamasaki, K. Senga, and S. Okamoto,Plastic Optical Fiber (Kyoritu, 1997).

Nakamura, K.

T. Yamamoto, S. Takahashi, T. Kaino, Y. Koike, K. Nakamura, M. Eto, T. Yamashita, A. Tanaka, H. Kobayashi, S. Taneichi, M. Nishiguchi, Y. Takezawa, S. Toyoshima, K. Naito, M. Ishiharada, S. Muto, N. Sakura, K. Kohayoshi, F. Miyasaka, H. Matagi, M. Kyozo, H. Yuuki, K. Asada, S. Takagi, K. Nakamura, T. Yamasaki, K. Senga, and S. Okamoto,Plastic Optical Fiber (Kyoritu, 1997).

T. Yamamoto, S. Takahashi, T. Kaino, Y. Koike, K. Nakamura, M. Eto, T. Yamashita, A. Tanaka, H. Kobayashi, S. Taneichi, M. Nishiguchi, Y. Takezawa, S. Toyoshima, K. Naito, M. Ishiharada, S. Muto, N. Sakura, K. Kohayoshi, F. Miyasaka, H. Matagi, M. Kyozo, H. Yuuki, K. Asada, S. Takagi, K. Nakamura, T. Yamasaki, K. Senga, and S. Okamoto,Plastic Optical Fiber (Kyoritu, 1997).

Nihei, E.

Nishiguchi, M.

T. Yamamoto, S. Takahashi, T. Kaino, Y. Koike, K. Nakamura, M. Eto, T. Yamashita, A. Tanaka, H. Kobayashi, S. Taneichi, M. Nishiguchi, Y. Takezawa, S. Toyoshima, K. Naito, M. Ishiharada, S. Muto, N. Sakura, K. Kohayoshi, F. Miyasaka, H. Matagi, M. Kyozo, H. Yuuki, K. Asada, S. Takagi, K. Nakamura, T. Yamasaki, K. Senga, and S. Okamoto,Plastic Optical Fiber (Kyoritu, 1997).

Nosu, K.

K. Nosu and R. Watanabe, "Slab waveguide star coupler for multimode optical fibers," Electron. Lett. 16, 608-609 (1980).
[CrossRef]

Ohtsuka, Y.

Okamoto, S.

T. Yamamoto, S. Takahashi, T. Kaino, Y. Koike, K. Nakamura, M. Eto, T. Yamashita, A. Tanaka, H. Kobayashi, S. Taneichi, M. Nishiguchi, Y. Takezawa, S. Toyoshima, K. Naito, M. Ishiharada, S. Muto, N. Sakura, K. Kohayoshi, F. Miyasaka, H. Matagi, M. Kyozo, H. Yuuki, K. Asada, S. Takagi, K. Nakamura, T. Yamasaki, K. Senga, and S. Okamoto,Plastic Optical Fiber (Kyoritu, 1997).

Pennings, E. C. M.

L. B. Soldano and E. C. M. Pennings, "Optical multi-mode interference devices based on self-imaging: principles and applications," J. Lightwave Technol. 13, 615-627 (1995).
[CrossRef]

Persechini, D. L.

G. L. Tangonan, O. G. Ramer, H. R. Friedrich, C. K. Asawa, D. L. Persechini, and L. E. Gorre, "Planar multimode devices for fiber optics," in Proceedings of Fifth European Conference on Optical Communication ( ECOC, 1979), pp. 21.5-1.

Ramer, O. G.

G. L. Tangonan, O. G. Ramer, H. R. Friedrich, C. K. Asawa, D. L. Persechini, and L. E. Gorre, "Planar multimode devices for fiber optics," in Proceedings of Fifth European Conference on Optical Communication ( ECOC, 1979), pp. 21.5-1.

Sakura, N.

T. Yamamoto, S. Takahashi, T. Kaino, Y. Koike, K. Nakamura, M. Eto, T. Yamashita, A. Tanaka, H. Kobayashi, S. Taneichi, M. Nishiguchi, Y. Takezawa, S. Toyoshima, K. Naito, M. Ishiharada, S. Muto, N. Sakura, K. Kohayoshi, F. Miyasaka, H. Matagi, M. Kyozo, H. Yuuki, K. Asada, S. Takagi, K. Nakamura, T. Yamasaki, K. Senga, and S. Okamoto,Plastic Optical Fiber (Kyoritu, 1997).

Samoc, A.

D. R. Beltrami, J. D. Love, A. Durandet, A. Samoc, M. Samoc, B. Luther-Davies, and R. W. Boswell, "Planar graded-index (GRIN) PECVD lens," Electron. Lett. 32, 549-550 (1996).
[CrossRef]

Samoc, M.

D. R. Beltrami, J. D. Love, A. Durandet, A. Samoc, M. Samoc, B. Luther-Davies, and R. W. Boswell, "Planar graded-index (GRIN) PECVD lens," Electron. Lett. 32, 549-550 (1996).
[CrossRef]

Senga, K.

T. Yamamoto, S. Takahashi, T. Kaino, Y. Koike, K. Nakamura, M. Eto, T. Yamashita, A. Tanaka, H. Kobayashi, S. Taneichi, M. Nishiguchi, Y. Takezawa, S. Toyoshima, K. Naito, M. Ishiharada, S. Muto, N. Sakura, K. Kohayoshi, F. Miyasaka, H. Matagi, M. Kyozo, H. Yuuki, K. Asada, S. Takagi, K. Nakamura, T. Yamasaki, K. Senga, and S. Okamoto,Plastic Optical Fiber (Kyoritu, 1997).

Soldano, L. B.

L. B. Soldano and E. C. M. Pennings, "Optical multi-mode interference devices based on self-imaging: principles and applications," J. Lightwave Technol. 13, 615-627 (1995).
[CrossRef]

Steier, W. H.

Takagi, S.

T. Yamamoto, S. Takahashi, T. Kaino, Y. Koike, K. Nakamura, M. Eto, T. Yamashita, A. Tanaka, H. Kobayashi, S. Taneichi, M. Nishiguchi, Y. Takezawa, S. Toyoshima, K. Naito, M. Ishiharada, S. Muto, N. Sakura, K. Kohayoshi, F. Miyasaka, H. Matagi, M. Kyozo, H. Yuuki, K. Asada, S. Takagi, K. Nakamura, T. Yamasaki, K. Senga, and S. Okamoto,Plastic Optical Fiber (Kyoritu, 1997).

Takahashi, S.

T. Yamamoto, S. Takahashi, T. Kaino, Y. Koike, K. Nakamura, M. Eto, T. Yamashita, A. Tanaka, H. Kobayashi, S. Taneichi, M. Nishiguchi, Y. Takezawa, S. Toyoshima, K. Naito, M. Ishiharada, S. Muto, N. Sakura, K. Kohayoshi, F. Miyasaka, H. Matagi, M. Kyozo, H. Yuuki, K. Asada, S. Takagi, K. Nakamura, T. Yamasaki, K. Senga, and S. Okamoto,Plastic Optical Fiber (Kyoritu, 1997).

Takezawa, Y.

T. Yamamoto, S. Takahashi, T. Kaino, Y. Koike, K. Nakamura, M. Eto, T. Yamashita, A. Tanaka, H. Kobayashi, S. Taneichi, M. Nishiguchi, Y. Takezawa, S. Toyoshima, K. Naito, M. Ishiharada, S. Muto, N. Sakura, K. Kohayoshi, F. Miyasaka, H. Matagi, M. Kyozo, H. Yuuki, K. Asada, S. Takagi, K. Nakamura, T. Yamasaki, K. Senga, and S. Okamoto,Plastic Optical Fiber (Kyoritu, 1997).

Tanaka, A.

T. Yamamoto, S. Takahashi, T. Kaino, Y. Koike, K. Nakamura, M. Eto, T. Yamashita, A. Tanaka, H. Kobayashi, S. Taneichi, M. Nishiguchi, Y. Takezawa, S. Toyoshima, K. Naito, M. Ishiharada, S. Muto, N. Sakura, K. Kohayoshi, F. Miyasaka, H. Matagi, M. Kyozo, H. Yuuki, K. Asada, S. Takagi, K. Nakamura, T. Yamasaki, K. Senga, and S. Okamoto,Plastic Optical Fiber (Kyoritu, 1997).

Taneichi, S.

T. Yamamoto, S. Takahashi, T. Kaino, Y. Koike, K. Nakamura, M. Eto, T. Yamashita, A. Tanaka, H. Kobayashi, S. Taneichi, M. Nishiguchi, Y. Takezawa, S. Toyoshima, K. Naito, M. Ishiharada, S. Muto, N. Sakura, K. Kohayoshi, F. Miyasaka, H. Matagi, M. Kyozo, H. Yuuki, K. Asada, S. Takagi, K. Nakamura, T. Yamasaki, K. Senga, and S. Okamoto,Plastic Optical Fiber (Kyoritu, 1997).

Tangonan, G. L.

G. L. Tangonan, O. G. Ramer, H. R. Friedrich, C. K. Asawa, D. L. Persechini, and L. E. Gorre, "Planar multimode devices for fiber optics," in Proceedings of Fifth European Conference on Optical Communication ( ECOC, 1979), pp. 21.5-1.

Tateda, M.

M. Ikeda, M. Tateda, and H. Yoshikiyo, "Refractive index profile of a graded index fiber: measurement by a reflection method," Appl. Opt. 4, 814-815 (1975).
[CrossRef]

Toyoshima, S.

T. Yamamoto, S. Takahashi, T. Kaino, Y. Koike, K. Nakamura, M. Eto, T. Yamashita, A. Tanaka, H. Kobayashi, S. Taneichi, M. Nishiguchi, Y. Takezawa, S. Toyoshima, K. Naito, M. Ishiharada, S. Muto, N. Sakura, K. Kohayoshi, F. Miyasaka, H. Matagi, M. Kyozo, H. Yuuki, K. Asada, S. Takagi, K. Nakamura, T. Yamasaki, K. Senga, and S. Okamoto,Plastic Optical Fiber (Kyoritu, 1997).

Tsushima, H.

K. Imoto, H. Tsushima, and E. Watanabe, "Photo-bleaching type waveguide and its fabrication method," Annual Meeting of IEICE of Japan (Institute of Electronics, Information, and Communications Engineers, 2002), p. 519.

Watanabe, E.

K. Imoto, H. Tsushima, and E. Watanabe, "Photo-bleaching type waveguide and its fabrication method," Annual Meeting of IEICE of Japan (Institute of Electronics, Information, and Communications Engineers, 2002), p. 519.

Watanabe, R.

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Yamasaki, T.

T. Yamamoto, S. Takahashi, T. Kaino, Y. Koike, K. Nakamura, M. Eto, T. Yamashita, A. Tanaka, H. Kobayashi, S. Taneichi, M. Nishiguchi, Y. Takezawa, S. Toyoshima, K. Naito, M. Ishiharada, S. Muto, N. Sakura, K. Kohayoshi, F. Miyasaka, H. Matagi, M. Kyozo, H. Yuuki, K. Asada, S. Takagi, K. Nakamura, T. Yamasaki, K. Senga, and S. Okamoto,Plastic Optical Fiber (Kyoritu, 1997).

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Figures (9)

Fig. 1
Fig. 1

Mechanism of photodecomposition providing large refractive index change of polysilane.

Fig. 2
Fig. 2

Cross section of an analytical rectangular WG model with vertical GI and horizontal SI profiles covered by cladding and coordinates. (a) and (b) A vertical GI slab and a horizontal SI slab indicating components of the field in a GI MMI, which has solutions depending only on x and z and solutions depending only on y and z with separable form. A darker color indicates a higher index.

Fig. 3
Fig. 3

Three-dimensional BPM simulation model of a MM WG based on GI MMI and a vertical index profile using polysilane with photobleaching properties. A darker color indicates a higher index.

Fig. 4
Fig. 4

X Z -sliced propagation fields at the vertical center (bottom part) and X Y -sliced fields at comparably selected propagation distances (0, 2000, 10,000, 15,000, 19,000, 25,000, 30,000, 37,000, 39,000 μ m ) (upper part) inside the MM WGs based on (a) SI MMI and (b) GI MMI in the case of a symmetrical single input from GI50 fiber, calculated by 3D BPM. A darker color indicates a higher light intensity.

Fig. 5
Fig. 5

(a) Δ (circles) versus total insertion loss on connecting with the output GI50 slab and (b) Δ (circles) versus total insertion loss on connecting with the output GI50 fiber. Δ 0 is 0.0240 in the case of GI50 fiber; Δ p is Δ of the GI slab fabricated with the present successful photobleaching conditions, 0.0456; and Δ c is 0.0869 in the case of the GI slab on a glass substrate.

Fig. 6
Fig. 6

Fabrication process of the GI slab using polysilane with photobleaching properties. A darker color indicates a higher index.

Fig. 7
Fig. 7

Schematic of a technique for evaluating the features of a planar two-way MM splitter based on the GI MMI profiling measurement. Two images are input and output field profiles when a planar two-way MM splitter works. SMF, single-mode fiber; PC, personal computer.

Fig. 8
Fig. 8

Normalized refractive index profiles by the vertical center for (a) a GI slab and (b) a SI slab (three layers) using polysilane with photobleaching properties. Dotted curves indicate an approximating quadratic curve. Transmitted field images of white light are shown as well.

Fig. 9
Fig. 9

Normalized output field profiles (solid curve) measured with a CCD camera along the transverse coordinate through two peaks at 37,000 μ m propagating distance, in which normalized output field profiles (dashed curve) is calculated with 3D BPM.

Tables (3)

Tables Icon

Table 1 Length of Planar N-Way MM Splitter Based on GI MMI

Tables Icon

Table 2 Physical Behavior of GI50 Fiber and GI Rectangular Waveguide

Tables Icon

Table 3 Optimal Length of Planar Two-Way MM Splitter Based on GI MMI by Using Analytical Results

Equations (16)

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n ( x , y ) 2 = n 0 2 ( 1 g 2 y 2 ) ; b x b , a y a ,
E p q x ( x , y , z , t ) = E cos ( k p x + φ x ) H q ( ξ + φ y ) π 1 2 2 q q ! exp [ ( ξ + φ y ) 2 2 ] exp [ j ( β p q z ω t ) ] ,
k x p 2 + k y q 2 + β p q 2 = n 2 k 0 2 ,
k x p = ( p + 1 ) π W x p ,
k y q 2 = n 2 k 0 2 [ n 0 2 k 0 2 ( 2 q + 1 ) n 0 k 0 g ] ,
W x p W x 0 2 b + λ 0 π 1 [ n 0 2 ( 1 g 2 y 2 ) n c 2 ] 1 2 [ n c n 0 ( 1 g 2 y 2 ) 1 2 ] 2 σ ,
β p q n 0 k 0 ( p + 1 ) 2 π 2 2 n 0 k 0 W x 0 2 ( 2 q + 1 ) g 2 .
Ψ ( x , y , z , t ) = p , q = 0 n 1 c p q ψ p ( x ) ϕ q ( y ) exp [ j ( ω t β 00 z ) ] exp [ j ( β 00 β p q ) z ] ,
c p q = Ψ ( x , y , z , t ) ψ p ( x ) ϕ q ( y ) d n d y [ ψ p ( x ) 2 ϕ q ( y ) 2 d x d y ] 1 2 ,
exp [ j ( β 00 β p q ) z ] = exp { j [ π 2 p ( p + 2 ) 2 n 0 k 0 W x 0 2 + q g ] z } .
[ π 2 p ( p + 2 ) 2 n 0 k 0 W x 0 2 + q g ] L 1 = m π ,
Ψ ( x , y , z , t ) = ( 1 ) m exp ( j β 00 z ) Ψ ( x , y , 0 , t ) .
L 1 = m x 2 n 0 k 0 W x 0 2 π = m y π g ,
L 1 = m x 2 n 0 k 0 W x 0 2 π .
n 0 ( 2 Δ ) 1 2 = sin θ 0 c sin θ i = n i ( 2 Δ i ) 1 2 ,
Δ n i 2 n 0 2 Δ i = Δ 0 ,

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