Nano-mechanical tuning and imaging of a photonic crystal micro-cavity resonance

: We show that nano-mechanical interaction using atomic force microscopy (AFM) can be used to map out mode-patterns of an optical micro-resonator with high spatial accuracy. Furthermore we demonstrate how the Q-factor and center wavelength of such resonances can be sensitively modified by both horizontal and vertical displacement of an AFM tip consisting of either Si 3 N 4 or Si material. With a silicon tip we are able to tune the resonance wavelength by 2.3 nm, and to set Q between values of 615 and zero, by expedient positioning of the AFM tip. We find full on/off switching for less than 100 nm vertical, and for 500 nm lateral displacement at the strongest resonance antinode locations.


Introduction
Nano-mechanical interactions with the evanescent field of photonic crystal (PhC) microcavities (MCs) enable tuning of important resonator properties such as quality-factor (Q) and resonance wavelength. The fabrication of high-Q silicon-on-insulator (SOI) based PhCs demands sophisticated nanometer-scale-precision [1][2][3], and has driven the search for alternative resonator tuning strategies. These include using heaters to achieve thermo-optic tuning [4,5], and pore infiltration by liquids [6], polymers [7] or liquid crystals [8] to achieve a broad tuning range. The progress in micrometer-scale integrated optics has led to an increase in attention for mechanical tuning [9][10][11][12]. Mechano-optical interactions have been utilized in for example sensor [13] and actuator [14] applications to modulate the evanescent field. Two types of interaction can be effected, namely changing the modal amplitude through the attenuation constant (leaking or scattering of light, which can been used for scanning nearfield microscopy [15]), or changing its phase through the phase constant (changing the effective refractive index). In traditional mechano-optical approaches, the size of the object placed in the evanescent field is much larger than the optical wavelength [14] to obtain a sufficiently large phase shift while avoiding strong attenuation. In this case, boundary effects causing out of plane scattering can be neglected. However, if we use a resonant cavity that provides a strongly enhanced field in a small volume (that is, a high quality factor to modal volume ratio Q/V [16]), then an object as small as 10 nm in close proximity to the resonator can strongly affect the transfer properties [17,18]. Although the analysis of nano-mechanooptical transduction is more involved than that of the classical configuration, we demonstrate that it also offers many more opportunities for manipulation of light. We explore this manipulation experimentally in great detail using a high Q/V micro-cavity in a photonic crystal slab.

Design and realization
For the experiments reported here, we designed a PhC MC in SOI (220 nm device layer thickness on 1 μ m buried oxide) with a triangular lattice of periodicity a = 440 nm and a hole radius r = 270 nm. We chose a relatively large cavity, designed to have a resonance near 1550 nm wavelength, and a medium Q-factor of 650 with a high finesse to have a good wavelength separation of adjacent resonances. In principle the MC could be made smaller and optimized for high Q [19], but this is not needed due to the strong interaction of the probe with the cavity resonance. The Fabry-Pérot-type cavity is defined in a W1 line-defect waveguide (1 row left out), providing optical access for transmission measurements. We calculated the resonant field distribution using a finite-difference time-domain method. Although accurate modeling requires full 3D calculations [20] and consequently high computer resources, we relied on (fast) 2D calculations, which have been qualitatively validated by a 3D calculation. The pattern shows 8 fringes with two distinct major peaks in the field amplitude within the resonator, close to the entrance and exit of the cavity [see Fig. 1(a)]. One may expect that a disturbance at these two peaks will have the largest effect on two essential resonance properties: central resonance wavelength and Q. The structure as shown in the SEM photo in Fig. 1(b), was fabricated (at IMEC, Belgium) using a process [21] involving deep UV lithography (λ = 248 nm) and reactive ion etching. The resonance wavelength λ r,0 of the fabricated cavity was measured to be 1539.25 nm.

Measurement principle and imaging results
To bring a nano-sized object in the field of the resonator in a controlled way, we combined a typical optical end-fire transmission setup with a stand alone scanning tip AFM stage [22] [ Fig. 2(a)]. For our first experiments we selected an AFM tip that is expected to have a relatively small impact on optical loss, by choosing a small size (minimum radius 10 nm) and a low-loss material Si 3 N 4 , with a refractive index (n Si3N4 ~ 2) lower than the effective index of the guided mode in the photonic crystal waveguide (n eff ~ 2.9). By raster scanning the AFM probe over the sample in contact mode and closed loop operation, we obtained both geometrical and optical transfer information from the AFM deflection data [ Fig. 2 We chose a 20 nm interpixel grid distance, resulting in a scanning window size of 5.2 x 5.2 micrometers. However, grid sizes as small as 1 nm or less can be selected when needed. By combining both the deflection and optical transmission data, the exact locations of strong interaction of the probe with the optical field in the cavity can be visualized, as shown in Fig.  2(d), where the topographic data has been enhanced in order to improve the visibility of the holes. The figure shows how the transmitted optical power is affected by the tip through both detuning the cavity and causing scattering loss [17]. A simple intuitive model, taking into account only the tuning effect, predicts a decrease in transmitted optical power if the source wavelength λ s is set to a value smaller than the undisturbed resonance wavelength λ r,0 , because the resonance wavelength λ r is shifted further away from λ s (to longer wavelengths). Conversely, if λ s is longer than λ r,0 , an increase in transmitted power will be detected (moving up the transmission-wavelength curve of the resonance). Note, however, that this model is rather simplified, an issue addressed experimentally below.  Figs. 2(d) and 1(a) shows that that the method can be used to find the maximum field locations of a cavity resonance. Moreover it proves that these locations are indeed the "hottest spots" for tuning [17,18] as predicted by the simulations [ Fig. 1(a)]. We have further used this innovative method of visualizing the resonator properties to study the wavelength dependent cavity disturbance. Figure 3(a) shows the transmission result for λ s =λ r,0 which confirms the expected decrease in power transmission at the locations of field maxima in the cavity. For λ s slightly larger than λ r,0 we find an interesting complex pattern, shown in Fig. 3(b), with reduced transmission at some probe locations and increased transmission at others. This complex pattern can be explained by the wavelength dependence of each extreme in the MC on the resonance wavelength shift and induced loss. Increasing λ s further to a value larger than λ r,0 , we find the inverse image of Fig. 3(a), as shown in Fig. 3(c).

Cavity tuning method and results
A stronger response can be expected when the Si 3 N 4 tip is replaced by a Si one, due to its much larger refractive index (n Si ~ 3.45). We used a Si tip with minimum radius of only 7.5 nm. In order to explore the height dependence of the mechano-optical interaction, we used the AFM in tapping mode. By adjusting the tapping amplitude we obtained control of the average height (in time) above the surface. The very high sensitivity of transmission to the average tip height is shown in Figs. 3(d)-3(f). Another advantage of tapping mode is that the tip wears out at a much lower pace compared to contact mode. After locating the field maxima at resonance in tapping mode, we placed the tip exactly in the middle of the largest maximum at the input side [labeled A in the inset of Fig. 4(a)], switched to contact mode, and measured the spectrum [ Fig. 4(a)]. We found a full drop of about 7 dB in the transmitted power (black curve) for this cavity. After moving the tip to point B, we measured the spectrum again. The new spectrum (red), compared to the undisturbed one (blue) shows a shift in λ r of about 2 nm and a reduction of Q by a factor of about 2, while the transmission has dropped by ~ 4 dB. To find the exact lateral dependence of the transmitted power [in the y direction as shown by the dotted line in the inset of Fig. 4(a)] for a wavelength at λ r,0 , we plotted the transmitted power versus vertical tip displacement, see Fig. 4(b). The graph shows that the cavity resonance is highly sensitive to tip displacement and can be switched on and off by a lateral tip displacement of about 500 nm.  Fig. 4(b)]. The wavelength dependency of each point in the resonator could be found by performing 2D scans in the XY plane for wavelengths ranging from 1538 nm to 1544 nm with a step of 0.25 nm, using both a Si 3 N 4 and an Si tip in contact mode. Using these results, fitted to the expected Lorentzian response, we mapped the shift of the resonance wavelength and the change in Q as a function of the displacement from the center position of the antinode. The results for the Si 3 N 4 tip are shown in Fig. 5(a). A maximum detuning of λ r by 1.8 nm (0.12 % of λ s ) is found together with a maximum Q change of 50 %. The shape of the Q-factor curve is less smooth due to the larger uncertainty in the width parameter found by applying the fitting procedure. The experiments with the Si tip show that a further detuning is possible [ Fig. 5(b)]. However for tip positions too close to the field maximum, it was not possible to fit the data because the power had dropped below the noise level, as is also shown by the black curve in Fig. 4(a). We found a maximum detuning of λ r by ~ 2.3 nm (0.15 % of λ s ) and a maximum change of Q by 65 %.

Conclusion
In conclusion, we have shown experimentally that an AFM probe can be used to map out the resonance pattern of a PhC MC with, to our knowledge, the highest resolution reported so far. The results show the exciting complex behavior that follows from the interaction of a nano-tip with the resonator mode, which is an interesting subject for future theoretical and experimental studies. Furthermore we have shown that the two important parameters (Qfactor and resonance wavelength) of a PhC MC can be nano-mechanically tuned over a considerable range. The results strongly motivate further exploitation of the tip-resonator mode interaction, which may be used for designing many new complex optical structures, such as a mechano-optically integrated reconfigurable PhC add-drop multiplexer. Another implication of our study is that near-field probing on high Q (or bandwidth limited ultra slow light [23]) structures cannot be performed without appreciably changing the optical properties of the device under study (while maintaining the same spatial resolution). Finally we mention that the strong advantage of this tuning is the ability to compensate for inevitable small fabrication errors, i.e. shifting the resonance wavelengths or changing the Q-value to the desired values.