Abstract

Significant efforts are being made to increase optical network capacity in response to ever-growing data traffic. One promising candidate is mode-division multiplexing (MDM) in few-mode fibers. A fundamental element for MDM is a modal transformer. Modal transformation can be implemented in a free-space basis by using multiregion phase plates. In this work, we show that efficient monolithic binary phase plates can be fabricated by ion exchange in glass and used for MDM tasks. We present an optical characterization method of such plates, which is based on a combination of the inverse Wentzel–Kramers–Brillouin (IWKB) method and Mach–Zehnder interferometric techniques. The IWKB method allows us to design and characterize the phase plates in an easy and fast way, whereas interferometry gives us a precise measurement of the phase step. Far-field optical intensities are measured, and a high-quality mode transformation is confirmed.

© 2013 Optical Society of America

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References

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  1. D. Qian, M. F. Huang, E. Ip, Y. K. Huang, Y. Shao, J. Hu, and T. Wang, “101.7  Tb/s (370−294  Gb/s) PDM-128QAM-OFDM transmission over 3–55 km SSMF using pilot-based phase noise mitigation,” in Proceedings of Optical Fiber Communication Conference and Exposition (OFC/NFOEC), 2011, and the National Fiber Optic Engineers Conference (IEEE, 2011), paper PDPB5.
  2. A. Li, A. A. Amin, X. Chen, and W. Shieh, “Transmission of 107  Gb/s mode and polarization multiplexed CO-OFDM signal over a two-mode fiber,” Opt. Express 19, 8808–8814 (2011).
    [CrossRef]
  3. E. Ip, N. Bai, Y. Huang, E. Mateo, F. Yaman, M. Li, S. Bickham, S. Ten, S. J. Liñares, C. Montero, V. Moreno, X. Prieto, V. Tse, K. M. Chung, A. Lau, H. Tam, C. Lu, Y. Luo, G. Peng, and G. Li, “88×3×112  Gb/s WDM transmission over 50 km of three-mode fiber with inline few-mode fiber amplifier,” in European Conference and Exhibition on Optical Communication (ECOC), OSA Technical Digest (CD) (Optical Society of America, 2011), paper Th.13.C.2.
  4. S. Randel, R. Ryf, A. Sierra, P. J. Winzer, A. H. Gnauck, C. A. Bolle, R. Essiambre, D. W. Peckham, A. McCurdy, and R. Lingle, “6×56  Gb/s mode-division multiplexed transmission over 33 km few-mode fiber enabled by 6×6 mimo equalization,” Opt. Express 19, 16697–16707 (2011).
    [CrossRef]
  5. J. Liñares, C. Montero, and X. Prieto, “Graded-index bifocal spectacle lenses produced by ion-exchange in glass: paraxial designing,” Pure Appl. Opt. 4, 695–699 (1995).
    [CrossRef]
  6. S. I. Najafi, ed., Introduction to Glass Integrated Optics(Artech House, 1992).
  7. J. Liñares, C. Montero, V. Moreno, M. C. Nistal, X. Prieto, J. R. Salgueiro, and D. Sotelo, “Glass processing by ion exchange to fabricate integrated optical planar components: applications,” Proc. SPIE 3936, 227–238 (2000).
    [CrossRef]
  8. D. J. Butler, S. Hippler, S. Egner, W. Xu, and J. Bähr, “Broadband, static wave-front generation: Na-Ag ion-exchange phase screens and telescope emulation,” Appl. Opt. 43, 2813–2823 (2004).
    [CrossRef]
  9. D. L. Lee, Electromagnetic Principles of Integrated Optics(Wiley, 1986).
  10. J. Liñares, X. Prieto, and C. Montero, “A novel refractive index profile for optical characterization of nonlinear diffusion processes and planar waveguides in glass,” Opt. Materials 3, 229–236 (1994).
    [CrossRef]
  11. X. Prieto and J. Liñares, “An approximated solution for the non-linear diffusion equation for planar waveguides: a new refractive-index profile,” in 10th Topical Meeting on Gradient-Index Optical Systems, OSA Technical Digest (University Publishers, 1992), paper PD9.T6.
  12. V. Moreno, S. Bara, M. V. Perez, C. Gomez-Reino, and J. H. Garcia, “Tilting and shearing determination in the alignment of a Mach–Zehnder interferometer by zone plates,” Opt. Laser Technol. 20, 89–94 (1988).
    [CrossRef]
  13. T. Kreiss, Handbook of Holographic Interferometry (Wiley-VCH, 2005).

2011 (2)

2004 (1)

2000 (1)

J. Liñares, C. Montero, V. Moreno, M. C. Nistal, X. Prieto, J. R. Salgueiro, and D. Sotelo, “Glass processing by ion exchange to fabricate integrated optical planar components: applications,” Proc. SPIE 3936, 227–238 (2000).
[CrossRef]

1995 (1)

J. Liñares, C. Montero, and X. Prieto, “Graded-index bifocal spectacle lenses produced by ion-exchange in glass: paraxial designing,” Pure Appl. Opt. 4, 695–699 (1995).
[CrossRef]

1994 (1)

J. Liñares, X. Prieto, and C. Montero, “A novel refractive index profile for optical characterization of nonlinear diffusion processes and planar waveguides in glass,” Opt. Materials 3, 229–236 (1994).
[CrossRef]

1988 (1)

V. Moreno, S. Bara, M. V. Perez, C. Gomez-Reino, and J. H. Garcia, “Tilting and shearing determination in the alignment of a Mach–Zehnder interferometer by zone plates,” Opt. Laser Technol. 20, 89–94 (1988).
[CrossRef]

Amin, A. A.

Bähr, J.

Bai, N.

E. Ip, N. Bai, Y. Huang, E. Mateo, F. Yaman, M. Li, S. Bickham, S. Ten, S. J. Liñares, C. Montero, V. Moreno, X. Prieto, V. Tse, K. M. Chung, A. Lau, H. Tam, C. Lu, Y. Luo, G. Peng, and G. Li, “88×3×112  Gb/s WDM transmission over 50 km of three-mode fiber with inline few-mode fiber amplifier,” in European Conference and Exhibition on Optical Communication (ECOC), OSA Technical Digest (CD) (Optical Society of America, 2011), paper Th.13.C.2.

Bara, S.

V. Moreno, S. Bara, M. V. Perez, C. Gomez-Reino, and J. H. Garcia, “Tilting and shearing determination in the alignment of a Mach–Zehnder interferometer by zone plates,” Opt. Laser Technol. 20, 89–94 (1988).
[CrossRef]

Bickham, S.

E. Ip, N. Bai, Y. Huang, E. Mateo, F. Yaman, M. Li, S. Bickham, S. Ten, S. J. Liñares, C. Montero, V. Moreno, X. Prieto, V. Tse, K. M. Chung, A. Lau, H. Tam, C. Lu, Y. Luo, G. Peng, and G. Li, “88×3×112  Gb/s WDM transmission over 50 km of three-mode fiber with inline few-mode fiber amplifier,” in European Conference and Exhibition on Optical Communication (ECOC), OSA Technical Digest (CD) (Optical Society of America, 2011), paper Th.13.C.2.

Bolle, C. A.

Butler, D. J.

Chen, X.

Chung, K. M.

E. Ip, N. Bai, Y. Huang, E. Mateo, F. Yaman, M. Li, S. Bickham, S. Ten, S. J. Liñares, C. Montero, V. Moreno, X. Prieto, V. Tse, K. M. Chung, A. Lau, H. Tam, C. Lu, Y. Luo, G. Peng, and G. Li, “88×3×112  Gb/s WDM transmission over 50 km of three-mode fiber with inline few-mode fiber amplifier,” in European Conference and Exhibition on Optical Communication (ECOC), OSA Technical Digest (CD) (Optical Society of America, 2011), paper Th.13.C.2.

Egner, S.

Essiambre, R.

Garcia, J. H.

V. Moreno, S. Bara, M. V. Perez, C. Gomez-Reino, and J. H. Garcia, “Tilting and shearing determination in the alignment of a Mach–Zehnder interferometer by zone plates,” Opt. Laser Technol. 20, 89–94 (1988).
[CrossRef]

Gnauck, A. H.

Gomez-Reino, C.

V. Moreno, S. Bara, M. V. Perez, C. Gomez-Reino, and J. H. Garcia, “Tilting and shearing determination in the alignment of a Mach–Zehnder interferometer by zone plates,” Opt. Laser Technol. 20, 89–94 (1988).
[CrossRef]

Hippler, S.

Hu, J.

D. Qian, M. F. Huang, E. Ip, Y. K. Huang, Y. Shao, J. Hu, and T. Wang, “101.7  Tb/s (370−294  Gb/s) PDM-128QAM-OFDM transmission over 3–55 km SSMF using pilot-based phase noise mitigation,” in Proceedings of Optical Fiber Communication Conference and Exposition (OFC/NFOEC), 2011, and the National Fiber Optic Engineers Conference (IEEE, 2011), paper PDPB5.

Huang, M. F.

D. Qian, M. F. Huang, E. Ip, Y. K. Huang, Y. Shao, J. Hu, and T. Wang, “101.7  Tb/s (370−294  Gb/s) PDM-128QAM-OFDM transmission over 3–55 km SSMF using pilot-based phase noise mitigation,” in Proceedings of Optical Fiber Communication Conference and Exposition (OFC/NFOEC), 2011, and the National Fiber Optic Engineers Conference (IEEE, 2011), paper PDPB5.

Huang, Y.

E. Ip, N. Bai, Y. Huang, E. Mateo, F. Yaman, M. Li, S. Bickham, S. Ten, S. J. Liñares, C. Montero, V. Moreno, X. Prieto, V. Tse, K. M. Chung, A. Lau, H. Tam, C. Lu, Y. Luo, G. Peng, and G. Li, “88×3×112  Gb/s WDM transmission over 50 km of three-mode fiber with inline few-mode fiber amplifier,” in European Conference and Exhibition on Optical Communication (ECOC), OSA Technical Digest (CD) (Optical Society of America, 2011), paper Th.13.C.2.

Huang, Y. K.

D. Qian, M. F. Huang, E. Ip, Y. K. Huang, Y. Shao, J. Hu, and T. Wang, “101.7  Tb/s (370−294  Gb/s) PDM-128QAM-OFDM transmission over 3–55 km SSMF using pilot-based phase noise mitigation,” in Proceedings of Optical Fiber Communication Conference and Exposition (OFC/NFOEC), 2011, and the National Fiber Optic Engineers Conference (IEEE, 2011), paper PDPB5.

Ip, E.

D. Qian, M. F. Huang, E. Ip, Y. K. Huang, Y. Shao, J. Hu, and T. Wang, “101.7  Tb/s (370−294  Gb/s) PDM-128QAM-OFDM transmission over 3–55 km SSMF using pilot-based phase noise mitigation,” in Proceedings of Optical Fiber Communication Conference and Exposition (OFC/NFOEC), 2011, and the National Fiber Optic Engineers Conference (IEEE, 2011), paper PDPB5.

E. Ip, N. Bai, Y. Huang, E. Mateo, F. Yaman, M. Li, S. Bickham, S. Ten, S. J. Liñares, C. Montero, V. Moreno, X. Prieto, V. Tse, K. M. Chung, A. Lau, H. Tam, C. Lu, Y. Luo, G. Peng, and G. Li, “88×3×112  Gb/s WDM transmission over 50 km of three-mode fiber with inline few-mode fiber amplifier,” in European Conference and Exhibition on Optical Communication (ECOC), OSA Technical Digest (CD) (Optical Society of America, 2011), paper Th.13.C.2.

Kreiss, T.

T. Kreiss, Handbook of Holographic Interferometry (Wiley-VCH, 2005).

Lau, A.

E. Ip, N. Bai, Y. Huang, E. Mateo, F. Yaman, M. Li, S. Bickham, S. Ten, S. J. Liñares, C. Montero, V. Moreno, X. Prieto, V. Tse, K. M. Chung, A. Lau, H. Tam, C. Lu, Y. Luo, G. Peng, and G. Li, “88×3×112  Gb/s WDM transmission over 50 km of three-mode fiber with inline few-mode fiber amplifier,” in European Conference and Exhibition on Optical Communication (ECOC), OSA Technical Digest (CD) (Optical Society of America, 2011), paper Th.13.C.2.

Lee, D. L.

D. L. Lee, Electromagnetic Principles of Integrated Optics(Wiley, 1986).

Li, A.

Li, G.

E. Ip, N. Bai, Y. Huang, E. Mateo, F. Yaman, M. Li, S. Bickham, S. Ten, S. J. Liñares, C. Montero, V. Moreno, X. Prieto, V. Tse, K. M. Chung, A. Lau, H. Tam, C. Lu, Y. Luo, G. Peng, and G. Li, “88×3×112  Gb/s WDM transmission over 50 km of three-mode fiber with inline few-mode fiber amplifier,” in European Conference and Exhibition on Optical Communication (ECOC), OSA Technical Digest (CD) (Optical Society of America, 2011), paper Th.13.C.2.

Li, M.

E. Ip, N. Bai, Y. Huang, E. Mateo, F. Yaman, M. Li, S. Bickham, S. Ten, S. J. Liñares, C. Montero, V. Moreno, X. Prieto, V. Tse, K. M. Chung, A. Lau, H. Tam, C. Lu, Y. Luo, G. Peng, and G. Li, “88×3×112  Gb/s WDM transmission over 50 km of three-mode fiber with inline few-mode fiber amplifier,” in European Conference and Exhibition on Optical Communication (ECOC), OSA Technical Digest (CD) (Optical Society of America, 2011), paper Th.13.C.2.

Liñares, J.

J. Liñares, C. Montero, V. Moreno, M. C. Nistal, X. Prieto, J. R. Salgueiro, and D. Sotelo, “Glass processing by ion exchange to fabricate integrated optical planar components: applications,” Proc. SPIE 3936, 227–238 (2000).
[CrossRef]

J. Liñares, C. Montero, and X. Prieto, “Graded-index bifocal spectacle lenses produced by ion-exchange in glass: paraxial designing,” Pure Appl. Opt. 4, 695–699 (1995).
[CrossRef]

J. Liñares, X. Prieto, and C. Montero, “A novel refractive index profile for optical characterization of nonlinear diffusion processes and planar waveguides in glass,” Opt. Materials 3, 229–236 (1994).
[CrossRef]

X. Prieto and J. Liñares, “An approximated solution for the non-linear diffusion equation for planar waveguides: a new refractive-index profile,” in 10th Topical Meeting on Gradient-Index Optical Systems, OSA Technical Digest (University Publishers, 1992), paper PD9.T6.

Liñares, S. J.

E. Ip, N. Bai, Y. Huang, E. Mateo, F. Yaman, M. Li, S. Bickham, S. Ten, S. J. Liñares, C. Montero, V. Moreno, X. Prieto, V. Tse, K. M. Chung, A. Lau, H. Tam, C. Lu, Y. Luo, G. Peng, and G. Li, “88×3×112  Gb/s WDM transmission over 50 km of three-mode fiber with inline few-mode fiber amplifier,” in European Conference and Exhibition on Optical Communication (ECOC), OSA Technical Digest (CD) (Optical Society of America, 2011), paper Th.13.C.2.

Lingle, R.

Lu, C.

E. Ip, N. Bai, Y. Huang, E. Mateo, F. Yaman, M. Li, S. Bickham, S. Ten, S. J. Liñares, C. Montero, V. Moreno, X. Prieto, V. Tse, K. M. Chung, A. Lau, H. Tam, C. Lu, Y. Luo, G. Peng, and G. Li, “88×3×112  Gb/s WDM transmission over 50 km of three-mode fiber with inline few-mode fiber amplifier,” in European Conference and Exhibition on Optical Communication (ECOC), OSA Technical Digest (CD) (Optical Society of America, 2011), paper Th.13.C.2.

Luo, Y.

E. Ip, N. Bai, Y. Huang, E. Mateo, F. Yaman, M. Li, S. Bickham, S. Ten, S. J. Liñares, C. Montero, V. Moreno, X. Prieto, V. Tse, K. M. Chung, A. Lau, H. Tam, C. Lu, Y. Luo, G. Peng, and G. Li, “88×3×112  Gb/s WDM transmission over 50 km of three-mode fiber with inline few-mode fiber amplifier,” in European Conference and Exhibition on Optical Communication (ECOC), OSA Technical Digest (CD) (Optical Society of America, 2011), paper Th.13.C.2.

Mateo, E.

E. Ip, N. Bai, Y. Huang, E. Mateo, F. Yaman, M. Li, S. Bickham, S. Ten, S. J. Liñares, C. Montero, V. Moreno, X. Prieto, V. Tse, K. M. Chung, A. Lau, H. Tam, C. Lu, Y. Luo, G. Peng, and G. Li, “88×3×112  Gb/s WDM transmission over 50 km of three-mode fiber with inline few-mode fiber amplifier,” in European Conference and Exhibition on Optical Communication (ECOC), OSA Technical Digest (CD) (Optical Society of America, 2011), paper Th.13.C.2.

McCurdy, A.

Montero, C.

J. Liñares, C. Montero, V. Moreno, M. C. Nistal, X. Prieto, J. R. Salgueiro, and D. Sotelo, “Glass processing by ion exchange to fabricate integrated optical planar components: applications,” Proc. SPIE 3936, 227–238 (2000).
[CrossRef]

J. Liñares, C. Montero, and X. Prieto, “Graded-index bifocal spectacle lenses produced by ion-exchange in glass: paraxial designing,” Pure Appl. Opt. 4, 695–699 (1995).
[CrossRef]

J. Liñares, X. Prieto, and C. Montero, “A novel refractive index profile for optical characterization of nonlinear diffusion processes and planar waveguides in glass,” Opt. Materials 3, 229–236 (1994).
[CrossRef]

E. Ip, N. Bai, Y. Huang, E. Mateo, F. Yaman, M. Li, S. Bickham, S. Ten, S. J. Liñares, C. Montero, V. Moreno, X. Prieto, V. Tse, K. M. Chung, A. Lau, H. Tam, C. Lu, Y. Luo, G. Peng, and G. Li, “88×3×112  Gb/s WDM transmission over 50 km of three-mode fiber with inline few-mode fiber amplifier,” in European Conference and Exhibition on Optical Communication (ECOC), OSA Technical Digest (CD) (Optical Society of America, 2011), paper Th.13.C.2.

Moreno, V.

J. Liñares, C. Montero, V. Moreno, M. C. Nistal, X. Prieto, J. R. Salgueiro, and D. Sotelo, “Glass processing by ion exchange to fabricate integrated optical planar components: applications,” Proc. SPIE 3936, 227–238 (2000).
[CrossRef]

V. Moreno, S. Bara, M. V. Perez, C. Gomez-Reino, and J. H. Garcia, “Tilting and shearing determination in the alignment of a Mach–Zehnder interferometer by zone plates,” Opt. Laser Technol. 20, 89–94 (1988).
[CrossRef]

E. Ip, N. Bai, Y. Huang, E. Mateo, F. Yaman, M. Li, S. Bickham, S. Ten, S. J. Liñares, C. Montero, V. Moreno, X. Prieto, V. Tse, K. M. Chung, A. Lau, H. Tam, C. Lu, Y. Luo, G. Peng, and G. Li, “88×3×112  Gb/s WDM transmission over 50 km of three-mode fiber with inline few-mode fiber amplifier,” in European Conference and Exhibition on Optical Communication (ECOC), OSA Technical Digest (CD) (Optical Society of America, 2011), paper Th.13.C.2.

Nistal, M. C.

J. Liñares, C. Montero, V. Moreno, M. C. Nistal, X. Prieto, J. R. Salgueiro, and D. Sotelo, “Glass processing by ion exchange to fabricate integrated optical planar components: applications,” Proc. SPIE 3936, 227–238 (2000).
[CrossRef]

Peckham, D. W.

Peng, G.

E. Ip, N. Bai, Y. Huang, E. Mateo, F. Yaman, M. Li, S. Bickham, S. Ten, S. J. Liñares, C. Montero, V. Moreno, X. Prieto, V. Tse, K. M. Chung, A. Lau, H. Tam, C. Lu, Y. Luo, G. Peng, and G. Li, “88×3×112  Gb/s WDM transmission over 50 km of three-mode fiber with inline few-mode fiber amplifier,” in European Conference and Exhibition on Optical Communication (ECOC), OSA Technical Digest (CD) (Optical Society of America, 2011), paper Th.13.C.2.

Perez, M. V.

V. Moreno, S. Bara, M. V. Perez, C. Gomez-Reino, and J. H. Garcia, “Tilting and shearing determination in the alignment of a Mach–Zehnder interferometer by zone plates,” Opt. Laser Technol. 20, 89–94 (1988).
[CrossRef]

Prieto, X.

J. Liñares, C. Montero, V. Moreno, M. C. Nistal, X. Prieto, J. R. Salgueiro, and D. Sotelo, “Glass processing by ion exchange to fabricate integrated optical planar components: applications,” Proc. SPIE 3936, 227–238 (2000).
[CrossRef]

J. Liñares, C. Montero, and X. Prieto, “Graded-index bifocal spectacle lenses produced by ion-exchange in glass: paraxial designing,” Pure Appl. Opt. 4, 695–699 (1995).
[CrossRef]

J. Liñares, X. Prieto, and C. Montero, “A novel refractive index profile for optical characterization of nonlinear diffusion processes and planar waveguides in glass,” Opt. Materials 3, 229–236 (1994).
[CrossRef]

X. Prieto and J. Liñares, “An approximated solution for the non-linear diffusion equation for planar waveguides: a new refractive-index profile,” in 10th Topical Meeting on Gradient-Index Optical Systems, OSA Technical Digest (University Publishers, 1992), paper PD9.T6.

E. Ip, N. Bai, Y. Huang, E. Mateo, F. Yaman, M. Li, S. Bickham, S. Ten, S. J. Liñares, C. Montero, V. Moreno, X. Prieto, V. Tse, K. M. Chung, A. Lau, H. Tam, C. Lu, Y. Luo, G. Peng, and G. Li, “88×3×112  Gb/s WDM transmission over 50 km of three-mode fiber with inline few-mode fiber amplifier,” in European Conference and Exhibition on Optical Communication (ECOC), OSA Technical Digest (CD) (Optical Society of America, 2011), paper Th.13.C.2.

Qian, D.

D. Qian, M. F. Huang, E. Ip, Y. K. Huang, Y. Shao, J. Hu, and T. Wang, “101.7  Tb/s (370−294  Gb/s) PDM-128QAM-OFDM transmission over 3–55 km SSMF using pilot-based phase noise mitigation,” in Proceedings of Optical Fiber Communication Conference and Exposition (OFC/NFOEC), 2011, and the National Fiber Optic Engineers Conference (IEEE, 2011), paper PDPB5.

Randel, S.

Ryf, R.

Salgueiro, J. R.

J. Liñares, C. Montero, V. Moreno, M. C. Nistal, X. Prieto, J. R. Salgueiro, and D. Sotelo, “Glass processing by ion exchange to fabricate integrated optical planar components: applications,” Proc. SPIE 3936, 227–238 (2000).
[CrossRef]

Shao, Y.

D. Qian, M. F. Huang, E. Ip, Y. K. Huang, Y. Shao, J. Hu, and T. Wang, “101.7  Tb/s (370−294  Gb/s) PDM-128QAM-OFDM transmission over 3–55 km SSMF using pilot-based phase noise mitigation,” in Proceedings of Optical Fiber Communication Conference and Exposition (OFC/NFOEC), 2011, and the National Fiber Optic Engineers Conference (IEEE, 2011), paper PDPB5.

Shieh, W.

Sierra, A.

Sotelo, D.

J. Liñares, C. Montero, V. Moreno, M. C. Nistal, X. Prieto, J. R. Salgueiro, and D. Sotelo, “Glass processing by ion exchange to fabricate integrated optical planar components: applications,” Proc. SPIE 3936, 227–238 (2000).
[CrossRef]

Tam, H.

E. Ip, N. Bai, Y. Huang, E. Mateo, F. Yaman, M. Li, S. Bickham, S. Ten, S. J. Liñares, C. Montero, V. Moreno, X. Prieto, V. Tse, K. M. Chung, A. Lau, H. Tam, C. Lu, Y. Luo, G. Peng, and G. Li, “88×3×112  Gb/s WDM transmission over 50 km of three-mode fiber with inline few-mode fiber amplifier,” in European Conference and Exhibition on Optical Communication (ECOC), OSA Technical Digest (CD) (Optical Society of America, 2011), paper Th.13.C.2.

Ten, S.

E. Ip, N. Bai, Y. Huang, E. Mateo, F. Yaman, M. Li, S. Bickham, S. Ten, S. J. Liñares, C. Montero, V. Moreno, X. Prieto, V. Tse, K. M. Chung, A. Lau, H. Tam, C. Lu, Y. Luo, G. Peng, and G. Li, “88×3×112  Gb/s WDM transmission over 50 km of three-mode fiber with inline few-mode fiber amplifier,” in European Conference and Exhibition on Optical Communication (ECOC), OSA Technical Digest (CD) (Optical Society of America, 2011), paper Th.13.C.2.

Tse, V.

E. Ip, N. Bai, Y. Huang, E. Mateo, F. Yaman, M. Li, S. Bickham, S. Ten, S. J. Liñares, C. Montero, V. Moreno, X. Prieto, V. Tse, K. M. Chung, A. Lau, H. Tam, C. Lu, Y. Luo, G. Peng, and G. Li, “88×3×112  Gb/s WDM transmission over 50 km of three-mode fiber with inline few-mode fiber amplifier,” in European Conference and Exhibition on Optical Communication (ECOC), OSA Technical Digest (CD) (Optical Society of America, 2011), paper Th.13.C.2.

Wang, T.

D. Qian, M. F. Huang, E. Ip, Y. K. Huang, Y. Shao, J. Hu, and T. Wang, “101.7  Tb/s (370−294  Gb/s) PDM-128QAM-OFDM transmission over 3–55 km SSMF using pilot-based phase noise mitigation,” in Proceedings of Optical Fiber Communication Conference and Exposition (OFC/NFOEC), 2011, and the National Fiber Optic Engineers Conference (IEEE, 2011), paper PDPB5.

Winzer, P. J.

Xu, W.

Yaman, F.

E. Ip, N. Bai, Y. Huang, E. Mateo, F. Yaman, M. Li, S. Bickham, S. Ten, S. J. Liñares, C. Montero, V. Moreno, X. Prieto, V. Tse, K. M. Chung, A. Lau, H. Tam, C. Lu, Y. Luo, G. Peng, and G. Li, “88×3×112  Gb/s WDM transmission over 50 km of three-mode fiber with inline few-mode fiber amplifier,” in European Conference and Exhibition on Optical Communication (ECOC), OSA Technical Digest (CD) (Optical Society of America, 2011), paper Th.13.C.2.

Appl. Opt. (1)

Opt. Express (2)

Opt. Laser Technol. (1)

V. Moreno, S. Bara, M. V. Perez, C. Gomez-Reino, and J. H. Garcia, “Tilting and shearing determination in the alignment of a Mach–Zehnder interferometer by zone plates,” Opt. Laser Technol. 20, 89–94 (1988).
[CrossRef]

Opt. Materials (1)

J. Liñares, X. Prieto, and C. Montero, “A novel refractive index profile for optical characterization of nonlinear diffusion processes and planar waveguides in glass,” Opt. Materials 3, 229–236 (1994).
[CrossRef]

Proc. SPIE (1)

J. Liñares, C. Montero, V. Moreno, M. C. Nistal, X. Prieto, J. R. Salgueiro, and D. Sotelo, “Glass processing by ion exchange to fabricate integrated optical planar components: applications,” Proc. SPIE 3936, 227–238 (2000).
[CrossRef]

Pure Appl. Opt. (1)

J. Liñares, C. Montero, and X. Prieto, “Graded-index bifocal spectacle lenses produced by ion-exchange in glass: paraxial designing,” Pure Appl. Opt. 4, 695–699 (1995).
[CrossRef]

Other (6)

S. I. Najafi, ed., Introduction to Glass Integrated Optics(Artech House, 1992).

E. Ip, N. Bai, Y. Huang, E. Mateo, F. Yaman, M. Li, S. Bickham, S. Ten, S. J. Liñares, C. Montero, V. Moreno, X. Prieto, V. Tse, K. M. Chung, A. Lau, H. Tam, C. Lu, Y. Luo, G. Peng, and G. Li, “88×3×112  Gb/s WDM transmission over 50 km of three-mode fiber with inline few-mode fiber amplifier,” in European Conference and Exhibition on Optical Communication (ECOC), OSA Technical Digest (CD) (Optical Society of America, 2011), paper Th.13.C.2.

D. Qian, M. F. Huang, E. Ip, Y. K. Huang, Y. Shao, J. Hu, and T. Wang, “101.7  Tb/s (370−294  Gb/s) PDM-128QAM-OFDM transmission over 3–55 km SSMF using pilot-based phase noise mitigation,” in Proceedings of Optical Fiber Communication Conference and Exposition (OFC/NFOEC), 2011, and the National Fiber Optic Engineers Conference (IEEE, 2011), paper PDPB5.

D. L. Lee, Electromagnetic Principles of Integrated Optics(Wiley, 1986).

X. Prieto and J. Liñares, “An approximated solution for the non-linear diffusion equation for planar waveguides: a new refractive-index profile,” in 10th Topical Meeting on Gradient-Index Optical Systems, OSA Technical Digest (University Publishers, 1992), paper PD9.T6.

T. Kreiss, Handbook of Holographic Interferometry (Wiley-VCH, 2005).

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Figures (6)

Fig. 1.
Fig. 1.

Geometrical and optical characteristics of a dielectric plate.

Fig. 2.
Fig. 2.

Refractive index profiles using G (+) (dashed line) and L (×) (solid line) models.

Fig. 3.
Fig. 3.

Mach–Zender interferometer to characterize binary phase plates.

Fig. 4.
Fig. 4.

Four interferograms of the IR2 phase plate for four phase steps of the reference beam.

Fig. 5.
Fig. 5.

Retrieval phase of plate IR2 (the gradient in vertical direction is not relevant).

Fig. 6.
Fig. 6.

(a) Measured diffracted optical field (solid line) for a plate with ΔΦ=0.985π and Gauss and Dawson functions (dotted line). (b) Measured (solid line) and theoretical (dotted line) diffracted optical field for ΔΦ0.37π.

Tables (1)

Tables Icon

Table 1. Parameters (Wavelength, Diffusion Time, and Phase-Step) of the Characterized Ion-Exchanged Glass Binary Phase Plates

Equations (21)

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ΦAC=k0{ndcosθ+d(tanθ0tanθ)sinθ0}=k0{ndcosθ+dtanθ0sinθ0}.
ΔΦ=ΦAC2ΦAC1=k0d{n2cosθ2n1cosθ1}.
ΔΦ=ΦAC2ΦAC12πλ0n1(n12sin2θ0)1/2Δnd.
n2(z)=ns+Δn(z).
ΔΦ=Φ2Φ12πλ0ns(ns2sin2θ0)1/20zpΔn(z)dz.
n2(z,t)=ns+Δn(z,t)=ns+Δnc(z,t).
c(z,t)=erfc(z/2Dt)=erfc(z/d),
d=2Dt.
c(z,t)=1γ[1(1γ)erfc(z/2Dt)],
c(z,t)=1αlog[1+(eα1)erfc(z/2Dt)],
c(z,t)=ez2/4Dt=ez2/d2.
ΔΦ(t)=2πλ0nsΔnd(ns2sin2θ0)1/20zp/dc(z)dz
ΔΦ(t)=2πλ0nsΔnd(ns2sin2θ0)1/20ez2dz=2πλ0nsΔnd(ns2sin2θ0)1/2π2.
ΔΦ(t)=2πλ0nsΔnd(ns2sin2θ0)1/20log(1+(eα1)erfcz)αdz=2πλ0nsΔnd(ns2sin2θ0)1/2I(α).
ΔΦ(t)2πλ0nsΔnd(ns2sin2θ0)1/2(0.1306α+0.5725).
ΦR=arccosI1I2+I3I42(I2I3).
Φ(x,y)=arctanI3I2+(I1I3)cosΦ¯R+(I2I1)cos2Φ¯R(I1I3)sinΦ¯R+(I2I1)sin2Φ¯R+32Φ¯R.
Ψ(x0,y0,z)=ieik0zeiΔΦ2λ0z{eiΔΦ20++ex2+y2a2eik02z[(x0x)2+(y0y)2]eik02f(x2+y2)dxdy+eiΔΦ20+ex2+y2a2eik02z[(x0x)2+(y0y)2]eik02f(x2+y2)dxdy}.
Ψ(x0,y0,z)=Cek0y02A24z2{cos(ΔΦ2)0+ex2A2(eik0x0xz+eik0x0xz)dx+isin(ΔΦ2)0+ex2A2(eik0x0xzeik0x0xz)dx}.
Ψ(x0,y0,z)=C{cos(ΔΦ2)ek0(x02+y02)a24f2+sin(ΔΦ2)ek0(x02+y02)a24f2erfi(k0ax02f)},
Ψ(x0,y0,z)=Cek0y02a24f2{cos(ΔΦ2)G(k0x0a/2f)sin(ΔΦ2)D(k0x0a/2f)}.

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