## 400-Channel 25-GHz-spacing SOI-based planar waveguide demultiplexer employing a concave grating across C- and L-bands

Optics Express, Vol. 18, Issue 6, pp. 6108-6115 (2010)

http://dx.doi.org/10.1364/OE.18.006108

Acrobat PDF (480 KB)

### Abstract

The 400-channel 25-GHz-spacing SOI-based planar waveguide demultiplexer employing a concave grating across C- and L-bands is proposed in this paper. For the high polarization dependence, the waveguides are designed for supporting the TE mode only. To reduce the spherical aberration of the concave grating, the values of the maximum half divergent angle of the light source and minimum effective half width of the fundamental mode of the ridge waveguide are determined. We use a design example to show the spectral characteristics of the proposed design. Simulation results show that the proposed design provides better spectral characteristics and smaller die size.

© 2010 Optical Society of America

## 1. Introduction

2. K. Takada, M. Ade, T. Shibita, and K. Okamoto, “A 25-GHz-spaced 1080-channel tandem multi/demultiplexer covering the S-, C-, and L-bands using an arrayed-waveguide grating with Gaussian passbands as primary filter,” IEEE Photon. Technol. Lett. **14**(5), 648–650 (2002). [CrossRef]

7. K. A. McGreer, “Theory of concave gratings based on a recursive definition of facet positions,” Appl. Opt. **35**(30), 5904–5910 (1996). [CrossRef] [PubMed]

## 2. Design and Simulation

7. K. A. McGreer, “Theory of concave gratings based on a recursive definition of facet positions,” Appl. Opt. **35**(30), 5904–5910 (1996). [CrossRef] [PubMed]

*μ*m-thick buried oxide layer, and a 500-

*μ*m-thick silicon substrate while the light is transmitted in the top silicon layer. Therefore, the top silicon layer is the core layer and the buried oxide layer is the cladding layer. The refractive indices of the silicon and oxide materials, considered in this paper, are 3.50 and 1.45, respectively, and the cross-sectional view of the ridge waveguide (input and output waveguides) is shown in Fig. 2. The width and thickness of the core layer for the ridge waveguide are denoted as

*w*

_{si}and

*t*

_{si}, respectively. Since the effective indices of the TE and TM modes are highly polarization-dependent, the waveguide structures are designed for supporting the TE mode only without the design of the polarization compensator [5

5. D. Dai and S. He, “Design of a polarization-insensitive arrayed waveguide grating demultiplexer based on silicon photonic wires,” Opt. Lett. **31**(13), 1988–1990 (2006). [CrossRef] [PubMed]

8. J.-J. He, E. S. Koteles, B. Lamontagne, L. Erickson, A. Delâge, and M. Davies, “Integrated Polarization Compensator for WDM Waveguide Demultiplexers,” IEEE Photon. Technol. Lett. **11**(2), 321–322 (1999). [CrossRef]

*t*

_{si}of the core layer for the ridge and slab waveguides are specifically designed for the low propagation loss of the TE mode but high propagation loss of the TM mode.

*α*is the incident angle of the light at the grating pole,

*β*is the diffraction angle of the light at the grating pole,

*R*is the effective radius of the grating curvature,

*r*

_{1,0}is the distance between A and P, and

*r*

_{2,0}is the distance between A and Q. For the triangles ACX and BPX, we can obtain

*δγ*, the arc length AB can be approximated as the tangent length

*δγ*,

*δσ*, and

*δρ*are small, they can be expressed as

*n*

_{eff}is the effective index in the slab waveguide,

*d*is the grating period along the grating chord,

*m*is the diffraction order, and

*λ*is the wavelength of the light. After we differentiate Eq. (7), we can obtain

*δγ*

_{max}must be determined so we define the deviation function

*f*(

*δγ*) of the approximation as [14]

*f*(

*δγ*) lower than 0.1 % the arc angle

*δγ*must be lower than 8.8° as shown in Fig. 4. For simplification, the maximum arc angle

*δγ*

_{max}, the maximum half central angle of the grating curvature, is chosen as 8.0° and then maximum

*δσ*

_{max}, the maximum half divergent angle of the light source as [13]

*λ*

_{0}is chosen as 1570 nm. By using the effective-index method [15], Fig. 5 shows the propagation losses due to the leakages to the silicon substrate versus the thickness

*t*

_{si}of the core layer (top silicon layer) for both modes at a center wavelength of 1570 nm when the thickness of the cladding layer (buried oxide layer) is chosen as 1

*μ*m. It shows that when the thickness

*t*

_{si}of the core layer is lower than 220 nm, the propagation loss of the TM mode dramatically increases from about 9.0 dB/cm. So the thickness

*t*

_{si}is chosen as 220 nm for supporting the TE mode only as in [10

10. J. Brouckaert, W. Bogaerts, P. Dumon, D. V. Thourhout, and R. Baets, “Planar concave grating demultiplexer fabricated on a nanophotonic silicon-on-insulator platform,” J. Lightwave Technol. **25**(5), 1269–1275 (2007). [CrossRef]

16. W. Bogaerts, R. Baets, P. Dumon, V. Wiaux, S. Beckx, D. Taillaert, B. Luyssaert, J. V. Campenhout, P. Bienstman, and D. V. Thourhout, “Nanophotonic waveguides in silicon-on-insulator fabricated with CMOS technology,” J. Lightwave Technol. **23**(1), 401–412 (2005). [CrossRef]

*w*

_{si}of the core layer must be smaller than 500 nm [16

16. W. Bogaerts, R. Baets, P. Dumon, V. Wiaux, S. Beckx, D. Taillaert, B. Luyssaert, J. V. Campenhout, P. Bienstman, and D. V. Thourhout, “Nanophotonic waveguides in silicon-on-insulator fabricated with CMOS technology,” J. Lightwave Technol. **23**(1), 401–412 (2005). [CrossRef]

*w*

_{si}is chosen as 500 nm as in [10

10. J. Brouckaert, W. Bogaerts, P. Dumon, D. V. Thourhout, and R. Baets, “Planar concave grating demultiplexer fabricated on a nanophotonic silicon-on-insulator platform,” J. Lightwave Technol. **25**(5), 1269–1275 (2007). [CrossRef]

16. W. Bogaerts, R. Baets, P. Dumon, V. Wiaux, S. Beckx, D. Taillaert, B. Luyssaert, J. V. Campenhout, P. Bienstman, and D. V. Thourhout, “Nanophotonic waveguides in silicon-on-insulator fabricated with CMOS technology,” J. Lightwave Technol. **23**(1), 401–412 (2005). [CrossRef]

*w*

_{0}of the fundamental mode of the ridge waveguide along the

*x*′-axis can be obtained from the Beam-PROP software (RSoft, Inc.) as 237 nm. The 500-nm-wide silicon photonic wire waveguides with a bending radius of few micrometers allow further reduce the die size [10

10. J. Brouckaert, W. Bogaerts, P. Dumon, D. V. Thourhout, and R. Baets, “Planar concave grating demultiplexer fabricated on a nanophotonic silicon-on-insulator platform,” J. Lightwave Technol. **25**(5), 1269–1275 (2007). [CrossRef]

**23**(1), 401–412 (2005). [CrossRef]

*n*

_{eff,TE0}of the fundamental TE mode in the slab waveguide can be obtained as 2.85 with the negligible propagation loss.

*d*is large as compared to the wavelength of the light, so

*d*is chosen as 10

*μ*m. For the FSR larger than the bandwidth across the C- and L-bands, the diffraction order

*m*is chosen as 18 and the FSR (=

*λ*

_{0}/

*m*) can be obtained as 87 nm as in [3

3. 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**(6), 1090–1101 (2002). [CrossRef]

*α*of the input waveguide at the grating pole is chosen as 32.0°. When

*n*

_{eff,TE0},

*d*,

*α*,

*m*, and

*λ*

_{0}are determined, the diffraction angle

*β*

_{0}of the design output waveguide at the grating pole can be obtained from Eq. (7) as 27.5°. For the small die size with the acceptable crosstalk between adjacent channels, the distance

*r*

_{1,0}and

*r*

_{2,0}are chosen as 45 mm (

*r*

_{1,0}=

*r*

_{2,0}= 45 mm). When the grating pole is chosen at the origin of the coordinates, the coordinate positions, (

*a*

_{1},

*b*

_{1}) and (

*a*

_{2},

*b*

_{2}), of the ends of the input and center output waveguides can be obtained as (

*r*

_{1,0}· sin

*α*,

*r*

_{1,0}· cos

*α*) and (

*r*

_{2,0}· sin

*β*

_{0},

*r*

_{2,0}· cos

*β*

_{0}), respectively, as shown in Fig. 6. For the design of the concave grating, the grating period

*d*is constant along the grating chord. When the

*x*-axis coordinate position

*x*of the center of the

_{i}*i*th grating facet is chosen as

*x*=

_{i}*i*·

*d*, the

*y*-axis coordinate position

*y*of the center of the

_{i}*i*th grating facet can be obtained from the root of the constraint function [7

7. K. A. McGreer, “Theory of concave gratings based on a recursive definition of facet positions,” Appl. Opt. **35**(30), 5904–5910 (1996). [CrossRef] [PubMed]

*α*,

*β*

_{0},

*r*

_{1,0}, and

*r*

_{2,0}are determined, the effective radius

*R*of the grating curvature can then be obtained from Eq. (9) as 51.87 mm. Then the maximum arc angle

*δσ*

_{max}can be obtained from Eq. (12) as 7.8°. According to the theory of the guided wave [15], the half angle

*δσ*of the Gaussian beam divergence at 1/

*e*amplitude on the

*x*′

*y*′-plane can be expressed as

*w*

_{0,min}can be obtained as 1.287

*μ*m. Therefore, we need a spot size converters to change the effective half width

*w*

_{0}from 237 nm to 1.287

*μ*m. For a 2-

*μ*m-wide 40-nm-shallow-etched waveguide, the effective half width

*w*′

_{0}of the fundamental mode along the

*x*′- or

*x*″-axis can be obtained from the BeamPROP software (RSoft, Inc.) as 1.287

*μ*m. The spot size converters can be achieved by a two-step etch process at the ends of the input and output waveguides as shown in Fig. 7. It can also reduce the transition losses between the ridge waveguide and slab waveguide [10

**25**(5), 1269–1275 (2007). [CrossRef]

*δσ*

_{max}of 7.8°, the total illuminated grating periods

*N*can be obtained as 1446. Figure 8 shows the simulated TE-mode spectral responses of 400 channels with a channel spacing of 25 GHz (0.2 nm), which are obtained from the overlap integral of the image field at the end of the output waveguide and the fundamental mode field of the output waveguide [9

9. Z. Shi and S. He, “A three-focal-point method for the optimal design of a flat-top planar waveguide demultiplexer,” IEEE J. Sel. Top. Quantum Electron. **8**(6), 1179–1185 (2002). [CrossRef]

11. C.-T. Lin, Y.-T. Huang, and J.-Y. Huang, “Quantitative analysis of a flat-top planar waveguide demultiplexer,” J. Lightwave Technol. **27**(5), 552–558 (2009). [CrossRef]

3. 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**(6), 1090–1101 (2002). [CrossRef]

^{2}, while that of the demultiplexer employing an AWG in [3

3. 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**(6), 1090–1101 (2002). [CrossRef]

^{2}. So the proposed design provides an alternative to a planar waveguide demultiplexer with higher spectral resolution, lower crosstalk, and smaller die size compared with those in [3

**8**(6), 1090–1101 (2002). [CrossRef]

## 3. Conclusion

^{2}. The proposed design provides an alternative to a planar waveguide demultiplexer with higher spectral resolution, lower crosstalk, and smaller die size.

## References and links

1. | S. V. Kartalopoulos, |

2. | K. Takada, M. Ade, T. Shibita, and K. Okamoto, “A 25-GHz-spaced 1080-channel tandem multi/demultiplexer covering the S-, C-, and L-bands using an arrayed-waveguide grating with Gaussian passbands as primary filter,” IEEE Photon. Technol. Lett. |

3. | 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. |

4. | A. Kaneko, T. Goh, H. Yamada, T. Tanaka, and I. Ogawa, “Design and applications of silica-based planar lightwave circuits,” IEEE J. Sel. Top. Quantum Electron. |

5. | D. Dai and S. He, “Design of a polarization-insensitive arrayed waveguide grating demultiplexer based on silicon photonic wires,” Opt. Lett. |

6. | K. Maru and Y. Abe, “Low-loss, flat-passband and athermal arrayed-waveguide grating multi/demultiplexer,” Opt. Express |

7. | K. A. McGreer, “Theory of concave gratings based on a recursive definition of facet positions,” Appl. Opt. |

8. | J.-J. He, E. S. Koteles, B. Lamontagne, L. Erickson, A. Delâge, and M. Davies, “Integrated Polarization Compensator for WDM Waveguide Demultiplexers,” IEEE Photon. Technol. Lett. |

9. | Z. Shi and S. He, “A three-focal-point method for the optimal design of a flat-top planar waveguide demultiplexer,” IEEE J. Sel. Top. Quantum Electron. |

10. | J. Brouckaert, W. Bogaerts, P. Dumon, D. V. Thourhout, and R. Baets, “Planar concave grating demultiplexer fabricated on a nanophotonic silicon-on-insulator platform,” J. Lightwave Technol. |

11. | C.-T. Lin, Y.-T. Huang, and J.-Y. Huang, “Quantitative analysis of a flat-top planar waveguide demultiplexer,” J. Lightwave Technol. |

12. | C.-T. Lin, Y.-T. Huang, J.-Y. Huang, and H.-H. Lin, “Integrated planar waveguide concave gratings for high density WDM systems,” in |

13. | M. C. Hutley, |

14. | C.-T. Lin, “A Study on Design and Fabrication of Micro Concave Grating,” Master’s thesis, Institute of Electro-physics, National Chiao Tung University, Hsinchu 30010, Taiwan (2002). |

15. | H. Kogelnik, “Theory of Optical Waveguides,” in |

16. | W. Bogaerts, R. Baets, P. Dumon, V. Wiaux, S. Beckx, D. Taillaert, B. Luyssaert, J. V. Campenhout, P. Bienstman, and D. V. Thourhout, “Nanophotonic waveguides in silicon-on-insulator fabricated with CMOS technology,” J. Lightwave Technol. |

**OCIS Codes**

(050.1950) Diffraction and gratings : Diffraction gratings

(060.4230) Fiber optics and optical communications : Multiplexing

(060.4510) Fiber optics and optical communications : Optical communications

(130.2790) Integrated optics : Guided waves

(130.3120) Integrated optics : Integrated optics devices

(230.7370) Optical devices : Waveguides

**ToC Category:**

Integrated Optics

**History**

Original Manuscript: January 5, 2010

Revised Manuscript: March 1, 2010

Manuscript Accepted: March 3, 2010

Published: March 11, 2010

**Citation**

Chun-Ting Lin, "400-Channel 25-GHz-spacing SOI-based planar waveguide demultiplexer employing a concave grating across Cand L-bands," Opt. Express **18**, 6108-6115 (2010)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-6-6108

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### References

- S. V. Kartalopoulos, Introduction to DWDM Technology (IEEE Press, New York, 2000).
- K. Takada, M. Ade, T. Shibita, and K. Okamoto, "A 25-GHz-spaced 1080-channel tandem multi/demultiplexer covering the S-, C-, and L-bands using an arrayed-waveguide grating with Gaussian passbands as primary filter," IEEE Photon. Technol. Lett. 14(5), 648-650 (2002). [CrossRef]
- Y. Hibino, "Recent advances in high-density and large-scale AWG multi/demultiplexers with higher indexcontrast silica-based PLCs," IEEE J. Sel. Top. Quantum Electron 8(6), 1090-1101 (2002). [CrossRef]
- A. Kaneko, T. Goh, H. Yamada, T. Tanaka, and I. Ogawa, "Design and applications of silica-based planar lightwave circuits," IEEE J. Sel. Top. Quantum Electron 5(5), 1227-1236 (1999). [CrossRef]
- D. Dai and S. He, "Design of a polarization-insensitive arrayed waveguide grating demultiplexer based on silicon photonic wires," Opt. Lett. 31(13), 1988-1990 (2006). [CrossRef] [PubMed]
- K. Maru and Y. Abe, "Low-loss, flat-passband and athermal arrayed-waveguide grating multi/demultiplexer," Opt. Express 15(26), 18351-18356 (2007). [CrossRef] [PubMed]
- K. A. McGreer, "Theory of concave gratings based on a recursive definition of facet positions," Appl. Opt. 35(30), 5904-5910 (1996). [CrossRef] [PubMed]
- J.-J. He, E. S. Koteles, B. Lamontagne, L. Erickson, A. Delˆage, and M. Davies, "Integrated Polarization Compensator for WDM Waveguide Demultiplexers," IEEE Photon. Technol. Lett. 11(2), 321-322 (1999). [CrossRef]
- Z. Shi and S. He, "A three-focal-point method for the optimal design of a flat-top planar waveguide demultiplexer," IEEE J. Sel. Top. Quantum Electron 8(6), 1179-1185 (2002). [CrossRef]
- J. Brouckaert, W. Bogaerts, P. Dumon, D. V. Thourhout, and R. Baets, "Planar concave grating demultiplexer fabricated on a nanophotonic silicon-on-insulator platform," J. Lightwave Technol. 25(5), 1269-1275 (2007). [CrossRef]
- C.-T. Lin, Y.-T. Huang, and J.-Y. Huang, "Quantitative analysis of a flat-top planar waveguide demultiplexer," J. Lightwave Technol. 27(5), 552-558 (2009). [CrossRef]
- C.-T. Lin, Y.-T. Huang, J.-Y. Huang, and H.-H. Lin, "Integrated planar waveguide concave gratings for high density WDM systems," in 2005 Optical Communications Systems and Networks (OCSN 2005), pp. 98-102 (Banff, Alberta, Canada, 2005).
- M. C. Hutley, Diffraction Gratings (Academic Press, London, 1982).
- C.-T. Lin, "A Study on Design and Fabrication of Micro Concave Grating," Master’s thesis, Institute of Electrophysics, National Chiao Tung University, Hsinchu 30010, Taiwan (2002).
- H. Kogelnik, "Theory of OpticalWaveguides," in Guided-Wave Optoelectronics, T. Tamir, ed., (Springer-Verlag, Berlin, Germany, 1990) Chap. 2.
- W. Bogaerts, R. Baets, P. Dumon, V. Wiaux, S. Beckx, D. Taillaert, B. Luyssaert, J. V. Campenhout, P. Bienstman, and D. V. Thourhout, "Nanophotonic waveguides in silicon-on-insulator fabricated with CMOS technology," J. Lightwave Technol. 23(1), 401-412 (2005). [CrossRef]

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