Mapping the refractive index of optically transparent ... - OSA Publishing

Mapping the refractive index of optically transparent samples by means of optical nanoantenna attached to fiber microaxicon Aleksandr A. Kuchmizhak,1 Dmitriy V. Pavlov,2 Yuri N. Kulchin,1,2 and Oleg B. Vitrik1,2 1

Institute for Automation and Control Processes, Far Eastern Branch, Russian Academy of Science, 5 Radio str., Vladivostok 690041, Russia 2 Far Eastern Federal University, 8 Sukhanova Str., Vladivostok 690041, Russia * [email protected]

Abstract: We demonstrate analytically and numerically that the detection of the spectral response of a single spherical Au nanoantenna allows one to map very small (down to 5·10−4 RIU) variations of the refractive index of an optically transparent sample. Spectral shift of the dipole local plasmon resonance wavelength of the nanoantenna and the spectral sensitivity of the method developed was estimated by using simple analytical quasi-static model. A pointed scanning probe based on fiber microaxicon with the Au spherical nanoantenna attached to its tip was proposed to realize the RI mapping method. Finite-difference time-domain numerical simulations of the spectral properties of the proposed probe are in good agreement with the theoretical quasi-electrostatic estimations for a radius of the nanoantenna not exceeding the skin depth of Au. ©2014 Optical Society of America OCIS codes: (250.5403) Plasmonics; (260.3910) Metal optics; (260.5740) Resonance; (000.4430) Numerical approximation and analysis.

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#209237 - $15.00 USD Received 31 Mar 2014; revised 14 May 2014; accepted 17 May 2014; published 22 May 2014 (C) 2014 OSA 2 June 2014 | Vol. 22, No. 11 | DOI:10.1364/OE.22.013146 | OPTICS EXPRESS 13146

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1. Introduction The state-of-the-art development and fabrication level of various nanodevices imposes stringent requirements on the microscopic analysis methods of their critical dimensions, chemical composition, topography and local optical properties [1]. The analysis of the structural and topographical sample properties can be efficiently implemented by using atomic force (AFM) and scanning electron microscopy (SEM) methods, while detecting small changes in refractive index (RI), which fully determines the local chemical composition and optical properties of the sample, is usually based on the interaction of the sample surface with a light field localized at nanoscale [2]. Light radiation is difficult to focus on the sample under study by means of far-field optics due to the fundamental diffraction limit. Optical nanoantennas exhibit higher performance in light control and localization at nanoscale [2], thus giving opportunities for practical applications of optical manipulation for nano-objects [3], nanolithography [4], excitation and detection of single-molecule fluorescence at 20-nm resolution [5], as well as subwavelength RI microscopy [6]. In the letter case the development of such a superresolution technique for refractometric studying of the optically transparent samples opens up broad prospective for novel practical applications in integrated optics for the characterization of various nanophotonic devices recorded in the photosensitive materials, in microbiology for nonfluorescent study of the biological samples, etc. To control the “nanoantenna - sample” distance as well as to simultaneously map the local RI changes, the nanoantenna should be placed at the extremity of the scanning probe. With the aperture-type scanning near-field optical microscopy such a nanoantenna typically represents a localized light source, fabricated in the form of the through nanosized aperture on the end of a tapered optical fiber coated with an opaque metal film [7]. The described


approach is widely used in subwavelength optical microscopy of different samples with a lateral resolution down to 50 nm, however, the low throughput of the nanoaperture greatly limits the sensitivity of a-SNOM in RI mapping at nanoscale. The use of resonant apertures with higher throughput (bowtie apertures [4,8], C-shaped apertures [9], and apertures surrounded by concentric grooves [10]) can improve the lateral resolution of the a-SNOM (down to 20 nm), however, is not able to provide the significant sensitivity increase in detecting small RI changes (12-% intensity signal change at extremely high RI variation Δn~2 refractive index units (RIU) [6]). With the scattering-type near-field optical microscopy (s-SNOM) the metal tip of the AFM cantilever placed in the focal spot of the laser source and focused the radiation due to the “lighting rod effect” serves us such nanoantenna [11]. The radiation localized near the tip of such a “probe-like” nanoantenna is scattered owing to its interaction with the sample surface. The scattered signal intensity varies with the topographic and local optical properties of the surface [11] or even sub-surface [12] of the samples, which provides to s-SNOM with the possibility to detect sample chemical composition. However, the extended focal spot irradiated the tip adds the background contribution to the nanoantenna signal. This problem is solved by detection of nonlinear processes or by modulation techniques [13], which greatly complicate the practical realization of high-resolution refractometers based on the s-SNOM. Furthermore, in some applications the presence of the broad focal spot on the sample surface is highly undesirable [5]. It also should be noted that the metalized cantilever tip can be approximately considered us pointed nanoantenna owing to its infinite size does not support geometrical resonances [5]. Recently to avoid this drawback resonant probes (also referred to as “pointed probes”) based on the dipole or monopole nanoantennas were proposed and mapping and enhancement of the single-molecule fluorescence with a lateral resolution down to 20 nm were demonstrated [14,15]. However, the scattered radiation intensity from the resonant nanoantenna, as for the case of a-SNOM with resonant apertures, weakly dependents on the sample RI local changes preventing the usage of the nonfluorescent methods in studying the optically transparent samples. It is known that the use of spectrally-based signal processing techniques in SNOM systems, instead of amplitude ones, can increase the sensitivity of these systems [16]. Similar approach based on the detection of the nanoantenna’s spectral response rather than the scattered signal intensity seems to increase the sensitivity of the SNOM methods as well as provides them with the possibility to detect small RI changes of the optically transparent samples. Such an approach could be based on the fact that the metal nanoparticles have a pronounced spectral dependence of the local plasmon resonance (LPR) on the surrounding media RI [17]. Therefore, the metal nanoparticle placed at the extremity of the scanning probe can act as the pointed nanoantenna. The detection of the spectral response of this nanoantenna can provide the high-precision mapping of RI changes of the optically transparent samples. In this paper, by detecting the spectral response of the simplest nanoantenna - spherical Au nanoparticle placed at the extremity of the transparent dielectric probe fabricated in the form of a fiber microaxicon (FMA), we will theoretically demonstrate the possibility of mapping the extremely small RI variations (down to 5·10−4 RIU under ideal conditions) with the lateral resolution comparable to the nanoantenna diameter. We will show that the use of the FMA as a scanning probe provides an efficient excitation of dipole LPR in the nanoantenna by the diffraction-limited focal spot as well as the collection of the nanoantenna signal. The results of numerical simulations based on the 3D finite-difference time-domain (FDTD) method are in good agreement with the theoretical quasi-electrostatic estimations for the radius of the nanoantenna not exceeding the skin depth of Au. 2. Theoretical estimations To estimate the LPR spectral response of the spherical nanoantenna placed in the close proximity with the optically transparent sample surface we use a quasi-electrostatic theory. It is known that the impact of an electromagnetic wave with an electric field amplitude E on the spherical Au nanoparticles with a radius a and a dielectric permittivity εAu and a permeability #209237 - $15.00 USD Received 31 Mar 2014; revised 14 May 2014; accepted 17 May 2014; published 22 May 2014 (C) 2014 OSA 2 June 2014 | Vol. 22, No. 11 | DOI:10.1364/OE.22.013146 | OPTICS EXPRESS 13148

μ = 1, surrounded by a transparent homogeneous dielectric medium with the dielectric permittivity εm = 1 leads to its polarization with a dipole moment p = 4π a 3ε 0

ε Au − 1 E. ε Au + 2

(1)

We further assume a semi-infinite medium with a plane boundary and the dielectric permittivity εm and permeability the μ = 1 placed at a distance d = z0–a from the nanoantenna’s center (Fig. 1(a)). The incident electromagnetic field is assumed to be polarized in the direction perpendicular (s-polarization) to the medium surface (Fig. 1(a)).

Fig. 1. (a) Spherical Au nanoantenna illuminated by the s-polarized plane wave and its image dipole located at a distance d in the semi-infinite homogeneous medium with the dielectric permittivity εm; (b) Equivalent dielectric medium polarized by uniform electric field; (c) Sketch of the FMA with the attached Au nanoantenna.

In this case, the polarized nanoantenna will induce surface charges in the medium. The electromagnetic field of these surface charges can be described by an equivalent field of an image dipole [18] with dipole moment pekv = αp, α = (εm-1)/(εm + 1), located inside the medium at a distance 2z0 from the nanoantenna’s center (Fig. 1(a)). This field will affect the nanoantenna in turn. In this case, we can show that the dipole moment of the nanoantenna will affect only the longitudinal component (directed along the z-axis in Fig. 1(a)) generated by the reflected component of the dipole electric field, which can be written as: Eekv =

1 a 3 ε Au -1 E. α 4 z03 ε Au + 2

(2)

On the other hand, the Eekv can be expressed in term of the field-related charges in the equivalent medium (Fig. 1(b)) polarized by the E field and surrounded the nanoantenna from all sides [18] Eekv =

ε ekv − 1 E. 2ε ekv + 1

(3)

where εekv is the dielectric permittivity of the equivalent medium. By equating the Eqs. (2) and (3) we can found that the relationship between the εekv and the dielectric permittivity εm of the semi-infinite medium located at the distance z0 can be expressed by the following equation

ε ekv

a 3 (ε m − 1) (ε Au − 1) + (ε Au + 2) 4 z03 (ε m + 1) = . a 3 (ε − 1) 4− 3 m ε Au 4 z0 (ε m + 1)

(4)

The spectral dependence of the dielectric permittivity of the Au nanoantenna is assumed to follow the Drude-Lorentz model [18]:


ε Au (λ ) = ε ∞ −

1 , λ (1/ λ + i / γ p λ ) 2 p

2

(5)

where ε∞ is a high-frequency limit dielectric constant, λp - plasma wavelength, and γr - damping parameter. By neglecting the εekv dispersion, assuming (εm - 1)