Near-field probing of slow Bloch modes on photonic crystals with a nanoantenna

: We study the near-ﬁeld probing of the slow Bloch laser mode of a photonic crystal by a bowtie nano-aperture (BNA) positioned at the end of a metal-coated ﬁber probe. We show that the BNA acts as a polarizing nanoprobe allowing us to extract information about the polarization of the near-ﬁeld of the slow-light mode, without causing any signiﬁcant perturbation of the lasing process. Near-ﬁeld experiments reveal a spatial resolution better than λ / 20 and a polarization ratio as strong as 110. We also demonstrate that the collection efﬁciency is two orders of magnitude larger for the BNA than for a 200 nm large circular aperture opened at the apex of the same metal-coated ﬁber tip. The BNA allows for overcoming one of the main limitations of SNOM linked to


Introduction
For more than fifteen years, 2D photonic crystals (PCs) have been used to control optical fields down to the nanoscale [1]. Given the complex, vectorial nature of optical fields associated with subwavelength structures, a complete and precise knowledge of the electromagnetic field near a PC is difficult to gain. While theoretical models can predict vector field maps near an ideal PC structure, finding a reliable experimental technique to study the vectorial nature of confined optical fields near an actual 2D PC device remains both highly desirable and challenging, especially considering how difficult it is for a near-field probe not to perturb the optical signature of the sample . Beyond the novel experimental insight given by mapping the polarization state of the fields, a more precise analysis of the optical properties of a PC would make it possible to better assess the performance of a device, by comparing not only spatial intensity profiles but also local polarization states with theoretical models. With this in prospect, scanning Near-field Optical Microscopy (SNOM) has been widely used to investigate the optical properties of 2D PC structures [2][3][4][5][6][7][8][9][10] including to access vectorial information about the optical modes [11,12]. However, SNOM probes used in these experiments are not ideal for the accurate and reliable measurement of optical near-fields. On the one hand, the signal detected by conventional metalcoated aperture and apertureless probes is usually a "mixture" of electric and magnetic components. In this case, the probe apex can be viewed as nanoscale optical antenna [13] with electric and magnetic dipole moments which convert both electric and magnetic near-field information into free space propagating modes, albeit with a rather low conversion efficiency [14][15][16][17][18][19]. This is a serious issue for the accurate interpretation of results since the subwavelength spatial profiles of the electric and magnetic fields may be different. Only bare dielectric tips, which can be represented by an electric dipole moment only, are known to selectively collect the electric optical field [20,21], but at the cost of a modest spatial resolution. On the other hand, conventional SNOM probes have difficulties faithfully mapping the near-field of 2D PCs showing a strong vertical emission, i.e. operating at or near the Γ-point (center) of the Brillouin zone [22][23][24]. It has been shown that the nature of the coupling between the probe and the slow Bloch mode (SBM) is very critical, in particular due to the large propagating component of the field which interferes with the evanescent contribution and swamps some of the finer details [8].
Recently, resonant nanoantennas have been proposed as a way of establishing a two-way communication channel between optical nano-structures and free space radiation modes, thus enhancing dramatically light-matter interaction down to the nanoscale [25]. Among the various configurations of nanoantennas proposed so far, the bowtie [26, 27] and bowtie-aperture nanoantennas [28,29] were shown to be very efficient designs for creating highly confined and enhanced electric optical fields in the small gap between their two triangular metal particles.
Their resonant optical properties, defined by a huge optical capacitive effect within the air gap, are governed by an electric dipole moment oriented along the metal triangles. This means that these nanoantennas interact mainly with a single vector component of the electric field and light re-emission by the antenna is due to electric optical processes. As detailed in a recent theoretical work, BNAs may be used as high resolution polarizing nanocollectors with little sensitivity to the magnetic optical fields [30].
In this article, we propose to use BNAs integrated at the apex of SNOM fiber tips as nanoprobes for mapping the vectorial components of the electric near-field of 2D-PC slow Bloch laser mode. We consider surface addressable PC exploiting SBMs emitting in the vertical direction, i.e. operating at the Γ-point of the Brillouin zone. Near this point, low curvature flat bands give rise to delocalized, stationary optical modes. These modes have attracted much attention recently as they lead to versatile photonic structures not restricted to operate in the traditional in-plane, wave-guiding regime but suitable for coupling to free-space radiation [31,32]. SBMs at the Γ-point have already been exploited to directly achieve vertical laser emission with peculiar polarization states, such as azimuthal or radial polarizations [8,33]. So far, the investigation of the potential of BNAs as near-field optical nanoprobes has been limited to the nano-imaging of simple test-objects and only their resolution and collection efficiency have been investigated [30,34]. The issue of the local and vectorial imaging of the modes of complex nanophotonic structures, such as photonic crystal based devices, with a nanoantenna tip has not been addressed yet. Here, we experimentally demonstrate the potential of BNAs integrated at the apex of SNOM fiber probes for polarization-resolved optical mapping of the electric field with unprecedented signal-to-noise ratios and without perturbation of the laser emission. We also show that the resonance properties of the BNA lead to high resolution abilities in SNOM imaging with high collection efficiencies, in opposition to conventional circular nano-apertures for which any improvement of resolution is associated with a loss of collection efficiency.

Nanoantenna probe
In order to produce the BNA-on-tip, polymer tips (30μm) are first grown by photopolymerization at the cleaved end facet of a monomode (1.55 micron wavelength) glass fiber [35]. Next, the probes are metal coated with a few nanometer thick titanium adhesion layer followed by a 100 nm thick aluminum layer. Aluminum is chosen for its high conductivity at infrared frequencies leading to a strong antenna effect. Finally, a 220 nm wide BNA with square gap smaller than 40 nm and 45 • flare angles is opened at the rounded apex of the tip by Focused Ion Beam (FIB) milling. Figure 1(a) and Fig. 1(b) display scanning electron micrographs of a resulting fiber device. The BNA is designed to be resonant at λ =1.55 microns when it is in contact with an air/InP interface. The design process is performed using three dimensional Finite Difference in Time Domain method (3D FDTD) [36]. Figure 1(c) shows the collection spectrum of the BNA probe placed 10 nm away from a semi-infinite medium of InP, in air. Note that the presence of this high-index semi-infite medium has a strong impact on the resonance properties of the BNA and has to be taken into account in the design of the BNA. In the simulation, the BNA is excited by a single dipole positioned 5 nm below the gap of the BNA, orthogonal to the common median of the triangles, and radiating a single temporal pulse. The time-varying Poynting vector flow is calculated inside the probe, integrated over a transverse cross-section located 2 microns away from the BNA. The spectrum of the collected power is calculated by Fourier-transforming this result. The BNA resonance, of quality factor about 6, is large enough to allow an efficient nanocollection of the optical signal at wavelengths ranging from 1450 nm to 1650 nm. The polarization ratio of the BNA probe with dipolar excitation has been predicted a.u. to be about 1:170 in a previous study but can vary with the nature of the optical fields probed by the BNA [30].

Photonic crystal structure
The PC design consists of a honeycomb lattice of cylindrical air holes (with a lattice parameter A=730 nm and a 245 nm hole diameter) patterned in a 240 nm thick InP slab bonded on top of a transparent SiO 2 substrate (see Fig. 2(a) and Fig. 2(c)). The PC structure is designed to support a low curvature band-edge mode at the Γ-point of the first Brillouin zone. This SBM radiates in the vertical direction and will be labelled M-mode, in reference with the monopolar symmetry of the magnetic field [8]. The light distribution of the M-mode at the surface of the 2D-PC was modelled using 3D FDTD and is presented in Fig. 2(a). In the simulation, the mode expansion is limited by the edges of the PC-structure. The light intensity is maximum at the center of the PC and its global envelope is gaussian. In addition, simulations indicate that the intensity is distributed in each unit cell of the honeycomb lattice in a "doughnut" shape of about 260 nm of outer radius and 90 nm of inner radius ( Fig. 2(b)). The polarization of the electric field inside each unit cell is azimuthal : the zero of the intensity of the field at the center of each hexagon is due to a phase singularity. These axially-polarized nano-doughnut beams are actually ideal test beds for assessing the polarization sensitivity of nano-objects such as single molecules

Experimental set up
PC structures are optically pumped at λ =780 nm with a laser diode. In our set-up, we used an inverted microscope to pump the sample from the back side. The pump laser beam is focused onto the 2D-PC through the silica substrate with a corrected objective of numerical aperture (NA) equal to 0.75. Its position and shape are perfectly controlled : the excitation spot at the PC surface has a Gaussian profile and a surface area smaller than 10 μm by 10 μm (Fig.  3(a)). Simultaneously to far-field measurements, SNOM acquisitions are carried out in collection mode with a stand alone commercial head (NT-MDT SMENA) positioned at the top of the inverted microscope (detailed experimental set up can be found in [8]). Near-field images are recorded by collecting locally the optical information through the BNA fiber probe during raster scan across the PC structure. After collection by the probe, the pump light is filtered out by a long-pass filter (cutoff wavelength 1100 nm). A monochromator with a 1 nm resolution in the infrared, and a thermo-electrically cooled InGaAs photodetector are used for spectral measurements. The distance between the probe and the sample is regulated using a non-optical shear-force feedback loop that keeps the probe less than 10 nm away from the sample. In our experiments, the orientation of the BNA is kept fixed with respect to the scan direction. To probe the different polarization components of the SBM, we simply rotate the sample. For comparison, near-field measurements have also been conducted with conventional SNOM probes: metallized probes with 200 nm large circular aperture. These apertures have been engineered at the apex of the same polymer tips that we use for the BNA.

Results and discussion
Under these excitation conditions, the M-mode is lasing. The laser beam emitted by the PC structure is imaged in far-field with the same objective coupled to an infrared camera ( Fig.  3(b)): it takes the shape of a large doughnut and is found to be azimuthally polarized [8]. Figure  3 shows the topographic shear-force images of the structure and the optical near-field images recorded with the BNA-on-tip at the lasing wavelength λ =1611 nm. In this study, the BNA is oriented along two characteristic orthogonal axes of the honeycomb lattice unit cell, called x-axis and y-axis in the following (see insets of Fig. 3). In Fig. 3(c) and Fig. 3(e), the two triangles of the BNA-on tip are aligned with the y-axis whereas in Fig. 3(d) and Fig. 3(f), the sample has been rotated by 90 • so that the BNA-on-tip is oriented along the x-axis. The hole pattern of the 2D-PC is clearly visible in Fig. 3(c) and Fig. 3(d) which demonstrates the ability of the tip to yield the correct topography of the PC. Figure 3(e) and Fig. 3(f) show that the optical contrast is excellent for the two orientations of the BNA tip. Laser emission is achieved in both configurations, which demonstrates that any loss induced by the presence of the BNAon-tip in the near-field of the PC is small enough not to hinder the lasing process. Moreover, the lasing wavelength and the far-field pattern of the laser mode remain unchanged irrespective of whether the BNA tip is present. This is a very good indication that the tip does not perturb the M-mode. Unlike cavity (defect) modes, large stationary modes such as slow band-edge mode are more robust to small perturbations such as a single BNA-on-tip [40]. Figure 4 shows the comparison between simulation (3D FDTD) and experiment (SNOM) for the electric field intensity of the M-mode mode across a few unit cells of the PC. The SNOM images over a given area are captured with either a BNA or a 200 nm large circular nano-aperture. Figure 4(a) and Fig. 4(b) show the simulation of the total electric intensity (|E x | 2 + |E y | 2 ) and the near-field optical image recorded with a 200 nm aperture tip, respectively. The circular aperture tip is able to resolve the light distribution inside a unit cell, revealing the doughnut shape of the optical field [8]. The convenional-tip resolution is estimated by comparing the computed and the experimental maps and found to be of the order of λ /7. This figure is in good agreement with the aperture size which is about 200 nm. Note that the sensitivity of the SNOM tips to the electric and/or magnetic optical fields cannot be determined experimentally with the SBM for which the transverse electric and transverse magnetic intensities overlap and lead to the same light patterns. Figure 4(c) and Fig. 4(e) display the simulations of the intensity distributions |E x | 2 and |E y | 2 , respectively. The corresponding SNOM images with the BNA tip oriented along the x-axis and y-axis are reported in Fig. 4(d) and Fig. 4(f), respectively. Experimental maps are recorded on the same structure as in Fig. 3. The theoretical results are in excellent agreement with the experimental results despite the fact that the tip is not taken into account in the simulations. It clearly demonstrates the ability of the nanoantenna to provide accurate subwavelength information on the vectorial properties of the SBM. Note that the orientation of the BNA-on-tip with respect to the PC can be directly inferred from the experimental acquisitions because of the azimuthal polarization [37,38].To estimate the performances of the BNA-on-tip as polarizing nanocollector, cross sections of Fig. 4(d) and Fig. 4(f), taken along the x and y-axis over a unit cell (≈ 1.5μm

Conclusion
In conclusion, we have used a bow-tie aperture nanoantenna (BNA) to perform a local, nearfield optical probing of the electric field polarization of a slow Bloch laser mode (SBM) in a photonic crystal. The high sensitivity of the BNA to the electric field and its polarization filtering properties yield optical near-field probes with a high spatial resolution and an enhanced collection efficiency compared to conventional, metal coated optical fiber probers. The BNA probe's ability to discriminate between near-field polarization states on a subwavelength scale has been demonstrated by measuring the experimental SBM spatial profile and comparing it to 3D FDTD simulations. An excellent agreement was found which highlights the fact that the BNA near-field probe does not generate any significant perturbation of the optical mode of the photonic crystal. We have also shown that the BNA can overcome one of the main limitations of SNOM, linked to the well-known trade off between resolution and signal-tonoise ratio. In future studies, the coupling of BNA probes with heterodyne detection SNOM would allow for the full vectorial characterization of optical modes at the surface of PCs, for both the electric and magnetic fields [38]. The present investigation also paves the way for emerging nanophotonic architectures aiming at integrating nanoantennas [44,45] on top of a PC resonator. Nanoantenna-on-fiber devices could also be seen as an optimized interface for out-coupling optical energy from PC structures toward fiber networks.