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The coherent excitation of optical device through the interference effect of multiple beam provides a practical way to enhance the degree of real-time control of the optical response of device. In this work, the coherent control of polarization transformation of Bloch surface wave supported by dielectric multilayer is studied. The grooves are introduced into the top layer of the dielectric multilayer to achieve the polarization transformations of Bloch surface wave. Two coherent beams of Bloch surface waves are incident on the grooves from the left side and the right side of the structure, respectively. The polarization transformation efficiency of Bloch surface wave can be controlled in real time by designing the phase difference of polarization transformation coefficients and the phase delay of the incident coherent beams. Moreover, the output ports of polarization transformation of Bloch surface waves can be selectively excited. By using the proposed method, the controllable port transmission of Bloch surface wave related polarization component can be achieved. In this work, the design of phase difference from the polarization transformation coefficients is achieved by changing the separation distance of grooves. The predicted polarization transformation phenomena under the excitation of coherent beams are evidenced by the rigorous electromagnetic simulation. The research results have potential applications in on-chip integration of photonic circuitry.
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Keywords:
- Bloch surface waves /
- polarization transformation /
- dielectric multilayers /
- coherent control
[1] Zhao R Z, Geng G Z, Wei Q S, Liu Y, Zhou H Q, Zhang X, He C, Li X, Li X W, Wang Y T, Li J J, Huang L L 2022 Adv. Opt. Mater. 10 2102596
Google Scholar
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Google Scholar
[3] Luo W, Abbasi S A, Zhu S, Li X, Ho H P, Yuan W 2023 Nanophotonics 12 1797
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[4] Zhang X G, Yu Q, Jiang W X, Sun Y L, Bai L, Wang Q, Qiu C W, Cui T J 2020 Adv. Sci. 7 1903382
Google Scholar
[5] Zhang Y, Feng Y, Zhao J 2020 Carbon 163 244
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[6] Baranov D G, Krasnok A, Shegai T, Alù A, Chong Y 2017 Nat. Rev. Mater. 2 17064
Google Scholar
[7] Zhang J, MacDonald K F, Zheludev N I 2012 Light-Sci. Appl. 1 e18.
Google Scholar
[8] Baldacci L, Zanotto S, Biasiol G, Sorba L, Tredicucci A 2015 Opt. Express 23 9202
Google Scholar
[9] Yoon J W, Koh G M, Song S H, Magnusson 2012 Phys. Rev. Lett. 109 257402
Google Scholar
[10] Rao S M, Heitz J J F, Roger T, Westerberg N, Faccio D 2014 Opt. Lett. 39 5345
Google Scholar
[11] Fan Y, Liu Z, Zhang F, Zhao Q, Wei Z, Fu Q, Li J, Gu C, Li H 2015 Sci. Rep. 5 13956
Google Scholar
[12] Kang M, Chong Y D 2015 Phys. Rev. A 92 043826
Google Scholar
[13] Kang M, Zhang Z, Wu T, Zhang X, Xu Q, Krasnok A, Han J, Alù A 2022 Nat. Commun. 13 4536
Google Scholar
[14] Zhang H, Kang M, Zhang X, Guo W, Lv C, Li Y, Zhang W, Han J 2017 Adv. Mater. 29 1604252
Google Scholar
[15] Zhang Z, Kang M, Zhang X, Feng X, Xu Y, Chen X, Zhang H, Xu Q, Tian Z, Zhang W, Krasnok A, Han J, Alù A 2020 Adv. Mater. 32 2002341
Google Scholar
[16] Pirruccio G, Ramezani M, Rodriguez S R K, Rivas J G, 2016 Phys. Rev. Lett. 116 103002
Google Scholar
[17] Yeh P, Yariv A, Hong C S 1977 J. Opt. Soc. Am. 67 423
Google Scholar
[18] Kang X B, Lu H, Wang Z G 2018 Opt. Express 26 12769
Google Scholar
[19] Sinibaldi A, Danz N, Descrovi E, Munzert P, Schulz U, Sonntag F, Dominici L, Michelotti F 2012 Sens. Actuators B 174 292
Google Scholar
[20] Badugu R, Nowaczyk K, Descrovi E, Lakowicz J R 2013 Anal. Biochem. 442 83
Google Scholar
[21] Yang Q, Zhang C, Wu S, Li S, Bao Q, Giannini V, Maier S A, Li X 2018 Nano Energy 48 161
Google Scholar
[22] Nong J, Zhao B, Xiao X, Min C, Yuan X, Somekh M, Feng F 2022 Opt. Express 30 35085
Google Scholar
[23] Descrovi E, Sfez T, Quaglio M, Brunazzo D, Dominici L, Michelotti F, Herzig H P, Martin O J F, Giorgis F 2010 Nano Letters 10 2087
Google Scholar
[24] Luo H, Tang X, Lu Y, Wang P 2021 Phys. Rev. Appl. 16 014064
Google Scholar
[25] Perani T, Liscidini M 2020 Opt. Lett. 45 6534
Google Scholar
[26] Xiang Y, Lu Q, Wang R 2023 Opt. Express 31 22102
Google Scholar
[27] Wang M, Zhang H, Kovalevich T, Salut R, Kim M S, Suarez M A, Bernal M P, Herzig H P, Lu H, Grosjean T 2018 Light-Sci. Appl. 7 24
Google Scholar
[28] Deng C Z, Ho Y L, Clark J K, Yatsui T, Delaunay J J 2020 ACS Photonics 7 2915
Google Scholar
[29] Bezus E A, Bykov D A, Doskolovich L L 2021 Nanophotonics 10 4331
Google Scholar
[30] Safronov K R, Gulkin D N, Antropov I M, Abrashitova K A, Bessonov V O, Fedyanin A A 2020 ACS Nano 14 10428
Google Scholar
[31] Rodriguez G A, Aurelio D, Liscidini M, Weiss S M 2019 Appl. Phys. Lett. 115 011101
Google Scholar
[32] Chen J, Zhang D, Wang P, Ming H, Lakowicz J R 2018 Phys. Rev. Appl. 9 024008
Google Scholar
[33] Wang R, Chen J, Xiang Y, Kuai Y, Wang P, Ming H, Lakowicz J R, Zhang D 2018 Phys. Rev. Appl. 10 024032
Google Scholar
[34] Derudder H, Olyslager F, De Zutter D, Van den Berghe S 2001 IEEE Trans. Antennas Propag. 49 185
Google Scholar
[35] Liscidini M, Sipe J E 2009 J. Opt. Soc. Am. B 26 279
Google Scholar
[36] Moharam M G, Gaylord T K, Grann E B, Pommet D A 1995 J. Opt. Soc. Am. A 12 1068
Google Scholar
[37] Silberstein E, Lalanne P, Hugonin J P, Cao Q 2001 J. Opt. Soc. Am. A 18 2865
Google Scholar
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图 1 (a)多层结构的示意图; (b) 结构对应的输入和输出端口示意图
Figure 1. (a) Schematic diagram of the considered dielectric multilayer; (b) the schematic diagram of input and output ports in the structure.
图 2 单束TE-BSW入射到单个凹槽上的情况, 偏振转换系数rsp的幅度随TE-BSW的入射角度和凹槽宽度的变化
Figure 2. Amplitude of polarization transformation coefficient rsp as a function of the incidence angle of TE-BSW and the width of groove. Here, a single TE-BSW beam is incident on a single groove.
图 3 (a) 偏振转换系数
$ {r^{{\text{sp}}}} $ 和$ {t^{{\text{sp}}}} $ 的幅度随凹槽间距L的变化; (b)偏振转换系数的相位差$ {\theta _{{\text{r, sp}}}} - {\theta _{{\text{t, sp}}}} $ 随凹槽间距L的变化. 凹槽的宽度和深度都为250 nm, TE-BSW的入射角度θi = 49°Figure 3. (a) Amplitude of polarization transformation coefficients
$ {r^{{\text{sp}}}} $ and$ {t^{{\text{sp}}}} $ versus the separation distance L; (b) the phase difference of polarization transformation coefficients$ {\theta _{{\text{r, sp}}}} - {\theta _{{\text{t, sp}}}} $ versus the separation distance L. The width and depth of grooves are 250 nm, the incidence angle of TE-BSW is 49°.
图 4 (a)偏振转换强度(Rsp 和Tsp)随入射TE-BSW的延迟相位ψ的变化; (b)反射率(Rss)和透射率(Tss)随入射TE-BSW的延迟相位ψ的变化. 其中, 凹槽的间距L = 530 nm, 入射角度 θi = 49°
Figure 4. (a) Polarization transformation intensities Rsp and Tsp versus the phase delay ψ of incident TE-BSWs; (b) the reflectance Rss and transmittance Tss of TE-BSW versus the phase delay ψ of incident TE-BSWs. The separation distance L = 530 nm, the incidence angle θi = 49°.
图 5 当相位延迟(a)
$ \psi = {{\text{π }} \mathord{\left/ {\vphantom {{\text{π }} 2}} \right. } 2} $ 和 (b)$ \psi = {{3{\text{π }}} \mathord{\left/ {\vphantom {{3{\text{π }}} 2}} \right. } 2} $ 时, 结构的电场振幅分布. 其中凹槽的间距L = 530 nm, 入射角度θi = 49°, 白色的点线表示凹槽所在的区域Figure 5. Electric field amplitude distribution of structure for different phase delay (a)
$ \psi = {{\text{π }} \mathord{\left/ {\vphantom {{\text{π }} 2}} \right. } 2} $ and (b)$ \psi = {{3{\text{π }}} \mathord{\left/ {\vphantom {{3{\text{π }}} 2}} \right. } 2} $ . The separation distance L = 530 nm and the incidence angle θi = 49°, the dot lines denote the zone of grooves.
图 6 (a) 偏振转换强度(Rsp 和Tsp)随入射TE-BSW的延迟相位的变化; (b)反射(Rss)和透射(Tss)强度随入射TE-BSW的延迟相位的变化关系. 其中, 凹槽的间距L = 453 nm, 入射角度θi = 49°
Figure 6. (a) Polarization transformation intensity Rsp and Tsp versus the phase delay of the incident TE-BSWs; (b) the reflectance Rss and transmittance Tss versus the phase delay. The separation distance L = 453 nm and the incidence angle θi = 49°.
图 7 相位延迟
$ \psi = {\text{π }} $ 时, 结构的电场振幅分布, 其中凹槽的间距L = 453 nm, 入射角度θi = 49°, 白色的点线表示凹槽所在的区域Figure 7. Electric field amplitude distribution of structure for phase delay
$ \psi = {\text{π}}$ , the separation distance L = 453 nm and the incidence angle θi = 49°. The dotted lines dente the zone of grooves. -
[1] Zhao R Z, Geng G Z, Wei Q S, Liu Y, Zhou H Q, Zhang X, He C, Li X, Li X W, Wang Y T, Li J J, Huang L L 2022 Adv. Opt. Mater. 10 2102596
Google Scholar
[2] Ghosh S K, Das S, Bhattacharyya S 2022 J. Lightwave Technol. 40 6676
Google Scholar
[3] Luo W, Abbasi S A, Zhu S, Li X, Ho H P, Yuan W 2023 Nanophotonics 12 1797
Google Scholar
[4] Zhang X G, Yu Q, Jiang W X, Sun Y L, Bai L, Wang Q, Qiu C W, Cui T J 2020 Adv. Sci. 7 1903382
Google Scholar
[5] Zhang Y, Feng Y, Zhao J 2020 Carbon 163 244
Google Scholar
[6] Baranov D G, Krasnok A, Shegai T, Alù A, Chong Y 2017 Nat. Rev. Mater. 2 17064
Google Scholar
[7] Zhang J, MacDonald K F, Zheludev N I 2012 Light-Sci. Appl. 1 e18.
Google Scholar
[8] Baldacci L, Zanotto S, Biasiol G, Sorba L, Tredicucci A 2015 Opt. Express 23 9202
Google Scholar
[9] Yoon J W, Koh G M, Song S H, Magnusson 2012 Phys. Rev. Lett. 109 257402
Google Scholar
[10] Rao S M, Heitz J J F, Roger T, Westerberg N, Faccio D 2014 Opt. Lett. 39 5345
Google Scholar
[11] Fan Y, Liu Z, Zhang F, Zhao Q, Wei Z, Fu Q, Li J, Gu C, Li H 2015 Sci. Rep. 5 13956
Google Scholar
[12] Kang M, Chong Y D 2015 Phys. Rev. A 92 043826
Google Scholar
[13] Kang M, Zhang Z, Wu T, Zhang X, Xu Q, Krasnok A, Han J, Alù A 2022 Nat. Commun. 13 4536
Google Scholar
[14] Zhang H, Kang M, Zhang X, Guo W, Lv C, Li Y, Zhang W, Han J 2017 Adv. Mater. 29 1604252
Google Scholar
[15] Zhang Z, Kang M, Zhang X, Feng X, Xu Y, Chen X, Zhang H, Xu Q, Tian Z, Zhang W, Krasnok A, Han J, Alù A 2020 Adv. Mater. 32 2002341
Google Scholar
[16] Pirruccio G, Ramezani M, Rodriguez S R K, Rivas J G, 2016 Phys. Rev. Lett. 116 103002
Google Scholar
[17] Yeh P, Yariv A, Hong C S 1977 J. Opt. Soc. Am. 67 423
Google Scholar
[18] Kang X B, Lu H, Wang Z G 2018 Opt. Express 26 12769
Google Scholar
[19] Sinibaldi A, Danz N, Descrovi E, Munzert P, Schulz U, Sonntag F, Dominici L, Michelotti F 2012 Sens. Actuators B 174 292
Google Scholar
[20] Badugu R, Nowaczyk K, Descrovi E, Lakowicz J R 2013 Anal. Biochem. 442 83
Google Scholar
[21] Yang Q, Zhang C, Wu S, Li S, Bao Q, Giannini V, Maier S A, Li X 2018 Nano Energy 48 161
Google Scholar
[22] Nong J, Zhao B, Xiao X, Min C, Yuan X, Somekh M, Feng F 2022 Opt. Express 30 35085
Google Scholar
[23] Descrovi E, Sfez T, Quaglio M, Brunazzo D, Dominici L, Michelotti F, Herzig H P, Martin O J F, Giorgis F 2010 Nano Letters 10 2087
Google Scholar
[24] Luo H, Tang X, Lu Y, Wang P 2021 Phys. Rev. Appl. 16 014064
Google Scholar
[25] Perani T, Liscidini M 2020 Opt. Lett. 45 6534
Google Scholar
[26] Xiang Y, Lu Q, Wang R 2023 Opt. Express 31 22102
Google Scholar
[27] Wang M, Zhang H, Kovalevich T, Salut R, Kim M S, Suarez M A, Bernal M P, Herzig H P, Lu H, Grosjean T 2018 Light-Sci. Appl. 7 24
Google Scholar
[28] Deng C Z, Ho Y L, Clark J K, Yatsui T, Delaunay J J 2020 ACS Photonics 7 2915
Google Scholar
[29] Bezus E A, Bykov D A, Doskolovich L L 2021 Nanophotonics 10 4331
Google Scholar
[30] Safronov K R, Gulkin D N, Antropov I M, Abrashitova K A, Bessonov V O, Fedyanin A A 2020 ACS Nano 14 10428
Google Scholar
[31] Rodriguez G A, Aurelio D, Liscidini M, Weiss S M 2019 Appl. Phys. Lett. 115 011101
Google Scholar
[32] Chen J, Zhang D, Wang P, Ming H, Lakowicz J R 2018 Phys. Rev. Appl. 9 024008
Google Scholar
[33] Wang R, Chen J, Xiang Y, Kuai Y, Wang P, Ming H, Lakowicz J R, Zhang D 2018 Phys. Rev. Appl. 10 024032
Google Scholar
[34] Derudder H, Olyslager F, De Zutter D, Van den Berghe S 2001 IEEE Trans. Antennas Propag. 49 185
Google Scholar
[35] Liscidini M, Sipe J E 2009 J. Opt. Soc. Am. B 26 279
Google Scholar
[36] Moharam M G, Gaylord T K, Grann E B, Pommet D A 1995 J. Opt. Soc. Am. A 12 1068
Google Scholar
[37] Silberstein E, Lalanne P, Hugonin J P, Cao Q 2001 J. Opt. Soc. Am. A 18 2865
Google Scholar
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