Letter pubs.acs.org/NanoLett
Dielectric Metasurface as a Platform for Spatial Mode Conversion in Nanoscale Waveguides David Ohana,† Boris Desiatov,† Noa Mazurski,† and Uriel Levy*,† †
Department of Applied Physics, The Benin School of Engineering and Computer Science, The Center for Nanoscience and Nanotechnology, The Hebrew University of Jerusalem, Jerusalem, 91904, Israel
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S Supporting Information *
ABSTRACT: We experimentally demonstrate a nanoscale mode converter that performs coupling between the first two transverse electric-like modes of a silicon-on-insulator waveguide. The device operates by introducing a nanoscale periodic perturbation in its effective refractive index along the propagation direction and a graded effective index profile along its transverse direction. The periodic perturbation provides phase matching between the modes, while the graded index profile, which is realized by the implementation of nanoscale dielectric metasurface consisting of silicon features that are etched into the waveguide taking advantage of the effective medium concept, provides the overlap between the modes. Following the device design and numerical analysis using three-dimensional finite difference time domain simulations, we have fabricated the device and characterized it by directly measuring the modal content using optical imaging microscopy. From these measurements, the mode purity is estimated to be 95% and the transmission relative to an unperturbed strip waveguide is as high as 88%. Finally, we extend this approach to accommodate for the coupling between photonic and plasmonic modes. Specifically, we design and numerically demonstrate photonic to plasmonic mode conversion in a hybrid waveguide in which photonic and surface plasmon polariton modes can be guided in the silicon core and in the silicon/metal interface, respectively. The same method can also be used for coupling between symmetric and antisymmetric plasmonic modes in metal−insulator− metal or insulator−metal−insulator structures. On the basis of the current demonstration, we believe that such nanoscale dielectric metasurface-based mode converters can now be realized and become an important building block in future nanoscale photonic and plasmonic devices. Furthermore, the demonstrated platform can be used for the implementation of other chip scale components such as splitters, combiners couplers, and more. KEYWORDS: Dielectric metasurface, waveguide, mode converter, nanoscale, effective medium
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antennas, and motivated the realization of mode converters between these modes.4,5 Additionally, the high confinement of plasmonic modes, and in particular gap plasmons modes, makes them suitable for applications such as nanoscale optoelectronics integrated circuits (ICs),6−8 light-matter interactions,9 nanoantennas,10 enhancement of nonlinear processes,11,12 nanolithography,13 nanomemories,14 and nanodetectors15 to name a few. Their high propagation loss, however, is an obvious bottleneck. Therefore, it seems attractive to combine photonic devices with plasmonic components in order to take advantage of the low loss of photonic devices. Crossing the bridge between these two fields is possible by making use of photonic to plasmonic mode converters. Various schemes have been proposed for applying photonic/ photonic,16−21 plasmonic/plasmonic,4,5,22 and photonic/plasmonic23−26 mode conversion. Recently,27 we have proposed a
he ability to manipulate light in the form of converting its spatial shape between different eigenmodes of optical waveguides is of central importance in future nanoscale photonic and plasmonic information systems. In photonics, mode converters are key components for the realization of, for example, on chip mode division multiplexing (MDM) optical nanocircuits.1 Moreover, different waveguide modes have distinct properties that can be exploited for a variety of applications. For example, it was shown2 that the first antisymmetric transverse electric (TE) mode of a silicon strip waveguide behaves as the one-dimensional (1D) equivalent of a radially polarized beam, and hence has the ability to enhance the energy density at the apex of a nanoscale metallic tip that is very useful for nanofocusing applications. Similarly, the symmetric and antisymmetric plasmonic modes in metal− insulator−metal (MIM) or insulator−metal−insulator (IMI) structures have different properties in terms of mode confinement, effective index, and losses (or propagation length).3 These properties can be exploited in controlling light enhancement and propagation, for example, in nano© 2016 American Chemical Society
Received: October 11, 2016 Revised: November 8, 2016 Published: November 14, 2016 7956
DOI: 10.1021/acs.nanolett.6b04264 Nano Lett. 2016, 16, 7956−7961
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couples to the other desired mode. This coupling length is inversely proportional to the coupling coefficient between the modes which in turn is proportional to the spatial integration of the term Em*(x,y)·Δñ(q)(x,y)·Ej(x,y), where Em*(x,y) and Ej(x,y) are the transverse cross sections of electric field of the mth and jth eigenmodes, respectively, and Δñ(q)(x,y) is the qth coefficient in the Fourier series of Δn(x,y,z). Therefore, a proper choice of the transverse profile Δn ← (x,y) will maximize the coupling coefficient and minimize the coupling length. We refer to the above expression as the “field overlap” integral. For clarity we summarize that “phase matching” is satisfied by choosing the appropriate period of the perturbation along propagation direction. Once “phase matching” had been established, proper choice of the graded index profile along the transverse direction is essential in order to achieve short coupling length. Realization of the graded index profile in a waveguide is achieved by the implementation of a dielectric metasurface consisting of nanoscale features that are etched into the waveguide. The desired refractive index profile is related to the grating features by the effective medium theory (EMT) approximation.29 According to this theory, a subwavelength periodic structure consisting of alternating layers of n1 and n2 refractive indices, acts as if it has an average refractive index over its spatial dimensions instead of rapid index variations. Up to the second order approximation, the average refractive index is related to n1 and n2, the period Λ of the layers, the duty cycle, and the wavelength. If the period is constant but the duty cycle varies locally along the structure, one can obtain a graded index profile as required. It was shown theoretically27 that by using the aforementioned method, mode conversion between different photonic modes (symmetric and antisymmetric) of a silicon waveguide can be achieved. The nanoscale dielectric metasurface consists of a periodic structure in transverse direction made of alternating layers of silicon and air with period on the order of hundreds of nanometers and minimum features (air gap or silicon) size as low as few tens of nanometers. As mentioned before, the strength of this method is that the same design concept can be implemented for the realization of plasmonic/ plasmonic, or photonic/plasmonic mode conversion. An example of photonic to SPP mode conversion is studied numerically in the Supporting Information. Next we provide an experimental proof for the capability of the proposed approach to perform efficient mode conversion. To do so, we have focused our efforts on demonstrating nanoscale metasurface based mode converter in a silicon rib waveguide. The waveguide cross sectional dimensions are 1 μm width and 220 nm height with SiO2 and air as bottom and upper claddings, respectively. With these core dimensions at 1.55 μm wavelength, we found that the waveguide supports the first two TE polarized modes (designated as TE0 and TE1). Following our previous design procedure,27 we found that the suitable design parameters of the converter are n0 = 3.29 and Δnmax = 0.08 with rectangular grating of period δ = 4.29 μm and duty cycle of 50% along the propagation direction. n0 is the unperturbed refractive index and Δnmax represents the amplitude of the periodic perturbation Δn(x,y,z) along the propagation direction (z-axis). The choice of Δnmax = 0.08 is a compromise between too low index modulation, which results in insufficient coupling and longer device, and too high index modulation, which might lead to mode mismatch and high scattering. As explained before, the index profile along the
generic approach based on nanoscale dielectric structures that could be implemented for the application of photonic mode conversion. While the approach could be criticized for its challenging implementation, we have now faced the challenge as we experimentally demonstrate an operating mode converter with highly promising metrics. Furthermore, we show the generality of our approach for performing not only photonic/ photonic mode conversion but also other conversions of interest, for example, photonic/plasmonic mode conversion. The operation principles of the metasurface-based mode converter are explained in detail in our previous publication27 and thus will be described here briefly. In short, the propagation of electromagnetic field in a perturbed dielectric structure can be approximated by the coupled mode theory (CMT).28 According to CMT, periodic perturbation in the dielectric media acts as a grating that diffracts the incident mode into another mode by providing phase matching, that is, by changing its wave vector as to fit to the wave vector of the output mode. The metasurface based mode converter is sketched in Figure 1. We designate the periodic perturbation
Figure 1. (a) The desired refractive index profile of the device. It is consisting of a rectangular periodic profile along the propagation direction and continuous graded index profile along its transverse direction. (b) Binary height profile of the metasurface device. (c) A 3D conceptual model of the physical binary grating structure. Si fraction relative to air varies across the x-axis and creates the required graded index profile along that direction.
as Δn(x,y,z), having its periodicity of period δ along the z-axis, which is also the light propagation direction. We designate βm as the propagation constant in the z-direction corresponding to the mth guided mode. Its coupling to the jth mode occurs if “phase matching” condition is satisfied, that is, (βm − βj − 2πq/ δ) = 0 where q is the diffraction order q = 0, ±1, ±2, and so forth. In other words, the grating period should be chosen as to compensate for the β mismatch of the two modes. Nevertheless, while phase matching is needed, it is not a sufficient condition for efficient coupling to occur. Clearly, one needs to take into consideration also the coupling length, that is, the position along the z -axis in which 100% of the mode power 7957
DOI: 10.1021/acs.nanolett.6b04264 Nano Lett. 2016, 16, 7956−7961
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Nano Letters transverse direction is realized by the implementation of nanoscale dielectric metasurface consisting of air features that are etched into the silicon waveguide with a constant period of Λ = 333 nm and variable duty cycle calculated using the EMT. Etching depth is 70 nm. Thus, the end result is a waveguide with nanoscale air patterns along both the transverse and the longitudinal axes, partially etched to 70 nm depth. Figure 1a shows the required refractive index profile of the device with rectangular variation along the propagation direction. Figure 1b shows the height profile of the dielectric metasurface device. In Figure 1c, we show a 3D conceptual model of the actual physical structure of the metasurface to be implemented in the silicon waveguide in order to obtain the required refractive index profile via the EMT approximation. Note that the actual device is longer than that shown in Figure 1 (see Figure 2a).
by reactive ion etching (RIE) process. Because of the height difference between the waveguide and the mode converter, two consecutive steps of lithography and etching with high precision alignment were performed. The first step was aimed to produce the waveguide pattern while the second step is used for the definition of the mode converter pattern over the waveguide. Clearly, achieving nanoscale alignment accuracy is important. SEM images of a fabricated device are shown in Figure 3.
Figure 2. TE0 to TE1 mode conversion with EMT based graded index rectangular grating. (a) Refractive index profile of the device. The right and left uniform sections represent the input and output waveguides, and the intermediate segment between them is the converter section. (b) Analytic calculation of the power exchange between the two modes. Calculation method is described in ref 27 (c) A 3D FDTD simulation of the Ex̂ field (in-plane) propagation in the device.
Figure 3. SEM images of a fabricated device which composed of input and output waveguides and TE0 to TE1 mode converter. (a) Slant view. (b) Top view.
Following device fabrication, we turn into its experimental characterization. The main optical parameters we aim to characterize experimentally are the mode purity and transmission. In order to quantify the mode purity parameter, we excite the fundamental mode at the input section of the waveguide. The light is coupled via polarization maintain (PM) fiber to a lensed fiber which is used to inject the light into the input waveguide. The near field intensity of the mode at the output waveguide is then imaged onto an IR camera using a “home built” optically corrected microscope with ∼300× magnification and effective numerical aperture (NA) of 0.3. We can analyze the modal content of the output mode by fitting the measured intensity to the calculated one while assuming a near field of the form E(x,y) = a·TE0(x,y) + (1 − a)TE1(x,y), where TE0(x,y) and TE1(x,y) are the electric field profiles of the TE0 and TE1 modes, respectively, and a denotes the weight factor (0 ≤ a ≤ 1). Transmission measurement is performed by replacing the microscope and camera of the imaging setup by an additional lensed fiber which is connected to a power meter. When simulating the image of the output mode the difference between the near-field and far-field intensities needs to be taken into consideration. Ideally, one would like to image the near-field profile as it appears on the external facet of the output waveguide. Clearly, the near-field differs from the far-field intensity, which is actually obtained at the image plane of the microscope due to two major reasons. The first is related to the total internal reflection (TIR) experienced by light at the output facet of the waveguide. Calculating the Fourier transform of the TE0 or TE1 mode profiles in the silicon waveguide reveals that it consists of a spectrum of plane waves
On the basis of the design parameters, we performed a 3D FDTD simulation30 to study light propagation through the device after being excited by the TE0 mode at the input section of the waveguide. The results are shown in Figure 2. Indeed, one can clearly observe the conversion into the TE1 mode. Decomposition of the numerically computed output field in the basis of the waveguide eigenmodes enables us to determine the power transmission of each mode through the device. We make use of these results in order to compute the “Mode purity”, defined as the ratio between output mode power (TE1 in our case) and the total transmitted power. With the aforementioned design parameters and with mode converter length of 23 μm we are expecting for mode purity of 96.5%, and total transmission (that is, the ratio between total transmitted and the incident power) of 92%. Our simulations also indicate that reduced mode conversion due to fabrication imperfections such as inaccuracy of the etching depth, deviation in the features dimensions or misalignment between the converter and the waveguides, can be mostly compensated via modifying the mode converter length. Thus, we fabricated mode converters with different lengths. The devices were fabricated using silicon-on-insulator (SOI) substrate with device layer of 220 nm on top of 2 μm buried oxide (BOX). The waveguide width is 1 μm and SiO2 and air serve as bottom and upper claddings, respectively. Both the waveguide and the superimposed mode converter were defined with standard electron-beam (EBEAM) lithography followed 7958
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Figure 4. (a) Calculated far-field intensity of TE0 mode of a strip waveguide using NA = 0.3 while assuming near field of the form 1TE0 + 0TE1. (b) Measured far field intensity of the output from the strip waveguide as obtained in the IR camera. (c) Cross section of (b) at Y = 0 μm. (d) Calculated far field intensity of TE1 mode using NA = 0.3 while assuming near field of the form 0.05TE0 + 0.95TE1. (e) Measured far field intensity of the output from the fabricated device as obtained in the IR camera. (f) Cross section of (e) at Y = 0 μm. The magnification was 270× and the images were scaled in both dimensions with respect to the object plane (that is, the waveguide output facet plane) in order to be comparable to the calculated images.
waveguide of the mode converter. We perform this measurement in order to confirm that the modal content is as expected. Our expectation to find approximately 100% of the fundamental TE0 mode is indeed verified as can be seen in Figure 4a−c, where the calculated and measured far field intensities and their cross sections are presented and compared. The calculated far-field presented in Figure 4a is based on that the near-field is composed of 100% of the TE0 mode (that is, a = 1). Next, we use the same imaging system to measure the intensity at the output of the mode converter device. We measured several devices and found that optimal conversion is achieved with mode converter length of 22.5 μm and at wavelength of 1556 nm. The slight deviation from the nominal design of 23 μm length at wavelength of 1550 nm can be attributed to fabrication tolerances. In Figure 4d−f, we present the calculated and measured far-field intensities and their cross sections. By fitting the heights of the brighter and darker lobs of the calculated image to the measured one, as can be seen in Figure 4f, we estimate that the mode purity of the output field is ∼95%, that is, that the overlap integral of the obtained field with the TE1 mode, normalized to the overlap integral with all modes is 0.95. Accordingly, the calculated far-field presented at Figure 4d is based on the assumption that the near-field is composed of 95% of the TE1 mode (that is, a = 0.05). The asymmetry in Figure 4d,e is a direct result of the interference between desired antisymmetric mode and the undesired “leftovers” of the symmetric mode. The asymmetry is enhanced by the transfer function of the imaging system being
propagating inside the waveguides with different wavenumbers kx, ky in (x,y) plane. Remembering that31 the propagation constant is expressed as β = (k 0ncore)2 − kx2 − k y2 = k 0ncore cos ϕ, where k0 is the wavenumber in vacuum and ncore is the core refractive index. This means that each plane waves is propagating with unique angle ϕ relative to the propagation direction z. Careful investigation shows that there is a range of angles that are larger than the critical transmission angle at silicon/air interface, and therefore the corresponding plane waves are evanescent in the air medium that is, decay after propagation distance of few wavelengths. These waves does not reach the microscope entrance pupil and therefore do not contribute to the image captured at the focal plane. In that manner the output facet of the waveguide serves as a low pass filter of spatial frequencies. In fact this is the same as to say that the image is formed by a microscope having NA of 1, while the NA of the silicon waveguide appears to be larger. A realistic microscope (which is not oil immersed) has NA lower than 1. This will further reduce image resolution due to diffraction, and this is the second reason for the difference between the near field intensity and the final image. Actually, the final image can be calculated as the Fourier transform of the truncated far field amplitude at the entrance pupil of the objective lens.32 Using the previous method, we measured the mode purity of a reference device, consisting of a strip waveguide (that is, waveguide that does not incorporate the mode converter structure), which was fabricated with the same parameters and under the same conditions and procedures as the input 7959
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a symmetric low pass filter. As a result, the antisymmetric mode (having high spatial frequencies) is greatly attenuated by the system, whereas the symmetric mode (having lower spatial frequencies) is experiencing less attenuation and is thus more dominant in the measured image. Transmission characterization of the device was also conducted by measuring the transmitted power of the fabricated device with respect to that of a reference waveguide of the same length. By comparing the average output power in the two measurements, we conclude that that transmission of the mode converter relative to a strip waveguide is 88% ± 15%. The theoretical value from the 3D FDTD simulation is 92%. The slight difference and the relative error in the measurement are primarily attributed to the nonperfect fabrication process (e.g., different roughness relative to the reference waveguide, nonuniformity of the etched features dimensions, and shift from their expected position) and the setup stability (e.g., its sensitivity to the fibers position with respect to the measured device). We believe that this result can be improved by carefully optimizing the fabrication process and by improvement of the setup stability. Furthermore, the theoretical value can also be improved by applying an adiabatically varying structures. In conclusion, we designed, fabricated, and experimentally demonstrated a nanoscale mode converter enabling the conversion of TE0 to TE1 mode in a 1 μm × 220 nm silicon waveguide. The device has a periodic variation in its refractive index along the propagation direction and a graded index profile along the transverse direction. The graded index profile is realized by the implementation of nanoscale dielectric metasurface consisting of silicon features that are etched into the waveguide based on the concept of effective medium theory. Mode coupling is analyzed in the framework of the coupled mode theory (CMT). The device was tested by directly measuring the modal content in the far field intensity obtained from a reference waveguide and from the mode converter, using optical imaging microscopy. The measured mode purity is estimated to be 95% and the transmission relative to a strip waveguide is about 88%. These results are in good agreement with 3D FDTD simulation results of the device. We believe that this demonstration lays the foundations for the realization of this concept for conversion of photonic to plasmonic modes or of different plasmonic modes in MIM/IMI structures. Furthermore, our device offers robustness and relaxed tolerances to fabrication imperfections, which is a direct result of the analytic design approach. This is an important advantage compared with previously published mode converter devices,33−35 which are mostly based on numerical optimization that tends to be more sensitive to fabrication imperfections. The analytic design approach was also shown to be useful for the demonstration of chip scale metamaterials for focusing applications.36,37 As such, while this paper was focused on the demonstration of mode converters, our approach can also be used to implement other nanoscale devices, for example, splitters, combiners, couplers, and more. Finally, it should be noted that the approach demonstrated here expands the capabilities of metasurface significantly. Following the large body of work in metasurfaces operating in free space configuration,38−56 the ability to implement metasurfaces in guided mode configuration paves the way for efficient implementation of such devices in chip scale applications.
Letter
ASSOCIATED CONTENT
S Supporting Information *
The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.nanolett.6b04264. Mode conversion from photonic to plasmonic modes (PDF)
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AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. ORCID
Uriel Levy: 0000-0002-5918-1876 Author Contributions
D.O. designed and simulated the device, performed the experiments, analyzed the data and wrote the paper; B.D. performed the experiments and supported the fabrication of the device; N.M. fabricated the device; and U.L. supervised the project and wrote the paper. All authors have given approval to the final version of the manuscript. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS We thank Liron Stern for fruitful discussions. The devices were fabricated at the Center for Nanoscience and Nanotechnology, The Hebrew University of Jerusalem.
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