## Demonstration of channelized tunable optical dispersion compensator based on arrayed-waveguide grating and liquid crystal on silicon |

Optics Express, Vol. 18, Issue 18, pp. 18565-18579 (2010)

http://dx.doi.org/10.1364/OE.18.018565

Acrobat PDF (2407 KB)

### Abstract

We propose and demonstrate a multi-channel tunable optical dispersion compensator (TODC) that consists of an arrayed-waveguide grating (AWG) and liquid crystal on silicon (LCOS). By utilizing the AWG with a large angular dispersion and the LCOS with a flexible phase setting, we can construct a compact and flexible TODC that has a wide tuning range of chromatic dispersion. We confirmed experimentally that the TODC could realize channel-by-channel CD compensation for six WDM channels with a ± 800 ps/nm range and a 3 dB bandwidth of 24 GHz. We believe that the multi-channel operation of this TODC will help to reduce the cost and power consumption of high-speed optical transmission systems.

© 2010 OSA

## 1. Introduction

1. K. Takiguchi, K. Okamoto, and K. Moriwaki, “Planar lightwave circuit dispersion equalizer,” J. Lightwave Technol. **14**(9), 2003–2011 (1996). [CrossRef]

3. C. R. Doerr, L. W. Stulz, S. Chandrasekhar, and R. Pafchek, “colorless tunable dispersion compensator with 400-ps/nm range integrated with a tunable noise filter,” IEEE Photon. Technol. Lett. **15**(9), 1258–1260 (2003). [CrossRef]

10. M. A. F. Roelens, S. Frisken, J. A. Bolger, D. Abakoumov, G. Baxter, S. Poole, and B. J. Eggleton, “Dispersion trimming in a reconfigurable wavelength selective switch,” J. Lightwave Technol. **26**(1), 73–78 (2008). [CrossRef]

8. T. Sano, T. Iwashima, M. Kitayama, T. Kanie, M. Harumoto, M. Shigehara, H. Suganuma, and M. Nishimura, “Novel multichannel tunable chromatic dispersion compensator based on MEMS and diffraction grating,” IEEE Photon. Technol. Lett. **15**(8), 1109–1110 (2003). [CrossRef]

9. D. T. Neilson, R. Ryf, F. Pardo, V. A. Aksyuk, M. E. Simon, D. O. Lopez, D. M. Marom, and S. Chandrasekhar, “MEMS-based channelized dispersion compensator with flat passbands,” J. Lightwave Technol. **22**(1), 101–105 (2004). [CrossRef]

10. M. A. F. Roelens, S. Frisken, J. A. Bolger, D. Abakoumov, G. Baxter, S. Poole, and B. J. Eggleton, “Dispersion trimming in a reconfigurable wavelength selective switch,” J. Lightwave Technol. **26**(1), 73–78 (2008). [CrossRef]

11. M. Shirasaki, A. N. Akhter, and C. Lin, “Virtually imaged phased array with graded reflectivity,” IEEE Photon. Technol. Lett. **11**(11), 1443–1445 (1999). [CrossRef]

12. H. Takenouchi, T. Ishii, and T. Goh, “8 THz bandwidth dispersion-slope compensator module for multiband 4Gbit/s WDM transmission systems using an AWG and spatial phase filter,” Electron. Lett. **37**(12), 777–778 (2001). [CrossRef]

14. K. Takada, M. Abe, T. Shibata, and K. Okamoto, “1-GHz-spaced 16-channel arrayed-waveguide grating for a wavelength reference standard in DWDM network systems,” J. Lightwave Technol. **20**(5), 850–853 (2002). [CrossRef]

11. M. Shirasaki, A. N. Akhter, and C. Lin, “Virtually imaged phased array with graded reflectivity,” IEEE Photon. Technol. Lett. **11**(11), 1443–1445 (1999). [CrossRef]

15. K. Seno, K. Suzuki, K. Watanabe, N. Ooba, M. Ishii, and S. Mino, “Channel-by-channel tunable optical dispersion compensator consisting of arrayed-waveguide grating and liquid crystal on silicon,” in *Proceedings of Optical Fiber Communication Conference and Exposition* (Optical Society of America, 2008), paper OWP4.

## 2. Principle and design of spectrometer-based TODC using LCOS

### 2.1 Principle

*x*direction by the focusing lens. The LCOS, which has a large number of fine pixels, is in the wavelength dispersion axis of the AWG. Thus the LCOS spatially modulates the wavefront of the incoming light, reflects the signal back in the opposite direction, and returns it to the same input waveguide of the AWG. Finally the output signal travels in a lower direction via a circulator.

*x*axis. Therefore there are typically hundreds of pixels in each channel. As a result we can modulate the wavefront of the incoming light signal very flexibly, as described in more detail later in this section.

#### 2.1.1 Chromatic Dispersion value CD

*x*is

*Φ*, the group delay

_{SLM}(x)*τ*is obtained bywhere

*ω*,

*c*and

*λ*are the angular frequency of the signal, the speed of light in a vacuum, and the signal wavelength, respectively. Thus, the CD provided by the system is given by

*dx/dλ*in the first part of Eq. (2) represents the dispersion of the AWG on the LCOS surface, and this can be increased by increasing the diffraction order. This can be given with the AWG design by the equation:where

*n*is the group index of the effective index

_{g}*n*of the array waveguide,

_{c}*f*is the focal length of the focusing lens,

*ΔL*is the path length difference between neighboring array waveguides, and

*d*is the array waveguide separation in the output region [16]. The

*ΔL*is not in the bulk grating, and is a characteristic of the AWG, which is given by

*ΔL = λ*, where

_{c}m/n_{c}*m*is the diffraction order. Equation (3) means that the linear dispersion can be increased by

*ΔL*, and that this increase corresponds to higher order diffraction. The

*d*value in an AWG is typically about 10 μm, and

*m*can be above 100, and these parameters can be designed flexibly. On the other hand, in a typical bulk diffraction grating,

*d*is 1 μm, and

*m*is 2. Thus the

*dx/dλ*value of the AWG can be increased by one order compared with that of a typical bulk grating. Therefore, the CD value using the AWG is much larger than that with a bulk-type diffraction grating.

*d*is the quadratic coefficient of the phase function. As mentioned above, the phase shift setting in a LCOS can be given in each pixel by employing an electrical voltage. As a result, the necessary phase distribution along the dispersion

^{2}/dx^{2}Φ_{SLM}(x)*x*axis can be set flexibly. Here the phase shift in the LCOS is in the 0 to 2π range. Thus if the necessary phase shift is above 2π, we can give the phase function in the folded every 2π as shown in Fig. 1(b). Therefore, a large CD value can be obtained by combining the AWG and the LCOS. At the same time, we can set different CD values in the different channels, and this enables us to realize channel-by-channel TODC operation.

#### 2.1.2 Transmission bandwidth BW

11. M. Shirasaki, A. N. Akhter, and C. Lin, “Virtually imaged phased array with graded reflectivity,” IEEE Photon. Technol. Lett. **11**(11), 1443–1445 (1999). [CrossRef]

*CD*and a 3-dB transmission bandwidth

*BW*is expressed by (A5)Here, an AWG is advantageous as regards designing a wide transmission bandwidth

*BW*, because

*dx/dλ*can be increased as mentioned above, and

*W*can be suitably designed by designing

_{SLM}*W*. The Gaussian beam spot radius on the LCOS

_{out}*W*can be evaluated from the AWG output light

_{SLM}*W*in the following equation.As shown in Eq. (4), our spectrometer-based TODC requires a small

_{out}*W*if we are to obtain a large

_{SLM}*CD**

*BW*value. With a typical AWG,

*W*is several millimeters long. This means that

_{out}*W*is some tens of microns according to Eq. (5) assuming a focusing length of around 100 mm. This means that an AWG with a wide

_{SLM}*W*is preferable in terms of obtaining a small

_{out}*W*value. If we realize in the normal space optics, we must, for example, install a beam expander (a pair of prisms) to increase the beam width from a typical beam size of around 200 μm. We can easily increase

_{SLM}*W*by increasing the number of arrayed waveguides, and acquire better

_{out}*CD**

*BW*values.

*W*, and reduce the

_{out}*W*compared with the LCOS pixel pitch

_{SLM}*T*, we can no longer ignore the LCOS pixel discontinuity because we approximate the continuous curvature of the phase function. As a result, ripples appear in the transmission spectrum and in the group delay characteristics. We investigate this effect of LCOS pixel discontinuity on the group delay characteristics numerically in sub-section 2.2.2.

### 2.2 Design and numerical estimation

*CD*and transmission bandwidth

*BW*by assuming the experimental parameters described in sub-section 2.2.1. In addition, we evaluate the effect of the diffraction because of the discretely pixelized LCOS cells by calculating the overlap integral of the electric field between the incident and reflected Gaussian beams in sub-section 2.2.2. Based on these calculations, we confirm that this TODC, which consists of an AWG and LCOS, can deal with large dispersion values in a sufficient bandwidth in multi-channel operation.

#### 2.2.1 Relationship between chromatic dispersion CD and bandwidth BW

*CD*and bandwidth

*BW*as a parameter of diffraction order

*m*. We summarize the parameters we used in Table 1 .

*CD*and the transmission bandwidth

*BW*as a parameter of the diffraction order

*m*. In Fig. 2(a) and 2(b), the ratio of the beam spot sizes on the LCOS

*W*and LCOS pixel pitch

_{SLM}*T*(hereafter overlap) are 4 and 8, respectively. Here we also calculate a typical bulk grating as a reference in which the grating pitch is 1 μm and the diffraction order is 2 assuming the same

*W*. As shown in Eq. (3), compared with the bulk grating, the AWG can provide a large

_{SLM}*CD*BW*product because of the large linear dispersion (

*dx/dλ*) originating from high diffraction order m. This

*CD*BW*product can be increased as the spot beam size on the LCOS is decreased.

*CD*. Figure 3 shows the results when the diffraction order

*m*is 200. As expected with Eq. (4), the bandwidth becomes larger as the spot size

*W*decreases. If we need the dispersion compensation value

_{SLM}/T*CD*of the 600 ps/nm bandwidth required for a 40 Gb/s optical signal, we have to design the spot size

*W*to be less than 8. Since

_{SLM}/T*T*is equal to around 5-15 μm, this value can be easily designed in practice.

*W*decreases. As a result, ripples appear in the transmission and group delay characteristics around the pixel boundary. We discuss this LCOS pixel discrepancy effect numerically in the next section.

_{SLM}/T#### 2.2.2 LCOS discrepancy effect

*φ*(

*x*) and the field reflected by the LCOS

*ϕ*(

*x*). The electric field of the incoming light

*φ*(

*x*) and the field spatially modulated and reflected by the LCOS

*ϕ*(

*x*) are expressed as where

*A*,

*x, ω*and

*θ*are the electric field intensity, the position on the LCOS in the

_{SLM}(x)*x*direction, the beam spot size on the LCOS surface, and the phase distribution (hereafter phase function) of the LCOS, respectively. The phase of the output signal

*Φ*(

*x*) and the group delay

*τ*are obtained byHere, we calculate

*τ*(

*λ*) in Eq. (9) instead of Eq. (1).This expression is a more general formula than Eq. (4) and takes account of the diffraction effect.

*W*increases, and falls to a sufficiently small value of less than 2 ps by the time the beam width reaches twice the pixel size. This result indicates that if we can adopt a

_{SLM}*W*/

_{SLM}*T*of more than 4, the LCOS discrepancy effect becomes negligible.

*CD*BW*value can be realized when we utilize the higher order diffraction of the AWG. Typically, we could attain a

*CD*of 800 ps/nm in a 40 GHz bandwidth in a multi-channel TODC, when we used a diffraction order of 200 and an overlap of 4 pixels of the LCOS. The LCOS discrepancy effect is less than ± 2 ps when the overlap is more than 2 pixels.

## 3. Experimental results and discussions for channelized TODC

*CD*BW*value, it is adequate for investigating the validity of our design described in the previous section. The focal length of the focusing lens was set at 100 mm. The beam waist was set at eight times the pixel size. The pixel number was set at 256, which corresponds to a WDM channel with a bandwidth of 0.84 nm. These parameters are based on the discussion in section 2. Multi-channel operation (6 channels) can be achieved by using 1536 LCOS pixels. For the phase setting in the LCOS, we applied voltage to these pixels with complementary metal oxide semiconductor (CMOS) circuits through dozens of electrical I/O interfaces. For our purpose, this voltage is in the 0 to 5 V range and is capable of fine resolution.

*CD*and 3 dB bandwidth

*BW*is examined for ch. 3 to confirm the detailed correspondence between the design in Sec. 2 and the results with this setup. In addition, it is shown that channel-by-channel operation has been achieved according to the design in Sec. 3.2. We clarified that ripples that appeared in the transmittance and group delay spectra when we analyzed these results. The analysis of the cause of the ripples and a corrective strategy are discussed in Sec. 3.3. Moreover, Sec. 3.4 demonstrates the ability to prescribe third-order dispersion compensation. We confirmed experimentally that a feature of our TODC is that the optical phase is programmable.

### 3.1 Single channel characteristics

17. A. Sugita, A. Kaneko, K. Okamoto, M. Itoh, A. Himeno, and Y. Ohmori, KM Okamoto, A Itoh, Himeno, and Y Ohmori, “Very low insertion loss arrayed-waveguide grating with vertically tapered waveguides,” IEEE Photon. Technol. Lett. **12**(9), 1180–1182 (2000). [CrossRef]

### 3.2 Channel-by-channel operation

*W*, and proportional to the linear dispersion on the LCOS. Therefore, to preserve the same characteristics in each channel, we must reduce

_{SLM}*W*. However, it should be noted that the overlap,

_{SLM}*W*, should be two or more pixels, as described in sub-section 2.2.2. Therefore, we can expand up to 20 channels with this method. If we want to design a TODC with 20 or more channels, we have to change the number of pixels and the pixel gap of the LCOS.

_{SLM}/T9. D. T. Neilson, R. Ryf, F. Pardo, V. A. Aksyuk, M. E. Simon, D. O. Lopez, D. M. Marom, and S. Chandrasekhar, “MEMS-based channelized dispersion compensator with flat passbands,” J. Lightwave Technol. **22**(1), 101–105 (2004). [CrossRef]

18. K. Suzuki, N. Ooba, M. Ishii, K. Seno, T. Shibata, and S. Mino, “40-wavelength channelized tunable optical dispersion compensator with increased bandwidth consisting of arrayed waveguide gratings and liquid crystal on silicon,” in *Proceedings of Optical Fiber Communication Conference and Exposition* (Optical Society of America, 2009), paper OThB3.

19. K. Seno, K. Suzuki, N. Ooba, T. Watanabe, M. Itoh, S. Mino, and T. Sakamoto, “50-wavelength channel-by-channel tunable optical dispersion compensator using combination of arrayed-waveguide and bulk gratings,” in *Proceedings of Optical Fiber Communication Conference and Exposition* (Optical Society of America, 2010), paper OMT7.

### 3.3 Cause of ripples in the group delay and the transmission spectra

*T*and

*S*are the pixel pitch of the LCOS and the space between adjacent pixels, respectively.

### 3.4 High order dispersion

## 4. Conclusion

## 5. Appendix

## References and links

1. | K. Takiguchi, K. Okamoto, and K. Moriwaki, “Planar lightwave circuit dispersion equalizer,” J. Lightwave Technol. |

2. | Y. Painchaud, M. Lapointe, F. Trepanier, R. L. Lachance, C. Paquet, and M. Guy, “Recent progress on FBG-based tunable dispersion compensators for 40 Gb/s applications,” in |

3. | C. R. Doerr, L. W. Stulz, S. Chandrasekhar, and R. Pafchek, “colorless tunable dispersion compensator with 400-ps/nm range integrated with a tunable noise filter,” IEEE Photon. Technol. Lett. |

4. | M. Shirasaki, and S. Cao, “Compensation of chromatic dispersion and dispersion slope using a virtually imaged phased array,” in |

5. | C. R. Doerr, “Polarization-independent tunable dispersion compensator comprised of a silica arrayed waveguide grating and a polymer slab,” in |

6. | D. M. Marom, C. R. Doerr, M. A. Cappuzzo, E. Y. Chen, A. Wong-Foy, L. T. Gomez, and S. Chandrasekhar, “Compact colorless tunable dispersion compensator with 1000-ps/nm tuning range for 40-Gb/s data rates,” J. Lightwave Technol. |

7. | G.-H. Lee, S. Xiao, and A. M. Weiner, “Optical dispersion compensator with >4000-ps/nm tuning range using a virtually imaged phased array (VIPA) and spatial light modulator (SLM),” IEEE Photon. Technol. Lett. |

8. | T. Sano, T. Iwashima, M. Kitayama, T. Kanie, M. Harumoto, M. Shigehara, H. Suganuma, and M. Nishimura, “Novel multichannel tunable chromatic dispersion compensator based on MEMS and diffraction grating,” IEEE Photon. Technol. Lett. |

9. | D. T. Neilson, R. Ryf, F. Pardo, V. A. Aksyuk, M. E. Simon, D. O. Lopez, D. M. Marom, and S. Chandrasekhar, “MEMS-based channelized dispersion compensator with flat passbands,” J. Lightwave Technol. |

10. | M. A. F. Roelens, S. Frisken, J. A. Bolger, D. Abakoumov, G. Baxter, S. Poole, and B. J. Eggleton, “Dispersion trimming in a reconfigurable wavelength selective switch,” J. Lightwave Technol. |

11. | M. Shirasaki, A. N. Akhter, and C. Lin, “Virtually imaged phased array with graded reflectivity,” IEEE Photon. Technol. Lett. |

12. | H. Takenouchi, T. Ishii, and T. Goh, “8 THz bandwidth dispersion-slope compensator module for multiband 4Gbit/s WDM transmission systems using an AWG and spatial phase filter,” Electron. Lett. |

13. | K. Seno, N. Ooba, K. Suzuki, K. Watanabe, M. Ishii, and S. Mino, “tunable dispersion compensator consisting of simple optics with arrayed-waveguide grating and flat mirror,” in |

14. | K. Takada, M. Abe, T. Shibata, and K. Okamoto, “1-GHz-spaced 16-channel arrayed-waveguide grating for a wavelength reference standard in DWDM network systems,” J. Lightwave Technol. |

15. | K. Seno, K. Suzuki, K. Watanabe, N. Ooba, M. Ishii, and S. Mino, “Channel-by-channel tunable optical dispersion compensator consisting of arrayed-waveguide grating and liquid crystal on silicon,” in |

16. | K. Okamoto, |

17. | A. Sugita, A. Kaneko, K. Okamoto, M. Itoh, A. Himeno, and Y. Ohmori, KM Okamoto, A Itoh, Himeno, and Y Ohmori, “Very low insertion loss arrayed-waveguide grating with vertically tapered waveguides,” IEEE Photon. Technol. Lett. |

18. | K. Suzuki, N. Ooba, M. Ishii, K. Seno, T. Shibata, and S. Mino, “40-wavelength channelized tunable optical dispersion compensator with increased bandwidth consisting of arrayed waveguide gratings and liquid crystal on silicon,” in |

19. | K. Seno, K. Suzuki, N. Ooba, T. Watanabe, M. Itoh, S. Mino, and T. Sakamoto, “50-wavelength channel-by-channel tunable optical dispersion compensator using combination of arrayed-waveguide and bulk gratings,” in |

20. | D. Sinefeld, C. R. Doerr, and D. M. Marom, “Photonic spectral processor employing two-dimensional wdm channel separation and a phase LCoS modulator,” in |

**OCIS Codes**

(230.7390) Optical devices : Waveguides, planar

(130.2035) Integrated optics : Dispersion compensation devices

(070.6120) Fourier optics and signal processing : Spatial light modulators

**ToC Category:**

Integrated Optics

**History**

Original Manuscript: June 16, 2010

Revised Manuscript: August 5, 2010

Manuscript Accepted: August 5, 2010

Published: August 16, 2010

**Citation**

Kazunori Seno, Kenya Suzuki, Naoki Ooba, Kei Watanabe, Motohaya Ishii, Hirotaka Ono, and Shinji Mino, "Demonstration of channelized tunable optical dispersion compensator based on arrayed-waveguide grating and liquid crystal on silicon," Opt. Express **18**, 18565-18579 (2010)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-18-18565

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### References

- K. Takiguchi, K. Okamoto, and K. Moriwaki, “Planar Lightwave Circuit Dispersion Equalizer,” J. Lightwave Technol. 14(9), 2003–2011 (1996). [CrossRef]
- Y. Painchaud, M. Lapointe, F. Trepanier, R. L. Lachance, C. Paquet, and M. Guy, “Recent Progress on FBG-based Tunable Dispersion Compensators for 40 Gb/s Applications,” in Proceedings of Optical Fiber Communication Conference and Exposition (Optical Society of America, 2007), paper OThP3.
- C. R. Doerr, L. W. Stulz, S. Chandrasekhar, and R. Pafchek, “Colorless Tunable Dispersion Compensator with 400-ps/nm Range Integrated With a Tunable Noise Filter,” IEEE Photon. Technol. Lett. 15(9), 1258–1260 (2003). [CrossRef]
- M. Shirasaki, and S. Cao, “Compensation of Chromatic Dispersion and Dispersion Slope Using a Virtually Imaged Phased Array,” in Proceedings of Optical Fiber Communication Conference and Exposition (Optical Society of America, 2001), paper TuS1.
- C. R. Doerr, “Polarization-Independent Tunable Dispersion Compensator Comprised of a Silica Arrayed Waveguide Grating and a Polymer Slab,” in Proceedings of Optical Fiber Communication Conference and Exposition (Optical Society of America, 2006), paper PDP9.
- D. M. Marom, C. R. Doerr, M. A. Cappuzzo, E. Y. Chen, A. Wong-Foy, L. T. Gomez, and S. Chandrasekhar, “Compact Colorless Tunable Dispersion Compensator With 1000-ps/nm Tuning Range for 40-Gb/s Data Rates,” J. Lightwave Technol. 24(1), 237–241 (2006). [CrossRef]
- G.-H. Lee, S. Xiao, and A. M. Weiner, “Optical Dispersion Compensator With >4000-ps/nm Tuning Range Using a Virtually Imaged Phased Array (VIPA) and Spatial Light Modulator (SLM),” IEEE Photon. Technol. Lett. 18(17), 1819–1821 (2006). [CrossRef]
- T. Sano, T. Iwashima, M. Kitayama, T. Kanie, M. Harumoto, M. Shigehara, H. Suganuma, and M. Nishimura, “Novel Multichannel Tunable Chromatic Dispersion Compensator Based on MEMS and Diffraction Grating,” IEEE Photon. Technol. Lett. 15(8), 1109–1110 (2003). [CrossRef]
- D. T. Neilson, R. Ryf, F. Pardo, V. A. Aksyuk, M. E. Simon, D. O. Lopez, D. M. Marom, and S. Chandrasekhar, “MEMS-Based Channelized Dispersion Compensator With Flat Passbands,” J. Lightwave Technol. 22(1), 101–105 (2004). [CrossRef]
- M. A. F. Roelens, S. Frisken, J. A. Bolger, D. Abakoumov, G. Baxter, S. Poole, and B. J. Eggleton, “Dispersion Trimming in a Reconfigurable Wavelength Selective Switch,” J. Lightwave Technol. 26(1), 73–78 (2008). [CrossRef]
- M. Shirasaki, A. N. Akhter, and C. Lin, “Virtually Imaged Phased Array with Graded Reflectivity,” IEEE Photon. Technol. Lett. 11(11), 1443–1445 (1999). [CrossRef]
- H. Takenouchi, T. Ishii, and T. Goh, “8 THz Bandwidth Dispersion-Slope Compensator Module for Multiband 4Gbit/s WDM Transmission Systems Using an AWG and Spatial Phase Filter,” Electron. Lett. 37(12), 777–778 (2001). [CrossRef]
- K. Seno, N. Ooba, K. Suzuki, K. Watanabe, M. Ishii, and S. Mino, “Tunable Dispersion Compensator Consisting of Simple Optics with Arrayed-Waveguide Grating and Flat Mirror,” in Proceedings of IEEE Lasers and Electro-Optics Society Annual Meeting, (Academic, Newport Beach, CA., 2008), WE1.
- K. Takada, M. Abe, T. Shibata, and K. Okamoto, “1-GHz-spaced 16-channel Arrayed-Waveguide Grating for a Wavelength Reference Standard in DWDM Network Systems,” J. Lightwave Technol. 20(5), 850–853 (2002). [CrossRef]
- K. Seno, K. Suzuki, K. Watanabe, N. Ooba, M. Ishii, and S. Mino, “Channel-by-Channel Tunable Optical Dispersion Compensator Consisting of Arrayed-Waveguide Grating and Liquid Crystal on Silicon,” in Proceedings of Optical Fiber Communication Conference and Exposition (Optical Society of America, 2008), paper OWP4.
- K. Okamoto, Fundamentals of Optical Waveguides, 2nd ed., (Elsevier, 2006), Chap. 9, Sec. 9.3.1.
- A. Sugita, A. Kaneko, K. Okamoto, M. Itoh, A. Himeno, and Y. Ohmori, KM Okamoto, A Itoh, Himeno, and Y Ohmori, “Very Low Insertion Loss Arrayed-Waveguide Grating with Vertically Tapered Waveguides,” IEEE Photon. Technol. Lett. 12(9), 1180–1182 (2000). [CrossRef]
- K. Suzuki, N. Ooba, M. Ishii, K. Seno, T. Shibata, and S. Mino, “40-Wavelength Channelized Tunable Optical Dispersion Compensator with Increased Bandwidth Consisting of Arrayed Waveguide Gratings and Liquid Crystal on Silicon,” in Proceedings of Optical Fiber Communication Conference and Exposition (Optical Society of America, 2009), paper OThB3.
- K. Seno, K. Suzuki, N. Ooba, T. Watanabe, M. Itoh, S. Mino, and T. Sakamoto, “50-Wavelength Channel-by-Channel Tunable Optical Dispersion Compensator Using Combination of Arrayed-Waveguide and Bulk Gratings,” in Proceedings of Optical Fiber Communication Conference and Exposition (Optical Society of America, 2010), paper OMT7.
- D. Sinefeld, C. R. Doerr, and D. M. Marom, “Photonic Spectral Processor Employing Two-Dimensional WDM Channel Separation and a Phase LCoS Modulator,” in Proceedings of Optical Fiber Communication Conference and Exposition (Optical Society of America, 2010), paper OMP5.

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