Ultrashort and efficient adiabatic waveguide taper ... - OSA Publishing

Vol. 25, No. 17 | 21 Aug 2017 | OPTICS EXPRESS 19894

Ultrashort and efficient adiabatic waveguide taper based on thin flat focusing lenses JINGJING ZHANG,1,2 JUNBO YANG,1,2,* HE XIN,1,2 JIE HUANG,1,2 DINGBO CHEN,1,2 AND ZHANG ZHAOJIAN1,2 1

College of Science, National University of Defense Technology, Changsha 410073, China Center of Material Science, National University of Defense Technology, Changsha 410073, China * yangjunbo008@sohu.com 2

Abstract: A new structure is reported, which realizes the flat focusing by introducing the silicon subwavelength slits into the waveguide. The subwavelength silicon-air slits, with variable widths to match the phase compensation, makes possible to focus a plane wave. The flat lens proposed here demonstrates relatively high power gain at the focal point or two focal points. By using such a design, we demonstrate a grating coupler with an ultrashort taper of 22.5-μm to connect a 10-μm-wide input waveguide and a 0.5-μm-wide output waveguide, achieving a transmission up to nearly 95.4% numerically in the communication band. The length of which is one-twentieth of that for the traditional taper. To our best knowledge, this work is the first demonstration of an ultrashort taper based on flat lens, which significantly improves the integration of the photonics integrated circuits, and indicates an effective solution for potential applications in compactly integrated micro/nano optical devices. © 2017 Optical Society of America OCIS codes: (130.0130) Integrated optics; (230.7405) Wavelength conversion devices; (220.3630) Lenses.

References and links 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15.

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#297663 Journal © 2017

https://doi.org/10.1364/OE.25.019894 Received 8 Jun 2017; revised 21 Jul 2017; accepted 31 Jul 2017; published 8 Aug 2017 Corrected: 22 Aug 2017


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1. Introduction With the development of the integrated optics, micro lens, a key component in the on-chip optical imaging systems, is enabled to have a miniaturized size. While the conventional lens with large footprint is shown to have a limitation on compact integration, the thin flat lens developed recently can solve such an awkward problem. In the past decade, lenses based on the subwavelength metasurface (consist of subwavelength structure array in the film) are studied diffusely, where numerous structures have been proposed with an operating wavelength ranging from the visible light spectral band to the Herizian band [1–10]. Based on these structures, one can realize the beam focusing, deflection, holography and polarization handle. For example, the gradient index (GRIN) metamaterial lens can change the beam propagation direction, when the electric field and the magnetic field property of the medium are appropriately designed based on the transformation optics [11]. More specifically, Ref [11] demonstrates a focusing at 9.45 GHz using a lens fabricated with commercial dielectric materials. This design is implemented by stacking dielectric layers, yet the length of the lens, 19.05mm, is not suitable for on-chip integration. Moreover, by taking the wavelength dependence into account, achromatic metasurface structures are designed [12–14]. Ref [12] presents a multi-wavelength achromatic metasurface at visible light, introducing multiple metallic nano-groove gratings to enhance diffractions for transverse magnetic polarization in an ultrawide incident angle ranges, but brings extra loss. Ref [13] shows silicon metasurfaces at visible band, which is capable of wave front manipulation for red, green, and blue light simultaneously. This report also provides a method of full phase-control, that is, by independently changing the in-plane orientations of the corresponding nanoblocks, the required geometric phases at communication band are induced. A two-wavelength lens at terahertz band with independent phase and amplitude control is introduced in Ref [14], while an achromatic flat focusing based on all-dielectric silicon subwavelength metasurface operating at a spectral range of 8-10 µm is demonstrated in Ref [15]. However, the operating wavelength of these structures detunes far from the communication band, therefore cannot be applied to the optical integrated circuit especially for on-chip communication applications. Although a lens based on surface palsmon polaritons (SPP) metallic-insulator-metal (MIM) waveguide realizes achromatic structure at spectral range from 1µm to 2µm, it suffers from significantly energy loss [16]. As most of the previous research focus on the nature analysis of the lens or the simple indication of the potential applications, it is also worth more noticing to introduce the flat lens in to the silicon-on-insulator (SOI) waveguide in order to realize the


functionalists such as wavelength division multiplexing, beam splitters, compact integrated optical circuits, and so on. In this paper, we introduce a single focus lens and a two focus lens based on SOI chip for communication band. Since there is no metallic structure introduced, high transmission efficiency which is the ratio of energy of the incident light to the output light can be achieved. Grating couplers [17,18] helps to connect the waveguide and the optical fiber. The light is coupled from the fiber, collected by the grating coupler on a multi-mode waveguide (~10-μmwide), and then coupled into a single-mode waveguide. As the mode mismatching between the multi-mode and the single-mode waveguides results a large extra loss, it remains a challenge to achieve high coupling efficiency. Although by carefully designing the dimension of the waveguide taper can partly solve such a problem, the adiabatic propagation between the multi-mode waveguide the single-mode waveguides requires a long optical length. For example, the suitable taper length needs to be larger than 400μm [19] for efficient connection between a 12-μm-wide multi-mode waveguide and a 0.5-μm-wide single-mode waveguide. Such a long taper not only brings extra propagation loss, but also degrades the compact of the photonic integrated circuits due to their large footprint. On the other hand, by using focusing grating couplers [20], the taper length can be shortened to tens of microns, yet remains the problems of unstable polarization of the output light and the difficulty of the fabrication approaches. Recently, a focusing subwavelength grating (SWG) for efficient coupling of a suspended membrane germanium (Ge) photonic integrated circuits (PICs), which enables mid-infrared applications in the entire fingerprint region, is reported in [21], but not practical for most silicon photonic integrated circuits. Ultra-broadband grating couplers with focusing curved subwavelength structures for silicon photonics optical interfaces are demonstrated in Ref [22]. The device footprint is miniaturized to only 40 µm × 20 µm, yet the coupling efficiency is only -4.7 dB near 1.55μm. Focusing grating couplers both in SOI and the goldon-SOI platform is presented in Ref [23], with a coupling efficiency of only 20% and a large footprint of 18.5µm × 28µm. A compact lens-assisted focusing tapers fabricated on SOI is proposed in Ref [24]. By introducing a symmetric bi-concave lens with a radius of curvature of 6µm, the refractive index is engineered to realize compact focusing tapers with length of ranging from 10µm to 20µm. However, the loss of the tapers for transverse electric (TE) polarization is as large as 1dB and the production process is particularly complicated. The difference of etching height between waveguide and lens brings difficulty to fabricate the structure through a single step of etching. Ref [25] demonstrates an ultracompact taper between a linear grating coupler and a single-mode SOI waveguide. Using a quadratic sinusoidal function, they propose a taper with a length of merely 15 µm and have an insertion loss as low as 0.22 dB at 1.55μm; however the exhibited structure is more complex than the adiabatic waveguide taper. Hence, we motivate to have a one-step etching structure, which is more practical than that in Ref [24], preferable to have a more reliable and more reproducible performance than Ref [25]. In this paper, we presented an electrically thin GRIN lens which was composed of period dielectric layers (slit and block) based on SOI technology. The operating wavelength was centered at 1.55μm. By designing subwavelength silicon-air slits array with variable widths to match the phase compensation, the proposed structure can modulate the wave front of light and further consequently focus a plane wave at a point. According to the identical principle,, the two focus lens making the light focus at two points, are proposed according to the identical principle, which works as a beams splitter. At last, we introduce the flat lens into a 22.5-μm-long taper to couple the input light from a 10-μm-wide multi-mode waveguide to a 0.5-μm-wide single-mode waveguide. The transmission efficiency is achieved 95.4% in the communication band. Differ from the traditional taper using a gradient structure to make the power field in the multi-mode waveguide match with in the single-mode waveguide, this process is adiabatic. As we introduce lens into the taper, the length of taper is reduced significantly, while the energy intensity is enlarged. In addition, due to the same etching


height of the waveguide and lens, 220nm, we can fabricate our structure through a single step of etching. The structure is shown in Fig. 1.

lens

taper

Fig. 1. The proposed structure consists of grating couplers, thin lens and a taper. The incident light is coupled from the fiber to the slab waveguide by the grating couplers; input light is coupled from multi-mode waveguide to single-mode waveguide by the taper with the lens; the black dotted line represents the detection area, where the micro-nano devices can be placed for testing. Where Pin is the input power, pout is the output power. The transmission efficiency (T) is defined as the ratio of outputs to inputs (T = Pout/Pin) Our structure is based on an SOI wafer with a 220-nm-thickness top silicon layer and a 2-μm-height silica.

2. Principle and design

Fig. 2. (a) Schematic of the metasurface lens with one focus; (b) Schematic of the metasurface lens with two focus.

The principle of the phase compensation is also called Fermat principle described by Fig. 2, which is also the principle diagram of the lens. It is composed of periodic subwavelength silicon block and air slit units. Each unit has uniform period (T) and the lens thickness (d), but different slit width (w). In order to coverage the incident rays paralleling with the optical axis to a focus, the value of effective refractive index for each layer is determined by the following relation, nd + F = nm d + bm

(1)

where n is the effective refractive index of the central layer; nm is that of the mth layer; F is the distance from the lens to the focus; and bm is the distance between the midpoints of the mth layer and the focus. Equation (1) indicates that the optical path of parallel ray incident from the center layer to the focus is equal for all of the layers, as shown in Fig. 2(a). The two focus lens, based on the same principle, is a mirror symmetric structure of single-focus structures, as shown in Fig. 2(b). By introducing the subwavelength structure into the dielectric waveguide, one can tailor the effective refractive index of incident light in the waveguide. After etching air slit in the multi-mode waveguide, N can be calculated by the Eq. (2) TE N eff =

2 fnAir + (1 − f ) nSi2

(2)


where f (f = w/T) is the filling factor of the layers, determined by the ratio of the width (w) of slit and the period (T) for a layer. The material refractive index is set at nSi = 3.48 and nAir = 1 for silicon and air, respectively. According to Eqs. (1) and (2), we calculate the proposed filling factors for 20 unit cells. The values of f are shown in Fig. 3(a). We also show the corresponding effective refractive index of each cell according to their filling factor in Fig. 3(b) and the phase-shift Φ at the plane of the lens in Fig. 3(c).

Fig. 3. (a) The filling factors of each cell; (b) The effective refractive index of each cell; (c) The flat lens induce the phase shift Φ of each cell with the period T = 0.5μm, the width d = 0.5μm and the etching height H = 220nm.

According to Eq. (1), the effective refractive index and the phase-shift Φ should behave as parabolic distribution in Figs. 3(b) and 3(c). Since the period number of the lens is limited by the waveguide width while the periodic boundary is not strictly satisfied, the effective refractive index and the phase-shift Φ given by Eq. (2) can be simply approximated to the calculation shown in Figs. 3(b) and 3(c). Therefore the light passing through a flat lens focuses to a point in X axis. We introduce a thin flat lens to 10-μm-wide multi-mode waveguide. The period of each cell is 500nm; the thickness (d) of the lens is 500nm; the focal length is 16µm. We use the FDTD solution to simulate our design. The result is shown in Fig. 4. The light is converged to


about 2 microns spot at the focus. The theoretical computing is agreed with the simulation results. https://www.lumerical.com/tcad-products/fdtd/

Fig. 4. (a) Magnitude of the simulated x directed Poynting vector over the x–y plane; (b) The cross section of the optical field distribution for input; (c) the cross section of the optical field distribution for the output.

Figure 4 shows the Poynting vector and the cross section of the optical field distribution for the input and the output at 1.55μm. Field concentrates around the focus distanced 16μm from the plane of lens. The size of flare distributed in the waveguide is clearly reduced as shown in Figs. 4(b) and 4(c). A ~8-μm-width input field is reduced to a ~2-μm-width field, with an absolute transmission efficiency of 89.7% at 1.55μm. The two focus lens is also designed, the simulation result of which is shown in Fig. 5. The two focus lens consists of a mirror single-focus lens-pair, which are mirror symmetrically structured. The parallel ray incident from the center of the lens is converged into two beams at each focus. Furthermore, the multi-focus lens can be designed using the same conception, that is, a series of singlefocus lens aligned along the vertical direction of the light is designed.

Fig. 5. Magnitude of the simulated x directed Poynting vector over the x–y plane for two focus design.


The width of the air slit is a key parameter for the lens designing. From the phase compensation, a phase shift is induced when adjusting the value of the width d. TE-polarized incident light is focused at different point along x direction and achieves different transmissivity at wavelength λ = 1.55μm. The impact of d on lens performance is revealed in Fig. 6. Figure 6(a) indicates that the length of focal point for parameter d in value range from 0.3μm to 1.0μm is changed. When the width d varies from 0.3μm to 0.8μm, focal points are roughly at the same position, where the light is gathered at the location of 16μm away from the plane of the lens. This is because we calculate effective refractive index only considering filling factor (f), when the thickness of lens (d) is largely less than the focal length (F). The silicon- air slit provides compensation of the optical path difference for the beams propagation at different layer. When the thickness of the lens changed from 0.3μm to 0.8μm, the compensation-induced optical path reflected a negligible difference in the focal point distance. In addition, the transmission efficiency of our design with parameter d changing fluctuates negligibly as can be seen from Fig. 6(b).

Fig. 6. (a) The focus position changed with d; (b) The transmission efficiency of the lens changed with d.

We choose d = 0.5μm to design an ultrashort adiabatic waveguide taper under the roles shown in Eq. (3) [19]

θ