Abstract

In this work, we present a generalized design of broadband optical waveguide couplers with arbitrary coupling ratios on the silicon-on-insulator platform. The device is segmented into 34 short sections, where the propagation constant and the coupling coefficient of each section are viewed as variables during the optimization process. The optimal variable combination is determined by a genetic algorithm. We can achieve a performance superior to that of other design methods with fewer degrees of freedom. For 75%/25%, 50%/50%, 25%/75%, and 0%/100% couplers, the device lengths are 34 μm and the ±2% bandwidths are all in excess of 100 nm at the central wavelength of 1580 nm.

© 2016 Optical Society of America

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References

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2016 (6)

2015 (1)

2014 (3)

2013 (3)

2012 (2)

2010 (1)

J. Marqués-Hueso, L. Sanchis, B. Cluzel, F. de Fornel, and J. P. Martínez-Pastor, “Genetic algorithm designed silicon integrated photonic lens operating at 1550 nm,” Appl. Phys. Lett. 97, 071115 (2010).
[Crossref]

2009 (2)

2005 (4)

C. R. Doerr, M. Cappuzzo, E. Chen, A. Wong-Foy, L. Gomez, A. Griffin, and L. Buhl, “Bending of a planar lightwave circuit 2 × 2 coupler to desensitize it to wavelength, polarization, and fabrication changes,” IEEE Photon. Technol. Lett. 17, 1211–1213 (2005).
[Crossref]

A. Liu, R. Wu, and Y. Lin, “A compact design of W-band high-pass waveguide filter using genetic algorithms and full-wave finite element analysis,” IEICE T. Electron. E88-C, 1764–1771 (2005).
[Crossref]

A. Håkansson, P. Sanchis, J. Sánchez-Dehesa, and J. Martí, “High-efficiency defect-based photonic-crystal tapers designed by a genetic algorithm,” J. Lightw. Technol. 23, 3881–3888 (2005).
[Crossref]

A. Håkansson and J. Sánchez-Dehesa, “Inverse designed photonic crystal de-multiplex waveguide coupler,” Opt. Express 13, 5440–5449 (2005).
[Crossref] [PubMed]

2004 (1)

L. Sanchis, A. Håkansson, D. Lopez-Zanón, J. Bravo-Abad, and J. Sánchez-Dehesa, “Integrated optical devices design by genetic algorithm,” Appl. Phys. Lett. 84, 4460–4462 (2004).
[Crossref]

2003 (1)

D. Correia, J. da Silva, and H. Hernandez-Figueroa, “Genetic algorithm and finite-element design of short single-section passive polarization converter,” IEEE Photon. Technol. Lett. 15, 915–917 (2003).
[Crossref]

1994 (1)

1993 (1)

H. Li, “Refractive index of silicon and germanium and its wavelength and temperature derivatives,” J. Phys. Chem. Ref. Data 9, 561–658 (1993).
[Crossref]

1992 (1)

A. Takagi, K. Jinguji, and M. Kawachi, “Wavelength characteristics of (2 × 2) optical channel-type directional couplers with symmetric or nonsymmetric coupling structures,” J. Lightwave Technol. 10, 735–746 (1992).
[Crossref]

1990 (1)

A. Takagi, K. Jinguji, and M. Kawachi, “Broadband silica-based optical waveguide coupler with asymmetric structure,” Electron. Lett. 26, 132–133, (1990).
[Crossref]

1965 (1)

Absil, P.

Aitchison, J.

Alloatti, L.

Assefa, S.

Baehr-Jones, T.

C. Chen, X. Zhu, Y. Liu, K. Wen, M. Chik, T. Baehr-Jones, M. Hochberg, and K. Bergman, “Programmable dynamically-controlled silicon photonic switch fabric,” J. Lightw. Technol. 34, 2952–2958 (2016).
[Crossref]

Baets, R.

Bahrami, F.

Beeckman, J.

Bergman, K.

C. Chen, X. Zhu, Y. Liu, K. Wen, M. Chik, T. Baehr-Jones, M. Hochberg, and K. Bergman, “Programmable dynamically-controlled silicon photonic switch fabric,” J. Lightw. Technol. 34, 2952–2958 (2016).
[Crossref]

Bogaerts, W.

Bravo-Abad, J.

L. Sanchis, A. Håkansson, D. Lopez-Zanón, J. Bravo-Abad, and J. Sánchez-Dehesa, “Integrated optical devices design by genetic algorithm,” Appl. Phys. Lett. 84, 4460–4462 (2004).
[Crossref]

Buhl, L.

C. R. Doerr, M. Cappuzzo, E. Chen, A. Wong-Foy, L. Gomez, A. Griffin, and L. Buhl, “Bending of a planar lightwave circuit 2 × 2 coupler to desensitize it to wavelength, polarization, and fabrication changes,” IEEE Photon. Technol. Lett. 17, 1211–1213 (2005).
[Crossref]

Campenhout, J.

Cappuzzo, M.

C. R. Doerr, M. Cappuzzo, E. Chen, A. Wong-Foy, L. Gomez, A. Griffin, and L. Buhl, “Bending of a planar lightwave circuit 2 × 2 coupler to desensitize it to wavelength, polarization, and fabrication changes,” IEEE Photon. Technol. Lett. 17, 1211–1213 (2005).
[Crossref]

Cheben, P.

Chen, C.

C. Chen, X. Zhu, Y. Liu, K. Wen, M. Chik, T. Baehr-Jones, M. Hochberg, and K. Bergman, “Programmable dynamically-controlled silicon photonic switch fabric,” J. Lightw. Technol. 34, 2952–2958 (2016).
[Crossref]

Chen, E.

C. R. Doerr, M. Cappuzzo, E. Chen, A. Wong-Foy, L. Gomez, A. Griffin, and L. Buhl, “Bending of a planar lightwave circuit 2 × 2 coupler to desensitize it to wavelength, polarization, and fabrication changes,” IEEE Photon. Technol. Lett. 17, 1211–1213 (2005).
[Crossref]

Chen, L.

Chen, S.

Chen, X.

Chen, Y.

Chen, Z.

Cheng, N.

Chiang, T.

Chik, M.

C. Chen, X. Zhu, Y. Liu, K. Wen, M. Chik, T. Baehr-Jones, M. Hochberg, and K. Bergman, “Programmable dynamically-controlled silicon photonic switch fabric,” J. Lightw. Technol. 34, 2952–2958 (2016).
[Crossref]

Chrostowski, L.

Y. Wang, Z. Lu, M. Ma, H. Yun, F. Zhang, N. A. F. Jaeger, and L. Chrostowski, “Compact broadband directional couplers using subwavelength gratings,” IEEE Photon. J. 8, 7101408 (2016).
[Crossref]

Z. Lu, H. Yun, Y. Wang, Z. Chen, F. Zhang, N. Jaeger, and L. Chrostowski, “Broadband silicon photonic directional coupler using asymmetric-waveguide based phase control,” Opt. Express 23, 3795–3808 (2015).
[Crossref] [PubMed]

Chuang, S.

S. Chuang, Physics of Optoelectronic Devices (Wiley, 2009).

Cluzel, B.

J. Marqués-Hueso, L. Sanchis, B. Cluzel, F. de Fornel, and J. P. Martínez-Pastor, “Genetic algorithm designed silicon integrated photonic lens operating at 1550 nm,” Appl. Phys. Lett. 97, 071115 (2010).
[Crossref]

Correia, D.

D. Correia, J. da Silva, and H. Hernandez-Figueroa, “Genetic algorithm and finite-element design of short single-section passive polarization converter,” IEEE Photon. Technol. Lett. 15, 915–917 (2003).
[Crossref]

da Silva, J.

D. Correia, J. da Silva, and H. Hernandez-Figueroa, “Genetic algorithm and finite-element design of short single-section passive polarization converter,” IEEE Photon. Technol. Lett. 15, 915–917 (2003).
[Crossref]

Dai, D.

de Fornel, F.

J. Marqués-Hueso, L. Sanchis, B. Cluzel, F. de Fornel, and J. P. Martínez-Pastor, “Genetic algorithm designed silicon integrated photonic lens operating at 1550 nm,” Appl. Phys. Lett. 97, 071115 (2010).
[Crossref]

Deng, Q.

Doerr, C. R.

C. R. Doerr, M. Cappuzzo, E. Chen, A. Wong-Foy, L. Gomez, A. Griffin, and L. Buhl, “Bending of a planar lightwave circuit 2 × 2 coupler to desensitize it to wavelength, polarization, and fabrication changes,” IEEE Photon. Technol. Lett. 17, 1211–1213 (2005).
[Crossref]

Fernandez, F.

Fu, P.

Gomez, L.

C. R. Doerr, M. Cappuzzo, E. Chen, A. Wong-Foy, L. Gomez, A. Griffin, and L. Buhl, “Bending of a planar lightwave circuit 2 × 2 coupler to desensitize it to wavelength, polarization, and fabrication changes,” IEEE Photon. Technol. Lett. 17, 1211–1213 (2005).
[Crossref]

Green, W.

Griffin, A.

C. R. Doerr, M. Cappuzzo, E. Chen, A. Wong-Foy, L. Gomez, A. Griffin, and L. Buhl, “Bending of a planar lightwave circuit 2 × 2 coupler to desensitize it to wavelength, polarization, and fabrication changes,” IEEE Photon. Technol. Lett. 17, 1211–1213 (2005).
[Crossref]

Håkansson, A.

A. Håkansson, P. Sanchis, J. Sánchez-Dehesa, and J. Martí, “High-efficiency defect-based photonic-crystal tapers designed by a genetic algorithm,” J. Lightw. Technol. 23, 3881–3888 (2005).
[Crossref]

A. Håkansson and J. Sánchez-Dehesa, “Inverse designed photonic crystal de-multiplex waveguide coupler,” Opt. Express 13, 5440–5449 (2005).
[Crossref] [PubMed]

L. Sanchis, A. Håkansson, D. Lopez-Zanón, J. Bravo-Abad, and J. Sánchez-Dehesa, “Integrated optical devices design by genetic algorithm,” Appl. Phys. Lett. 84, 4460–4462 (2004).
[Crossref]

Halir, R.

He, S.

Hernandez-Figueroa, H.

D. Correia, J. da Silva, and H. Hernandez-Figueroa, “Genetic algorithm and finite-element design of short single-section passive polarization converter,” IEEE Photon. Technol. Lett. 15, 915–917 (2003).
[Crossref]

Hillerkuss, D.

Hochberg, M.

C. Chen, X. Zhu, Y. Liu, K. Wen, M. Chik, T. Baehr-Jones, M. Hochberg, and K. Bergman, “Programmable dynamically-controlled silicon photonic switch fabric,” J. Lightw. Technol. 34, 2952–2958 (2016).
[Crossref]

Huang, D.

Huang, W.

Iiyama, K.

Jaeger, N.

Jaeger, N. A. F.

Y. Wang, Z. Lu, M. Ma, H. Yun, F. Zhang, N. A. F. Jaeger, and L. Chrostowski, “Compact broadband directional couplers using subwavelength gratings,” IEEE Photon. J. 8, 7101408 (2016).
[Crossref]

James, R.

Jiang, X.

Jinguji, K.

A. Takagi, K. Jinguji, and M. Kawachi, “Wavelength characteristics of (2 × 2) optical channel-type directional couplers with symmetric or nonsymmetric coupling structures,” J. Lightwave Technol. 10, 735–746 (1992).
[Crossref]

A. Takagi, K. Jinguji, and M. Kawachi, “Broadband silica-based optical waveguide coupler with asymmetric structure,” Electron. Lett. 26, 132–133, (1990).
[Crossref]

Kawachi, M.

A. Takagi, K. Jinguji, and M. Kawachi, “Wavelength characteristics of (2 × 2) optical channel-type directional couplers with symmetric or nonsymmetric coupling structures,” J. Lightwave Technol. 10, 735–746 (1992).
[Crossref]

A. Takagi, K. Jinguji, and M. Kawachi, “Broadband silica-based optical waveguide coupler with asymmetric structure,” Electron. Lett. 26, 132–133, (1990).
[Crossref]

Komorowska, K.

Korn, D.

Lepage, G.

Leuthold, J.

Li, H.

H. Li, “Refractive index of silicon and germanium and its wavelength and temperature derivatives,” J. Phys. Chem. Ref. Data 9, 561–658 (1993).
[Crossref]

Li, X.

Lin, Y.

A. Liu, R. Wu, and Y. Lin, “A compact design of W-band high-pass waveguide filter using genetic algorithms and full-wave finite element analysis,” IEICE T. Electron. E88-C, 1764–1771 (2005).
[Crossref]

Liu, A.

A. Liu, R. Wu, and Y. Lin, “A compact design of W-band high-pass waveguide filter using genetic algorithms and full-wave finite element analysis,” IEICE T. Electron. E88-C, 1764–1771 (2005).
[Crossref]

Liu, B.

Liu, L.

Liu, R.

Liu, Y.

C. Chen, X. Zhu, Y. Liu, K. Wen, M. Chik, T. Baehr-Jones, M. Hochberg, and K. Bergman, “Programmable dynamically-controlled silicon photonic switch fabric,” J. Lightw. Technol. 34, 2952–2958 (2016).
[Crossref]

Lopez-Zanón, D.

L. Sanchis, A. Håkansson, D. Lopez-Zanón, J. Bravo-Abad, and J. Sánchez-Dehesa, “Integrated optical devices design by genetic algorithm,” Appl. Phys. Lett. 84, 4460–4462 (2004).
[Crossref]

Lu, Z.

Y. Wang, Z. Lu, M. Ma, H. Yun, F. Zhang, N. A. F. Jaeger, and L. Chrostowski, “Compact broadband directional couplers using subwavelength gratings,” IEEE Photon. J. 8, 7101408 (2016).
[Crossref]

Z. Lu, H. Yun, Y. Wang, Z. Chen, F. Zhang, N. Jaeger, and L. Chrostowski, “Broadband silicon photonic directional coupler using asymmetric-waveguide based phase control,” Opt. Express 23, 3795–3808 (2015).
[Crossref] [PubMed]

Ma, M.

Y. Wang, Z. Lu, M. Ma, H. Yun, F. Zhang, N. A. F. Jaeger, and L. Chrostowski, “Compact broadband directional couplers using subwavelength gratings,” IEEE Photon. J. 8, 7101408 (2016).
[Crossref]

Ma, Y.

Maese-Novo, A.

Maisonneuve, M.

Malitson, I.

Mao, J.

Marqués-Hueso, J.

J. Marqués-Hueso, L. Sanchis, B. Cluzel, F. de Fornel, and J. P. Martínez-Pastor, “Genetic algorithm designed silicon integrated photonic lens operating at 1550 nm,” Appl. Phys. Lett. 97, 071115 (2010).
[Crossref]

Martí, J.

A. Håkansson, P. Sanchis, J. Sánchez-Dehesa, and J. Martí, “High-efficiency defect-based photonic-crystal tapers designed by a genetic algorithm,” J. Lightw. Technol. 23, 3881–3888 (2005).
[Crossref]

Martínez-Pastor, J. P.

J. Marqués-Hueso, L. Sanchis, B. Cluzel, F. de Fornel, and J. P. Martínez-Pastor, “Genetic algorithm designed silicon integrated photonic lens operating at 1550 nm,” Appl. Phys. Lett. 97, 071115 (2010).
[Crossref]

Maruyama, T.

Meunier, M.

Michalewicz, Z.

Z. Michalewicz, Genetic Algorithms + Data Structures = Evolution Programs, 2nd ed. (Springer-Verlag, 1994).
[Crossref]

Miller, D.

D. Miller, “Designing linear optical components,” Opt. Photon. News 24, 38 (2013).
[Crossref]

Mojahedi, M.

Molina-Fernández, I.

Morino, H.

Neyts, K.

Ortega-Moñux, A.

Pan, T.

Pantouvaki, M.

Pérez-Galacho, D.

Qiu, C.

Romero-García, S.

Sánchez-Dehesa, J.

A. Håkansson and J. Sánchez-Dehesa, “Inverse designed photonic crystal de-multiplex waveguide coupler,” Opt. Express 13, 5440–5449 (2005).
[Crossref] [PubMed]

A. Håkansson, P. Sanchis, J. Sánchez-Dehesa, and J. Martí, “High-efficiency defect-based photonic-crystal tapers designed by a genetic algorithm,” J. Lightw. Technol. 23, 3881–3888 (2005).
[Crossref]

L. Sanchis, A. Håkansson, D. Lopez-Zanón, J. Bravo-Abad, and J. Sánchez-Dehesa, “Integrated optical devices design by genetic algorithm,” Appl. Phys. Lett. 84, 4460–4462 (2004).
[Crossref]

Sanchis, L.

J. Marqués-Hueso, L. Sanchis, B. Cluzel, F. de Fornel, and J. P. Martínez-Pastor, “Genetic algorithm designed silicon integrated photonic lens operating at 1550 nm,” Appl. Phys. Lett. 97, 071115 (2010).
[Crossref]

L. Sanchis, A. Håkansson, D. Lopez-Zanón, J. Bravo-Abad, and J. Sánchez-Dehesa, “Integrated optical devices design by genetic algorithm,” Appl. Phys. Lett. 84, 4460–4462 (2004).
[Crossref]

Sanchis, P.

A. Håkansson, P. Sanchis, J. Sánchez-Dehesa, and J. Martí, “High-efficiency defect-based photonic-crystal tapers designed by a genetic algorithm,” J. Lightw. Technol. 23, 3881–3888 (2005).
[Crossref]

Shi, Y.

Su, Y.

Takagi, A.

A. Takagi, K. Jinguji, and M. Kawachi, “Wavelength characteristics of (2 × 2) optical channel-type directional couplers with symmetric or nonsymmetric coupling structures,” J. Lightwave Technol. 10, 735–746 (1992).
[Crossref]

A. Takagi, K. Jinguji, and M. Kawachi, “Broadband silica-based optical waveguide coupler with asymmetric structure,” Electron. Lett. 26, 132–133, (1990).
[Crossref]

Tremblay, C.

Tseng, S.

Van Campenhout, J.

Vanbrabant, P.

Verheyen, P.

Vlasov, Y.

Wang, Y.

Y. Wang, Z. Lu, M. Ma, H. Yun, F. Zhang, N. A. F. Jaeger, and L. Chrostowski, “Compact broadband directional couplers using subwavelength gratings,” IEEE Photon. J. 8, 7101408 (2016).
[Crossref]

Z. Lu, H. Yun, Y. Wang, Z. Chen, F. Zhang, N. Jaeger, and L. Chrostowski, “Broadband silicon photonic directional coupler using asymmetric-waveguide based phase control,” Opt. Express 23, 3795–3808 (2015).
[Crossref] [PubMed]

Wangüemert-Pérez, J.

Wen, K.

C. Chen, X. Zhu, Y. Liu, K. Wen, M. Chik, T. Baehr-Jones, M. Hochberg, and K. Bergman, “Programmable dynamically-controlled silicon photonic switch fabric,” J. Lightw. Technol. 34, 2952–2958 (2016).
[Crossref]

Wen, R.

Wong-Foy, A.

C. R. Doerr, M. Cappuzzo, E. Chen, A. Wong-Foy, L. Gomez, A. Griffin, and L. Buhl, “Bending of a planar lightwave circuit 2 × 2 coupler to desensitize it to wavelength, polarization, and fabrication changes,” IEEE Photon. Technol. Lett. 17, 1211–1213 (2005).
[Crossref]

Wu, J.

Wu, R.

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Figures (17)

Fig. 1
Fig. 1

Schematic of an optically coupled system in general view.

Fig. 2
Fig. 2

Mode profiles of the quasi-TM polarization of (a) a single strip waveguide, (b) even and (c) odd modes of coupled waveguides.

Fig. 3
Fig. 3

ψ and ψ′ versus |Δβ| at λ = 1580 nm and G =300 nm.

Fig. 4
Fig. 4

Plots of lookup tables of (a) Δβ(λ, w) and (b) κ(λ, G) calculated by the FEM.

Fig. 5
Fig. 5

The kth section of the device.

Fig. 6
Fig. 6

Evolution of the best fitness value for the generic algorithm.

Fig. 7
Fig. 7

(a) Normalized power output of the bar and cross ports of the optimal design of a broadband 50%/50% coupler, the initial population, and a conventional directional coupler for the quasi-TM mode where h = 320 nm, = 320 nm, and λ = 1530 – 1630 nm. (b) Δβ, (c) κ, (d) w0, (e) w1, and (f) G versus z.

Fig. 8
Fig. 8

(a) Normalized power output of the bar and cross ports of the optimal design of a broadband 75%/25% coupler, the initial population, and a conventional directional coupler for the quasi-TM mode where h = 320 nm, = 320 nm, and λ = 1530 – 1630 nm. (b) Δβ, (c) κ, (d) w0, (e) w1, and (f) G versus z.

Fig. 9
Fig. 9

(a) Normalized power output of the bar and cross ports of the optimal design of broadband 25%/75% coupler, the initial population, and a conventional directional coupler for the quasi-TM mode where h = 320 nm, = 320 nm, and λ = 1530 – 1630 nm. (b) Δβ, (c) κ, (d) w0, (e) w1, and (f) G versus z.

Fig. 10
Fig. 10

(a) Normalized power output of the bar and cross ports of the optimal design of a broadband 0%/100% coupler, the initial population, and a conventional directional coupler for the quasi-TM mode where h = 320 nm, = 320 nm, and λ = 1530 – 1630 nm. (b) Δβ, (c) κ, (d) w0, (e) w1, and (f) G versus z.

Fig. 11
Fig. 11

(a) Normalized power output of the bar and cross ports of the optimal design of a broadband 50%/50% coupler, the initial population, and a conventional directional coupler for the quasi-TM mode where h = 320 nm, = 320 nm, and λ = 1480 – 1680 nm. (b) Δβ, (c) κ, (d) w0, (e) w1, and (f) G versus z.

Fig. 12
Fig. 12

(a) Normalized power output of the bar and cross ports of the optimal design of a broadband 50%/50% coupler, the initial population, and a conventional directional coupler for the quasi-TE mode where h = 320 nm, = 320 nm, and λ = 1530 – 1630 nm. (b) Δβ, (c) κ, (d) w0, (e) w1, and (f) G versus z.

Fig. 13
Fig. 13

(a) Normalized power output of the bar and cross ports of the optimal design of a broadband 50%/50% coupler, the initial population, and a conventional directional coupler for the quasi-TE mode where h = 220 nm, = 350 nm, and λ = 1530 – 1630 nm. (b) Δβ, (c) κ, (d) w0, (e) w1, and (f) G versus z.

Fig. 14
Fig. 14

Normalized optical power distribution fields of the optimal design for λ = 1530, 1580, and 1630 nm.

Fig. 15
Fig. 15

P0 and P1 versus wavelength for λ = 1500–1660 nm calculated by the CMT, BEM, and FEM.

Fig. 16
Fig. 16

Fabrication tolerance versus Δw for λ = 1530, 1580, and 1630 nm.

Fig. 17
Fig. 17

(a) Δβ and (b) κ versus z at λ = 1580 nm for different values of Δw.

Tables (1)

Tables Icon

Table 1 w0,i, w1,i, and Gi of the initial and final populations.

Equations (7)

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z [ A 0 ( λ , z ) A 1 ( λ , z ) ] = j [ β ¯ ( λ , z ) + Δ β ( λ , z ) κ ( λ , z ) κ ( λ , z ) β ¯ ( λ , z ) Δ β ( λ , z ) ] [ A 0 ( λ , z ) A 1 ( λ , z ) ] ,
A 0 ( λ , z ) = ( A 0 ( λ , 0 ) ( cos ( ψ z ) j Δ β sin ( ψ z ) ψ A 1 ( λ , 0 ) j κ sin ( ψ z ) ψ ) ) e j β ¯ z ,
A 1 ( λ , z ) = ( A 0 ( λ , 0 ) j κ sin ( ψ z ) ψ + A 1 ( λ , 0 ) ( cos ( ψ z ) + j Δ β sin ( ψ z ) ψ ) ) e j β ¯ z ,
[ A 0 , k + 1 A 1 , k + 1 ] = e j β ¯ Δ z [ cos ( ψ k Δ z ) j Δ β k sin ( ψ k Δ z ) ψ k j κ k sin ( ψ k Δ z ) ψ k j κ k sin ( ψ k Δ z ) ψ k cos ( ψ k Δ z ) + j Δ β k sin ( ψ k Δ z ) ψ k ] [ A 0 , k A 1 , k ]
V = [ G 1 G 2 G 17 w 0 , 1 w 0 , 2 w 0 , 17 ] .
F 50 / 50 = l = 0 10 ( P 0 ( λ l ) 0.5 ) 2 ,
V child = V 1 + R ( V 2 V 1 ) ,

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