## Details

Originalsprache | Englisch |
---|---|

Seiten (von - bis) | 1125-1128 |

Seitenumfang | 4 |

Fachzeitschrift | Optics letters |

Jahrgang | 49 |

Ausgabenummer | 5 |

Publikationsstatus | Veröffentlicht - 20 Feb. 2024 |

## Abstract

Optical beam splitters are essential for classical and quantum photonic on-chip systems. In integrated optical technology, a beam splitter can be implemented as a beam coupler with two input and two output ports. The output phases are constrained by the conservation of energy. In lossless beam splitters, the phase shift between the output fields is π and zero for excitation from the first and second input ports, respectively. Therefore, for excitation from both inputs, the phase between the output fields, defined as beam splitter phase (BSP), is π. The BSP leads to several phenomena, such as the quantum interference between two photons, known as the Hong–Ou–Mandel effect. By introducing losses, BSP values different than π become theoretically possible, but the design of 2 × 2 beam couplers with an arbitrary phase is elusive in integrated optics. Inspired by the growing interest on fundamental limits in electromagnetics and inverse design, here we explore the theoretical limits of symmetrical integrated beam splitters with an arbitrary BSP via adjoint-based topology optimization. Optimized 2D designs accounting for fabrication constraints are obtained for several combinations of loss and phase within the theoretical design space. Interestingly, the algorithm does not converge for objectives outside of the theoretical limits. Designs of beam splitters with arbitrary phase may find use in integrated optics for quantum information processing.

## ASJC Scopus Sachgebiete

- Physik und Astronomie (insg.)
**Atom- und Molekularphysik sowie Optik**

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**Exploring the fundamental limits of integrated beam splitters with arbitrary phase via topology optimization.**/ Nanda, Abhishek; Kues, Michael; Calà Lesina, Antonio.

in: Optics letters, Jahrgang 49, Nr. 5, 20.02.2024, S. 1125-1128.

Publikation: Beitrag in Fachzeitschrift › Letter › Forschung › Peer-Review

*Optics letters*, Jg. 49, Nr. 5, S. 1125-1128. https://doi.org/10.1364/OL.512100

}

TY - JOUR

T1 - Exploring the fundamental limits of integrated beam splitters with arbitrary phase via topology optimization

AU - Nanda, Abhishek

AU - Kues, Michael

AU - Calà Lesina, Antonio

N1 - Funding Information: Funding. European Research Council (QFreC project, Grant agreement ID 947603); Deutsche Forschungsgemeinschaft (EXC 2122, Project ID 390833453). Simulations were performed, in part, on the central computing cluster operated by Leibniz University IT Services (LUIS), which is funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation), project number INST 187/742-1 FUGG. We also acknowledge the computing time granted by the Resource Allocation Board and provided on the supercomputer Lise and Emmy at NHR@ZIB and NHR@Göttingen as part of the NHR infrastructure (calculations were conducted with computing resources under the project nip00059).

PY - 2024/2/20

Y1 - 2024/2/20

N2 - Optical beam splitters are essential for classical and quantum photonic on-chip systems. In integrated optical technology, a beam splitter can be implemented as a beam coupler with two input and two output ports. The output phases are constrained by the conservation of energy. In lossless beam splitters, the phase shift between the output fields is π and zero for excitation from the first and second input ports, respectively. Therefore, for excitation from both inputs, the phase between the output fields, defined as beam splitter phase (BSP), is π. The BSP leads to several phenomena, such as the quantum interference between two photons, known as the Hong–Ou–Mandel effect. By introducing losses, BSP values different than π become theoretically possible, but the design of 2 × 2 beam couplers with an arbitrary phase is elusive in integrated optics. Inspired by the growing interest on fundamental limits in electromagnetics and inverse design, here we explore the theoretical limits of symmetrical integrated beam splitters with an arbitrary BSP via adjoint-based topology optimization. Optimized 2D designs accounting for fabrication constraints are obtained for several combinations of loss and phase within the theoretical design space. Interestingly, the algorithm does not converge for objectives outside of the theoretical limits. Designs of beam splitters with arbitrary phase may find use in integrated optics for quantum information processing.

AB - Optical beam splitters are essential for classical and quantum photonic on-chip systems. In integrated optical technology, a beam splitter can be implemented as a beam coupler with two input and two output ports. The output phases are constrained by the conservation of energy. In lossless beam splitters, the phase shift between the output fields is π and zero for excitation from the first and second input ports, respectively. Therefore, for excitation from both inputs, the phase between the output fields, defined as beam splitter phase (BSP), is π. The BSP leads to several phenomena, such as the quantum interference between two photons, known as the Hong–Ou–Mandel effect. By introducing losses, BSP values different than π become theoretically possible, but the design of 2 × 2 beam couplers with an arbitrary phase is elusive in integrated optics. Inspired by the growing interest on fundamental limits in electromagnetics and inverse design, here we explore the theoretical limits of symmetrical integrated beam splitters with an arbitrary BSP via adjoint-based topology optimization. Optimized 2D designs accounting for fabrication constraints are obtained for several combinations of loss and phase within the theoretical design space. Interestingly, the algorithm does not converge for objectives outside of the theoretical limits. Designs of beam splitters with arbitrary phase may find use in integrated optics for quantum information processing.

UR - http://www.scopus.com/inward/record.url?scp=85186318650&partnerID=8YFLogxK

U2 - 10.1364/OL.512100

DO - 10.1364/OL.512100

M3 - Letter

C2 - 38426954

AN - SCOPUS:85186318650

VL - 49

SP - 1125

EP - 1128

JO - Optics letters

JF - Optics letters

SN - 0146-9592

IS - 5

ER -