300
J. Eur. Opt. Society-Rapid Publ. 21, 28( 2025)
Figure 2. Dependence of effective mode index on chemical potential and number of graphene layers at s = 50 ps, t = 100 nm and l = 0.2 eV.
where r is the graphene conductivity as reported in [ 31 ]: By applying Equations( 18) and( 19) to the proposed waveguide structure, the following matrix is obtained:
2 32
3
6 4 b 11
b 21 b 31
b 41 b 51
b 61 b 12
b 22 b 32
b 42 b 52
b 62 b 13
b 23 b 33
b 43 b 53
b 63 b 14
b 24 b 34
b 44 b 54
b 64 b 15
b 25 b 35
b 45 b 55
b 65 b 16
b 26 b 36
b 46 b 56
b 66
76 54 c 1
c 2 c 3
c 4 c 5
c 6
¼ 0:
7 5 ð20Þ
Here, b 11 = 0, b 12 = �j( f + ba 1) u 1 � M( b � da 1) u 1, b 13 = 0,
b 14 ¼�jðf þ ba 2 Þu 2 � Mðb � da 2 Þu 2, b 15 ¼ 0, b 16 ¼ 0, b 21 ¼ M þ ja 1, b 22 ¼ 0, b 23 ¼ M þ ja 2, b 24 ¼ 0, b 25 ¼ 0, b 26 ¼ 0, b 31 ¼�jðf þ ba 1 Þu 1 sin½tu 1 Š, b 32 ¼ jðf þ ba 1 Þ cos½tu 1 Šu 1, b 33 ¼�jðf þ ba 2 Þu 2 sin½tu 2 Š, b 34 ¼ jðf þ ba 2 Þu 2 cos½tu 2 Š, b 35 ¼ e �tu 1 ð�r þðf þ ba 1 Þu 1 Þ, b 36 ¼ e �tq 2 ð�r þðf þ ba2 Þu 2 Þ, b 41 ¼�j cos½tu 1 Ša 1, b 42 ¼ �j sin ½ tu 1 Ša 1, b 43 ¼�j cos½tu 2 Ša 2, b 44 ¼�j sin½tu 2 Ša 2, b 45 ¼ e �tu1 ðja 1 þ rðb � da 1 Þu 1 Þ, b 46 ¼ e �tu2 ðja 2 þ rðb � da 2 Þu 2 Þ, b 51 ¼�ðb � da 1 Þu 1 sin½tu 1 Š, b 52 ¼ cos½tu 1 Šðb � da 1 Þu 1, b 53 ¼ � sin½tu 2 Šu 2 ðb � da 2 Þ, b 54 ¼ cos½tu 2 Šu 2 ðb � da 2 Þ, b 55 ¼ e �tðu 1þu 2 Þ e tu 2 ðb � da 1 Þu 1, b 56 ¼ e tu1 ðb � da 2 Þu 2 e �tðu1þu2Þ, b 61 ¼�cos½tu 1 Š, b 62 ¼�sin½tu 1 Š, b 63 ¼�cos½tu 2 Š, b 64 ¼ � sin½tu 2 Š, b 65 ¼ e �tu 1
, b 66 ¼ e �tu 2.
Results
This section numerically examines dispersion equation( 20) for a sandwiched structure at the magnetized plasma – graphene – magnetized plasma – PMC planar interface to explore the novel SPPs in the THz frequency region. Figure 2a illustrates the relationship between the effective mode index and propagation frequency for different chemical potentials. In graphene, the optical conductivity varies with the chemical potential. In response to an increase in chemical potential, the real part of optical conductivity increases, thereby resulting in a stronger interaction with the EM field. As a result, the optical mode becomes more confined within or near the graphene layer, resulting in a higher effective mode index. Figure 2 also shows that as the magnitude of the chemical potential increases, the dispersion curves shift from the low-frequency to the highfrequency region, and the propagation frequency decreases. It is observed that the slope of the dispersion curve is smaller for lower chemical potential values. Furthermore, at lower propagation frequencies, the dispersion curves exhibit less significant behaviors. The dependence of the effective mode index on the number of graphene layers versus the propagation frequency is analyzed in Figure 2b. It is clearly seen that the effective mode index increases but the cutoff frequency decreases for multilayer graphene. An increase in the number of graphene layers results in an increase in the overall thickness of the waveguide structure. Moreover, the multilayer graphene structure interacts more strongly with the EM field than the single-layer graphene structure. In addition, the multilayers enhance graphene’ s ability to support SPPs or guided modes, increasing the effective mode index. Thedependenceoftheeffectivemodeindexontheplasma frequency and cyclotron frequency versus the propagation frequency is analyzed in Figures 3a and 3b, respectively. According to Figure 3a, the cutoff frequency and effective mode index increase with the plasma frequency. An increase in plasma frequency results in an increase in electron density. As a result, the EM wave and the plasma are more strongly coupled.
Increasing the effective mode index signifies a decrease in the phase velocity of the wave, thereby indicating stronger confinement and slower propagation of the wave through the magnetized plasma. Furthermore, the slope of the dispersion curve decreases with the plasma frequency. Figure 3b illustrates the dependence of the effective mode index on the cyclotron frequency versus the propagation