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Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 18, Iss. 6 — Mar. 15, 2010
  • pp: 6108–6115
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400-Channel 25-GHz-spacing SOI-based planar waveguide demultiplexer employing a concave grating across C- and L-bands

Chun-Ting Lin  »View Author Affiliations


Optics Express, Vol. 18, Issue 6, pp. 6108-6115 (2010)
http://dx.doi.org/10.1364/OE.18.006108


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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

With the explosive growth of Internet, the copper coaxial cable can not meet the increasing demand for the bandwidth while the optical fiber can provide greater bandwidth. In a wavelength division multiplexing (WDM) system, each wavelength is treated as a separate channel and it is possible to increase the bandwidth by increasing the channel number rather than increasing the bit rate. When the channel spacing is less than 100 GHz (0.8 nm), the technology is well know as dense wavelength division multiplexing (DWDM) [1

1. S. V. Kartalopoulos, Introduction to DWDM Technology (IEEE Press, New York, 2000).

]. International Telecommunication Union Telecommunication (ITU-T) Standardization Sector recommends several bands for lower transmission losses in a silica-based single-mode fiber, including S-, C-, and L-bands [1–3

1. S. V. Kartalopoulos, Introduction to DWDM Technology (IEEE Press, New York, 2000).

]. The maximum channel number in these bands depends greatly on what kinds of the demultiplexers are used. In recent years, there has been considerable interest in developing integrated planar waveguide demultiplexers, such as arrayed waveguide gratings (AWGs) [2–6

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]

] and planar waveguide concave gratings [7–11

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]

], due to the advantages of low insertion loss, low crosstalk, high possibilities of mass production, and high spectral resolution. However, AWGs has inherent limits due to larger die size, lower free spectral range (FSR), and greater sensitivity to the environment. The purpose of this research us to design a planar waveguide demultiplexer employing a concave grating. This research may provide an alternative to a planar waveguide demultiplexer with the high channel number and narrow channel spacing in an optical communication system.

2. Design and Simulation

In this paper, we do the research on a planar waveguide concave grating demultiplexer which is designed on a silicon-on-insulator (SOI) wafer. The concave grating is based on the recursive definition of the centers of the facet positions, which was first proposed by McGreer in 1996 [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]

]. There are three types of the concave gratings in the literature including Rowland circle, Taylor expansion, and recursive definition types, respectively [12

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 2005 Optical Communications Systems and Networks (OCSN 2005), pp. 98–102 (Banff, Alberta, Canada, 2005).

]. Simulation results showed that the recursive definition type suffers from less spherical aberration than the other two types. The schematic figure of the planar waveguide demultiplexer employing a concave grating is shown in Fig. 1. The single-mode SOI wafer consists of a 200-to-300-nm-thick top silicon layer, and a 1-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 wsi and tsi, 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

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]

]. So the thicknesses tsi 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.

Fig. 1. Schematic figure of the planar waveguide demultiplexer employing a concave grating.
Fig. 2. Cross-sectional view of the ridge waveguide.

Fig. 3 shows the light diffracted and focused by the concave grating, where A is the grating pole, B is the boundary of the concave grating on one side, C is the center of the grating curvature, P is the position of the light source, Q is the position of the focal point, 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, r1,0 is the distance between A and P, and r2,0 is the distance between A and Q. For the triangles ACX and BPX, we can obtain

α+δγ=α+δα+δσ,
(1)

and

δα=δγδσ.
(2)

Similarly, we can obtain

δβ=δγδρ.
(3)

For the small arc angle δγ, the arc length AB can be approximated as the tangent length AB¯. When the arc angles δγ, δσ, and δρ are small, they can be expressed as

δα=ABR¯,
(4)
Fig. 3. Schematic figure of the light diffracted and focused by the concave grating.
δσ=AB¯cosαr1,0,
(5)
δρ=AB¯cosβr2,0.
(6)

The diffraction equation of the grating can be expressed as

neff·d(sinα+sinβ)=,
(7)

where neff 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

cosαδα+cosβδβ=0.
(8)

Taking Eqs. (2) to (6) into Eq. (8), we can obtain

cosαRcos2αr1,0+cosβRcos2βr2,0=0,
(9)

which is the so-called focal equation of the concave grating [13

13. M. C. Hutley, Diffraction Gratings (Academic Press, London, 1982).

]. To reduce the spherical aberration of the concave grating, the maximum arc angle δγmax must be determined so we define the deviation function f(δγ) of the approximation as [14

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).

]

f(δγ)=ABAB¯AB=R·δγ2R·sin(δγ2)R·δγ.
(10)

Simulation results show that for the value of 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 δγmax, the maximum half central angle of the grating curvature, is chosen as 8.0° and then maximum AB¯max can be obtained from Eq. (4) as

AB¯max=R·8.0°.
(11)

Taking Eq. (11) into Eq. (5), we can obtain the maximum arc angle δσmax, the maximum half divergent angle of the light source as [13

13. M. C. Hutley, Diffraction Gratings (Academic Press, London, 1982).

]

δσmax=R·8.0°·cosαr1,0.
(12)
Fig. 4. Deviation function of the approximation.

The scalar diffraction theory is valid when the grating period 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 (= λ0/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]

]. For no overlaps of the positions of the input waveguide and all the output waveguides, the incident angle α of the input waveguide at the grating pole is chosen as 32.0°. When neff,TE0, d, α, m, and λ0 are determined, the diffraction angle β0 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 r1,0 and r2,0 are chosen as 45 mm (r1,0 = r2,0 = 45 mm). When the grating pole is chosen at the origin of the coordinates, the coordinate positions, (a1, b1) and (a2, b2), of the ends of the input and center output waveguides can be obtained as (r1,0 · sinα, r1,0 · cosα) and (r2,0 · sinβ0, r2,0 · cosβ0), 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 xi of the center of the ith grating facet is chosen as xi = i·d, the y-axis coordinate position yi of the center of the ith 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]

]. When α, β0, r1,0, and r2,0 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 δσmax can be obtained from Eq. (12) as 7.8°. According to the theory of the guided wave [15

15. H. Kogelnik, “Theory of Optical Waveguides,” in Guided-Wave Optoelectronics, T. Tamir, ed., chap. 2 (Springer-Verlag, Berlin, Germany, 1990).

], the half angle δσ of the Gaussian beam divergence at 1/e amplitude on the xy′-plane can be expressed as

δσ=λ0πneffw0.
(13)
Fig. 5. Propagation losses versus the thickness tsi of the core layer at a center wavelength of 1570 nm.
Fig. 6. Schematic figure of the light propagating in the slab waveguide and then diffracted by the concave grating.

From Eqs. (12) and (13), the minimum effective half width w0,min can be obtained as 1.287 μ m. Therefore, we need a spot size converters to change the effective half width w0 from 237 nm to 1.287 μ m. For a 2-μ m-wide 40-nm-shallow-etched waveguide, the effective half width w0 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

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]

].

Fig. 7. Cross-sectional views of the ridge waveguide and the spot size converter.

For a maximum arc angle δσmax 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

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]

]. The simulated insertion losses of 400 channels, which include the propagation loss, undesired-order loss, and the excess loss, range from 6.20 to 6.75 dB. In our case, the propagation loss of the TE mode is negligible. The undesired-order loss of the center channel, which comes from the diffraction of the light into the undesired adjacent four orders, is 5.92 dB. The excess loss of the center channel, which comes from the amplitude mismatch between the image field at the end of the output waveguide and the fundamental mode field of the output waveguide, is 0.28 dB. The crosstalk between adjacent channels is defined as the maximum signal received from adjacent channels within -1-dB passband bandwidth. For the same center wavelength, diffraction order, channel spacing, and channel number, the worst crosstalk in our case is -30 dB, while that 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]

] is -20 dB. And the die size of the proposed demultiplexer employing a concave grating is 41 × 32 mm2, 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]

] is 124 × 64 mm2. 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

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]

].

Fig. 8. Spectral responses of 400 channel with a channel spacing of 25 GHz (0.2 nm).

3. Conclusion

In this paper, 400-channel 25-GHz spacing SOI-based planar waveguide demultiplexer employing a concave grating across C- and L-bands is proposed. For the high polarization dependence, the thickness and width of the ridge waveguide are specifically designed for supporting the TE mode only. To reduce the spherical aberration of the concave grating, we determine 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. The spot size converters are used at the end of the input and output waveguides to change the effective half width of the fundamental mode of the ridge waveguide. For a design example, simulation results show that the proposed design provides a worst crosstalk between adjacent channels of -30 dB and a remarkable die size of 41 × 32 mm2. 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, Introduction to DWDM Technology (IEEE Press, New York, 2000).

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]

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]

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(5), 1227–1236 (1999). [CrossRef]

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]

6.

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]

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]

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]

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]

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]

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]

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 2005 Optical Communications Systems and Networks (OCSN 2005), pp. 98–102 (Banff, Alberta, Canada, 2005).

13.

M. C. Hutley, Diffraction Gratings (Academic Press, London, 1982).

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 Guided-Wave Optoelectronics, T. Tamir, ed., chap. 2 (Springer-Verlag, Berlin, Germany, 1990).

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]

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

  1. S. V. Kartalopoulos, Introduction to DWDM Technology (IEEE Press, New York, 2000).
  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]
  3. 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]
  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(5), 1227-1236 (1999). [CrossRef]
  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]
  6. 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]
  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]
  8. 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]
  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]
  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]
  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]
  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 2005 Optical Communications Systems and Networks (OCSN 2005), pp. 98-102 (Banff, Alberta, Canada, 2005).
  13. M. C. Hutley, Diffraction Gratings (Academic Press, London, 1982).
  14. 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).
  15. H. Kogelnik, "Theory of OpticalWaveguides," in Guided-Wave Optoelectronics, T. Tamir, ed., (Springer-Verlag, Berlin, Germany, 1990) Chap. 2.
  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]

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