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Enhanced nonlinear optical effects based on strong coupling between epsilon-near-zero mode and gap surface plasmons

## Enhanced nonlinear optical effects based on strong coupling between epsilon-near-zero mode and gap surface plasmons

Guo Qi-Qi, Chen Yi-Hang
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• #### Abstract

Optical nonlinear effect plays an important role in optical communication, optical detection, quantum information and other areas. However, it is constrained by the weakness of the nonlinear optical response of the common materials. The enhancement of the optical nonlinear response on a nanoscale becomes a critical challenge. Over the years, several ways to enhance the optical nonlinear effects have been suggested. In fact, these technologies can slightly enhance the optical nonlinear response. Recently, some research groups focused on the materials with vanished permittivity, which is called epsilon-near-zero (ENZ) material, showing that it can exhibit large optical nonlinearity due to the field enhancement in the material of this type. However, the ENZ material only holds a large optical nonlinear response in a limited spectral range. In order to overcome this limitation, here in this paper we report the ENZ mode which is excited by the ITO film and strongly coupled to the gap surface plasmons excited by the metal-dielectric-metal structure. To acquire the nonlinear refractive index n2, we first calculate the ITO permittivity through the Drude-Lorentz model and find the wavelength of the ENZ material. Then we calculate the time-dependent electron temperature and lattice temperature of ITO by the two-temperature model. According to the elevated electron temperature, we can calculate the plasma frequency ${\omega _{\rm p}}$, and by taking it into the Drude-Lorentz model, we can obtain a new permittivity of ITO compared with the initial one. Finally, we can calculate the variation of the refractive index $\Delta n$, and the nonlinear refractive index ${n_2} = \Delta n/{I_0}$. In this paper, our coupled structure exhibits a broadband (～1000 nm bandwidth) enhancement of the nonlinear optical effect in the near-infrared spectrum, a maximum nonlinear refractive index n2 as large as 3.02 cm2·GW–1, which is nearly 3 orders larger than the previously reported nonlinear refractive index of bare ITO film. As a result, it is possible to realize a dramatically large variation of nonlinear refractive index under a low-power optical field. It is expected to be used in the nano photonic devices such as optical storage, all-optical switches, etc.

#### References

 [1] Boyd R W, Gehr R J, Fischer G L, Sipe J E 1996 Pure Appl. Optics J. European Optical Society Part A 5 505 [2] Boyd R W, Sipe J E 1994 J. Opt. Soc. Am. B 11 297 [3] Sarychev A K, Shalaev V M 2000 Phys. Rep. 335 275 [4] Abb M, Albella P, Aizpurua J, Muskens O L 2011 Nano Lett. 11 2457 [5] Abb M, Wang Y, De Groot CH, Muskens O L 2014 Nat.Commun. 5 4869 [6] Lee J, Tymchenko M, Argyropoulos C, Chen P Y, Lu F, Demmerle F, Boehm G, Amann MC, Alù A, Belkin M A 2014 Nature 511 65 [7] Yang Y, Wang W, Boulesbaa A, Kravchenko I I, Briggs D P, Puretzky A, Geohegan D, Valentine J 2015 Nano Lett. 15 7388 [8] Alexander E M, Andrey E M, Anton Y B, Tatiana V M, Dragomir N N, Yuri S K 2015 Laser Photonics Rev. 9 195 [9] Engheta N 2013 Science 340 286 [10] Liberal I, Mahmoud A M, Li Y, Edwards B, Engheta N 2017 Science 355 1058 [11] Maas R, Parsons J, Engheta N, Polman A 2013 Nat. Photonics 7 907 [12] Capretti A, Wang Y, Engheta N, Dal Negro L 2015 Opt. Lett. 40 1500 [13] Capretti A, Wang Y, Engheta N, Dal Negro L 2015 Acs Photonics 2 1584 [14] Caspani L, Kaipurath R, Clerici M, Ferrera M, Roger T, Kim J, Kinsey N, Pietrzyk M, Falco AD, Shalaev V 2016 Phys. Rev. Lett. 116 233901 [15] Alam M Z, Leon I D, Boyd R W 2016 Science 352 795 [16] Vassant S, Hugonin J P, Marquier F, Greffet J J 2012 Opt. Express 20 23971 [17] Campione S, Brener I, Marquier F 2015 Phys. Rev. B 91 121408 [18] Hendrickson J R, Vangala S, Dass C K, Gibson R, Goldsmith J, Leedy K D, Walker D, Cleary J, Kim W, Guo J 2018 ACS Photonics 5 776 [19] Luk T S, Ceglia D D, Liu S, Keeler G A, Prasankumar R P, Vincenti M A, Scalora M, Sinclair M B, Campione S 2015 Appl. Phys. Lett. 106 151103 [20] Zhou Y, Alam M Z, Karimi M, Upham J, Boyd R W 2020 Nat. Commun. 11 2180 [21] Vial A, Grimault A S, Macias D, Barchiesi D, Chapelle M L D L 2005 Phys. Rev. B 71 85416 [22] Alam M Z, Schulz S A, Upham J, De Leon I, Boyd R W 2018 Nat. Photonics 12 79 [23] Carpene E 2006 Phys. Rev. B 74 4301 [24] Törmä1 P, Barnes W L 2015 Rep. Prog. Phys. 78 013901 [25] Runnerstrom E L, Kelley K P, Folland T, Nolen J R, Engheta N, Caldwell J D, Jon-Paul M 2019 Nano Lett. 19 948 [26] Palik, Edward D 1985 Handbook of optical constants of solids (Academic Press) pp350, 749 [27] Smith D R, Vier D C, Koschny T, Soukoulis C M 2005 Phys. Rev. E: Stat. Nonlinear, Soft Matter Phys. 72 036617

#### Cited By

• 图 1  器件结构设计图, 包含银圆盘、ITO材料层、二氧化硅介质层、银膜层以及硅基底(未画出)　(a)三维结构图; (b)平面结构图及对应参数的示意图

Figure 1.  Design of the device, including the silver disc, the ITO material layer, the SiO2 dielectric spacer layer, the silver film layer, and the silicon substrate (not drawn in the figure): (a) Three-dimensional structure; (b) the planar graph and parameter of the structure.

图 2  ITO材料的介电常数的实部(黑色线)与虚部(红色线)

Figure 2.  Real part (black line) and the imaginary part (red line) of permittivity of the ITO.

图 3  FDTD模拟扫描计算得到的耦合结构的反射率随银圆盘半径的变化　(a)无ITO材料层; (b)有ITO材料层; (c)由单独ENZ模式与单独间隙表面等离激元的色散曲线(红色点划线)得到的强耦合作用产生的上支和下支色散曲线(黑色实线)

Figure 3.  Reflectance of the coupled structure vs. the radius of the silver disc by using FDTD solutions: (a) Without ITO material layer; (b) with ITO material layer; (c) theoretical dispersion curves of coupled upper branch and lower branch (black solid lines) resulting from strong coupling obtained by the bare ENZ mode and GPP dispersion curves (red dot dash lines).

图 4  ITO中激发的ENZ模式与间隙表面等离极化激元强耦合的电磁场分布图　(a)−(d)负失谐; (e)−(h)零失谐; (i)−(l)正失谐

Figure 4.  Electric and magnetic field distribution of the strong coupling between the ENZ mode that excited in the ITO film and the GPP: (a)−(d) Negative detuning; (e)−(h) zero detuning; (i)−(l) positive detuning.

图 5  (a)耦合结构的反射谱; (b)−(d)主共振位置(1180 nm)处总电场、电场x分量以及z分量分布

Figure 5.  (a) Reflectance spectrum of the coupled structure; (b)−(d) the total electric field, the x-component, the z-component distribution at the main resonance (1180 nm) respectively.

图 6  (a)通过双温模型计算得到的电子温度Te(t)和晶格温度Tl(t); (b)非线性折射率n 2, 黑线为文中结构的非线性折射率, 红点为文献[15]报道的单层ITO薄膜的n 2值乘以200倍, 蓝色点线为文献[15]单层ITO薄膜结构通过双温模型理论计算得到的n 2值乘以200倍

Figure 6.  (a) Calculated electron temperature and lattice temperature through the two-temperature model; (b) nonlinear refractive index n 2, where the black line represents the n 2 of the coupled structure, the red dots represent 200 times of the n 2 of bare ITO film reported in Ref. [15], the blue dot line represents 200 times of the calculated theoretical value of n 2 of bare ITO film reported in Ref. [15] by two-temperature model.

•  [1] Boyd R W, Gehr R J, Fischer G L, Sipe J E 1996 Pure Appl. Optics J. European Optical Society Part A 5 505 [2] Boyd R W, Sipe J E 1994 J. Opt. Soc. Am. B 11 297 [3] Sarychev A K, Shalaev V M 2000 Phys. Rep. 335 275 [4] Abb M, Albella P, Aizpurua J, Muskens O L 2011 Nano Lett. 11 2457 [5] Abb M, Wang Y, De Groot CH, Muskens O L 2014 Nat.Commun. 5 4869 [6] Lee J, Tymchenko M, Argyropoulos C, Chen P Y, Lu F, Demmerle F, Boehm G, Amann MC, Alù A, Belkin M A 2014 Nature 511 65 [7] Yang Y, Wang W, Boulesbaa A, Kravchenko I I, Briggs D P, Puretzky A, Geohegan D, Valentine J 2015 Nano Lett. 15 7388 [8] Alexander E M, Andrey E M, Anton Y B, Tatiana V M, Dragomir N N, Yuri S K 2015 Laser Photonics Rev. 9 195 [9] Engheta N 2013 Science 340 286 [10] Liberal I, Mahmoud A M, Li Y, Edwards B, Engheta N 2017 Science 355 1058 [11] Maas R, Parsons J, Engheta N, Polman A 2013 Nat. Photonics 7 907 [12] Capretti A, Wang Y, Engheta N, Dal Negro L 2015 Opt. Lett. 40 1500 [13] Capretti A, Wang Y, Engheta N, Dal Negro L 2015 Acs Photonics 2 1584 [14] Caspani L, Kaipurath R, Clerici M, Ferrera M, Roger T, Kim J, Kinsey N, Pietrzyk M, Falco AD, Shalaev V 2016 Phys. Rev. Lett. 116 233901 [15] Alam M Z, Leon I D, Boyd R W 2016 Science 352 795 [16] Vassant S, Hugonin J P, Marquier F, Greffet J J 2012 Opt. Express 20 23971 [17] Campione S, Brener I, Marquier F 2015 Phys. Rev. B 91 121408 [18] Hendrickson J R, Vangala S, Dass C K, Gibson R, Goldsmith J, Leedy K D, Walker D, Cleary J, Kim W, Guo J 2018 ACS Photonics 5 776 [19] Luk T S, Ceglia D D, Liu S, Keeler G A, Prasankumar R P, Vincenti M A, Scalora M, Sinclair M B, Campione S 2015 Appl. Phys. Lett. 106 151103 [20] Zhou Y, Alam M Z, Karimi M, Upham J, Boyd R W 2020 Nat. Commun. 11 2180 [21] Vial A, Grimault A S, Macias D, Barchiesi D, Chapelle M L D L 2005 Phys. Rev. B 71 85416 [22] Alam M Z, Schulz S A, Upham J, De Leon I, Boyd R W 2018 Nat. Photonics 12 79 [23] Carpene E 2006 Phys. Rev. B 74 4301 [24] Törmä1 P, Barnes W L 2015 Rep. Prog. Phys. 78 013901 [25] Runnerstrom E L, Kelley K P, Folland T, Nolen J R, Engheta N, Caldwell J D, Jon-Paul M 2019 Nano Lett. 19 948 [26] Palik, Edward D 1985 Handbook of optical constants of solids (Academic Press) pp350, 749 [27] Smith D R, Vier D C, Koschny T, Soukoulis C M 2005 Phys. Rev. E: Stat. Nonlinear, Soft Matter Phys. 72 036617
•  Citation:
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• Abstract views:  396
• Cited By: 0
##### Publishing process
• Received Date:  07 February 2021
• Accepted Date:  30 April 2021
• Available Online:  07 June 2021
• Published Online:  20 September 2021

## Enhanced nonlinear optical effects based on strong coupling between epsilon-near-zero mode and gap surface plasmons

###### Corresponding author: Chen Yi-Hang, yhchen@scnu.edu.cn
• Guangdong Provincial Key Laboratory of Quantum Engineering and Quantum Materials, School of Physics and Telecommunication Engineering, South China Normal University, Guangzhou 510006, China

Abstract: Optical nonlinear effect plays an important role in optical communication, optical detection, quantum information and other areas. However, it is constrained by the weakness of the nonlinear optical response of the common materials. The enhancement of the optical nonlinear response on a nanoscale becomes a critical challenge. Over the years, several ways to enhance the optical nonlinear effects have been suggested. In fact, these technologies can slightly enhance the optical nonlinear response. Recently, some research groups focused on the materials with vanished permittivity, which is called epsilon-near-zero (ENZ) material, showing that it can exhibit large optical nonlinearity due to the field enhancement in the material of this type. However, the ENZ material only holds a large optical nonlinear response in a limited spectral range. In order to overcome this limitation, here in this paper we report the ENZ mode which is excited by the ITO film and strongly coupled to the gap surface plasmons excited by the metal-dielectric-metal structure. To acquire the nonlinear refractive index n2, we first calculate the ITO permittivity through the Drude-Lorentz model and find the wavelength of the ENZ material. Then we calculate the time-dependent electron temperature and lattice temperature of ITO by the two-temperature model. According to the elevated electron temperature, we can calculate the plasma frequency ${\omega _{\rm p}}$, and by taking it into the Drude-Lorentz model, we can obtain a new permittivity of ITO compared with the initial one. Finally, we can calculate the variation of the refractive index $\Delta n$, and the nonlinear refractive index ${n_2} = \Delta n/{I_0}$. In this paper, our coupled structure exhibits a broadband (～1000 nm bandwidth) enhancement of the nonlinear optical effect in the near-infrared spectrum, a maximum nonlinear refractive index n2 as large as 3.02 cm2·GW–1, which is nearly 3 orders larger than the previously reported nonlinear refractive index of bare ITO film. As a result, it is possible to realize a dramatically large variation of nonlinear refractive index under a low-power optical field. It is expected to be used in the nano photonic devices such as optical storage, all-optical switches, etc.

Reference (27)

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