Integrated 2D-Graded Index Plasmonic Lens on a Silicon Waveguide

Integrated 2D-Graded Index Plasmonic Lens on a Silicon Waveguide for Operation in the Near Infrared Domain Yulong Fan,† Xavier Le Roux,† Alexander Korovin,† Anatole Lupu,† and Andre de Lustrac*,†,‡ †

Univ. Paris-Sud, Université Paris-Saclay, C2N, 91405 Orsay, Cedex, France Université Paris Nanterre, 92410 Ville d’Avray, France

‡

ABSTRACT: In this article we address the nanoscale engineering of the effective index of silicon on insulator waveguides by using plasmonic metasurface resonances to realize a graded index lens. We report the design, implementation, and experimental demonstration of this plasmonic metasurface-based graded index lens integrated on a silicon waveguide for operation in the near-infrared domain. The 2D-graded index lens consists of an array of gold cut wires fabricated on the top of a silicon waveguide. These gold cut wires modify locally the effective index of the silicon waveguide and allow the realization of this gradient lens. The reported solution represents a promising alternative to the bulky or multilayered metamaterials approach in the near IR domain. This enabling technology may have found its place in silicon photonic applications by exploiting the plasmonic resonances to control the light at nanoscale. KEYWORDS: lens, plasmon, metamaterial, metasurface, photonics, silicon Yet another opportunity for taming the light flow offered by the metasurfaces is to consider their use in a guided wave configuration by means of their integration on a dielectric slab waveguide.25−28 The great advantages of such a solution are (i) simplified technology, only single metamaterial layer fabrication is required; (ii) reduced propagation losses, only the evanescent tail of the mode interacts with plasmonic resonators. Following this approach, a number of useful functionalities as for instance light reception,29 emission,30 wavelength demultiplexing,31 sensing,32 or absorption33,34 have been either theoretically or experimentally demonstrated. One of such functionalities of major importance for transformation optics applications is the control of the hybrid metal-dielectric waveguide effective index by the localized surface plasmon resonances.35,36 As it was evidenced by our theoretical results, an array of gold cut wires placed on the top of a silicon waveguide allows achieving a significant index variation in the vicinity of the metamaterial resonance. It can serve as a building block for the implementation of number of optical functions based on the local variation of waveguide effective index. The aim of the current work is to make a step further in this direction and bring an experimental demonstration of a functional integrated optics device exploiting the concept of

T

he advent of metamaterials during the past decennia has generated an intense research activity on the study of these artificial optical media that exhibit unusual properties that do not exist in the “natural” materials.1,2 The interest in the exploration of these structures was motivated by the possibility of an unconventional control of the propagation of electromagnetic waves, leading to a number of astonishing demonstrations, such as the invisibility cloak,3−7 perfect lens based on metamaterials with a negative index,2,8,9 concentrators,7 rotators,10 wormholes.11 The ultimate goal of such an approach is the implementation of light manipulations at the nanoscale for the further miniaturization of optical devices.12 For the time being most of the demonstrations exploiting the concept of effective electromagnetic medium have been performed in the microwave domain. Despite the tremendous progresses in nanofabrication technologies13 the fabrication of 3D metal nanostructures for the optical domain yet remains a major challenge because of the essentially planar character of standard electron-beam lithography and lift-off metal deposition techniques. The technological difficulties for the fabrication of large-scale optical metamaterials and the need to overcome metal related losses motivated the past year’s interest to the 2D arrays of subwavelength resonators also known as metasurfaces. The essential of the work performed in this direction was oriented to achieve a spatially resolved phase and amplitude control on the free space propagating light impinging on metasurface.14−24 © 2017 American Chemical Society

Received: January 8, 2017 Accepted: May 2, 2017 Published: May 2, 2017 4599

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refractive index is close to that of a slab dielectric waveguide. This provides the ability to engineer the composite metaldielectric slab effective refractive index by an appropriate positioning of the CWs resonance with respect to the operating frequency. To avoid the harmful effects of losses inherent to the absorption of metal CWs it is preferable to operate not exactly at the resonance but in its near vicinity and find an optimal trade-off between index variation and loss. As detailed in,36 the resonance frequency depends on many material and geometrical parameters of the CWs array. However, the most relevant parameters for the control of the resonance frequency are the length of the CWs associated with its fundamental plasmonic mode and the substrate refractive index. Here it is namely the length of the CWs that was chosen as tuning parameter for the implementation of a graded index profile. For a given CW length the effective index of the hybrid metallo-dielectric waveguide can be readily determined by means of numerical modeling with subsequent retrieval procedure.42,43 Figure 2a shows the frequency dependence of the effective index of the composite SOI-metasurface waveguide for selected lengths of CWs corresponding to our technological realization. Another important parameter is the distance s between the wires in the direction of wave propagation. Figure 2b shows the variation of the effective index of the composite SOI-

the control of waveguide local effective index by means of localized plasmon resonances. In this letter we report the design, fabrication, and experimental demonstration of a 2Dgraded index (GRIN) focusing lens for the NIR domain. The schematic of this hybrid metallo-dielectric GRIN lens operating in a guided wave configuration is shown in Figure 1. The local

Figure 1. Schematic of a 2D hybrid metallo-dielectric GRIN lens. Light propagation direction indicated by arrows.

change of the effective index is achieved by the integration of a 2D array of gold cut-wires (CWs) nanoresonators of different lengths on the top of the 220 nm thick silicon on insulator (SOI) waveguide covered by 10 nm thick silicon dioxide layer in order to increase CWs resonance frequency.36 The polarization of the light must be parallel to the wires. Our aim is the numerical and experimental demonstration of light focusing properties of such a 2D plasmonic GRIN lens.

RESULTS AND DISCUSSION To this end we start by considering the design of a generic GRIN focusing length integrated on a 220 nm thick SOI slab waveguide and operating at 190 THz corresponding to ∼1.58 μm wavelength. The width of the lens is w = 7.2 μm and the thickness d = 4 μm. For a paraxial approximation the refractive index profile of a GRIN lens follows a parabola law:37 n2(r ) = n02[1 − (gr )2 ]

(1)

where r is the distance from the center of the device, n0 is the index in the center of the lens, n(r) the index at the distance r from the center, and g is the gradient constant. The general approach for the engineering of the gradient refractive index structures made from composite materials is to perform a local variation of the effective index by changing the concentration of some inclusions, as for instance doping elements in glasses38,39 size or density of artificial defects like air holes on photonic crystals.40,41 In our case the important difference with respect to conventional approaches stems from the resonant nature of artificial inclusions made of CWs plasmonic nanoresonators and from the fact that the inclusions are not in the bulk but on the surface of the material. By consequence the resonance frequency of the CWs becomes one of the primary importance parameters for the engineering of local effective index. The effective permittivity εeff of a hybrid metal/dielectric slab waveguide can be approximated by a Lorentzian-type dispersion formula.36 The refractive index is higher than that of the dielectric slab below the resonance frequency and lower above it. Far from the resonance the

Figure 2. (a) Frequency dependence of the composite SOImetasurface waveguides effective index for different lengths of the resonant CWs element. The distance s between CWs is 50 nm. (b) Variation of the effective index of the composite SOI-metasurface waveguide for different distance s between CWs. CWs dimensions 180 × 50 × 50 nm, frequency f = 190 THz. 4600

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ACS Nano Table 1. Parameters of CWs Used for GRIN Lens Design at 190 THz half structure of GRIN lens (190 THz) CWs resonance frequency (THz) CWs length (nm) CWs width (nm) CWs height (nm) longitudinal separation distance between adjacent CWs lateral separation distance between adjacent CWs number of CWs in the array

area 1 n1 = area 2 n2 = area 3 n3 = 3.02 2.99 2.96

area 4 n1 = 2.94

area 5 n5 = 2.92

area 6 n6 = area 7 n7 = area 8 n8 = 2.89 2.87 2.84

area 9 n9 = 2.83

235.1 180 50 50 50

239.0 175 50 50 50

244.4 170 50 50 50

250.7 165 50 50 50

257.6 160 50 50 50

272.1 150 50 50 50

286.7 140 50 50 50

338.1 110 50 50 50

367.1 100 50 50 50

100

100

100

100

100

100

100

100

100

4 × 40

2 × 40

1 × 40

1 × 40

1 × 40

1 × 40

1 × 40

1 × 40

4 × 40

Figure 3. (a) Target (blue curve) and step-like discretized (red curve) GRIN lens index profiles. (b) Full 3D simulation of the light propagation across the GRIN lens at 190 THz.

metasurface waveguide as a function of separation distance s between CWs. In the given example the dimensions of the CWs corresponding to their length, l, width, w, and height, h, are 180 × 50 × 50 nm, respectively. The operation frequency f = 190 THz. We can observe that the effective index becomes higher as the distance between CWs is decreased. To avoid proximity effects related to e-beam lithography step and achieve high and reliable fabrication yield the distance s between CWs along the wave propagation direction was fixed to 50 nm. The resulting spatial periodicity p = w + s = 100 nm along the direction of wave propagation is small enough as compared to the Bragg period ≈290 nm at 190 THz for silicon slab waveguide. So the choice of s = 50 nm is also compliant with design considerations by satisfying the criteria for the validity of the homogenization approach. For distances between CWs approaching the Bragg condition (s > 200 nm) the model of effective material is no longer valid. This explains the choice for the distance s = 50 nm between CWs. The totality of the geometrical dimensions of the CWs array used for the lens design and corresponding refractive index at operation frequency of 190 THz are summarized in the Table 1. The parameters of Au, Si, and SiO2 used in HFSS numerical simulations are those given by Palik.44

The parameters of the GRIN lens to be used in a parabola index profile at 190 THz deduced from the data for composite slab effective index are approximately: n0 = 3.018 and g = 0.1149 μm−2. The parabola index profile given by eq 1 and its approximation by a step-like index variation using arrays of CWs with parameters listed in the Table 1 are shown Figure 3a. To verify the validity of the effective medium approach used for the GRIN lens design we performed full 3D HFSS45 simulations with same parameters of SOI slab waveguide (2 μm thick buried SiO2 underclad, 220 nm thick Si core, 10 nm thick SiO2 overclad). The parameters of CWs used for GRIN lens design are those listed in Table 1. The calculated distribution of light intensity at 190 THz propagating across the plasmonic GRIN lens is shown in Figure 3b. A clear focalization effect is observed at 14−18 μm distance from the rear end of the GRIN lens to the right end of the figure. Figure 4a shows a scanning electron microscope (SEM) view of the fabricated device. The fabrication of the sample is detailed in the Methods Section. The light is collected at the output of the lens using 9 waveguides. Varying the distance D between the lens and the waveguides allows the investigation of the focalization of the light beam. 4601

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Figure 4. SEM image views: (a) CWs-based GRIN lens. The eight areas evidenced by rectangles correspond to arrays with different CWs length (180, 175, 170 160, 140, 110, and 100 nm) located from the center to the border of the symmetric lens. (b) Enlarged view of the plasmonic GRIN lens showing the nine output waveguides (width 700 nm, separation distance 300 nm) used for collection of the transmitted light and intensity distribution measurements. (c) Plasmonic GRIN lens and output D = 4.2 μm distance from the plasmonic lens to the waveguides fan-shaped region. (d) Same as D but with output plane distance D = 13.2 μm.

shaped output waveguides varying from Dmin = 0.6 μm to Dmax = 24 μm with a step ΔD = 0.6 μm have been fabricated on the same wafer. The measurements of intensity distribution performed in such a way revealed that efficient focalization occurs for a separation distance from the rear end of the GRIN lens and the input end of the fan-shaped region about 10−14 μm. This focalization distance is a little smaller than the simulation result (14−18 μm) shown in the Figure 3b but the form of the transverse mode at the focal distance in a good agreement. The distribution of the light intensity profile corresponding to the distance D = 10.8 μm is displayed in Figure 6a. It can be observed that the light intensity in the waveguide corresponding to the center of the GRIN lens is order of magnitude higher as compared to its neighbors. The intensity distribution is markedly different from that of a blank structure without CWs GRIN lens shown in Figure 6c. Furthermore, the evolution with wavelength of the distribution of light intensity at the output plane of D = 10.8 μm from the lens is displayed as colormap in Figure 6b shows that focalization effect is wide-band and occurs in the frequency range 183−195 THz (1.54−1.64 μm wavelength). For higher frequencies (λ-1.5 μm) the light transmission becomes highly attenuated, especially in the region corresponding to the central part of the lens. The observed behavior fully agrees with that expected from the frequency dependence of composite waveguide effective index shown in Figure 2. Indeed, the CWs elements in the central part of the GRIN lens are having lower resonance frequency. By consequence above the resonance frequency the wavefront transmitted across the central part of the lens is heavily attenuated. At the same time the frequency of the resonant elements at the border of the lens being higher, the attenuation of light traveling across these regions is lower. In contrast, for the blank structure without lens the intensity distribution in the whole spectral range practically does not depend of the wavelength (Figure 6d).

The experimental characterization based on an end-fire coupling setup is shown in Figure 5. This experimental setup is detailed in the Methods Section.

Figure 5. Schematic of end-fire optical bench setup.

Special care was taken in the design of the SOI waveguide structure bearing CWs GRIN lens to ensure light propagation only in the fundamental TE mode. This point was especially critical since at a 10 μm width the waveguide is intrinsically multimode. To demonstrate the focalization properties of the CWs GRIN lens we employed a technique similar to that used in the early experiences on the photonic crystals “superprism”.46,47 The light transmitted through the CWs GRIN lens is collected by a fan-shaped set of 0.7 μm wide waveguides (Figure 4b−d), which is imaged by means of a 32× objective on a 1D CCD array camera. The role of the fan-shaped region is to rapidly increase the separation distance between output waveguides in order to avoid coupling and energy transfer between them. To determine the focus position a set of 40 structures with identical CWs GRIN lens design but a different distance D between the rear end of the GRIN lens and fan4602

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Figure 6. (a) Distribution of light intensity at 190 THz (1.58 μm) for a GRIN lens with output plane distance D = 10.8 μm. (b) Colormap of light intensity distribution as a function of frequency for a GRIN lens with output plane distance D = 10.8 μm. The focalization effect occurs from 183 to 195 THz. (c) Distribution of light intensity at 190 THz (1.58 μm) for a 10 μm wide SOI waveguide without GRIN lens. (d) Colormap of light intensity distribution as a function of frequency for a 10 μm wide SOI waveguide without GRIN lens.

Figure 7. Evolution of the distribution of light intensity with the variation of output plane distance D at different operation frequencies: (a) 200 THz (1.5 μm); (b) 195 THz (1.54 μm); (c) 190 THz (1.58 μm); (d) 185 THz (1.62 μm).

light intensity with the variation of output plane distance D. Figure 7 shows the evolution of light intensity distribution with distance from the rear end plasmonic lens at the frequencies of

To further evidence the focusing properties of plasmonic lens we reconstructed from the whole set of experimental data on the 40 fabricated structures the evolution of the distribution of 4603

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ACS Nano 200, 195, 190, 185 THz (1.5, 1.54, 1.58, 1.62 μm, respectively). The experimental results are in good agreement with 3D numerical simulations. As it can be seen the focalization effect is wideband (183−195THz), with a large focus range (10−16 μm) meaning increased robustness and tolerance with respect to the fabrication imperfections. Furthermore, despite the propagation across the 40 periods of CWs arrays, the additional losses induced by the presence of plasmonic nanoresonators are rather low (∼2−4 dB) making the considered approach viable for many practical applications, in particular for silicon photonics, especially what concerns optical interconnects applications. The great advantage of the considered approach is that realization of the index variation in this case does not require an etching procedure. By consequence the fabrication of waveguides and other passive optical elements for clock signal distribution in optical interconnects can be implemented on the same level used for transistors fabrication.

32× objective with 0.6 numerical aperture and is either measured with large area photodetector or high sensitivity 1D CCD array IR camera providing the spatial distribution of the transmitted light.

AUTHOR INFORMATION Corresponding Author

*E-mail: [email protected]. ORCID

Andre de Lustrac: 0000-0002-3814-1226 Notes

The authors declare no competing financial interest.

ACKNOWLEDGMENTS We would like to thank the C2N Orsay Cleanroom staff for their technological support.

CONCLUSIONS The demonstration of the focusing effect produced by CWs GRIN lens unambiguously proves the ability for taming the light flow in the guided wave structures through engineering of the local effective index by plasmonic CW nanoresonators. The great advantages of the considered solution with respect to the conventional multilayered metamaterials approach are simplified technology and reduced propagation losses. In contrast to photonic crystals approach, the resonant nature of plasmonic nanoresonators inclusions allows a much higher degree of freedom for the control of effective index. Depending on the operation with respect to the resonance frequency, effective index either higher or lower as that of the host slab waveguide can be obtained. The amplitude of the variation of the effective index depends of the quality factor of nanoresonators. By consequence there is room to augment the variation of the effective index well beyond that of natural materials by operating at lower frequencies and either considering MIR or THz photonic applications. The considered approach is quite generic and can be adapted to different type of planar lightwave circuits platforms: silicon, GaN/AlN, InGaAsP/InP, doped silica glass etc. The reported enabling technology brings the opportunity for the creation of a family of optical devices based on the use of plasmonic resonances to control the light at nanoscale.

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METHODS For the fabrication of the sample we use an undoped SOI wafer from SOITEC with a 220 nm thick top silicon film separated from the Si substrate by a 2 μm buried SiO2. The CWs pattern was defined with a NB4 electron-beam lithography process using PMMA positive resist. After the resist development, double step e-beam evaporation was performed to obtain a first 2 nm film of chromium and 50 nm film of gold. This metallization step followed by a lift-off serves to fabricate both the CWs and the metal alignment marks used for the second lithography step devoted to the waveguides definition. Waveguides pattern definition is also performed with a NB4 electron-beam lithography process using ZEP520A positive resist. Remaining resist after development is used as a soft mask for silicon etching. The silicon etching down to buried SiO2 is performed by using an inductive coupled plasma (ICP) process with a C4F8/SF6 gas mixture. For characterization, we use the setup of the Figure 5. Three tunable semiconductor lasers of the T100S series from Yenista Optics are used to scan a spectral range from 1250 to 1640 nm. A linearly polarized light beam is coupled into an input waveguide using a polarization maintaining lensed fiber. The output light is collected by a 4604

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