## Diffractive slit patterns for focusing surface plasmon polaritons

Optics Express, Vol. 16, Issue 12, pp. 8969-8980 (2008)

http://dx.doi.org/10.1364/OE.16.008969

Acrobat PDF (978 KB)

### Abstract

We propose a design method of diffractive slit patterns for focusing surface plasmon polaritons. A scalar model of surface plasmon polariton excitation and interference is adopted, based on which the design method of diffractive slit patterns is built up. The validity of the proposed scalar model-based design is discussed through the comparison of the simulation results of the scalar model and the rigorous three-dimensional vectorial electromagnetic model using the rigorous coupled wave analysis.

© 2008 Optical Society of America

## 1. Introduction

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

4. L. Yin, V. K. Vlasko-Vlasov, J. Pearson, J. M. Miller, J. Hua, U. Welp, D. E. Brown, and C. W. Kimball, “Subwavelength focusing and guiding of surface plasmons,” Nano Lett. **5**, 1399–1402 (2005). [CrossRef] [PubMed]

4. L. Yin, V. K. Vlasko-Vlasov, J. Pearson, J. M. Miller, J. Hua, U. Welp, D. E. Brown, and C. W. Kimball, “Subwavelength focusing and guiding of surface plasmons,” Nano Lett. **5**, 1399–1402 (2005). [CrossRef] [PubMed]

9. H. Kim, J. Hahn, and B. Lee,“Focusing properties of surface plasmon polariton floatig dielectric lenses,” Opt. Express 16, 3049–3057 (2008). [CrossRef] [PubMed]

10. L. Feng, K. A. Tetz, B. Slutsky, V. Lomakin, and Y. Fainman, “Fourier plasmonics: Diffractive focusing of in-plane surface plasmon polariton waves,” Appl. Phys. Lett. **91**, 081101 (2007). [CrossRef]

9. H. Kim, J. Hahn, and B. Lee,“Focusing properties of surface plasmon polariton floatig dielectric lenses,” Opt. Express 16, 3049–3057 (2008). [CrossRef] [PubMed]

11. H. Kim, J. Hahn, and B. Lee, “Mathematical modeling of triangle-mesh-modeled three-dimensional surface objects for digital holography,” Appl. Opt. **47**, D117–D127 (2008). [CrossRef] [PubMed]

12. R. Zia and M. L. Brongersma, “Surface plasmon polariton analogue to Young’s double-slit experiment,” Nat. Nanotechnol. **2**, 426–429 (2007). [CrossRef]

13. H. Kim, I.-M. Lee, and B. Lee, “Extended scattering-matrix method for efficient full parallel implementation of rigorous coupled-wave analysis,” J. Opt. Soc. Am. A **24**, 2313–2327 (2007). [CrossRef]

14. H. Kim and B. Lee, “Mathematical modeling of crossed nanophotonic structures with generalized scattering-matrix method and local Fourier modal analysis,” J. Opt. Soc. Am. B **25**, 518–544 (2008). [CrossRef]

## 2. Diffractive slit patterns and scalar model of surface plasmon polariton interference

*x*,

_{m}*y*) is the spot center of a point sources.

_{m}*k*is the wavenumber of SPP given by

_{SPP}*λ*is free space wavelength,

*ε*is the permittivity of air,

_{a}*ε*is the permittivity of metal (Au) substrate, and

_{m}*λ*is the SPP wavelength on air/metal interface.

_{SPP}*k*and

^{r}_{SPP}*k*are the real and imaginary parts of

^{i}_{SPP}*k*. In general, SPP propagates with inherent damping due to the ohmic loss of metallic media, which is indicated by the term,

_{SPP}*k*in Eq. (1a). In this paper, we assume that

^{i}_{SPP}*λ*,

*ε*, and

_{a}*ε*are 650nm, 1, and -9.8492+

_{m}*j*1.0572, respectively. Then the SPP wavelength,

*λ*, is given by 616.5nm-j3.7nm. Let us define the complementary field

_{SPP}*G*(

*x*,

*y*) of

*F*(

*x*,

*y*) as

*a*(

*x*,

*y*) and

*ϕ*(

*x*,

*y*) are the amplitude and phase functions of the composite optical field

*G*(

*x*,

*y*).

*G*(

*x*,

*y*) is composed of the circular wave components with the counterdirectional wavenumber, -

*k*, that are exponentially increasing from the spot centers (

_{SPP}*x*,

_{m}*y*).

_{m}*R*

_{1}and

*R*

_{2}. Then let the intersections of the constant phase contours of the phase function,

*ϕ*(

*x*,

*y*) (for phase values of 0 and -

*π*) and the concentric band be denoted by Ω

^{+}and Ω

^{-}, respectively. Ω

^{+}and Ω

^{-}are mathematically expressed by the set forms given, respectively, by

^{+}and Ω

^{-}, of which subsets become a part of diffractive slit patterns for multiple SPP focal spots. In addition, let the amplitude profiles of Ω

^{+}and Ω

^{-}be defined by A

^{+}and A

^{-}as

*x*,

_{c}*y*), at (0,0) and (1.5µm, 1.5µm), are presented in Fig. 1(a) and 1(b), respectively. In this paper,

_{c}*R*

_{1}and

*R*

_{2}of the concentric band are chosen as 3.89µm and

*R*

_{1}-

*λ*, respectively,

^{r}_{SPP}*λ*is the real part of

^{r}_{SPP}*λ*. The rectangle region of 9µm×9µm size is concerned. In Fig. 1(c), the phase distribution of a composite field of two point sources with the centers at (1.5µm, 1.5µm) and (-1.5µm, -1.5µm) is shown. The amplitude profiles of Figs. 1(a), 1(b), and 1(c) are shown in Figs. 1(d), 1(e), and 1(f), respectively. The concentric band is indicated by white dashed lines in Figs. 1(a), 1(b) and 1(c) and by black dashed lines in Figs. 1(d), 1(e), and 1(f).

_{SPP}^{+}and Ω

^{-}, Ω

^{+}and Ω

^{-}of a single 2-D point source with its center at (0,0) are represented by the red circles in Figs. 2(a) and 2(c), respectively. In both figures, the concentric band is indicated by white dashed lines. If a subwavelength curved slit pattern is formed following the path of Ω

^{+}or Ω

^{-}in a thin metal film placed on the

*x*-

*y*plane (

*z*=0) and an

*x*-directional polarization plane wave is normally incident on the backside of the metal film, SPPs excited on the front surface of the metal film by the curved slit propagate and produce complex interference patterns on the metal surface. In the cases shown in Fig. 2, it is expected for SPP to form a focused spot on the origin, (0,0) because of the circular symmetry of the circular slit pattern. However, in understanding the SPP focusing, we should necessarily consider the polarity of SPP excitation. Because the incident optical field is

*x*-directional linear polarized, the SPP excited on the slit in the region of

*x*≤0 and that in the region of

*x*>0 have different polarity, that is,

*π*-phase difference. In Figs. 2(b) and 2(d), the plus and minus signs are used to visually indicate the polarity of SPP in the inner region in

*x*≤0 and in the inner region in

*x*>0, respectively. In the case of Ω

^{+}, the plus-signed half circle and minus-signed half circle are denoted by a black and white half circles, respectively in Fig. 2(b), while in the case of Ω

^{-}the plus signed half circle and minus-signed half circle are denoted by a white and black half circle, respectively, in Fig. 2(d).

12. R. Zia and M. L. Brongersma, “Surface plasmon polariton analogue to Young’s double-slit experiment,” Nat. Nanotechnol. **2**, 426–429 (2007). [CrossRef]

*U*(

*x*,

*y*), is represented by

*C*,

**p**and

**n**are the polarization vector of the illuminating plane wave and the outer normal vector of the slit curve

*C*, and

*ds*is the differential length along the slit curve

*C*.

*π*-phase difference in SPPs excited on the upper part and lower part of the circle slit, the destructive interference occurs at the origin. Thus, we can see the dual point SPP focus pattern. However, if we make a slit by combining two half circles with different polarities, for example, the white half circle of Ω

^{+}circle and the black half circle of Ω

^{-}, we can make a slit pattern with the

*π*-phase difference compensated. The resulting slit pattern and its SPP interference pattern are shown in Fig. 3(c) and 3(d), respectively. As shown in Fig. 3(d), at the origin, the constructive interference occurs. The maximum SPP field intensity around the focal point of the phase compensated slit is about 1.5 times higher than that of the circle slit without the compensation of the

*π*-phase difference.

*x*,

_{m}*y*). First, the intersection sets of the constant phase contours and the concentric band, Ω

_{m}^{+}and Ω

^{-}, should be extracted, for which numerical calculations are necessary. This is the phase contour extraction stage. Second, the parity of SPP excitation is analyzed with the inspection of the sign of the inner product of the outward normal vector of the slit curve,

**n**, and the polarization vector,

**p**. The outward normal vector of the slit curve,

**n**, is obtained by the gradient vector of the phase function

*ϕ*(

*x*,

*y*)

*ϕ*(

*x*,

*y*) is given by

*ϕ*(

*x*,

*y*)/∂

*x*and ∂

*ϕ*(

*x*,

*y*)/∂

*y*are obtained, respectively, as

**n**is given by the normalized gradient vector

**n**=∇Ω

^{±}/|∇Ω

^{±}|. Let the x-directional linear polarization vector of the incident optical field be denoted by

**p**=(1, 0). The sign of the inner product of

**p**and the gradient vector ∇Ω

^{±}may be plus or minus. According to the sign of this inner product, the Ω

^{+}is divided into Ω

^{+}

_{p}and Ω

^{+}

_{n}and Ω

^{-}is divided into Ω

^{-}

_{p}and Ω

^{-}

_{n}. The subsets, Ω

^{+}

_{p}, Ω

^{+}

_{n}, Ω

^{-}

_{p}, and Ω

^{-}

_{n}, are defined, respectively, as

*π*-phase difference compensated is obtained as the unions of the subsets, Ω

^{+}

_{p}◡Ω

^{-}

_{n}or Ω

^{-}

_{p}◡Ω

^{+}

_{n}. The slit pattern shown in Fig. 3(c) is Ω

^{+}

_{p}◡Ω

^{-}

_{n}. We can also define the amplitude profiles of Ω

^{+}

_{p}, Ω

^{+}

_{n}, Ω

^{-}

_{p}, and Ω

^{-}

_{n}by A

^{+}

_{p}, A

^{+}

_{n}, A

^{-}

_{p}, and A

^{-}

_{n}, respectively, by the same manner of the definition of Eqs. (3c) and (3d).

^{+}and Ω

^{-}, of this case are presented by the red lines in Figs. 4(a) and 4(d), respectively. The polarities of the SPP excitation are distinguished by white and black curves in Figs. 4(b) and 4(e) according to the above stated method. In Fig. 4(c) and 4(d), the amplitude profiles of Ω

^{+}and Ω

^{-}defined in Eqs. (3c) and (3d) are shown, respectively.

*k*≠0) and its consideration in the proposed slit design method. In the framework addressed above, the complementary field

^{i}_{SPP}*G*(

*x*,

*y*) with both counterdirectional wavenumber and exponential amplification property is used to extract the diffractive slit pattern. If SPP is excited on the extracted slit

*C*with the definite amplitude profile proportional to the amplified amplitude profile

*a*(

*x*,

*y*), the amplitude profile

*a*(

*x*,

*y*) would effectively compensate the damping loss of SPP propagating along the metal/dielectric interface and as a result, we may obtain desired SPP focusing profiles. In this case, the SPP interference pattern,

*U*(

*x*,

*y*), is represented by

**p**·

**n**, of the polarization,

**p**, and the outer normal vector,

**n**, at a local point on the slit as shown in Eq. (5), the SPP interference pattern should take the form

**p**is not a constant vector but a spatial vector function. Since the proposed slit pattern design method is based on the simple scalar model, the polarization of the incident beam is not taken into account in the design stage. In the analysis of the constructed SPP field distribution, the polarization effect is considered as shown in Eq. (8b), where the polarization vector

**p**is a general spatial polarization vector function.

*a*(

*x*,

*y*). However, in practice, it would be very difficult to realize the SPP amplitude modulation profiled by

*a*(

*x*,

*y*). This problem requires further research. In diffractive optics, it is well known that the diffractive or interferometric optical field synthesis is more strongly influenced by phase distribution than by amplitude distribution. In diffractive field synthesis problems [11

11. H. Kim, J. Hahn, and B. Lee, “Mathematical modeling of triangle-mesh-modeled three-dimensional surface objects for digital holography,” Appl. Opt. **47**, D117–D127 (2008). [CrossRef] [PubMed]

11. H. Kim, J. Hahn, and B. Lee, “Mathematical modeling of triangle-mesh-modeled three-dimensional surface objects for digital holography,” Appl. Opt. **47**, D117–D127 (2008). [CrossRef] [PubMed]

*R*

_{1}and

*R*

_{2}, of a concentric band (on the metal surface) increase and the focal spot pattern becomes complex, the amount of unevenness of the amplitude profile

*a*(

*x*,

*y*) becomes larger and, as a result, the influence of the amplitude profile will be significant. The phase only optical slit pattern design with the constant amplitude profile requires specifically devised nonlinear optimization algorithm, which is an advanced problem that is posed from this paper. The simple and efficient scalar model such as Eq. (5) is inevitable for building up the optimal design method of phase only diffractive slit pattern.

*π*-phase difference compensation are shown, respectively. The resulting SPP interference patterns from respective slit patterns with the uniform SPP excitation on the slit curve are presented in Figs. 5(b) and 5(d), respectively. In the case of the circle slit shown in Fig. 5(a), the resulting SPP interference pattern is dual point SPP focus pattern as seen in Fig. 5(b). Because of the

*π*-phase difference between SPPs excited on the Ω

^{+}

_{p}and Ω

^{+}

_{n}parts of the slit, the destructive interference occurs at the focal point. However, if we make a slit by combining the half circles with different polarities, for example, the white lined part of Ω

^{+}and the white lined part of Ω

^{-}, that is, using Ω

^{+}

_{p}◡Ω

^{-}

_{n}, we can make the slit pattern with the

*π*-phase difference compensated. The resulting slit pattern and its resulting SPP interference pattern are shown in Figs. 5(c) and 5(d), respectively. As shown in Fig. 5(d), at the focal point, the constructive interference occurs.

*π*-phase difference compensation are shown in Figs. 6(a) and 6(c), respectively. The resulting SPP interference patterns from respective slit patterns are presented in Figs. 6(b) and 6(d), respectively. In the case of the circle slit shown in Fig. 6(a), the resulting SPP interference pattern is dual point SPP focus pattern as seen in Fig. 6(b). The

*π*-phase difference between SPPs excited on the Ω

^{+}

_{p}and Ω

^{+}

_{n}parts of the slit lead to the destructive interference at the focal points. However, the slit pattern with the

*π*-phase difference compensated is extracted from the form Ω

^{+}

_{p}◡Ω

^{-}

_{n}. The resulting slit pattern and its resulting SPP interference pattern are shown in Figs. 6(c) and 6(d), respectively. As shown in Fig. 6(d), at the focal points, the constructive interference occurs.

## 3. Numerical results of rigorous coupled wave analysis

*x*-directional linear polarization backside incidence, the slit width is kept constant along the

*x*-direction without any width variation for specifically modulating the SPP amplitude profile on the slit curves.

*x*-directional and

*y*-directional Fourier spatial harmonics is set to 61×61 which is the maximum number of harmonics manageable in our personal computer (64bit CPU and 8Gb memory), fortunately, which is the truncation order showing weak convergence, and both the

*x*-directional and

*y*-directional supercell periods,

*T*and

_{x}*T*, are chosen as a same value of 9µm. Under this setting, the field representation resolution in the 9µm×9µm region with 61×61 Fourier spatial harmonics is 150nm×150nm. In the RCWA simulation, the silt width of the tested slit patterns is set to 250nm and the real part of the SPP wavelength,

_{y}*λ*, is 616.5nm. The RCWA resolution of 150nm is sufficient to represent the SPP eigenmode on the metal dielectric interface, that is,

^{r}_{SPP}*z*-directional evanescent 2-D plane waves. Thus the setting is reasonable in representing the slit pattern structures and the generated SPP field distribution inside the concentric band.

*z*-directional polarization electric field distribution on the surface inside the concentric band can be represented by the scalar expression as

*b*(

*x*,

*y*) is the exact SPP excitation complex coefficient with amplitude and phase values, which can be only obtained by the rigorous vectorial electromagnetic method as the 3-D RCWA. Also, in

*b*(

*x*,

*y*), the multiple reflections between slit patterns, diffraction, and scattering are taken into considered. It is noted that we cannot analyze the complex amplitude

*b*(

*x*,

*y*) using only the scalar analysis. As shown in Eq. (8b), we can only assume the SPP excitation model of Eq. (5) with the aid of physical intuition, where

*b*(

*x*,

*y*) is simply assumed as

**p**·

**n**. Therefore, in the analysis of diffractive slit patterns, the most distinction point of using the 3D RCWA from using the scalar model should be placed on the fact that the 3D RCWA can provide the exact consideration of

*b*(

*x*,

*y*). The RCWA result shows that the SPP field inside the concentric band is a scalar field with

*b*(

*x*,

*y*) considered fully. It should be understood that the possible difference between the results provided by the scalar model and the rigorous model with respect to the meaning of

*b*(

*x*,

*y*). In fact, the field distributions presented here cannot said to be fully convergent. In general, the convergence of 3D RCWA is practically a hard thing to be attained by conventional personal computers, using which the number of Fourier harmonics retained in computation is seriously limited. However, definitely, as the truncation order increases, the obtained result will be converged at a certain level. However, we can expect that the general focusing feature shown in this paper would not change seriously.

*π*-phase difference compensated that generate the single SPP focus at the origin and off-origin are examined with the RCWA. Figures 7(a) and 8(a) show the slit patterns extracted from the prototype slit patterns shown in Figs. 3(a) and 3(c), respectively. In practice, we should find the optimal slit width for efficient SPP excitation. The optimal slit width can be found by repeating parametric simulation with variation in the slit width. After parametric study with the RCWA, we adopted the optimal slit width of 250nm. The inner rim of the slit pattern is equal to the prototype slit curve, but the outer rim is obtained by translating the inner rim by the slit width, 250nm. The translation direction is outward from the origin.

*x*-polarization,

*y*-polarization, and

*z*-polarization electric field intensity distributions on the front surface of the metal film with the slit without the

*π*-phase difference compensation, respectively, that is analyzed by the 3-D RCWA. In this case, as expected in the scalar model, dual point focus pattern in the

*z*-polarization electric field distribution is observed. In Figs. 8(b), 8(c), and 8(d), the

*x*-polarization,

*y*-polarization, and

*z*-polarization electric field intensity distributions obtained from the slit with the

*π*-phase difference compensation are presented, respectively. In this case, because the

*π*-phase difference is compensated in the slit pattern, a single focus pattern appear where the constructive interference occurs at the origin as expected.

*x*-polarization,

*y*-polarization, and

*z*-polarization electric field intensity distributions obtained by the RCWA, are shown, respectively. A single SPP focal spot is formed at the specific position, which is the same position expected by the scalar model. Figure 10 shows the RCWA results of the slit pattern generating two SPP focal spots, of which prototype pattern is shown in Fig. 6(c). In Fig. 10(a), the slit pattern is shown and the

*x*-polarization,

*y*-polarization, and

*z*-polarization electric field intensity distributions are shown in Figs. 10(b), 10(c), and 10(d), respectively. In Fig. 10(d), we can see that two SPP focal spots appear clearly in the

*z*-polarization electric field distribution.

## 3. Conclusion

## Acknowledgment

## References and links

1. | W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature |

2. | E. Ozbay, “Plasmonics: Merging photonics and electronics at nanoscale dimensions,” Science |

3. | P. Berini, R. Charbonneau, and N. Lahoud, “Long-range surface plasmons on ultrathin membranes,” Nano Lett. |

4. | L. Yin, V. K. Vlasko-Vlasov, J. Pearson, J. M. Miller, J. Hua, U. Welp, D. E. Brown, and C. W. Kimball, “Subwavelength focusing and guiding of surface plasmons,” Nano Lett. |

5. | I. P. Radko, S. I. Bozhevolnyi, A. B. Evlyukhin, and A. Boltasseva, “Surface plasmon polariton beam focusing with parabolic nanoparticle chains,” Opt. Express |

6. | H. L. Offerhaus, B. van den Bergen, M. Escalante, F. B. Segerink, J. P. Korterik, and N. F. van Hulst, “Creating focused plasmons by noncollinear phasematching on functional gratings,” Nano Lett. |

7. | Z. Liu, J. M. Steele, W. Srituravanich, Y. Pikus, C. Sun, and X. Zhang, “Focusing surface plasmons with plasmonic lens,” Nano Lett. |

8. | Z. Liu, J. M. Steele, H. Lee, and X. Zhang, “Tuning the focus of a plasmonic lens by the incident angle,” Appl. Phys. Lett. |

9. | H. Kim, J. Hahn, and B. Lee,“Focusing properties of surface plasmon polariton floatig dielectric lenses,” Opt. Express 16, 3049–3057 (2008). [CrossRef] [PubMed] |

10. | L. Feng, K. A. Tetz, B. Slutsky, V. Lomakin, and Y. Fainman, “Fourier plasmonics: Diffractive focusing of in-plane surface plasmon polariton waves,” Appl. Phys. Lett. |

11. | H. Kim, J. Hahn, and B. Lee, “Mathematical modeling of triangle-mesh-modeled three-dimensional surface objects for digital holography,” Appl. Opt. |

12. | R. Zia and M. L. Brongersma, “Surface plasmon polariton analogue to Young’s double-slit experiment,” Nat. Nanotechnol. |

13. | H. Kim, I.-M. Lee, and B. Lee, “Extended scattering-matrix method for efficient full parallel implementation of rigorous coupled-wave analysis,” J. Opt. Soc. Am. A |

14. | H. Kim and B. Lee, “Mathematical modeling of crossed nanophotonic structures with generalized scattering-matrix method and local Fourier modal analysis,” J. Opt. Soc. Am. B |

**OCIS Codes**

(240.6680) Optics at surfaces : Surface plasmons

(250.5300) Optoelectronics : Photonic integrated circuits

**ToC Category:**

Optics at Surfaces

**History**

Original Manuscript: March 20, 2008

Revised Manuscript: May 17, 2008

Manuscript Accepted: May 30, 2008

Published: June 3, 2008

**Citation**

Hwi Kim and Byoungho Lee, "Diffractive slit patterns for focusing surface
plasmon polaritons," Opt. Express **16**, 8969-8980 (2008)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-12-8969

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### References

- W. L. Barnes, A. Dereux, and T. W. Ebbesen, "Surface plasmon subwavelength optics," Nature 424, 824-830 (2003). [CrossRef] [PubMed]
- E. Ozbay, "Plasmonics: Merging photonics and electronics at nanoscale dimensions," Science 311, 189-193 (2006). [CrossRef] [PubMed]
- P. Berini, R. Charbonneau, and N. Lahoud, "Long-range surface plasmons on ultrathin membranes," Nano Lett. 7, 1376-1380 (2007). [CrossRef] [PubMed]
- L. Yin, V. K. Vlasko-Vlasov, J. Pearson, J. M. Miller, J. Hua, U. Welp, D. E. Brown, and C. W. Kimball, "Subwavelength focusing and guiding of surface plasmons," Nano Lett. 5, 1399-1402 (2005). [CrossRef] [PubMed]
- I. P. Radko, S. I. Bozhevolnyi, A. B. Evlyukhin, and A. Boltasseva, "Surface plasmon polariton beam focusing with parabolic nanoparticle chains," Opt. Express 15, 6576-6582 (2007). [CrossRef] [PubMed]
- H. L. Offerhaus, B. van den Bergen, M. Escalante, F. B. Segerink, J. P. Korterik, and N. F. van Hulst, "Creating focused plasmons by noncollinear phasematching on functional gratings," Nano Lett. 5, 2144-2148 (2005). [CrossRef] [PubMed]
- Z. Liu, J. M. Steele, W. Srituravanich, Y. Pikus, C. Sun, and X. Zhang, "Focusing surface plasmons with plasmonic lens," Nano Lett. 5, 1726-1729 (2005). [CrossRef] [PubMed]
- Z. Liu, J. M. Steele, H. Lee, and X. Zhang, "Tuning the focus of a plasmonic lens by the incident angle," Appl. Phys. Lett. 88, 121108 (2006).
- H. Kim, J. Hahn, and B. Lee, "Focusing properties of surface plasmon polariton floatig dielectric lenses," Opt. Express 16, 3049-3057 (2008). [CrossRef] [PubMed]
- L. Feng, K. A. Tetz, B. Slutsky, V. Lomakin, and Y. Fainman, "Fourier plasmonics: Diffractive focusing of in-plane surface plasmon polariton waves," Appl. Phys. Lett. 91, 081101 (2007). [CrossRef]
- H. Kim, J. Hahn, and B. Lee, "Mathematical modeling of triangle-mesh-modeled three-dimensional surface objects for digital holography," Appl. Opt. 47, D117-D127 (2008). [CrossRef] [PubMed]
- R. Zia and M. L. Brongersma, "Surface plasmon polariton analogue to Young???s double-slit experiment," Nat. Nanotechnol. 2, 426-429 (2007). [CrossRef]
- H. Kim, I.-M. Lee, and B. Lee, "Extended scattering-matrix method for efficient full parallel implementation of rigorous coupled-wave analysis," J. Opt. Soc. Am. A 24, 2313-2327 (2007). [CrossRef]
- H. Kim and B. Lee, "Mathematical modeling of crossed nanophotonic structures with generalized scattering-matrix method and local Fourier modal analysis," J. Opt. Soc. Am. B 25, 518-544 (2008). [CrossRef]

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