---
title: "Long-range propagation of plasmon polaritons in a thin metal film on a one-dimensional photonic crystal surface"
authors: ["Valery N. Konopsky", "Elena V. Alieva"]
affiliation: "Institute of Spectroscopy, Russian Academy of Sciences, Troitsk, Moscow region, 142190, Russia -."
journal: "Physical Review Letters"
year: 2006
volume: "97"
issue: "25"
article_number: "253904"
pages: ""
doi: "10.1103/PhysRevLett.97.253904"
type: journal-article
site_group: "Surface plasmons and photonic bandgaps"
url_abstract: "https://valery.konopsky.com/paper/PRL2006/PRL2006.htm"
url_pdf: "https://valery.konopsky.com/kvnlocal/PhysRevLett_97_253904.pdf"
language: en
source_tex: "Z:\\ValeryData\\Valery_New\\my_articles\\PhysRevLett2006\\PhysRevLett\\Sent\\Konopsky2PRL.tex"
source_pdf: "Z:\\ValeryData\\Valery_New\\my_articles\\PhysRevLett2006\\PhysRevLett\\published\\PhysRevLett_97_253904.pdf"
---
## Abstract

We present experimental results on the ultra-long-range surface plasmon-polaritons, propagating along thin metal film on the photonic crystal surface over a distance of several millimeters. This propagation length is about two orders of magnitude higher than the one in the ordinary Kretschmann configuration at the same optical frequency. We show that a long-range surface plasmon-polaritons propagation may take place not only in a (quasi-)symmetrical scheme, where a thin metal film is located between two media with (approximately) the same refraction index, but also in a scheme where the thin metal film is located between an appropriate 1-D photonic crystal and an arbitrary (air, water, etc.) medium. The ultra-long-range surface plasmon-polaritons are potentially important for biosensors, plasmonics and other applications.

Surface plasmon-polaritons (SPPs) are bound electromagnetic modes that may exist at a metal/di­electric interface [1] . They are finding ever-widening applications in many fields, ranging from biosensors for detection biomolecules and bioreactions on the surface [2] to plasmonics – a young field devoted to guiding optical waves through metal nanostructures [3, 4, 5]. One of the main obstacles in developing these fields is an intrinsic damping of the surface plasmon-polaritons in the metal and, consequently, a limiting propagation distance of the surface plasmon-polaritons (about ten micrometers in the optical frequency range). In the early 1980s, it was first predicted [6] and then demonstrated [7] that in thin metal films, imbedded between two identical dielectrics (Fig. 1a), a long-range surface plasmon-polariton (LRSPP) mode may appear as a result of a coupling between SPPs from both film interfaces. Compared with conventional SPPs, LRSPPs have higher surface electric field strengths, longer propagation lengths and, consequently, narrower angular resonance curves. Several attempts have been made to exploit LRSPPs instead of SPPs in typical SPP applications, such as surface plasmon resonance biosensors [8, 9] and surface-plasmon-enhanced high-harmonic generation [10]. A drawback of LRSPP applications is the more complicated scheme for LRSPP excitation (Fig. 1b) compared to the ordinary Kretschmann scheme for SPP excitation, because a matching layer (usually a matching fluid) is needed to match the refraction indexes of the medium on both sides of the film. For many media under investigation that have low refraction index $n_e$ (for example, water), this approach is hardly applicable and becomes impractical for $n_e=1$ (air), since a freely suspended thin film is needed in this case.

In this Letter we describe LRSPPs that may propagate at interfaces of metal/air, metal/water, etc., and have a propagation length of about two orders of magnitude higher than one in the ordinary Kretschmann configuration at the same optical frequency. The above objective is attained by using an appropriate 1-D photonic crystal instead of the matching layer, as shown in Fig. 1(c). Here we show that this scheme may support even more long-range SPPs (i.e., ultra-long-range SPPs) than the usual symmetrical scheme for LRSPPs.

![Structures supported the long-range surface plasmon-polaritons propagation. (a) The symmetric scheme with two identical dielectrics at both sides of the thin metal film. (b) The Kretschmann-like quasisymmetric scheme for LRSPP excitation by the frustrated TIR on the prism. For the drawbacks of this scheme, refer to the text. (c) The presented scheme – a thin metal film on the 1-D photonic crystal. The external medium may have any RI in the range 1 ≤ ne < n0, subject to an appropriate choosing of the photonic crystal structure.](media/PRL2006/Konopsky_fig1.eps)

*Structures supported the long-range surface plasmon-polaritons propagation. (a) The symmetric scheme with two identical dielectrics at both sides of the thin metal film. (b) The Kretschmann-like quasisymmetric scheme for LRSPP excitation by the frustrated TIR on the prism. For the drawbacks of this scheme, refer to the text. (c) The presented scheme – a thin metal film on the 1-D photonic crystal. The external medium may have any RI in the range 1 ≤ ne < n0, subject to an appropriate choosing of the photonic crystal structure.*

First it is important to note that the main reason for the long-range plasmon propagation is the presence of a minimum of electric field strength in the thin film as a result of a destructive interference of SPPs from both film interfaces. We consider this problem more generally: When does the modulus of the electric field strength have a minimum equal to zero in the thin metal film? In this essay, let p-polarized electromagnetic field be an incident on the metal film with complex refraction index $n_M$ and thickness $d_M$ at an angle $\theta_0$ from internal medium with refraction index (RI) $n_0$. Hereafter we will use a numerical aperture $\rho=n_0\sin(\theta_0)$ as an angle variable instead of angles $\theta_j$ in different layers. This will be a unified angle variable for all layers since, according to Snell’s law, $\rho=n_0\sin(\theta_0)=n_j\sin(\theta_j)$, for any layer $j$. We will consider the case $\rho\geq n_e$, which is total internal reflection from the external medium with refraction index $n_e$. Assuming that $d_m<<\lambda$, $|n_{M}|>n_{e}$ and looking for the zero minimum of the electric field modulus $|E_p|$ in the thin film, one can find that the zero minimum takes place at the incident angle
``` math
\begin{equation}
\rho_{\alpha}= n_e+2{\alpha}^{2}\,{\frac {{
n_e}^{3}{d_M}^{2}{\pi}^{2}}{{\lambda}^{2}}}\; , 
\end{equation}
```
where $\alpha=(d_M-z_0)/d_M$ is the coordinate of the zero minimum $z_0$ in terms of film thickness $d_M$. When $z_0=0$ ($\alpha=1$), and the angle of incidence is $\rho=\rho_{1}$, the zero minimum of the electric field modulus $|E_p|$ takes place at an internal border of the film. When $z_0=d_M/2$ ($\alpha=1/2$), the zero minimum occurs at
``` math
\begin{equation}
\rho_{1/2}=
n_e+\frac{1}{2}\,{\frac {{
n_e}^{3}{d_M}^{2}{\pi}^{2}}{{\lambda}^{2}}}\; , 
\end{equation}
```
in the center of the film. When $z_0\rightarrow d_M$ ($\alpha\rightarrow 0$), the zero minimum of the electric field modulus $|E_p|$ is located at an external border of the film, and this takes place at $\rho_0$ infinitesimally close to $n_e$ (i.e. near the angle of total internal reflection).

Therefore we have the next answer of our first question: the modulus of the electric field strength $|E_p|$ has a minimum equal to zero when the p-polarized electromagnetic wave incident on the thin metal film is in the angular range from $\rho_{1}$ to $\rho_0$. In this case, the point where $|E_p|=0$ is changed in the range from internal to external border of the film and is located in the center of the film at $\rho=\rho_{1/2}$.

Now we face the second question: Can some electromagnetic surface modes have the wavevector in the range: $k
=[\frac{\omega}{c}\rho_{1} \dots \frac{\omega}{c}\rho_0]$? If yes, one may expect that these modes will be long-range propagated surface modes, since they may be excited by the p-polarized waves incident on the film in angular range $\rho
=[\rho_{1}\dots\rho_0]$ and these modes have the zero minimum of $|E_p|$ inside the metal film.

One example of such a mode is already familiar to readers – the LRSPP in thin film embedded between two identical dielectrics (Fig. 1a). It is known that the dispersion curve of SPPs splits as a result of a coupling between SPPs from both film interfaces, and the LRSPP wavevector shifts (at given frequency) to a light curve. The value of the LRSPP wavevector is $k\simeq\frac{\omega}{c}\rho_{1/2}$ [11], where $\rho_{1/2}$ is given by (2), and the zero minimum of $|E_p|$ is always located in the center of the film.

Here we present another example of electromagnetic surface modes that can propagate along thin metal films and have a wavevector in the range of $k =[\frac{\omega}{c}\rho_{1} \dots
\frac{\omega}{c}\rho_0]$ – optical surface waves on the photonic crystal surface. Photonic crystals are materials that possess a periodic modulation of their refraction index on the scale of the wavelength of light [12]. Such materials can exhibit photonic band gaps that are very much like the electronic band gaps for electron waves travelling in the periodic potential of the crystal. In both cases, frequency intervals exist where the wave propagation is forbidden. This analogy may be extended [13] to include surface levels, which can exist in band gaps of electronic crystals. In photonic crystals it will be the optical surface wave, which dispersion curve is located inside the photonic band gap.

The 1-D photonic crystal is a simple dielectric multilayer mirror. Optical surface modes in 1-D photonic crystals were studied in the 1970s by the Yariv group both theoretically [14] and experimentally [15]. Twenty years later, Robertson et al. experimentally studied the excitation of optical surface waves in a Kretschmann-like configuration [16, 17]. All of these works dealt with s-polarized optical surface waves. We will exploit p-polarized optical surface waves on the 1-D photonic crystal ended by the thin metal film.

We have prepared the test photonic crystal structure and measured angles of the SPP excitation at different wavelengths. The next photonic crystal structure was used: substrate/$(HL)^{14}H_1M$/air, where $H$ is $Ta_2O_5$ layer with thickness 100.0 nm, $L$ is $SiO_2$ layer with thickness 155.7 nm, $H_1$ is $Ta_2O_5$ layer with thickness 98.4 nm, and $M$ is a 5 nm thick gold layer. The prism and substrate were made from VK-7 glass. The refraction indexes of the substrate, $Ta_2O_5$, $SiO_2$ and $Au$ at $\lambda=710$ nm, were $n_0=1.513$, $n_1=2.13$, $n_2=1.45$ and $n_M=0.2+i4.14$ correspondingly. The RIs at other wavelengths were derived using dispersion data presented by Palik [18]. The $Ta_2O_5/SiO_2$ multilayer was deposited by ion sputtering. The gold film was deposited by an ion-assisted RF-frequency diode sputtering. The specific electrical resistance of our sputtered gold film was measured to be $16.3 \mu\Omega$cm, which is 7.4 times higher than the specific resistance of bulk gold $2.2 \mu\Omega$cm. According to Fuchs’ formula [19], the specific resistance of the 5 nm gold film at room temperature should be about 6 times higher than that of bulk gold, which is in good agreement with the measured value, taking into account the imperfections of the sputtered gold film.

The calculated dispersion of our test structure is presented in Fig. 2 as the logarithm of optical field enhancement in the external medium near the structure. Good correspondence is seen between experimental points (white pentagrams) and the calculated dispersion curve of the optical surface mode [^1].

![The calculated dispersion of the test photonic crystal structure and measured experimental points (white pentagrams) at different wavelengths. The photonic band gap is clearly seen as light areas with an enhancement much less than 1. The photonic band gap is vanished near Brewster’s angle (ρBr ≃ 1.249 in this system) where no reflection of the p-polarized wave takes place from SiO2/Ta2O5 interface. The optical surface mode is seen as a dark curve with an enhancement more than 100 inside the band gap. The white pentagrams are experimental points measured at λ = 633 nm (He-Ne laser), λ = 690 nm (diode laser) and λ = 704.5 nm, λ = 710.1 nm, λ = 715.25 nm (Ti-sapphire laser). One can see that, at wavelengths in the range λ ∼ [704…718] nm, the optical surface mode dispersion curve approaches the line of the total internal reflection (TIR) (ρ → ρTIR ≡ ne = 1). Therefore, LRSPPs at these wavelengths are possible.](media/PRL2006/Konopsky_fig2.eps)

*The calculated dispersion of the test photonic crystal structure and measured experimental points (white pentagrams) at different wavelengths. The photonic band gap is clearly seen as light areas with an enhancement much less than 1. The photonic band gap is vanished near Brewster’s angle (ρBr ≃ 1.249 in this system) where no reflection of the p-polarized wave takes place from SiO2/Ta2O5 interface. The optical surface mode is seen as a dark curve with an enhancement more than 100 inside the band gap. The white pentagrams are experimental points measured at λ = 633 nm (He-Ne laser), λ = 690 nm (diode laser) and λ = 704.5 nm, λ = 710.1 nm, λ = 715.25 nm (Ti-sapphire laser). One can see that, at wavelengths in the range λ ∼ [704…718] nm, the optical surface mode dispersion curve approaches the line of the total internal reflection (TIR) (ρ → ρTIR ≡ ne = 1). Therefore, LRSPPs at these wavelengths are possible.*

Figure 2 illustrates that the optical surface mode dispersion curve approaches the line of the total internal reflection (TIR) ($\rho_{TIR}\equiv n_e=1$) at wavelengths in the range of $\lambda\sim [704\dots718]~nm$. Therefore, at these wavelengths we can excite the SPP at $\rho\rightarrow n_e$ and expect it to be LRSPP. At $\rho=\rho_{1/2}$ (in our structure it takes place at $\lambda\simeq 711$ nm), the zero minimum of $|E_p|$ occurs in the center of 5 nm gold film. Moreover, at $\lambda\rightarrow 718$ nm $\rho=
\rho_0\rightarrow n_e$ and we can excite LRSPPs with $|E_p|=0$ at the external interface of the gold film. It may be shown, that the intrinsic extinction of LRSPPs decreased and the propagation length increased when $\alpha$ from equation (1) goes to zero. Therefore, contrary to intuitive expectations, modes with $\rho= \rho_0\rightarrow
n_e$ ($|E_p|=0$ at the external interface of the film) are more long-range propagated than the mode with $\rho=\rho_{1/2}$ ($|E_p|=0$ in the center of the film). To confirm this statement experimentally we have recorded the angular resonance curves of LRSPPs at different wavelengths.

![. Angular resonance curves at different wavelengths. Each curve is up-shifted by 0.6 a.u. from the previous one for good visibility. The diode array was shaded at θ0 ≤ 41.28 to mark the zero level. The interference near the plasmon resonance curves at λ &gt; 714 nm is a new distinguishing feature of ultra-long-range SPPs in the Kretschmann-like configuration (see text for details).](media/PRL2006/Konopsky_fig3.eps)

*. Angular resonance curves at different wavelengths. Each curve is up-shifted by 0.6 a.u. from the previous one for good visibility. The diode array was shaded at θ0 ≤ 41.28 to mark the zero level. The interference near the plasmon resonance curves at λ &gt; 714 nm is a new distinguishing feature of ultra-long-range SPPs in the Kretschmann-like configuration (see text for details).*

Angular resonance curves [^2] are presented in Fig. 3. One can see that the angular curve width at $\lambda= 710$ nm is $\delta\theta= 6\cdot
10^{-4}$ rad, which corresponds to the SPP propagation length (length of $1/e$ intensity decreasing) $L_{710}\simeq 160~\mu$m. This is about twenty times higher than the SPP propagation in the ordinary Kretschmann configuration at optimal film thickness at the same wavelength ($L_{SPP}\simeq
8~\mu$m). As we increase the wavelength, the resonance angle shifts to the TIR angle ($\theta^{TIR}_0=\arcsin(1/n_0)\simeq 
41.37$ grad) and the resonance curve width decreases (hence the propagation length increases). For instance, at $\lambda= 715.2$ nm, the propagation length is estimated to be $L_{715}\simeq 0.8$ mm, which is about two orders of magnitude higher than $L_{SPP}$ in the ordinary Kretschmann scheme. Moreover, a new distinguishing feature of ultra-long-range SPPs in the Kretschmann-like configuration appears: an interference near the plasmon resonance curve. This interference cannot be theoretically predicted from Fresnel-based calculations of reflection curves since the incident field is approximated as an infinite flat front in these calculations, and the limited propagation of SPPs is compared with infinity. However, describing the reflection of a focused restricted Gaussian laser beam, the interference appears when the angular width of the plasmon resonance curve becomes comparable with the diffracted beam divergency of a laser beam. In other words, the interference in the angular distribution of the reflected beam appears when propagation length $L$ is comparable with the laser beam diameter $d$. In our experiments, we used a laser beam with diameter $d=2$ mm and, consequently, $(\delta\theta)_{diff}\simeq\lambda/d=3.5\cdot 10^{-4}$ rad.

![(color). The photographs of the focussed laser beam near the SPP resonance: (a) slightly off resonance and (b) in resonance. The plotting paper is placed near the laser focus on the film for calibration. The photographs were made from the external side of the film (from the upper side of Fig. 1c). Ideally, no light must be seen from this side since total internal reflection of all light occurs. However, in actual practice, light is scattered on imperfections, which are always present on real surfaces, and this scattered light may be detected from the external side.](media/PRL2006/Konopsky_fig4.eps)

*(color). The photographs of the focussed laser beam near the SPP resonance: (a) slightly off resonance and (b) in resonance. The plotting paper is placed near the laser focus on the film for calibration. The photographs were made from the external side of the film (from the upper side of Fig. 1c). Ideally, no light must be seen from this side since total internal reflection of all light occurs. However, in actual practice, light is scattered on imperfections, which are always present on real surfaces, and this scattered light may be detected from the external side.*

When the propagation length of LRSPP reaches such large values, the propagation of LRSPPs may easily be seen by the naked eye. Fig. 4 presents photographs of the laser beam focused using a lens with focal length $f=435$ mm both out of resonance (Fig. 4a) and in resonance (Fig. 4b). One can see in Fig. 4(b), as different scratches and roughnesses are visualized by the plasmon field while the SPPs travel the several-millimeter distance.

It is worth noting here that the scattering of SPPs to light by the surface imperfections is a prominent extinction mechanism of LRSPPs in the current study. The reason for this is the close proximity of the SPP dispersion curve and the light line ($\rho_{TIR}=n_e=1$) in the system. Therefore, even small amplitude roughness may transform the LRSPP to a free-propagated light. This is not a typical situation for SPPs – where the intrinsic damping in the metal is the major extinction mechanism [1, 20]. In the current study, the intrinsic damping is dramatically reduced due to the presence of $|E_p|=0$ inside the metal film, and the role of extinction, due to the plasmon-photon scattering, is increased. This is confirmed by our theoretical calculations, which show that taking into account only internal damping in the metal, we should obtain a propagation length of about one order more that we experimentally measured. The measured propagation length, consequently, is determined by the plasmon-photon scattering rather than by the internal damping. Therefore, improving the smoothness of the metal film (which is purely a technological problem) should result in a propagation length in the centimeter range, which is about three order of magnitude more than in ordinary Kretschmann schemes at the same wavelength.

In conclusion, we have used unique tunable properties of photonic crystals for the excitation of SPPs along a thin metal film in that wavevector range where they become ultra-long-range SPPs and may exist in an asymmetric configuration.

## Acknowledgments

This work was partly supported by the European Network of Excellence, NMP3-CT-2005-515703-2. Authors thank V.O. Kompanets for a technical assistance at work with the Ti-sapphire laser.

H. Raether, *Surface Plasmons* (Springer-Verlag, Berlin, 1988).

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E. Ozbay, Science **311**, 189 (2006).

M. Quinten, A. Leitner, J. R. Krenn, and F. R. Aussenegg, Opt. Lett. **23**, 1331 (1998).

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, J.-Y. Laluet, and T. W. Ebbesen, Nature **440**, 508 (2006).

D. Sarid, Phys. Rev. Lett. **47**, 1927 (1981).

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## References

1. H. Raether, *Surface Plasmons (Springer-Verlag, Berlin, 1988).

2. J. Homola, S. S. Yee, and G. Gauglitz, Sensors and Actuators B **54, 3 (1999).

3. E. Ozbay, Science **311, 189 (2006).

4. M. Quinten, A. Leitner, J. R. Krenn, and F. R. Aussenegg, Opt. Lett. **23, 1331 (1998).

5. S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, J.-Y. Laluet, and T. W. Ebbesen, Nature **440, 508 (2006).

6. D. Sarid, Phys. Rev. Lett. **47, 1927 (1981).

7. A. E. Craig, G. A. Olson, and D. Sarid, Opt. Lett. **8, 380 (1983).

8. G. Nenninger, P. Tobiv ska, J. Homola, and S. Yee, Sensors and Actuators B **74, 145 (2001).

9. A. W. Wark, H. J. Lee, and R. M. Corn, Anal. Chem. **77, 3904 (2005).

10. H. J. Simon, Y. Wang, L.-B. Zhou, and Z. Chen, Opt. Lett. **17, 1268 (1992).

11. F. Yang, J. R. Sambles, and G. W. Bradberry, Phys. Rev. B **44, 5855 (1991).

12. E. Yablonovitch, J. Opt. Soc. Am. B **10, 283 (1993).

13. D. Kossel, J. Opt. Soc. Am. **56, 1434 (1966).

14. P. Yeh, A. Yariv, and C.-S. Hong, J. Opt. Soc. Am. **67, 423 (1977).

15. P. Yeh, A. Yariv, and A. Y. Cho, Appl. Phys. Lett. **32, 104 (1978).

16. W. M. Robertson and M. S. May, Appl. Phys. Lett. **74, 1800 (1999).

17. W. M. Robertson, J. Lightwave Tech. **17, 2013 (1999).

18. E. D. Palik, *Handbook of Optical Constants of Solids (Academic, London, 1985).

19. D. C. Larson, in *Physics of Thin Films, edited by M. H. Francombe and R. W. Hoffman (Academic, London, 1971), vol. VI, chap. 2.

20. D. L. Mills, Phys. Rev. B **12, 4036 (1975). thebibliography.

[^1]: The excitation angles of the optical surface waves, indicated as white pentagrams in Fig. 2, were experimentally measured with an angular accuracy of $\pm 1'$ by parallel laser beam at specified laser wavelengths.

[^2]: The angular resonance curves in Fig. 3 were measured by focusing the laser light on the structure, in Kretschmann-like geometry, with the objective of a focal length of $f=220$ mm and detecting the intensity distribution of reflected light by 512-pixels Hamamatsu photodiode array.

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