Analytical analysis of modulated signal in apertureless scanning near-field optical microscopy C. H. Chuang and Y. L. Lo *

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1 Research Volume 5 Issue 10 - October 3, 2008 [ ] Analytical analysis of modulated signal in apertureless scanning near-field optical microscopy C. H. Chuang and Y. L. Lo * Department of Mechanical Engineering, National Cheng Kung University, Tainan, Taiwan * loyl@mail.ncku.edu.tw Optics Express, Vol. 15, No. 24, pp (2007) 1. Introduction For many years, the resolution of optical microscopy was limited to the order of approximately 1/2λ as a result of the far-field diffraction effect. Most popular equipment to break down the diffraction limit is scanning near-field optical microscopy (SNOM), a metallic aperture is used to confine the near-field light emanating from or entering the probe tip. However, the resolution is limited to approximately 50 nm since the tapered glass fiber tip causes a waveguide cut-off effect. Accordingly, an alternative SNOM configuration was proposed in which the optical fiber was replaced with small scatter, yielding an enhanced resolution of approximately 10 nm depending on the tip diameter. In this configuration, the incident light illuminates the small scatter and induces an enhanced electric field between the tip and the sample whose magnitude depends on the dipole effect. Measuring the near-field interaction electric field is the operating principle. This device is conventionally referred to as the apertureless scanning near-field optical microscope (A- SNOM). However, in A-SNOM, the near-field electric field is seriously affected by a background interference electric field and therefore it is necessary to develop techniques for eliminating the background-scattering noise from the detected signal in order to improve the imaging resolution. This paper develops a detailed analytical model of the detected A-SNOM signal and investigates the variation in the signal contrast and intensity as a function of the phase modulation depth, the wavelength and angle of the incident light, and the amplitude of the AFM tip vibration. The analytical results are intended to clarify the factors determining the detection signal contrast such that the imaging capabilities of A-SNOM can be further improved. As comparison with the fore-experimental results, the authors adopted higher order harmonic radian frequency in order to improve signal contrast, and it consists with ones of our major findings. 1 of 5

2 Fig.1 Model of A-SNOM near-field region. 2. Analytical model of A-SNOM Fig. 1 presents a schematic illustration of the A-SNOM near-field region. Note that to simplify the analytical model used in this study, an assumption is made that both the incident light and the detection light pass through the same objective lens. As shown, the incident angle of the electric field is denoted by θ. The most important, yet the weakest, is the interaction signal between the AFM tip and the sample. This interaction (or enhancement) effect can be described using the general model of quasielectrostatic theory. = (1) where is the interaction electric field, α eff is the effective polarizability, E i is the amplitude of the incident electric field, and ω and are the frequency and initial phase of the interaction electric field, respectively. Of these parameters, is a critically important factor in A-SNOM since it contains all the necessaries to predict the relative contrasts observable in A-SNOM. The value of α eff is determined by the tip radius, the dielectric constants of the AFM tip and the sample, respectively, and the distance between them. During the imaging process, the AFM drives the probe with a vertical cosine displacement around a mean position Z0, with an amplitude A and radian frequency of ω0, respectively. Therefore, the position of the probe at any time t can be written as Z(t)=Z 0 +Acos(ω 0 t) (2) 2 of 5

3 An assumption is made that the AFM tip does not perturb the near-field region. As a result, the scattering electric field from the tip (See Fig. 1) can be expressed as = (3) where E T and are the amplitude and initial phase of the scattering electric field, respectively, ω is the radian frequency, and K is the wave number of the incident light (given by 2π/λ). The third electric field in the near-field region is the scattering light from the sample surface. Since this light is not modulated by the AFM tip, it can be described simply as (4) where E S and are the amplitude and initial phase of the scattering light from the sample surface. 3. Modulation signals of A-SNOM As described above, the incident electric field with an incident angle θ generates three major electric fields in the near-field and far-field detection regions, namely the electromagnetic interaction electric field between the AFM tip and the sample, the scattering electric field from the AFM tip, and the scattering electric field from the sample. Thus, the total electric field coupled into the objective lens is equal to the sum of the three individual electric fields, i.e. (5) Applying the Fourier-Bessel series expansion and assuming that ψ 1 = - +2Ksin(θ)Z0, ψ 2 = - +2Ksin(θ)Z0 and ψ 3 =2Ksin(θ)A I(t) can then be decomposed into the following major terms: + High Order Modulation Frequency Terms (6) Although Eq. (6) still appears complicated, it provides some indications as to how to deal with the three 3 of 5

4 different electric fields,,, and, within the detected signal. 4. Wavelength and incident angle effects in A-SNOM In optical systems, the longer wavelength results in the poorer resolution, and thus electron microscopes provide a far better resolution. In previous A-SNOM investigations, researchers have claimed that the resolution is independent of the wavelength of the incident light and have suggested that the key factors determining the resolution are actually the aperture and tip size in SNOM and A-SNOM, respectively. The qualitative observation that using the longer wavelength improves the signal contrast for a constant order of modulation radian frequency is found. In our study, a quantitative model is presented and given for more detail discussion in wavelength influence. To test this claim, this study examines the effect of the wavelength on the contrast and intensity of the various components in the A-SNOM lock-in detected signal. The relationships ψ 3 =2Ksin(θ)A and K=2π/λ are substituted into Eq. (6) in order to get the relation between wavelength and signal contrast. Note that in accordance with the experimental results, the incident angle θ is specified as π/4 and the amplitude A of the tip vibration is set to 60 nm. Therefore, Fig. 2 plots the results obtained for the variation of the signal contrast (S1/S2) with the wavelength of the incident light. From the results in Fig. 3, it is clear that the angle of the incident light is not as influential as the wavelength in the lock-in detection technique, i.e. since I2ω 0, I3ω 0, and I4ω 0 have very similar signal contrasts. However, the incident angle is known to have a key effect on the tip enhancement in A-SNOM Overall, combining the results presented here with those reported in the literature it can be inferred that a smaller incident angle provides both a better tip enhancement and an improved intensity contrast. Fig.2 Variation of signal contrast with incident wavelength in A-SNOM. 4 of 5

5 Fig. 3 Variation of signal contrast in different order of modulated frequency with incident angle. 5. Conclusions This study has presented a comprehensive modulation analysis of the detected signal in A-SNOM. A mathematical model has been constructed to describe the interference among the electromagnetic interaction field between the AFM tip and the sample, the scattering electric field from the AFM tip, and the scattering electric field from the sample surface. In conclusion, the analytical formulae and results presented in this study provide new insights into the complex phenomena of A-SNOM and indicate potential techniques for improving the signal resolution of A-SNOM measurement systems. 5 of 5