Abstract

We suggest optimally designed one-dimensional metal/photonic crystal structures for the excitation of optical Tamm plasmon polaritons, which show strongly enhanced electromagnetic field intensities compared to those due to conventional surface plasmon excitations. We assume that the photonic crystal is made of weakly nonlinear optical materials and calculate the reflectance and the electromagnetic field distribution precisely, using the invariant imbedding method generalized to nonlinear media. We find field intensity enhancement factors as large as 3,000 at the metal/photonic crystal interface. We verify that due to this strong enhancement, nonlinear optical effects such as optical bistability can be observed for very small values of the incident wave power. Our results imply that using our structure, very strong surface enhanced Raman scattering signals can be achieved and optical switching devices can be operated in much lower threshold light intensities.

© 2013 OSA

1. Introduction

The strong local enhancement of the electromagnetic fields due to the excitation of surface plasmon polaritons (SPPs) is one of the key phenomena in plasmonics [13]. It plays a major role in various nonlinear optical applications of plasmonics. More recently, a different kind of surface electromagnetic waves called optical Tamm plasmon polaritons (TPPs) have been actively studied [413]. TPPs can be excited at the surface of a photonic crystal and are simple analogies of the Tamm states proposed as localized electronic states at the edge of a truncated periodic potential. They show characteristics similar to conventional propagating SPPs, but can be generated in all-dielectric multilayer structures. Unlike SPPs, they can be excited by incident s waves as well as p waves. Their dielectric loss is much smaller than that of conventional SPPs, leading to sharper coupling resonances, higher surface fields, and longer propagation distances than those for SPPs [5, 9]. These features are advantageous for current and future applications in plasmonics.

In this paper, we suggest optimally designed one-dimensional metal/photonic crystal structures for the generation of optical TPPs, which have strongly enhanced field intensities compared to those due to conventional propagating surface plasmon excitations. We assume that the photonic crystal is made of weakly nonlinear optical materials. Using the invariant imbedding method generalized to nonlinear media [14], we calculate the reflectance and the electromagnetic field distribution precisely. We find extremely large field intensity enhancement factors as large as 3,000 at the metal/photonic crystal interface. Due to this strong enhancement, various nonlinear optical effects including optical bistability can be observed for rather small values of the incident wave power. Our results imply that using our structure, very strong surface enhanced Raman scattering signals can be achieved and optical switching devices can be operated in much lower threshold light intensities.

2. Model and theoretical method

We consider a multilayered structure consisting of a one-dimensional photonic crystal coated with silver film. The photonic crystal is made of GaAs and AlAs multilayers the refractive indices of which are taken to be 3.7 and 3 respectively. Due to the possibility of a precise control of the deposition thicknesses by molecular beam epitaxy, GaAs and AlAs are commonly used to fabricate photonic crystals for the excitation of TPPs in the infrared region. In our calculations, the Drude model

ε=1ωp2ω(ω+iγ)
with h̄ωp = 9.01 eV and h̄γ = 0.0048 eV is used to describe the dielectric permittivity of silver film, where ωp is the plasma frequency and γ is the collision frequency. GaAs layers are considered to have a Kerr-type optical nonlinearity, the strength of which is given by the third-order nonlinear optical coefficient χ(3) ≈ 10−10 esu [15].

We assume that linearly-polarized electromagnetic waves are obliquely incident on the structure from the metal side. The wave equation describing the propagation of these waves in nonlinear media with a Kerr nonlinearity can be solved in a numerically precise and efficient manner using a generalized version of the invariant imbedding method [14]. Though it can be applied to both s and p waves, we focus here on the propagation of p waves of frequency ω incident on a multilayered structure, where the dielectric permittivity ε varies only in the z direction. We assume that the structure lies in 0 ≤ zL and the wave propagates in the xz plane. The magnetic field amplitude H = H(z) satisfies

d2Hdz21ε(z)dεdzdHdz+[ω2c2ε(z)kx2]H=0,
where kx is the x component of the wave vector. The wave is assumed to be incident from z > L and transmitted to z < 0. ε is equal to ε1 and ε2 in the incident and transmissive regions respectively, whereas in 0 ≤ zL, it is given by
ε(z)=εL(z)+β(z)|E(z)|2,
where εL is the linear part of the dielectric permittivity and β describes the strength of the Kerr-type nonlinearity. E(z) is the electric field amplitude.

The reflection coefficient r is defined by the wave function in the incident region

H(z)=vε1[eikz(Lz)+r(L)eikz(zL)],
where |v|2 (≡ w) is the electric field intensity of the incident wave and kz is the z component of the wave vector. r and w are considered as functions of L in our invariant imbedding method, using which we derive exact differential equations satisfied by them:
1kzdrdl=2iε˜(l)ri2[ε˜(l)1][1tan2θε˜(l)](1+r)2,1kzdwdl=Im{2ε˜(l)[ε˜(l)1][1tan2θε˜(l)](1+r)}w,
where θ is the incident angle and ε̃(l) [≡ ε(l)/ε1] is obtained from
ε(l)=εL(l)+β(l)w(l)[ε12|ε(l)|2|1+r(l)|2sin2θ+|1r(l)|2cos2θ].
They are supplemented with the initial conditions for r and w:
r(0)=ε2ε1cosθε1ε2ε1sin2θε2ε1cosθ+ε1ε2ε1sin2θ,w(0)=w0.
The constant w0 is chosen such that the final solution for w(L) is the same as the physical input intensity. The fact that in general, there are several w0 values corresponding to a given w(L) value gives a natural explanation of optical multistability. The reflectance R is given by R = |r(L)|2.

The invariant imbedding method can also be used in calculating the normalized magnetic field amplitude u(z) = H(z)/v. We consider the u field as a function of both z and l: u = u(z, l). Then we have

1kzul=iε˜(l)ui2[ε˜(l)1][1tan2θε˜(l)][1+r(l)]u.
For a given z (0 < z < L), u(z, L) is obtained by integrating this equation, together with Eq. (5), from l = z to l = L using the initial condition u(z, z) = 1 + r(z).

3. Numerical results

We consider the linear cases first. The number of photonic crystal periods, the thickness of one period and the metal layer thickness are denoted by N, Λ and dm respectively. Then the total thickness of the structure is L = NΛ + dm. We assume Λ = 187 nm and the optical thicknesses of GaAs and AlAs layers are equal to 309.8 nm. In the normal incidence case, the photonic bandgap is formed between h̄ω = 0.94 eV and 1.06 eV. We expect the resonance energy of the TPP, h̄ωT, lies inside this bandgap. In order to obtain the largest field enhancement, we tune dm by varying it from 40 to 60 nm. In Fig. 1, we show the profile of the real part of the refractive index, nR, along the z direction when N = 20.

 

Fig. 1 Profile of the real part of the refractive index along the z direction when N = 20.

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In all calculations presented in this section, the incident wave is assumed to be p-polarized. In Fig. 2(a), we plot the reflectance as a function of the incident angle, when N = 20 and h̄ωT = 0.96, 0.97, 0.98, 0.99 eV. For each value of ωT, the metal layer thickness dm has been chosen to maximize the field enhancement. We find that when h̄ωT = 0.96 eV, the TPP is excited at θ = 8.26°. This angle shifts toward higher values as ωT increases. In Fig 2(b), we show the spatial distributions of the magnetic field intensity corresponding to the four reflectance minima shown in Fig. 2(a). We find that the field intensity near the the metal/photonic crystal interface is greatly enhanced with respect to that of the incident wave. This enhancement is much larger than that due to conventional propagating surface plasmon excitations.

 

Fig. 2 (a) Reflectance versus incident angle, when N = 20 and h̄ωT = 0.96, 0.97, 0.98, 0.99 eV. The metal layer thickness dm chosen to maximize the field enhancement for each ωT is denoted on the figure. (b) Spatial distributions of the magnetic field intensity corresponding to the four reflectance minima shown in (a). A magnified view of the field distribution near the metal/photonic crystal interface is shown in the inset. The field intensity is normalized with respect to that of the incident wave.

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In Fig. 3, we show the reflectance and the magnetic field distribution for four different values of N when h̄ωT = 0.96 eV. For N = 20, the TPP is excited at θ = 8.26°. The excitation angle decreases to smaller values, 5.68°, 4.96° and 4.63°, as N increases to 25, 30 and 40 respectively. We also find that the the value of dm chosen to maximize the field enhancement increases as N increases and converges to about 55 nm. In Fig. 3(b), we observe that an extremely large enhancement occurs at the interface between the photonic crystal and the metal layer. We note that the intensity of the incident wave is 1, therefore an enhancement factor as large as 3,000 can be achieved.

 

Fig. 3 (a) Reflectance versus incident angle, when h̄ωT = 0.96 eV and N = 20, 25, 30, 40. The metal layer thickness dm chosen to maximize the field enhancement for each N is denoted on the figure. (b) Spatial distributions of the normalized magnetic field intensity corresponding to the five reflectance minima shown in (a).

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In Fig. 4, we plot the maximum value of the normalized magnetic field intensity, which occurs at the interface between the photonic crystal and the metal layer, versus N, when h̄ωT = 0.96 eV. The enhancement factor increases monotonically and converges to about 3,000 as N increases. This value is much larger than the field ebhancement factor due to the excitation of conventional SPPs [16, 17]. This implies that stronger nonlinear optical effects including more strongly enhanced Raman scattering signals can be obtained due to the excitation of optical TPPs. In the inset of Fig. 4, the metal layer thickness dm chosen to maximize the field enhancement is plotted versus N. We notice that dm converges to about 55 nm.

 

Fig. 4 Maximum value of the normalized magnetic field intensity, which occurs at the interface between the photonic crystal and the metal layer, versus N, when h̄ωT = 0.96 eV. In the inset, the metal layer thickness dm chosen to maximize the field enhancement is plotted versus N.

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We now turn to the nonlinear case. In Fig. 5, we turn on the nonlinearity of GaAs and plot the reflectance versus incident angle for several values of βw, when h̄ωT = 0.96 eV, N = 40 and dm = 55 nm. β is a quantity proportional to χ(3) and w is a quantity proportional to the power of incident laser light. The parameter βw is the measure of the strength of optical nonlinearity. More specifically, it is straightforward to derive the identity

βw=24π2c107χ(3)I0.079χ(3)I,
where χ(3) is measured in esu and I is the intensity of the incident wave measured in W/cm2 [17]. As shown in Fig. 5, we find that optical bistability begins to appear from βw ≈ 10−4. This value is much smaller than that for conventional SPPs given by βw ≈ 0.005 [17]. This fact suggests that it is feasible to design sensitive optical switches operating at very small powers based on the giant field enhancement. When χ(3) ≈ 10−10 esu, the I value corresponding to βw ≈ 10−4 is approximately 13 MW/cm2.

 

Fig. 5 Reflectance versus incident angle when h̄ωT = 0.96 eV, N = 40, dm = 55 nm and βw = 0, 0.00003, 0.00005, 0.0001.

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4. Conclusion

In this paper, we have suggested optimally designed one-dimensional metal/photonic crystal structures for the generation of optical TPPs, which have strongly enhanced field intensities compared to those due to conventional surface plasmon excitations. Assuming that the photonic crystal is made of weakly nonlinear optical materials, we have calculated the reflectance and the electromagnetic field distribution precisely, using the invariant imbedding method generalized to nonlinear media. We have obtained extremely large field intensity enhancement factors, which are as large as 3,000 at the metal/photonic crystal interface. Due to this strong enhancement, we have shown that nonlinear optical effects such as optical bistability can be observed for rather small values of the incident wave power.

Acknowledgments

This work has been supported by the National Research Foundation of Korea Grant ( NRF-2012R1A1A2044201) funded by the Korean Government and by CNRS-Ewha International Research Center Program.

References and links

1. W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424, 824–830 (2003). [CrossRef]   [PubMed]  

2. E. Ozbay, “Plasmonics: Merging photonics and electronics at nanoscale dimensions,” Science 311, 189–193 (2006). [CrossRef]   [PubMed]  

3. A. V. Zayats, I. I. Smolyaninov, and A. A. Maradudin, “Nano-optics of surface plasmon polaritons,” Phys. Rep. 408, 131–314 (2005). [CrossRef]  

4. V. A. Kavokin, I. A. Shelykh, and G. Malpuech, “Lossless interface modes at the boundary between two periodic dielectric structures,” Phys. Rev. B 72, 233102 (2005). [CrossRef]  

5. M. Kaliteevski, I. Iorsh, S. Brand, R. A. Abram, J. M. Chamberlian, A. V. Kavokin, and I. A. Shelykh, “Tamm plasmon-polaritons: Possible electromagnetic states at the interface of a metal and a dielectric Bragg mirror,” Phys. Rev. B 76, 165415 (2007). [CrossRef]  

6. S. Brand, M. Kaliteevski, and R. A. Abram, “Optical Tamm states above the bulk plasma frequency at a Bragg stack/metal interface,” Phys. Rev. B 79, 085416 (2009). [CrossRef]  

7. N. Malkova and C. Z. Ning, “Shockley and Tamm surface states in photonic crystals,” Phys. Rev. B 73, 113113 (2006). [CrossRef]  

8. S. H. Tsang, S. F. Yu, X. F. Li, H. Y. Yang, and H. K. Liang, “Observation of Tamm plasmon polaritons in visible regime from ZnO/Al2O3distributed Bragg reflector-Ag interface,” Opt. Commun. 284, 1890–1892 (2011). [CrossRef]  

9. M. E. Sasin, R. P. Seisyan, M. Kaliteevski, S. Brand, R. A. Abram, J. M. Chamberlain, A. Yu. Egorov, A. P. Vasil’ev, V. S. Mikhrin, and A. V. Kavokin, “Tamm plasmon polaritons: Slow and spatially compact light,” Appl. Phys. Lett. 92, 251112 (2008). [CrossRef]  

10. I. Iorsh, P. V. Panicheva, I. A. Slovinskii, and M. A. Kaliteevski, “Coupled Tamm plasmons,” Tech. Phys. Lett. 38, 351–353 (2012). [CrossRef]  

11. R. Brückner, M. Sudzius, S. I. Hintschich, H. Fröb, V. G. Lyssenko, M. A. Kaliteevski, I. Iorsh, R. A. Abram, A. V. Kavokin, and K. Leo, “Parabolic polarization splitting of Tamm states in a metal-organic microcavity,” Appl. Phys. Lett. 100, 062101 (2012). [CrossRef]  

12. C.-H. Xue, H.-T. Jiang, H. Lu, G.-Q. Du, and H. Chen, “Efficient third-harmonic generation based on Tamm plasmon polaritons,” Opt. Lett. 38, 959–961 (2013). [CrossRef]   [PubMed]  

13. I. V. Treshin, V. V. Klimov, P. N. Melentiev, and V. I. Balykin, “Optical Tamm state and extraordinary light transmission through a nanoaperture,” Phys. Rev. A 88, 023832 (2013). [CrossRef]  

14. K. Kim, D. K. Phung, F. Rotermund, and H. Lim, “Propagation of electromagnetic waves in stratified media with nonlinearity in both dielectric and magnetic responses,” Opt. Express 16, 1150–1164 (2008). [CrossRef]   [PubMed]  

15. R. W. Boyd, Nonlinear Optics, 2nd ed. (Academic, 2003).

16. Y. Liu, S. Xu, X. Xuyang, B. Zhao, and W. Xu, “Long-range surface plasmon field-enhanced Raman scattering spectroscopy based on evanescent field excitation,” J. Phys. Chem. Lett. 2, 2218–2222 (2011). [CrossRef]  

17. K. Kim, D. K. Phung, F. Rotermund, and H. Lim, “Strong influence of nonlinearity and surface plasmon excitations on the lateral shift,” Opt. Express 16, 15506–15513 (2008). [CrossRef]   [PubMed]  

References

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  1. W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424, 824–830 (2003).
    [CrossRef] [PubMed]
  2. E. Ozbay, “Plasmonics: Merging photonics and electronics at nanoscale dimensions,” Science 311, 189–193 (2006).
    [CrossRef] [PubMed]
  3. A. V. Zayats, I. I. Smolyaninov, and A. A. Maradudin, “Nano-optics of surface plasmon polaritons,” Phys. Rep. 408, 131–314 (2005).
    [CrossRef]
  4. V. A. Kavokin, I. A. Shelykh, and G. Malpuech, “Lossless interface modes at the boundary between two periodic dielectric structures,” Phys. Rev. B 72, 233102 (2005).
    [CrossRef]
  5. M. Kaliteevski, I. Iorsh, S. Brand, R. A. Abram, J. M. Chamberlian, A. V. Kavokin, and I. A. Shelykh, “Tamm plasmon-polaritons: Possible electromagnetic states at the interface of a metal and a dielectric Bragg mirror,” Phys. Rev. B 76, 165415 (2007).
    [CrossRef]
  6. S. Brand, M. Kaliteevski, and R. A. Abram, “Optical Tamm states above the bulk plasma frequency at a Bragg stack/metal interface,” Phys. Rev. B 79, 085416 (2009).
    [CrossRef]
  7. N. Malkova and C. Z. Ning, “Shockley and Tamm surface states in photonic crystals,” Phys. Rev. B 73, 113113 (2006).
    [CrossRef]
  8. S. H. Tsang, S. F. Yu, X. F. Li, H. Y. Yang, and H. K. Liang, “Observation of Tamm plasmon polaritons in visible regime from ZnO/Al2O3distributed Bragg reflector-Ag interface,” Opt. Commun. 284, 1890–1892 (2011).
    [CrossRef]
  9. M. E. Sasin, R. P. Seisyan, M. Kaliteevski, S. Brand, R. A. Abram, J. M. Chamberlain, A. Yu. Egorov, A. P. Vasil’ev, V. S. Mikhrin, and A. V. Kavokin, “Tamm plasmon polaritons: Slow and spatially compact light,” Appl. Phys. Lett. 92, 251112 (2008).
    [CrossRef]
  10. I. Iorsh, P. V. Panicheva, I. A. Slovinskii, and M. A. Kaliteevski, “Coupled Tamm plasmons,” Tech. Phys. Lett. 38, 351–353 (2012).
    [CrossRef]
  11. R. Brückner, M. Sudzius, S. I. Hintschich, H. Fröb, V. G. Lyssenko, M. A. Kaliteevski, I. Iorsh, R. A. Abram, A. V. Kavokin, and K. Leo, “Parabolic polarization splitting of Tamm states in a metal-organic microcavity,” Appl. Phys. Lett. 100, 062101 (2012).
    [CrossRef]
  12. C.-H. Xue, H.-T. Jiang, H. Lu, G.-Q. Du, and H. Chen, “Efficient third-harmonic generation based on Tamm plasmon polaritons,” Opt. Lett. 38, 959–961 (2013).
    [CrossRef] [PubMed]
  13. I. V. Treshin, V. V. Klimov, P. N. Melentiev, and V. I. Balykin, “Optical Tamm state and extraordinary light transmission through a nanoaperture,” Phys. Rev. A 88, 023832 (2013).
    [CrossRef]
  14. K. Kim, D. K. Phung, F. Rotermund, and H. Lim, “Propagation of electromagnetic waves in stratified media with nonlinearity in both dielectric and magnetic responses,” Opt. Express 16, 1150–1164 (2008).
    [CrossRef] [PubMed]
  15. R. W. Boyd, Nonlinear Optics, 2nd ed. (Academic, 2003).
  16. Y. Liu, S. Xu, X. Xuyang, B. Zhao, and W. Xu, “Long-range surface plasmon field-enhanced Raman scattering spectroscopy based on evanescent field excitation,” J. Phys. Chem. Lett. 2, 2218–2222 (2011).
    [CrossRef]
  17. K. Kim, D. K. Phung, F. Rotermund, and H. Lim, “Strong influence of nonlinearity and surface plasmon excitations on the lateral shift,” Opt. Express 16, 15506–15513 (2008).
    [CrossRef] [PubMed]

2013 (2)

I. V. Treshin, V. V. Klimov, P. N. Melentiev, and V. I. Balykin, “Optical Tamm state and extraordinary light transmission through a nanoaperture,” Phys. Rev. A 88, 023832 (2013).
[CrossRef]

C.-H. Xue, H.-T. Jiang, H. Lu, G.-Q. Du, and H. Chen, “Efficient third-harmonic generation based on Tamm plasmon polaritons,” Opt. Lett. 38, 959–961 (2013).
[CrossRef] [PubMed]

2012 (2)

I. Iorsh, P. V. Panicheva, I. A. Slovinskii, and M. A. Kaliteevski, “Coupled Tamm plasmons,” Tech. Phys. Lett. 38, 351–353 (2012).
[CrossRef]

R. Brückner, M. Sudzius, S. I. Hintschich, H. Fröb, V. G. Lyssenko, M. A. Kaliteevski, I. Iorsh, R. A. Abram, A. V. Kavokin, and K. Leo, “Parabolic polarization splitting of Tamm states in a metal-organic microcavity,” Appl. Phys. Lett. 100, 062101 (2012).
[CrossRef]

2011 (2)

Y. Liu, S. Xu, X. Xuyang, B. Zhao, and W. Xu, “Long-range surface plasmon field-enhanced Raman scattering spectroscopy based on evanescent field excitation,” J. Phys. Chem. Lett. 2, 2218–2222 (2011).
[CrossRef]

S. H. Tsang, S. F. Yu, X. F. Li, H. Y. Yang, and H. K. Liang, “Observation of Tamm plasmon polaritons in visible regime from ZnO/Al2O3distributed Bragg reflector-Ag interface,” Opt. Commun. 284, 1890–1892 (2011).
[CrossRef]

2009 (1)

S. Brand, M. Kaliteevski, and R. A. Abram, “Optical Tamm states above the bulk plasma frequency at a Bragg stack/metal interface,” Phys. Rev. B 79, 085416 (2009).
[CrossRef]

2008 (3)

2007 (1)

M. Kaliteevski, I. Iorsh, S. Brand, R. A. Abram, J. M. Chamberlian, A. V. Kavokin, and I. A. Shelykh, “Tamm plasmon-polaritons: Possible electromagnetic states at the interface of a metal and a dielectric Bragg mirror,” Phys. Rev. B 76, 165415 (2007).
[CrossRef]

2006 (2)

E. Ozbay, “Plasmonics: Merging photonics and electronics at nanoscale dimensions,” Science 311, 189–193 (2006).
[CrossRef] [PubMed]

N. Malkova and C. Z. Ning, “Shockley and Tamm surface states in photonic crystals,” Phys. Rev. B 73, 113113 (2006).
[CrossRef]

2005 (2)

A. V. Zayats, I. I. Smolyaninov, and A. A. Maradudin, “Nano-optics of surface plasmon polaritons,” Phys. Rep. 408, 131–314 (2005).
[CrossRef]

V. A. Kavokin, I. A. Shelykh, and G. Malpuech, “Lossless interface modes at the boundary between two periodic dielectric structures,” Phys. Rev. B 72, 233102 (2005).
[CrossRef]

2003 (1)

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424, 824–830 (2003).
[CrossRef] [PubMed]

Abram, R. A.

R. Brückner, M. Sudzius, S. I. Hintschich, H. Fröb, V. G. Lyssenko, M. A. Kaliteevski, I. Iorsh, R. A. Abram, A. V. Kavokin, and K. Leo, “Parabolic polarization splitting of Tamm states in a metal-organic microcavity,” Appl. Phys. Lett. 100, 062101 (2012).
[CrossRef]

S. Brand, M. Kaliteevski, and R. A. Abram, “Optical Tamm states above the bulk plasma frequency at a Bragg stack/metal interface,” Phys. Rev. B 79, 085416 (2009).
[CrossRef]

M. E. Sasin, R. P. Seisyan, M. Kaliteevski, S. Brand, R. A. Abram, J. M. Chamberlain, A. Yu. Egorov, A. P. Vasil’ev, V. S. Mikhrin, and A. V. Kavokin, “Tamm plasmon polaritons: Slow and spatially compact light,” Appl. Phys. Lett. 92, 251112 (2008).
[CrossRef]

M. Kaliteevski, I. Iorsh, S. Brand, R. A. Abram, J. M. Chamberlian, A. V. Kavokin, and I. A. Shelykh, “Tamm plasmon-polaritons: Possible electromagnetic states at the interface of a metal and a dielectric Bragg mirror,” Phys. Rev. B 76, 165415 (2007).
[CrossRef]

Balykin, V. I.

I. V. Treshin, V. V. Klimov, P. N. Melentiev, and V. I. Balykin, “Optical Tamm state and extraordinary light transmission through a nanoaperture,” Phys. Rev. A 88, 023832 (2013).
[CrossRef]

Barnes, W. L.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424, 824–830 (2003).
[CrossRef] [PubMed]

Boyd, R. W.

R. W. Boyd, Nonlinear Optics, 2nd ed. (Academic, 2003).

Brand, S.

S. Brand, M. Kaliteevski, and R. A. Abram, “Optical Tamm states above the bulk plasma frequency at a Bragg stack/metal interface,” Phys. Rev. B 79, 085416 (2009).
[CrossRef]

M. E. Sasin, R. P. Seisyan, M. Kaliteevski, S. Brand, R. A. Abram, J. M. Chamberlain, A. Yu. Egorov, A. P. Vasil’ev, V. S. Mikhrin, and A. V. Kavokin, “Tamm plasmon polaritons: Slow and spatially compact light,” Appl. Phys. Lett. 92, 251112 (2008).
[CrossRef]

M. Kaliteevski, I. Iorsh, S. Brand, R. A. Abram, J. M. Chamberlian, A. V. Kavokin, and I. A. Shelykh, “Tamm plasmon-polaritons: Possible electromagnetic states at the interface of a metal and a dielectric Bragg mirror,” Phys. Rev. B 76, 165415 (2007).
[CrossRef]

Brückner, R.

R. Brückner, M. Sudzius, S. I. Hintschich, H. Fröb, V. G. Lyssenko, M. A. Kaliteevski, I. Iorsh, R. A. Abram, A. V. Kavokin, and K. Leo, “Parabolic polarization splitting of Tamm states in a metal-organic microcavity,” Appl. Phys. Lett. 100, 062101 (2012).
[CrossRef]

Chamberlain, J. M.

M. E. Sasin, R. P. Seisyan, M. Kaliteevski, S. Brand, R. A. Abram, J. M. Chamberlain, A. Yu. Egorov, A. P. Vasil’ev, V. S. Mikhrin, and A. V. Kavokin, “Tamm plasmon polaritons: Slow and spatially compact light,” Appl. Phys. Lett. 92, 251112 (2008).
[CrossRef]

Chamberlian, J. M.

M. Kaliteevski, I. Iorsh, S. Brand, R. A. Abram, J. M. Chamberlian, A. V. Kavokin, and I. A. Shelykh, “Tamm plasmon-polaritons: Possible electromagnetic states at the interface of a metal and a dielectric Bragg mirror,” Phys. Rev. B 76, 165415 (2007).
[CrossRef]

Chen, H.

Dereux, A.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424, 824–830 (2003).
[CrossRef] [PubMed]

Du, G.-Q.

Ebbesen, T. W.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424, 824–830 (2003).
[CrossRef] [PubMed]

Fröb, H.

R. Brückner, M. Sudzius, S. I. Hintschich, H. Fröb, V. G. Lyssenko, M. A. Kaliteevski, I. Iorsh, R. A. Abram, A. V. Kavokin, and K. Leo, “Parabolic polarization splitting of Tamm states in a metal-organic microcavity,” Appl. Phys. Lett. 100, 062101 (2012).
[CrossRef]

Hintschich, S. I.

R. Brückner, M. Sudzius, S. I. Hintschich, H. Fröb, V. G. Lyssenko, M. A. Kaliteevski, I. Iorsh, R. A. Abram, A. V. Kavokin, and K. Leo, “Parabolic polarization splitting of Tamm states in a metal-organic microcavity,” Appl. Phys. Lett. 100, 062101 (2012).
[CrossRef]

Iorsh, I.

R. Brückner, M. Sudzius, S. I. Hintschich, H. Fröb, V. G. Lyssenko, M. A. Kaliteevski, I. Iorsh, R. A. Abram, A. V. Kavokin, and K. Leo, “Parabolic polarization splitting of Tamm states in a metal-organic microcavity,” Appl. Phys. Lett. 100, 062101 (2012).
[CrossRef]

I. Iorsh, P. V. Panicheva, I. A. Slovinskii, and M. A. Kaliteevski, “Coupled Tamm plasmons,” Tech. Phys. Lett. 38, 351–353 (2012).
[CrossRef]

M. Kaliteevski, I. Iorsh, S. Brand, R. A. Abram, J. M. Chamberlian, A. V. Kavokin, and I. A. Shelykh, “Tamm plasmon-polaritons: Possible electromagnetic states at the interface of a metal and a dielectric Bragg mirror,” Phys. Rev. B 76, 165415 (2007).
[CrossRef]

Jiang, H.-T.

Kaliteevski, M.

S. Brand, M. Kaliteevski, and R. A. Abram, “Optical Tamm states above the bulk plasma frequency at a Bragg stack/metal interface,” Phys. Rev. B 79, 085416 (2009).
[CrossRef]

M. E. Sasin, R. P. Seisyan, M. Kaliteevski, S. Brand, R. A. Abram, J. M. Chamberlain, A. Yu. Egorov, A. P. Vasil’ev, V. S. Mikhrin, and A. V. Kavokin, “Tamm plasmon polaritons: Slow and spatially compact light,” Appl. Phys. Lett. 92, 251112 (2008).
[CrossRef]

M. Kaliteevski, I. Iorsh, S. Brand, R. A. Abram, J. M. Chamberlian, A. V. Kavokin, and I. A. Shelykh, “Tamm plasmon-polaritons: Possible electromagnetic states at the interface of a metal and a dielectric Bragg mirror,” Phys. Rev. B 76, 165415 (2007).
[CrossRef]

Kaliteevski, M. A.

R. Brückner, M. Sudzius, S. I. Hintschich, H. Fröb, V. G. Lyssenko, M. A. Kaliteevski, I. Iorsh, R. A. Abram, A. V. Kavokin, and K. Leo, “Parabolic polarization splitting of Tamm states in a metal-organic microcavity,” Appl. Phys. Lett. 100, 062101 (2012).
[CrossRef]

I. Iorsh, P. V. Panicheva, I. A. Slovinskii, and M. A. Kaliteevski, “Coupled Tamm plasmons,” Tech. Phys. Lett. 38, 351–353 (2012).
[CrossRef]

Kavokin, A. V.

R. Brückner, M. Sudzius, S. I. Hintschich, H. Fröb, V. G. Lyssenko, M. A. Kaliteevski, I. Iorsh, R. A. Abram, A. V. Kavokin, and K. Leo, “Parabolic polarization splitting of Tamm states in a metal-organic microcavity,” Appl. Phys. Lett. 100, 062101 (2012).
[CrossRef]

M. E. Sasin, R. P. Seisyan, M. Kaliteevski, S. Brand, R. A. Abram, J. M. Chamberlain, A. Yu. Egorov, A. P. Vasil’ev, V. S. Mikhrin, and A. V. Kavokin, “Tamm plasmon polaritons: Slow and spatially compact light,” Appl. Phys. Lett. 92, 251112 (2008).
[CrossRef]

M. Kaliteevski, I. Iorsh, S. Brand, R. A. Abram, J. M. Chamberlian, A. V. Kavokin, and I. A. Shelykh, “Tamm plasmon-polaritons: Possible electromagnetic states at the interface of a metal and a dielectric Bragg mirror,” Phys. Rev. B 76, 165415 (2007).
[CrossRef]

Kavokin, V. A.

V. A. Kavokin, I. A. Shelykh, and G. Malpuech, “Lossless interface modes at the boundary between two periodic dielectric structures,” Phys. Rev. B 72, 233102 (2005).
[CrossRef]

Kim, K.

Klimov, V. V.

I. V. Treshin, V. V. Klimov, P. N. Melentiev, and V. I. Balykin, “Optical Tamm state and extraordinary light transmission through a nanoaperture,” Phys. Rev. A 88, 023832 (2013).
[CrossRef]

Leo, K.

R. Brückner, M. Sudzius, S. I. Hintschich, H. Fröb, V. G. Lyssenko, M. A. Kaliteevski, I. Iorsh, R. A. Abram, A. V. Kavokin, and K. Leo, “Parabolic polarization splitting of Tamm states in a metal-organic microcavity,” Appl. Phys. Lett. 100, 062101 (2012).
[CrossRef]

Li, X. F.

S. H. Tsang, S. F. Yu, X. F. Li, H. Y. Yang, and H. K. Liang, “Observation of Tamm plasmon polaritons in visible regime from ZnO/Al2O3distributed Bragg reflector-Ag interface,” Opt. Commun. 284, 1890–1892 (2011).
[CrossRef]

Liang, H. K.

S. H. Tsang, S. F. Yu, X. F. Li, H. Y. Yang, and H. K. Liang, “Observation of Tamm plasmon polaritons in visible regime from ZnO/Al2O3distributed Bragg reflector-Ag interface,” Opt. Commun. 284, 1890–1892 (2011).
[CrossRef]

Lim, H.

Liu, Y.

Y. Liu, S. Xu, X. Xuyang, B. Zhao, and W. Xu, “Long-range surface plasmon field-enhanced Raman scattering spectroscopy based on evanescent field excitation,” J. Phys. Chem. Lett. 2, 2218–2222 (2011).
[CrossRef]

Lu, H.

Lyssenko, V. G.

R. Brückner, M. Sudzius, S. I. Hintschich, H. Fröb, V. G. Lyssenko, M. A. Kaliteevski, I. Iorsh, R. A. Abram, A. V. Kavokin, and K. Leo, “Parabolic polarization splitting of Tamm states in a metal-organic microcavity,” Appl. Phys. Lett. 100, 062101 (2012).
[CrossRef]

Malkova, N.

N. Malkova and C. Z. Ning, “Shockley and Tamm surface states in photonic crystals,” Phys. Rev. B 73, 113113 (2006).
[CrossRef]

Malpuech, G.

V. A. Kavokin, I. A. Shelykh, and G. Malpuech, “Lossless interface modes at the boundary between two periodic dielectric structures,” Phys. Rev. B 72, 233102 (2005).
[CrossRef]

Maradudin, A. A.

A. V. Zayats, I. I. Smolyaninov, and A. A. Maradudin, “Nano-optics of surface plasmon polaritons,” Phys. Rep. 408, 131–314 (2005).
[CrossRef]

Melentiev, P. N.

I. V. Treshin, V. V. Klimov, P. N. Melentiev, and V. I. Balykin, “Optical Tamm state and extraordinary light transmission through a nanoaperture,” Phys. Rev. A 88, 023832 (2013).
[CrossRef]

Mikhrin, V. S.

M. E. Sasin, R. P. Seisyan, M. Kaliteevski, S. Brand, R. A. Abram, J. M. Chamberlain, A. Yu. Egorov, A. P. Vasil’ev, V. S. Mikhrin, and A. V. Kavokin, “Tamm plasmon polaritons: Slow and spatially compact light,” Appl. Phys. Lett. 92, 251112 (2008).
[CrossRef]

Ning, C. Z.

N. Malkova and C. Z. Ning, “Shockley and Tamm surface states in photonic crystals,” Phys. Rev. B 73, 113113 (2006).
[CrossRef]

Ozbay, E.

E. Ozbay, “Plasmonics: Merging photonics and electronics at nanoscale dimensions,” Science 311, 189–193 (2006).
[CrossRef] [PubMed]

Panicheva, P. V.

I. Iorsh, P. V. Panicheva, I. A. Slovinskii, and M. A. Kaliteevski, “Coupled Tamm plasmons,” Tech. Phys. Lett. 38, 351–353 (2012).
[CrossRef]

Phung, D. K.

Rotermund, F.

Sasin, M. E.

M. E. Sasin, R. P. Seisyan, M. Kaliteevski, S. Brand, R. A. Abram, J. M. Chamberlain, A. Yu. Egorov, A. P. Vasil’ev, V. S. Mikhrin, and A. V. Kavokin, “Tamm plasmon polaritons: Slow and spatially compact light,” Appl. Phys. Lett. 92, 251112 (2008).
[CrossRef]

Seisyan, R. P.

M. E. Sasin, R. P. Seisyan, M. Kaliteevski, S. Brand, R. A. Abram, J. M. Chamberlain, A. Yu. Egorov, A. P. Vasil’ev, V. S. Mikhrin, and A. V. Kavokin, “Tamm plasmon polaritons: Slow and spatially compact light,” Appl. Phys. Lett. 92, 251112 (2008).
[CrossRef]

Shelykh, I. A.

M. Kaliteevski, I. Iorsh, S. Brand, R. A. Abram, J. M. Chamberlian, A. V. Kavokin, and I. A. Shelykh, “Tamm plasmon-polaritons: Possible electromagnetic states at the interface of a metal and a dielectric Bragg mirror,” Phys. Rev. B 76, 165415 (2007).
[CrossRef]

V. A. Kavokin, I. A. Shelykh, and G. Malpuech, “Lossless interface modes at the boundary between two periodic dielectric structures,” Phys. Rev. B 72, 233102 (2005).
[CrossRef]

Slovinskii, I. A.

I. Iorsh, P. V. Panicheva, I. A. Slovinskii, and M. A. Kaliteevski, “Coupled Tamm plasmons,” Tech. Phys. Lett. 38, 351–353 (2012).
[CrossRef]

Smolyaninov, I. I.

A. V. Zayats, I. I. Smolyaninov, and A. A. Maradudin, “Nano-optics of surface plasmon polaritons,” Phys. Rep. 408, 131–314 (2005).
[CrossRef]

Sudzius, M.

R. Brückner, M. Sudzius, S. I. Hintschich, H. Fröb, V. G. Lyssenko, M. A. Kaliteevski, I. Iorsh, R. A. Abram, A. V. Kavokin, and K. Leo, “Parabolic polarization splitting of Tamm states in a metal-organic microcavity,” Appl. Phys. Lett. 100, 062101 (2012).
[CrossRef]

Treshin, I. V.

I. V. Treshin, V. V. Klimov, P. N. Melentiev, and V. I. Balykin, “Optical Tamm state and extraordinary light transmission through a nanoaperture,” Phys. Rev. A 88, 023832 (2013).
[CrossRef]

Tsang, S. H.

S. H. Tsang, S. F. Yu, X. F. Li, H. Y. Yang, and H. K. Liang, “Observation of Tamm plasmon polaritons in visible regime from ZnO/Al2O3distributed Bragg reflector-Ag interface,” Opt. Commun. 284, 1890–1892 (2011).
[CrossRef]

Vasil’ev, A. P.

M. E. Sasin, R. P. Seisyan, M. Kaliteevski, S. Brand, R. A. Abram, J. M. Chamberlain, A. Yu. Egorov, A. P. Vasil’ev, V. S. Mikhrin, and A. V. Kavokin, “Tamm plasmon polaritons: Slow and spatially compact light,” Appl. Phys. Lett. 92, 251112 (2008).
[CrossRef]

Xu, S.

Y. Liu, S. Xu, X. Xuyang, B. Zhao, and W. Xu, “Long-range surface plasmon field-enhanced Raman scattering spectroscopy based on evanescent field excitation,” J. Phys. Chem. Lett. 2, 2218–2222 (2011).
[CrossRef]

Xu, W.

Y. Liu, S. Xu, X. Xuyang, B. Zhao, and W. Xu, “Long-range surface plasmon field-enhanced Raman scattering spectroscopy based on evanescent field excitation,” J. Phys. Chem. Lett. 2, 2218–2222 (2011).
[CrossRef]

Xue, C.-H.

Xuyang, X.

Y. Liu, S. Xu, X. Xuyang, B. Zhao, and W. Xu, “Long-range surface plasmon field-enhanced Raman scattering spectroscopy based on evanescent field excitation,” J. Phys. Chem. Lett. 2, 2218–2222 (2011).
[CrossRef]

Yang, H. Y.

S. H. Tsang, S. F. Yu, X. F. Li, H. Y. Yang, and H. K. Liang, “Observation of Tamm plasmon polaritons in visible regime from ZnO/Al2O3distributed Bragg reflector-Ag interface,” Opt. Commun. 284, 1890–1892 (2011).
[CrossRef]

Yu, S. F.

S. H. Tsang, S. F. Yu, X. F. Li, H. Y. Yang, and H. K. Liang, “Observation of Tamm plasmon polaritons in visible regime from ZnO/Al2O3distributed Bragg reflector-Ag interface,” Opt. Commun. 284, 1890–1892 (2011).
[CrossRef]

Yu. Egorov, A.

M. E. Sasin, R. P. Seisyan, M. Kaliteevski, S. Brand, R. A. Abram, J. M. Chamberlain, A. Yu. Egorov, A. P. Vasil’ev, V. S. Mikhrin, and A. V. Kavokin, “Tamm plasmon polaritons: Slow and spatially compact light,” Appl. Phys. Lett. 92, 251112 (2008).
[CrossRef]

Zayats, A. V.

A. V. Zayats, I. I. Smolyaninov, and A. A. Maradudin, “Nano-optics of surface plasmon polaritons,” Phys. Rep. 408, 131–314 (2005).
[CrossRef]

Zhao, B.

Y. Liu, S. Xu, X. Xuyang, B. Zhao, and W. Xu, “Long-range surface plasmon field-enhanced Raman scattering spectroscopy based on evanescent field excitation,” J. Phys. Chem. Lett. 2, 2218–2222 (2011).
[CrossRef]

Appl. Phys. Lett. (2)

M. E. Sasin, R. P. Seisyan, M. Kaliteevski, S. Brand, R. A. Abram, J. M. Chamberlain, A. Yu. Egorov, A. P. Vasil’ev, V. S. Mikhrin, and A. V. Kavokin, “Tamm plasmon polaritons: Slow and spatially compact light,” Appl. Phys. Lett. 92, 251112 (2008).
[CrossRef]

R. Brückner, M. Sudzius, S. I. Hintschich, H. Fröb, V. G. Lyssenko, M. A. Kaliteevski, I. Iorsh, R. A. Abram, A. V. Kavokin, and K. Leo, “Parabolic polarization splitting of Tamm states in a metal-organic microcavity,” Appl. Phys. Lett. 100, 062101 (2012).
[CrossRef]

J. Phys. Chem. Lett. (1)

Y. Liu, S. Xu, X. Xuyang, B. Zhao, and W. Xu, “Long-range surface plasmon field-enhanced Raman scattering spectroscopy based on evanescent field excitation,” J. Phys. Chem. Lett. 2, 2218–2222 (2011).
[CrossRef]

Nature (1)

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424, 824–830 (2003).
[CrossRef] [PubMed]

Opt. Commun. (1)

S. H. Tsang, S. F. Yu, X. F. Li, H. Y. Yang, and H. K. Liang, “Observation of Tamm plasmon polaritons in visible regime from ZnO/Al2O3distributed Bragg reflector-Ag interface,” Opt. Commun. 284, 1890–1892 (2011).
[CrossRef]

Opt. Express (2)

Opt. Lett. (1)

Phys. Rep. (1)

A. V. Zayats, I. I. Smolyaninov, and A. A. Maradudin, “Nano-optics of surface plasmon polaritons,” Phys. Rep. 408, 131–314 (2005).
[CrossRef]

Phys. Rev. A (1)

I. V. Treshin, V. V. Klimov, P. N. Melentiev, and V. I. Balykin, “Optical Tamm state and extraordinary light transmission through a nanoaperture,” Phys. Rev. A 88, 023832 (2013).
[CrossRef]

Phys. Rev. B (4)

V. A. Kavokin, I. A. Shelykh, and G. Malpuech, “Lossless interface modes at the boundary between two periodic dielectric structures,” Phys. Rev. B 72, 233102 (2005).
[CrossRef]

M. Kaliteevski, I. Iorsh, S. Brand, R. A. Abram, J. M. Chamberlian, A. V. Kavokin, and I. A. Shelykh, “Tamm plasmon-polaritons: Possible electromagnetic states at the interface of a metal and a dielectric Bragg mirror,” Phys. Rev. B 76, 165415 (2007).
[CrossRef]

S. Brand, M. Kaliteevski, and R. A. Abram, “Optical Tamm states above the bulk plasma frequency at a Bragg stack/metal interface,” Phys. Rev. B 79, 085416 (2009).
[CrossRef]

N. Malkova and C. Z. Ning, “Shockley and Tamm surface states in photonic crystals,” Phys. Rev. B 73, 113113 (2006).
[CrossRef]

Science (1)

E. Ozbay, “Plasmonics: Merging photonics and electronics at nanoscale dimensions,” Science 311, 189–193 (2006).
[CrossRef] [PubMed]

Tech. Phys. Lett. (1)

I. Iorsh, P. V. Panicheva, I. A. Slovinskii, and M. A. Kaliteevski, “Coupled Tamm plasmons,” Tech. Phys. Lett. 38, 351–353 (2012).
[CrossRef]

Other (1)

R. W. Boyd, Nonlinear Optics, 2nd ed. (Academic, 2003).

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Figures (5)

Fig. 1
Fig. 1

Profile of the real part of the refractive index along the z direction when N = 20.

Fig. 2
Fig. 2

(a) Reflectance versus incident angle, when N = 20 and h̄ωT = 0.96, 0.97, 0.98, 0.99 eV. The metal layer thickness dm chosen to maximize the field enhancement for each ωT is denoted on the figure. (b) Spatial distributions of the magnetic field intensity corresponding to the four reflectance minima shown in (a). A magnified view of the field distribution near the metal/photonic crystal interface is shown in the inset. The field intensity is normalized with respect to that of the incident wave.

Fig. 3
Fig. 3

(a) Reflectance versus incident angle, when h̄ωT = 0.96 eV and N = 20, 25, 30, 40. The metal layer thickness dm chosen to maximize the field enhancement for each N is denoted on the figure. (b) Spatial distributions of the normalized magnetic field intensity corresponding to the five reflectance minima shown in (a).

Fig. 4
Fig. 4

Maximum value of the normalized magnetic field intensity, which occurs at the interface between the photonic crystal and the metal layer, versus N, when h̄ωT = 0.96 eV. In the inset, the metal layer thickness dm chosen to maximize the field enhancement is plotted versus N.

Fig. 5
Fig. 5

Reflectance versus incident angle when h̄ωT = 0.96 eV, N = 40, dm = 55 nm and βw = 0, 0.00003, 0.00005, 0.0001.

Equations (9)

Equations on this page are rendered with MathJax. Learn more.

ε = 1 ω p 2 ω ( ω + i γ )
d 2 H d z 2 1 ε ( z ) d ε d z d H d z + [ ω 2 c 2 ε ( z ) k x 2 ] H = 0 ,
ε ( z ) = ε L ( z ) + β ( z ) | E ( z ) | 2 ,
H ( z ) = v ε 1 [ e i k z ( L z ) + r ( L ) e i k z ( z L ) ] ,
1 k z d r d l = 2 i ε ˜ ( l ) r i 2 [ ε ˜ ( l ) 1 ] [ 1 tan 2 θ ε ˜ ( l ) ] ( 1 + r ) 2 , 1 k z d w d l = Im { 2 ε ˜ ( l ) [ ε ˜ ( l ) 1 ] [ 1 tan 2 θ ε ˜ ( l ) ] ( 1 + r ) } w ,
ε ( l ) = ε L ( l ) + β ( l ) w ( l ) [ ε 1 2 | ε ( l ) | 2 | 1 + r ( l ) | 2 sin 2 θ + | 1 r ( l ) | 2 cos 2 θ ] .
r ( 0 ) = ε 2 ε 1 cos θ ε 1 ε 2 ε 1 sin 2 θ ε 2 ε 1 cos θ + ε 1 ε 2 ε 1 sin 2 θ , w ( 0 ) = w 0 .
1 k z u l = i ε ˜ ( l ) u i 2 [ ε ˜ ( l ) 1 ] [ 1 tan 2 θ ε ˜ ( l ) ] [ 1 + r ( l ) ] u .
β w = 24 π 2 c 10 7 χ ( 3 ) I 0.079 χ ( 3 ) I ,

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