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
Photonic crystal (PhC) membranes  provide a highly promising environment for optical quantum technologies . On the one hand, fundamental optical components such as ultra-high quality resonators [3–5], low-loss waveguides  and power splitters  can be realized in PhCs. On the other hand, by coupling PhC cavities to single quantum emitters, such as quantum dots  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 .
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 terminating the PhC waveguide with a size of only ∼ 1.6μm2. 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 
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 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 (Si3N4, 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 ≈ 261nm and r ≈ 92nm. For the grating coupler, a ring width of w ≈ 317nm and a ring separation of v ≈ 156nm 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 wavelength of 0.320 Å in protective N2 atmosphere to avoid beam damage. Figure 3 shows the 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 . 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 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 4f -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 ≈ 630nm. 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 1d-case 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.
Using this technique, transmission spectra were recorded (Fig. 6, top). The measured spectra show high transmission intensities in the wavelength range of the photonic band gap and below (note that the cut-off at 500 nm is due to the laser source), as well as transmission at around 700 nm. This behavior is in good agreement with numerical results (Fig. 6, bottom) on the coupler and waveguide transmission obtained using a flux-monitor based scheme in FDTD-calculations (MEEP ). At wavelengths below 610 nm, the waveguide exhibits good transmission, while a stop band is located from between 610 nm and 670 nm. Consequently, no light arrives at the coupler and the transmitted intensities vanish in this wavelength range. At about 700 nm the waveguide has a good performance again, due to index-guided modes. In the waveguide’s transmission windows, the coupler exhibits transmission efficiencies to the positive vertical direction of about 30 %. This value is close to the theoretical maximum of 50 % for unidirectional transmission in a z-symmetric structure. Note that the oscillations in the coupler’s transmission are a numerical artefact caused by reflections at the boundaries implemented as perfectly matched layers. Additionally, the simulations showed that the coupler’s ring supports reduce the overall transmission by roughly 5 %. Also note that the experimental results are not normalized to the incident power, resulting in an underestimation of the index-guided low frequency transmission. The agreement between simulation and measurement data in the spectral position of the bandgap and the index-guided mode band of the waveguide show that the simulations give a good approximation for the real system. According to this we attribute the same validity to the calculated value for the absolute coupling efficiency. A direct measurement of this quantity is challenging, since the flux incident to the coupler needs to be known. One possible solution to tackle this issue is to compare to the transmission of nominally identical PhC waveguides, directly coupled to dielectric waveguides being accessible on the chips edge. However, such a comparison would be very sensitive to fabrication tolerances and might be speculative. Hence, we rely on the numerical simulations to estimate the coupling efficiency.
We demonstrated that Bragg-like grating structures with a very small footprint of only ∼ 1.6μm2 can be utilized to efficiently scatter light from photonic crystal waveguides to the far field in near-vertical direction. If designed properly, these systems can achieve good directionalities for a specific wavelength range and high scattering efficiencies over a wide spectral range – for example covering the complete photonic bandgap. In comparison to many alternative approaches, such coupling devices do not need any extra processing steps or additional materials. Standard technologies can be used to detect the resulting signal. Our work thus significantly increases the knowledge on ring grating couplers as used e.g. in Refs. [19, 20], in particular with respect to their directionality and efficiency properties.
Our studies proved that the directional properties of the coupling behavior can be well understood from a 1d analogy. In addition, our results allow to improve the design in view of a maximum coupling efficiency and directivity for future experiments. Thus, our study paves the way for future quantum optics devices, including on-chip integrated two-photon interference  or entanglement [25, 26] experiments.
We acknowledge financial support from DFG through project IQuOSuPla ( AI 92/3) and Sfb951 (HIOS). For helpful discussions regarding numerical problems, we like to thank Prof. Dr. Kurt Busch and his group. We further acknowledge the ESRF for provision of synchrotron radiation facilities and we would like to thank M. Mezger and Ch. Weber for help with the x-ray experiments at beamline ID 15C.
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