## Design of guided-wave grating-assisted tunable filters for telecommunications systems

Optics Express, Vol. 10, Issue 23, pp. 1354-1360 (2002)

http://dx.doi.org/10.1364/OE.10.001354

Acrobat PDF (205 KB)

### Abstract

In this paper, a number of critical aspects in the design and performance of guided-wave grating-assisted tunable filters for dense telecommunications systems are investigated by using a rigorous numerical approach. It is shown how highly narrow filters, with the potential to be tunable over a large number of channels (> 50), can be accurately designed by using well-selected apodization windows.

© 2002 Optical Society of America

## 1. Introduction

1. C.R. Doerr, M. Zirngibl, C.H. Joyner, L.W. Stulz, and H.M. Presby, “Polarization Diversity Waveguide Grating Receiver with Integrated Optical Preamplifiers,” IEEE Photon. Tech. Lett. **9**, 85–87 (1997). [CrossRef]

2. J. Sapriel, D. Charissoux, V. Voloshinov, and V. Molchanov, “Tunable Acoustooptic Filters and Equalizers for WDM Applications,” J. Lightwave Technol. **20**, 864–871 (2002). [CrossRef]

## 2. Design considerations

6. W. P. Huang, J. Hong, and Z. M. Mao, “Improved coupled-mode formulation based on composite modes for parallel grating-assisted co-directional couplers,” IEEE J. Quantum Electron. **29**, 2805–2812 (1993). [CrossRef]

*k*in the GADC filter, which can be written as:

*E*

_{A}

*, E*

_{B}are the normalized wavefunctions of the two compound modes of unperturbed structure (A even and B odd mode, respectively), Δ

*t*

_{g}is the grating thickness. Since the grating profile is a periodic index distribution along the GADC, its permittivity change depends on the coefficients of its own Fourier series expansion. In particular, in Eq. (1), only one coefficient is dominant, i.e. the series expansion coefficient

*n*= 1 which minimizes the phase change between the two coupled waves. Therefore, the permittivity change for a rectangular profile becomes:

*n*

_{g}

*,n*

_{o}are the grating and overlay refractive indices, respectively, Λ is the grating period, and

*w*/Λ the duty cycle of the grating profile, being

*w*the groove width. Therefore, the coupling strength can be appropriately modulated along the grating by changing its duty cycle.

*Han*(

*n*) = 0.5[1 - cos(2

*πn*/(

*N*-1))] (Hanning)

*Ham*(

*n*) = 0.54 - 0.46 cos(2

*πn*/(

*N*-1)) (Hamming)

*Blac*(

*n*) = 0.42 - 0.5 cos(2

*πn*/(

*N*- 1)) + 0.08cos(4

*πn*/(

*N*- 1)) (Blackman)

7. V.M.N. Passaro and M.N. Armenise, “Analysis of Radiation Loss in Grating-Assisted Codirectional Couplers,” IEEE J. Quantum Electron. **31**, 1691–1697 (1995). [CrossRef]

8. N.-H. Sun, J.K. Butler, G.A. Evans, L. Pang, and P. Congdon, “Analysis of Grating-Assisted Directional Couplers Using the Floquet-Bloch Theory,” J. Lightwave Technol. **15**, 2301–2314 (1997). [CrossRef]

9. V.M.N. Passaro, “Optimal Design of Grating-Assisted Directional Couplers,” J. Lightwave Technol. **18**, 973–984 (2000). [CrossRef]

*f*

^{A}

_{0}), and mode B by space harmonics (0,+1) with normalized field distributions (

*f*

^{B}

_{+1}), respectively. In Eq. (3),

*c*

_{0},

*c*

_{1}designate the fundamental and first-order coefficient of the grating profile Fourier series expansion, respectively.

*c*

_{0},

*c*

_{1}coefficients of the profile series expansion and the real field distributions in the device. For example, for rectangular profiles where

*c*

_{0}=

*w*/Λ and

*c*

_{1}=(

*w*/Λ) sin

*c*(

*w*/Λ), it can be easily proved by using Eq. (3) that the coupling coefficient is proportional to the duty cycle even for

*w*/Λ≤0.4[3

3. H. Sakata, “Sidelobe suppression in grating-assisted wavelength-selective couplers,” Opt. Lett. **17**, 463–465 (1992). [CrossRef] [PubMed]

*k*can be obtained by LMP rather than CMT approach for design purposes. The evaluation of accurate values of k means to strongly increase the filter fabrication precision in terms of the grating duty cycle apodization and, then, the filter performance in terms of bandwidth and SSR. The comparison of different grating profiles, made in Fig. 2(a), demonstrates that some shapes, i.e. rectangular or trapezoidal, allow to obtain the same coupling coefficient with two different values of duty cycles. There is no ambiguity in this circumstance, since only one value of duty cycle is practically chosen during the fabrication process, on the basis of the required fabrication tolerances. Moreover, Fig. 2(b) shows the coupling efficiency distribution along the GADC length, as apodized by a number of different functions. The apodization windows are always symmetric with respect to the centre of the GADC length.

8. N.-H. Sun, J.K. Butler, G.A. Evans, L. Pang, and P. Congdon, “Analysis of Grating-Assisted Directional Couplers Using the Floquet-Bloch Theory,” J. Lightwave Technol. **15**, 2301–2314 (1997). [CrossRef]

10. Yu-H. Jan, G.A. Fish, L.A. Coldren, and S. P. DenBaars, “Widely tunable integrated filter/receiver with apodized grating-assisted codirectional coupler,” Proc. SPIE **3290**, 258–261 (1997). [CrossRef]

*n*

_{o}=3.18,

*n*

_{g}= 3.482,

*n*

_{slab1}=3.482,

*n*

_{gap}=3.18,

*n*

_{slab2}=3.282,

*n*

_{sub}=3.18 and thicknesses

*t*

_{slab1}=0.3 μm,

*t*

_{gap}=1.1 μm,

*t*

_{slab2}= 0.26 μm,

*t*

_{g}= 35 nm, at the wavelength of 1550 nm (see parameters in Fig. 1). The resonance occurs at Λ =16.8 μm in case of squared profile (

*w*/Λ = 0.5 , TE polarization), instead of 18 μm as evaluated in [10

10. Yu-H. Jan, G.A. Fish, L.A. Coldren, and S. P. DenBaars, “Widely tunable integrated filter/receiver with apodized grating-assisted codirectional coupler,” Proc. SPIE **3290**, 258–261 (1997). [CrossRef]

*k*= 26.5 cm

^{-1}, quite different from that obtained by CMT, i.e.

*k*=19.3 cm

^{-1}. In Fig. 4(a) the wavelength spectra (dB) relevant to some apodization windows are sketched at the output of the one-stage filter. The best SSR is clearly obtained by the Blackman function, but at the expenses of a larger bandwidth. A narrower bandwidth can be obtained by triangular or Hamming functions. Table I summarizes the most significant parameters of various windows, together with the main requirements of DWDM systems (red section).

*n*

_{s}= 3.18 ,

*n*

_{slab1}= 3.482 and

*n*

_{s}= 3.18 (TM-polarized wave). The numerical results assert that if the upper slab has a transverse size

*t*

_{trans,slab1}= 10 μm, the TE-polarized wave field distribution and its effective index are not practically influenced by the waveguide sidewalls. In fact, in that case only the refractive index change “seen” along the GADC depth influences the field distribution of the two compound modes of the structure, coupled by the GADC grating. This result has been substantially confirmed by more accurate simulations performed by the beam propagation method [12]. In Fig. 5 the field distribution in the transverse section of the GADC filter (as in Fig. 3) is sketched, showing the negligible effect of the sidewalls along the horizontal direction.

## 3. Conclusions

## References and links

1. | C.R. Doerr, M. Zirngibl, C.H. Joyner, L.W. Stulz, and H.M. Presby, “Polarization Diversity Waveguide Grating Receiver with Integrated Optical Preamplifiers,” IEEE Photon. Tech. Lett. |

2. | J. Sapriel, D. Charissoux, V. Voloshinov, and V. Molchanov, “Tunable Acoustooptic Filters and Equalizers for WDM Applications,” J. Lightwave Technol. |

3. | H. Sakata, “Sidelobe suppression in grating-assisted wavelength-selective couplers,” Opt. Lett. |

4. | R. C. Alferness and P.S. Cross, “Filter characteristics of codirectionally coupled waveguides with weighted coupling,” IEEE J. Quantum Electron. |

5. | B. E. Little, C. Wu, and W.-P. Huang, “Synthesis of codirectional couplers with ultralow sidelobes and minimum bandwidth,” Opt. Lett. |

6. | W. P. Huang, J. Hong, and Z. M. Mao, “Improved coupled-mode formulation based on composite modes for parallel grating-assisted co-directional couplers,” IEEE J. Quantum Electron. |

7. | V.M.N. Passaro and M.N. Armenise, “Analysis of Radiation Loss in Grating-Assisted Codirectional Couplers,” IEEE J. Quantum Electron. |

8. | N.-H. Sun, J.K. Butler, G.A. Evans, L. Pang, and P. Congdon, “Analysis of Grating-Assisted Directional Couplers Using the Floquet-Bloch Theory,” J. Lightwave Technol. |

9. | V.M.N. Passaro, “Optimal Design of Grating-Assisted Directional Couplers,” J. Lightwave Technol. |

10. | Yu-H. Jan, G.A. Fish, L.A. Coldren, and S. P. DenBaars, “Widely tunable integrated filter/receiver with apodized grating-assisted codirectional coupler,” Proc. SPIE |

11. | Yu-H. Jan, G.A. Fish, L.A. Coldren, and S. P. DenBaars, “Demonstration of InP-InGaAsP Vertical Grating-Assisted Codirectional Coupler Filters and Receivers with Tapered Coupling Coefficient Distributions,” IEEE Photon. Tech. Lett. |

12. | BeamProp by Rsoft Inc., 1999. |

**OCIS Codes**

(050.2770) Diffraction and gratings : Gratings

(130.2790) Integrated optics : Guided waves

(230.3120) Optical devices : Integrated optics devices

**ToC Category:**

Research Papers

**History**

Original Manuscript: October 28, 2002

Revised Manuscript: November 11, 2002

Published: November 18, 2002

**Citation**

Vittorio Passaro, "Design of guided-wave grating-assisted tunable filters for telecommunications systems," Opt. Express **10**, 1354-1360 (2002)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-10-23-1354

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### References

- C. R. Doerr, M. Zirngibl, C. H. Joyner, L. W. Stulz, and H.M. Presby, �??Polarization DiversityWaveguide Grating Receiver with Integrated Optical Preamplifiers,�?? IEEE Photon. Tech. Lett. 9, 85-87 (1997). [CrossRef]
- J. Sapriel, D. Charissoux, V. Voloshinov and V. Molchanov, �??Tunable Acoustooptic Filters and Equalizers for WDM Applications,�?? J. Lightwave Technol. 20, 864-871 (2002). [CrossRef]
- H. Sakata, �??Sidelobe suppression in grating-assisted wavelength-selective couplers,�?? Opt. Lett. 17, 463-465 (1992). [CrossRef] [PubMed]
- R. C. Alferness and P. S. Cross, �??Filter characteristics of codirectionally coupled waveguides with weighted coupling,�?? IEEE J. Quantum Electron. QE-14, 843-847 (1978). [CrossRef]
- B. E. Little, C. Wu, and W.-P. Huang, �??Synthesis of codirectional couplers with ultralow sidelobes and minimum bandwidth,�?? Opt. Lett. 20, 1259-1261 (1995). [CrossRef] [PubMed]
- W. P. Huang, J. Hong, and Z. M. Mao, �??Improved coupled-mode formulation based on composite modes for parallel grating-assisted co-directional couplers,�?? IEEE J. Quantum Electron. 29, 2805-2812 (1993). [CrossRef]
- V. M. N. Passaro and M. N. Armenise, �??Analysis of Radiation Loss in Grating-Assisted Codirectional Couplers,�?? IEEE J. Quantum Electron. 31, 1691-1697 (1995). [CrossRef]
- N. -H. Sun, J. K. Butler, G. A. Evans, L. Pang, and P. Congdon, �??Analysis of Grating-Assisted Directional Couplers Using the Floquet-Bloch Theory,�?? J. Lightwave Technol. 15, 2301-2314 (1997). [CrossRef]
- V. M. N. Passaro, �??Optimal Design of Grating-Assisted Directional Couplers,�?? J. Lightwave Technol. 18, 973-984 (2000). [CrossRef]
- Yu-H. Jan, G. A. Fish, L. A. Coldren, S. P. DenBaars, �??Widely tunable integrated filter/receiver with apodized grating-assisted codirectional coupler,�?? Proc. SPIE 3290, 258-261 (1997). [CrossRef]
- Yu-H. Jan, G. A. Fish, L. A. Coldren, S. P. DenBaars, �??Demonstration of InP-InGaAsP Vertical Grating-Assisted Codirectional Coupler Filters and Receivers with Tapered Coupling Coefficient Distributions,�?? IEEE Photon. Tech. Lett. 9, 994-996 (1997). [CrossRef]
- BeamProp by Rsoft Inc., 1999.

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