Miniaturized Bragg-grating couplers for SiN-photonic crystal slabs ¨ Carlo Barth,1,∗ Janik Wolters,1 Andreas W. Schell,1 Jurgen Probst,2 Max Schoengen,2 Bernd L¨ochel,2 Stefan Kowarik,3 and Oliver Benson1 1 Nano-Optics,
Institute of Physics, Humboldt-Universit¨at zu Berlin, Newtonstr. 15, D-12489 Berlin, Germany 2 Optical Technology, Institute for Nanometer Optics and Technology, Helmholtz-Zentrum Berlin f¨ur Materialien und Energie GmbH, Albert-Einstein-Str. 15, D-12489 Berlin, Germany 3 Coherent Optics with X-rays – Time Resolved Surface Science, Institute of Physics, Humboldt-Universit¨at zu Berlin, Newtonstr. 15, D-12489 Berlin, Germany ∗ [email protected]
Abstract: We report on an experimental and theoretical investigation of an integrated Bragg-like grating coupler for near-vertical scattering of light from photonic crystal waveguides with an ultra-small footprint of a few lattice constants only. Using frequency-resolved measurements, we find the directional properties of the scattered radiation and prove that the coupler shows a good performance over the complete photonic bandgap. The results compare well to analytical considerations regarding 1d-scattering phenomena as well as to FDTD simulations. © 2015 Optical Society of America OCIS codes: (050.1950) Diffraction gratings; (050.5298) Photonic crystals.
References and links 1. S. G. Johnson, S. Fan, P. Villeneuve, J. D. Joannopoulos, and L. Kolodziejski, “Guided modes in photonic crystal slabs,” Phys. Rev. B 60, 5751–5758 (1999). 2. J. L. O’Brien, A. Furusawa, and J. Vuˇckovi´c, “Photonic quantum technologies,” Nat. Photonics 3, 687–695 (2009). 3. B.-S. Song, S. Noda, T. Asano, and Y. Akahane, “Ultra-high-Q photonic double-heterostructure nanocavity,” Nat. Mater. 4, 207–210 (2005). 4. E. Kuramochi, M. Notomi, S. Mitsugi, A. Shinya, T. Tanabe, and T. Watanabe, “Ultrahigh-Q photonic crystal nanocavities realized by the local width modulation of a line defect,” Appl. Phys. Lett. 88, 041112 (2006). 5. K. J. Vahala, “Optical microcavities,” Nature 424, 839–846 (2003). 6. S. G. Johnson, P. R. Villeneuve, S. Fan, and J. D. Joannopoulos, “Linear waveguides in photonic-crystal slabs,” Phys. Rev. B 62, 8212–8222 (2000). 7. S. Fan, S. G. Johnson, J. D. Joannopoulos, C. Manolatou, and H. A. Haus, “Waveguide branches in photonic crystals,” J. Opt. Soc. Am. B 18, 162 (2001). 8. D. Englund, D. Fattal, E. Waks, G. Solomon, B. Zhang, T. Nakaoka, Y. Arakawa, Y. Yamamoto, and J. Vuˇckovi´cc, “Controlling the spontaneous emission rate of single quantum dots in a two-dimensional photonic crystal,” Phys. Rev. Lett. 95, 013904 (2005). 9. J. Wolters, A. W. Schell, G. Kewes, N. Nuesse, M. Schoengen, H. Doescher, T. Hannappel, B. Loechel, M. Barth, and O. Benson, “Enhancement of the zero phonon line emission from a single nitrogen vacancy center in a nanodiamond via coupling to a photonic crystal cavity,” Appl. Phys. Lett. 97, 141108 (2010). 10. J. Wolters, G. Kewes, A. W. Schell, N. N¨usse, M. Schoengen, B. L¨ochel, T. Hanke, R. Bratschitsch, A. Leitenstorfer, T. Aichele, and O. Benson, “Coupling of single nitrogen-vacancy defect centers in diamond nanocrystals to optical antennas and photonic crystal cavities,” Phys. Status Solidi 249, 918–924 (2012). 11. K. Asakawa, Y. Sugimoto, Y. Watanabe, N. Ozaki, A. Mizutani, Y. Takata, Y. Kitagawa, H. Ishikawa, N. Ikeda, K. Awazu, X. Wang, A. Watanabe, S. Nakamura, S. Ohkouchi, K. Inoue, M. Kristensen, O. Sigmund, P. I. Borel, and R. Baets, “Photonic crystal and quantum dot technologies for all-optical switch and logic device,” New J. Phys. 8, 208–208 (2006).
#228369 - $15.00 USD (C) 2015 OSA
Received 5 Jan 2015; revised 11 Mar 2015; accepted 11 Mar 2015; published 9 Apr 2015 20 Apr 2015 | Vol. 23, No. 8 | DOI:10.1364/OE.23.009803 | OPTICS EXPRESS 9803
12. A. Faraon, A. Majumdar, D. Englund, E. Kim, M. Bajcsy, and J. Vuckovic, “Integrated quantum optical networks based on quantum dots and photonic crystals,” New J. Phys. 13, 055025 (2011). 13. T. Yoshie, A. Scherer, J. Hendrickson, G. Khitrova, H. M. Gibbs, G. Rupper, C. Ell, O. B. Shchekin, and D. G. Deppe, “Vacuum Rabi splitting with a single quantum dot in a photonic crystal nanocavity,” Nature 432, 200–3 (2004). 14. J. Wolters, N. Nikolay, M. Schoengen, A. W. Schell, J. Probst, B. L¨ochel, and O. Benson, “Thermo-optical response of photonic crystal cavities operating in the visible spectral range,” Nanotechnol. 24, 315204 (2013). 15. K. Nozaki, T. Tanabe, A. Shinya, S. Matsuo, T. Sato, H. Taniyama, and M. Notomi, “Sub-femtojoule all-optical switching using a photonic-crystal nanocavity,” Nat. Photonics 4, 477–483 (2010). 16. G. Roelkens, D. Vermeulen, F. Van Laere, S. Selvaraja, S. Scheerlinck, D. Taillaert, W. Bogaerts, P. Dumon, D. Van Thourhout, and R. Baets, “Bridging the gap between nanophotonic waveguide circuits and single mode optical fibers using diffractive grating structures,” J. Nanosci. Nanotechnol. 10, 1551–1562 (2010). 17. D. Taillaert, F. Van Laere, M. Ayre, W. Bogaerts, D. Van Thourhout, P. Bienstman, and R. Baets, “Grating couplers for coupling between optical fibers and nanophotonic waveguides,” Japanese J. Appl. Physics, Part 1 Regul. Pap. Short Notes Rev. Pap. 45, 6071–6077 (2006). 18. S. L. Portalupi, M. Galli, C. Reardon, T. F. Krauss, L. O’Faolain, L. C. Andreani, and D. Gerace, “Planar photonic crystal cavities with far-field optimization for high coupling efficiency and quality factor,” Opt. Express 18, 16064–73 (2010). 19. A. Faraon, I. Fushman, D. Englund, N. Stoltz, P. Petroff, and J. Vuˇckovi´c, “Dipole induced transparency in waveguide coupled photonic crystal cavities,” Opt. Express 16, 12154–12162 (2008). 20. M. Arcari, I. S¨ollner, A. Javadi, S. L. Hansen, S. Mahmoodian, J. Liu, H. Thyrrestrup, E. H. Lee, J. D. Song, S. r. Stobbe, and P. Lodahl, “Near-unity coupling efficiency of a quantum emitter to a photonic-crystal waveguide,” Phys. Rev. Lett. 113, 093603 (2014). 21. C. Toninelli, K. Early, J. Bremi, A. Renn, S. G¨otzinger, and V. Sandoghdar, “Near-infrared single-photons from aligned molecules in ultrathin crystalline films at room temperature,” Opt. Express 18, 6577–82 (2010). 22. L. G. Parratt, “Surface studies of solids by total reflection of x-rays,” Phys. Rev. 95, 359–369 (1954). 23. A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “Meep: A flexible free-software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Commun. 181, 687–702 (2010). 24. C. K. Hong, Z. Y. Ou, and L. Mandel, “Measurement of subpicosecond time intervals between two photons by interference,” Phys. Rev. Lett. 59, 2044–2046 (1987). 25. S. Barrett and P. Kok, “Efficient high-fidelity quantum computation using matter qubits and linear optics,” Phys. Rev. A 71, 060310 (2005). 26. J. Wolters, J. Kabuss, A. Knorr, and O. Benson, “Deterministic and robust entanglement of nitrogen-vacancy centers using low-Q photonic-crystal cavities,” Phys. Rev. A 89, 060303 (2014).
1.
Introduction
Photonic crystal (PhC) membranes [1] provide a highly promising environment for optical quantum technologies [2]. On the one hand, fundamental optical components such as ultrahigh quality resonators [3–5], low-loss waveguides [6] and power splitters [7] can be realized in PhCs. On the other hand, by coupling PhC cavities to single quantum emitters, such as quantum dots [8] or color centers in diamond [9, 10], single photons can effectively be generated on-chip. Hence, integrated circuits implementing functionalities such as photon blockade or all-optical switching [11–15] can be realized, giving an idea of the possibilities of future optical quantum devices on PhC platforms. For all applications which could feature such functionalities, efficient out of plane coupling of photons is crucial either for communication between different parts of the chip or for detection by detectors located above the PhC membrane. A standard approach to this coupling problem is to use extended Bragg gratings [16, 17] coupled via dielectric on-chip waveguides. However, this approach is unfavorable due to a comparably large footprint and the need for an additional interface between photonic crystal and dielectric waveguide. To tackle this problem, either miniaturized Bragg grating structures, or photonic crystal superlattices have been proposed [18]. In this letter, we present a study of a miniaturized grating directly interfacing a photonic crystal waveguide. A similar geometry, but designed for infrared wavelength on a GaAs platform is used in Refs. [19, 20]. Its geometry is depicted in Fig. 1, consisting of a double-ring grating #228369 - $15.00 USD (C) 2015 OSA
Received 5 Jan 2015; revised 11 Mar 2015; accepted 11 Mar 2015; published 9 Apr 2015 20 Apr 2015 | Vol. 23, No. 8 | DOI:10.1364/OE.23.009803 | OPTICS EXPRESS 9804
Supports
a
b Output PhC Waveguide Input
r0
z y x y x
Grating Coupler
w
v
w
Fig. 1. a, Geometry of the grating coupler design consisting of a double-ring grating (ring width w, ring separation v, inner circle diameter r0 ) which terminates a PhC waveguide (SiN in gray). Supports are necessary for mechanical stability. b, Sketch of the input-output principle when using the coupler. For a z-symmetric coupler the unidirectional efficiency is limited to 50 %.
terminating the PhC waveguide with a size of only ∼ 1.6 µm2 . For specific wavelengths, it is expected that interference effects cause a dominant vertical scattering, for reasons of symmetry identically to both +z and −z-direction. The efficiency and angular distribution of the scattered light may additionally strongly depend on the mode profile. This specific design was chosen for phenomenological reasons and the initial guess for the optimum relations between target wavelength λtune , ring width w and ring separation v is [19] w = λtune /2,
v = λtune /(2n).
(1)
This is motivated by the fact that for the 1d-case (propagation along x-direction) a lattice constant of the grating of Λ = w + v = λ /(2nair ) + λ /(2nSiN ) = λ /(navg. )
(2)
results in perfectly vertical scattering, for an incoming wave of a wavelength of λ = λ . For assessment of the coupling efficiency, the angular distribution and the absolute transmission of the coupler have to be considered in combination. This means, one needs to i) maximize the fraction of incident power which is scattered out of plane, i.e. which is not reflected from or passing the coupler; ii) minimize the angular widening of the scattered radiation; and iii) achieve a main scattering angle of ≈ 90°. In the following, feature i) will be referred to as transmission, while the combination of ii) and iii) will be called directionality. The directionality properties determine the maximum distance and the necessary size of a detector located above the coupler. If we assume a perfect detection of all photons which are scattered out of plane, the transmission corresponds to the probability with which a photon incident to the coupler is detected. 2.
Fabricated chip and measurement setup
Figure 2(a) shows a sketch of a PhC sample including a grating coupler. The design is chosen such that laser light can be coupled to a dielectric waveguide which in turn couples to the photonic crystal. For proper incoupling, a relatively wide (10 µm) dielectric waveguide is necessary. This waveguide then is tapered in two steps to a final width of 300 nm. This transition #228369 - $15.00 USD (C) 2015 OSA
Received 5 Jan 2015; revised 11 Mar 2015; accepted 11 Mar 2015; published 9 Apr 2015 20 Apr 2015 | Vol. 23, No. 8 | DOI:10.1364/OE.23.009803 | OPTICS EXPRESS 9805
b
a
SEM Image
10μ m
500 nm
Fig. 2. a, View of dielectric incoupling waveguide and a single PhC waveguide and grating coupler. The dielectric waveguide is tapered in two steps from 10 µm to 300 nm and a 90°curve is used to avoid scattering light (PhC and coupler not to scale). b, Scanning electron micrograph of a channel with coupler.
from a multi-mode to a single-mode waveguide scatters out light except light in the fundamental mode. A 90° curve after the second tapered region is used to prevent the non-guided light from reaching the PhC. To experimentally characterize the coupler, a chip was fabricated using silicon nitride (Si3 N4 , n ≈ 2) as dielectric material. This allows for operation wavelengths in the visible, as needed to access the zero-phonon-line emission of nitrogen vacancy centers or single organic molecules [9, 10, 21]. The structuring was applied using electron beam lithography, reactive ion etching and a final underetching step using 7:1 buffered hydrofluoric acid (BHF). This way we achieve a textured z-symmetric SiN-membrane suspended in air. To characterize the lattice constant a and the hole radius r, scanning electron microscopy was utilized (Fig. 2(b)), resulting in a ≈ 261 nm and r ≈ 92 nm. For the grating coupler, a ring width of w ≈ 317 nm and a ring separation of v ≈ 156 nm was found. When referring to the initial design parameters (Eq. (1)), a target wavelength λtune in the range of 625 nm to 635 nm would thus be expected. The SiN thickness as an important input parameter for simulations regarding the PhC was determined using x-ray reflectivity measurements. The measurements were performed at beamline ID 15C of the European Synchrotron Radiation Facility (ESRF, Grenoble, France) at an x-ray
1E-3
X-ray
BHF etching qz
212 nm
X-ray reflectivity
X-ray reflectivity
Reference Sample
organic residuals 230 nm
SiN SiO2
1E-4
SiN
1E-3
SiO2
1E-4
1E-5
0.08
0.10
0.12
0.14
qz [Å–1 ]
0.16
0.18
1E-5 0.08
0.10
0.12
0.14
0.16
0.18
qz [Å–1 ]
Fig. 3. X-ray reflectivity data (black dots) and fit (red line) to the data using the SiN thicknesses of 230 nm for the reference sample (top) and 212 nm for the BHF etched sample (bottom). The inset shows the sample with the scattering geometry of incident x-ray wave vector, specularly reflected x-ray wavevector, and the wavevector transfer qz .
#228369 - $15.00 USD (C) 2015 OSA
Received 5 Jan 2015; revised 11 Mar 2015; accepted 11 Mar 2015; published 9 Apr 2015 20 Apr 2015 | Vol. 23, No. 8 | DOI:10.1364/OE.23.009803 | OPTICS EXPRESS 9806
a Supercontinuum Source
Nikon
NA=0.3
Positioning Platform
Fiber Coupled Spectrometer
Lamp
Incoupling Objective
Aperture (removable)
f'
Mitutoyyo
NA=0.9
Chip Detection Objective
b
Flip Lens
Beam splitter f
f
f
Flip Mirror
CCDCamera
f
CCD-Camera Images without coupler
with coupler
mode cleaner radiation
zoom
zoom
Fig. 4. a, Experimental setup for transmission and back focal plane (BFP) measurements, for which a supercontinuum source is used to illuminate the samples. The signal can either be analyzed using a CCD-camera or a fiber-coupled spectrometer. An aperture is used to clip the image if necessary. Using a 4 f -alignment, the BFP of the detection objective can be projected to the CCD-chip to study the angular distribution of the scattered light. b, CCD images of a channel without (left) and a channel with coupler (right). A bright spot appears at the coupler position, which is completely missing in the image without coupler.
˚ in protective N2 atmosphere to avoid beam damage. Figure 3 shows the wavelength of 0.320 A specular x-ray reflectivity (incident angle θ = exit angle θ ) as a function of the wavevector transfer qz = (4π /λ ) sin(θ ). Rapid Kiessig oscillations in the reflectivity are clearly visible for both samples, which are due to interference between reflections from the top and bottom SiN interfaces. For the reference sample with a thin layer of organic residuals on top, a second, slow oscillation period is visible as well, corresponding to interferences due to the organic layer. The experimental data was fitted using the optical matrix method for layered media [22]. The resulting layer thicknesses for the reference sample are (230 ± 1) nm for the SiN and (6.5 ± 0.1) nm for the organic layer, with interface roughness below 1 nm for all interfaces. For the BHF etched sample a SiN layer thickness of (212 ± 1) nm was found with an interface roughness of (0.3 ± 0.3) nm at the SiO2 – SiN interface and a roughness of (0.6 ± 0.3) nm at the SiN – air interface. The measurement setup used to optically characterize the sample is depicted in Fig. 4(a). A fiber-coupled supercontinuum white-light source was used to illuminate the incoupling dielectric waveguides through a high working distance objective (incoupling objective, NA = 0.3). Using a 6-axes positioning platform, the incoupling and the position of the chip in front of a second objective (detection objective, NA = 0.9) could be adjusted separately. An LED-lamp #228369 - $15.00 USD (C) 2015 OSA
Received 5 Jan 2015; revised 11 Mar 2015; accepted 11 Mar 2015; published 9 Apr 2015 20 Apr 2015 | Vol. 23, No. 8 | DOI:10.1364/OE.23.009803 | OPTICS EXPRESS 9807
was used for direct illumination in order to orientate on the chip. The resulting signal was analyzed using a CCD-camera. In subsequent sections it will be explained how the flip elements in the setup were utilized to obtain spectral and back focal plane (BFP) measurements. Figure 4(b) shows images produced using the CCD-camera to measure the directly scattered light from the samples. The left hand image depicts a channel without a coupler – the waveguide is abruptly terminated. There is no scattering light visible at the area of termination. For a channel with coupler, the right hand image shows a bright spot at the coupler position, illustrating the extreme improvement achieved using our coupler. 3.
Back focal plane measurements
To characterize the directionality properties of the coupler experimentally, back focal plane measurements were used. Light scattered by the coupler into a specific direction is focused in a well-determined point in the BFP, so that the angular distribution of the coupler light can be studied. For this purpose, a 4 f -configuration was realized in the setup (Fig. 4(a)), so that the CCD-chip of the camera is aligned with the BFP and the flip lens was used to toggle between real and k-space. The numerical aperture of the detection objective determines the maximum angle ϕmax under which signals can be measured (in our case NA = 0.9 → ϕmax ≈ 64°) and the aperture in the image plane was used to optionally clip the image in order to exclusively analyze the light coming from the coupler. The frequency resolved BFP measurement data obtained using a tunable supercontinuum source (PicoQuant Solea) is illustrated in Fig. 5(a). For each tuning frequency, the source provided a bandwidth of about 3 nm. For 600 nm, most light from the coupler is scattered to the forward direction with angles between 40° and 60°, while for 656 nm the light is backscattered with angles of about 60° (note that in this notation an angle of 0° means vertical scattering). In between, patterns are visible (≈616 nm to 632 nm), which show a good directionality with main scattering angles between 10° and 25°, as well as comparatively small widening angles. The narrow feature at shallow angles in backward direction might be due to TM-modes, which are not confined by the PhC-waveguide. Note, that from Fig. 5(b) it is clear that these features are not due to second order backscattered effects, since these can exclusively occur for forward scattered modes (i.e. λmode < λtune ). The optimum wavelengths are close to the approximate target wavelength of λtune ≈ 630 nm. Accordingly, Eq. (Eq. (1)) seems to hold in view of the directionality properties of the coupler. The observed behavior fits the expectation which is obtained from the 1d-case, as already explained in the introduction. A smaller wavelength – effectively equaling a larger lattice constant Λ of the grating – would produce scattering angles > 90°, thus forward scattering. The opposite applies for larger wavelengths. Obviously, the 1dcase is able to give a good estimation for the grating coupler’s behavior. Actually, the measured optimum wavelength seems to be slightly smaller than the estimated value of 630 nm, which might arise from the fact that the guided modes extend to the region outside the dielectric. This would cause an effectively smaller refractive index and from Eq. (2) – with constant Λ and decreased navg. – we find that λ would decrease as well. 4.
Measurements and simulations regarding the coupler transmission
The back focal plane measurements alone do not contain enough information on the absolute intensity, hence no statement is possible in view of the coupler’s transmission properties. To get additional insight in the spectral transmission properties of the coupler, independent measurements were necessary. To this end, the fiber coupled spectrometer depicted in Fig. 4(a) was used. The signal was clipped to the light coming from the coupler using the aperture and was directed to the fiber using the flip mirror. The flip lens must be used in this case, since the measurement should be performed in real space. #228369 - $15.00 USD (C) 2015 OSA
Received 5 Jan 2015; revised 11 Mar 2015; accepted 11 Mar 2015; published 9 Apr 2015 20 Apr 2015 | Vol. 23, No. 8 | DOI:10.1364/OE.23.009803 | OPTICS EXPRESS 9808
a
λ = 600 nm
b
λ = 616 nm
λ1 > λ2 > λ3 Λ
1
k1
z x
λ = 632 nm
k1 = 2π /λ
0
forward λ1
Institute of Physics, Humboldt-Universit¨at zu Berlin, Newtonstr. 15, D-12489 Berlin, Germany 2 Optical Technology, Institute for Nanometer Optics and Technology, Helmholtz-Zentrum Berlin f¨ur Materialien und Energie GmbH, Albert-Einstein-Str. 15, D-12489 Berlin, Germany 3 Coherent Optics with X-rays – Time Resolved Surface Science, Institute of Physics, Humboldt-Universit¨at zu Berlin, Newtonstr. 15, D-12489 Berlin, Germany ∗ [email protected]
Abstract: We report on an experimental and theoretical investigation of an integrated Bragg-like grating coupler for near-vertical scattering of light from photonic crystal waveguides with an ultra-small footprint of a few lattice constants only. Using frequency-resolved measurements, we find the directional properties of the scattered radiation and prove that the coupler shows a good performance over the complete photonic bandgap. The results compare well to analytical considerations regarding 1d-scattering phenomena as well as to FDTD simulations. © 2015 Optical Society of America OCIS codes: (050.1950) Diffraction gratings; (050.5298) Photonic crystals.
References and links 1. S. G. Johnson, S. Fan, P. Villeneuve, J. D. Joannopoulos, and L. Kolodziejski, “Guided modes in photonic crystal slabs,” Phys. Rev. B 60, 5751–5758 (1999). 2. J. L. O’Brien, A. Furusawa, and J. Vuˇckovi´c, “Photonic quantum technologies,” Nat. Photonics 3, 687–695 (2009). 3. B.-S. Song, S. Noda, T. Asano, and Y. Akahane, “Ultra-high-Q photonic double-heterostructure nanocavity,” Nat. Mater. 4, 207–210 (2005). 4. E. Kuramochi, M. Notomi, S. Mitsugi, A. Shinya, T. Tanabe, and T. Watanabe, “Ultrahigh-Q photonic crystal nanocavities realized by the local width modulation of a line defect,” Appl. Phys. Lett. 88, 041112 (2006). 5. K. J. Vahala, “Optical microcavities,” Nature 424, 839–846 (2003). 6. S. G. Johnson, P. R. Villeneuve, S. Fan, and J. D. Joannopoulos, “Linear waveguides in photonic-crystal slabs,” Phys. Rev. B 62, 8212–8222 (2000). 7. S. Fan, S. G. Johnson, J. D. Joannopoulos, C. Manolatou, and H. A. Haus, “Waveguide branches in photonic crystals,” J. Opt. Soc. Am. B 18, 162 (2001). 8. D. Englund, D. Fattal, E. Waks, G. Solomon, B. Zhang, T. Nakaoka, Y. Arakawa, Y. Yamamoto, and J. Vuˇckovi´cc, “Controlling the spontaneous emission rate of single quantum dots in a two-dimensional photonic crystal,” Phys. Rev. Lett. 95, 013904 (2005). 9. J. Wolters, A. W. Schell, G. Kewes, N. Nuesse, M. Schoengen, H. Doescher, T. Hannappel, B. Loechel, M. Barth, and O. Benson, “Enhancement of the zero phonon line emission from a single nitrogen vacancy center in a nanodiamond via coupling to a photonic crystal cavity,” Appl. Phys. Lett. 97, 141108 (2010). 10. J. Wolters, G. Kewes, A. W. Schell, N. N¨usse, M. Schoengen, B. L¨ochel, T. Hanke, R. Bratschitsch, A. Leitenstorfer, T. Aichele, and O. Benson, “Coupling of single nitrogen-vacancy defect centers in diamond nanocrystals to optical antennas and photonic crystal cavities,” Phys. Status Solidi 249, 918–924 (2012). 11. K. Asakawa, Y. Sugimoto, Y. Watanabe, N. Ozaki, A. Mizutani, Y. Takata, Y. Kitagawa, H. Ishikawa, N. Ikeda, K. Awazu, X. Wang, A. Watanabe, S. Nakamura, S. Ohkouchi, K. Inoue, M. Kristensen, O. Sigmund, P. I. Borel, and R. Baets, “Photonic crystal and quantum dot technologies for all-optical switch and logic device,” New J. Phys. 8, 208–208 (2006).
#228369 - $15.00 USD (C) 2015 OSA
Received 5 Jan 2015; revised 11 Mar 2015; accepted 11 Mar 2015; published 9 Apr 2015 20 Apr 2015 | Vol. 23, No. 8 | DOI:10.1364/OE.23.009803 | OPTICS EXPRESS 9803
12. A. Faraon, A. Majumdar, D. Englund, E. Kim, M. Bajcsy, and J. Vuckovic, “Integrated quantum optical networks based on quantum dots and photonic crystals,” New J. Phys. 13, 055025 (2011). 13. T. Yoshie, A. Scherer, J. Hendrickson, G. Khitrova, H. M. Gibbs, G. Rupper, C. Ell, O. B. Shchekin, and D. G. Deppe, “Vacuum Rabi splitting with a single quantum dot in a photonic crystal nanocavity,” Nature 432, 200–3 (2004). 14. J. Wolters, N. Nikolay, M. Schoengen, A. W. Schell, J. Probst, B. L¨ochel, and O. Benson, “Thermo-optical response of photonic crystal cavities operating in the visible spectral range,” Nanotechnol. 24, 315204 (2013). 15. K. Nozaki, T. Tanabe, A. Shinya, S. Matsuo, T. Sato, H. Taniyama, and M. Notomi, “Sub-femtojoule all-optical switching using a photonic-crystal nanocavity,” Nat. Photonics 4, 477–483 (2010). 16. G. Roelkens, D. Vermeulen, F. Van Laere, S. Selvaraja, S. Scheerlinck, D. Taillaert, W. Bogaerts, P. Dumon, D. Van Thourhout, and R. Baets, “Bridging the gap between nanophotonic waveguide circuits and single mode optical fibers using diffractive grating structures,” J. Nanosci. Nanotechnol. 10, 1551–1562 (2010). 17. D. Taillaert, F. Van Laere, M. Ayre, W. Bogaerts, D. Van Thourhout, P. Bienstman, and R. Baets, “Grating couplers for coupling between optical fibers and nanophotonic waveguides,” Japanese J. Appl. Physics, Part 1 Regul. Pap. Short Notes Rev. Pap. 45, 6071–6077 (2006). 18. S. L. Portalupi, M. Galli, C. Reardon, T. F. Krauss, L. O’Faolain, L. C. Andreani, and D. Gerace, “Planar photonic crystal cavities with far-field optimization for high coupling efficiency and quality factor,” Opt. Express 18, 16064–73 (2010). 19. A. Faraon, I. Fushman, D. Englund, N. Stoltz, P. Petroff, and J. Vuˇckovi´c, “Dipole induced transparency in waveguide coupled photonic crystal cavities,” Opt. Express 16, 12154–12162 (2008). 20. M. Arcari, I. S¨ollner, A. Javadi, S. L. Hansen, S. Mahmoodian, J. Liu, H. Thyrrestrup, E. H. Lee, J. D. Song, S. r. Stobbe, and P. Lodahl, “Near-unity coupling efficiency of a quantum emitter to a photonic-crystal waveguide,” Phys. Rev. Lett. 113, 093603 (2014). 21. C. Toninelli, K. Early, J. Bremi, A. Renn, S. G¨otzinger, and V. Sandoghdar, “Near-infrared single-photons from aligned molecules in ultrathin crystalline films at room temperature,” Opt. Express 18, 6577–82 (2010). 22. L. G. Parratt, “Surface studies of solids by total reflection of x-rays,” Phys. Rev. 95, 359–369 (1954). 23. A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “Meep: A flexible free-software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Commun. 181, 687–702 (2010). 24. C. K. Hong, Z. Y. Ou, and L. Mandel, “Measurement of subpicosecond time intervals between two photons by interference,” Phys. Rev. Lett. 59, 2044–2046 (1987). 25. S. Barrett and P. Kok, “Efficient high-fidelity quantum computation using matter qubits and linear optics,” Phys. Rev. A 71, 060310 (2005). 26. J. Wolters, J. Kabuss, A. Knorr, and O. Benson, “Deterministic and robust entanglement of nitrogen-vacancy centers using low-Q photonic-crystal cavities,” Phys. Rev. A 89, 060303 (2014).
1.
Introduction
Photonic crystal (PhC) membranes [1] provide a highly promising environment for optical quantum technologies [2]. On the one hand, fundamental optical components such as ultrahigh quality resonators [3–5], low-loss waveguides [6] and power splitters [7] can be realized in PhCs. On the other hand, by coupling PhC cavities to single quantum emitters, such as quantum dots [8] or color centers in diamond [9, 10], single photons can effectively be generated on-chip. Hence, integrated circuits implementing functionalities such as photon blockade or all-optical switching [11–15] can be realized, giving an idea of the possibilities of future optical quantum devices on PhC platforms. For all applications which could feature such functionalities, efficient out of plane coupling of photons is crucial either for communication between different parts of the chip or for detection by detectors located above the PhC membrane. A standard approach to this coupling problem is to use extended Bragg gratings [16, 17] coupled via dielectric on-chip waveguides. However, this approach is unfavorable due to a comparably large footprint and the need for an additional interface between photonic crystal and dielectric waveguide. To tackle this problem, either miniaturized Bragg grating structures, or photonic crystal superlattices have been proposed [18]. In this letter, we present a study of a miniaturized grating directly interfacing a photonic crystal waveguide. A similar geometry, but designed for infrared wavelength on a GaAs platform is used in Refs. [19, 20]. Its geometry is depicted in Fig. 1, consisting of a double-ring grating #228369 - $15.00 USD (C) 2015 OSA
Received 5 Jan 2015; revised 11 Mar 2015; accepted 11 Mar 2015; published 9 Apr 2015 20 Apr 2015 | Vol. 23, No. 8 | DOI:10.1364/OE.23.009803 | OPTICS EXPRESS 9804
Supports
a
b Output PhC Waveguide Input
r0
z y x y x
Grating Coupler
w
v
w
Fig. 1. a, Geometry of the grating coupler design consisting of a double-ring grating (ring width w, ring separation v, inner circle diameter r0 ) which terminates a PhC waveguide (SiN in gray). Supports are necessary for mechanical stability. b, Sketch of the input-output principle when using the coupler. For a z-symmetric coupler the unidirectional efficiency is limited to 50 %.
terminating the PhC waveguide with a size of only ∼ 1.6 µm2 . For specific wavelengths, it is expected that interference effects cause a dominant vertical scattering, for reasons of symmetry identically to both +z and −z-direction. The efficiency and angular distribution of the scattered light may additionally strongly depend on the mode profile. This specific design was chosen for phenomenological reasons and the initial guess for the optimum relations between target wavelength λtune , ring width w and ring separation v is [19] w = λtune /2,
v = λtune /(2n).
(1)
This is motivated by the fact that for the 1d-case (propagation along x-direction) a lattice constant of the grating of Λ = w + v = λ /(2nair ) + λ /(2nSiN ) = λ /(navg. )
(2)
results in perfectly vertical scattering, for an incoming wave of a wavelength of λ = λ . For assessment of the coupling efficiency, the angular distribution and the absolute transmission of the coupler have to be considered in combination. This means, one needs to i) maximize the fraction of incident power which is scattered out of plane, i.e. which is not reflected from or passing the coupler; ii) minimize the angular widening of the scattered radiation; and iii) achieve a main scattering angle of ≈ 90°. In the following, feature i) will be referred to as transmission, while the combination of ii) and iii) will be called directionality. The directionality properties determine the maximum distance and the necessary size of a detector located above the coupler. If we assume a perfect detection of all photons which are scattered out of plane, the transmission corresponds to the probability with which a photon incident to the coupler is detected. 2.
Fabricated chip and measurement setup
Figure 2(a) shows a sketch of a PhC sample including a grating coupler. The design is chosen such that laser light can be coupled to a dielectric waveguide which in turn couples to the photonic crystal. For proper incoupling, a relatively wide (10 µm) dielectric waveguide is necessary. This waveguide then is tapered in two steps to a final width of 300 nm. This transition #228369 - $15.00 USD (C) 2015 OSA
Received 5 Jan 2015; revised 11 Mar 2015; accepted 11 Mar 2015; published 9 Apr 2015 20 Apr 2015 | Vol. 23, No. 8 | DOI:10.1364/OE.23.009803 | OPTICS EXPRESS 9805
b
a
SEM Image
10μ m
500 nm
Fig. 2. a, View of dielectric incoupling waveguide and a single PhC waveguide and grating coupler. The dielectric waveguide is tapered in two steps from 10 µm to 300 nm and a 90°curve is used to avoid scattering light (PhC and coupler not to scale). b, Scanning electron micrograph of a channel with coupler.
from a multi-mode to a single-mode waveguide scatters out light except light in the fundamental mode. A 90° curve after the second tapered region is used to prevent the non-guided light from reaching the PhC. To experimentally characterize the coupler, a chip was fabricated using silicon nitride (Si3 N4 , n ≈ 2) as dielectric material. This allows for operation wavelengths in the visible, as needed to access the zero-phonon-line emission of nitrogen vacancy centers or single organic molecules [9, 10, 21]. The structuring was applied using electron beam lithography, reactive ion etching and a final underetching step using 7:1 buffered hydrofluoric acid (BHF). This way we achieve a textured z-symmetric SiN-membrane suspended in air. To characterize the lattice constant a and the hole radius r, scanning electron microscopy was utilized (Fig. 2(b)), resulting in a ≈ 261 nm and r ≈ 92 nm. For the grating coupler, a ring width of w ≈ 317 nm and a ring separation of v ≈ 156 nm was found. When referring to the initial design parameters (Eq. (1)), a target wavelength λtune in the range of 625 nm to 635 nm would thus be expected. The SiN thickness as an important input parameter for simulations regarding the PhC was determined using x-ray reflectivity measurements. The measurements were performed at beamline ID 15C of the European Synchrotron Radiation Facility (ESRF, Grenoble, France) at an x-ray
1E-3
X-ray
BHF etching qz
212 nm
X-ray reflectivity
X-ray reflectivity
Reference Sample
organic residuals 230 nm
SiN SiO2
1E-4
SiN
1E-3
SiO2
1E-4
1E-5
0.08
0.10
0.12
0.14
qz [Å–1 ]
0.16
0.18
1E-5 0.08
0.10
0.12
0.14
0.16
0.18
qz [Å–1 ]
Fig. 3. X-ray reflectivity data (black dots) and fit (red line) to the data using the SiN thicknesses of 230 nm for the reference sample (top) and 212 nm for the BHF etched sample (bottom). The inset shows the sample with the scattering geometry of incident x-ray wave vector, specularly reflected x-ray wavevector, and the wavevector transfer qz .
#228369 - $15.00 USD (C) 2015 OSA
Received 5 Jan 2015; revised 11 Mar 2015; accepted 11 Mar 2015; published 9 Apr 2015 20 Apr 2015 | Vol. 23, No. 8 | DOI:10.1364/OE.23.009803 | OPTICS EXPRESS 9806
a Supercontinuum Source
Nikon
NA=0.3
Positioning Platform
Fiber Coupled Spectrometer
Lamp
Incoupling Objective
Aperture (removable)
f'
Mitutoyyo
NA=0.9
Chip Detection Objective
b
Flip Lens
Beam splitter f
f
f
Flip Mirror
CCDCamera
f
CCD-Camera Images without coupler
with coupler
mode cleaner radiation
zoom
zoom
Fig. 4. a, Experimental setup for transmission and back focal plane (BFP) measurements, for which a supercontinuum source is used to illuminate the samples. The signal can either be analyzed using a CCD-camera or a fiber-coupled spectrometer. An aperture is used to clip the image if necessary. Using a 4 f -alignment, the BFP of the detection objective can be projected to the CCD-chip to study the angular distribution of the scattered light. b, CCD images of a channel without (left) and a channel with coupler (right). A bright spot appears at the coupler position, which is completely missing in the image without coupler.
˚ in protective N2 atmosphere to avoid beam damage. Figure 3 shows the wavelength of 0.320 A specular x-ray reflectivity (incident angle θ = exit angle θ ) as a function of the wavevector transfer qz = (4π /λ ) sin(θ ). Rapid Kiessig oscillations in the reflectivity are clearly visible for both samples, which are due to interference between reflections from the top and bottom SiN interfaces. For the reference sample with a thin layer of organic residuals on top, a second, slow oscillation period is visible as well, corresponding to interferences due to the organic layer. The experimental data was fitted using the optical matrix method for layered media [22]. The resulting layer thicknesses for the reference sample are (230 ± 1) nm for the SiN and (6.5 ± 0.1) nm for the organic layer, with interface roughness below 1 nm for all interfaces. For the BHF etched sample a SiN layer thickness of (212 ± 1) nm was found with an interface roughness of (0.3 ± 0.3) nm at the SiO2 – SiN interface and a roughness of (0.6 ± 0.3) nm at the SiN – air interface. The measurement setup used to optically characterize the sample is depicted in Fig. 4(a). A fiber-coupled supercontinuum white-light source was used to illuminate the incoupling dielectric waveguides through a high working distance objective (incoupling objective, NA = 0.3). Using a 6-axes positioning platform, the incoupling and the position of the chip in front of a second objective (detection objective, NA = 0.9) could be adjusted separately. An LED-lamp #228369 - $15.00 USD (C) 2015 OSA
Received 5 Jan 2015; revised 11 Mar 2015; accepted 11 Mar 2015; published 9 Apr 2015 20 Apr 2015 | Vol. 23, No. 8 | DOI:10.1364/OE.23.009803 | OPTICS EXPRESS 9807
was used for direct illumination in order to orientate on the chip. The resulting signal was analyzed using a CCD-camera. In subsequent sections it will be explained how the flip elements in the setup were utilized to obtain spectral and back focal plane (BFP) measurements. Figure 4(b) shows images produced using the CCD-camera to measure the directly scattered light from the samples. The left hand image depicts a channel without a coupler – the waveguide is abruptly terminated. There is no scattering light visible at the area of termination. For a channel with coupler, the right hand image shows a bright spot at the coupler position, illustrating the extreme improvement achieved using our coupler. 3.
Back focal plane measurements
To characterize the directionality properties of the coupler experimentally, back focal plane measurements were used. Light scattered by the coupler into a specific direction is focused in a well-determined point in the BFP, so that the angular distribution of the coupler light can be studied. For this purpose, a 4 f -configuration was realized in the setup (Fig. 4(a)), so that the CCD-chip of the camera is aligned with the BFP and the flip lens was used to toggle between real and k-space. The numerical aperture of the detection objective determines the maximum angle ϕmax under which signals can be measured (in our case NA = 0.9 → ϕmax ≈ 64°) and the aperture in the image plane was used to optionally clip the image in order to exclusively analyze the light coming from the coupler. The frequency resolved BFP measurement data obtained using a tunable supercontinuum source (PicoQuant Solea) is illustrated in Fig. 5(a). For each tuning frequency, the source provided a bandwidth of about 3 nm. For 600 nm, most light from the coupler is scattered to the forward direction with angles between 40° and 60°, while for 656 nm the light is backscattered with angles of about 60° (note that in this notation an angle of 0° means vertical scattering). In between, patterns are visible (≈616 nm to 632 nm), which show a good directionality with main scattering angles between 10° and 25°, as well as comparatively small widening angles. The narrow feature at shallow angles in backward direction might be due to TM-modes, which are not confined by the PhC-waveguide. Note, that from Fig. 5(b) it is clear that these features are not due to second order backscattered effects, since these can exclusively occur for forward scattered modes (i.e. λmode < λtune ). The optimum wavelengths are close to the approximate target wavelength of λtune ≈ 630 nm. Accordingly, Eq. (Eq. (1)) seems to hold in view of the directionality properties of the coupler. The observed behavior fits the expectation which is obtained from the 1d-case, as already explained in the introduction. A smaller wavelength – effectively equaling a larger lattice constant Λ of the grating – would produce scattering angles > 90°, thus forward scattering. The opposite applies for larger wavelengths. Obviously, the 1dcase is able to give a good estimation for the grating coupler’s behavior. Actually, the measured optimum wavelength seems to be slightly smaller than the estimated value of 630 nm, which might arise from the fact that the guided modes extend to the region outside the dielectric. This would cause an effectively smaller refractive index and from Eq. (2) – with constant Λ and decreased navg. – we find that λ would decrease as well. 4.
Measurements and simulations regarding the coupler transmission
The back focal plane measurements alone do not contain enough information on the absolute intensity, hence no statement is possible in view of the coupler’s transmission properties. To get additional insight in the spectral transmission properties of the coupler, independent measurements were necessary. To this end, the fiber coupled spectrometer depicted in Fig. 4(a) was used. The signal was clipped to the light coming from the coupler using the aperture and was directed to the fiber using the flip mirror. The flip lens must be used in this case, since the measurement should be performed in real space. #228369 - $15.00 USD (C) 2015 OSA
Received 5 Jan 2015; revised 11 Mar 2015; accepted 11 Mar 2015; published 9 Apr 2015 20 Apr 2015 | Vol. 23, No. 8 | DOI:10.1364/OE.23.009803 | OPTICS EXPRESS 9808
a
λ = 600 nm
b
λ = 616 nm
λ1 > λ2 > λ3 Λ
1
k1
z x
λ = 632 nm
k1 = 2π /λ
0
forward λ1
