# High-Resolution Arrayed-Waveguide-Gratings in Astronomy: Design and Fabrication Challenges

^{*}

## Abstract

**:**

_{2}platform. To evaluate the fabrication challenges of such high-resolution AWGs, effects of random perturbations of the effective refractive index (RI) distribution in the free propagation region (FPR), as well as small variations of the array waveguide optical lengths are numerically investigated. The results of the investigation show a dramatic degradation of the point spread function (PSF) for a random effective RI distribution with variance values above $\sim {10}^{-4}$ for both the FPR and the waveguide array. Based on the results, requirements on the fabrication technology for high-resolution AWG-based spectrographs are given in the end.

## 1. Introduction

## 2. Principle of the AWG-Based IPS

## 3. Features of the AWG Design

#### 3.1. Target Application and Material Platform

_{3}N

_{4}on SiO

_{2}. Although low-loss, fibre compatible high-index waveguide structures have been demonstrated [16,17], their fabrication involves additional steps and requires modifications of the traditional lithographic processes. In order to avoid complications, Silica-on-Silicon (SoS) material platform with a refractive index contrast of 1.5% was chosen for the AWG design due to good fibre compatibility, low absorption in the NIR wavelength range and low propagation losses of $\sim 0.01\phantom{\rule{0.166667em}{0ex}}\mathrm{dB}/\mathrm{cm}$ [18], amongst other advantages.

#### 3.2. General Structure of the AWG

_{2}buffer and cladding is 1.443 and the core refractive index is 1.466 ($\mathsf{\Delta}=0.015$) at the central wavelength of 1630 nm. The mode field diameter equals 4.7 $\mathsf{\mu}$m. Circular waveguide bends with a fixed radius of 3000 $\mathsf{\mu}$m, which is the minimal radius at the longest expected wavelength of 1800 nm, are used to minimize systematic phase errors. The physical path length difference between adjacent waveguides is 111.2 $\mathsf{\mu}$m, which corresponds to a grating order of 99 and an FSR of $16.15$ nm.

#### 3.3. Customized Input Waveguide Interface

#### 3.4. Loss Reduction by Modification of the FPR-Array Interface

## 4. Fabrication-Tolerance Investigation

#### 4.1. Effects of Random Perturbations of the Refractive Index Distribution in the FPR

#### 4.2. Effects of Random Effective RI Variations in the Waveguide Array Region

## 5. Discussion

_{2}platform has been introduced in this work. Optimization of the geometrical structure resulted in a footprint of 5.5 cm × 3.93 cm with 800 arrayed waveguides and a focal length of 24 mm. An application-specific input interface with three separate groups of input access waveguides was designed. A modification of the FPR-array transition region was devised in order to reduce coupling losses due to higher order mode excitation in the taper waveguides of the interface by $2\%$–$4.9\%$ in the H-band wavelength range (1500 nm–1800 nm).

## 6. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 1.**Schematic depiction of an arrayed-waveguide-grating (AWG)-based spectrograph assembly with cross-dispersive optics.

**Figure 3.**Cross-section of the rectangular buried channel waveguide core used in the AWG design. Core thickness is 3.5 $\mathsf{\mu}$m with variable core widths of 3.5 $\mathsf{\mu}$m (arrayed waveguides)—16.03 $\mathsf{\mu}$m (widest taper).

**Figure 6.**Illustration of simulated coupling between the free propagation regions (FPR) and the waveguide array with standard linear tapers (

**left**) and discontinuous MMI tapers (

**right**). The beating pattern in the left image indicates two-mode interference. Waveguide core boundaries are highlighted in yellow colour.

**Figure 7.**Comparison between the standard linear taper and the multimode interference (MMI) taper. Simulations were performed for TE and TM polarization in the wavelength range 1500 nm–1800 nm.

**Figure 10.**Figure of merit (FOM) maps for waveguide arrays of various sizes and propagation lengths. 800 waveguides, L = 10.5 cm (

**a**); 600 waveguides, L = 8.3 cm (

**b**); 400 waveguides, L = 6 cm (

**c**); 200 waveguides, L = 3.8 cm (

**d**).

λ/Δλ | 20 k | 25 k | 30 k | 35 k | 40 k | 45 k | 50 k | 55 k | 60 k |
---|---|---|---|---|---|---|---|---|---|

Width (μm) | 16.03 | 12.42 | 10.02 | 8.30 | 7.01 | 6.01 | 5.20 | 4.55 | 3.5 |

Location (μm) | −80 | 80 | −60 | 60 | −40 | 40 | −20 | 20 | 0 |

**Table 2.**Critical thresholds of the refractive index distribution $RMS$ for various values of ${L}_{C}$ and target resolving power R.

R | 60 k | 45 k | 30 k | 15 k | |
---|---|---|---|---|---|

L_{c} | |||||

100 $\mathsf{\mu}$m | $5.14\times {10}^{-5}$ | $5.7\times {10}^{-5}$ | $6.56\times {10}^{-5}$ | $8\times {10}^{-5}$ | |

500 $\mathsf{\mu}$m | $2\times {10}^{-5}$ | $2.5\times {10}^{-5}$ | $2.95\times {10}^{-5}$ | $3.77\times {10}^{-5}$ | |

1000 $\mathsf{\mu}$m | $1.52\times {10}^{-5}$ | $1.7\times {10}^{-5}$ | $2\times {10}^{-5}$ | $3.2\times {10}^{-5}$ | |

3000 $\mathsf{\mu}$m | $1.14\times {10}^{-5}$ | $1.4\times {10}^{-5}$ | $1.86\times {10}^{-5}$ | $3.6\times {10}^{-5}$ |

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**MDPI and ACS Style**

Stoll, A.; Zhang, Z.; Haynes, R.; Roth, M.
High-Resolution Arrayed-Waveguide-Gratings in Astronomy: Design and Fabrication Challenges. *Photonics* **2017**, *4*, 30.
https://doi.org/10.3390/photonics4020030

**AMA Style**

Stoll A, Zhang Z, Haynes R, Roth M.
High-Resolution Arrayed-Waveguide-Gratings in Astronomy: Design and Fabrication Challenges. *Photonics*. 2017; 4(2):30.
https://doi.org/10.3390/photonics4020030

**Chicago/Turabian Style**

Stoll, Andreas, Ziyang Zhang, Roger Haynes, and Martin Roth.
2017. "High-Resolution Arrayed-Waveguide-Gratings in Astronomy: Design and Fabrication Challenges" *Photonics* 4, no. 2: 30.
https://doi.org/10.3390/photonics4020030