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Multi-frequency near-field scanning optical microscopy

This content has been downloaded from IOPscience. Please scroll down to see the full text. 2014 Nanotechnology 25 035203 (http://iopscience.iop.org/0957-4484/25/3/035203) View the table of contents for this issue, or go to the journal homepage for more

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Nanotechnology Nanotechnology 25 (2014) 035203 (6pp)

doi:10.1088/0957-4484/25/3/035203

Multi-frequency near-field scanning optical microscopy ´ Greusard2 , Sergey Sukhov1 , Dana C Kohlgraf-Owens1 , Leo 2 Yannick De Wilde and Aristide Dogariu1 1 2

CREOL, The College of Optics and Photonics, University of Central Florida, Orlando, FL 32816, USA Institut Langevin, CNRS UMR7587, F-75005 Paris, France

E-mail: [email protected] Received 11 October 2013, in final form 12 November 2013 Published 17 December 2013 Abstract

We demonstrate a new multi-frequency approach for mapping near-field optically induced forces with subwavelength spatial resolution. The concept relies on oscillating a scanning probe at two different frequencies. Oscillations at one frequency are driven electrically to provide positional feedback regulation. Modulations at another frequency are induced optically and are used to measure the mechanical action of the optical field on the probe. Because the measurement is based on locally detecting the force of the electromagnetic radiation acting on the probe, the new method does not require a photodetector to map the radiation distribution and, therefore, can provide true broadband detection of light with a single probe. Keywords: optical force, near-field scanning optical microscopy, opto-mechanics, scanning probe microscopy, atomic force microscopy S Online supplementary data available from stacks.iop.org/Nano/25/035203/mmedia (Some figures may appear in colour only in the online journal)

1. Introduction

preserving the high spatial resolution across the sample [7–9]. In this paper we introduce multi-frequency near-field scanning optical microscopy (MF-NSOM) that permits simultaneous measurement of the topography of a surface and the spatial distribution of optically induced forces acting on the probe.

Detecting light with a spatial resolution that overcomes the diffraction limit is of interest in many areas including the design and characterization of metamaterials and plasmonic nanostructures as well as in various biophotonics applications [1–3]. In typical near-field scanning optical microscopy (NSOM), a sharp probe or small aperture is used to scatter the electromagnetic field close to the surface of a sample where high spatial resolution information is contained in the evanescent fields. The probe converts the field structured at subwavelength scales into a propagating one which is then measured with a photodetector in the far-field. We have recently shown that light can also be detected via the gradient of the optical force exerted on the scanning probe [4–6]. This opens up new possibilities for detecting electromagnetic fields, not by energy transfer in a photon detector but by means of optically induced forces. In scanning probe microscopy, multi-frequency operation provides access to different physical properties while 0957-4484/14/035203+06$33.00

2. Methods and experimental details 2.1. Tuning-fork-based NSOM

The surface topography is recorded in the usual manner using an oscillating quartz tuning fork having a sharp probe rigidly fixed to one of its arms. When the probe is brought close to an interface, the resonance frequency of the tuning fork and/or the dissipation rate are affected by surface forces, which change the amplitude and/or the phase of the induced oscillations. A feedback loop maintains a constant phase of the piezoelectric signal relative to the driving voltage and establishes a constant tip–sample separation in the proximity of the sample. The presence of an optical field induces 1

c 2014 IOP Publishing Ltd Printed in the UK

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Figure 1. (a) MF-NSOM operation: two voltage generators are used to modulate the electrical driving of a tuning fork and the light

intensity. (b) Typical amplitude and phase of probe oscillations caused by optically induced forces observed at a higher order resonance of the tuning fork.

additional forces acting on the same probe. When this field is modulated, it can induce probe oscillations that can be measured via the same piezoelectric effect on the tuning fork. A second lock-in detection system may be used to separate and measure the amplitude and phase of the oscillations induced by optical forces. In this paper, we demonstrate that this combined electrical and optical multi-frequency operation is indeed possible. The concept is illustrated schematically in figure 1. The first mechanical resonance of a tuning fork is used to provide the feedback for distance regulation while the light intensity illuminating the probe is modulated at a frequency ωopt , which is scanned across a second, higher order resonance. In the experiment depicted in figure 1(a), a standard gold-coated pulled fiber NSOM probe with a manufacturer specified 100 nm diameter aperture connected to a Nanonics MultiView 4000 is illuminated from beneath with 635 nm laser light coupled out of a single mode fiber. The peak average intensity at the fiber face was maintained at a moderate level of 0.36 mW µm−2 and the probe was placed 2 µm above the surface. As can be seen in figure 1(b), the signal from the tuning fork, demodulated at the frequency ωopt , exhibits a clear resonance signature, which provides a direct measure of the optical force acting on the tip.

frequency of the laser source illuminating the sample, ωopt . A feedback loop on the signal demodulated at ωe is used to maintain constant modulation amplitude of the cantilever. This signal is used to measure the topography as in standard atomic force microscope measurements. The amplitude and phase of the signal demodulated at ωopt relate to the optical force driving the cantilever probe as explained further in the text.

2.2. Cantilever-based NSOM

where m is the equivalent mass of the oscillator. The probe’s position z = z0 + a around its undeflected position z0 oscillates with an amplitude a ≈ ae + aopt = Ae exp(iωe t + iφe ) + Aopt exp(iωopt t + iφopt ). Thus, the probe is modulated electrically and optically at the frequencies ωe and ωopt , respectively. The eigenfrequencies and the quality factors of the closest resonances are denoted by ω0 and Q. The oscillator is driven electrically by a force fe = Fe exp(iωe t) applied to the tuning fork and by a component fs = (∂Fs /∂z)a of the tip–sample interaction force which contributes to the signal at both frequencies ωe and ωopt . In general, these are typical surface contributions due to van der Waals/Casimir forces, meniscus forces, etc. In addition, the motion of the probe is also affected by an optically induced force fopt = fopt mod + fopt avg = Fopt mod exp(iωopt t) + (∂Fopt avg /∂z)a which has a component Fopt mod modulated at ωopt and a gradient component ∂Fopt avg /∂z due to the nonzero average optical

2.3. Multi-frequency detection concept

The physical origin of the measured signals can be understood by considering the NSOM probe as a damped, driven harmonic oscillator [12] (a detailed description is included in the supplemental materials available at stacks.iop.org/Nano/ 25/035203/mmedia). The coupled equations of motion along the direction of the probe’s oscillation are   ω0e 2 m a¨ e + i a˙ e + ω0e ae = fe (t) + fs (r) Qe + fopt (r, t)   (1) ω0opt 2 a˙ opt + ω0opt aopt = fe (t) + fs (r) m a¨ opt + i Qopt + fopt (r, t)

To demonstrate the generality of the proposed method, similar measurements were performed with a cantilever-based setup shown in figure 2. A detailed description of this setup can be found elsewhere [10]. For the force measurements, an AFM highly doped silicon tip (apex ∼ 20 nm) is mounted on a top-coated cantilever [11]. The system ‘cantilever + tip’ is then set on a piezoplate. The latter is driven electrically at a typical resonance frequency around 70 kHz, which makes the tip oscillate vertically. The control of the probe-sample distance relies on a beam-deflection laser system (λ = 980 nm) where the beam reflected off the cantilever is then sent onto a four-quadrant detector, which measures the ‘T-B’ signal as shown in figure 2. Two lock-in detectors are used to demodulate the signal at the electrical driving frequency, ωe , and the modulation 2

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Figure 2. Cantilever-based setup to measure the optically induced forces (OIFs): the optical field studied is modulated in intensity at ωopt

while a standard AFM silicon tip is mechanically excited at ωe . The tip–sample distance is controlled with a deflection-beam laser (λ = 980 nm) which is sent onto the top side of a cantilever where it is then reflected to a four-quadrant photodiode. The latter delivers a ‘T-B’ signal which is divided into two beams. One is demodulated at ωe for the topography. The other is demodulated at ωopt and gives the OIF measurements.

3. Results

intensity intrinsically incident on the probe. For conceptual clarity, we have assumed in the equations above that the surface and the optically induced force gradients are constant over the probe’s oscillation cycle such that a two term Taylor expansion can be used for both forces fs and fopt . Quantitative analysis requires rigorous computation of the forces over the probe oscillation cycle, however the essential physics remains the same [13]. The signal collected from the oscillating tuning fork or cantilever is demodulated at the electrical and optical driving frequencies. At the optical modulation frequency, the measured amplitude Aopt and phase φopt of the oscillation relative to the optical driving signal are given by   Fopt mod (r) 1 ∂Ftot (r) 2 2 2 Aopt (r) = ω0opt − ωopt − m m ∂z  2 − 1 2 ω0opt (2) + ωopt Qopt   (ω0opt ωopt )/Qopt ϕopt (r) = tan−1 2 2 − 1 ∂Ftot (r) ω0opt − ωopt m ∂z

To demonstrate the subwavelength resolution of tuning fork based MF-NSOM, we used a Nanonics MultiView 4000 instrument to measure a gold nanosphere lithography (NSL) sample with better than λ/50 resolution. To illuminate the sample, we placed it over the face of a single mode fiber from which 1550 nm light was coupled out using a setup similar to the one shown in figure 1(a). The illumination had an average intensity at the center of the spot of 0.26 mW µm−2 and was modulated at 218.43 kHz, a frequency near a higher order resonance of the Cr-coated AFM probe used in this experiment. The NSL sample was made using 0.453 µm spheres, corresponding to the triangles having a center to center spacing of about 260 nm [14]. In figure 3 we present the NSL topography measured at ωe as well as the amplitude and phase of the signal measured at the optical modulation frequency ωopt . To better clarify the spatial location of the amplitude signal relative to the topographic features of the sample, in figure 3(d) the amplitude color map is superimposed onto the 3D topography. To demonstrate the general nature of the MF-NSOM concept outlined here, we repeated the above experiment with a cantilever-based system. Typical results are shown in figure 4. The only differences in comparison with the data presented in figure 3 are the 633 nm operation wavelength and the optical modulation frequency which is now 109 Hz and thus significantly below the lowest mechanical resonance of the cantilever. As can be seen, the results in figures 3 and 4 are quite similar. Specifically, one can clearly note that, again, the amplitude is the lowest over the pads, moderate over glass, and highest near the vertices. These examples demonstrate that both tuning fork and cantilever-based systems can be used in MF-NSOM to

where ∂Ftot /∂z = ∂Fs /∂z + ∂Fopt avg /∂z. From equation (2), we observe that amplitude variations measured at ωopt are due to changes in the strength of both the modulated optical force Fopt mod and the gradient of the total interaction force ∂Ftot /∂z, which acts to shift the resonance frequency of the probe and thus the compliance of the tuning fork at the driving frequency. Likewise, variations in the phase are due to the same force gradient induced changes in the resonance frequency. In principle, by combining these two signals for a well characterized system, it is possible to extract both the magnitude of the optical force acting on the probe and its gradient. 3

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Figure 3. The NSL topography (a) measured at ωe , and the amplitude (b) and phase (c) of the tuning fork signal measured at the optical driving frequency ωopt . (d) Color coded amplitude in (b) mapped on the three-dimensional topography of the NSL sample.

Figure 4. The NSL topography (a) and the corresponding optical force amplitude (b) measured with a cantilever-based NSOM. The

measurement was performed in conditions similar to figure 3(b).

measure near-field optical forces with high spatial resolution. Because of their higher quality factor, tuning fork systems need to be operated close to their mechanical resonances, a requirement which is not so stringent in the case of cantilevers. However, higher quality factors mean that the off-resonance, background contributions are more efficiently suppressed.

interaction force arising from the high sensitivity of the phase to local topographic variations. Changes in the measured amplitude, on the other hand, have two possible origins: variations in the optically induced force Fopt mod and modifications of the effective resonance frequency due to the same force gradients discussed before. In this context, two features of the data in figure 3 are worth noting. First, the oscillation amplitude is lower when the probe scans over the gold regions and is higher over the bare glass where the intensity is also stronger. The second observation relates to the locations of the highest oscillation amplitudes, i.e. the hot-spots seen near the particle vertices. In these areas, the optical forces Fopt mod are strongest because their magnitude is directly proportional to the strength of the electric field distribution. One can conclude that the changes in the signal’s amplitude are mainly due to variations in the magnitude of optically induced forces; thus the image in figure 3(b) demonstrates the possibility of measuring optical force distributions with very high spatial resolution. Similar conclusions can be reached from finite element calculations of the field, optical force, and optical force gradient acting on a dipole probe. In this case, the time

4. Discussion

Let us now interpret these observations in view of the model outlined here. As can be seen in figure 3, the measured amplitude is lowest over the gold pads, moderate over the glass, and is highest near the corners of the NSL sample. The phase, on the other hand, closely follows the topography. First, according to equation (2), changes in the phase signal arise due to shifts in the resonance frequencies which, in turn, are determined by the gradient of the total interaction force. Because the measured phase closely follows the topography, one can infer that changes in the phase signal are mainly determined by variations in the local gradient of the surface 4

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manner similar to a lock-in detector designed to extract the desired information from the nonlinear interaction between the scanning probe and its environment. Thus it is in principle possible for such a resonator to act as a detector of electromagnetic radiation with an integrated lock-in in a single, compact device. Therefore, the multi-frequency operation demonstrated here could provide the framework for designing novel detectors based on the exchange of energy between optical radiation and mechanical probes. While the ability to tune a mechanical resonance frequency is still limited, the possibility of detecting electromagnetic radiation via direct optomechanical action on resonators is a topic of considerable interest.

averaged optical force along the direction of probe oscillation, hFz i, is given by hFz i = 12 Re(αE(∂E∗ /∂z)) where α is the probe polarizability [15]. This means that the optically induced force is proportional to both the local field E and its gradient ∂E∗ /∂z. Our calculations, included in the supplemental materials (available at stacks.iop.org/Nano/25/ 035203/mmedia), indicate that the forces are strongest at the vertices and also along the edges of the triangles, which is consistent with our experimental findings. We also note that, as no attempt was made to align the polarization state of the incident light with respect to the NSL sample, it may be assumed that the incident polarization state is mixed and, therefore, all three vertices should show strong force effects, as we actually see figure 3(b). It is worth stressing again that the force acting on the probe depends not only on the local strength of the electric field but also on its gradient. This is important because it provides an inherent amplification of the probe’s sensitivity when measuring, with high spatial resolution, distributions of optical near fields which naturally exhibit not only large magnitudes but also strong field gradients. As a consequence, an effective suppression of the influence of propagating fields is achieved without having to detect the harmonics of the driving frequency, as required for scattering NSOM where background suppression is obtained at the expense of significantly reduced signal strength [16]. When measuring the properties of an optical field close to an interface, the desired information as well as influences from surface topography and other possible interactions are all encoded in the highly nonlinear dynamics of the probe. The bimodal operation where two mechanical eigenmodes of the probe are excited independently allows one in principle to isolate the topography from other interactions affecting the probe. In our case, the excitation of a higher eigenmode is achieved by modulating the strength of the optical interaction, i.e. by modulating precisely the magnitude of the physical quantity to be measured. As is also apparent from equation (2), the detection sensitivity depends on both the quality factor of the mechanical resonator and the coupling between the probe and the local optical field. While typical quality factors for tuning forks go up to about 104 [17], specialized resonators such as the ones based on whispering galleries can reach factors as high as 109 [18]. The optical response, or the effective polarizability, can also be enhanced considerably by structuring the probe following strategies similar to the ones used in designing nano-antennas [19]. Therefore, one can anticipate that specialized probe designs could achieve significantly higher performance in detecting optical fields with very high spatial resolution, over a broad range of wavelengths, and without using photodetectors. This should be especially appealing in the far-IR and THz regions where there is a recognized lack of a competitive alternative for radiation detection. Similarly, because the resonator (i.e. tuning fork or cantilever) acts as a filter with a certain Q factor, it acts to suppress excitations at frequencies off the mechanical resonances of the resonator. Thus, MF-NSOM operates in a

5. Conclusion

We have demonstrated a novel measurement approach that allows detection of near-field optical forces. It relies on exciting the probe’s oscillation at two different frequencies: one driven electrically, to assist the topographical measurement of a surface, and another one driven optically, which provides a measurement of the optically induced forces acting on the probe. We have shown that such multi-frequency near-field scanning measurements can be performed with very high spatial resolution (better than λ/50) and can be effectively performed with both tuning fork and cantilever-based systems. Furthermore, we have demonstrated that detection of optically induced forces is possible even for all dielectric systems, where thermally induced effects are insignificant. This operation modality provides an attractive alternative to standard near-field scanning optical microscopy in cases where photodetectors are impractical to use, such as in the long wavelength regime, or when it is desirable to use a single probe for sensing a broad range of wavelengths, potentially ranging from the THz to the visible. Acknowledgment

Part of this work is supported by LABEX WIFI (Laboratory of Excellence within the French Program ‘Investments for the Future’) under reference ANR-10-IDEX-0001-02 PSL*. References [1] Novotny L and Hecht B 2006 Principles of Nano-Optics (Cambridge: Cambridge University Press) [2] Shvets G and Tsukerman I 2011 Plasmonics and Plasmonic Metamaterials: Analysis and Applications (Singapore: World Scientific) [3] Stebounova L, Paulite M, Walker G C and Fakhraai Z 2011 2.10—biological imaging using near-field scanning optical microscopy Comprehensive Nanoscience and Technology ed D L Andrews, G D Scholes and G P Wiederrecht (Amsterdam: Academic) pp 263–85 [4] Kohlgraf-Owens D C, Sukhov S and Dogariu A 2011 Optical-force-induced artifacts in scanning probe microscopy Opt. Lett. 36 4758 [5] Kohlgraf-Owens D C, Sukhov S and Dogariu A 2011 Mapping the mechanical action of light Phys. Rev. A 84 011807 5

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[6] Kohlgraf-Owens D C, Sukhov S and Dogariu A 2012 Discrimination of field components in optical probe microscopy Opt. Lett. 37 3606–8 [7] Garcia R and Herruzo E T 2012 The emergence of multifrequency force microscopy Nature Nanotechnol. 7 217–26 [8] Proksch R 2010 Multi-frequency atomic force microscopy Scanning Probe Microscopy of Functional Materials: Nanoscale Imaging and Spectroscopy (Berlin: Springer) [9] Forchheimer D, Platz D, Thol´en E A and Haviland D B 2012 Model-based extraction of material properties in multifrequency atomic force microscopy Phys. Rev. B 85 195449 [10] Costantini D et al 2012 In situ generation of surface plasmon polaritons using a near-infrared laser diode Nano Lett. 12 4693–7 [11] Nanoworld 2013 Arrow-FMRTM http://nanoworld.com/ force-modulation-reflex-coated-afm-tip-arrow-fmr [12] Ruiter A G T, Veerman J A, van der Werf K O and van Hulst N F 1997 Dynamic behavior of tuning fork shear-force feedback Appl. Phys. Lett. 71 28–30

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Multi-frequency near-field scanning optical microscopy.

We demonstrate a new multi-frequency approach for mapping near-field optically induced forces with subwavelength spatial resolution. The concept relie...
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