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Second harmonic generation using IMI grating structure
Optik - International Journal for Light and Electron Optics 183 (2019) 247–252
Contents lists available at ScienceDirect
Optik journal homepage: www.elsevier.com/locate/ijleo
Original research article
Second harmonic generation using IMI grating structure Hamed Kaveha, Alireza Karimib, a b
⁎
T
Department of Electrical Engineering, Bandar Abbas branch, Islamic Azad University, Bandar Abbas, Iran Department of Electrical Engineering, Shiraz branch, Islamic Azad University, Shiraz, Iran
A R T IC LE I N F O
ABS TRA CT
Keywords: Plasmonics Second harmonic generation IMI structure
In this paper, the nonlinear effect of second harmonic generation (SHG) in insulator-metal-insulator plasmonic waveguides was investigated. Initially, an IMI plasmonic waveguide was simulated and its SHG effect was considered, then an IMI grating structure was proposed to increase the SHG effect and reduce its loss. Finally, it is realized that the proposed structure can enhance the SHG effect and the frequency spectra compared to the fundamental structure.
1. Introduction The field of Plasmonic is an important part of nanophotonics that has attracted much attention and has indicated various applications in the last decade. Metallic nanoparticles have massive oscillations of plasmons and support localized plasmon resonances. These resonances can be set from UV to mid-range infrared frequencies, depending on the geometry, dimensions and environments in which the nanoparticles are embedded. Large local electromagnetic fields could be generated by plasmon resonances, where the nanoparticles affect light, resulting in unique optical properties. Plasmonic nanoparticles have provided many optical capabilities, such as surface-enhanced molecule sensing, solar energy, chemical photocatalysis, cancer therapy, environment sensing and infrared photo-detection. One of the most interesting applications could be generating strong nonlinear optical effects by low excitation powers when the fields are enhanced and confined in a small volume [1]. The studies of surface electromagnetic (EM) waves commenced in the early 1900′s. In 1907 initially the surface wave property “Zenneck wave” was analyzed theoretically. In 1909, the possibility of radio waves propagating around the earth was realized by Sommerfield. Then the existence of surface plasmons at a metal surface was proposed theoretically and experimentally in 1941. In 1968 Otto and Kretschmann and Raether observed SPPs optically in the attenuated total reflection (ATR) experiments. Since then SPPs have been extensively explored for several decades for their potentials in nanophotonics, metamaterials and biosensing. The surface localization property of SPs, confining the optical mode to subwavelength scale and minimizing the optical mode size, therefore, conventional dielectric-based waveguides could be replaced by plasmonic waveguides an intriguing [2]. Nonlinear optical effects occur when electronic mobility in a strong electromagnetic field cannot be considered harmonic. The incident fields can be mixed by growth of the anharmonicity as power series in the field strength creating new fields that oscillate at the sums and differences of the incident frequencies which can propagate in various directions. The second and third order are the most prominent impacts for different applications. Hence, nonlinear optical phenomena could be beneficial to various applications, such as ultrafast switching, optical signal processing, production of ultra-short pulses, and frequency conversion [3]. Amongst the nonlinear phenomena, Second Harmonic Generation (SHG) has proven to be a surface sensitive measurement tool, hence it has been used for a number of research over the last decades [4]. Second harmonic generation (SHG) is one the most interesting and important nonlinear phenomena, in which two photons are
⁎
Corresponding author. E-mail addresses: [email protected] (H. Kaveh), [email protected] (A. Karimi).
https://doi.org/10.1016/j.ijleo.2019.02.138 Received 18 January 2019; Accepted 24 February 2019 0030-4026/ © 2019 Elsevier GmbH. All rights reserved.
Optik - International Journal for Light and Electron Optics 183 (2019) 247–252
H. Kaveh and A. Karimi
Fig. 1. The schematic of the planar IMI plasmonic waveguide.
Fig. 2. Ey distributions of the pulse at a propagation distance in the nonlinear material sandwiching a silver film (d = 20 nm) in three time steps (a) 30 fs (b) 60 fs (c) 90 fs. 248
Optik - International Journal for Light and Electron Optics 183 (2019) 247–252
H. Kaveh and A. Karimi
Fig. 3. IMI plasmonic waveguide with grating structure.
destroyed in a frequency such as f and replaced by a photon in 2f with half the incident wavelength [5]. For the first time, Peter Franken, A. E. Hill, C. W. Peters, and G. Weinreich introduced second harmonic generation, at the University of Michigan, in 1961 [6]. According to the last research, the nonlinear response of the surface of the metal is associated with understanding the surface structure of the way it was formed and can be designed by geometry of the metal layer. In addition, considering its feature, environments that provide field enhancement are able to increase SHG efficiency [7]. Some of the applications of SHG could be an appropriate assistance of research on material science [8], and laser industry [9]. Over the past few years, several articles regarding SHG enhancement have been presented such as, how hybrid plasmonic waveguides could improve second harmonic generation [10], Second-order nonlinear frequency conversion processes in plasmonic slot waveguides [11]. In this study, SHG, one of the important nonlinear effects, was investigated in IMI waveguides. For this purpose, a grating structure has been used and it has been determined how this structure modify the enhancement of SHG.
2. The structure of IMI waveguide Two planar structures could be described as propagation of a plasmonic wave: insulator-metal-insulator waveguides (IMI) and metal-insulator-metal waveguides (MIM). In both of them, there is a slight gap between two surface plasmons or plasmon polartions supporting dielectric-metal interfaces. Surface plasmon polaritons (SPP) on each interface can be coupled across the two interfaces. Therefore, the gap between them is small enough and the guided optical modes can be achieved for the waveguide. Since the efficiency of most nonlinear phenomena can be remarkably increased, the improvement of the resulting field makes them favorable for surface nonlinear optics [12]. Fig. 1 shows the schematic of a planar IMI plasmonic waveguide for the investigating of SHG enhancement, known as fundamental plasmonic waveguide. In this waveguide, a thin silver film sandwiched by two nonlinear media and a propagation length of 20 μm for a SPP mode with a thickness of d = 20 nm [13]. In this research we should focus the light to the smallest spot. Consider a Gaussian TM beam incident from the left side, the y component of the electric field is described as: ⎛
Ey = E 0 *
y2 ⎞
⎜− y 2 ⎞ − (t − t 0) w0 2⎟ * e⎝ w (x ) ⎠ * cos ⎛ω0 * t − k 0 * x + η (x ) − k 0 * * e Δt 2 w (x ) 2 * R (x ) ⎠ ⎝ ⎜
2
⎟
(1)
Where In these expressions, k is the wave number which means the spatial frequency of the wave, y is the in-plane transverse coordinate, ω is the angular frequency, w(x) is proportional to the width of the beam, and the constant w0 is called the minimum waist. The wave front of the beam is not exactly planar; it propagates like a spherical wave with radius R(x) and η(x) is known as Gouy phase shift which slightly shifts the phase of the wave front of the wave as a whole. [14]. The parameters in the simulation described as: the center frequency f0 = 2.84 × 1014 Hz, the pulse width Δt = 10 fs, the pulse time delay t0 = 25 fs, the time step 0.02 fs, and the peak electric field E0 = 30 kV. We assumed the metal is silver for the simulations with ωD = 1.38 × 1016 Hz, γ = 2.73 × 1013 Hz. Where γ is the damping in time and ωD is the plasma frequency [15]. The nonlinear properties for second harmonic generation in a material can be defined with the following matrix,
Fig. 4. The frequency spectra of the pulse having propagated in IMI grating waveguide including triangles (a) with 200 nm depth (b) with 250 nm depth (c) with 300 nm depth. 249
Optik - International Journal for Light and Electron Optics 183 (2019) 247–252
H. Kaveh and A. Karimi
Fig. 5. The frequency spectra of the pulse having propagated in IMI grating waveguide including (a) one slot (b) four slots (c) 10 slots.
⎡ d11 d12 d13 d14 d15 d16 ⎤ ⎢ d21 d22 d23 d24 d25 d26 ⎥. ⎢ ⎦ ⎣ d31 d32 d33 d34 d35 d36 ⎥
2 ⎡ Ex ⎤ ⎢ Ey 2 ⎥ ⎢ 2 ⎥ ⎢ Ez ⎥ ⎢ 2EzEy ⎥ ⎢ 2EzEx ⎥ ⎢ 2ExEy ⎥ ⎣ ⎦
(2) −17
We set the second-order nonlinear susceptibility coefficient d22 = 10 F/V, and all the rest as zero, since the main component of the electric field is oriented towards the y direction. Fig.2 indicates Ey distributions of the pulse after propagation in three time steps (30 fs, 60 fs, and 90 fs) in the nonlinear material described by the Drude model. 3. Enhancement of SHG in IMI waveguides In Fig. 3 a new structure is proposed, introducing an IMI grating plasmonic waveguide. According to the figure, a thin silver film with a thickness of 20 nm is sandwiched by two nonlinear media from two sides. Moreover, the structure has right triangle slots on both sides known as grating, which facilitates the further connection between photons and plasmons [16]. In order to reach the most enhanced SHG, different triangles with different depths are simulated. It is revealed that the best measure for the depth and length of triangles would be 250 nm and 500 nm, respectively. Fig. 4 illustrates the SHG effect in the grating structure with different depth. Furthermore, the gap between the right triangles is calculated in order to achieve the maximum second harmonic generation. In other words, different numbers of slots are simulated so as to achieve the enhanced SHG. The simulations is carried out from 13 slots to one slot on each side and according to Fig.5 it could be observed that the SHG effect increases due to decreasing the number of triangles. Therefore, the growth continues until the number of slots reaches four. Afterwards, declining the number of slots from four to one is equivalent to the gradual reduction of SHG enhancement. Thus, the most appropriate structure for the SHG enhancement could be the Fig.3. Thus, in this waveguide, the number of slots and the intervals between triangles were considered 4 and 5000 nm, respectively. As a result, adjusting the intervals is associated with optimizing the number of slots. Fig. 6 shows the Ey distribution of the pulse after propagation within 3 time steps (30 fs, 60 fs, and 90 fs) in a nonlinear material with a grating structure. It can be seen that a significant increase in the electric field peak of the SHG occurred due to the stimulation of SPPs. Furthermore, in time domain simulation thorough the Comsol software, a point probe is set on the dielectric surface to measure the pulse’s electric field along the metal surface and the results are utilized to calculate the frequency spectrum with Fast Fourier Transforms. Regarding Fig.7, a second harmonic wave is generated at the central frequency of 5.68 * 1014 Hz, and the electric field improvement is resulted in SHG enhancement consequently as evidenced by the growth in the second harmonic component. 4. Conclusion In this research, we have simulated the Drude model in time-domain study through the Comsol software in order to analyze the grating influence on SHG optimization in an IMI plasmonic waveguide. This study investigated SHG effect in the fundamental and proposed IMI plasmonic waveguides. With regard to above mentioned, a nonlinear medium was used as dielectric. These two IMI plasmonic waveguides were studied, and their SHG simulation outcomes have been presented. The proposed waveguide had right triangles geometries on both sides of the nonlinear media and the quantity of slots was calculated to reach the highest SHG. As it was explained previously, the length of the waveguide is 20 μm and the quantity of triangles changed in this distance. Hence, the quantity of triangles is considered to be four here. Looking more closely at the given figures predicting a significant second harmonic wave could be generated in the grating 250
Optik - International Journal for Light and Electron Optics 183 (2019) 247–252
H. Kaveh and A. Karimi
Fig. 6. Ey distributions of the pulse at a propagation distance in the nonlinear material with a grating structure in three time steps (a) 30 fs (b) 60 fs (c) 90 fs.
plasmonic waveguides. Figs. 2 and 6 illustrated the amplitude of electric field diagrams for both the fundamental and proposed plasmonic waveguides. As shown in Fig. 8, throughout the waveguide, the electric field amplitude diagram has considerably increased in the grating structure. It can be observed in the middle of the diagram that there is a slight discrepancy between the two trends. In contrast, at the end of the grating waveguide a dramatic enhancement has occurred in the amount of electric filed as compared to the trend of the fundamental structure. Figs. 7 and 8 show the frequency spectrum and Ey distribution of different structures, respectively. As displayed in the figures, the peak electric field of the proposed structure is remarkably enhanced as a result of stimulation of SPPs. In general, it is logical to conclude that this proposed waveguide could be favorable in the enhancement of SHG. Therefore, the proposed structure is an appropriate plasmonic waveguide for future applications of SHG.
251
Optik - International Journal for Light and Electron Optics 183 (2019) 247–252
H. Kaveh and A. Karimi
Fig. 7. The frequency spectra of the pulse having propagated in (a) fundamental IMI waveguide (b) grating IMI structure.
Fig. 8. Ey distributions amplitude within three time steps in comparison.
References [1] Y. Zhang, Nonlinear nanophotonic systems for harmonic generation, parametric amplification, Optical Processing and Single-Molecule Detection (2015) 2–3 Retrieved from http://hdl.handle.net/1911/90374. [2] J. Chen, Metal-insulator-insulator-metal Plasmonic Waveguides and Devices, p. 1 (2009) Retrieved from http://digitalrepository.unm.edu/ece_etds/48. [3] M. Kauranen, A.V. Zayats, Nonlinear plasmonics. Handbook of Surface Science, (2012), https://doi.org/10.1016/B978-0-444-59526-3.00011-2. [4] Wunderlich, S., & Peschel, U. (2013). Plasmonic enhancement of second harmonic generation on metal coated nanoparticles, 21(16), 6622–6625. https://doi. org/10.1364/OE.21.018611. [5] N.M. Jassim, A review: optical second – harmonic generation enhancement via plasmonic surface - theory and applications, Adv. Res. 7 (6) (2016) 1–17, https:// doi.org/10.9734/AIR/2016/27351. [6] P. Franken, A. Hill, C. Peters, G. Weinreich, Generation of optical harmonics, Phys. Rev. Lett. 7 (4) (1961) 118–119, https://doi.org/10.1103/PhysRevLett.7.118. [7] R. Chandrasekar, N.K. Emani, A. Lagutchev, V.M. Shalaev, C. Ciracì, D.R. Smith, A.V. Kildishev, Second harmonic generation with plasmonic metasurfaces: direct comparison of electric and magnetic resonances, Opt. Mater. Express (2015), https://doi.org/10.1364/OME.5.002682. [8] V.K. Valev, Characterization of nanostructured plasmonic surfaces with second harmonic generation, Langmuir 28 (44) (2012) 15454–15471, https://doi.org/ 10.1021/la302485c PMID 22889193. [9] S. Favre, T.C. Sidler, R. Salathé, S. Member, High-power long-pulse second harmonic generation and optical damage with free-running Nd : YAG laser, IEEE J. Sel. Top. Quantum Electron. 39 (6) (2003) 733–740. [10] M.Z. Alam, J.S. Aitchison, M. Mojahedi, A marriage of convenience: Hybridization of surface plasmon and dielectric waveguide modes, Laser Photon. Rev. 408 (3) (2014) 394–408, https://doi.org/10.1002/lpor.201300168. [11] S.B. Hasan, C. Rockstuhl, T. Pertsch, F. Lederer, Second-order nonlinear frequency conversion processes in plasmonic slot waveguides, J. Opt. Soc. Am. B (2012), https://doi.org/10.1364/JOSAB.29.001606. [12] M. Soltani, M. Nikoufard, M. Dousti, Enhancement of second harmonic generation in metal-insulator-Metal plasmonic waveguides, Plasmonics (2017), https:// doi.org/10.1007/s11468-016-0445-5. [13] H. Li, N. Zhu, H. Zhang, Z. Chen, T. Mei, Nonlocal effects on second harmonic generation in nanofilm plasmonic structure, Opt. Commun. (2015), https://doi. org/10.1016/j.optcom.2014.11.055. [14] E.J. Galvez, Gaussian Beams, Retrieved from (2009), p. p. 6 http://www.colgate.edu/portaldata/imagegallerywww/98c178dc-7e5b-4a04-b0a1-a73abf7f13d5. [15] A. Wiener, A.I. Fernández-Domínguez, A.P. Horsfield, J.B. Pendry, S.A. Maier, Nonlocal effects in the nanofocusing performance of plasmonic tips, Nano Lett. (2012), https://doi.org/10.1021/nl301478n. [16] T. Ning, H. Pietarinen, O. Hyvärinen, R. Kumar, T. Kaplas, M. Kauranen, G. Genty, Efficient second-harmonic generation in silicon nitride resonant waveguide gratings, Opt. Lett. (2012), https://doi.org/10.1364/OL.37.004269.
252
Contents lists available at ScienceDirect
Optik journal homepage: www.elsevier.com/locate/ijleo
Original research article
Second harmonic generation using IMI grating structure Hamed Kaveha, Alireza Karimib, a b
⁎
T
Department of Electrical Engineering, Bandar Abbas branch, Islamic Azad University, Bandar Abbas, Iran Department of Electrical Engineering, Shiraz branch, Islamic Azad University, Shiraz, Iran
A R T IC LE I N F O
ABS TRA CT
Keywords: Plasmonics Second harmonic generation IMI structure
In this paper, the nonlinear effect of second harmonic generation (SHG) in insulator-metal-insulator plasmonic waveguides was investigated. Initially, an IMI plasmonic waveguide was simulated and its SHG effect was considered, then an IMI grating structure was proposed to increase the SHG effect and reduce its loss. Finally, it is realized that the proposed structure can enhance the SHG effect and the frequency spectra compared to the fundamental structure.
1. Introduction The field of Plasmonic is an important part of nanophotonics that has attracted much attention and has indicated various applications in the last decade. Metallic nanoparticles have massive oscillations of plasmons and support localized plasmon resonances. These resonances can be set from UV to mid-range infrared frequencies, depending on the geometry, dimensions and environments in which the nanoparticles are embedded. Large local electromagnetic fields could be generated by plasmon resonances, where the nanoparticles affect light, resulting in unique optical properties. Plasmonic nanoparticles have provided many optical capabilities, such as surface-enhanced molecule sensing, solar energy, chemical photocatalysis, cancer therapy, environment sensing and infrared photo-detection. One of the most interesting applications could be generating strong nonlinear optical effects by low excitation powers when the fields are enhanced and confined in a small volume [1]. The studies of surface electromagnetic (EM) waves commenced in the early 1900′s. In 1907 initially the surface wave property “Zenneck wave” was analyzed theoretically. In 1909, the possibility of radio waves propagating around the earth was realized by Sommerfield. Then the existence of surface plasmons at a metal surface was proposed theoretically and experimentally in 1941. In 1968 Otto and Kretschmann and Raether observed SPPs optically in the attenuated total reflection (ATR) experiments. Since then SPPs have been extensively explored for several decades for their potentials in nanophotonics, metamaterials and biosensing. The surface localization property of SPs, confining the optical mode to subwavelength scale and minimizing the optical mode size, therefore, conventional dielectric-based waveguides could be replaced by plasmonic waveguides an intriguing [2]. Nonlinear optical effects occur when electronic mobility in a strong electromagnetic field cannot be considered harmonic. The incident fields can be mixed by growth of the anharmonicity as power series in the field strength creating new fields that oscillate at the sums and differences of the incident frequencies which can propagate in various directions. The second and third order are the most prominent impacts for different applications. Hence, nonlinear optical phenomena could be beneficial to various applications, such as ultrafast switching, optical signal processing, production of ultra-short pulses, and frequency conversion [3]. Amongst the nonlinear phenomena, Second Harmonic Generation (SHG) has proven to be a surface sensitive measurement tool, hence it has been used for a number of research over the last decades [4]. Second harmonic generation (SHG) is one the most interesting and important nonlinear phenomena, in which two photons are
⁎
Corresponding author. E-mail addresses: [email protected] (H. Kaveh), [email protected] (A. Karimi).
https://doi.org/10.1016/j.ijleo.2019.02.138 Received 18 January 2019; Accepted 24 February 2019 0030-4026/ © 2019 Elsevier GmbH. All rights reserved.
Optik - International Journal for Light and Electron Optics 183 (2019) 247–252
H. Kaveh and A. Karimi
Fig. 1. The schematic of the planar IMI plasmonic waveguide.
Fig. 2. Ey distributions of the pulse at a propagation distance in the nonlinear material sandwiching a silver film (d = 20 nm) in three time steps (a) 30 fs (b) 60 fs (c) 90 fs. 248
Optik - International Journal for Light and Electron Optics 183 (2019) 247–252
H. Kaveh and A. Karimi
Fig. 3. IMI plasmonic waveguide with grating structure.
destroyed in a frequency such as f and replaced by a photon in 2f with half the incident wavelength [5]. For the first time, Peter Franken, A. E. Hill, C. W. Peters, and G. Weinreich introduced second harmonic generation, at the University of Michigan, in 1961 [6]. According to the last research, the nonlinear response of the surface of the metal is associated with understanding the surface structure of the way it was formed and can be designed by geometry of the metal layer. In addition, considering its feature, environments that provide field enhancement are able to increase SHG efficiency [7]. Some of the applications of SHG could be an appropriate assistance of research on material science [8], and laser industry [9]. Over the past few years, several articles regarding SHG enhancement have been presented such as, how hybrid plasmonic waveguides could improve second harmonic generation [10], Second-order nonlinear frequency conversion processes in plasmonic slot waveguides [11]. In this study, SHG, one of the important nonlinear effects, was investigated in IMI waveguides. For this purpose, a grating structure has been used and it has been determined how this structure modify the enhancement of SHG.
2. The structure of IMI waveguide Two planar structures could be described as propagation of a plasmonic wave: insulator-metal-insulator waveguides (IMI) and metal-insulator-metal waveguides (MIM). In both of them, there is a slight gap between two surface plasmons or plasmon polartions supporting dielectric-metal interfaces. Surface plasmon polaritons (SPP) on each interface can be coupled across the two interfaces. Therefore, the gap between them is small enough and the guided optical modes can be achieved for the waveguide. Since the efficiency of most nonlinear phenomena can be remarkably increased, the improvement of the resulting field makes them favorable for surface nonlinear optics [12]. Fig. 1 shows the schematic of a planar IMI plasmonic waveguide for the investigating of SHG enhancement, known as fundamental plasmonic waveguide. In this waveguide, a thin silver film sandwiched by two nonlinear media and a propagation length of 20 μm for a SPP mode with a thickness of d = 20 nm [13]. In this research we should focus the light to the smallest spot. Consider a Gaussian TM beam incident from the left side, the y component of the electric field is described as: ⎛
Ey = E 0 *
y2 ⎞
⎜− y 2 ⎞ − (t − t 0) w0 2⎟ * e⎝ w (x ) ⎠ * cos ⎛ω0 * t − k 0 * x + η (x ) − k 0 * * e Δt 2 w (x ) 2 * R (x ) ⎠ ⎝ ⎜
2
⎟
(1)
Where In these expressions, k is the wave number which means the spatial frequency of the wave, y is the in-plane transverse coordinate, ω is the angular frequency, w(x) is proportional to the width of the beam, and the constant w0 is called the minimum waist. The wave front of the beam is not exactly planar; it propagates like a spherical wave with radius R(x) and η(x) is known as Gouy phase shift which slightly shifts the phase of the wave front of the wave as a whole. [14]. The parameters in the simulation described as: the center frequency f0 = 2.84 × 1014 Hz, the pulse width Δt = 10 fs, the pulse time delay t0 = 25 fs, the time step 0.02 fs, and the peak electric field E0 = 30 kV. We assumed the metal is silver for the simulations with ωD = 1.38 × 1016 Hz, γ = 2.73 × 1013 Hz. Where γ is the damping in time and ωD is the plasma frequency [15]. The nonlinear properties for second harmonic generation in a material can be defined with the following matrix,
Fig. 4. The frequency spectra of the pulse having propagated in IMI grating waveguide including triangles (a) with 200 nm depth (b) with 250 nm depth (c) with 300 nm depth. 249
Optik - International Journal for Light and Electron Optics 183 (2019) 247–252
H. Kaveh and A. Karimi
Fig. 5. The frequency spectra of the pulse having propagated in IMI grating waveguide including (a) one slot (b) four slots (c) 10 slots.
⎡ d11 d12 d13 d14 d15 d16 ⎤ ⎢ d21 d22 d23 d24 d25 d26 ⎥. ⎢ ⎦ ⎣ d31 d32 d33 d34 d35 d36 ⎥
2 ⎡ Ex ⎤ ⎢ Ey 2 ⎥ ⎢ 2 ⎥ ⎢ Ez ⎥ ⎢ 2EzEy ⎥ ⎢ 2EzEx ⎥ ⎢ 2ExEy ⎥ ⎣ ⎦
(2) −17
We set the second-order nonlinear susceptibility coefficient d22 = 10 F/V, and all the rest as zero, since the main component of the electric field is oriented towards the y direction. Fig.2 indicates Ey distributions of the pulse after propagation in three time steps (30 fs, 60 fs, and 90 fs) in the nonlinear material described by the Drude model. 3. Enhancement of SHG in IMI waveguides In Fig. 3 a new structure is proposed, introducing an IMI grating plasmonic waveguide. According to the figure, a thin silver film with a thickness of 20 nm is sandwiched by two nonlinear media from two sides. Moreover, the structure has right triangle slots on both sides known as grating, which facilitates the further connection between photons and plasmons [16]. In order to reach the most enhanced SHG, different triangles with different depths are simulated. It is revealed that the best measure for the depth and length of triangles would be 250 nm and 500 nm, respectively. Fig. 4 illustrates the SHG effect in the grating structure with different depth. Furthermore, the gap between the right triangles is calculated in order to achieve the maximum second harmonic generation. In other words, different numbers of slots are simulated so as to achieve the enhanced SHG. The simulations is carried out from 13 slots to one slot on each side and according to Fig.5 it could be observed that the SHG effect increases due to decreasing the number of triangles. Therefore, the growth continues until the number of slots reaches four. Afterwards, declining the number of slots from four to one is equivalent to the gradual reduction of SHG enhancement. Thus, the most appropriate structure for the SHG enhancement could be the Fig.3. Thus, in this waveguide, the number of slots and the intervals between triangles were considered 4 and 5000 nm, respectively. As a result, adjusting the intervals is associated with optimizing the number of slots. Fig. 6 shows the Ey distribution of the pulse after propagation within 3 time steps (30 fs, 60 fs, and 90 fs) in a nonlinear material with a grating structure. It can be seen that a significant increase in the electric field peak of the SHG occurred due to the stimulation of SPPs. Furthermore, in time domain simulation thorough the Comsol software, a point probe is set on the dielectric surface to measure the pulse’s electric field along the metal surface and the results are utilized to calculate the frequency spectrum with Fast Fourier Transforms. Regarding Fig.7, a second harmonic wave is generated at the central frequency of 5.68 * 1014 Hz, and the electric field improvement is resulted in SHG enhancement consequently as evidenced by the growth in the second harmonic component. 4. Conclusion In this research, we have simulated the Drude model in time-domain study through the Comsol software in order to analyze the grating influence on SHG optimization in an IMI plasmonic waveguide. This study investigated SHG effect in the fundamental and proposed IMI plasmonic waveguides. With regard to above mentioned, a nonlinear medium was used as dielectric. These two IMI plasmonic waveguides were studied, and their SHG simulation outcomes have been presented. The proposed waveguide had right triangles geometries on both sides of the nonlinear media and the quantity of slots was calculated to reach the highest SHG. As it was explained previously, the length of the waveguide is 20 μm and the quantity of triangles changed in this distance. Hence, the quantity of triangles is considered to be four here. Looking more closely at the given figures predicting a significant second harmonic wave could be generated in the grating 250
Optik - International Journal for Light and Electron Optics 183 (2019) 247–252
H. Kaveh and A. Karimi
Fig. 6. Ey distributions of the pulse at a propagation distance in the nonlinear material with a grating structure in three time steps (a) 30 fs (b) 60 fs (c) 90 fs.
plasmonic waveguides. Figs. 2 and 6 illustrated the amplitude of electric field diagrams for both the fundamental and proposed plasmonic waveguides. As shown in Fig. 8, throughout the waveguide, the electric field amplitude diagram has considerably increased in the grating structure. It can be observed in the middle of the diagram that there is a slight discrepancy between the two trends. In contrast, at the end of the grating waveguide a dramatic enhancement has occurred in the amount of electric filed as compared to the trend of the fundamental structure. Figs. 7 and 8 show the frequency spectrum and Ey distribution of different structures, respectively. As displayed in the figures, the peak electric field of the proposed structure is remarkably enhanced as a result of stimulation of SPPs. In general, it is logical to conclude that this proposed waveguide could be favorable in the enhancement of SHG. Therefore, the proposed structure is an appropriate plasmonic waveguide for future applications of SHG.
251
Optik - International Journal for Light and Electron Optics 183 (2019) 247–252
H. Kaveh and A. Karimi
Fig. 7. The frequency spectra of the pulse having propagated in (a) fundamental IMI waveguide (b) grating IMI structure.
Fig. 8. Ey distributions amplitude within three time steps in comparison.
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