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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 18, Iss. 19 — Sep. 13, 2010
  • pp: 19495–19503
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Theory of enhanced optical transmission through a metallic nano-slit surrounded with asymmetric grooves under oblique incidence

Lin Cai, Guangyuan Li, Feng Xiao, Zhonghua Wang, and Anshi Xu  »View Author Affiliations


Optics Express, Vol. 18, Issue 19, pp. 19495-19503 (2010)
http://dx.doi.org/10.1364/OE.18.019495


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Abstract

A metallic nano-slit surrounded with asymmetric grooves is proposed as the plasmonic concentrator for oblique incident light. A theoretical model based on the surface plasmon polariton (SPP) coupled-mode method is derived for the extraordinary optical transmission (EOT) through such a structure under oblique incidence. The model is quantitatively validated with the finite element method. With the model, the physical insight of the EOT is then interpreted, i.e., the major contributions to the transmission include the vertical Fabry-Perot resonance of the slit, and the interference among slit modes excited by the incident light, by SPPs generated from groove arrays and their first-order reflections. This is quite different from the EOT through a nano-slit surrounded with symmetric grooves under normal incidence.

© 2010 Optical Society of America

1. Introduction

Since the first experimental report of the extraordinary optical transmission (EOT) phenomenon [1

1. T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff. “Extraordinary optical transmission through subwavelength hole arrays,” Nature 391, 667–669 (1998). [CrossRef]

], surface plasmon polaritons (SPPs) have attracted world-wide attention in fundamental research as well as in optoelectronic applications. A metallic nano-slit surrounded with symmetric periodic corrugations on the illuminated surface, which acts as the plasmonic concentrator, is particularly attractive in applications such as the near-field scanning optical microscopy, the high-density optical storage, and the high-speed photodetector [2–4

2. Z. Yu, G. Veronis, S. Fan, and M. L. Brongersma, “Design of midinfrared photodetectors enhanced by surface plasmons on grating structures,” Appl. Phys. Lett. 89, 151116 (2006). [CrossRef]

]. To maximize the optical transmission through such a structure, there has been a lot of research in the structure optimization and the underlying physics [5–11

5. T. Thio, K. M. Pellerin, R. A. Linke, H. J. Lezec, and T. W. Ebbesen, “Enhanced light transmission through a single subwavelength aperture,” Opt. Lett. 26, 1972–1974 (2001). [CrossRef]

]. It has been widely accepted that the slit-groove distance plays a key role in the transmission, and different distances may lead to enhanced or suppressed transmission. Based on the phenomena, it was believed that the interference between the incident light and the SPPs generated by grooves was responsible for the EOT [8

8. B. Ung and Y. Sheng, “Interference of surface waves in a metallic nanoslit,” Opt. Express 15, 1182–1190 (2007). [CrossRef] [PubMed]

, 9

9. O. T. A. Janssen, H. P. Urbach, and G.W. ’t Hooft, “Giant optical transmission of a subwavelength slit optimized using the magnetic field phase,” Phys. Rev. Lett. 99, 043902 (2007). [CrossRef] [PubMed]

]. However, the interference effect was soon challenged and claimed to be incorrect [10

10. Y. X. Cui and S. L. He, “A theoretical re-examination of giant transmission of light through a metallic nano-slit surrounded with periodic grooves,” Opt. Express 17, 13995–14000 (2009). [CrossRef] [PubMed]

]. The debate continued until quite recently, the authors found that the horizontal Fabry-Perot (F-P) resonance effect of SPPs due to the reflection by surrounding grooves also plays a key role and finally clarified that the EOT originates from the interference between the slit fundamental modes excited by the incident light and by groove-generated SPPs, where SPPs are modulated by the horizontal F-P resonance effect [11

11. L. Cai, G. Li, Z. Wang, and A. Xu, “Interference and horizontal Fabry-Perot resonance on extraordinary transmission through a metallic nano-slit surrounded with grooves,” Opt. Lett. 35, 127–129 (2010). [CrossRef] [PubMed]

].

In all those works, the incident plane wave is limited to normal incidence, and the grooves surrounding the slit are symmetric accordingly. However, in applications such as the photodetector array used in biological or chemical sensing, the light scattered by the sample may obliquely impinge upon detectors. In this case, the plasmonic concentrator in front of the detector should be capable to collect light of oblique incidence. In this work, we propose a nano-slit surrounded with asymmetric grooves to realize such a plasmonic concentrator for obliquely incident light for the first time to our knowledge, as illustrated in Fig. 1. A theoretical model for the EOT through the structure will be derived and quantitatively validated with numerical calculations. With the model, the physical insights will be also interpreted.

Fig. 1. Application of the proposed structure composed of a nano-slit surrounded with asymmetric grooves acting as the plasmonic concentrator in the photodetector for oblique incident light.

2. Theoretical model

As SPPs are shown to be the primary vector in the visible or near infrared regime [12

12. P. Lalanne, J. P. Hugonin, H. T. Liu, and B. Wang, “A microscopic view of the electromagnetic properties of sub-λ metallic surfaces,” Surf. Sci. Rep. 64, 453–469 (2009). [CrossRef]

], we only consider SPP-assisted transmission and neglect the contributions of other electro-magnetic fields such as quasi-cylindrical waves (CWs) mentioned in [12

12. P. Lalanne, J. P. Hugonin, H. T. Liu, and B. Wang, “A microscopic view of the electromagnetic properties of sub-λ metallic surfaces,” Surf. Sci. Rep. 64, 453–469 (2009). [CrossRef]

]. To efficiently excite SPPs under oblique incidence of angle θ, the period of a groove array should be properly chosen to compensate the missing momentum between SPPs and the incident TM-polarized free-space light [13

13. C. Genet and T. W. Ebbesen, “Light in tiny holes,” Nature 445, 39–46 (2007). [CrossRef] [PubMed]

],

k0nsp=k0sinθ+m2πp,
(1)

where nsp is the effective refractive index of the SPP mode at a air-metal interface, and m is an integer. If the periods of grooves on the left and the right sides are set as p 1 = /(Re(nsp)− sin θ) and p 2 = /(Re(nsp) + sin θ) with “Re” referring to the real part, respectively, the generated SPPs by grooves on both sides will propagate toward the central slit under oblique incidence, as shown in Fig. 2(a). As a result, grooves surrounding the nano-slit in the proposed structure are asymmetric. Such structures are widely used in the optical off-axis beaming [14–16

14. D.-Z. Lin, T.-D. Cheng, C.-K. Chang, J.-T. Yeh, J.-M. Liu, C.-S. Yeh, and C.-K. Lee, “Directional light beaming control by a subwavelength asymmetric surface structure,” Opt. Express 15, 2585–2591 (2007). [CrossRef] [PubMed]

]. However, the physical mechanism of off-axis beaming is different from that of the EOT under oblique incidence, which has not been studied yet.

As stated in [9

9. O. T. A. Janssen, H. P. Urbach, and G.W. ’t Hooft, “Giant optical transmission of a subwavelength slit optimized using the magnetic field phase,” Phys. Rev. Lett. 99, 043902 (2007). [CrossRef] [PubMed]

, 11

11. L. Cai, G. Li, Z. Wang, and A. Xu, “Interference and horizontal Fabry-Perot resonance on extraordinary transmission through a metallic nano-slit surrounded with grooves,” Opt. Lett. 35, 127–129 (2010). [CrossRef] [PubMed]

], there may be enhanced or suppressed transmission even when the surrounding grooves are designed to maximize the SPPs’ excitation efficiency. The key lies in the slit-groove distances. To analyze the EOT through the nano-slit surrounded with asymmetric grooves, we propose a theoretical model, in which the groove arrays are treated as “black boxes” that generate and reflect SPPs, as shown in Fig. 2. A 1 (B 2) is the complex amplitude of the superposition of the left-going (right-going) SPP modes starting from the edge of the slit, A 2 (B 1) is that of the left-going (right-going) SPP modes starting from the edge of the right (left) grooves, D (U) is that of the fundamental slit mode propagating downward (upward). Here we use the Hz component instead of Ex or Ey to model the EOT, because the incident, the scattered, and the transmitted fields have strong Hz components [9

9. O. T. A. Janssen, H. P. Urbach, and G.W. ’t Hooft, “Giant optical transmission of a subwavelength slit optimized using the magnetic field phase,” Phys. Rev. Lett. 99, 043902 (2007). [CrossRef] [PubMed]

].

The main elementary scattering processes involved in the proposed model are shown in Figs. 2(b) to 2(g). r s1 and r s2 are the respective reflectance coefficients of the slit fundamental modes at the top and the bottom openings. ρ and τ are the reflectance coefficient and the transmittance coefficient of the SPP mode at the slit, respectively. The SPP mode at the air-metal interface and the slit fundamental mode can be converted to each other with a conversion coefficient α, as shown in Figs. 2(b) and 2(d). The SPP generation coefficients and reflectance coefficients of the left and the right groove arrays are β 1(θ), r g1 and β 2(θ), r g2, respectively. t 0(θ), βs(−θ), and βs(θ) are the respective generation coefficients of the slit fundamental mode, the left-going and the right-going SPP modes by a single silt under the illumination of a plane wave with amplitude I 0 and angle θ. Since the slits considered are very small (usually wsl < λ/2), we only take into account the slit fundamental mode with the effective complex refractive index nsl. Finally, the coupled-mode equations lead to

Fig. 2. (a) Schematic of the proposed model for the metallic nano-slit surrounded with asymmetric periodic grooves. The groove periods, slit-groove distances, and the duty cycles for the left and the right arrays are p 1,d 1, f 1 and p 2,d 2, f 2, respectively. The depths for grooves on both sides are h. The electromagnetic quantities A 1,B 1,A 2,B 2,U,D are all defined in the text. (b)–(g) show the main elementary scattering processes involved in the EOT. (b) and (c) show the scattering coefficients under the fundamental slit mode illumination. (d) is the scattering of incident SPP mode by a nano-slit. (e) and (f) show the generation and reflectance of the SPP mode by a groove array, respectively. (g) shows the generation of the SPP modes and the slit fundamental mode by a nano-slit.
B1=rg1w1A1+β1(θ)I0,
(2a)
A1=τw2A2+βs(θ)I0+αvU+ρw1B1,
(2b)
A2=rg2w2B2+β2(θ)I0,
(2c)
B2=τw1B1+βs(θ)I0+αvU+ρw2A2,
(2d)
D=rs1vU+t0(θ)I0+αw1B1+αw2A2,
(2e)
U=rs2vD,
(2f)

where w 1 = exp(ik 0 nspd 1), w 2 = exp(ik 0 nspd 2), and v = exp(ik 0 nslt). Instead of the slit-groove center-to-center distances, we use the slit-groove edge-to-edge distances d 1 and d 2, which are more convenient for the analysis as they are independent from the widths of the slit and grooves. Note that we set the phase of the incident magnetic field at the center of the slit’s upper opening (x = y = 0) to zero. As a result, β 1(θ) includes a phase difference of the obliquely incident field exp[−ik 0 sin θ(d 1 + wsl/2)], β 2(−θ) includes exp[ik 0 sin θ(d 2 + wsl/2)], and βs(±θ) includes exp(∓ik 0 sin θwsl/2). One should notice that βsθ) can be omitted in practice due to ∣βsθ)∣ ≫ ∣β 1(θ)∣ and ∣βsθ)∣ ≫ ∣β 2(−θ)∣ for any given θ when the groove number N is large enough (for example, N > 5).

Equation (2a) can be interpreted as follows. The right-going SPP modes away from the left grooves are composed of the reflection of left-going ones and those generated by the left grooves. Equation (2b) indicates the left-going SPP modes propagating toward the left grooves are composed of those transmitted from the right grooves, those generated by the slit, those excited by the slit fundamental modes propagating upward, and reflections of right-going SPPs away from the left grooves. Equation (2e) means the slit fundamental modes propagating downward are excited by the reflection of those propagating upward, by the incident light, and by the right-going and the left-going SPPs. Other equations in Eq. (2) can be understood similarly. The definitions of B 1,A 1,B 2,A 2,D,U and the coupling among them indicate that multiple reflections and conversions are automatically incorporated in Eq. (2).

Note that the influences of groove parameters are contained in r g1, r g2 and β 1, β 2. Of course, the grooves can also be further modeled using the coupled-mode equations in terms of the contribution of every groove. However, in this case, the resulted equation system is so complex that there will be no closed-form solutions. A vivid example is on the SPP’s reflectance coefficient rg [18

18. G. Li, L. Cai, F. Xiao, Y. Pei, and A. Xu, “A quantitative theory and the generalized Bragg condition for surface plasmon Bragg reflectors,” Opt. Express 18, 10487–10499 (2010). [CrossRef] [PubMed]

].

From Eq. (2), we further neglect trivial terms of high-order coupling coefficients such as α 2 r g1 r s2 w 2 1 ν and α 2 r g2 r s2 w 2 2 ν, then obtain

D=I01rs1rs2v2{t0(θ)+α[1+(τρ)δ2]w1β1(θ)+α[1+(τρ)δ1]w2β2(θ)(1ρδ1)(1ρδ2)τ2δ1δ2},
(3)

where δ 1 = r g1 w 2 1 and δ 2 = r g2 w 2 2. Specially, for a slit surrounded with symmetric groove arrays under normal incidence, we have r g1 = r g2 = rg, w 1 = w 2 = w, β 1 = β 2 = β, and δ 1 = δ 2 = rgw 2. Equation (3) is then reduced into

D=I01rs1rs2v2[t0+2αwβ1(τ+ρ)rgw2],
(4)

3. Results and discussions

3.1. Model validations

In this section, we first validate the theoretical model by quantitatively comparing ∣D2 predicted by the model with the transmission efficiency η calculated by the finite element method (FEM) [19

19. G. Li and A. Xu, “Phase shift of plasmons excited by slits in a metal film illuminated by oblique incident TM plane wave,” Proc SPIE 7135, 71350T (2008). [CrossRef]

]. The coefficients involved in the model are calculated as follows. The mode conversion coefficients, α and t 0(θ), are obtained analytically [20

20. P. Lalanne, J. P. Hugonin, and J. C. Rodier, “Approximate model for surface-plasmon generation at slit apertures,” J. Opt. Soc. Am. A 23, 1608–1615 (2006). [CrossRef]

]. The reflectance coefficients r s1, r s2, ρ, r g1, r g2 and the transmittance coefficient τ are calculated by the a-FMM [17

17. E. Silberstein, P. Lalanne, J. P. Hugonin, and Q. Cao, “Use of grating theories in integrated optics,” J. Opt. Soc. Am. A 18, 2865–2875 (2001). [CrossRef]

]. The SPP generation coefficients β 1(θ) and β 2(θ) can be calculated by either the method combining the a-FMM with the reciprocity theorem [21

21. H. Liu, P. Lalanne, X. Yang, and J. P. Hugonin, “Surface plasmon generation by subwavelength isolated objects,” IEEE J. Sel. Top. Quantum Electron. 14, 1522–1529 (2008). [CrossRef]

]. The wavelength of λ = 800 nm, the substrate of silica with permittivity εd = 1.46, and gold with relative permittivity εm = −26.2 + 1.85i [22

22. E. D. Palik, Handbook of Optical Constants of Solids (Academic, 1985).

] are used to illustrate our discussions throughout the paper.

Fig. 3. (a) ∣D2 predicted by the proposed model as a function of slit-groove distances d 1 and d 2. The calculations are performed for N = 10, wsl = 100 nm, t = 174 nm, h = 70 nm, and θ = 20°. The period and the duty cycle are p 1 = 1180 nm, f 1 = 0.38 for the grooves on the left side, and p 2 = 588 nm, f 2 = 0.5 for those on the right side. (b) and (c) show the comparisons between ∣D2 predicted by the model and the transmission efficiency η calculated by FEM simulations. The calculations are performed along the vertical green line with d 1 = 160 nm and the horizontal white line with d 2 = 100 nm in (a), respectively. (d) and (e) show the scattered magnetic field ∣Hz2 calculated by the FEM. The slit-groove distances for (d) and (e) correspond to the point “Q” (d 1 = 160 nm, d 2 = 80 nm) and the point “P” (d 1 = 160 nm, d 2 = 360 nm) in (a), respectively.

3.2. Physical interpretations

To have a better understanding of the EOT under oblique incidence, we further simplify Eq. (3) by neglecting ρ, which is usually very small (∣ρ∣ < 0.1) compared with τ (∣τ∣ > 0.85) for small slits (wsl < λ/2) [23

23. O. T. A. Janssen, H. P. Urbach, and G. W.’t Hooft, “On the phase of plasmons excited by slits in a metal film,” Opt. Express 14, 11823–11832 (2006). [CrossRef] [PubMed]

], leading to,

D=I01rs1rs2v2[t0+αw1β1(1+τδ2)+αw2β2(1+τδ1)1τ2δ1δ2].
(5)

Equation (5) is intuitively meaningful. The first term, i.e., I 0/(1 − r s1 r s2 ν 2), represents the vertical F-P resonance effect of the cavity formed by the top and the bottom openings of the slit, as mentioned in Ref. 24

24. A. Krishnan, T. Thio, T. J. Kima, H. J. Lezec, T. W. Ebbesen, P. A. Wolff, J. Pendry, L. Martin-Moreno, and F. J. Garcia-Vidal, “Evanescently coupled resonance in surface plasmon enhanced transmission,” Opt. Commun. 200, 1–7 (2001). [CrossRef]

, and the maximum transmission is achieved when

2k0Re(nsl)t+arg(rs1)+arg(rs2)=2qπ,
(6)

where the function “arg” refers to the argument of a complex number, and q is an integer. Hereafter, we set wsl = 100 nm to illustrate our discussions. Calculated by the a-FMM, the reflectance coefficients are r s1 = −0.2389 − 0.4411i and r s2 = 0.1081 − 0.4125i, and the effective refractive index of the silt fundamental mode is nsl = 1.2346 + 0.0082i. According to Eq. (6), the resonant film thickness should be t = 174 nm (q = 0).

Fig. 4. Interference interpretation of the term αw 1 β 1(1 + τδ 2) in Eq. (5).

Now let us consider the term αw 1 β 1(1 + τδ 2), and rewrite it as αw 1 β 1 + αw 1 β 1 τr g2 w 2 2. This term means the interference between slit fundamental modes, which are generated by the part of SPPs propagating from the left grooves directly coupled into the slit, and the part crossing over the slit, reflected back by the right groove array, and then coupled into the slit from the right side, respectively, as illustrated in Fig. 4. The term αw 2 β 2(1 + τδ 1) can be understood similarly. The corresponding constructive interference conditions for αw 1 β 1(1 + τr g2 w 2 2) and αw 2 β 2(1+ τr g1 w 2 1) are given by

2k0Re(nsp)d2+arg(rg2)+arg(τ)=2m2π,
(7a)
2k0Re(nsp)d1+arg(rg1)+arg(τ)=2m1π,
(7b)

where m 1 and m 2 are integers. Obviously, the periods of these terms as functions of slit-groove distances are λsp/2, where λsp = λ/Re(nsp) is the wavelength of the SPP mode.

D=I01rs1rs2v2[t0+αw1β1(1+τδ2)+αw2β2(1+τδ1)].
(8)

From Eq. (8), it is easy to infer that the major contributions to the EOT through the proposed structure under oblique incidence are the vertical F-P resonance of the slit, the interference among slit modes excited by the incident light, by SPPs generated from groove arrays and their first-order reflections. This is quite different from the EOT through the nano-slit surrounded with symmetric grooves under normal incidence, which is due to the vertical F-P resonance of the slit, the interference between the slit modes excited by the incident light and by the groovegenerated SPPs which are modulated by the horizontal F-P resonance effect [11

11. L. Cai, G. Li, Z. Wang, and A. Xu, “Interference and horizontal Fabry-Perot resonance on extraordinary transmission through a metallic nano-slit surrounded with grooves,” Opt. Lett. 35, 127–129 (2010). [CrossRef] [PubMed]

], as indicated by Eq. (4).

With these interpretations, let us reconsider the different behaviors of d 1 and d 2 in Figs. 3(a) to 3(c), where the peak separations are quite different. For grooves used in Fig. 3, r g1 = −0.3036 + 0.0377i, and r g2 = −0.0362 − 0.1077i. Then r g2 τw 2 2 can be further neglected because of small r g2, indicating that the first-order reflection of SPPs propagating from grooves on the left side makes little contribution. As a result, we rewrite Eq. (8) as

D=I01rs1rs2v2[t0+αw1β1+αw2β2(1+τδ1)].
(9)

From Eq. (9), it is not difficult to understand the differences between Figs. 3(b) and 3(c): given d 1 (or w 1), the separation between peaks of ∣D2 as a function of d 2 is approximate to λsp; however, given d 2 (or w 2), this peak separation, as a function of d 1, is approximate to λsp/2 because of the term 1 + τδ 1.

From the above discussions, the slit-grating distances di(i = 1,2) paly key roles in the interference between SPPs generated from groove arrays on the left and the right sides, and their first-order reflections. As a result, one can use different di to compensate the different phases of the SPPs launched from the left and the right to maximize the transmission.

4. Concluding remarks

The field-of-view (FOV) of the plasmonic concentrator is very important in applications such as photodetectors and the optical storage. The structure with symmetric surrounding grooves, which is designed for the normal incident light, is very sensitive to the incidence angle θ, as illustrated in Fig. 5. Its transmission efficiency reaches the maximum at the designed angle, i.e. θ = 0°, but decreases rapidly when θ deviates from 0°, resulting a narrow FOV. The angular performance is similar for the proposed structure with asymmetric surrounding grooves, which is designed for the oblique incident light. It is clear that the angular pattern of the transmission efficiency for different structures are almost the same, except that transmission peaks are shifted to the designed angles.

Fig. 5. Angular transmission efficiencies for the plasmonic concentrators designed for θ = 0° (black), θ = 10° (red), θ = 20° (green) and θ = 30° (blue). The calculations are performed for p 1=p 2=785nm, f 1=f 2=0.52, d 1=d 2=240nm; p 1=946nm, p 2=670nm, f 1=0.46, f 2=0.5, d 1=200nm, d 2=130nm; p 1=1180nm, p 2=588nm, f 1=0.38, f 2=0.5, d 1=160nm, d 2=80nm; and p 1=1540nm, p 2=526nm, f 1=0.5, f 2=0.56, d 1=400nm, d 2=120nm, respectively. Other parameters are the same as those used in Fig. 3. The parameters p 1 and p 2 are chosen according to Eq. (1), d 1 and d 2 are predicted by the proposed model.

As shown in Fig. 5, the peak values of transmission efficiency for plasmonic concentrators designed for different angles are very close to one another. If an array of such structures, each of which is designed for a specific angle of incidence, are integrated in a chip, a wide FOV with almost flat transmission efficiency would be realized.

In conclusion, we have proposed a plasmonic concentrator composed of a nano-slit surrounded with asymmetric grooves under oblique incidence. A SPP coupled-mode model was derived to describe the EOT through such a structure. Comparisons of the model predictions with FEM computational data quantitatively showed that the general trend of the transmission efficiency is well captured by the model. The physical insight of the EOT was interpreted, i.e. the major contributions to the transmission enhancement are the vertical F-P resonance of the slit, the interference among slit modes excited by the incident light, by SPPs generated from groove arrays and their first-order reflections. With the proposed plasmonic concentrator for obliquely incident light, we believe the wide FOV optical receiver will be realized with a photodetector array integrated with an array of plasmonic concentrators, each of which is responsible for a specific angle of incidence.

Acknowledgements

This work was supported by the National Natural Science Foundation of China under grant 60772002, and by State Key Laboratory of Advanced Optical Communication Systems and Networks, China.

References and links

1.

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff. “Extraordinary optical transmission through subwavelength hole arrays,” Nature 391, 667–669 (1998). [CrossRef]

2.

Z. Yu, G. Veronis, S. Fan, and M. L. Brongersma, “Design of midinfrared photodetectors enhanced by surface plasmons on grating structures,” Appl. Phys. Lett. 89, 151116 (2006). [CrossRef]

3.

R. D. Bhat, N. C. Panoiu, S. R. Brueck, and R. M. Osgood, “Enhancing the signal-to-noise ratio of an infrared photodetector with a circular metal grating,” Opt. Express 16, 4588–4596 (2008). [CrossRef] [PubMed]

4.

L. A. Dunbar, M. Guillaumée, F. de León-Pérez, C. Santschi, E. Grenet, R. Eckert, F. López-Tejeira, F. J. García-Vidal, L. Martín-Moreno, and R. P. Stanley, “Enhanced transmission from a single subwavelength slit aperture surrounded by grooves on a standard detector,” Appl. Phys. Lett. 95, 011113 (2009). [CrossRef]

5.

T. Thio, K. M. Pellerin, R. A. Linke, H. J. Lezec, and T. W. Ebbesen, “Enhanced light transmission through a single subwavelength aperture,” Opt. Lett. 26, 1972–1974 (2001). [CrossRef]

6.

F. J. Garcia-Vidal, H. J. Lezec, T. W. Ebbesen, and L. Martin-Moreno, “Multiple paths to enhance optical transmission through a single subwavelength slit,” Phys. Rev. Lett. 90, 213901 (2003). [CrossRef] [PubMed]

7.

A. Degiron and T.W. Ebbesen, “Analysis of the transmission process through single apertures surrounded by periodic corrugations,” Opt. Express 12, 3694–3700 (2004). [CrossRef] [PubMed]

8.

B. Ung and Y. Sheng, “Interference of surface waves in a metallic nanoslit,” Opt. Express 15, 1182–1190 (2007). [CrossRef] [PubMed]

9.

O. T. A. Janssen, H. P. Urbach, and G.W. ’t Hooft, “Giant optical transmission of a subwavelength slit optimized using the magnetic field phase,” Phys. Rev. Lett. 99, 043902 (2007). [CrossRef] [PubMed]

10.

Y. X. Cui and S. L. He, “A theoretical re-examination of giant transmission of light through a metallic nano-slit surrounded with periodic grooves,” Opt. Express 17, 13995–14000 (2009). [CrossRef] [PubMed]

11.

L. Cai, G. Li, Z. Wang, and A. Xu, “Interference and horizontal Fabry-Perot resonance on extraordinary transmission through a metallic nano-slit surrounded with grooves,” Opt. Lett. 35, 127–129 (2010). [CrossRef] [PubMed]

12.

P. Lalanne, J. P. Hugonin, H. T. Liu, and B. Wang, “A microscopic view of the electromagnetic properties of sub-λ metallic surfaces,” Surf. Sci. Rep. 64, 453–469 (2009). [CrossRef]

13.

C. Genet and T. W. Ebbesen, “Light in tiny holes,” Nature 445, 39–46 (2007). [CrossRef] [PubMed]

14.

D.-Z. Lin, T.-D. Cheng, C.-K. Chang, J.-T. Yeh, J.-M. Liu, C.-S. Yeh, and C.-K. Lee, “Directional light beaming control by a subwavelength asymmetric surface structure,” Opt. Express 15, 2585–2591 (2007). [CrossRef] [PubMed]

15.

S. Kim, H. Kim, Y. Lim, and B. Lee, “Off-axis directional beaming of optical field diffracted by a single subwavelength metal slit with asymmetric dielectric surface gratings,” Appl. Phys. Lett. 90, 051113 (2007). [CrossRef]

16.

Y. Lim, J. Hahn, S. Kim, J. Park, H. Kim, and B. Lee, “Plasmonic light beaming manipulation and its detection using holographic microscopy,” IEEE J. Quantum Electron. 46, 300–305 (2010). [CrossRef]

17.

E. Silberstein, P. Lalanne, J. P. Hugonin, and Q. Cao, “Use of grating theories in integrated optics,” J. Opt. Soc. Am. A 18, 2865–2875 (2001). [CrossRef]

18.

G. Li, L. Cai, F. Xiao, Y. Pei, and A. Xu, “A quantitative theory and the generalized Bragg condition for surface plasmon Bragg reflectors,” Opt. Express 18, 10487–10499 (2010). [CrossRef] [PubMed]

19.

G. Li and A. Xu, “Phase shift of plasmons excited by slits in a metal film illuminated by oblique incident TM plane wave,” Proc SPIE 7135, 71350T (2008). [CrossRef]

20.

P. Lalanne, J. P. Hugonin, and J. C. Rodier, “Approximate model for surface-plasmon generation at slit apertures,” J. Opt. Soc. Am. A 23, 1608–1615 (2006). [CrossRef]

21.

H. Liu, P. Lalanne, X. Yang, and J. P. Hugonin, “Surface plasmon generation by subwavelength isolated objects,” IEEE J. Sel. Top. Quantum Electron. 14, 1522–1529 (2008). [CrossRef]

22.

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

23.

O. T. A. Janssen, H. P. Urbach, and G. W.’t Hooft, “On the phase of plasmons excited by slits in a metal film,” Opt. Express 14, 11823–11832 (2006). [CrossRef] [PubMed]

24.

A. Krishnan, T. Thio, T. J. Kima, H. J. Lezec, T. W. Ebbesen, P. A. Wolff, J. Pendry, L. Martin-Moreno, and F. J. Garcia-Vidal, “Evanescently coupled resonance in surface plasmon enhanced transmission,” Opt. Commun. 200, 1–7 (2001). [CrossRef]

25.

F. López-Tejeira, F. J. García-Vidal, and L. Martín-Moreno, “Scattering of surface plasmons by one-dimensional periodic nanoindented surfaces,” Phys. Rev. B 72, 161405 (2005). [CrossRef]

OCIS Codes
(050.1220) Diffraction and gratings : Apertures
(250.5403) Optoelectronics : Plasmonics

ToC Category:
Diffraction and Gratings

History
Original Manuscript: June 29, 2010
Revised Manuscript: August 19, 2010
Manuscript Accepted: August 19, 2010
Published: August 30, 2010

Citation
Lin Cai, Guangyuan Li, Feng Xiao, Zhonghua Wang, and Anshi Xu, "Theory of enhanced optical transmission through a metallic nano-slit surrounded with asymmetric grooves under oblique incidence," Opt. Express 18, 19495-19503 (2010)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-19-19495


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References

  1. T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff. “Extraordinary optical transmission through subwavelength hole arrays,” Nature 391,667–669 (1998). [CrossRef]
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  4. L. A. Dunbar, M. Guillaumée, F. de León-Pérez, C. Santschi, E. Grenet, R. Eckert, F. López-Tejeira, F. J. García-Vidal, L. Martín-Moreno, and R. P. Stanley, “Enhanced transmission from a single subwavelength slit aperture surrounded by grooves on a standard detector,” Appl. Phys. Lett. 95,011113 (2009). [CrossRef]
  5. T. Thio, K. M. Pellerin, R. A. Linke, H. J. Lezec, and T. W. Ebbesen, “Enhanced light transmission through a single subwavelength aperture,” Opt. Lett. 26,1972–1974 (2001). [CrossRef]
  6. F. J. Garcia-Vidal, H. J. Lezec, T. W. Ebbesen, and L. Martin-Moreno, “Multiple paths to enhance optical transmission through a single subwavelength slit,” Phys. Rev. Lett. 90,213901 (2003). [CrossRef] [PubMed]
  7. A. Degiron and T.W. Ebbesen, “Analysis of the transmission process through single apertures surrounded by periodic corrugations,” Opt. Express 12,3694–3700 (2004). [CrossRef] [PubMed]
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  9. O. T. A. Janssen, H. P. Urbach, and G.W. ’t Hooft, “Giant optical transmission of a subwavelength slit optimized using the magnetic field phase,” Phys. Rev. Lett. 99,043902 (2007). [CrossRef] [PubMed]
  10. Y. X. Cui and S. L. He, “A theoretical re-examination of giant transmission of light through a metallic nano-slit surrounded with periodic grooves,” Opt. Express 17,13995–14000 (2009). [CrossRef] [PubMed]
  11. L. Cai, G. Li, Z. Wang, and A. Xu, “Interference and horizontal Fabry-Perot resonance on extraordinary transmission through a metallic nano-slit surrounded with grooves,” Opt. Lett. 35,127–129 (2010). [CrossRef] [PubMed]
  12. P. Lalanne, J. P. Hugonin, H. T. Liu, and B. Wang, “A microscopic view of the electromagnetic properties of sub-⌊ metallic surfaces,” Surf. Sci. Rep. 64,453–469 (2009). [CrossRef]
  13. C. Genet and T. W. Ebbesen, “Light in tiny holes,” Nature 445,39–46 (2007). [CrossRef] [PubMed]
  14. D.-Z. Lin, T.-D. Cheng, C.-K. Chang, J.-T. Yeh, J.-M. Liu, C.-S. Yeh, and C.-K. Lee, “Directional light beaming control by a subwavelength asymmetric surface structure,” Opt. Express 15,2585–2591 (2007). [CrossRef] [PubMed]
  15. S. Kim, H. Kim, Y. Lim, and B. Lee, “Off-axis directional beaming of optical field diffracted by a single subwavelength metal slit with asymmetric dielectric surface gratings,” Appl. Phys. Lett. 90,051113 (2007). [CrossRef]
  16. Y. Lim, J. Hahn, S. Kim, J. Park, H. Kim, and B. Lee, “Plasmonic light beaming manipulation and its detection using holographic microscopy,” IEEE J. Quantum Electron. 46,300–305 (2010). [CrossRef]
  17. E. Silberstein, P. Lalanne, J. P. Hugonin, and Q. Cao, “Use of grating theories in integrated optics,” J. Opt. Soc. Am. A 18,2865–2875 (2001). [CrossRef]
  18. G. Li, L. Cai, F. Xiao, Y. Pei, and A. Xu, “A quantitative theory and the generalized Bragg condition for surface plasmon Bragg reflectors,” Opt. Express 18,10487–10499 (2010). [CrossRef] [PubMed]
  19. G. Li and A. Xu, “Phase shift of plasmons excited by slits in a metal film illuminated by oblique incident TM plane wave,” Proc SPIE 7135,71350T (2008). [CrossRef]
  20. P. Lalanne, J. P. Hugonin, and J. C. Rodier, “Approximate model for surface-plasmon generation at slit apertures,” J. Opt. Soc. Am. A 23,1608–1615 (2006). [CrossRef]
  21. H. Liu, P. Lalanne, X. Yang, and J. P. Hugonin, “Surface plasmon generation by subwavelength isolated objects,” IEEE J. Sel. Top. Quantum Electron. 14,1522–1529 (2008). [CrossRef]
  22. E. D. Palik, Handbook of Optical Constants of Solids (Academic, 1985).
  23. O. T. A. Janssen, H. P. Urbach, and G. W. ’t Hooft, “On the phase of plasmons excited by slits in a metal film,” Opt. Express 14,11823–11832 (2006). [CrossRef] [PubMed]
  24. A. Krishnan, T. Thio, T. J. Kima, H. J. Lezec, T. W. Ebbesen, P. A. Wolff, J. Pendry, L. Martin-Moreno, and F. J. Garcia-Vidal, “Evanescently coupled resonance in surface plasmon enhanced transmission,” Opt. Commun. 200,1–7 (2001). [CrossRef]
  25. F. López-Tejeira, F. J. García-Vidal, and L. Martín-Moreno, “Scattering of surface plasmons by one-dimensional periodic nanoindented surfaces,” Phys. Rev. B 72,161405 (2005). [CrossRef]

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