Non-universal behavior of leaky surface waves in a one dimensional asymmetric plasmonic grating
Summary (1 min read)
INTRODUCTION
- From early 1980s,1,2 surface plasmon3,4 based optical sensors have been exhibiting a great potential in evaluating physical, chemical, and biological parameters.
- These applications are dependent on the sensitivity of surface plasmon polaritons (SPPs) to the refractive index (RI) of the medium adjacent to the metal surface.
- 3,4,13,18 Among the various types, grating structure can be compact and robust, which are desirable characteristics for integration into other devices6 apart from the tunability of the spectral response through geometrical parameters.
- The grating parameters were optimized10,19 to maximize the absorption of propagating SPPs (surface wave).
GRATING STRUCTURE AND COMPUTATIONAL DETAILS
- Svempati01@qub.ac.uk and tahir.awan@uog.edu.pk b)S. Vempati and T. Iqbal contributed equally to this work, also known as Electronic addresses.
- The gradient condition increases the number of data points as the spatial distribution of the field becomes more complicated.
- The source-field and the reflection in the far-field were at a distance of 1500 nm and 1000 nm when measured from the top of the analyte, respectively.
- In the present case, the relevant parameters were optimized (results not shown here) in such a way that the FP-like resonances were suppressed in the region of spectral interest10,19 while maximizing the absorption for surface waves.
RESULTS AND DISCUSSION
- The activation of surface modes requires either evanescent or grating coupling, where the latter introduces additional wave-vector along the parallel direction.
- It is notable that the grating parameters were optimized such that the slits are in anti-resonant condition at the wavelengths in which the RS (iii) associated with the two interfaces occur (1st and 2nd order FP modes 1150 nm and 509 nm, respectively).
- As h value increases, the minimum becomes prominent and red-shifts, where the shift is governed by the effective RI.
- Significant changes in the effective RI induce additional (k1, k2, and k3) sets of surface wave modes on Au/analyte interface.
- Since k1, k2, and k3 are not integer multiples of k0, the possibility of the former being higher order surface modes of the latter can be ruled out.
CONCLUSIONS
- It is known that the surface plasmons are quite sensitive to the changes in the RI, so is the case with surface waves on 1D asymmetric grating.
- Essentially, the resonance wavelength red-shifts with increasing h value while after a certain h value, new sets of surface waves emerge.
- The authors believe that this study not only provides new insights in designing the plasmonic sensors but also has fundamental importance in the context of behavior of plasmonic surface waves.
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Frequently Asked Questions (17)
Q2. Why are the resonance modes dependent on the contrast of RI of the surrounding media?
Due to the asymmetry,22 the resonance modes seen in the reflection spectra are highly dependent on the contrast of RI of the (two) surrounding media (i.e., analyte and Si).
Q3. What is the effect of the resonance wavelength on the surface waves?
the resonance wavelength red-shifts with increasing h value while after a certain h value, new sets of surface waves emerge.
Q4. What are the advantages of asymmetric gratings?
3,4,13,18 Among the various types, grating structure can be compact and robust, which are desirable characteristics for integration into other devices6 apart from the tunability of the spectral response through geometrical parameters.
Q5. What is the effect of the coupling between the SPPs on the other side?
Having said that as the h increases further (>2200 nm), there is apossibility that the FP mode may occur (due to the change in the effective RI) and hence a coupling between the SPPs on either side may be expected.
Q6. What is the effect of the FP mode on the slit?
To emphasize, FP mode within the slit is highly dependent on the geometry (k¼ 2t effective RI) of the single slit10 although the effective RI changes with h.
Q7. What is the simplest explanation for the reflection spectrum?
A metal grating surrounded by a dielectric medium supports three resonant states (RS), which can be identified in a reflection spectrum.
Q8. What is the spectral shift of FP and plasmonic resonances?
RS (iii) are bound to the surface of the grating however, can generate a leaky mode by coupling through the slits depending on the availability of a FP-like cavity mode.10 Essentially, for wavelengths close to K, the reflection minimum of 1D grating follows the dispersion relation of bound surface waves.
Q9. What are the characteristics of a leaky surface waveguide?
These surface waves become leaky for k< 2K where their dispersion is determined by the geometrical parameters andthe finite conductivity29 of the metal.
Q10. What are the resonant states of a metal grating?
These RS are (i) waveguide formed within the metal strips (broad band resonance, metal-insulator-metal structure),10 similar to FP cavity mode, (ii) propagating SPPs, and (iii) involve the whole grating periodicity depending on the availability of FP cavity modes.
Q11. Why are SPPs excited at the input and output interfaces?
On the other hand, because of the asymmetry, SPP modes are excited at the input and output interfaces in addition to FP cavity modes.
Q12. What is the effect of the h value on the surface waves?
the red-shift saturates exponentially in all cases however, with different time constants, i.e., the surface waves respond non-universally to the changes in the effective RI.
Q13. What is the reason why the FP mode does not exist on both sides at once?
In other words, this mode does not exist on both the sides at once due to the lack of coupling between the two interfaces, which is achieved by depleting the FP mode within the wavelength range of interest.
Q14. How far away was the reflection from the source-field?
The source-field and the reflection in the far-field were at a distance of 1500 nm and 1000 nm when measured from the top of the analyte, respectively.
Q15. What is the characteristic wavelength of the present grating design?
This characteristic wavelength (y0) depends on the grating parameters, which were optimized to suppress the FP modes while supporting the surface waves within the wavelength range.
Q16. What is the reason why dk/dh may not be zero?
dk/dh may approach zero for ki (i> 3) and h values exceeding 2200 nm, i.e., no red-shift with increasing h, which essentially suggests two plausible reasons.
Q17. What are the differential red-shifts with respect to h?
By considering the first two resonance wavelengths in each set, the differential red-shifts with respect to h are (dk/dh) 0.59, 0.23, and 0.09 for k0, k1, and k2, respectively.