## Novel dispersive and focusing device configuration based on curved waveguide grating (CWG)

Optics Express, Vol. 14, Issue 19, pp. 8630-8637 (2006)

http://dx.doi.org/10.1364/OE.14.008630

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### Abstract

Configuration of a novel compact dispersive and focusing device based on a Curved Waveguide Grating (CWG) is presented, which is essentially an integrated optic wavelength demultiplexer consisting of a curved stripe waveguide with tilted grating, a slab waveguide adjacent to it, and a set of output waveguides locate on focal line of the curved waveguide. Underlying wavelength demultiplexing mechanism of CWG is theoretically illustrated by employing the Fourier optics approach. Analysis shows that device based on CWG possesses fine wavelength resolution, compact configuration, and potentially low cost as well, which make it a promising wavelength demultiplexer, or a network performance monitor, in DWDM optical networks.

© 2006 Optical Society of America

## 1. Introduction

1. M. K. Smit and C. van Dam, “PHASAR-based WDM-devices: Principles, design and application,” IEEE J. Sel. Top Quantum. Electron. **2**, 236–250 (1996). [CrossRef]

2. E. Gini, W. Hunziker, and H. Melchior, “Polarization independent InP WDM multiplexer/demultiplexer module,” IEEE J. Lightwave Technol. **16**, 625–630 (1998). [CrossRef]

3. C. K. Madsen, J. Wagener, T. A. Strasser, D. Muehlner, M. A. Milbrodt, E. J. Laskowski, and J. DeMarco, “Planar waveguide optical spectrum analyzer using a UV-induced grating,” IEEE J. Sel. Top Quantum. Electron. **4**, 925–929 (1998). [CrossRef]

## 2. Device descriptions

3. C. K. Madsen, J. Wagener, T. A. Strasser, D. Muehlner, M. A. Milbrodt, E. J. Laskowski, and J. DeMarco, “Planar waveguide optical spectrum analyzer using a UV-induced grating,” IEEE J. Sel. Top Quantum. Electron. **4**, 925–929 (1998). [CrossRef]

## 3. Theoretical model

### 3.1. Bragg diffraction of waveguide with grating

4. A. Yariv and M. Nakamura, “Periodic structures for integrated optics,” IEEE J. Quantum. Electron. **13**, 233–252 (1977). [CrossRef]

*n*is effective index of the guided mode,

_{eff}*n*is the refractive index of stripe waveguide cladding layer,

_{c}*λ*is wavelength in vacuum, Λ is the grating period, as shown in Fig. 1,

*m*is known as grating order.

*θ=π/2*, correspondingly, the grating period can be determined from Eq. (1).

*λ*and

_{0}*ν*are the design wavelength and frequency, respectively.

_{0}### 3.2. Dispersive and focusing mechanism of CWG

5. H. Takenouchi, H. Tsuda, and T. Kurokawa, “Analysis of optical signal processing using an arrayed waveguide grating,” Opt. Express **6**, 124–135 (2000). [CrossRef] [PubMed]

6. P. Munoz, D. Pastor, and J. Capmany, “Analysis and design of arrayed waveguide gratings with MMI coupler,” Opt. Express **9**, 328–338 (2001). [CrossRef] [PubMed]

7. P. Munoz, D. Pastor, and J. Capmany, “Modeling and design of arrayed waveguide gratings,” IEEE J. Lightwave. Technol. **20**, 661–674 (2002). [CrossRef]

#### 3.2.1. Field at the input waveguide

*y*is the coordinate perpendicular to the stripe waveguide in the wafer plane, as shown in Fig. 1,

*f*is the power normalized spatial field profile,

_{0}(y)*U(x*is amplitude factor,

_{0})*β*is propagation constant of the stripe waveguide.

*f*can be approximately expressed as a power normalized Gaussian function

_{0}(y)*ω*is the mode field radius, which depends on particular waveguide parameters, including core layer dimensions, as well as refractive index profile.

_{0}#### 3.2.2. Diffraction field of the grating in waveguide

*C*. Therefore, amplitude factor of the guided mode is expressed as

*2N+1*grating lines in the arc-shaped waveguide, with the

*N+1*th one at

*x*.

_{0}=0*ε*and

*µ*are permittivity and permeability, of the waveguide material, respectively.

_{0}*x*, phase factor of diffractive light can be written as

_{0}*κ*represents phase shift of diffraction light with respect to the guided light, due to “reflection” at each single grating line.

*δ*is a summation of delta functions.

_{Λ}(x_{0})*g(x*is the spatial field distribution of the central grating line (at

_{0})*x0=0*), which is determined by the specific grating structure on the waveguide, and will be discussed in more detail in section 4.

#### 3.2.3. Spatial distribution on the focal plane

*x*

_{1}, the Fourier transformation of (15) is calculated, yielding

*u*is the spatial frequency domain variable of the Fourier transformation and

*α*is equivalent to the wavelength focal length product in Fourier optics propagation

_{ν}*n*is refractive index of the slab waveguide,

_{s}*L*is focal length (radius of curvature) of the arc-shaped waveguide grating.

_{f}*ν-ν*, the approximation

_{0}≪ν_{0}*ν=ν*holds, and then

_{0}*r*, known as the diffraction order.

*r*and

*γ*. The Frequency Spatial Dispersion Parameter (FSDP) given by

*E*, the term

_{1}(x_{1})*G(x*introduces the loss nonuniformity, and the term

_{1})*φ(ν)*incorporates the phase delay information.

*ν*by two consecutive diffractions (i.e.,

*k*and

*k+1*), can be acquired from Eq. (25) and given as

## 4. Discussion

*W*and

_{T}*W*are projection of grating line in the direction perpendicular to the propagation direction of the guided light and the diffracted light, respectively.

_{L}*f*is the power normalized spatial field profile, as given in Eq. (5).

_{0}(x_{0})*rect(x*is given by

_{0}/W_{T})*π/4, W*, and grating lines with sufficiently large length to partially “reflect” guided light over all its transverse section spatially,

_{T}=W_{L}*g(x*can be reasonably approximated as a power normalized Gaussian function

_{0})*ω*the field radius of diffracted light at

_{g}*x*.

_{0}3. C. K. Madsen, J. Wagener, T. A. Strasser, D. Muehlner, M. A. Milbrodt, E. J. Laskowski, and J. DeMarco, “Planar waveguide optical spectrum analyzer using a UV-induced grating,” IEEE J. Sel. Top Quantum. Electron. **4**, 925–929 (1998). [CrossRef]

**4**, 925–929 (1998). [CrossRef]

**4**, 925–929 (1998). [CrossRef]

**4**, 925–929 (1998). [CrossRef]

**4**, 925–929 (1998). [CrossRef]

**4**, 925–929 (1998). [CrossRef]

*L*, slab waveguide refractive index

_{f}=107mm*n*, center wavelength

_{s}=1.45*λ*, grating length

_{0}=1540nm*L*. As shown in Fig. 6, for grating length of 10mm, resulted spots sizes are in good agreement with corresponding diffraction-limited values; for grating length of 20mm, resulted spot sizes deviate gradually from diffraction-limited values as wavelength depart from center wavelength, owning to imaging aberration of Rowland circle configuration. However, the spot sizes deviation from diffraction limited value over 1515~1565nm is sufficiently slight, a good reason for the CWG configuration to be regarded as diffraction-limited. In addition, for grating length of 10mm, the focused spot size is

_{g}=10mm, 20mm*22.9 µ m*, much finer in contrast with corresponding value of ~100

*µ m*in Ref. [3

**4**, 925–929 (1998). [CrossRef]

*E*possesses big sidelobes, as shown in Fig. 4, which means reduced coupling efficiency from grating to output waveguides, and high cross-talk between adjacent channels. Therefore, apodization approaches, through chirping or other technologies, are indispensable for obtaining high performance devices. Obviously,

_{1}(x_{1})*U*could be tailored by designing a grating with a varying coupling coefficient in its longitude direction. One possible approach is to tailor

_{d}(x_{0})*U*, envelop of the grating diffraction field amplitude factor, to a Gaussian profile, or a truncated Gaussian profile, as that at the end of the arrayed waveguide in AWG. Correspondingly, according to Eq. (18), we can get a

_{d}(x_{0})*E*of the form of a Gaussian form, or M function, as shown in Ref. [7

_{1}(x_{1})7. P. Munoz, D. Pastor, and J. Capmany, “Modeling and design of arrayed waveguide gratings,” IEEE J. Lightwave. Technol. **20**, 661–674 (2002). [CrossRef]

## 5. Conclusions

## References and links

1. | M. K. Smit and C. van Dam, “PHASAR-based WDM-devices: Principles, design and application,” IEEE J. Sel. Top Quantum. Electron. |

2. | E. Gini, W. Hunziker, and H. Melchior, “Polarization independent InP WDM multiplexer/demultiplexer module,” IEEE J. Lightwave Technol. |

3. | C. K. Madsen, J. Wagener, T. A. Strasser, D. Muehlner, M. A. Milbrodt, E. J. Laskowski, and J. DeMarco, “Planar waveguide optical spectrum analyzer using a UV-induced grating,” IEEE J. Sel. Top Quantum. Electron. |

4. | A. Yariv and M. Nakamura, “Periodic structures for integrated optics,” IEEE J. Quantum. Electron. |

5. | H. Takenouchi, H. Tsuda, and T. Kurokawa, “Analysis of optical signal processing using an arrayed waveguide grating,” Opt. Express |

6. | P. Munoz, D. Pastor, and J. Capmany, “Analysis and design of arrayed waveguide gratings with MMI coupler,” Opt. Express |

7. | P. Munoz, D. Pastor, and J. Capmany, “Modeling and design of arrayed waveguide gratings,” IEEE J. Lightwave. Technol. |

**OCIS Codes**

(050.0050) Diffraction and gratings : Diffraction and gratings

(130.0130) Integrated optics : Integrated optics

**ToC Category:**

Integrated Optics

**History**

Original Manuscript: June 19, 2006

Revised Manuscript: July 30, 2006

Manuscript Accepted: August 6, 2006

Published: September 18, 2006

**Citation**

Yinlei Hao, Yaming Wu, Jianyi Yang, Xiaoqing Jiang, and Minghua Wang, "Novel dispersive and focusing device configuration based on curved waveguide grating (CWG)," Opt. Express **14**, 8630-8637 (2006)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-14-19-8630

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### References

- M. K. Smit and C. van Dam, "PHASAR-based WDM-devices: Principles, design and application," IEEE J. Sel. Top Quantum.Electron. 2, 236-250 (1996). [CrossRef]
- E. Gini, W. Hunziker, H. Melchior, "Polarization independent InP WDM multiplexer/demultiplexer module," IEEE J. Lightwave Technol. 16, 625-630 (1998). [CrossRef]
- C. K. Madsen, J. Wagener, T. A. Strasser, D. Muehlner, M. A. Milbrodt, E. J. Laskowski, and J. DeMarco, "Planar waveguide optical spectrum analyzer using a UV-induced grating," IEEE J. Sel. Top Quantum Electron. 4, 925-929 (1998). [CrossRef]
- A. Yariv, M. Nakamura, "Periodic structures for integrated optics," IEEE J. Quantum. Electron. 13, 233-252 (1977). [CrossRef]
- H. Takenouchi, H. Tsuda and T. Kurokawa, "Analysis of optical signal processing using an arrayed-waveguide grating," Opt. Express 6, 124-135 (2000). [CrossRef] [PubMed]
- P. Munoz, D. Pastor and J. Capmany, "Analysis and design of arrayed waveguide gratings with MMI coupler," Opt. Express 9, 328-338 (2001). [CrossRef] [PubMed]
- P. Munoz, D. Pastor and J. Capmany, "Modeling and design of arrayed waveguide gratings," IEEE J. Lightwave. Technol. 20, 661-674 (2002). [CrossRef]

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