Utilizing Shift-or-Shrink Method to Optimize Multisegment Structures of Bent Optical Waveguides

The authors utilized a heuristic shift-or-shrink method that is associated with the beam propagation method to design an optimal multisegment bent optical waveguide. By transforming the shape of each segment, the multisegment structure of the bent waveguide can be optimized. In addition to achieving maximal transmission efficiency, only four segments are sufficient to satisfactorily improve the transmission performance. Moreover, the optimal path of each of these multisegment bent waveguides remains similar to each other waveguide's optimal path even though the number of the segments increases.

Index Terms
shift-or-shrink method; beam propagation method; BPM; bent waveguide

Authorship

Ruei-Chang Lu

Department of Electronic Engineering, National I-Lan University, I-Lan City, I-Lan County, Taiwan, ROC, E-mail: rclu@ems.niu.edu.twNational I-Lan UniversityROCI-Lan City, Taiwan, ROCDepartment of Electronic Engineering, National I-Lan University, I-Lan City, I-Lan County, Taiwan, ROC, E-mail: rclu@ems.niu.edu.tw

http://orcid.org/0000-0001-6331-9359

Keh-Yi Lee

Department of Electrical Engineering, Chinese Culture University, Taipei, Taiwan, ROC, E-mail: kyleentu@ms52.hinet.netChinese Culture UniversityROCTaipei, Taiwan, ROCDepartment of Electrical Engineering, Chinese Culture University, Taipei, Taiwan, ROC, E-mail: kyleentu@ms52.hinet.net

http://orcid.org/0000-0002-2660-9274

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Figures

Figures (7)

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Fig. 1
Flowchart of the SOS algorithm.

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Fig. 2
(a) A searching polyhedron for obtaining the extremum of f(x₁, x₂) in the 2D space. In this special case, the searching polyhedron is a square. (b) Shift operation. The value of f(x₁, x₂) at the vertex P4 was assumed to be the extremum. The original searching square is depicted using dashed squares. The new square is depicted as a solid square. (c) Shrink operation. All the new vertices uniformly move toward the center.

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Fig. 3
Centers of the searching squares from the first round to the 11th round of the SOS procedure for determing the location of the minimum of

f (x, y) = {(x - 2)}^{2} + {(y - 3)}^{2}

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Fig. 4
(a) Conventional 2D optical waveguide. The straight-but-oblique section is connected to both upright input and output waveguides with the same width W. The straight-but-oblique section was divided into six (m = 3) segments. (b) C_k and C_6−k (1 ≤ k ≤ 2) move horizontally. Each segment is transformed into a new shape, but the initial width W and original height L/6 are maintained. The dash lines in this subfigure represent the pattern of the initial and conventional 2D optical waveguide.

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Fig. 5
(a) Initial bent waveguide structure. (b) BPM simulation of the propagating lightwave intensity distribution along the initial bent waveguide structure. (c) The optimal four-segment structure of the bent waveguide. (d) BPM simulation of the incident lightwave propagating along the optimal four-segment structure of the bent waveguide. (e) The transmission efficiencies calculated using the SOS method converges to the same maximum regardless of whether the initial value of h is 3.2 μm (blue dot) or 2.4 μm (green square).

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Fig. 6
Optimal multisegment bent waveguides and their respective BPM simulation results of the incident lightwave propagating along them in the case of a (a) six-segment structure, (b) eight-segment structure, (c) ten-segment structure, and (d) 12-segment structure.

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Fig. 7
Comparison between the optical paths of the conventional (blue dotted line), optimal four-segment (green curve), optimal eight-segment (red dash curve), and optimal 12-segment (black dash-dot curve) bent waveguide structures.

Fig. 1 Flowchart of the SOS algorithm.

Fig. 2 (a) A searching polyhedron for obtaining the extremum of f(x₁, x₂) in the 2D space. In this special case, the searching polyhedron is a square. (b) Shift operation. The value of f(x₁, x₂) at the vertex P4 was assumed to be the extremum. The original searching square is depicted using dashed squares. The new square is depicted as a solid square. (c) Shrink operation. All the new vertices uniformly move toward the center.

Fig. 3 Centers of the searching squares from the first round to the 11th round of the SOS procedure for determing the location of the minimum of $f (x, y) = {(x - 2)}^{2} + {(y - 3)}^{2}$ .

Fig. 4 (a) Conventional 2D optical waveguide. The straight-but-oblique section is connected to both upright input and output waveguides with the same width W. The straight-but-oblique section was divided into six (m = 3) segments. (b) C_k and C_6−k (1 ≤ k ≤ 2) move horizontally. Each segment is transformed into a new shape, but the initial width W and original height L/6 are maintained. The dash lines in this subfigure represent the pattern of the initial and conventional 2D optical waveguide.

Fig. 5 (a) Initial bent waveguide structure. (b) BPM simulation of the propagating lightwave intensity distribution along the initial bent waveguide structure. (c) The optimal four-segment structure of the bent waveguide. (d) BPM simulation of the incident lightwave propagating along the optimal four-segment structure of the bent waveguide. (e) The transmission efficiencies calculated using the SOS method converges to the same maximum regardless of whether the initial value of h is 3.2 μm (blue dot) or 2.4 μm (green square).

Fig. 6 Optimal multisegment bent waveguides and their respective BPM simulation results of the incident lightwave propagating along them in the case of a (a) six-segment structure, (b) eight-segment structure, (c) ten-segment structure, and (d) 12-segment structure.

Fig. 7 Comparison between the optical paths of the conventional (blue dotted line), optimal four-segment (green curve), optimal eight-segment (red dash curve), and optimal 12-segment (black dash-dot curve) bent waveguide structures.

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Utilizing Shift-or-Shrink Method to Optimize Multisegment Structures of Bent Optical Waveguides

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