### Abstract

Using nonlinear programing and the geometry projection method, the quality factor of the monopole mode of a single defect photonic crystal laser cavity is improved from 38 000 to 87 000. Beginning with a design that considers only round air holes shifted away from the cavity, the radius of the nearest neighbor and of the surrounding air holes are optimized while satisfying a constraint on the resonant frequency. The total reflectivity of the photonic crystal laser structure is then defined, and it is shown that this quantity correlates strongly to the total quality factor. The reflectivity of the structure is improved by altering the shape of the holes immediately surrounding the cavity, thus leading to an improvement in quality factor. The geometry projection method is used to define the shape of the holes and the finite element and adjoint methods are used to compute the objective function and sensitivities required by the optimizer. This work demonstrates one way to optimize the Q factor of a photonic crystal laser by altering the hole shape.

Original language | English (US) |
---|---|

Article number | 033102 |

Journal | Journal of Applied Physics |

Volume | 103 |

Issue number | 3 |

DOIs | |

State | Published - Feb 22 2008 |

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### ASJC Scopus subject areas

- Physics and Astronomy(all)

### Cite this

*Journal of Applied Physics*,

*103*(3), [033102]. https://doi.org/10.1063/1.2838173

**Optimization of a single defect photonic crystal laser cavity.** / Frei, Walter R.; Johnson, H. T.; Choquette, Kent D.

Research output: Contribution to journal › Article

*Journal of Applied Physics*, vol. 103, no. 3, 033102. https://doi.org/10.1063/1.2838173

}

TY - JOUR

T1 - Optimization of a single defect photonic crystal laser cavity

AU - Frei, Walter R.

AU - Johnson, H. T.

AU - Choquette, Kent D.

PY - 2008/2/22

Y1 - 2008/2/22

N2 - Using nonlinear programing and the geometry projection method, the quality factor of the monopole mode of a single defect photonic crystal laser cavity is improved from 38 000 to 87 000. Beginning with a design that considers only round air holes shifted away from the cavity, the radius of the nearest neighbor and of the surrounding air holes are optimized while satisfying a constraint on the resonant frequency. The total reflectivity of the photonic crystal laser structure is then defined, and it is shown that this quantity correlates strongly to the total quality factor. The reflectivity of the structure is improved by altering the shape of the holes immediately surrounding the cavity, thus leading to an improvement in quality factor. The geometry projection method is used to define the shape of the holes and the finite element and adjoint methods are used to compute the objective function and sensitivities required by the optimizer. This work demonstrates one way to optimize the Q factor of a photonic crystal laser by altering the hole shape.

AB - Using nonlinear programing and the geometry projection method, the quality factor of the monopole mode of a single defect photonic crystal laser cavity is improved from 38 000 to 87 000. Beginning with a design that considers only round air holes shifted away from the cavity, the radius of the nearest neighbor and of the surrounding air holes are optimized while satisfying a constraint on the resonant frequency. The total reflectivity of the photonic crystal laser structure is then defined, and it is shown that this quantity correlates strongly to the total quality factor. The reflectivity of the structure is improved by altering the shape of the holes immediately surrounding the cavity, thus leading to an improvement in quality factor. The geometry projection method is used to define the shape of the holes and the finite element and adjoint methods are used to compute the objective function and sensitivities required by the optimizer. This work demonstrates one way to optimize the Q factor of a photonic crystal laser by altering the hole shape.

UR - http://www.scopus.com/inward/record.url?scp=39349115291&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=39349115291&partnerID=8YFLogxK

U2 - 10.1063/1.2838173

DO - 10.1063/1.2838173

M3 - Article

AN - SCOPUS:39349115291

VL - 103

JO - Journal of Applied Physics

JF - Journal of Applied Physics

SN - 0021-8979

IS - 3

M1 - 033102

ER -