**Silicon Photonics Laboratory**

Name of the course | Online | Lecture | Exercises^{[1]} |
Lab |
---|---|---|---|---|

Silicon Photonics Lab | ✓ | ✓ | ✗ (✓) | ✓ |

The Silicon Photonics Laboratory is a twelve-weeks course for master or bachelor programs, where level of complexity and workload of the course depend on the program. It is organized in two parts. Part One is an virtual classroom education on the Finite Difference Time Domain Method (FDTD), the Vector Wave Propagation Method (VWPM) and a very brief introduction to the Python language. Part Two is the practical lab training where students design and simulate selected silicon photonic standard components with the FDTD and/or the VWPM.

Each lab is focussed on a specific photonic building block as shown in the table below. The contents are incremental and build up on each other. After a brief introduction to the theory of the building blocks, participants model and simulate photonic components and prepare a report at the end of each exercise.

The course utilizes the software packages MEEP and VWPM. Both simulators are available for single and multiprocessor Linux systems and free of charge. Versions of OptiFDTD and VWPM are available for Windows systems but students are highly recommended to use Linux tools as those are supported by the course material. All required software packages are available for download on participants personal computers.

Conceptually, the course is set up as an online course and participants are not tied to a classroom at all. The course is offered in a master and bachelor version. While the master version has a focus on theory and programming of simulators, the bachelor version utilizes existing simulators to design and optimize silicon photonic building blocks. To successfully complete the master course, it is an advantage have completed the course Optics and Photonics or at least have a basic knowledge in the relevant theory. Programming skills are absolutely required in both versions of the course.

Lecture | Content | |
---|---|---|

1 | Classification of problems and finite differencing | [PDF*] |

2 | Classification of systems and introduction to Fourier optics | [PDF*] |

3 | Finite differencing schemes for partial differential equations | [PDF] |

4 | The Finite Difference Time Domain Method | [PDF] |

5 | The Beam Propagation Method | [PDF*] |

6 | The Wave Propagation Method | [PDF] |

7 | The Vector Wave Propagation Method | [PDF] |

Lab | Content | Download |
---|---|---|

1 | Plane Wave and Gaussian Sources | [.tar.gz] |

2 | Reflection at plane interface | [.tar.gz] |

3 | Waveguides | [.tar.gz] |

4 | Splitters & Tapers | [.tar.gz] |

5 | Grating Couplers | - |

6 | Fabry Perot and Ring Resonators | - |

# 1. Free Space Propagation

Free space propagation of **Continous and Gaussian Sources** with variations in the propagation vector, wavelength (frequency) and spectral width. Perform a spectral analysis of plane waves and Gaussian beams for vertical and oblique incidence. Align the results with the Fourier Theory and investigate the effect of **Perfectly Matched Layer** (PML) or **Absorbing Boundary Conditions** (ABC). Simulate with time stepping and cw-solver. Discuss symmetry settings.

# 2. Plane Interface

Derive the **Fresnel Coefficients** from a simulation of reflected and transmitted field amplitudes over a range of spatial frequencies. Use a **Gaussian Pulse** to obtain the **impulse response** of the interface. Derive reflected and transmitted field amplitudes over the angle of incidence. Compared results to a simulation with **plane waves**. Develop an **anti-reflection coating** from impulse response analysis.

# 3. Waveguide

Model a **Straight Waveguide** and calculate radiation losses. Perform a variation of wavelength and **contrast**, i.e. refractive index ratio of core and cladding. Verify that mode confinement is only reached with total internal reflection and that only a discrete set of modes are carried by the waveguide due to phase alignment (resonance/standing wave) conditions at the waveguide boundaries. Optimize the waveguide for monomode propagation and analyze the energy flux. Plot transmittance and reflectance over spectral range.

Model and simulate a rectangular and circular **Waveguide Bend** and analyze the energy flux. Parametrize the bend and determine the maximum bend angle for mode confinement. Determine the normalized energy flux of transmitted fields over spatial frequency and determine the waveguide losses. Compare the performance of orthogonal and circular bend. **Photonic Crystal Waveguides** are optional if time permits.

# 4. Splitter & Taper

Model and optimize a **Waveguide Splitter** to achieve a maximum trans- mittance and compare performance for two design points. Optimize a **Waveguide Taper** to achieve a maximum transmittance. Understand how taper and splitter shapes (linear, exponential, etc.) affect their operability. Investigate how device performance is influenced by source misalignments. Perform parameter variations and performance evaluations.

# 5. Grating Coupler

Model and optimize a one-dimensional **Grating Coupler**. Analyze the spectrum of transmitted and reflected beam. Show the dependency of grating parameters to diffraction orders. Attach a waveguide to the grating and analyze the coupling efficiency. Explore the design space and identify an optimal solution for a maximum transmission. Investigate the interdependency of wavelength, angle of incidence and grating pitch (width).

# 6. Fabry Perot & Ring Resonator

Investigate the theory of Fabry Perot resonators. Develop a **Ring Resonator** to selectively filter wavelengths. Use the theory of ring resonators to verify the conditions of resonance. Engineer a design to selectively filter one of two wavelengths. Use two Gaussian sources and perform a **mode analysis** of the input and output spectrum. Evaluate the results and optimize the design for a maximum **mode separation**. Use the material parameters and dimensions of a **standard CMOS SOI technology**.

# 7. Nonlinear optimization of a bragg-grating outcoupler

This exercise is intended for participants with a solid background in Silicon Photonics, Optics and experience in Pyton and Shell programming. A bragg-grating outcoupler shall to be designed in three dimensions. An optimal parameter set shall be found for a maximum outcoupling power by using a nonlinear optimizer, e.g. nlopt. Radiation patterns shall be derived from the Poynting vector gained from the spatial field distribution and a far-field analysis. The optimizer is supposed find a power maximum for a specific range of angles.

## Helpful Links

[1] MEEP install guide[2] Python documentation for MEEP

[3] Python documentation for HDF5-Format

[4] Managing Python libraries with Anaconda

[5] MIT Photonic Bands (MPB)

[6] Python documentation for MIT Photonic Bands (MPB)

[7] NumPy Reference, a scientific computing package for Python

[8] About MEEP and VWPM.

## Literature

[1] Principles Of Optics, Born & Wolf, Cambridge University Press, ISBN 0-521-64222-1[2] Fourier Optics, Goodman, Roberts Publ., ISBN 0-974-70772-4

[3] The Finite-Difference Time-Domain Method, Taflove, Artech House Inc., ISBN 1-580-53832-0

[4] Engineering Optics With Matlab, Poon & Kim, World Scientific Publ. Co, ISBN 9-789-812-56873-1

[5] Optics, Hecht, Addison-Wesley Publ., ISBN 9-780-805-38566-3