## Two-dimensional wavelength demultiplexing employing multilevel arrayed waveguides

Optics Express, Vol. 12, Issue 6, pp. 1084-1089 (2004)

http://dx.doi.org/10.1364/OPEX.12.001084

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### Abstract

Two-dimensional (2D) optical wavelength demultiplexing is demonstrated by employing multilevel arrayed waveguides as a 2D diffraction grating, named the 2D arrayed waveguide grating (2D-AWG). Since the monochromatic lightwave is diffracted by the 2D-AWG to a series of periodic spots with 2D diffraction orders in both x and y directions while the dispersion direction is never parallel to the x or y direction, we can obtain 2D wavelength demultiplexing exploiting diffraction orders of either the x or y direction. One of the two dispersion components is designed much larger than the other, and the correspondent spatial free spectral range component is set properly to ensure high diffraction efficiency. The input and output ports can also be designed based on the multilevel lightwave circuit (MLC), and their level planes can be tuned parallel to that of the MLC-based 2D-AWG, which makes it feasible to integrate the 2D-AWG with the input port and/or the output port. It provides a promising way to realize large-scale and high-density optical multiplexers/demultiplexers.

© 2004 Optical Society of America

## 1. Introduction

6. M. Smit and C. van Dam, “Phasar-based WDM-devices: principles, design and applications” IEEE J. Sel. Top. Quantum Electron. **2**, 236–250 (1996) [CrossRef]

3. C. Cremer, G. Ebbinghaus, G. Heise, R. Muller-Nawrath, M. Schienle, and L. Stoll. “Grating spectrograph in InGaAs/InP for dense wavelength division multiplexing” Appl. Phys. Lett. **59**, 627–629 (1991) [CrossRef]

4. J. He, B. Lamontagne, A. Delage, L. Erickson, M. Davies, and E. Kotels, “Monolithic integrated wavelength demultiplexer based on a waveguide Rowland circle grating in InGaAsP/InP,” J. Lightwave Technol. **16**, 631–638 (1998) [CrossRef]

5. M. Smit, “New focusing and dispersive planar component based on an optical phased array,” Electron. Lett. **24**, 385–386 (1988) [CrossRef]

7. Y. Hibino, “Recent advances in high-density and large-scale AWG multi/demultiplexers with higher index-contrast silica-based PLCs,” IEEE J. Sel. Top. Quantum Electron. **8**, 1090–1101 (2002) [CrossRef]

8. Y. Hida, Y. Hibino, T. Kitoh, Y. Inoue, M. Itoh, T. Shibata, and A. Himeno, “400-channel 25-GHz spacing arrayed-waveguide grating covering a full range of C- and L-bands,” in *OSA Trends in Optics and Photonics (TOPS) Vol. 54, Optical Fiber Communication Conference*, Technical Digest, Postconference Edition (Optical Society of America, Washington, DC, 2001), 3, pp. WB2-1–WB2-3

7. Y. Hibino, “Recent advances in high-density and large-scale AWG multi/demultiplexers with higher index-contrast silica-based PLCs,” IEEE J. Sel. Top. Quantum Electron. **8**, 1090–1101 (2002) [CrossRef]

9. K. Takada, M. Abe, T. Shibata, and K. Okamoto, “10-GHz-spaced 1010-channel tandem AWG filter consisting of one primary and ten secondary AWGs,” IEEE Photon. Technol. Lett. **13**, 577–578 (2001) [CrossRef]

## 2. Diffraction of 2D-AWG

*d*and

_{x}*d*, respectively.

_{y}*d*also indicates the level thickness of the 2D-AWG. The number of the waveguides in every level is assumed to be

_{y}*N*and the total number of the levels is

_{x}*N*. The length of the lth waveguide in the

_{y}*k*th level can be described as:

*L*

_{0}=

*L*

_{11}is the length of the first waveguide in the first level, and Δ

*L*

_{x}and Δ

*L*

_{y}are the length differences between every two adjacent waveguides in the same level and between two correspondent waveguides of two adjacent levels, respectively. Figure 1(c) shows the schematic waveguide layout of a waveguide level of the 2D-AWG. The input and output ports, as shown in Fig. 1(a), are used to couple light into or out of the optical system, respectively.

*x*=

_{l}*x*

_{1}+

*ld*(

_{x}*l*=1,2,…,

*N*) and

_{x}*y*=

_{l}*y*

_{1}+

*kd*(

_{y}*k*=1,2,…,

*N*) indicate the position of the

_{y}*l*th waveguide in the

*k*th level in the output end surface of the 2D-AWG,

*υ*is the frequency of the input light,

*c*is the light speed in vacuum,

*n*is the effective index of the optical waveguides,

_{eff}*L*is the focal length of the two lenses,

_{f}*C*is the normalized optical power in the

_{lk}*l*th waveguide in the

*k*th level, and

*G*(

*x,y*) is the far field of the optical waveguide mode of the individual waveguides of the 2D-AWG. Here it is assumed that

*L*>>

_{f}*d*and

_{x}*d*. With this equation, we can obtain that the input light at a certain frequency

_{y}*υ*is diffracted to a series of spots distributed in two dimensions in the focal plane, corresponding to two-dimensional diffraction orders (m

_{x}, m

_{y}) as shown in Fig. 2. These diffracted spots form a two-dimensional periodic pattern with a rectangular grid.

*r*

^{2}=

*x*

^{2}+

*y*

^{2},

*D*, respectively, and

_{λ}*m*th- and

_{x}*m*th-order diffractive central frequencies, respectively. As shown in Fig. 2, the dispersion direction is at an angle of

_{y}*θ*with respect to the x direction:

*m*th-order diffractive central frequency of

_{x}*υ*, spatial dispersion of

_{mx}*D*, and free spectral range (FSR) of

_{υx}*FSR*. Similarly, the y-direction correspondent waveguides in all levels form a series of y-direction 1D-AWGs, and have identical

_{υx}*m*th-order diffractive central frequency of

_{y}*υ*, spatial dispersion of

_{my}*D*, and FSR of

_{υy}*FSR*.

_{υy}## 3. Two-Dimensional Wavelength Demultiplexing

*m*or

_{x}*m*) are parallel to the y or x direction, respectively, we can always achieve two-dimensional wavelength demultiplexing employing a set of dispersion lines that have the same x-(or y-) direction diffraction order and continuous y-(or x-) direction diffraction orders. Figure 3 presents an output scheme for two-dimensional wavelength multiplexing, in which the diffraction lines have the same y-direction diffraction order and continuous x-direction diffraction orders.

_{y}*φ*with respect to the x direction:

*υ*(

_{i,j}*i*=1, 2, …,

*N*=1, 2, …,

_{u, j}*N*), as shown in Fig. 3, can be written as:

_{v}*N*is the total number of the designed channels along every dispersion line,

_{u}*N*is the total number of the dispersion lines, and Δ

_{v}*υ*is the designed frequency-based channel spacing. Then it can be derived that the light at the frequency

*m*)th,

_{x}-j*m*th)-order diffracted spot at the position (

_{y}*m*

_{x-j}+1)th,

*m*th)-order diffracted spot at the position (

_{y}*N*×

_{u}*N*two-dimensional wavelength demultiplexing with the fixed channel spacing of Δ

_{v}*υ*.

*G*(

*x,y*) in Eq. (2) and the angle

*φ*are important parameters to control the diffraction efficiency of the 2D-AWG-based optical DEMUX.

## 4. Demultiplexing Scheme for MLC-Based Integration

*FSR*is designed equal to

_{υx}*N*Δ

_{u}*υ, φ*will be 90°, given by Eq. (10), and the v direction will be in the y direction. Similarly, to tune the v-direction to be in the x-direction, we can choose a set of the diffraction lines that have the same x-direction diffraction order and continuous y-direction diffraction orders and set

*FSR*equal to

_{υy}*N*Δ

_{u}*υ*. A 2D-AWG-based optical DEMUX for MLC-based integration was designed and simulated, and its wavelength-demultiplexed two-dimensional output is shown in Fig. 5, which covers the wavelength band from 1523 nm to 1563 nm and has a channel spacing of 50 GHz.

11. S. Nolte, M. Will, J. Burghoff, and A. Tuennermann, “Femtosecond waveguide writing: a new avenue to three-dimensional integrated optics,” Appl. Phys. A-Mater. **77**, 109–111 (2003) [CrossRef]

12. Y. Sun, X. Jiang, J. Yang, Y. Tang, and M. Wang, “Experimental demonstration of 2-D MMI optical power splitter,” Chinese Phys. Lett. **20**, 2182–2184 (2003) [CrossRef]

## 5. Conclusion

## Acknowledgments

## References and links

1. | J. Laude and K. Lange, “Dense wavelength division multiplexer and routers using diffraction grating,” in |

2. | X. Deng, J. Yang, J. Zou, and R. T. Chen, “Design of hybrid free-space wavelength-division multiplexers for integration,” in |

3. | C. Cremer, G. Ebbinghaus, G. Heise, R. Muller-Nawrath, M. Schienle, and L. Stoll. “Grating spectrograph in InGaAs/InP for dense wavelength division multiplexing” Appl. Phys. Lett. |

4. | J. He, B. Lamontagne, A. Delage, L. Erickson, M. Davies, and E. Kotels, “Monolithic integrated wavelength demultiplexer based on a waveguide Rowland circle grating in InGaAsP/InP,” J. Lightwave Technol. |

5. | M. Smit, “New focusing and dispersive planar component based on an optical phased array,” Electron. Lett. |

6. | M. Smit and C. van Dam, “Phasar-based WDM-devices: principles, design and applications” IEEE J. Sel. Top. Quantum Electron. |

7. | Y. Hibino, “Recent advances in high-density and large-scale AWG multi/demultiplexers with higher index-contrast silica-based PLCs,” IEEE J. Sel. Top. Quantum Electron. |

8. | Y. Hida, Y. Hibino, T. Kitoh, Y. Inoue, M. Itoh, T. Shibata, and A. Himeno, “400-channel 25-GHz spacing arrayed-waveguide grating covering a full range of C- and L-bands,” in |

9. | K. Takada, M. Abe, T. Shibata, and K. Okamoto, “10-GHz-spaced 1010-channel tandem AWG filter consisting of one primary and ten secondary AWGs,” IEEE Photon. Technol. Lett. |

10. | C. Wachter, Th. Hennig, Th. Bauer, A. Brauer, and W. Karthe, “Integrated optics toward third dimension,” in |

11. | S. Nolte, M. Will, J. Burghoff, and A. Tuennermann, “Femtosecond waveguide writing: a new avenue to three-dimensional integrated optics,” Appl. Phys. A-Mater. |

12. | Y. Sun, X. Jiang, J. Yang, Y. Tang, and M. Wang, “Experimental demonstration of 2-D MMI optical power splitter,” Chinese Phys. Lett. |

**OCIS Codes**

(050.1940) Diffraction and gratings : Diffraction

(050.1950) Diffraction and gratings : Diffraction gratings

(060.1810) Fiber optics and optical communications : Buffers, couplers, routers, switches, and multiplexers

(130.2790) Integrated optics : Guided waves

(130.3120) Integrated optics : Integrated optics devices

(230.7370) Optical devices : Waveguides

**ToC Category:**

Research Papers

**History**

Original Manuscript: February 13, 2004

Revised Manuscript: March 11, 2004

Published: March 22, 2004

**Citation**

Jianyi Yang, Xiaoqing Jiang, Minghua Wang, and Yuelin Wang, "Two-dimensional wavelength demultiplexing employing multilevel arrayed waveguides," Opt. Express **12**, 1084-1089 (2004)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-12-6-1084

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### References

- J. Laude and K. Lange, �??�??Dense wavelength division multiplexer and routers using diffraction grating,�??�?? in Proceedings of 1999 National Fiber Optic Engineers Conference (Telcordia Technologies, Piscataway, New Jersey, 1999), 1, pp.83-86
- X. Deng, J. Yang, J. Zou, and R. T. Chen, "Design of hybrid free-space wavelength-division multiplexers for integration," in WDM and Photonic Switching Devices for Network Applications III, Proc. SPIE 4653, paper 25, 153-160 (2002)
- C. Cremer, G. Ebbinghaus, G. Heise, R. Muller-Nawrath, M. Schienle, and L. Stoll. �??Grating spectrograph in InGaAs/InP for dense wavelength division multiplexing�?? Appl. Phys. Lett. 59, 627-629 (1991) [CrossRef]
- J. He, B. Lamontagne, A. Delage, L. Erickson, M. Davies, E. Kotels, �??Monolithic integrated wavelength demultiplexer based on a waveguide Rowland circle grating in InGaAsP/InP,�?? J. Lightwave Technol. 16, 631-638 (1998) [CrossRef]
- M. Smit, �??New focusing and dispersive planar component based on an optical phased array,�?? Electron. Lett. 24, 385-386 (1988) [CrossRef]
- M. Smit, C. van Dam, �??Phasar-based WDM-devices: principles, design and applications�?? IEEE J. Sel. Top. Quantum Electron. 2, 236-250 (1996) [CrossRef]
- Y. Hibino, �??Recent advances in high-density and large-scale AWG multi/demultiplexers with higher index-contrast silica-based PLCs,�?? IEEE J. Sel. Top. Quantum Electron. 8, 1090-1101 (2002) [CrossRef]
- Y. Hida, Y. Hibino, T. Kitoh, Y. Inoue, M. Itoh, T. Shibata, and A. Himeno, "400-channel 25-GHz spacing arrayed-waveguide grating covering a full range of C- and L-bands," in OSA Trends in Optics and Photonics (TOPS) Vol. 54, Optical Fiber Communication Conference, Technical Digest, Postconference Edition (Optical Society of America, Washington, DC, 2001), 3, pp. WB2-1 �?? WB2-3
- K. Takada, M. Abe, T. Shibata, K. Okamoto, �??10-GHz-spaced 1010-channel tandem AWG filter consisting of one primary and ten secondary AWGs,�?? IEEE Photon. Technol. Lett. 13, 577 �??578 (2001) [CrossRef]
- C. Wachter, Th. Hennig, Th. Bauer, A. Brauer, W. Karthe, �??Integrated optics toward third dimension,�?? in Integrated Optic Devices II, G. Righini, S. Iraj Najafi, and B. Jalali, eds., Proc. SPIE 3278, 102�??111 (1998)
- S. Nolte, M. Will, J. Burghoff, A. Tuennermann, �??Femtosecond waveguide writing: a new avenue to three-dimensional integrated optics,�?? Appl. Phys. A - Mater. 77, 109-111 (2003) [CrossRef]
- Y. Sun, X. Jiang, J. Yang, Y. Tang, M. Wang, �??Experimental demonstration of 2-D MMI optical power splitter,�?? Chinese Phys. Lett. 20, 2182-2184 (2003) [CrossRef]

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