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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 20, Iss. 11 — May. 21, 2012
  • pp: 12521–12529
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SPPs coupling induced interference in metal/dielectric multilayer waveguides and its application for plasmonic lithography

Peng Zhu, Haofei Shi, and L. Jay Guo  »View Author Affiliations


Optics Express, Vol. 20, Issue 11, pp. 12521-12529 (2012)
http://dx.doi.org/10.1364/OE.20.012521


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Abstract

We present the analyses of surface plasmon polaritons (SPPs) coupling induced interference in metal/dielectric (M/D) multilayer metamaterials and techniques to improve the performance of sub-wavelength plasmonic lithography. Expressions of beam spreading angles and interference patterns are derived from analyses of numerical simulations and the coupled mode theory. The new understandings provide useful guidelines and design criteria for plasmonic lithography. With proper layer structure design, sub-wavelength uniform periodic patterns with feature size of 1/12 of the mask's period can be realized. High pattern contrast of 0.8 and large field depth of 80 nm are also demonstrated numerically by considering the SPPs coupling in the photoresist. Both high contrast and large image depth are crucial for practical application of plasmonic lithography.

© 2012 OSA

1. Introduction

In the past, effective medium theory (EMT) and transfer matrix method have been used to explain and analyze the sub-wavelength characteristic of the interference patterns formed by metal/dielectric metamaterials [12

12. T. Xu, Y. H. Zhao, J. X. Ma, C. T. Wang, J. H. Cui, C. L. Du, and X. G. Luo, “Sub-diffraction-limited interference photolithography with metamaterials,” Opt. Express 16(18), 13579–13584 (2008). [CrossRef] [PubMed]

]. The hyperbolic dispersion relation of the metamaterial indicates that field components in the x direction (parallel to the film surface) with high spatial frequency can be supported in the structures and part of the high wavevector can pass through the metamaterials and be enhanced according to the optical transfer function. However, the effective medium analysis completely ignores the unique field patterns in the metal/dielectric multilayer structures, and offers no information about the formation of the interference patterns, e.g. the intensity distribution of the patterns. Especially, the interference patterns within the multi-layer stack become more complex when gratings with large period are used to excite the SPPs. In addition, although the feature size of the patterns can be much smaller than the optical diffraction limit [8

8. X. F. Yang, B. B. Zeng, C. T. Wang, and X. G. Luo, “Breaking the feature sizes down to sub-22 nm by plasmonic interference lithography using dielectric-metal multilayer,” Opt. Express 17(24), 21560–21565 (2009). [CrossRef] [PubMed]

, 11

11. X. G. Luo and T. Ishihara, “Surface plasmon resonant interference nanolithography technique,” Appl. Phys. Lett. 84(23), 4780–4782 (2004). [CrossRef]

], currently the SPPs-assisted plasmonic lithography still suffers from the low pattern contrast and the shallow field depth, which seriously limit its practical application. Therefore, to advance the understanding and further exploration of this promising technique, analyses of properties of SPPs propagation in the metal/dielectric multi-layers are critically needed. Not only it gives intuitive understanding and mechanism of the generation of interference patterns, but also provides important criteria for the optimized design of plasmonic metal/dielectric structures.

2. Structure and simulation results

We consider a hypermedia that consists of 10 alternating layers of Ag and MgF2 thin films with a conventional chromium mask on top of the MDMW film stacks. We first analyze a basic structure with only one slit in the chromium mask as shown in Fig. 1
Fig. 1 Schematic diagram of the multilayer Ag/ MgF2 waveguide with an air slit. All the components are treated as semi-infinite in the y direction.
.The air slit sits at the center of the chromium layer and the width w is 80 nm. Each layer of Ag and MgF2 can be considered as a waveguide and the length Lw along x direction is chosen as 1.5 μm in the simulation. A 5 μm thick transparent glass is used as a substrate. The thicknesses of the chromium mask and MgF2 layer are hCr = 50 nm and hm = 30 nm, respectively. Thickness hd of Ag layer is varied in the following analyses. A normal incident TM polarized light (electrical field is parallel to x coordinate) from the top of the glass substrate is used to excite the SPPs and the wavelength is 442nm. The index of MgF2 is 1.39 and the permittivity of Ag is εAg=5.77+0.5i [13

13. M. J. Weber, Handbook of Optical Materials (CRC Press, 2003), Chap. 4, 352–355.

]. Finite element method software Multi-physics COMSOL 3.5a is used to simulate and analyze the field distribution of SPPs in the MDMW.

3. Analysis of propagation property by coupled mode theory

The propagation behaviors of electromagnetic field in discrete optical waveguide and meta/air waveguide array have been analyzed by the coupled mode theory [17

17. A. Locatelli, M. Conforti, D. Modotto, and C. De Angelis, “Diffraction engineering in arrays of photonic crystal waveguides,” Opt. Lett. 30(21), 2894–2896 (2005). [CrossRef] [PubMed]

, 18

18. H. S. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchison, “Discrete Spatial Optical Solitons in Waveguide Arrays,” Phys. Rev. Lett. 81(16), 3383–3386 (1998). [CrossRef]

]. A set of coupled differential equations are used to describe the electrical field in the nth waveguide in an infinite array that is coupled with adjacent waveguides [17

17. A. Locatelli, M. Conforti, D. Modotto, and C. De Angelis, “Diffraction engineering in arrays of photonic crystal waveguides,” Opt. Lett. 30(21), 2894–2896 (2005). [CrossRef] [PubMed]

]:
iddxEn+βEn+C(En+1+En1)=0,
(1)
whereEn represents the electrical field in the nth waveguide, x is the coordinate of the propagation direction of waveguide,β is the propagation constant of the waveguide mode and C is the coupling coefficient between adjacent waveguides. The solution for the nth waveguide with the boundary conditions E0(0)=A0 andEn0(0)=0 can be expressed as
En(x)=E0(i)nexp(iβx)Jn(2Cx),
(2)
where Jn represents the Bessel function of nth order. Equation (2) predicts that the light input into one waveguide in the array will fan out and spread into two main lobes because of the coupling of light in adjacent waveguides, as shown in Fig. 4(a)
Fig. 4 (a) Theoretical electric field distribution expressed by Eq. (1) and plotted by Matlab. (b) Total electric field distribution of the MDMW with one air slit simulated by COMSOL 3.5a. (c) Theoretical electric field distribution expressed by Eq. (3) with five excitation ports. The dashed lines are the intersections of the spreading beams. (d) Electric field distribution of the MDMW with five air slits calculated by COMSOL 3.5a. The distance between the neighboring slits is 600 nm and the thicknesses of Ag/MgF2 are 30 nm/20 nm.
. The phenomenon in our configuration in Fig. 1 can be described in a similar way because their physical mechanisms are the same, which are both based on the coupling process of light (or SPPs) in waveguide arrays. The minor difference is that the incident SPPs are launched from the center of the first layer of the waveguides along both + x and -x directions. Figure 4(b) reproduces the simulated beam spreading behavior as discussed above. Gray-scale images are presented here for a better comparison. The field pattern can be regarded as the result of two incident waves input at opposite directions in Fig. 4(a) and only the half of the bottom part is displayed.

The electrical field distribution excited by two or more slits can be considered as a superposition of the field excited by a single slit at different positions. We assume that the number of slits is m and the position of each slit is known, the total electrical field can be expressed as
E(x)=k=1mEk(x)=k=1mA0(i)nexp(iβx)Jn{2C[xL(k)]},
(3)
whereL(k) is the position of each slit and the calculated electrical field is shown in Fig. 4(c). The total electrical field distribution in the MDMW with multiple slits by COMSOL simulation is also presented in Fig. 4(d) for a comparison. The distance between the neighboring slits and the spreading angle will determine the position where the spreading beams meet and interfere with each other in the multilayer waveguide. Interference patterns can be expected in the overlapped regions between the spreading zones originated from the two neighboring slits. It is clearly shown in Fig. 4(d) that different intensity distributions can be obtained at different distance from the top of the waveguide during the downward coupling of SPPs. The intensity is stronger at the intersections where the spreading beams meet and will attenuate gradually in the following propagation. There is a position between the intersections, where uniform interference patterns can be formed, as shown in the dashed rectangular area in Fig. 4(d). By using periodic nano-slits on the chromium mask and designing the thickness of films, uniform field distribution can be realized at the bottom layer of the waveguide array for the lithography application where the photoresist layer is placed right at bottom.

The above model based on coupled mode theory gives the physical description of the propagation property of SPPs in MDMW and can provide some useful guidelines when applying it to SPPs lithography applications.

4. Applications in SPPs assisted interference lithography

To apply the coupling mechanism described above to SPPs-assisted lithography, we use a grating with a periodic narrow slits to represent the chromium mask pattern on top of the MDMW stack, and a layer of photoresist coated on a silicon substrate is placed below the multilayer waveguide for exposure, as shown in Fig. 5(a)
Fig. 5 Intensity of total electrical field on the photoresist in structures with different thicknesses of Ag/MgF2, 28 nm/30 nm in (a) and 20 nm/30 nm in (b); (c) thicknesses of Al/ MgF2 are 16 nm/16 nm. (d) Profile of the electrical field at a distance to 20 nm from the top of the photoresist of interference patterns in (c).
. The advantage offered by SPPs-assisted lithography is that much smaller line-width than optical diffraction limit can be obtained, down to ~1/10 of the wavelength. Here we further show that interference patterns with feature size of 1/12 of the period of the original mask can also be achieved. Such a capability can greatly relax the demand on making very high resolution patterns on the optical mask. The property of SPPs coupling in M/D multilayer waveguide can be considered to obtain a proper design of the hypermedia structure, especially the thicknesses of the metal and dielectric layers. For example, the structures in Fig. 5(a) and 5(b) have a 30 nm thick MgF2 layer, and 28 nm and 20 nm thick Ag layers, respectively. The yellow arrows represent the propagation direction of the coupling SPPs. As discussed above, the optical field distributions of interference patterns are mainly affected by the spreading angle of the propagating SPP waves, which is determined by the film thickness. Improper spreading angles will make most of the energy concentrated at certain regions, leading to very non-uniform interference patterns unsuitable for lithography application. Therefore the period of the mask pattern and the period of the interference pattern should be commensurate with each other and the spreading angle and film thickness should be chosen properly. According to the analysis in Fig. 4 and simulation results by COMSOL, uniform interference patterns will be generated at the center of the intersections of spreading beams. Figure 5(a) and 5(b) show the uniform and non-uniform interference patterns with the period of 100 nm (i.e. one sixth of the mask grating period) with different choice of film thicknesses. Interference patterns with smaller feature size (sub 22 nm) are also demonstrated in Fig. 5(c) and 5(d). The incident wavelength is reduced to 193nm (i.e. excimer laser wavelength currently used in lithography industry) in this case and Al is used instead of Ag because of its smaller loss at this deep UV wavelength. The permittivity of Al at 193nm is εAl = −4.69 + 0.485*i [13

13. M. J. Weber, Handbook of Optical Materials (CRC Press, 2003), Chap. 4, 352–355.

]. The thicknesses of Al/MgF2 are set as 16 nm/16 nm in order to support the SPPs modes with smaller wavelength. Multilayer films of such thicknesses are easily within reach by thin film deposition technologies. Figure 5(d) shows the field intensity profile of the interference patterns taken at a distance of 20 nm below the photoresist surface, with a contrast V=(|E|max2|E|min2)/(|E|max2+|E|min2)≈0.33.

We can notice that the field depth of the interference pattern is limited to the surface of photoresist and the contrast is only around 0.4 in the above designs. Most of the previously reported works also suffer from the same problems, which severely limits the applications of SPPs plasmonic lithography. Here, we use a modified configuration to further improve the contrast of the interference patterns and the field penetration depth in the resist layer. The strategy is to deposit a metal film on top of the silicon substrate below the photoresist in order to introduce SPPs coupling in the photoresist layer. This metal layer works as a plasmonic reflector [19

19. M. D. Arnold and R. J. Blaikie, “Subwavelength optical imaging of evanescent fields using reflections from plasmonic slabs,” Opt. Express 15(18), 11542–11552 (2007). [CrossRef] [PubMed]

]. SPPs are excited at the bottom photoresist/metal interface and then coupled with the SPPs from the top surface of photoresist, which produces an overall stronger field with higher contrast inside the photoresist layer. The metal of Al with permittivity εAl≈-28.34 + 6.43i at 442 nm is used for the enhancement of interference patterns with feature size of 50nm as shown in Fig. 6(a)
Fig. 6 (a) Intensity distribution of electrical field of the enhanced interference patterns with 50 nm feature size in the MDMW with a metal layer below photoresist;(b) Comparison of profiles of the cross section of the interference patterns with a distance of 40 nm from the top surface of photoresist in the structures with and without Al layer; (c) and (d) are the results for the interference patterns with feature size of 20 nm; (e) Schematic of the SPPs coupling in the photoresist. The red curve represents the coupled SPP modes on the top and bottom photoresist/metal interface. (f) Amplified intensity 2D electrical field distributions in the photoresist without and with metal film.
and the thickness of photoresist is 80 nm. A metamaterial with permittivity εm≈-9.6 + 0.62i at 193nm (can be calculated by effective media theory from metal/dielectric multilayer structure) is used for the patterns with 20 nm feature size in Fig. 6(c) and the thickness of photoresist is 40 nm. They all show that the electrical field of the interference patterns can penetrate through the whole photoresist layer and the field depths are larger than the previously reported SPPs patterns. Figure 6(b) and 6(d) compare the profiles of the electrical field in the center of the photoresist with and without metal layer under the photoresist for the two structures with different feature sizes. The field intensity drastically increases when the metal layer is coated under the photoresist and the contrast of the pattern is significantly improved to 0.8.

This technique has some limitations. It will make the lithography process more complex and expensive. Anyway, it can be useful when a metal grating or metamaterial with nano slits in large are needed for a device. The top photoresist pattern can be used as a mask for the etching of the metal. The SPPs coupling effect is schematically shown in Fig. 6(e). The red curve represents coupled SPPs mode. The coupling effect is affected by the thickness h of the photoresist. There is almost no enhancement when the thickness is too large, like 200 nm. In this case, it is similar to the situation where the photoresist is coated on the Si substrate directly because no SPPs can be generated at the bottom the photoresist/metal interface. Optimal results may be varied according to feature size of the interference patterns. Figure 6(f) shows the comparison of electrical fields in the photoresist with and without metal layer. We can see the obvious improvement of the interference patterns, especially at the deep depth in the photoresist.

5. Conclusion

In conclusion, we studied the mechanism and properties of SPPs coupling induced interference in metal/dielectric multilayer waveguides based on numerical simulations and the coupled mode theory. The phenomenon of beam spreading is caused by the horizontal propagation of the SPPs and the vertical coupling of SPPs between the adjacent waveguides. A relation of the wave propagation spreading angle, coupling length and film thickness is established by an approximate expression. Applications of the structures with multiple slits for SPP-assisted interference lithography are numerically demonstrated. Uniform interference patterns with small feature size (1/12 of the grating masks), high contrast of about 0.8 and large field depth of 80 nm (40 nm for 20 nm feature size) can be achieved by an optimal stack layer design based on the understanding of the coupling property of SPPs in MDMW. The contrast and the field penetration depth can be improved significantly by introducing a metal reflector layer beneath the resist. These analyses may also provide useful design principles for more plasmonic devices with involvement of SPPs and MDMW.

Acknowledgment

This work is supported by NSF funded CPHOM at the University of Michigan. P.Z. acknowledges the support from China Scholarship Council (CSC) and the University of Michigan.

References and links

1.

S. Thongrattanasiri and V. A. Podolskiy, “Hypergratings: nanophotonics in planar anisotropic metamaterials,” Opt. Lett. 34(7), 890–892 (2009). [CrossRef] [PubMed]

2.

W. S. Cai, D. A. Genov, and V. M. Shalaev, “Superlens based on metal-dielectric composites,” Phys. Rev. B 72(19), 193101 (2005). [CrossRef]

3.

X. B. Fan and G. P. Wang, “Nanoscale metal waveguide arrays as plasmon lenses,” Opt. Lett. 31(9), 1322–1324 (2006). [CrossRef] [PubMed]

4.

L. Verslegers, P. B. Catrysse, Z. F. Yu, and S. H. Fan, “Deep-subwavelength focusing and steering of light in an aperiodic metallic waveguide array,” Phys. Rev. Lett. 103(3), 033902 (2009). [CrossRef] [PubMed]

5.

X. Fan, G. P. Wang, J. C. W. Lee, and C. T. Chan, “All-angle broadband negative refraction of metal waveguide arrays in the visible range: theoretical analysis and numerical demonstration,” Phys. Rev. Lett. 97(7), 073901 (2006). [CrossRef] [PubMed]

6.

H. Shin and S. Fan, “All-angle negative refraction for surface plasmon waves using a metal-dielectric-metal structure,” Phys. Rev. Lett. 96(7), 073907 (2006). [CrossRef] [PubMed]

7.

T. Yang and K. B. Crozier, “Analysis of surface plasmon waves in metaldielectric- metal structures and the criterion for negative refractive index,” Opt. Express 17(2), 1136–1143 (2009). [CrossRef] [PubMed]

8.

X. F. Yang, B. B. Zeng, C. T. Wang, and X. G. Luo, “Breaking the feature sizes down to sub-22 nm by plasmonic interference lithography using dielectric-metal multilayer,” Opt. Express 17(24), 21560–21565 (2009). [CrossRef] [PubMed]

9.

W. Srituravanich, N. Fang, C. Sun, Q. Luo, and X. Zhang, “Plasmonic nanolithography,” Nano Lett. 4(6), 1085–1088 (2004). [CrossRef]

10.

Z. W. Liu, Q. H. Wei, and X. Zhang, “Surface plasmon interference nanolithography,” Nano Lett. 5(5), 957–961 (2005). [CrossRef] [PubMed]

11.

X. G. Luo and T. Ishihara, “Surface plasmon resonant interference nanolithography technique,” Appl. Phys. Lett. 84(23), 4780–4782 (2004). [CrossRef]

12.

T. Xu, Y. H. Zhao, J. X. Ma, C. T. Wang, J. H. Cui, C. L. Du, and X. G. Luo, “Sub-diffraction-limited interference photolithography with metamaterials,” Opt. Express 16(18), 13579–13584 (2008). [CrossRef] [PubMed]

13.

M. J. Weber, Handbook of Optical Materials (CRC Press, 2003), Chap. 4, 352–355.

14.

C. C. Yan, D. H. Zhang, Y. A. Zhang, D. D. Li, and M. A. Fiddy, “Metal-dielectric composites for beam splitting and far-field deep sub-wavelength resolution for visible wavelengths,” Opt. Express 18(14), 14794–14801 (2010). [CrossRef] [PubMed]

15.

B. Wang and G. P. Wang, “Surface plasmon polariton propagation in nanoscale metal gap waveguides,” Opt. Lett. 29(17), 1992–1994 (2004). [CrossRef] [PubMed]

16.

A. Yariv, “Coupled-mode theory for guided-wave optics,” IEEE J. Quantum Electron. 9(9), 919–933 (1973). [CrossRef]

17.

A. Locatelli, M. Conforti, D. Modotto, and C. De Angelis, “Diffraction engineering in arrays of photonic crystal waveguides,” Opt. Lett. 30(21), 2894–2896 (2005). [CrossRef] [PubMed]

18.

H. S. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchison, “Discrete Spatial Optical Solitons in Waveguide Arrays,” Phys. Rev. Lett. 81(16), 3383–3386 (1998). [CrossRef]

19.

M. D. Arnold and R. J. Blaikie, “Subwavelength optical imaging of evanescent fields using reflections from plasmonic slabs,” Opt. Express 15(18), 11542–11552 (2007). [CrossRef] [PubMed]

OCIS Codes
(230.7370) Optical devices : Waveguides
(240.6690) Optics at surfaces : Surface waves
(260.3160) Physical optics : Interference
(110.4235) Imaging systems : Nanolithography

ToC Category:
Optics at Surfaces

History
Original Manuscript: April 11, 2012
Manuscript Accepted: April 30, 2012
Published: May 17, 2012

Citation
Peng Zhu, Haofei Shi, and L. Jay Guo, "SPPs coupling induced interference in metal/dielectric multilayer waveguides and its application for plasmonic lithography," Opt. Express 20, 12521-12529 (2012)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-11-12521


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References

  1. S. Thongrattanasiri and V. A. Podolskiy, “Hypergratings: nanophotonics in planar anisotropic metamaterials,” Opt. Lett.34(7), 890–892 (2009). [CrossRef] [PubMed]
  2. W. S. Cai, D. A. Genov, and V. M. Shalaev, “Superlens based on metal-dielectric composites,” Phys. Rev. B72(19), 193101 (2005). [CrossRef]
  3. X. B. Fan and G. P. Wang, “Nanoscale metal waveguide arrays as plasmon lenses,” Opt. Lett.31(9), 1322–1324 (2006). [CrossRef] [PubMed]
  4. L. Verslegers, P. B. Catrysse, Z. F. Yu, and S. H. Fan, “Deep-subwavelength focusing and steering of light in an aperiodic metallic waveguide array,” Phys. Rev. Lett.103(3), 033902 (2009). [CrossRef] [PubMed]
  5. X. Fan, G. P. Wang, J. C. W. Lee, and C. T. Chan, “All-angle broadband negative refraction of metal waveguide arrays in the visible range: theoretical analysis and numerical demonstration,” Phys. Rev. Lett.97(7), 073901 (2006). [CrossRef] [PubMed]
  6. H. Shin and S. Fan, “All-angle negative refraction for surface plasmon waves using a metal-dielectric-metal structure,” Phys. Rev. Lett.96(7), 073907 (2006). [CrossRef] [PubMed]
  7. T. Yang and K. B. Crozier, “Analysis of surface plasmon waves in metaldielectric- metal structures and the criterion for negative refractive index,” Opt. Express17(2), 1136–1143 (2009). [CrossRef] [PubMed]
  8. X. F. Yang, B. B. Zeng, C. T. Wang, and X. G. Luo, “Breaking the feature sizes down to sub-22 nm by plasmonic interference lithography using dielectric-metal multilayer,” Opt. Express17(24), 21560–21565 (2009). [CrossRef] [PubMed]
  9. W. Srituravanich, N. Fang, C. Sun, Q. Luo, and X. Zhang, “Plasmonic nanolithography,” Nano Lett.4(6), 1085–1088 (2004). [CrossRef]
  10. Z. W. Liu, Q. H. Wei, and X. Zhang, “Surface plasmon interference nanolithography,” Nano Lett.5(5), 957–961 (2005). [CrossRef] [PubMed]
  11. X. G. Luo and T. Ishihara, “Surface plasmon resonant interference nanolithography technique,” Appl. Phys. Lett.84(23), 4780–4782 (2004). [CrossRef]
  12. T. Xu, Y. H. Zhao, J. X. Ma, C. T. Wang, J. H. Cui, C. L. Du, and X. G. Luo, “Sub-diffraction-limited interference photolithography with metamaterials,” Opt. Express16(18), 13579–13584 (2008). [CrossRef] [PubMed]
  13. M. J. Weber, Handbook of Optical Materials (CRC Press, 2003), Chap. 4, 352–355.
  14. C. C. Yan, D. H. Zhang, Y. A. Zhang, D. D. Li, and M. A. Fiddy, “Metal-dielectric composites for beam splitting and far-field deep sub-wavelength resolution for visible wavelengths,” Opt. Express18(14), 14794–14801 (2010). [CrossRef] [PubMed]
  15. B. Wang and G. P. Wang, “Surface plasmon polariton propagation in nanoscale metal gap waveguides,” Opt. Lett.29(17), 1992–1994 (2004). [CrossRef] [PubMed]
  16. A. Yariv, “Coupled-mode theory for guided-wave optics,” IEEE J. Quantum Electron.9(9), 919–933 (1973). [CrossRef]
  17. A. Locatelli, M. Conforti, D. Modotto, and C. De Angelis, “Diffraction engineering in arrays of photonic crystal waveguides,” Opt. Lett.30(21), 2894–2896 (2005). [CrossRef] [PubMed]
  18. H. S. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchison, “Discrete Spatial Optical Solitons in Waveguide Arrays,” Phys. Rev. Lett.81(16), 3383–3386 (1998). [CrossRef]
  19. M. D. Arnold and R. J. Blaikie, “Subwavelength optical imaging of evanescent fields using reflections from plasmonic slabs,” Opt. Express15(18), 11542–11552 (2007). [CrossRef] [PubMed]

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