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Quality factor and sensor characteristics of the modes

Parameters s=600 µm s=500 µm Resistance,R1 (Ω) 4.0 2.9 Inductance, L1 (f H) 60.5 38.1 Capacitance, C1 (pF) 5.8 5.65 Resistance,R2 (Ω) 0.5 0.3 Inductance, L2 (f H) 12.0 9.9 Capacitance, C2 (pF) 15.5 11.0

Table 2.1: Dierent parameters used in TL-RLC circuit for pyramidal corrugation.

can be attributed to the scattering, diffraction, and dispersion loss experienced by the wave as it propagates along with the corrugated pattern. These losses have a signifi- cant effect on signal loss and thus on the width of the spectrum. Losses due to these effects cannot be accurately included in the transmission line model. This model de- scribes a simple yet useful semi-analytical approach to account for resonant behavior, with a focus primarily on anti-resonance frequencies. The anti-resonance frequency corresponds to a sharp drop on the high frequency side of each resonance. Interest in anti-resonance frequencies arises because they are related parameters, not frequencies associated with the resonance peak [123, 124].

Further, we examine the field profiles of the terahertz modes supported by the pro- posed pyramidal structured plasmonic THz waveguide configuration. The results are shown in Fig.2.5 for two different planes i.e. zy-plane and xy-plane. Fig.2.5(a & b) represent the field profile at the resonant frequencies of the fundamental mode i.e. 0.27 THz in zy-plane and xy-plane respectively, however Fig.2.5(c&d) represents the field profile of the 2nd mode at 0.47 THz in the same plane. The structure exhibits strong confinement of all modes as it propagates along the waveguide. Fields are strongly confined at the resonant frequency and behaviour of the modes are apparent from the profile of modes.

(a) (b) (c) (d)

y z

y z

x z x


Min IntensityMax

f = 0.27 THz f = 0.47 THz f = 0.47 THz f = 0.27 THz

Figure 2.5: The eld proles of the pyramidal structured plasmonic waveguide for dierent THz modes i.e. a) Fundamental mode in zy -plane; b) Fundamental mode in zx-plane plane. It represents electric eld prole in the pyramidal groove at resonance frequency 0.27 THz; c)2nd mode in zy-plane; d) 2nd mode in zx-plane It represents electric eld prole in the pyramidal groove at resonance frequency 0.47 THz.

parameters to analyse the quality of the modes and the narrowness of the resonance.

The highQ-factor modes along with strong electric field confinement could be signifi- cant in the ultrasensitive sensing applications. The quality factor of a mode is defined as the ratio of resonance frequency (fr) and its band width (∆f). The band width is basically the full width at half maxima of the resonance. We have calculated the quality factor for the fundamental and high order resonance of our waveguide for dif- ferent transverse lengths (s) of the pyramidal grooves. The results have been shown

Q - factor

( μm ) s

0 300

30 60 90 120

400 500 600

2 modend

1 modest

Figure 2.6: Numerically calculatedQ-factor of the Fundamental mode and higher order modes of plasmonic waveguide having Pyramidal grooves.

in Fig.2.6. The red trace shows the quality factor for the fundamental mode, however blue trace represents for 2nd order mode. It may be noted that the quality factor (Q) of the fundamental mode decreases as the length of pyramidal grooves is increased.

Fors= 300µm, the Q-value is calculated to be 47.6, however it decreases to 33.8 as the

length of the groove is increased tos= 600µm. A similar trend is observed in the case of2ndorder mode. For2ndorder mode, as the length of the groove is increased froms= 400µm tos= 600µm, the quality factor is decreases 120.4 to 95.2 value. Our numerical observations also reveal that the Q-value of the2nd order mode is higher as compared to the fundamental mode owing to its narrow line width.

In order to examine the refractive index sensing capability of the modes in the pro- posed plasmonic waveguide, we filled pyramidal grooves with the analytes of differ- ent refractive indices. We measured the frequency shift of the fundamental as well as 2nd order mode with respect to the change in refractive index of the analyte. Precisely, we focused on a change in the anti-resonant frequency of the mode when grooves are filled with analyte with respect to the intrinsic anti-resonant frequencies (i.e. without any analyte). For our study, we varied refractive index values of the analyte as (n) = 1, 1.2, 1.4, 1.6, 2. The results of frequency shift versus refractive index are shown in Fig.2.7(a). When the refractive index of the analyte is increased, we observe a linear shift in the anti-resonance frequencies of the fundamental as well as 2nd order mode.

The shift in frequency is observed because of the interaction between the highly con- fined electric field of the modes at the surface and the analyte present there. Further, we

Frequency shift (THz)

0.05 0.10 0.15

s = 400 μm s = 600 μm 2 modend

1 modest

01 1.6 1.8 2.0

Refractive index (n) 1.2 1.4



Sensitivity (THz/ R.I)


0.01 0.015 0.025 0.03

0.14 0.21

Analyte volume ( mm ) 0.02 3 0.07

(b) 1 modest 2 modend

Figure 2.7: a) The variation of frequency shift of the fundamental mode& higher order mode versus refractive index of the polyimide substance for the plasmonic terahertz waveguides b) Numerically calculated variation of sensitivity versus quantity of the analyte lling the pyramidal grooves.

examine the sensitivity of the modes supported by our waveguide in order to compre-

hensively understand its sensing performance. The sensitivity is calculated by measur- ing frequency shift(∆f)with respect to the change in refractive index(∆n)for a given amount of analyte, and calculating the slope (∆f∆n) of this variation. Fig.2.7(b) shows the plot of sensitivity of the modes versus volume of analyte filled in the grooves. We have varied refractive index as (n) = 1, 1.2, 1.4, 1.6, 2.0 to calculate correspond fre- quency shift for several different volumes of analytes for groove length(s)= 600µm.

From the results, it is clear that sensitivity increases with the analyte quantity and this follows for fundamental as well as higher order modes. It may be observed from the plot that the2nd order mode results in higher sensitivity compared to the lower order mode. For 0.03mm3 of the analyte, the sensitivity for 2nd modes is calculated to be


∆n = 0.19T Hz/RIU, whereas for the same quantity of analyte, the sensitivity of 1st order modes turns out to be0.11T Hz/RIU.