## Binary encoded computer generated holograms for temporal phase shifting |

Optics Express, Vol. 19, Issue 23, pp. 23085-23096 (2011)

http://dx.doi.org/10.1364/OE.19.023085

Acrobat PDF (1782 KB)

### Abstract

The trend towards real-time optical applications predicates the need for real-time interferometry. For real-time interferometric applications, rapid processing of computer generated holograms is crucial as the intractability of rapid phase changes may compromise the input to the system. This paper introduces the design of a set of binary encoded computer generated holograms (CGHs) for real-time five-frame temporal phase shifting interferometry using a binary amplitude spatial light modulator. It is suitable for portable devices with constraints in computational power. The new set of binary encoded CGHs is used for measuring the phase of the generated electric field for a real-time selective launch in multimode fiber. The processing time for the new set of CGHs was reduced by up to 65% relative to the original encoding scheme. The results obtained from the new interferometric technique are in good agreement with the results obtained by phase shifting by means of a piezo-driven flat mirror.

© 2011 OSA

## 1. Introduction

1. K. Peters, “Polymer optical fiber sensors—a review,” Smart Mater. Struct. **20**(1), 1–17 (2011). [CrossRef]

4. T. Sibillano, A. Ancona, V. Berardi, and P. M. Lugarà, “A Real-Time Spectroscopic Sensor for Monitoring Laser Welding Processes,” Sensors (Basel Switzerland) **9**(5), 3376–3385 (2009). [CrossRef]

5. N. Kaneda, Q. Yang, X. Liu, S. Chandrasekhar, W. Shieh, and Y.-K. Chen, “Real-Time 2.5 GS/s Coherent Optical Receiver for 53.3-Gb/s Sub-Banded OFDM,” J. Lightwave Technol. **28**(4), 494–501 (2010). [CrossRef]

8. A. Leven, N. Kaneda, and S. Corteselli, “Real-Time Implementation of Digital Signal Processing for Coherent Optical Digital Communication Systems,” IEEE J. Sel. Top. Quantum Electron. **16**(5), 1227–1234 (2010). [CrossRef]

9. R. S. Maldonado, J. A. Izatt, N. Sarin, D. K. Wallace, S. Freedman, C. M. Cotten, and C. A. Toth, “Optimizing hand-held spectral domain optical coherence tomography imaging for neonates, infants, and children,” Invest. Ophthalmol. Vis. Sci. **51**(5), 2678–2685 (2010). [CrossRef] [PubMed]

12. W. Wieser, B. R. Biedermann, T. Klein, C. M. Eigenwillig, and R. Huber, “Multi-megahertz OCT: High quality 3D imaging at 20 million A-scans and 4.5 GVoxels per second,” Opt. Express **18**(14), 14685–14704 (2010). [CrossRef] [PubMed]

17. Y. Bitou, “Digital phase-shifting interferometer with an electrically addressed liquid-crystal spatial light modulator,” Opt. Lett. **28**(17), 1576–1578 (2003). [CrossRef] [PubMed]

19. C. Falldorf, M. Agour, C. V. Kopylow, and R. B. Bergmann, “Phase retrieval by means of a spatial light modulator in the Fourier domain of an imaging system,” Appl. Opt. **49**(10), 1826–1830 (2010). [CrossRef] [PubMed]

17. Y. Bitou, “Digital phase-shifting interferometer with an electrically addressed liquid-crystal spatial light modulator,” Opt. Lett. **28**(17), 1576–1578 (2003). [CrossRef] [PubMed]

19. C. Falldorf, M. Agour, C. V. Kopylow, and R. B. Bergmann, “Phase retrieval by means of a spatial light modulator in the Fourier domain of an imaging system,” Appl. Opt. **49**(10), 1826–1830 (2010). [CrossRef] [PubMed]

21. M. A. A. Neil, T. Wilson, and R. Juskaitis, “A wavefront generator for complex pupil function synthesis and point spread function engineering,” J. Microsc. **197**(3), 219–223 (2000). [CrossRef] [PubMed]

## 2. Mathematical derivation of binary encoded CGH for temporal phase shifting

*ϕ*is the phase of the test beam, γ is the fringe visibility, in radians and

*p*= π /2 radians is the induced phase shift.

*σ*= -π, -π/2, 0, π/2 and π respectively.

21. M. A. A. Neil, T. Wilson, and R. Juskaitis, “A wavefront generator for complex pupil function synthesis and point spread function engineering,” J. Microsc. **197**(3), 219–223 (2000). [CrossRef] [PubMed]

21. M. A. A. Neil, T. Wilson, and R. Juskaitis, “A wavefront generator for complex pupil function synthesis and point spread function engineering,” J. Microsc. **197**(3), 219–223 (2000). [CrossRef] [PubMed]

**197**(3), 219–223 (2000). [CrossRef] [PubMed]

**197**(3), 219–223 (2000). [CrossRef] [PubMed]

*x*and

*y*directions to the phase of the desired field,

*ξ*and the required phase shift,

*σ*, the new tilted wavefront is given bywhere

*a*(

*x*,

*y*) is the amplitude of the field and

*ξ*is the phase of the field. Letthen

*g(x, y)*is

*1*when the total phase is less than

*α*,where

*G(x, y)*, given in the first harmonic (

*n*= 1) has an amplitude,

*L1*Fourier transforms the first harmonic into the first diffraction order in the focal plane of the

*L1*. The first diffraction order is Fourier transformed again by

*L2*, and the image in the back focal plane of

*L2*is also has amplitude of

## 3. Demonstration of application of binary encoded CGH for temporal phase shifting

25. M. B. Shemirani and J. M. Kahn, “Higher-Order Modal Dispersion in Graded-Index Multimode Fiber,” J. Lightwave Technol. **27**(23), 5461–5468 (2009). [CrossRef]

26. L. Raddatz, I. H. White, D. G. Cunningham, and M. C. Nowell, “An experimental and theoretical study of the offset launch technique for the enhancement of the bandwidth of multimode fiber links,” J. Lightwave Technol. **16**(3), 324–331 (1998). [CrossRef]

33. N. Hanzawa, K. Saitoh, T. Sakamoto, T. Matsui, S. Tomita, and M. Koshiba, “Demonstration of mode-division multiplexing transmission over 10 km two-mode fiber with mode coupler,” in *The Optical Fiber Communication Conference and Exposition (OFC) and the National Fiber Optic Engineers Conference (NFOEC)**2011*, 2011)

31. M. Salsi, C. Koebele, D. Sperti, P. Tran, P. Brindel, H. Mardoyan, S. Bigo, A. Boutin, F. Verluise, P. Sillard, M. Astruc, L. Provost, F. Cerou, and G. Charlet, “Transmission at 2x100Gb/s, over Two Modes of 40km-long Prototype Few-Mode Fiber, using LCOS-based Mode Multiplexer and Demultiplexer,” in *The Optical Fiber Communication Conference and Exposition (OFC) and the National Fiber Optic Engineers Conference (NFOEC)**2011*, 2011)

37. A. Amphawan, “Holographic mode-selective launch for bandwidth enhancement in multimode fiber,” Opt. Express **19**(10), 9056–9065 (2011). [CrossRef] [PubMed]

37. A. Amphawan, “Holographic mode-selective launch for bandwidth enhancement in multimode fiber,” Opt. Express **19**(10), 9056–9065 (2011). [CrossRef] [PubMed]

*f*= 300mm (

_{1}*L1*) and

*f*= 100mm (

_{2}*L2*)] and a fiber collimator with an aspheric lens of

*f*= 11mm (

_{3}*L3*) were used. A visible 632.8nm Helium Neon laser was used to easily view modal field at various points along the system and to easily capture the interferograms. The MMF used was a 1km-long graded-index Thorlabs GIF625 [38], with a core diameter of 62.5μm

*c*(

*x*

_{1},

*y*

_{1}) was Fourier transformed, with zero-padding to increase the resolution of fine details. Next, a linear tilt of

*τ*= 88π in the horizontal direction and

_{x}*τ*= 120π in the vertical direction was added to the resultant field [21

_{y}**197**(3), 219–223 (2000). [CrossRef] [PubMed]

*x*

_{1}and

*y*

_{1}are spatial coordinates of the Fourier transformed field in the Fourier plane; and

*d*(

*x*

_{1},

*y*

_{1}) is the Fourier transform of the polarized modal electric field.

*d*(

*x*

_{1},

*y*

_{1}) may be binarized by first mapping the space of possible phase values

*ϕ*on the space g of binarized ones

*g (*

*ϕ*):

*x*→

*g*(

*ϕ*) using:where ξ(x

_{1}, y

_{1}) is the phase of the Fourier transform of the polarized modal electric field. Then, the real part of Eq. (22) is taken and approximated by a Fourier series given by the following expression:where a

_{o}is the constant term and a

_{n}is the Fourier cosine coefficient, b

_{n}is the Fourier sine coefficient. Only the real part of the complex field d (x

_{1}, y

_{1}) is required, thus b

_{n}= 0. Substituting Eq. (23) into Eq. (24) yields

*L1*. From Eq. (26), the Fourier transformed field in the back focal plane or Fourier plane of

*L1*is given as:where

*x*and

_{2}*y*are spatial coordinates in the Fourier plane of

_{2}*L1,** is the complex conjugate and

*M*(

_{n}*x*

_{1},

*y*

_{1}) is the

*n*-th diffraction order.

*M*was then spatially filtered using a pinhole located in the back focal plane of

_{1}*L1*. The combination of

*L2*and

*L3*then scales

*M*. Following this, the generated modal field was then interfered with the reference beam in the back focal plane of

_{1}*L2*. This was the closest location possible for the interference as

*L3*was connected directly to the input endface of the MMF using a fiber collimator [38]. The five binary encoded CGHs described in the previous section were displayed on the SLM sequentially to generate five interferograms of the phase-shifted electric field with respect to the reference beam.

## 4. Experimental results

*MSE*) between the retrieved phase distributions were calculated using:where

*θ*is the phase distribution from the first measurement,

_{1}*θ*is the phase distribution from the second measurement,

_{2}*t*is the index number for pixels on the horizontal axis,

*u*is the index number for pixels on the vertical axis,

*p = 128*is the total number of pixels on the horizontal axis, and

*q*= 128 is the total number of pixels on the vertical axis. Using Eq. (28), the MSEs of the second and third measured phase distributions relative to the first measured phase distribution were 0.014 and 0.009 respectively.

_{t }is the transverse field of a fiber mode, E

_{inc}is the incident electric field of the offset beam and A

_{core}is the cross sectional area of the fiber core. In the experimental setup in the power coupling efficiency is sensitive to the pitch, yaw, roll and distance of the SLM and lens with respect to the MMF. By measuring the phase at the end of the MMF prior to the launch, it is possible to adjust the pitch, yaw, roll and distance of the SLM and lens with respect to the MMF individually to find optimum power coupling into the desired mode.

## 5. Comparison to mechanical temporal phase shifting

## 6. Conclusion

## Acknowledgement

## References and links

1. | K. Peters, “Polymer optical fiber sensors—a review,” Smart Mater. Struct. |

2. | H. Su, M. Zervas, C. Furlong, and G. S. Fischer, “A Miniature MRI-Compatible Fiber-optic Force Sensor Utilizing Fabry-Perot Interferometer,” MEMS Nanotech. |

3. | V. Cortez-Retamozo, F. K. Swirski, P. Waterman, H. Yuan, J. L. Figueiredo, A. P. Newton, R. Upadhyay, C. Vinegoni, R. Kohler, J. Blois, A. Smith, M. Nahrendorf, L. Josephson, R. Weissleder, and M. J. Pittet, “Real-time assessment of inflammation and treatment response in a mouse model of allergic airway inflammation,” J. Clin. Invest. |

4. | T. Sibillano, A. Ancona, V. Berardi, and P. M. Lugarà, “A Real-Time Spectroscopic Sensor for Monitoring Laser Welding Processes,” Sensors (Basel Switzerland) |

5. | N. Kaneda, Q. Yang, X. Liu, S. Chandrasekhar, W. Shieh, and Y.-K. Chen, “Real-Time 2.5 GS/s Coherent Optical Receiver for 53.3-Gb/s Sub-Banded OFDM,” J. Lightwave Technol. |

6. | E. M. Ip and J. M. Kahn, “Fiber Impairment Compensation Using Coherent Detection and Digital Signal Processing,” J. Lightwave Technol. |

7. | B. Spinnler, “Equalizer Design and Complexity for Digital Coherent Receivers,” IEEE J. Sel. Top. Quantum Electron. |

8. | A. Leven, N. Kaneda, and S. Corteselli, “Real-Time Implementation of Digital Signal Processing for Coherent Optical Digital Communication Systems,” IEEE J. Sel. Top. Quantum Electron. |

9. | R. S. Maldonado, J. A. Izatt, N. Sarin, D. K. Wallace, S. Freedman, C. M. Cotten, and C. A. Toth, “Optimizing hand-held spectral domain optical coherence tomography imaging for neonates, infants, and children,” Invest. Ophthalmol. Vis. Sci. |

10. | N. Serbecic, S. C. Beutelspacher, F. C. Aboul-Enein, K. Kircher, A. Reitner, and U. Schmidt-Erfurth, “Reproducibility of high-resolution optical coherence tomography measurements of the nerve fibre layer with the new Heidelberg Spectralis optical coherence tomography,” Br. J. Ophthalmol. |

11. | S. Zotter, M. Pircher, T. Torzicky, M. Bonesi, E. Götzinger, R. A. Leitgeb, and C. K. Hitzenberger, “Visualization of microvasculature by dual-beam phase-resolved Doppler optical coherence tomography,” Opt. Express |

12. | W. Wieser, B. R. Biedermann, T. Klein, C. M. Eigenwillig, and R. Huber, “Multi-megahertz OCT: High quality 3D imaging at 20 million A-scans and 4.5 GVoxels per second,” Opt. Express |

13. | R. Tyson, |

14. | T. Kreis, |

15. | D. W. Robinson, |

16. | Z. Malacara and M. Servín, |

17. | Y. Bitou, “Digital phase-shifting interferometer with an electrically addressed liquid-crystal spatial light modulator,” Opt. Lett. |

18. | T. Meeser, C. v. Kopylow, and C. Falldorf, “Advanced Digital Lensless Fourier Holography by means of a Spatial Light Modulator,” in |

19. | C. Falldorf, M. Agour, C. V. Kopylow, and R. B. Bergmann, “Phase retrieval by means of a spatial light modulator in the Fourier domain of an imaging system,” Appl. Opt. |

20. | I. W. Jung, Spatial Light Modulators and Applications Spatial Light Modulators for Applications in Coherent Communication, Adaptive Optics and Maskless Lithography |

21. | M. A. A. Neil, T. Wilson, and R. Juskaitis, “A wavefront generator for complex pupil function synthesis and point spread function engineering,” J. Microsc. |

22. | S. Bois, |

23. | Cisco, “Cisco Visual Networking Index: Forecast and Methodology,” 2009-2014 (2010). |

24. | J. Gowar, |

25. | M. B. Shemirani and J. M. Kahn, “Higher-Order Modal Dispersion in Graded-Index Multimode Fiber,” J. Lightwave Technol. |

26. | L. Raddatz, I. H. White, D. G. Cunningham, and M. C. Nowell, “An experimental and theoretical study of the offset launch technique for the enhancement of the bandwidth of multimode fiber links,” J. Lightwave Technol. |

27. | A. Amphawan, F. Payne, D. O'Brien, and N. Shah, “Derivation of an analytical expression for the power coupling coefficient for offset launch into multimode fiber,” J. Lightwave Technol. |

28. | K. Balemarthy, A. Polley, and S. E. Ralph, “Electronic equalization of multikilometer 10-Gb/s multimode fiber links: mode-coupling effects,” J. Lightwave Technol. |

29. | C. Xia, M. Ajgaonkar, and W. Rosenkranz, “On the performance of the electrical equalization technique in MMF links for 10-gigabit ethernet,” J. Lightwave Technol. |

30. | R. Ryf, S. Randel, A. H. Gnauck, C. Bolle, R.-J. Essiambre, P. J. Winzer, D. W. Peckham, A. McCurdy, and J. R. Lingle, “Space-division multiplexing over 10 km of three-mode fiber using coherent 6 × 6 MIMO processing,” in |

31. | M. Salsi, C. Koebele, D. Sperti, P. Tran, P. Brindel, H. Mardoyan, S. Bigo, A. Boutin, F. Verluise, P. Sillard, M. Astruc, L. Provost, F. Cerou, and G. Charlet, “Transmission at 2x100Gb/s, over Two Modes of 40km-long Prototype Few-Mode Fiber, using LCOS-based Mode Multiplexer and Demultiplexer,” in |

32. | A. Li, A. A. Amin, X. Chen, and W. Shieh, “Reception of Mode and Polarization Multiplexed 107-Gb/s COOFDM Signal over a Two-Mode Fiber,” in |

33. | N. Hanzawa, K. Saitoh, T. Sakamoto, T. Matsui, S. Tomita, and M. Koshiba, “Demonstration of mode-division multiplexing transmission over 10 km two-mode fiber with mode coupler,” in |

34. | E. Alon, V. Stojanovic, J. M. Kahn, S. Boyd, and M. Horowitz, “Equalization of modal dispersion in multimode fiber using spatial light modulators,” in |

35. | P. L. Neo, J. P. Freeman, and T. D. Wilkinson, “Modal Control of a 50μm core diameter Multimode Fiber Using a Spatial Light Modulator,” in |

36. | G. Stepniak, L. Maksymiuk, and J. Siuzdak, “Increasing Multimode Fiber Transmission Capacity by Mode Selective Spatial Light Phase Modulation,” in |

37. | A. Amphawan, “Holographic mode-selective launch for bandwidth enhancement in multimode fiber,” Opt. Express |

38. | Thorlabs, “Tools of the Trade, Volume 20,” (Thorlabs Catalogue, 2009). |

**OCIS Codes**

(060.0060) Fiber optics and optical communications : Fiber optics and optical communications

(120.0120) Instrumentation, measurement, and metrology : Instrumentation, measurement, and metrology

(120.3180) Instrumentation, measurement, and metrology : Interferometry

(120.5050) Instrumentation, measurement, and metrology : Phase measurement

(280.4788) Remote sensing and sensors : Optical sensing and sensors

**ToC Category:**

Instrumentation, Measurement, and Metrology

**History**

Original Manuscript: August 11, 2011

Revised Manuscript: September 23, 2011

Manuscript Accepted: October 12, 2011

Published: October 31, 2011

**Citation**

Angela Amphawan, "Binary encoded computer generated holograms for temporal phase shifting," Opt. Express **19**, 23085-23096 (2011)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-23-23085

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### References

- K. Peters, “Polymer optical fiber sensors—a review,” Smart Mater. Struct. 20(1), 1–17 (2011). [CrossRef]
- H. Su, M. Zervas, C. Furlong, and G. S. Fischer, “A Miniature MRI-Compatible Fiber-optic Force Sensor Utilizing Fabry-Perot Interferometer,” MEMS Nanotech. 4, 131–136 (2011). [CrossRef]
- V. Cortez-Retamozo, F. K. Swirski, P. Waterman, H. Yuan, J. L. Figueiredo, A. P. Newton, R. Upadhyay, C. Vinegoni, R. Kohler, J. Blois, A. Smith, M. Nahrendorf, L. Josephson, R. Weissleder, and M. J. Pittet, “Real-time assessment of inflammation and treatment response in a mouse model of allergic airway inflammation,” J. Clin. Invest. 118(12), 4058–4066 (2008). [CrossRef] [PubMed]
- T. Sibillano, A. Ancona, V. Berardi, and P. M. Lugarà, “A Real-Time Spectroscopic Sensor for Monitoring Laser Welding Processes,” Sensors (Basel Switzerland) 9(5), 3376–3385 (2009). [CrossRef]
- N. Kaneda, Q. Yang, X. Liu, S. Chandrasekhar, W. Shieh, and Y.-K. Chen, “Real-Time 2.5 GS/s Coherent Optical Receiver for 53.3-Gb/s Sub-Banded OFDM,” J. Lightwave Technol. 28(4), 494–501 (2010). [CrossRef]
- E. M. Ip and J. M. Kahn, “Fiber Impairment Compensation Using Coherent Detection and Digital Signal Processing,” J. Lightwave Technol. 28(4), 502–519 (2010). [CrossRef]
- B. Spinnler, “Equalizer Design and Complexity for Digital Coherent Receivers,” IEEE J. Sel. Top. Quantum Electron. 16(5), 1180–1192 (2010). [CrossRef]
- A. Leven, N. Kaneda, and S. Corteselli, “Real-Time Implementation of Digital Signal Processing for Coherent Optical Digital Communication Systems,” IEEE J. Sel. Top. Quantum Electron. 16(5), 1227–1234 (2010). [CrossRef]
- R. S. Maldonado, J. A. Izatt, N. Sarin, D. K. Wallace, S. Freedman, C. M. Cotten, and C. A. Toth, “Optimizing hand-held spectral domain optical coherence tomography imaging for neonates, infants, and children,” Invest. Ophthalmol. Vis. Sci. 51(5), 2678–2685 (2010). [CrossRef] [PubMed]
- N. Serbecic, S. C. Beutelspacher, F. C. Aboul-Enein, K. Kircher, A. Reitner, and U. Schmidt-Erfurth, “Reproducibility of high-resolution optical coherence tomography measurements of the nerve fibre layer with the new Heidelberg Spectralis optical coherence tomography,” Br. J. Ophthalmol. 95(6), 804–810 (2011). [CrossRef] [PubMed]
- S. Zotter, M. Pircher, T. Torzicky, M. Bonesi, E. Götzinger, R. A. Leitgeb, and C. K. Hitzenberger, “Visualization of microvasculature by dual-beam phase-resolved Doppler optical coherence tomography,” Opt. Express 19(2), 1217–1227 (2011). [CrossRef] [PubMed]
- W. Wieser, B. R. Biedermann, T. Klein, C. M. Eigenwillig, and R. Huber, “Multi-megahertz OCT: High quality 3D imaging at 20 million A-scans and 4.5 GVoxels per second,” Opt. Express 18(14), 14685–14704 (2010). [CrossRef] [PubMed]
- R. Tyson, Principles of Adaptive Optics, 3rd Ed. (CRC Press, 2011).
- T. Kreis, Handbook of Holographic Interferometry: Optical and Digital Methods (Wiley-VCH, 2005).
- D. W. Robinson, Interferogram Analysis, Digital Fringe Pattern Measurement Techniques (Taylor & Francis, 1993).
- Z. Malacara and M. Servín, Interferogram Analysis For Optical Testing, Second Edition (Optical Science and Engineering) (CRC Press, 2005).
- Y. Bitou, “Digital phase-shifting interferometer with an electrically addressed liquid-crystal spatial light modulator,” Opt. Lett. 28(17), 1576–1578 (2003). [CrossRef] [PubMed]
- T. Meeser, C. v. Kopylow, and C. Falldorf, “Advanced Digital Lensless Fourier Holography by means of a Spatial Light Modulator,” in 3DTV-Conference: The True Vision - Capture, Transmission and Display of 3D Video (3DTV-CON),2010 2010), 1–4.
- C. Falldorf, M. Agour, C. V. Kopylow, and R. B. Bergmann, “Phase retrieval by means of a spatial light modulator in the Fourier domain of an imaging system,” Appl. Opt. 49(10), 1826–1830 (2010). [CrossRef] [PubMed]
- I. W. Jung, Spatial Light Modulators and Applications Spatial Light Modulators for Applications in Coherent Communication, Adaptive Optics and Maskless Lithography (VDM Verlag,2009).
- M. A. A. Neil, T. Wilson, and R. Juskaitis, “A wavefront generator for complex pupil function synthesis and point spread function engineering,” J. Microsc. 197(3), 219–223 (2000). [CrossRef] [PubMed]
- S. Bois, Next Generation Fibers and Standards (Corning Optical Fiber 2009).
- Cisco, “Cisco Visual Networking Index: Forecast and Methodology,” 2009-2014 (2010).
- J. Gowar, Optical communication systems, 2nd ed., Prentice-Hall international series in optoelectronics (Prentice Hall, New York, 1993), pp. xvi, 696.
- M. B. Shemirani and J. M. Kahn, “Higher-Order Modal Dispersion in Graded-Index Multimode Fiber,” J. Lightwave Technol. 27(23), 5461–5468 (2009). [CrossRef]
- L. Raddatz, I. H. White, D. G. Cunningham, and M. C. Nowell, “An experimental and theoretical study of the offset launch technique for the enhancement of the bandwidth of multimode fiber links,” J. Lightwave Technol. 16(3), 324–331 (1998). [CrossRef]
- A. Amphawan, F. Payne, D. O'Brien, and N. Shah, “Derivation of an analytical expression for the power coupling coefficient for offset launch into multimode fiber,” J. Lightwave Technol. 28(6), 861–869 (2010). [CrossRef]
- K. Balemarthy, A. Polley, and S. E. Ralph, “Electronic equalization of multikilometer 10-Gb/s multimode fiber links: mode-coupling effects,” J. Lightwave Technol. 24(12), 4885–4894 (2006). [CrossRef]
- C. Xia, M. Ajgaonkar, and W. Rosenkranz, “On the performance of the electrical equalization technique in MMF links for 10-gigabit ethernet,” J. Lightwave Technol. 23(6), 2001–2011 (2005). [CrossRef]
- R. Ryf, S. Randel, A. H. Gnauck, C. Bolle, R.-J. Essiambre, P. J. Winzer, D. W. Peckham, A. McCurdy, and J. R. Lingle, “Space-division multiplexing over 10 km of three-mode fiber using coherent 6 × 6 MIMO processing,” in The Optical Fiber Communication Conference and Exposition (OFC) and the National Fiber Optic Engineers Conference (NFOEC)2011, 2011)
- M. Salsi, C. Koebele, D. Sperti, P. Tran, P. Brindel, H. Mardoyan, S. Bigo, A. Boutin, F. Verluise, P. Sillard, M. Astruc, L. Provost, F. Cerou, and G. Charlet, “Transmission at 2x100Gb/s, over Two Modes of 40km-long Prototype Few-Mode Fiber, using LCOS-based Mode Multiplexer and Demultiplexer,” in The Optical Fiber Communication Conference and Exposition (OFC) and the National Fiber Optic Engineers Conference (NFOEC)2011, 2011)
- A. Li, A. A. Amin, X. Chen, and W. Shieh, “Reception of Mode and Polarization Multiplexed 107-Gb/s COOFDM Signal over a Two-Mode Fiber,” in The Optical Fiber Communication Conference and Exposition (OFC) and the National Fiber Optic Engineers Conference (NFOEC)2011, 2011)
- N. Hanzawa, K. Saitoh, T. Sakamoto, T. Matsui, S. Tomita, and M. Koshiba, “Demonstration of mode-division multiplexing transmission over 10 km two-mode fiber with mode coupler,” in The Optical Fiber Communication Conference and Exposition (OFC) and the National Fiber Optic Engineers Conference (NFOEC)2011, 2011)
- E. Alon, V. Stojanovic, J. M. Kahn, S. Boyd, and M. Horowitz, “Equalization of modal dispersion in multimode fiber using spatial light modulators,” in GLOBECOM '04. IEEE Global Telecommunications Conference, (IEEE, 2004), 1023- 1029.
- P. L. Neo, J. P. Freeman, and T. D. Wilkinson, “Modal Control of a 50μm core diameter Multimode Fiber Using a Spatial Light Modulator,” in Optical Fiber Communication and the National Fiber Optic Engineers Conference,2007. OFC/NFOEC 2007. Conference on, (Optical Society of America, 2007), 1–3.
- G. Stepniak, L. Maksymiuk, and J. Siuzdak, “Increasing Multimode Fiber Transmission Capacity by Mode Selective Spatial Light Phase Modulation,” in 36th European Conference on Optical Communications, 2010)
- A. Amphawan, “Holographic mode-selective launch for bandwidth enhancement in multimode fiber,” Opt. Express 19(10), 9056–9065 (2011). [CrossRef] [PubMed]
- Thorlabs, “Tools of the Trade, Volume 20,” (Thorlabs Catalogue, 2009).

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