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Letter
Vol. 40, No. 22 / November 15 2015 / Optics Letters
Biperiodic nanostructured waveguides for wavelength-selectivity of hybrid photonic devices A. TALNEAU,1,* X. POMMARÈDE,1 A. ITAWI,1 K. PANTZAS,1 A. LUPU,2
AND
H. BENISTY3
1
Laboratoire de Photonique et de Nanostructures, Route de Nozay, F-91460 Marcoussis, France IEF, CNRS, UMR 8622, Univ. Paris-Sud, 91405 Orsay Cedex, France 3 Laboratoire Charles Fabry, Institut d’Optique Graduate School, Univ PSud, 2 Avenue Augustin Fresnel, F-91127 Palaiseau, France *Corresponding author: [email protected] 2
Received 24 August 2015; revised 7 October 2015; accepted 10 October 2015; posted 12 October 2015 (Doc. ID 248520); published 2 November 2015
A biperiodic nanostructuration consisting of a superperiodicity added to a nanohole lattice of subwavelength pitch is demonstrated to provide both modal confinement and wavelength selectivity within a hybrid III-V on a silicon waveguide. The wavelength-selective behavior stems from finely tuned larger holes. Such biperiodic hybrid waveguides have been fabricated by oxide-free bonding III-V material on silicon and display well-defined stop bands. Such nanostructured waveguides offer the versatility for designing advanced optical functions within hybrid devices. Moreover, keeping the silicon waveguide surface planar, such nanostructured waveguides are compatible with electrical operation across the oxide-free hybrid interface. © 2015 Optical Society of America OCIS codes: (230.3120) Integrated optics devices; (130.7408) Wavelength filtering devices; (130.5296) Photonic crystal waveguides; (220.4241) Nanostructure fabrication. http://dx.doi.org/10.1364/OL.40.005148
Integrated photonics will boost the performances of optical networks links. Within photonics integrated circuits (PIC), emission/amplification and isolation are two major optical functions to be included. Si-based approaches can provide monomode sources, including rare-earth-doped waveguides operating under optical pumping [1], whereas a tandem-modulator-based isolator performs the optical isolation [2]. The most widely used approach leading to the best present performances relies upon hybrid silicon photonics, wherein III-V semiconductors provide light amplification and emission, while materials such as garnets provide optical isolation. When both materials are associated with a very thin intermediate layer to silicon, the optical guided mode is mainly selected by the chosen silicon structure, usually a rib waveguide [3,4]. If any advanced optical function is needed, an extra processing step is required to carve the adequate added structure; for instance, a grating on top of the guide [5] or a lateral grating [6] for wavelength-selective lasing operation. We propose here to carve the silicon guiding layer prior to bonding, specifically implementing guidance with a 2D photonic 0146-9592/15/225148-04$15/0$15.00 © 2015 Optical Society of America
crystal (PC) operating essentially below its photonic gap. When properly tailored, thanks to the huge range of effective indices that can be obtained in silicon/air composites, such a nanostructure can favor virtually any spatial or spectral characteristics for the propagated optical mode. A subwavelength below bandgap periodicity, in particular, is compatible with a broad range from the lasing long wavelength to the other shortwavelength limits (multimodal onset, silicon or III-V absorption, etc.). This sub-λ silicon waveguide patterning allows one to implement advanced optical functions in a single technological step and also retains a plane Si bonding surface that is oxidefree bonding compatible. This allows electrical injection through the hybrid interface, which is of great interest for the future of hybrid devices operation [7]. In this Letter, a sub-λ 2D photonic bandgap structuration is designed for modal confinement, and a biperiodic structuration in the propagation direction is added to provide wavelength selectivity. We calculate and demonstrate experimentally that this biperiodic patterned waveguide operates as a wavelength selection mechanism. For modal simulation, being in the subphotonic bandgap regime, effective medium theory (EMT) has been implemented to represent the nanopatterned material. EMT is of interest since simulation of the exact geometry requires a tiny meshing that leads to highly demanding computational resources. EMT allows fast and accurate investigation for large ranges of the several geometrical parameters under consideration. Then, a 2D modal analysis is performed to calculate the effective index of the fundamental mode. For the spectral behavior, a 3D finite-difference time-domain (FDTD) is performed to determine the geometry of the added super-periodicity. Both SOI waveguides, as well as hybrid InP/SOI oxide-free bonded waveguides, are fabricated and measured. Such a design has the potential of being included for singlemode longitudinal operation in hybrid III-V/SOI DFB lasers, providing on a single technological step both the modal confinement and the wavelength selectivity. More generally, according to the unit cell shape, a large number of optical functions can be addressed [8]. This approach offers a great potential of being compatible with any kind of hybrid environment. The optical waveguide has a generic shallow ridge shape, its core is not structured and both lateral claddings are composed
Letter of the same 2D PC operating below its photonic gap. Here, the 2D PC is a square array of air holes drilled in the silicon guiding layer. To investigate a large number of geometrical parameters with reasonable computing resources, the EMT is implemented to represent the 2D PC material [Fig. 1(a)] and propagation occurs along the z direction. EMT has been demonstrated to fully represent a periodic nanostructured medium when its pitch Λ is much smaller than the wavelength λ, α Λ∕λ ≪ 1 [9–11]. The nanostructured material behaves like a uniaxial material. For the electric field aligned with the direction of invariance (here, the y direction), the resulting permittivity of the extraordinary index ne is the mean value of the involved permittivities [9]. The ordinary index no is here obtained from the dispersion curve of a 2D PC calculated by a plane wave expansion method [Fig. 1(c)], the 2D PC period being 150 nm in the transverse direction and 110 nm in the longitudinal direction, already taking into account the specific geometry dedicated to wavelength-selective operation [12,13]. Both calculated ordinary and extraordinary indices are plotted in Fig. 1(b) versus the air-filling factor and show the basically uniaxial behavior of the patterned material. It can be seen in Fig. 1(c) that there is actually an in-plane anisotropy due to the technology-related choice of a rectangular lattice, but for the targeted air-filling factors (f ∼ 0.18) this anisotropy remains very limited. Hence, the cladding behaves almost as a homogenous material in a given polarization. The effective modal index of the fundamental guided mode is calculated with the commercial COMSOL RF mode solver module. We calculate the eigenmodes of both an SOI 2D PC nanopatterned claddings waveguide and a hybrid waveguide composed of the nanopatterned SOI waveguide with a 400-nmthick InP layer bonded to it [14]. The thickness of the Si guiding layer is a challenging choice within hybrid III-V/SOI active structures like lasers. We consider here a 550-nm-thick Si guiding
Fig. 1. (a) Schematic of the effective medium material operating as the waveguide lateral cladding sections; (b) extraordinary index and ordinary index versus areal air-filling factor. (c) In-plane TE photonic band structure (using a ≡ ΛDFB ∕2 as the reference period) for a 110 nm × 150 nm lattice of air holes in silicon (ΛEMT 150 nm ΛΛDFB 220 nm), and filling factors f 0.15 and 0.20, showing that operation at 1550 nm is in the effective index regime with only weak in-plane anisotropy between the two lattice directions. Only the first photonic band is shown in the two (y, z) symmetry directions with respective first Brillouin zone limits π∕ΛEMT and π∕ΛDFB ∕2.
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layer-based design that will not require any 3D taper for further implementation in a hybrid laser. For modal calculation, we do not include the geometrical detail of the added periodicity since its contribution to the modal effective index is marginal. Taking advantage of the EMT representation of the 2D PC, a parametric study is performed according to the PC waveguide width w, trench depth H , and air-filling factor f [Fig. 1(a)], the silicon guiding layer thickness being h 550 nm. The selected geometrical parameters w; H ; f are the ones that provide a large higher-order mode selectivity in TE polarization. For this selection, we have followed the approach proposed by Pogossian et al. [15]. We have generalized their approach in the case of a finite lateral confinement, since the number of rows limiting the shallow ridge is necessarily limited. We have considered here 20 rows of holes. Even though this number of rows is limited, it will not hamper the EMT approach because the structured material is a periodic one. A larger number of elements is required when random inclusions in the host material are considered [16]. A typical value of the modal effective index obtained by this procedure is 3.50. For wavelength-selective operation, a super-periodicity is added to the sub-λ 2D PC. It consists of a larger hole in every other longitudinal period, as shown in Fig. 2(a). When the effective index of the fundamental TE mode is obtained, the added super-periodicity ΛDFB is calculated to provide wavelength-selectivity at 1.55 μm. The 2D PC periodicity in the propagation direction is then obtained, being half of the superperiodicity: ΛEMT ΛDFB ∕2, about 110 nm. The 2D PC transverse periodicity is kept at 150 nm. The 2D PC thus becomes a rectangular array and the ordinary index of the EMT is then adjusted taking into account the rectangular geometry of the actual 2D PC. Note that in the present sub-λ regime well below the gap and with a small air-filling factor f , neff ≡ no is still isotropic in the plane, i.e., we can consider a uniaxial material even though the lattice is rectangular. The modal index is then recalculated to finely adjust the periodicity in the propagation direction. The geometry of the biperiodic array being fixed, a 3DFDTD simulation using the LUMERICAL commercial software is performed to determine the impact of the larger hole size on the transmission. An 80 rows-long waveguide is simulated. We plot in Fig. 2(b) the transmission versus wavelength for a larger hole size corresponding to 30%, 50%, and 70% increase versus the nominal hole diameter. The geometrical parameters of the structure are those leading to the largest higher-order mode rejection: a 2D PC longitudinal period ΛEMT 220 nm,
Fig. 2. (a) Super-periodicity added to provide a wavelength selection; (b) 3D FDTD transmission versus wavelength for an edge hole in the first row larger by the indicated amount (30%–50%–70%).
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a hole diameter of 60 nm, a hole depth H 380 nm, a waveguide width w 0.6 μm, the SOI waveguide is h 550 nm, and there is no InP layer bonded on top. The modest dip depth is due to the limited number of periods (80 rows 40ΛDFB ). The same trend versus enlarged hole size is obtained when a 400-nmthick InP layer is bonded on top of the SOI stack. The sub-λ 2D PC is fabricated on a SOI stack kindly provided by SOITEC. The hole geometry is designed by e-beam lithography in a PMMA resist mask, then transferred on the underlying SiO2 layer, which is used as the etching mask for ICP etching of the holes in the silicon guiding layer. Dry etching is performed on an ICP Sentech machine, with a Cl2 -H2 based process. A small amount of O2 is added to obtain vertical and smooth hole walls. The PC parameters obtained are close to the ones used for simulation: a longitudinal period of 220 nm, a transverse period of 150 nm, and a nominal hole diameter of 68 nm, slightly larger than the simulated one. The hole depth is close to the expected value. The larger hole diameter is 30% larger than the nominal diameter. Figure 3(a) shows a cleaved facet of a nanopatterned waveguide on SOI. The larger holes placed one every two periods are clearly visible. In the case of a hybrid waveguide, a 400-nm-thick InP membrane is heteroepitaxially bonded on top of the SOI nanopatterned device. This oxide-free bonding has been shown to preserve the hybrid interface at the atomic scale [14]. Figure 4(a) shows a cleaved facet of the hybrid waveguide. As for waveguide measurement, a thin resist layer has been added on top of the waveguide since the location of the waveguide center is no longer visible after bonding [Fig. 4(b)]. All the different waveguides are fabricated 20 μm apart one from another. Two cleaved facet waveguides 450-μm-long, Fig. 3(a) (SOI) and Figs. 4(a) and 4(b) (hybrid), including 20 rows of holes on both sides, have been measured on an end-fire setup including polarization-maintaining tunable sources and injection fiber for TE polarization. Collection is performed with a microscope objective allowing simultaneous observation of the guided mode and collection in the fiber. Measured transmissions are normalized to the spectrum obtained in the back-to-back situation taken as a reference. Figures 3(b), 3(c), and 4(c) show their transmissions versus wavelength, for w 0.6 μm. The feedback efficiency of the added periodicity provided by larger holes is visible both for the SOI waveguide, see Figs. 3(b) and 3(c), and for the hybrid waveguide, see Fig. 4(c). For modal behavior
Fig. 3. (a) SOI waveguide with cleaved facet; (b) transmission versus wavelength, for the larger holes in the first row, and (c) in the second row; (d) Fourier transform of the transmission spectrum for the second row.
Letter
Fig. 4. InP/Si oxide-free bonded waveguide; (a) cleaved facet; (b) resist line on top of the waveguide center; (c) transmission versus wavelength, for larger holes in the first row and in the inset a zoom of the transmission for larger holes in the second row; (d) Fourier transform of the transmission spectrum for the second row.
assessment, we perform a Fourier transform of the transmission. We plot this optical-length power-spectrum in the case of the SOI waveguide [Fig. 3(d)] and in the case of the hybrid waveguide [Fig. 4(d)] with larger holes in the second row. Both power spectra show a single peak, which is the signature of a monomode behavior. For the SOI waveguide, the stop band position is measured at 1547.7 nm, while for the hybrid waveguide it is shifted at a larger wavelength, 1563.2 nm, since the overall hybrid waveguide has a larger optical mode effective index that is due to the 400-nm-thick InP layer bonded on top. These spectral positions are in reasonable agreement with the simulations. Stop bands show a 20-dB transmission reduction, except for the hybrid waveguides with larger holes in the second row. In the case of larger holes in the first row, the dips are larger than what is expected from the 3D FDTD simulations. During the etching process, due to lag effect, the larger holes are also etched deeper than the nominal ones. This larger hole depth, which is not taken into account for the simulation due to the too large increase of computational resources related to the detailed design of all the holes, is most probably responsible for these relatively broad dips. Indeed, these larger holes being placed in the first row of holes limiting the waveguide have a strong feedback in the optical mode since the coupling strength is related to the proper Fourier component of the effective index modulation, at the ΛDFB period. Moving these larger holes in the second row has been considered, fabricated, and measured in the case of the SOI waveguide. The stop band visible in Fig. 3(c) is still 20-dB-deep but its width is much reduced due to the reduced feedback, the larger holes being further apart from the waveguide center. The second row configuration for the hybrid case [Fig. 4(c) inset] shows a narrow and comparatively shallow dip since the feedback is reduced both from holes far away from the waveguide center and looser confinement due to the upper InP layer. As for the power budget, transmission for hybrid waveguides is lower than for SOI waveguides. But propagation losses could not be unambiguously measured since the waveguides, being 20 μm apart, are close enough to experience sizable waveguide
Letter coupling. Such a cross talk occurring for shallow ridges fabricated on a thick Si guiding layer has been calculated by Malati et al. [17]; it was clearly assigned to sidewall-scattered waves having a very limited divergence due to the remaining silicon, and thus strongly influencing their neighbors. We have proposed and experimentally demonstrated the wavelength-selective operation of a biperiodic nanostructured III-V on a silicon hybrid waveguide. A super-periodicity is added in the propagation direction of the 2D PC material forming the waveguide cladding layers and operating below its bandgap. EMT has been implemented for the subwavelength structured material index calculation to investigate a large number of geometrical parameters with reasonable computing resources. Such a nanostructuration offers a large potential for the conception of any kind of hybrid waveguide dedicated to advanced optical functions, since a tailored geometry can be easily inserted in the hybrid oxide-free device because the silicon waveguide remains flat. The great advantage is that changing the geometry to obtain a new optical function does not require developing a new technology for material bonding, thus allowing several designs to be included within a hybrid device during a single bonding process. Funding. Agence Nationale de la Recherche (ANR). Acknowledgment. Part of the technological work was undertaken through the national RENATECH network.
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REFERENCES 1. M. Belt and D. J. Blumenthal, Opt. Express 22, 10655 (2014). 2. C. R. Doerr, L. Chen, and D. Vermeulen, Opt. Express 22, 4493 (2014). 3. S. Stankovic, R. Jones, M. S. Sysak, J. M. Heck, G. Roelkens, and D. VanThourhout, IEEE Photonics Technol. Lett. 23, 1781 (2011). 4. M. Lamponi, S. Keyvaninia, C. Jany, F. Poingt, F. Lelarge, G. de Valicourt, G. Roelkens, D. VanThourhout, S. Messaoudene, J.-M. Fedeli, and G. H. Duan, IEEE Photonics Technol. Lett. 24, 76 (2012). 5. A. W. Fang, E. Lively, Y.-H. Kuo, D. Liang, and J. E. Bowers, Opt. Express 16, 4413 (2008). 6. D. Inoue, J. Lee, T. Hiratani, Y. Atsuji, T. Amemiya, N. Nishiyama, and S. Arai, Opt. Express 23, 7771 (2015). 7. K. Tanabe, K. Watanabe, and Y. Arakawa, Sci. Rep. 2, 349 (2012). 8. M. D. Huntington, L. J. Lauhon, and T. W. Odom, Nano Lett. 14, 7195 (2014). 9. F. T. Chen and H. G. Craighead, Opt. Lett. 20, 121 (1995). 10. R. Brauer and O. Bryngdahl, Appl. Opt. 33, 7875 (1994). 11. P. Lalanne, Appl. Opt. 35, 5369 (1996). 12. C. Pang and H. Benisty, Photon. Nanostruct. Fundam. Applic. 11, 145 (2013). 13. K. Bougot-Robin, C. Pang, X. Pommarede, A. Itawi, A. Talneau, J.-P. Hugonin, and H. Benisty, J. Lightwave Technol. 32, 3283 (2014). 14. A. Talneau, C. Roblin, A. Itawi, O. Mauguin, L. Largeau, G. Beaudoin, I. Sagnes, G. Patriarche, C. Pang, and H. Benisty, Appl. Phys. Lett. 102, 212101 (2013). 15. S. P. Pogossian, L. Vescan, and A. Vonsovici, J. Lightwave Technol. 16, 1851 (1998). 16. M. Mishchenko, Z. Dlugach, and N. Zakharova, Opt. Lett. 39, 3935 (2014). 17. D. Melati, F. Morichetti, G. G. Gentili, and A. Melloni, Opt. Lett. 39, 3982 (2014).
Letter
Vol. 40, No. 22 / November 15 2015 / Optics Letters
Biperiodic nanostructured waveguides for wavelength-selectivity of hybrid photonic devices A. TALNEAU,1,* X. POMMARÈDE,1 A. ITAWI,1 K. PANTZAS,1 A. LUPU,2
AND
H. BENISTY3
1
Laboratoire de Photonique et de Nanostructures, Route de Nozay, F-91460 Marcoussis, France IEF, CNRS, UMR 8622, Univ. Paris-Sud, 91405 Orsay Cedex, France 3 Laboratoire Charles Fabry, Institut d’Optique Graduate School, Univ PSud, 2 Avenue Augustin Fresnel, F-91127 Palaiseau, France *Corresponding author: [email protected] 2
Received 24 August 2015; revised 7 October 2015; accepted 10 October 2015; posted 12 October 2015 (Doc. ID 248520); published 2 November 2015
A biperiodic nanostructuration consisting of a superperiodicity added to a nanohole lattice of subwavelength pitch is demonstrated to provide both modal confinement and wavelength selectivity within a hybrid III-V on a silicon waveguide. The wavelength-selective behavior stems from finely tuned larger holes. Such biperiodic hybrid waveguides have been fabricated by oxide-free bonding III-V material on silicon and display well-defined stop bands. Such nanostructured waveguides offer the versatility for designing advanced optical functions within hybrid devices. Moreover, keeping the silicon waveguide surface planar, such nanostructured waveguides are compatible with electrical operation across the oxide-free hybrid interface. © 2015 Optical Society of America OCIS codes: (230.3120) Integrated optics devices; (130.7408) Wavelength filtering devices; (130.5296) Photonic crystal waveguides; (220.4241) Nanostructure fabrication. http://dx.doi.org/10.1364/OL.40.005148
Integrated photonics will boost the performances of optical networks links. Within photonics integrated circuits (PIC), emission/amplification and isolation are two major optical functions to be included. Si-based approaches can provide monomode sources, including rare-earth-doped waveguides operating under optical pumping [1], whereas a tandem-modulator-based isolator performs the optical isolation [2]. The most widely used approach leading to the best present performances relies upon hybrid silicon photonics, wherein III-V semiconductors provide light amplification and emission, while materials such as garnets provide optical isolation. When both materials are associated with a very thin intermediate layer to silicon, the optical guided mode is mainly selected by the chosen silicon structure, usually a rib waveguide [3,4]. If any advanced optical function is needed, an extra processing step is required to carve the adequate added structure; for instance, a grating on top of the guide [5] or a lateral grating [6] for wavelength-selective lasing operation. We propose here to carve the silicon guiding layer prior to bonding, specifically implementing guidance with a 2D photonic 0146-9592/15/225148-04$15/0$15.00 © 2015 Optical Society of America
crystal (PC) operating essentially below its photonic gap. When properly tailored, thanks to the huge range of effective indices that can be obtained in silicon/air composites, such a nanostructure can favor virtually any spatial or spectral characteristics for the propagated optical mode. A subwavelength below bandgap periodicity, in particular, is compatible with a broad range from the lasing long wavelength to the other shortwavelength limits (multimodal onset, silicon or III-V absorption, etc.). This sub-λ silicon waveguide patterning allows one to implement advanced optical functions in a single technological step and also retains a plane Si bonding surface that is oxidefree bonding compatible. This allows electrical injection through the hybrid interface, which is of great interest for the future of hybrid devices operation [7]. In this Letter, a sub-λ 2D photonic bandgap structuration is designed for modal confinement, and a biperiodic structuration in the propagation direction is added to provide wavelength selectivity. We calculate and demonstrate experimentally that this biperiodic patterned waveguide operates as a wavelength selection mechanism. For modal simulation, being in the subphotonic bandgap regime, effective medium theory (EMT) has been implemented to represent the nanopatterned material. EMT is of interest since simulation of the exact geometry requires a tiny meshing that leads to highly demanding computational resources. EMT allows fast and accurate investigation for large ranges of the several geometrical parameters under consideration. Then, a 2D modal analysis is performed to calculate the effective index of the fundamental mode. For the spectral behavior, a 3D finite-difference time-domain (FDTD) is performed to determine the geometry of the added super-periodicity. Both SOI waveguides, as well as hybrid InP/SOI oxide-free bonded waveguides, are fabricated and measured. Such a design has the potential of being included for singlemode longitudinal operation in hybrid III-V/SOI DFB lasers, providing on a single technological step both the modal confinement and the wavelength selectivity. More generally, according to the unit cell shape, a large number of optical functions can be addressed [8]. This approach offers a great potential of being compatible with any kind of hybrid environment. The optical waveguide has a generic shallow ridge shape, its core is not structured and both lateral claddings are composed
Letter of the same 2D PC operating below its photonic gap. Here, the 2D PC is a square array of air holes drilled in the silicon guiding layer. To investigate a large number of geometrical parameters with reasonable computing resources, the EMT is implemented to represent the 2D PC material [Fig. 1(a)] and propagation occurs along the z direction. EMT has been demonstrated to fully represent a periodic nanostructured medium when its pitch Λ is much smaller than the wavelength λ, α Λ∕λ ≪ 1 [9–11]. The nanostructured material behaves like a uniaxial material. For the electric field aligned with the direction of invariance (here, the y direction), the resulting permittivity of the extraordinary index ne is the mean value of the involved permittivities [9]. The ordinary index no is here obtained from the dispersion curve of a 2D PC calculated by a plane wave expansion method [Fig. 1(c)], the 2D PC period being 150 nm in the transverse direction and 110 nm in the longitudinal direction, already taking into account the specific geometry dedicated to wavelength-selective operation [12,13]. Both calculated ordinary and extraordinary indices are plotted in Fig. 1(b) versus the air-filling factor and show the basically uniaxial behavior of the patterned material. It can be seen in Fig. 1(c) that there is actually an in-plane anisotropy due to the technology-related choice of a rectangular lattice, but for the targeted air-filling factors (f ∼ 0.18) this anisotropy remains very limited. Hence, the cladding behaves almost as a homogenous material in a given polarization. The effective modal index of the fundamental guided mode is calculated with the commercial COMSOL RF mode solver module. We calculate the eigenmodes of both an SOI 2D PC nanopatterned claddings waveguide and a hybrid waveguide composed of the nanopatterned SOI waveguide with a 400-nmthick InP layer bonded to it [14]. The thickness of the Si guiding layer is a challenging choice within hybrid III-V/SOI active structures like lasers. We consider here a 550-nm-thick Si guiding
Fig. 1. (a) Schematic of the effective medium material operating as the waveguide lateral cladding sections; (b) extraordinary index and ordinary index versus areal air-filling factor. (c) In-plane TE photonic band structure (using a ≡ ΛDFB ∕2 as the reference period) for a 110 nm × 150 nm lattice of air holes in silicon (ΛEMT 150 nm ΛΛDFB 220 nm), and filling factors f 0.15 and 0.20, showing that operation at 1550 nm is in the effective index regime with only weak in-plane anisotropy between the two lattice directions. Only the first photonic band is shown in the two (y, z) symmetry directions with respective first Brillouin zone limits π∕ΛEMT and π∕ΛDFB ∕2.
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layer-based design that will not require any 3D taper for further implementation in a hybrid laser. For modal calculation, we do not include the geometrical detail of the added periodicity since its contribution to the modal effective index is marginal. Taking advantage of the EMT representation of the 2D PC, a parametric study is performed according to the PC waveguide width w, trench depth H , and air-filling factor f [Fig. 1(a)], the silicon guiding layer thickness being h 550 nm. The selected geometrical parameters w; H ; f are the ones that provide a large higher-order mode selectivity in TE polarization. For this selection, we have followed the approach proposed by Pogossian et al. [15]. We have generalized their approach in the case of a finite lateral confinement, since the number of rows limiting the shallow ridge is necessarily limited. We have considered here 20 rows of holes. Even though this number of rows is limited, it will not hamper the EMT approach because the structured material is a periodic one. A larger number of elements is required when random inclusions in the host material are considered [16]. A typical value of the modal effective index obtained by this procedure is 3.50. For wavelength-selective operation, a super-periodicity is added to the sub-λ 2D PC. It consists of a larger hole in every other longitudinal period, as shown in Fig. 2(a). When the effective index of the fundamental TE mode is obtained, the added super-periodicity ΛDFB is calculated to provide wavelength-selectivity at 1.55 μm. The 2D PC periodicity in the propagation direction is then obtained, being half of the superperiodicity: ΛEMT ΛDFB ∕2, about 110 nm. The 2D PC transverse periodicity is kept at 150 nm. The 2D PC thus becomes a rectangular array and the ordinary index of the EMT is then adjusted taking into account the rectangular geometry of the actual 2D PC. Note that in the present sub-λ regime well below the gap and with a small air-filling factor f , neff ≡ no is still isotropic in the plane, i.e., we can consider a uniaxial material even though the lattice is rectangular. The modal index is then recalculated to finely adjust the periodicity in the propagation direction. The geometry of the biperiodic array being fixed, a 3DFDTD simulation using the LUMERICAL commercial software is performed to determine the impact of the larger hole size on the transmission. An 80 rows-long waveguide is simulated. We plot in Fig. 2(b) the transmission versus wavelength for a larger hole size corresponding to 30%, 50%, and 70% increase versus the nominal hole diameter. The geometrical parameters of the structure are those leading to the largest higher-order mode rejection: a 2D PC longitudinal period ΛEMT 220 nm,
Fig. 2. (a) Super-periodicity added to provide a wavelength selection; (b) 3D FDTD transmission versus wavelength for an edge hole in the first row larger by the indicated amount (30%–50%–70%).
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a hole diameter of 60 nm, a hole depth H 380 nm, a waveguide width w 0.6 μm, the SOI waveguide is h 550 nm, and there is no InP layer bonded on top. The modest dip depth is due to the limited number of periods (80 rows 40ΛDFB ). The same trend versus enlarged hole size is obtained when a 400-nmthick InP layer is bonded on top of the SOI stack. The sub-λ 2D PC is fabricated on a SOI stack kindly provided by SOITEC. The hole geometry is designed by e-beam lithography in a PMMA resist mask, then transferred on the underlying SiO2 layer, which is used as the etching mask for ICP etching of the holes in the silicon guiding layer. Dry etching is performed on an ICP Sentech machine, with a Cl2 -H2 based process. A small amount of O2 is added to obtain vertical and smooth hole walls. The PC parameters obtained are close to the ones used for simulation: a longitudinal period of 220 nm, a transverse period of 150 nm, and a nominal hole diameter of 68 nm, slightly larger than the simulated one. The hole depth is close to the expected value. The larger hole diameter is 30% larger than the nominal diameter. Figure 3(a) shows a cleaved facet of a nanopatterned waveguide on SOI. The larger holes placed one every two periods are clearly visible. In the case of a hybrid waveguide, a 400-nm-thick InP membrane is heteroepitaxially bonded on top of the SOI nanopatterned device. This oxide-free bonding has been shown to preserve the hybrid interface at the atomic scale [14]. Figure 4(a) shows a cleaved facet of the hybrid waveguide. As for waveguide measurement, a thin resist layer has been added on top of the waveguide since the location of the waveguide center is no longer visible after bonding [Fig. 4(b)]. All the different waveguides are fabricated 20 μm apart one from another. Two cleaved facet waveguides 450-μm-long, Fig. 3(a) (SOI) and Figs. 4(a) and 4(b) (hybrid), including 20 rows of holes on both sides, have been measured on an end-fire setup including polarization-maintaining tunable sources and injection fiber for TE polarization. Collection is performed with a microscope objective allowing simultaneous observation of the guided mode and collection in the fiber. Measured transmissions are normalized to the spectrum obtained in the back-to-back situation taken as a reference. Figures 3(b), 3(c), and 4(c) show their transmissions versus wavelength, for w 0.6 μm. The feedback efficiency of the added periodicity provided by larger holes is visible both for the SOI waveguide, see Figs. 3(b) and 3(c), and for the hybrid waveguide, see Fig. 4(c). For modal behavior
Fig. 3. (a) SOI waveguide with cleaved facet; (b) transmission versus wavelength, for the larger holes in the first row, and (c) in the second row; (d) Fourier transform of the transmission spectrum for the second row.
Letter
Fig. 4. InP/Si oxide-free bonded waveguide; (a) cleaved facet; (b) resist line on top of the waveguide center; (c) transmission versus wavelength, for larger holes in the first row and in the inset a zoom of the transmission for larger holes in the second row; (d) Fourier transform of the transmission spectrum for the second row.
assessment, we perform a Fourier transform of the transmission. We plot this optical-length power-spectrum in the case of the SOI waveguide [Fig. 3(d)] and in the case of the hybrid waveguide [Fig. 4(d)] with larger holes in the second row. Both power spectra show a single peak, which is the signature of a monomode behavior. For the SOI waveguide, the stop band position is measured at 1547.7 nm, while for the hybrid waveguide it is shifted at a larger wavelength, 1563.2 nm, since the overall hybrid waveguide has a larger optical mode effective index that is due to the 400-nm-thick InP layer bonded on top. These spectral positions are in reasonable agreement with the simulations. Stop bands show a 20-dB transmission reduction, except for the hybrid waveguides with larger holes in the second row. In the case of larger holes in the first row, the dips are larger than what is expected from the 3D FDTD simulations. During the etching process, due to lag effect, the larger holes are also etched deeper than the nominal ones. This larger hole depth, which is not taken into account for the simulation due to the too large increase of computational resources related to the detailed design of all the holes, is most probably responsible for these relatively broad dips. Indeed, these larger holes being placed in the first row of holes limiting the waveguide have a strong feedback in the optical mode since the coupling strength is related to the proper Fourier component of the effective index modulation, at the ΛDFB period. Moving these larger holes in the second row has been considered, fabricated, and measured in the case of the SOI waveguide. The stop band visible in Fig. 3(c) is still 20-dB-deep but its width is much reduced due to the reduced feedback, the larger holes being further apart from the waveguide center. The second row configuration for the hybrid case [Fig. 4(c) inset] shows a narrow and comparatively shallow dip since the feedback is reduced both from holes far away from the waveguide center and looser confinement due to the upper InP layer. As for the power budget, transmission for hybrid waveguides is lower than for SOI waveguides. But propagation losses could not be unambiguously measured since the waveguides, being 20 μm apart, are close enough to experience sizable waveguide
Letter coupling. Such a cross talk occurring for shallow ridges fabricated on a thick Si guiding layer has been calculated by Malati et al. [17]; it was clearly assigned to sidewall-scattered waves having a very limited divergence due to the remaining silicon, and thus strongly influencing their neighbors. We have proposed and experimentally demonstrated the wavelength-selective operation of a biperiodic nanostructured III-V on a silicon hybrid waveguide. A super-periodicity is added in the propagation direction of the 2D PC material forming the waveguide cladding layers and operating below its bandgap. EMT has been implemented for the subwavelength structured material index calculation to investigate a large number of geometrical parameters with reasonable computing resources. Such a nanostructuration offers a large potential for the conception of any kind of hybrid waveguide dedicated to advanced optical functions, since a tailored geometry can be easily inserted in the hybrid oxide-free device because the silicon waveguide remains flat. The great advantage is that changing the geometry to obtain a new optical function does not require developing a new technology for material bonding, thus allowing several designs to be included within a hybrid device during a single bonding process. Funding. Agence Nationale de la Recherche (ANR). Acknowledgment. Part of the technological work was undertaken through the national RENATECH network.
Vol. 40, No. 22 / November 15 2015 / Optics Letters
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