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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 19, Iss. 20 — Sep. 26, 2011
  • pp: 19093–19103
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Plasmonic and Mie scattering control of far-field interference for regular ripple formation on various material substrates

Go Obara, Naoki Maeda, Tomoya Miyanishi, Mitsuhiro Terakawa, Nikolay N. Nedyalkov, and Minoru Obara  »View Author Affiliations


Optics Express, Vol. 19, Issue 20, pp. 19093-19103 (2011)
http://dx.doi.org/10.1364/OE.19.019093


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Abstract

We present experimental and theoretical results on plasmonic control of far-field interference for regular ripple formation on semiconductor and metal. Experimental observation of interference ripple pattern on Si substrate originating from the gold nanosphere irradiated by femtosecond laser is presented. Gold nanosphere is found to be an origin for ripple formation. Arbitrary intensity ripple patterns are theoretically controllable by depositing desired plasmonic and Mie scattering far-field pattern generators. The plasmonic far-field generation is demonstrated not only by metallic nanostructures but also by the controlled surface structures such as ridge and trench structures on various material substrates.

© 2011 OSA

1. Introduction

In recent years, engineering science research using enhanced optical near field mediated with the light scattering by nanostructures has received much attention [1

1. S. Kawata, Near-Field Optics and Surface Plasmon Polaritons (Springer, 2001).

3

3. S. Carretero-Palacios, O. Mahboub, F. J. Garcia-Vidal, L. Martin-Moreno, S. G. Rodrigo, C. Genet, and T. W. Ebbesen, “Mechanisms for extraordinary optical transmission through bull’s eye structures,” Opt. Express 19(11), 10429–10442 (2011). [CrossRef] [PubMed]

]. In such a near-field engineering science, surface nanopatterning has been extensively investigated [4

4. S. M. Huang, M. H. Hong, B. S. Luk’yanchuk, Y. W. Zheng, W. D. Song, Y. F. Lu, and T. C. Chong, “Pulsed laser-assisted surface structuring with optical near-field enhanced effects,” J. Appl. Phys. 92(5), 2495–2500 (2002). [CrossRef]

15

15. Y. Tanaka, N. N. Nedyalkov, and M. Obara, “Enhanced near-field distribution inside substrates mediated with gold particle: optical vortex and bifurcation,” Appl. Phys., A Mater. Sci. Process. 97(1), 91–98 (2009). [CrossRef]

]. Plasmonic resonances in a metallic nanoscale system allow confinement of electric field power into spatial dimensions that are below the theoretical resolution limit determined by the Abbe criterion for far-field optics [2

2. C. Genet and T. W. Ebbesen, “Light in tiny holes,” Nature 445(7123), 39–46 (2007). [CrossRef] [PubMed]

,3

3. S. Carretero-Palacios, O. Mahboub, F. J. Garcia-Vidal, L. Martin-Moreno, S. G. Rodrigo, C. Genet, and T. W. Ebbesen, “Mechanisms for extraordinary optical transmission through bull’s eye structures,” Opt. Express 19(11), 10429–10442 (2011). [CrossRef] [PubMed]

]. The plasmonic nano-ablation processing using enhanced localized near field by gold particles [7

7. N. N. Nedyalkov, H. Takada, and M. Obara, “Nanostructuring of silicon surface by femtosecond laser pulse mediated with enhanced near-field of gold nanoparticles,” Appl. Phys., A Mater. Sci. Process. 85(2), 163–168 (2006). [CrossRef]

,8

8. N. N. Nedyalkov, T. Sakai, T. Miyanishi, and M. Obara, “Near field properties in the vicinity of gold nanoparticles placed on various substrates for precise nanostructuring,” J. Phys. D Appl. Phys. 39(23), 5037–5042 (2006). [CrossRef]

,11

11. G. Obara, Y. Tanaka, T. Miyanishi, and M. Obara, “Uniform plasmonic near-field nanopatterning by backward irradiation of femtosecond laser,” Appl. Phys., A Mater. Sci. Process. 102(3), 551–557 (2011). [CrossRef]

,14

14. T. Miyanishi, T. Sakai, N. N. Nedyalkov, and M. Obara, “Femtosecond-laser nanofabrication onto silicon surface with near-field localization generated by plasmon polaritons in gold nanoparticles with oblique irradiation,” Appl. Phys., A Mater. Sci. Process. 96(4), 843–850 (2009). [CrossRef]

,15

15. Y. Tanaka, N. N. Nedyalkov, and M. Obara, “Enhanced near-field distribution inside substrates mediated with gold particle: optical vortex and bifurcation,” Appl. Phys., A Mater. Sci. Process. 97(1), 91–98 (2009). [CrossRef]

], and enhanced near-field nanoprocessing by dielectric particles, in other words, resonant Mie scattering [6

6. H. Takada and M. Obara, “Fabrication of hexagonally arrayed nanoholes using femtosecond laser pulse ablation with template of subwavelength polystyrene particle array,” Jpn. J. Appl. Phys. 44, 7993–7997 (2005). [CrossRef]

,9

9. T. Sakai, Y. Tanaka, Y. Nishizawa, M. Terakawa, and M. Obara, “Size parameter effect of dielectric small particle mediated nano-hole patterning on silicon wafer by femtosecond laser,” Appl. Phys., A Mater. Sci. Process. 99(1), 39–46 (2010). [CrossRef]

,10

10. Y. Tanaka, G. Obara, A. Zenidaka, M. Terakawa, and M. Obara, “Femtosecond laser near-field nano-ablation patterning using Mie resonance high dielectric constant particle with small size parameter,” Appl. Phys. Lett. 96(26), 261103 (2010). [CrossRef]

,12

12. Y. Tanaka, G. Obara, A. Zenidaka, N. N. Nedyalkov, M. Terakawa, and M. Obara, “Near-field interaction of two-dimensional high-permittivity spherical particle arrays on substrate in the Mie resonance scattering domain,” Opt. Express 18(26), 27226–27237 (2010). [CrossRef] [PubMed]

,16

16. G. Mie, “Beiträ ge zur Optik trü ber Medien, speziell kolloidaler Metallö sungen,” Ann. Phys. 330(3), 377–445 (1908). [CrossRef]

] have been reported. Due to the surface plasmon polaritons, metallic nanoparticle can provide an enhanced near field in its vicinity even with small size Mie scattering parameter. In the meantime, high-permittivity dielectric particle (dielectric particle with high refractive index) with small size parameter can also provide a strong near-field enhancement mediated with the resonance Mie scattering. Many experiments were carried out with a normal incidence to the substrate, while an oblique incidence [14

14. T. Miyanishi, T. Sakai, N. N. Nedyalkov, and M. Obara, “Femtosecond-laser nanofabrication onto silicon surface with near-field localization generated by plasmon polaritons in gold nanoparticles with oblique irradiation,” Appl. Phys., A Mater. Sci. Process. 96(4), 843–850 (2009). [CrossRef]

] and backward irradiation [11

11. G. Obara, Y. Tanaka, T. Miyanishi, and M. Obara, “Uniform plasmonic near-field nanopatterning by backward irradiation of femtosecond laser,” Appl. Phys., A Mater. Sci. Process. 102(3), 551–557 (2011). [CrossRef]

] were also used. Such scattered optical field, which is governed by Mie scattering theory [16

16. G. Mie, “Beiträ ge zur Optik trü ber Medien, speziell kolloidaler Metallö sungen,” Ann. Phys. 330(3), 377–445 (1908). [CrossRef]

], by nanostructures and nanoparticles is numerically analyzed using Maxwell’s equations. The FDTD (Finite-Difference Time-Domain) simulation method is widely used to solve Maxwell’s equations. In this type of nanoprocessing, only the near field is of interest. In this technology, an unfocused laser pulse was irradiated upon a single-shot basis, whose fluence is much below the ablation threshold of the bulk substrate materials [8

8. N. N. Nedyalkov, T. Sakai, T. Miyanishi, and M. Obara, “Near field properties in the vicinity of gold nanoparticles placed on various substrates for precise nanostructuring,” J. Phys. D Appl. Phys. 39(23), 5037–5042 (2006). [CrossRef]

,9

9. T. Sakai, Y. Tanaka, Y. Nishizawa, M. Terakawa, and M. Obara, “Size parameter effect of dielectric small particle mediated nano-hole patterning on silicon wafer by femtosecond laser,” Appl. Phys., A Mater. Sci. Process. 99(1), 39–46 (2010). [CrossRef]

]. The sphere acts as a super metal lens and super dielectric Mie scattering lens to give an enhanced near-field zone, whose fluence becomes above the ablation threshold of the substrate [6

6. H. Takada and M. Obara, “Fabrication of hexagonally arrayed nanoholes using femtosecond laser pulse ablation with template of subwavelength polystyrene particle array,” Jpn. J. Appl. Phys. 44, 7993–7997 (2005). [CrossRef]

,15

15. Y. Tanaka, N. N. Nedyalkov, and M. Obara, “Enhanced near-field distribution inside substrates mediated with gold particle: optical vortex and bifurcation,” Appl. Phys., A Mater. Sci. Process. 97(1), 91–98 (2009). [CrossRef]

].

Ever since the development of the laser in 1960s, laser-induced damage of solid materials at or near the damage threshold has been investigated experimentally and theoretically. Grating-like laser damage patterns, resulting from irradiation with intense laser were observed at the surface of the target materials using cw (continuous wave) to picosecond laser sources, between 530 nm and 1060 nm. Sipe, Young, Peterson, and van Driel investigated theoretically and experimentally laser-induced periodic surface structures [27

27. J. Sipe, J. Young, J. Preston, and H. van Driel, “Laser-induced periodic surface structure. I. Theory,” Phys. Rev. B 27(2), 1141–1154 (1983). [CrossRef]

29

29. J. Young, J. Sipe, and H. van Driel, “Laser-induced periodic surface structure. III. Fluence regimes, the role of feedback, and details of the induced topography in germanium,” Phys. Rev. B 30, 2001–2015 (1984). [CrossRef]

]. They discussed the nature of the generated optical field structures and their relation to the simple “surface-scattered wave” model for periodic surface damage.

As for femtosecond laser induced periodic ripple structure formation, an initial random distribution of nanoscale ablation traces on diamond-like carbon (DLC) film is periodically structured with the increase of successive laser pulses irradiation or fluence on DLC film [21

21. G. Miyaji and K. Miyazaki, “Origin of periodicity in nanostructuring on thin film surfaces ablated with femtosecond laser pulses,” Opt. Express 16(20), 16265–16271 (2008). [CrossRef] [PubMed]

]. The formation of periodicity can be attributed to the excitation of surface plasmon polaritons to induce the periodic enhancement of local fields in the surface layer. Nanoscale ablation on DLC ridge-stripes arrays with 800 nm femtosecond laser was also reported [22

22. G. Miyaji and K. Miyazaki, “Nanoscale ablation on patterned diamondlike carbon film with femtosecond laser pulses,” Appl. Phys. Lett. 91(12), 123102 (2007). [CrossRef]

]. They reported that nanoscale ablation would preferentially be initiated by the enhancement of the localized plasmonic field on the stripe surface with high curvature.

The interference of the incident laser and the scattered plasmon polaritons far field (not near field) may be the origin of the ripple formation. Huang et al. considered that the ripples result from the initial surface plasmon and laser interference, and the subsequent grating-assisted surface plasmon-laser coupling [26

26. M. Huang, F. Zhao, Y. Cheng, N. Xu, and Z. Xu, “Origin of laser-induced near-subwavelength ripples: interference between surface plasmons and incident laser,” ACS Nano 3(12), 4062–4070 (2009). [CrossRef] [PubMed]

]. However, the origin of the surface plasmon generation was not evident.

There are many qualitative hypotheses of laser assisted ripple formation. The origin of ripples formation stems from surface roughness [19

19. T. Tomita, K. Kinoshita, S. Matsuo, and S. Hashimoto, “Effect of surface roughening on femtosecond laser-induced ripple structures,” Appl. Phys. Lett. 90(15), 153115 (2007). [CrossRef]

], spontaneous surface plasmon [21

21. G. Miyaji and K. Miyazaki, “Origin of periodicity in nanostructuring on thin film surfaces ablated with femtosecond laser pulses,” Opt. Express 16(20), 16265–16271 (2008). [CrossRef] [PubMed]

26

26. M. Huang, F. Zhao, Y. Cheng, N. Xu, and Z. Xu, “Origin of laser-induced near-subwavelength ripples: interference between surface plasmons and incident laser,” ACS Nano 3(12), 4062–4070 (2009). [CrossRef] [PubMed]

], surface scattering wave [30

30. H. Kumagai, M. Ezaki, K. Toyoda, and M. Obara, “Periodic submicrometer dot structure on n-GaAs substrates fabricated by laser-induced surface electromagnetic wave etching,” J. Appl. Phys. 73(4), 1971–1974 (1993). [CrossRef]

], laser-induced surface electromagnetic wave [31

31. M. Ezaki, H. Kumagai, K. Toyoda, and M. Obara, “Surface modification of III-V compound semiconductors using surface electromagnetic wave etching induced by ultraviolet lasers,” IEEE J. Sel. Top. Quantum Electron. 1(3), 841–847 (1995). [CrossRef]

], and others. Experimental ripple formation on semiconductors, dielectrics and metals were reported. These ripples were formed by spontaneous surface scattering wave originating from inherent surface roughness (nanostructured surface). The scattering far-field and near-field distributions are dependent on the polarization of the incident laser.

However, the far field of the surface plasmon polaritons was not directly observed previously for the ripple formation. After the initial weak ripples formed, the many subsequent laser pulses may couple with the formed surface grating to enhance the contrast of ripple structures via the self-organization process [20

20. G. Miyaji and K. Miyazaki, “Ultrafast dynamics of periodic nanostructure formation on diamondlike carbon films irradiated with femtosecond laser pulses,” Appl. Phys. Lett. 89(19), 191902 (2006). [CrossRef]

,23

23. D. Dufft, A. Rosenfeld, S. K. Das, R. Grunwald, and J. Bonse, “Femtosecond laser-induced periodic surface structures revisited: a comparative study on ZnO,” J. Appl. Phys. 105(3), 034908 (2009). [CrossRef]

,26

26. M. Huang, F. Zhao, Y. Cheng, N. Xu, and Z. Xu, “Origin of laser-induced near-subwavelength ripples: interference between surface plasmons and incident laser,” ACS Nano 3(12), 4062–4070 (2009). [CrossRef] [PubMed]

], while it was not externally controllable without feed-back loop. Wavy (not precisely periodic) ripples and non-regular ripples were experimentally observed in many reports [19

19. T. Tomita, K. Kinoshita, S. Matsuo, and S. Hashimoto, “Effect of surface roughening on femtosecond laser-induced ripple structures,” Appl. Phys. Lett. 90(15), 153115 (2007). [CrossRef]

23

23. D. Dufft, A. Rosenfeld, S. K. Das, R. Grunwald, and J. Bonse, “Femtosecond laser-induced periodic surface structures revisited: a comparative study on ZnO,” J. Appl. Phys. 105(3), 034908 (2009). [CrossRef]

,26

26. M. Huang, F. Zhao, Y. Cheng, N. Xu, and Z. Xu, “Origin of laser-induced near-subwavelength ripples: interference between surface plasmons and incident laser,” ACS Nano 3(12), 4062–4070 (2009). [CrossRef] [PubMed]

]. These ripples may be altered partially due to the input phase offset of the laser pulse. The CEP (carrier envelop phase) [32

32. A. Anderson, F. Lücking, T. Prikoszovits, M. Hofer, Z. Cheng, C. C. Neacsu, M. Scharrer, S. Rammler, P. S. J. Russell, G. Tempea, and A. Assion, “Multi-mJ carrier envelope phase stabilized few-cycle pulses generated by a tabletop laser system,” Appl. Phys. B 103, 531–536 (2011). [CrossRef]

,33

33. L. Bergé, C.-L. Soulez, C. Köhler, and S. Skupin, “Role of the carrier-envelop phase in laser filamentation,” Appl. Phys. B 103(3), 563–570 (2011). [CrossRef]

] modifies the polarization through the plasmon response. The CEPs in commercially available femtosecond laser systems are not controlled. The curvature and bend of the substrate surface may also be another origin of the wavy ripple formation. The fabricated surface ripples were not satisfactory for surface photonic device applications, because the fabricated ripples were not regular ripples.

We propose to control the optical field intensity interference pattern between the incident femtosecond laser and plasmonic far field induced with arbitrary artificial scattering structures. In this case, we change the concept of plasmonic noise induced spontaneously by the surface roughness into the coherent plasmonic signal generation using artificial plasmon generating structures or templates. Plasmon resonance originates from a low Q-factor resonator in terms of broad plasmon resonance spectral bandwidth, due to the inherent resistive nature of the metallic nanostructured materials. The low Q resonator is easy to induce multimode oscillation, and it is very difficult to choose only a single-mode oscillation without an additional mode selector. If we can successfully generate a coherent plasmon wave (far field) on the material surface by coherent femtosecond laser excitation, we can expect the precise periodic ripple formation. The effect of spatially partially coherent wave excitation of nanostructured objects was investigated recently [34

34. H. J. Hyvärinen, J. Turunen, and P. Vahimaa, “Elementary-field modeling of surface-plasmon excitation with partially coherent light,” Appl. Phys. B 101(1-2), 273–282 (2010). [CrossRef]

].

In this paper, we will report on the direct observation of the surface plasmon far field for the regular surface ripple formation by femtosecond laser irradiation of gold nanosphere on a silicon substrate. We explain the experimental results using FDTD simulation method. Then, we also describe the control of the plasmonic far field with artificial plasmon scattering nanostructures deposited on the substrate in advance in order to fabricate precise ripple structures on the material surface. In addition to the plasmonic nanostructures, it is found that nanoridge and trench on various substrates can serve as the far-field source of Mie scattering to form regular ripple structures.

2. Simulation procedure

We performed the numerical analysis of optical field distributions by three-dimensional (3D) FDTD simulation, whose software package is commercially available (Poynting, Fujitsu, Co., Japan). The simulation model consists of a single 200 nm diameter nanoparticle placed on a silicon substrate (xy plane). We also simulate many systems where a variety of nanostructures are on a silicon or metal substrate. A plane wave with circular polarization at the second harmonic wave (λ = 400 nm) of Ti:Al2O3 femtosecond laser is incident vertically (the k vector is along −z axis) to the particle system. The incident electric field strength is assumed as 1 V/m. The 400 nm pulsed laser illuminates uniformly a large area of 4000 x 4000 nm2. The simulated field intensity distribution just after a 400 nm or 800 nm femtosecond laser pulse irradiation of 21.6 fs is shown in this paper. 21.6 fs is the time when surface field becomes steady. The optical intensity is calculated as an average value of one cycle optical wave (2.7 fs for 800 nm, 1.35 fs for 400 nm). Optical constants of materials used in the simulation were taken from Refs [35

35. E. D. Palik, Handbook of Optical Constants of Solids (Academic, 1998).

37

37. A. R. Forouhi and I. Bloomer, “Optical dispersion relations for amorphous semiconductors and amorphous dielectrics,” Phys. Rev. B Condens. Matter 34(10), 7018–7026 (1986). [CrossRef] [PubMed]

]. The material characteristics of silicon with femtosecond laser irradiation at or near the bulk ablation threshold may change [24

24. J. Bonse, A. Rosenfeld, and J. Krüger, “On the role of surface plasmon polaritons in the formation of laser-induced periodic surface structures upon irradiation of silicon by femtosecond –laser pulse,” J. Appl. Phys. 106(10), 104910 (2009). [CrossRef]

]. Hence, the optical intensity interference distributions are simulated for both silicon (n = 3.688 + 0.006i) and metal-like silicon (n = 1.833 + 1.262i) [24

24. J. Bonse, A. Rosenfeld, and J. Krüger, “On the role of surface plasmon polaritons in the formation of laser-induced periodic surface structures upon irradiation of silicon by femtosecond –laser pulse,” J. Appl. Phys. 106(10), 104910 (2009). [CrossRef]

]. If the dielectric function by a Drude model approximation is changed with laser fluence, plasmon generation efficiency primarily changes.

3. Results and discussion

3.1 Direct observation of plasmonic far field interference by single gold particle on silicon substrate

To know the origin of ripple formation on a silicon substrate, gold spheres of 200 nm diameter were spin coated on the Si substrate. The Si single crystal surface roughness is less than 2 nm RMS. The 400 nm femtosecond laser with circular polarization illuminated normally the surface with 20 pulses (1 kHz repetition rate, 300 fs pulse duration). The laser fluence was as low as 80 mJ/cm2, which is below the bulk Si ablation threshold of 100 mJ/cm2 approximately. The SEM image of the silicon surface after the laser irradiation is shown in Fig. 1
Fig. 1 SEM images of the silicon surface after the laser irradiation. (a) Ripples. (b) Close-up picture near the center (different area) and nano-dotted substructure size is 30 nm approximately. The 400 nm femtosecond laser with circular polarization illuminated normally the surface with 20 pulses at 1 kHz. The laser fluence is 80 mJ/cm2, which is below the bulk silicon ablation threshold.
. The figure shows a gold sphere partially melted, and the sphere-generated spherical ripples. In addition, white dotted substructures (30 nm in diameter approximately) are observed. Due to the simulation results shown later in the paper, the first radial stripe indicates a strong field area, in which the substructure would be formed through modification change like amorphous silicon, or condensation into the substructure. At this moment, the underlying physics of the formation of the white dotted circular substructures is not elucidated. The period of the ripple is 400 nm approximately.

Figure 2
Fig. 2 SEM image of the silicon surface after the laser irradiation. The 400 nm femtosecond laser with circular polarization illuminated normally the surface with 20 pulses at 1 kHz. The laser fluence is 100 mJ/cm2, which is equivalent to the bulk silicon ablation threshold.
shows the SEM image after the 400 nm laser irradiation at 100 mJ/cm2. The spherical ripples of 400 nm periodicity approximately are observed from the center of gold nanosphere. There is no white dotted substructure on the surface at 100 mJ/cm2 , while in Fig. 1 white dotted substructures are observed at 80 mJ/cm2 fluence. At this moment, the fundamental physics for substructure fabrication as a function of laser fluence is not made clear.

Figure 3
Fig. 3 The simulated optical field intensity ripples induced by a single gold particle on silicon substrate. The incident electric field strength is 1 V/m at 400 nm. The circular polarization pulse is incident normally to the surface. (a) Irradiation schematic. (b) Optical intensity distribution on xy plane at z = −5 nm for silicon. (c) Optical intensity distribution on xy plane at z = − 5 nm for metal-like silicon.
shows a simulation result of interference intensity ripples on xy plane at z = − 5 nm. The field distribution just inside the substrate is more meaningful for the silicon modification and ablation than the one on the surface. Hence, we use the intensity at z = −5 nm throughout this paper. The simulated result is well consistent with the experimental result shown in Figs. 1 and 2. The simulation result cannot show the experimental result of dotted circular substructures. If the peak intensity of the ripples exceeds the ablation threshold or phase transition threshold, the substrate surface is periodically ablated or modified morphologically at the initial stages of the surface ripple growth process. The spherical pattern is observed in simulation, as shown in Fig. 3. The ripple intensity for metal-like silicon is higher than the one for silicon. The observed spherical ripple indicates the interference pattern between the plasmonic far field and the incident wave. As a result, the simulation result is validated by the experimental result.

3.2 Effect of particle material

In this simulation, the 800 nm fundamental wave of Ti:Al2O3 femtosecond laser is assumed. If the particle is made of silicon (not gold), the simulated ripple intensity is very low, as shown in Fig. 4(b)
Fig. 4 The simulated optical field intensity ripples induced by a single silicon particle (200 nm diameter) on silicon substrate. The circular polarization beam at 800 nm is incident normally to the surface. (a) Irradiation schematic. (b) Optical intensity ripple distribution on xy plane at z = −5 nm for silicon. (c) Optical field intensity distribution on xy plane at z = −5 nm for metal-like silicon.
. In this case, the material property of silicon is assumed to be kept constant during laser irradiation. Silicon is a semiconductor, which serves as the Mie scatterer. Since this size parameter is in the off-resonant Mie scattering domain, the scattered far field is weak [10

10. Y. Tanaka, G. Obara, A. Zenidaka, M. Terakawa, and M. Obara, “Femtosecond laser near-field nano-ablation patterning using Mie resonance high dielectric constant particle with small size parameter,” Appl. Phys. Lett. 96(26), 261103 (2010). [CrossRef]

,12

12. Y. Tanaka, G. Obara, A. Zenidaka, N. N. Nedyalkov, M. Terakawa, and M. Obara, “Near-field interaction of two-dimensional high-permittivity spherical particle arrays on substrate in the Mie resonance scattering domain,” Opt. Express 18(26), 27226–27237 (2010). [CrossRef] [PubMed]

]. If a silica (SiO2) particle is deposited on the Si wafer, the far-field ripple pattern is not observed, due to the low refractive index of SiO2, although the results are not shown. The non-resonant Mie scattering far field by a 200-nm diameter SiO2 is found to be weak.

3.3 Effect of nanoparticle shape

We simulate the effect of nanoparticle shape to know the ripple profiles originating from the shape of the scatter. Figure 5
Fig. 5 (a)The simulated optical field intensity ripples around a square mesa of silicon on silicon substrate. The silicon square mesa is 200 nm x 200 nm and is 200 nm high. (a) The linear polarization pulse is incident along x axis. (b) Optical field distribution on xy plane at z = −5 nm for metal-like silicon. (c) The optical field intensity profile along y axis (along the dotted line in Fig. 5(b)).
shows the simulated intensity ripple pattern when a square shape mesa structure of silicon is placed on the silicon substrate. The illumination wavelength is 800 nm with linear polarization. The linear ripples orthogonal to the incident polarization are experimentally formed with linearly polarized femtosecond laser irradiation. In this simulation, as shown in Fig. 5(b), in the silicon nanostructure’s vicinity the ripple pattern reflects the square shape elliptically along the polarization direction, and the outer ripples converge to the circular ripple pattern. The field intensity profile along the dotted line in Fig. 5(b) is shown in Fig. 5(c). The electric dipole is induced along the incident electric vector, and the near field at the center of the square shape is weak. The periodicity of the ripple is 800 nm approximately.

If there are two square mesa shaped structures on the silicon substrate, wavy ripples are observed, as shown in Fig. 6(b)
Fig. 6 (a) The simulated optical field intensity ripples around two square mesa structures (3200 nm distant) of silicon on silicon substrate. The incident linear polarization is along x axis. (b) Optical field distribution on xy plane at z = −5 nm for metal-like silicon. (c) The optical field intensity profile along y axis (along the dotted line in Fig. 6(b)).
. Due to the Huygens-Fresnel principle, the secondary ripple pattern is made by the superposition of the two primary wave sources. It is considered that when there are multiple identical scatteres randomly, far-field interference pattern becomes a line-like profile orthogonal to the incident polarization as the wave is getting away from the source. Figure 6(c) shows the intensity ripple profile along the dotted line shown in Fig. 6(b).

In summary, the intensity interference ripple patterns are found to depend upon the plasmonic nanostructures and polarization of the incoming laser pulse. In section 3.3, we proposed plasmonic and Mie scattering control of far-field interference for regular ripple formation on the silicon substrate, and in section 3.4 we will describe the controllability of intensity ripple pattern on a silicon substrate.

3.4 Plasmonic and Mie scattering control of far-field interference pattern for regular ripple formation on silicon substrate

In this section, we will control artificially the regular ripple patterns by depositing or writing plasmonic nanostructures and Mie scattering nanostructures on the silicon substrate prior to the laser irradiation. The artificial plasmonic and Mie scattering nanostructures will be able to generate coherent scattering far fields when excited by a coherent femtosecond laser. Consequently, one can design interference ripple patterns with 1D and 2D arrays.

Figure 7
Fig. 7 (Color online) The simulated optical field intensity ripples induced by a gold nano ridge structure on silicon substrate for silicon. The incident linear polarization is orthogonal to the ridge. (a) Irradiation schematic. (b) Optical field distribution on xy plane at z = −5 nm for silicon. (c) Optical field intensity profile along y axis at x = 0. Note that | E x|2 = 0 and |E z|2 = 0.
shows the simulated optical intensity distribution with a gold nano-ridge structure (200 nm height by 200 nm width) on the Si substrate. The incident laser polarization is linear at 800 nm and the electric vector is orthogonal to the linear nano-ridge. In Fig. 7(b), the intensity ripple pattern is observed on a parallel with the linear gold nano-structure, and in Fig. 7 (c) it is observed that |E| 2 ( = |E x|2 + |E y|2 + |E z|2) contains only |E y|2 component. This means the ripple is always formed orthogonal to the incident E vector, because the plasmonic far field is on xy plane. Of course, the near field E has E z component. This result is consistent with the experiment. If the linearly polarized laser beam is irradiated parallel to the gold nano-ridge line, the interference pattern is not induced, because no plasmonic far-field scattering in the orthogonal direction occurs.

When a silicon nano-ridge replaces the gold nano-ridge as the primary scatterer, the linear ripples are also observed, as shown in Fig. 8
Fig. 8 The simulated optical field intensity ripples induced by silicon nano-ridge structure on silicon substrate. The incident linear polarization is orthogonal to the ridge. (a) Irradiation schematic. (b) Optical field distribution on xy plane at z = −5 nm for metal-like silicon.
. The ridge dimension is the same as the gold structure. With the 200 x 200 nm2 silicon ridge, Mie scattering by this structure is off-resonant to the 800 nm wavelength. Hence, the scattered near field is weaker than the one by the gold structure. However, the observed far-field intensity is large. The excitation intensity at 800 nm wavelength is moderate below the ablation threshold of silicon substrate, and the ridge acts as the plasmonic and Mie scatterer.

A trench (valley) also behaves as the scatterer. If the trench is formed on the silicon surface and irradiated with a linearly polarized laser, the linear interference ripple pattern is induced, as shown in Fig. 9
Fig. 9 The simulated optical field intensity ripples induced by V-trench on silicon substrate. The linear polarization pulse is incident orthogonal to the trench. (a) Irradiation schematic. (b) Optical intensity distribution on xy plane at z = −5 nm for metal-like silicon.
. In this case, the two top edges and bottom edge act as the surface plasmon-polaritons sources for the near field. Therefore, the ripple pattern is different from the one in Figs. 7 and 8. The far-field interference pattern is seen to decay faster than the one by the silicon nano-ridge.

An L-shaped gold ridge or L-shaped trench is formed in advance on the silicon, and then it is illuminated with a circularly polarized beam. The simulation results are shown in Fig. 10
Fig. 10 The simulated optical field intensity ripples induced by (a) L-shaped gold ridge structure, and (b) L-shaped, V-trench both on Si substrate. The dimension of the gold nano-ridge is 200 nm width x 200 nm height x 4000 nm length. The dimension of the V-trench is 400 nm width and 200 nm depth. The circular polarization pulse is at normal incidence to the silicon surface. (a) Optical intensity distribution at z = −5 nm for gold ridge and metal-like silicon. (b) Optical intensity distribution at z = −5 nm for V-trench and metal-like silicon.
. 2D periodic dot arrays are induced in both systems. The circularly polarized beam has two components: E x and E y vectors. Each vector makes a linear interference pattern orthogonally, resulting in the formation of the 2D dotted arrays. The intensity of the 2D dotted array is larger by gold nano-ridge scatterer than the one by V-shaped trench.

In summary, both nanostructures made of gold and silicon are found to serve as the far-field scatterer. The interference ripple intensity is dependent upon the structure, size and material. If the dimensions of the nano-structures are optimized further to the plasmon resonant spectrum or resonant Mie scattering spectrum, more intense ripple profile will be achievable.

3.5 Control of far-field interference ripple pattern on metal substrates

In this section, we will present the far field ripple intensity on metal substrates. If the metal substrate is a complete conductor, the reflected electric field Er on the surface is Er = −Ei, and the magnetic field Br (Br = 2Bi) is twice the incident Bi field on the surface due to the Ampere’s law. If the trench is formed on a gold substrate and irradiated with a linearly polarized beam, the intensity ripple pattern is observed parallel to the trench direction, as shown in Fig. 11
Fig. 11 The simulated optical field intensity ripples induced by a trench on gold (Au) substrate. The dimension of the trench is 200 nm width and 200 nm depth. The incident linear polarization is orthogonal to the trench. (a) Irradiation schematic. (b) Optical field intensity on xy plane at z = −5 nm. (c) Optical field intensity along y axis (along the dotted black line in Fig. 11(b)).
. The trench dimensions used here have a nearly plasmon resonant spectrum for near-field generation. Hence, the ripple intensity is very large. Figure 12
Fig. 12 The simulated optical field intensity ripples induced by a trench on tungsten (W) substrate. The incident linear polarization pulse is orthogonal to the trench. (a) Irradiation schematic. (b) Optical field intensity on xy plane at z = −5 nm. (c) Optical field intensity along y axis (along the white dotted line in Fig. 12(b)).
shows the ripple profile when the trench is formed on a tungsten (W) surface. Due to the low electric conductivity of the tungsten substrate, the intensity ripple is very low and less than 40% of the one of gold substrate. As a result, the intensity ripple patterns are generated accurately on the metal and silicon substrate.

4. Conclusions

We presented experimental and theoretical results on plasmonic coherent control and Mie scattering control of far-field interference pattern for regular ripple formation on semiconductor and metals. We have directly observed the interference ripple pattern on the silicon substrate, which originates from the plasmonic scattering far field by gold nanosphere irradiated by femtosecond laser pulses. Arbitrary intensity ripple patterns were precisely controlled by placing a desired plasmonic and Mie scattering far-field pattern generators in advance. The far-field generation was demonstrated not only by metallic gold nanostructures but also by the controlled surface structures such as nano-ridge, nano-trench on the metal and silicon surfaces. This result indicates that in addition to the plasmonic scattering, the Mie scattering far field also serves as an origin of surface ripple formation at the initial stages. In this paper, we dealt with the low-spatial-frequency ripples of laser-induced periodic surface structures (LIPSS) [23

23. D. Dufft, A. Rosenfeld, S. K. Das, R. Grunwald, and J. Bonse, “Femtosecond laser-induced periodic surface structures revisited: a comparative study on ZnO,” J. Appl. Phys. 105(3), 034908 (2009). [CrossRef]

,26

26. M. Huang, F. Zhao, Y. Cheng, N. Xu, and Z. Xu, “Origin of laser-induced near-subwavelength ripples: interference between surface plasmons and incident laser,” ACS Nano 3(12), 4062–4070 (2009). [CrossRef] [PubMed]

]. High-spatial-frequency LIPSS [18

18. A. Borowiec and H. K. Haugen, “Subwavelength ripple formation on the surfaces of compound semiconductors irradiated with femtosecond laser pulses,” Appl. Phys. Lett. 82(25), 4462–4464 (2003). [CrossRef]

,26

26. M. Huang, F. Zhao, Y. Cheng, N. Xu, and Z. Xu, “Origin of laser-induced near-subwavelength ripples: interference between surface plasmons and incident laser,” ACS Nano 3(12), 4062–4070 (2009). [CrossRef] [PubMed]

] were also experimentally observed. The fundamental physics of this LIPSS will be published elsewhere.

Acknowledgments

This study is supported by the MEXT Japan Grant-in-Aid for Scientific Research (B-23360161). This study is also supported partially by a Grant-In-Aid for the Global Center of Excellence for High-Level Global Cooperation for Leading-Edge Platform on Access Spaces from the MEXT Japan. The authors thank Dr. M. Hasegawa, M.D. for his productive and warmest encouragement throughout this study. T. Miyanishi is grateful for the JSPS Fellowship for Young Scientists.

References and links

1.

S. Kawata, Near-Field Optics and Surface Plasmon Polaritons (Springer, 2001).

2.

C. Genet and T. W. Ebbesen, “Light in tiny holes,” Nature 445(7123), 39–46 (2007). [CrossRef] [PubMed]

3.

S. Carretero-Palacios, O. Mahboub, F. J. Garcia-Vidal, L. Martin-Moreno, S. G. Rodrigo, C. Genet, and T. W. Ebbesen, “Mechanisms for extraordinary optical transmission through bull’s eye structures,” Opt. Express 19(11), 10429–10442 (2011). [CrossRef] [PubMed]

4.

S. M. Huang, M. H. Hong, B. S. Luk’yanchuk, Y. W. Zheng, W. D. Song, Y. F. Lu, and T. C. Chong, “Pulsed laser-assisted surface structuring with optical near-field enhanced effects,” J. Appl. Phys. 92(5), 2495–2500 (2002). [CrossRef]

5.

A. Plech, V. Kotaidis, M. Lorenc, and J. Boneberg, “Femtosecond laser near-field ablation from gold nanoparticles,” Nat. Phys. 2(1), 44–47 (2006). [CrossRef]

6.

H. Takada and M. Obara, “Fabrication of hexagonally arrayed nanoholes using femtosecond laser pulse ablation with template of subwavelength polystyrene particle array,” Jpn. J. Appl. Phys. 44, 7993–7997 (2005). [CrossRef]

7.

N. N. Nedyalkov, H. Takada, and M. Obara, “Nanostructuring of silicon surface by femtosecond laser pulse mediated with enhanced near-field of gold nanoparticles,” Appl. Phys., A Mater. Sci. Process. 85(2), 163–168 (2006). [CrossRef]

8.

N. N. Nedyalkov, T. Sakai, T. Miyanishi, and M. Obara, “Near field properties in the vicinity of gold nanoparticles placed on various substrates for precise nanostructuring,” J. Phys. D Appl. Phys. 39(23), 5037–5042 (2006). [CrossRef]

9.

T. Sakai, Y. Tanaka, Y. Nishizawa, M. Terakawa, and M. Obara, “Size parameter effect of dielectric small particle mediated nano-hole patterning on silicon wafer by femtosecond laser,” Appl. Phys., A Mater. Sci. Process. 99(1), 39–46 (2010). [CrossRef]

10.

Y. Tanaka, G. Obara, A. Zenidaka, M. Terakawa, and M. Obara, “Femtosecond laser near-field nano-ablation patterning using Mie resonance high dielectric constant particle with small size parameter,” Appl. Phys. Lett. 96(26), 261103 (2010). [CrossRef]

11.

G. Obara, Y. Tanaka, T. Miyanishi, and M. Obara, “Uniform plasmonic near-field nanopatterning by backward irradiation of femtosecond laser,” Appl. Phys., A Mater. Sci. Process. 102(3), 551–557 (2011). [CrossRef]

12.

Y. Tanaka, G. Obara, A. Zenidaka, N. N. Nedyalkov, M. Terakawa, and M. Obara, “Near-field interaction of two-dimensional high-permittivity spherical particle arrays on substrate in the Mie resonance scattering domain,” Opt. Express 18(26), 27226–27237 (2010). [CrossRef] [PubMed]

13.

S. Imamova, A. Dikovska, N. Nedyalkov, P. Atanasov, M. Sawczak, R. Jendrzejewski, G. Sliwinski, and M. Obara, “Laser nanostructuring of thin Au films for application in surface enhanced Raman spectroscopy,” J. Optoelectron. Adv. Mater. 12, 500–504 (2010).

14.

T. Miyanishi, T. Sakai, N. N. Nedyalkov, and M. Obara, “Femtosecond-laser nanofabrication onto silicon surface with near-field localization generated by plasmon polaritons in gold nanoparticles with oblique irradiation,” Appl. Phys., A Mater. Sci. Process. 96(4), 843–850 (2009). [CrossRef]

15.

Y. Tanaka, N. N. Nedyalkov, and M. Obara, “Enhanced near-field distribution inside substrates mediated with gold particle: optical vortex and bifurcation,” Appl. Phys., A Mater. Sci. Process. 97(1), 91–98 (2009). [CrossRef]

16.

G. Mie, “Beiträ ge zur Optik trü ber Medien, speziell kolloidaler Metallö sungen,” Ann. Phys. 330(3), 377–445 (1908). [CrossRef]

17.

A. M. Ozkan, A. P. Malshe, T. A. Railkar, W. D. Brown, M. D. Shirk, and P. A. Molian, “Femtosecond laser-induced periodic structure writing on diamond crystals and microclusters,” Appl. Phys. Lett. 75(23), 3716–3718 (1999). [CrossRef]

18.

A. Borowiec and H. K. Haugen, “Subwavelength ripple formation on the surfaces of compound semiconductors irradiated with femtosecond laser pulses,” Appl. Phys. Lett. 82(25), 4462–4464 (2003). [CrossRef]

19.

T. Tomita, K. Kinoshita, S. Matsuo, and S. Hashimoto, “Effect of surface roughening on femtosecond laser-induced ripple structures,” Appl. Phys. Lett. 90(15), 153115 (2007). [CrossRef]

20.

G. Miyaji and K. Miyazaki, “Ultrafast dynamics of periodic nanostructure formation on diamondlike carbon films irradiated with femtosecond laser pulses,” Appl. Phys. Lett. 89(19), 191902 (2006). [CrossRef]

21.

G. Miyaji and K. Miyazaki, “Origin of periodicity in nanostructuring on thin film surfaces ablated with femtosecond laser pulses,” Opt. Express 16(20), 16265–16271 (2008). [CrossRef] [PubMed]

22.

G. Miyaji and K. Miyazaki, “Nanoscale ablation on patterned diamondlike carbon film with femtosecond laser pulses,” Appl. Phys. Lett. 91(12), 123102 (2007). [CrossRef]

23.

D. Dufft, A. Rosenfeld, S. K. Das, R. Grunwald, and J. Bonse, “Femtosecond laser-induced periodic surface structures revisited: a comparative study on ZnO,” J. Appl. Phys. 105(3), 034908 (2009). [CrossRef]

24.

J. Bonse, A. Rosenfeld, and J. Krüger, “On the role of surface plasmon polaritons in the formation of laser-induced periodic surface structures upon irradiation of silicon by femtosecond –laser pulse,” J. Appl. Phys. 106(10), 104910 (2009). [CrossRef]

25.

S. Sakabe, M. Hashida, S. Tokita, S. Namba, and K. Okamuro, “Mechanism of self-formation of periodic grating structures on a metal surface by a femtosecond laser pulse,” Phys. Rev. B 79(3), 033409 (2009). [CrossRef]

26.

M. Huang, F. Zhao, Y. Cheng, N. Xu, and Z. Xu, “Origin of laser-induced near-subwavelength ripples: interference between surface plasmons and incident laser,” ACS Nano 3(12), 4062–4070 (2009). [CrossRef] [PubMed]

27.

J. Sipe, J. Young, J. Preston, and H. van Driel, “Laser-induced periodic surface structure. I. Theory,” Phys. Rev. B 27(2), 1141–1154 (1983). [CrossRef]

28.

F. Jeff, “Young, J. F. Preston, H. M. van Driel, and J. E. Sipe, “Laser-induced periodic surface structure. II. Experiments on Ge, Si, Al, and brass,” Phys. Rev. B 27, 1155–1172 (1983).

29.

J. Young, J. Sipe, and H. van Driel, “Laser-induced periodic surface structure. III. Fluence regimes, the role of feedback, and details of the induced topography in germanium,” Phys. Rev. B 30, 2001–2015 (1984). [CrossRef]

30.

H. Kumagai, M. Ezaki, K. Toyoda, and M. Obara, “Periodic submicrometer dot structure on n-GaAs substrates fabricated by laser-induced surface electromagnetic wave etching,” J. Appl. Phys. 73(4), 1971–1974 (1993). [CrossRef]

31.

M. Ezaki, H. Kumagai, K. Toyoda, and M. Obara, “Surface modification of III-V compound semiconductors using surface electromagnetic wave etching induced by ultraviolet lasers,” IEEE J. Sel. Top. Quantum Electron. 1(3), 841–847 (1995). [CrossRef]

32.

A. Anderson, F. Lücking, T. Prikoszovits, M. Hofer, Z. Cheng, C. C. Neacsu, M. Scharrer, S. Rammler, P. S. J. Russell, G. Tempea, and A. Assion, “Multi-mJ carrier envelope phase stabilized few-cycle pulses generated by a tabletop laser system,” Appl. Phys. B 103, 531–536 (2011). [CrossRef]

33.

L. Bergé, C.-L. Soulez, C. Köhler, and S. Skupin, “Role of the carrier-envelop phase in laser filamentation,” Appl. Phys. B 103(3), 563–570 (2011). [CrossRef]

34.

H. J. Hyvärinen, J. Turunen, and P. Vahimaa, “Elementary-field modeling of surface-plasmon excitation with partially coherent light,” Appl. Phys. B 101(1-2), 273–282 (2010). [CrossRef]

35.

E. D. Palik, Handbook of Optical Constants of Solids (Academic, 1998).

36.

P. B. Johnson and R. W. Christy, “Optical Constants of the Noble Metals,” Phys. Rev. B 6(12), 4370–4379 (1972). [CrossRef]

37.

A. R. Forouhi and I. Bloomer, “Optical dispersion relations for amorphous semiconductors and amorphous dielectrics,” Phys. Rev. B Condens. Matter 34(10), 7018–7026 (1986). [CrossRef] [PubMed]

OCIS Codes
(290.4020) Scattering : Mie theory
(350.3390) Other areas of optics : Laser materials processing
(350.4238) Other areas of optics : Nanophotonics and photonic crystals
(220.4241) Optical design and fabrication : Nanostructure fabrication
(250.5403) Optoelectronics : Plasmonics

ToC Category:
Scattering

History
Original Manuscript: July 21, 2011
Revised Manuscript: August 6, 2011
Manuscript Accepted: August 18, 2011
Published: September 15, 2011

Virtual Issues
Vol. 6, Iss. 10 Virtual Journal for Biomedical Optics

Citation
Go Obara, Naoki Maeda, Tomoya Miyanishi, Mitsuhiro Terakawa, Nikolay N. Nedyalkov, and Minoru Obara, "Plasmonic and Mie scattering control of far-field interference for regular ripple formation on various material substrates," Opt. Express 19, 19093-19103 (2011)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-20-19093


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References

  1. S. Kawata, Near-Field Optics and Surface Plasmon Polaritons (Springer, 2001).
  2. C. Genet and T. W. Ebbesen, “Light in tiny holes,” Nature445(7123), 39–46 (2007). [CrossRef] [PubMed]
  3. S. Carretero-Palacios, O. Mahboub, F. J. Garcia-Vidal, L. Martin-Moreno, S. G. Rodrigo, C. Genet, and T. W. Ebbesen, “Mechanisms for extraordinary optical transmission through bull’s eye structures,” Opt. Express19(11), 10429–10442 (2011). [CrossRef] [PubMed]
  4. S. M. Huang, M. H. Hong, B. S. Luk’yanchuk, Y. W. Zheng, W. D. Song, Y. F. Lu, and T. C. Chong, “Pulsed laser-assisted surface structuring with optical near-field enhanced effects,” J. Appl. Phys.92(5), 2495–2500 (2002). [CrossRef]
  5. A. Plech, V. Kotaidis, M. Lorenc, and J. Boneberg, “Femtosecond laser near-field ablation from gold nanoparticles,” Nat. Phys.2(1), 44–47 (2006). [CrossRef]
  6. H. Takada and M. Obara, “Fabrication of hexagonally arrayed nanoholes using femtosecond laser pulse ablation with template of subwavelength polystyrene particle array,” Jpn. J. Appl. Phys.44, 7993–7997 (2005). [CrossRef]
  7. N. N. Nedyalkov, H. Takada, and M. Obara, “Nanostructuring of silicon surface by femtosecond laser pulse mediated with enhanced near-field of gold nanoparticles,” Appl. Phys., A Mater. Sci. Process.85(2), 163–168 (2006). [CrossRef]
  8. N. N. Nedyalkov, T. Sakai, T. Miyanishi, and M. Obara, “Near field properties in the vicinity of gold nanoparticles placed on various substrates for precise nanostructuring,” J. Phys. D Appl. Phys.39(23), 5037–5042 (2006). [CrossRef]
  9. T. Sakai, Y. Tanaka, Y. Nishizawa, M. Terakawa, and M. Obara, “Size parameter effect of dielectric small particle mediated nano-hole patterning on silicon wafer by femtosecond laser,” Appl. Phys., A Mater. Sci. Process.99(1), 39–46 (2010). [CrossRef]
  10. Y. Tanaka, G. Obara, A. Zenidaka, M. Terakawa, and M. Obara, “Femtosecond laser near-field nano-ablation patterning using Mie resonance high dielectric constant particle with small size parameter,” Appl. Phys. Lett.96(26), 261103 (2010). [CrossRef]
  11. G. Obara, Y. Tanaka, T. Miyanishi, and M. Obara, “Uniform plasmonic near-field nanopatterning by backward irradiation of femtosecond laser,” Appl. Phys., A Mater. Sci. Process.102(3), 551–557 (2011). [CrossRef]
  12. Y. Tanaka, G. Obara, A. Zenidaka, N. N. Nedyalkov, M. Terakawa, and M. Obara, “Near-field interaction of two-dimensional high-permittivity spherical particle arrays on substrate in the Mie resonance scattering domain,” Opt. Express18(26), 27226–27237 (2010). [CrossRef] [PubMed]
  13. S. Imamova, A. Dikovska, N. Nedyalkov, P. Atanasov, M. Sawczak, R. Jendrzejewski, G. Sliwinski, and M. Obara, “Laser nanostructuring of thin Au films for application in surface enhanced Raman spectroscopy,” J. Optoelectron. Adv. Mater.12, 500–504 (2010).
  14. T. Miyanishi, T. Sakai, N. N. Nedyalkov, and M. Obara, “Femtosecond-laser nanofabrication onto silicon surface with near-field localization generated by plasmon polaritons in gold nanoparticles with oblique irradiation,” Appl. Phys., A Mater. Sci. Process.96(4), 843–850 (2009). [CrossRef]
  15. Y. Tanaka, N. N. Nedyalkov, and M. Obara, “Enhanced near-field distribution inside substrates mediated with gold particle: optical vortex and bifurcation,” Appl. Phys., A Mater. Sci. Process.97(1), 91–98 (2009). [CrossRef]
  16. G. Mie, “Beiträ ge zur Optik trü ber Medien, speziell kolloidaler Metallö sungen,” Ann. Phys.330(3), 377–445 (1908). [CrossRef]
  17. A. M. Ozkan, A. P. Malshe, T. A. Railkar, W. D. Brown, M. D. Shirk, and P. A. Molian, “Femtosecond laser-induced periodic structure writing on diamond crystals and microclusters,” Appl. Phys. Lett.75(23), 3716–3718 (1999). [CrossRef]
  18. A. Borowiec and H. K. Haugen, “Subwavelength ripple formation on the surfaces of compound semiconductors irradiated with femtosecond laser pulses,” Appl. Phys. Lett.82(25), 4462–4464 (2003). [CrossRef]
  19. T. Tomita, K. Kinoshita, S. Matsuo, and S. Hashimoto, “Effect of surface roughening on femtosecond laser-induced ripple structures,” Appl. Phys. Lett.90(15), 153115 (2007). [CrossRef]
  20. G. Miyaji and K. Miyazaki, “Ultrafast dynamics of periodic nanostructure formation on diamondlike carbon films irradiated with femtosecond laser pulses,” Appl. Phys. Lett.89(19), 191902 (2006). [CrossRef]
  21. G. Miyaji and K. Miyazaki, “Origin of periodicity in nanostructuring on thin film surfaces ablated with femtosecond laser pulses,” Opt. Express16(20), 16265–16271 (2008). [CrossRef] [PubMed]
  22. G. Miyaji and K. Miyazaki, “Nanoscale ablation on patterned diamondlike carbon film with femtosecond laser pulses,” Appl. Phys. Lett.91(12), 123102 (2007). [CrossRef]
  23. D. Dufft, A. Rosenfeld, S. K. Das, R. Grunwald, and J. Bonse, “Femtosecond laser-induced periodic surface structures revisited: a comparative study on ZnO,” J. Appl. Phys.105(3), 034908 (2009). [CrossRef]
  24. J. Bonse, A. Rosenfeld, and J. Krüger, “On the role of surface plasmon polaritons in the formation of laser-induced periodic surface structures upon irradiation of silicon by femtosecond –laser pulse,” J. Appl. Phys.106(10), 104910 (2009). [CrossRef]
  25. S. Sakabe, M. Hashida, S. Tokita, S. Namba, and K. Okamuro, “Mechanism of self-formation of periodic grating structures on a metal surface by a femtosecond laser pulse,” Phys. Rev. B79(3), 033409 (2009). [CrossRef]
  26. M. Huang, F. Zhao, Y. Cheng, N. Xu, and Z. Xu, “Origin of laser-induced near-subwavelength ripples: interference between surface plasmons and incident laser,” ACS Nano3(12), 4062–4070 (2009). [CrossRef] [PubMed]
  27. J. Sipe, J. Young, J. Preston, and H. van Driel, “Laser-induced periodic surface structure. I. Theory,” Phys. Rev. B27(2), 1141–1154 (1983). [CrossRef]
  28. F. Jeff, “Young, J. F. Preston, H. M. van Driel, and J. E. Sipe, “Laser-induced periodic surface structure. II. Experiments on Ge, Si, Al, and brass,” Phys. Rev. B27, 1155–1172 (1983).
  29. J. Young, J. Sipe, and H. van Driel, “Laser-induced periodic surface structure. III. Fluence regimes, the role of feedback, and details of the induced topography in germanium,” Phys. Rev. B30, 2001–2015 (1984). [CrossRef]
  30. H. Kumagai, M. Ezaki, K. Toyoda, and M. Obara, “Periodic submicrometer dot structure on n-GaAs substrates fabricated by laser-induced surface electromagnetic wave etching,” J. Appl. Phys.73(4), 1971–1974 (1993). [CrossRef]
  31. M. Ezaki, H. Kumagai, K. Toyoda, and M. Obara, “Surface modification of III-V compound semiconductors using surface electromagnetic wave etching induced by ultraviolet lasers,” IEEE J. Sel. Top. Quantum Electron.1(3), 841–847 (1995). [CrossRef]
  32. A. Anderson, F. Lücking, T. Prikoszovits, M. Hofer, Z. Cheng, C. C. Neacsu, M. Scharrer, S. Rammler, P. S. J. Russell, G. Tempea, and A. Assion, “Multi-mJ carrier envelope phase stabilized few-cycle pulses generated by a tabletop laser system,” Appl. Phys. B103, 531–536 (2011). [CrossRef]
  33. L. Bergé, C.-L. Soulez, C. Köhler, and S. Skupin, “Role of the carrier-envelop phase in laser filamentation,” Appl. Phys. B103(3), 563–570 (2011). [CrossRef]
  34. H. J. Hyvärinen, J. Turunen, and P. Vahimaa, “Elementary-field modeling of surface-plasmon excitation with partially coherent light,” Appl. Phys. B101(1-2), 273–282 (2010). [CrossRef]
  35. E. D. Palik, Handbook of Optical Constants of Solids (Academic, 1998).
  36. P. B. Johnson and R. W. Christy, “Optical Constants of the Noble Metals,” Phys. Rev. B6(12), 4370–4379 (1972). [CrossRef]
  37. A. R. Forouhi and I. Bloomer, “Optical dispersion relations for amorphous semiconductors and amorphous dielectrics,” Phys. Rev. B Condens. Matter34(10), 7018–7026 (1986). [CrossRef] [PubMed]

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