Investigating factors affecting loss reduction in graphene-based plasmonic structures
الموضوعات : فصلنامه نانوساختارهای اپتوالکترونیکی
1 - Department of Electrical Engineering, Faculty of Engineering, Shahid Chamran University of Ahvaz, Ahvaz, Iran
الکلمات المفتاحية: Plasmon, Graphene, Losses, Propagation length, Chemical potential,
ملخص المقالة :
In graphene-based plasmonic structures, the path length traveled by surface plasmon polaritons (SPP) or the propagation length of plasmons is very important. So that the longer the plasmon propagation length in a structure is, the better that structure will perform. Therefore, it is very important to know the factors affecting the propagation length of plasmons. One of the effective factors in increasing the propagation length of plasmons is reducing the losses of the graphene-based plasmonic structure. The losses of these structures depend on the amount of chemical potential used for graphene and the material of the substrate used in the structure. Therefore, in this work, the effect of the chemical potential and the type of different substrates on the loss of the structure in the wavelength range of 8 to 12 micrometers has been investigated. According to the results obtained in this paper, by using a chemical potential of 1eV for graphene and using glass as a substrate, it is possible to reduce the losses of the structure and thus increase the emission length.
[1] J. Zhang, L. Zhang, and W. Xu, "Surface plasmon polaritons: physics and applications," Journal of Physics D: Applied Physics, vol. 45, no. 11, p. 113001, 2012.
[2] V. Belotelov, D. Bykov, L. Doskolovich, and A. Zvezdin, "On surface plasmon polariton wavepacket dynamics in metal–dielectric heterostructures," Journal of Physics: Condensed Matter, vol. 22, no. 39, p. 395301, 2010.
[3] P. Berini, "Long-range surface plasmon polaritons," Advances in optics and photonics, vol. 1, no. 3, pp. 484-588, 2009.
[4] K. S. Novoselov et al., "Electric field effect in atomically thin carbon films," science, vol. 306, no. 5696, pp. 666-669, 2004.
[5] X. Li et al., "Transfer of large-area graphene films for high-performance transparent conductive electrodes," Nano letters, vol. 9, no. 12, pp. 4359-4363, 2009.
[6] C. Lavorato and E. Fontananova, "An overview on exploitation of graphene-based membranes: From water treatment to medical industry, including recent fighting against COVID-19," Microorganisms, vol. 11, no. 2, p. 310, 2023.
[7] A. F. Mohsen Nasrolahi, Ashkan Horri, Hossein Hatami, "FDTD Analysis of a High-sensitivity refractive index sensing based on Fano resonances in a plasmonic planar split-ring resonators," Optoelectronical Nanostructures, vol. 9, no. 2, 2024, doi: 10.30495/jopn.2024.33499.1321.
[8] P. Rivero-Antúnez, C. Zamora-Ledezma, F. Sánchez-Bajo, J. C. Moreno-López, E. Anglaret, and V. Morales-Flórez, "Sol–gel method and reactive SPS for novel alumina–graphene ceramic composites," Journal of the European Ceramic Society, vol. 43, no. 3, pp. 1064-1077, 2023.
[9] S. Cai et al., "Understanding the high chemi-catalytic reactivity of graphene quantum dots to rapidly generate reactive oxygen species," Chemical Engineering Science, vol. 263, p. 118072, 2022.
[10] L. Cui, J. Wang, and M. Sun, "Graphene plasmon for optoelectronics," Reviews in Physics, vol. 6, p. 100054, 2021.
[11] F. Bagheri and M. Soroosh, "Design and simulation of subwavelength plasmonic D flip-flop with state remaining feature," Optical and Quantum Electronics, vol. 55, no. 5, p. 425, 2023.
[12] M. K. M.-F. Mehdi Dehghan, Mohsen GhaffariMiab, Masoud Jabbari, Ghafar Darvish, "Ultra-Compact Bidirectional Terahertz Switch Based on Resonance in Graphene Ring and Plate," Optoelectronical Nanostructures, vol. 4, 2019.
[13] B. A. A. Ali Moftakharzadeh , Mehdi Hosseini "Noise Equivalent Power Optimization of Graphene- Superconductor Optical Sensors in the Current Bias Mode," Optoelectronical Nanostructures, vol. 3, no. 3, 2018.
[14] H. M. Karim Milanchian "Modeling Graphene-based PIN-FET with Quantum Dot Channel," Optoelectronical Nanostructures, vol. 8, no. 4, 2023, doi: 10.30495/jopn.2024.32047.1292.
[15] R. F. Maedeh Akbari Eshkalak "A Computational Study on the Performance of Graphene Nanoribbon Field Effect Transistor," Optoelectronical Nanostructures, vol. 2, no. 3, 2017.
[16] M. Mohammadi, M. Soroosh, A. Farmani, and S. Ajabi, "High-performance plasmonic graphene-based multiplexer/demultiplexer," Diamond and Related Materials, vol. 139, p. 110365, 2023.
[17] G. Brodie, "Energy transfer from electromagnetic fields to materials," Electromagnetic Fields and Waves, pp. 1-18, 2019.
[18] J. Mikołajczyk et al., "Analysis of free-space optics development," Metrology and Measurement Systems, vol. 24, no. 4, pp. 653-674, 2017.
[19] F. Haddadan and M. Soroosh, "Design and simulation of a subwavelength 4-to-2 graphene-based plasmonic priority encoder," Optics & Laser Technology, vol. 157, p. 108680, 2023.
[20] F. Bagheri and M. Soroosh, "Design and simulation of compact graphene-based plasmonic flip-flop using a resonant ring," Diamond and Related Materials, vol. 136, p. 109904, 2023.
[21] S. A. Maier, Plasmonics: fundamentals and applications. Springer, 2007.
[22] M. H. Rezaei and A. Zarifkar, "Graphene-based plasmonic electro-optical SR flip-flop with an ultra-compact footprint," Optics Express, vol. 28, no. 17, pp. 25167-25179, 2020.
[23] J. Zheng, L. Yu, S. He, and D. Dai, "Tunable pattern-free graphene nanoplasmonic waveguides on trenched silicon substrate," Scientific reports, vol. 5, no. 1, p. 7987, 2015.
[24] P. S. Toth et al., "Electrochemistry in a drop: a study of the electrochemical behaviour of mechanically exfoliated graphene on photoresist coated silicon substrate," Chemical Science, vol. 5, no. 2, pp. 582-589, 2014.
[25] F. Haddadan, F. Bagheri, A. Basem, H. A. Kenjrawy, and M. Soroosh, "Evanescent field engineering to reduce cross-talk in pattern-free suspended graphene-based plasmonic waveguides using nano-strips," Optik, vol. 313, p. 171989, 2024.
[26] A. Badmaev, Y. Che, Z. Li, C. Wang, and C. Zhou, "Self-aligned fabrication of graphene RF transistors with T-shaped gate," ACS nano, vol. 6, no. 4, pp. 3371-3376, 2012.
[27] F. Bagheri, M. Soroosh, F. Haddadan, and Y. Seifi-Kavian, "Design and simulation of a compact graphene-based plasmonic D flip-flop," Optics & Laser Technology, vol. 155, p. 108436, 2022.
[28] L. Capua, S. Sheibani, S. Kamaei, J. Zhang, and A. Ionescu, "Extended-Gate FET cortisol sensor for stress disorders based on aptamers-decorated graphene electrode: fabrication, Experiments and Unified Analog Predictive Modeling," in 2020 IEEE International Electron Devices Meeting (IEDM), 2020: IEEE, pp. 35.2. 1-35.2. 4.
[29] B. Yan et al., "Optical response of tunable terahertz plasmon in a grating-gated graphene transistor," Chinese Physics B, vol. 26, no. 9, p. 097802, 2017.
[30] A. Celis et al., "Graphene nanoribbons: fabrication, properties and devices," Journal of Physics D: Applied Physics, vol. 49, no. 14, p. 143001, 2016.
[31] L. Zhou et al., "Surface structure of few layer graphene," Carbon, vol. 136, pp. 255-261, 2018.
[32] T. Iqbal, "Propagation length of surface plasmon polaritons excited by a 1D plasmonic grating," Current Applied Physics, vol. 15, no. 11, pp. 1445-1452, 2015.
[33] F. Bagheri and M. Soroosh, "Design and simulation of compact graphene-based plasmonic flip-flop using a resonant ring," Diamond and Related Materials, p. 109904, 2023.
Islamic Azad University
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Volume 10, Issue 1, Spring 2025, page 33-43 |
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Research Paper
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Investigating factors affecting loss reduction in graphene-based plasmonic structures
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Fereshte Bagheri*1 1 Department of Electrical Engineering, Shahid Chamran University of Ahvaz, Ahvaz, Iran | |||||||||
| Abstract In graphene-based plasmonic structures, the path length traveled by surface plasmon polaritons (SPP) or the propagation length of plasmons is very important. So that the longer the plasmon propagation length in a structure is, the better that structure will perform. Therefore, it is very important to know the factors affecting the propagation length of plasmons. One of the effective factors in increasing the propagation length of plasmons is reducing the losses of the graphene-based plasmonic structure. The losses of these structures depend on the amount of chemical potential used for graphene and the material of the substrate used in the structure. Therefore, in this work, the effect of the chemical potential and the type of different substrates on the loss of the structure in the wavelength range of 8 to 12 micrometers has been investigated. According to the results obtained in this paper, by using a chemical potential of 1eV for graphene and using glass as a substrate, it is possible to reduce the losses of the structure and thus increase the emission length. | ||||||||
Use your device to scan and read the article online
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Keywords: Plasmon, Graphene, Losses, Propagation length, Chemical potential
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1. INTRODUCTION
Surface plasmon polariton (SPP) is an electromagnetic excitation that occurs at the metal-semiconductor interface [1] and is used to control light flow at nanoscale [2]. The surface plasmons of metals have TM polarization and due to surface roughness and interband absorption, they will drop a lot and have a very short emission length [3], Therefore, in order for plasmons to have a longer propagation length, graphene is used instead of metal.
Graphene is a thin material with a thickness of one atom and a network in the shape of a honeycomb [4]. This material is a Pseudo-metal or a semiconductor with zero energy gap [5], which has attracted the attention of researchers in various fields of medicine [6], electrical [7], materials [8], chemistry [9], etc. due to its unique properties.
Features such as confinement of SPPs and having both TE and TM polarizations have made graphene-based plasmonic waveguides superior to other waveguides [10]. Also, according to the investigations, graphene is the only material that can well receive SPPs in the range of 0.1 to 10 terahertz and emit them with low losses. Therefore, today, the design of plasmonic devices based on graphene, such as flip-flop [11], switch [12], biosensor [7], sensor [13], transistor [14, 15], and multiplexer [16], has attracted the attention of researchers.
The terahertz range is a part of the electromagnetic spectrum that includes the wavelength range of 1mm to 700nm and the frequency range of 300GHz to 430THz [17]. The atmosphere passes part of the electromagnetic energy and the other part is absorbed by the molecules in the atmosphere (Such as ozone, carbon dioxide and water vapor) and converted into heat. The amount of energy absorption is different in different wavelengths of the electromagnetic spectrum. So that in the terahertz range, the wavelength range of 8µm to 12µm has the least absorption and the most transmission in the earth's atmosphere [18], hence the devices made in the terahertz range usually work in this wavelength range.
One of the important points in the design of graphene-based plasmonic devices is to design the structure in such a way that SPPs have the longest propagation length (Lspp), Because the increase in the Lspp of SPPs (Surface Plasmon Polaritons) leads to an improvement in the performance of the structure, one of the factors affecting the propagation length of SPPs is the losses in the structure. The lower the losses in the structure, the greater the propagation length of the SPPs will be. Therefore, identifying the factors that cause losses in graphene-based plasmonic structures is of great importance. Hence, this paper will investigate the factors that cause losses in graphene-based plasmonic structures. The focus of this research is on the impact of the substrate material and the chemical potential on the amount of losses.
It seems that by using the results of this research, it is possible to design an optical structure with minimal losses and maximum propagation length, and consequently a structure with good performance, by selecting the appropriate substrate and chemical potential.
2. LOSSES
Equation (1) is used to calculate losses [19]. Where C is The speed of light in vacuum, K(w) is The imaginary part of the refractive index (neff) and w is angular frequency.
(1) |
|
According to this equation, the loss depends on the neff, and the smaller the imaginary part of the neff, the lower the loss.
According to the equation (2), the neff is a complex parameter whose real part is called the effective neff and its imaginary part is called the absorption coefficient and is related to the absorption of light waves [20].
| (2) |
According to relation (3), the neff and electrical conductivity are related to each other, so according to relations (4) and (5), the real and imaginary part of the neff can be related to the real and imaginary part of the electrical permittivity.
(3) |
|
(4) |
|
(5) |
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The electrical conductivity of graphene consists of two parts, real and imaginary. Based on Kramers-Kronig’s method, the electrical conductivity can be obtained from the following relations [21].
(6) |
|
(7) |
|
where E is Radiant photon energy, hg=1nm is The thickness of the graphene layer, τ-1 is the dispersion rate of carriers which is usually considered equal to zero and µc is chemical potential.
The chemical potential or Fermi level is the factor that changes the conductivity of graphene. This parameter is calculated from equation (8).
∣µc∣≈ ћ 𝜈F | (8) |
where, ћ is the Planck's reduced constant, 𝜈F = 0.9⨯106 ms-1, a0=9⨯1016 m-2V-1, Vb is the bias voltage and V0 is the offset voltage caused by natural doping (V0=0.8 V).
2.1. LOSSES IN GRAPHEN
We know that for |µ𝑐| > ћ𝜔/2 the ɛimage is positive and graphene behaves like an extremely thin metal and TM polarization is established. For |µc| < ћω/2, the ɛimage is negative and graphene behaves like an dielectric and TE polarization is established [22].
Therefore, in order to reduce the losses in graphene, the ɛimage of the graphene surface should be positive. Therefore, according to the equation (7), it is expected that with the increase of the chemical potential, the ɛimage of the graphene surface will become more positive and as a result, the conductivity of graphene will increase (show in Fig.1a).
In Fig. 1b, the chemical potential diagram was drawn in terms of the neff of graphene. According to this diagram, with the increase in the chemical potential, the K(ω) decreases. Therefore, according to equation (1), with the increase in the chemical potential, the amount of losses decreases.
|
|
(a) | (b) |
Fig.1 (a) The graphene surface conductivity versus µc and (b) the neff versus the chemical potential | |
The selected wavelength for graphene is another factor that reduces losses in graphene. In order to achieve the lowest losses in graphene, the working wavelength of the input light must be selected in such a way that it is below the limit of optical phonon emission. Therefore, the working wavelength must be greater than the optical phonon wavelength, and due to the inverse relationship between wavelength and frequency (show in equation (9)), the working frequency must be smaller than the optical phonon emission frequency [23].
(9) | λ=υ/f |
where v is wave speed, f is wave frequency and λ is wavelength.
2.2. INVESTIGATING LOSSES SUBSTRATE USED IN THE DESIGN OF OPTICAL DEVICES
Due to the fact that the amount of losses of the substrate used in the design of optical devices is different in the range of 8µm to 12µm wavelengths, therefore, choosing the substrate that has the lowest losses in this wavelength range is of particular importance. Therefore, in this section, the amount of losses of conventional substrates in the design of optical structures in the wavelength range of 8µm to 12µm will be investigated.
In the design of plasmonic devices based on graphene, various substrates such as Si [24, 25] SiO2 [26], SnO2 [27], Glass [28], Al2O3 [29] are used, therefore, it is very important to determine which of these substrates has the lowest losses in the range of 8µm to 12µm wavelengths. To check the amount of losses of different substrate in this wavelength range, the structure in Fig. 2 was simulated in Lumerical software, and then the loss graph was drawn in terms of wavelength for different substrate (show in Fig.3). The waveguide width used in the proposed structure is 50 nm. According to the reference [30], fabrication of the graphene waveguides with a width of 50 nm is possible. The thickness of the graphene used for the waveguide is 2 nm [31].
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Fig. 2 A view of the structure used for simulation |
According to the obtained results, in the wavelength range of 8µm to 12µm, glass has the lowest losses and SiO2 has the highest losses, so it seems that using a glass substrate in graphene-based plasmonic structures is the best choice.
| |
(a) | |
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(c) | (b) |
Fig. 3 Loss versus the wavelength for different substrates at µc =1eV | |
One of the important points in the design of graphene-based plasmin structures is to have the maximum possible propagation length.
For the practical measurement of the propagation length, one can use the far field microscopes, PSTM-microscope, LRM-microscope [32], and equation (10) can be used to calculate it theoretically [33]:
(10) |
|
Where λ0 is Input wavelength. To ensure the results obtained in this article, the structure presented in Fig 2 was simulated for the glass substrate and the constant chemical potential of 1eV, and for the wavelength range of 8µm to 12µm graphs related to losses and propagation length were drawn. According to this diagram, as the wavelength increases, the loss decreases and the propagation length increases.
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Fig. 4 Propagation length and loss versus the wavelength at a chemical potential of 1eV |
3. CONCLUSION
One of the effective factors in increasing the propagation length of plasmons in graphene-based plasmonic structures is the reduction of losses. The losses of these structures depend on the amount of chemical potential applied to graphene and the type of substrate used. According to the results obtained in this article, by setting the chemical potential of graphene on 1eV and using glass as a substrate, the losses of graphene-based plasmonic structures can be minimized.
REFERENCES
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[19] F. Haddadan and M. Soroosh, "Design and simulation of a subwavelength 4-to-2 graphene-based plasmonic priority encoder," Optics & Laser Technology, vol. 157, p. 108680, 2023. https://www.sciencedirect.com/science/article/abs/pii/S003039922200826X
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[23] J. Zheng, L. Yu, S. He, and D. Dai, "Tunable pattern-free graphene nanoplasmonic waveguides on trenched silicon substrate," Scientific reports, vol. 5, no. 1, p. 7987, 2015. https://www.nature.com/articles/srep07987
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[25] F. Haddadan, F. Bagheri, A. Basem, H. A. Kenjrawy, and M. Soroosh, "Evanescent field engineering to reduce cross-talk in pattern-free suspended graphene-based plasmonic waveguides using nano-strips," Optik, vol. 313, p. 171989, 2024. https://www.sciencedirect.com/science/article/abs/pii/S0030402624003887
[26] A. Badmaev, Y. Che, Z. Li, C. Wang, and C. Zhou, "Self-aligned fabrication of graphene RF transistors with T-shaped gate," ACS nano, vol. 6, no. 4, pp. 3371-3376, 2012. https://pubs.acs.org/doi/abs/10.1021/nn300393c
[27] F. Bagheri, M. Soroosh, F. Haddadan, and Y. Seifi-Kavian, "Design and simulation of a compact graphene-based plasmonic D flip-flop," Optics & Laser Technology, vol. 155, p. 108436, 2022. https://www.sciencedirect.com/science/article/abs/pii/S003039922200593X
[28] L. Capua, S. Sheibani, S. Kamaei, J. Zhang, and A. Ionescu, "Extended-Gate FET cortisol sensor for stress disorders based on aptamers-decorated graphene electrode: fabrication, Experiments and Unified Analog Predictive Modeling," in 2020 IEEE International Electron Devices Meeting (IEDM), 2020: IEEE, pp. 35.2. 1-35.2. 4. https://ieeexplore.ieee.org/abstract/document/9372063/
[29] B. Yan et al., "Optical response of tunable terahertz plasmon in a grating-gated graphene transistor," Chinese Physics B, vol. 26, no. 9, p. 097802, 2017. https://iopscience.iop.org/article/10.1088/1674-1056/26/9/097802/meta
[30] A. Celis et al., "Graphene nanoribbons: fabrication, properties and devices," Journal of Physics D: Applied Physics, vol. 49, no. 14, p. 143001, 2016. https://iopscience.iop.org/article/10.1088/0022-3727/49/14/143001/meta
[31] L. Zhou et al., "Surface structure of few layer graphene," Carbon, vol. 136, pp. 255-261, 2018.
[32] T. Iqbal, "Propagation length of surface plasmon polaritons excited by a 1D plasmonic grating," Current Applied Physics, vol. 15, no. 11, pp. 1445-1452, 2015. https://iopscience.iop.org/article/10.1088/0022-3727/45/11/113001/meta
[33] F. Bagheri and M. Soroosh, "Design and simulation of compact graphene-based plasmonic flip-flop using a resonant ring," Diamond and Related Materials, p. 109904, 2023. https://www.sciencedirect.com/science/article/abs/pii/S0925963523002297
Citation: Fereshte Bagheri, Investigating factors affecting loss reduction in graphene-based plasmonic structures, Journal of Optoelectronical Nanostructures. 2025; 10(1): 33-43 |
