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Abstract: In this paper a far field optical technique we call polarization modulation thermal lens microscopy (PM-TLM) is used for imaging the orientation and dichroism of non-spherical nanoparticles. In PM-TLM, the polarization state of a pump beam is periodically modulated which in turn causes morphology related intensity fluctuations in a continuous probe beam, thus allowing high signal to noise ratio detection with using lock-in amplification. Since PM-TLM uses nanoparticle absorption as the contrast mechanism, it may be used to detect and image nanoparticles of far smaller dimensions than can be observed by conventional dark field optical microscopy. The technique, its implementation and experiment results are presented.
©2011 Optical Society of America
1. Introduction
The ability to measure and image the orientation of noble metal nanoparticles (NPs) has been shown to be useful in several studies [1,2]. While NPs possess the advantages of non-invasiveness and relative simplicity, conventional far field optical techniques are limited in their applicability because they rely on light scattering as the contrast mechanism. The scattering cross-section decreases with the sixth power of NP dimensions and this typically limits conventional microscopy techniques to NPs of 40 nm or greater. Additionally, when a scattering matrix such as tissue or cultured cells is present, the shot noise carried by stray light scattered from the sample soon overwhelms the light scattered by the nanoparticle (NP), the low signal to noise ratio makes the conventional microscopy unsuccessful.
The NP absorption cross-section, however, only decreases with the cube of NP dimension, so reduces far less rapidly as NP dimensions are shrunk. A gold nanosphere of 80 nm, for example, has comparable scattering and absorption, while a 20 nm nanosphere has an absorption cross-section that is 100 times greater than its scattering cross-section [3]. Furthermore for gold or silver nanoparticles, due to plasmonic properties, they will absorb much more optical energy than the surrounding medium if they are excited by an electromagnetic wave with a wavelength close to that of their resonance. Therefore, sensing optical absorption instead of scattering allows for higher signal to noise ratios when imaging very small gold or silver particles.
This observation has led to the development of novel optical modalities that rely on absorption of light rather than light scattering, the most prevalent of which are the closely related techniques of thermal lens microscopy (TLM) or photothermal heterodyne interferometry (PHI) [4,5]. TLM and PHI are pump-probe techniques which employ an intensity modulated pump beam to periodically heat the NPs through absorption. The NP then raises the temperature of its surrounding medium which, in turn, modifies the medium’s refractive index, typically reducing it. In PHI, fast modulation (MHz) is used such that the heated region around the NP is smaller than the probe beam size. The heated region diffracts and modulates part of the probe beam and this portion is interfered with the unmodulated, zero order portion which acts as a reference beam. In TLM, the modulation frequency is reduced so the heated region is larger than the probe beam and there is no zero order reference beam. Here, the heated region thus forms a “thermal lens” which deflects and removes energy from the probe beam. The periodic fluctuation in the probe beam is detected with a photodiode and a lock-in amplifier. Exploiting the relatively high absorption cross-sections of noble metal NPs has allowed PHI and TLM to detect NPs with dimensions down to a few nanometers [6,7].
NPs with non-spherical shapes, such as rods or spheroids are more interesting in biological and optical applications because of their rich optical characteristics [8–10]. We wish to characterize nano-structured surfaces and to employ functionalized non-spherical NPs as labels in live cell cultures and tissue sections. Knowledge of non-spherical NPs’ orientation could allow both rotational and translational diffusion coefficients to be calculated. This is not possible in existing TLM or PTI configurations which report either absorption parallel to the incident pump polarization, or integrate over orientation if circularly polarized or unpolarized light is used. In this paper we are going to present a polarization modulation technique and demonstrate how it can be incorporated into TLM to provide orientation and dichroism information when imaging non-spherical NPs. In previous work [11] TLM has been used to measure circular dichroism on bulk samples by switching between two states of circular polarization; in this paper we describe a method to quantify linear dichroism on particles far smaller than the optical spot size. Moreover, the need to perform a continuous measurement of the particle orientation rather than simply detect one of two states of circular dichroism requires a considerably more sophisticated lock-in measurement.
2. Theory
We present here a modification to the TLM technique that allows for the measurement and imaging of NP orientation and dichroism (degree of anisotropy). In polarization modulation thermal lens microscopy (PM-TLM), rather that modulating the intensity of the pump beam, we modulate its polarization state. Non-spherical noble metal NPs are strongly dichroic, that is their absorption (and scattering) cross-sections depend greatly on the polarization state of the illumination. The high absorption of noble metal NPs is a result of the illumination coupling to localized surface plasmon (LSPR) modes [12], with rod-like and cylindrical NPs, for example, having a strong longitudinal plus a weaker transverse mode. In order to excite either of these modes, the polarization state of the illumination must be aligned with the geometry of the NP.
We use a polarizer, a photoelastic modulator (PEM, Hinds Instruments, Oregon, USA) and a quarter wave plate configured to produce a linearly polarized pump beam where the polarization angle is sinusoidally modulated. Ignoring any constant phase offset, ϕ = Psin(ωt)/2 where ϕ is the instantaneous angle of polarization in radians, P is the peak amplitude of the rotation (determined by the drive setting of the PEM) and ω is the modulation angular frequency. In the case of a rod-like particle orientated at θ radians, the intensity absorbed can be expressed as
where I0 is the pump beam intensity at the particle, a and b are the particle absorption cross sections (m2) parallel and perpendicular to the particle axis respectively. As the particle is periodically heated by the polarization modulated pump beam, the refractive index of the medium around the particle is modulated at the same frequency. This is detected by the probe beam as the a.c. electrical signal V at a photo detector is proportional to Iabs. Representing the linear dichroism as σ = (a – b) and neglecting the d.c. term,where k is a system dependent constant parameter determined by the illumination intensity, amplifier gain and optical component losses, and Jn are Bessel functions of the first kind. Using phase sensitive detection to lock in to ω and 2ω, the outputs are which can be solved to obtain dichroism and orientation: In practice, optimum signal to noise ratio is obtained by setting the PEM such that P = 2.63 radians, so J1 (P) = J2 (P) and the orientation is then simply 0.5tan−1(Vω/V 2 ω).3. Experimental set up
A schematic of the PM-TLM instrument is shown in Fig. 1 . A HeNe laser (632.8 nm, JDS Uniphase 1136P) is used as a pump and a diode pumped solid-state laser (532 nm, B&W TEK INC. BWN-532-50E) generates the probe beam. A polarizer ensures the pump beam polarization is incident on the PEM at 45 degrees with respect to its optical axis. A quarter wave plate is aligned with the axis of the polarizer to obtain a linearly polarized output. In order to compensate for the effect on the polarization of non-ideal optical components in the illumination train, a simple calibration of the system is performed by placing a polarizer in the sample position and varying its orientation.
Fig. 1 Schematic of the PM-TLM microscope configuration, P- polarizer; PEM- photoelastic modulator; QW- quarter waveplate; M-mirror; BE-beam expander; DM- dichroic mirror; O1 and O2- objectives; F- filter; A- aperture. Two lock-in amplifiers are used to lock to the fundamental and second harmonic of the PEM modulation frequency. A widefield imaging channel (dashed squire) is used for sample location, RBS- removable beamsplitter; LED- light source; IO-illumination optics; BS- beamsplitter; TL-tube lens for imaging.
The microscope uses a co-axial mismatched arrangement [13], where the pump beam is tightly focused onto the sample by Objective 1 (Olympus 0.75NA, 40x) while the probe beam is slightly defocused. Objective 2 (Zeiss 0.7NA 50x) collects beams and a narrow interference bandpass filter (532 nm, Edmond Optics) is placed in front of the amplified photodetector (PDA100A-EC, Thorlabs) to exclude the pump beam. The output from a silicon photodetector is sent to two lock-in amplifiers (LIAs, SR844, Stanford Research) which are referenced to the fundamental and the second harmonic of the PEM (47 and 94 kHz respectively). An image is obtained by scanning the sample using an x-y linear stage (P-541.2CD Physik Instrumente). The widefield imaging channel is used to assist alignment and for initial location of the sample.
To demonstrate the PM-TLM technique, we used the microscope described above to image NPs of known orientation. An array of gold nanorods with nominal sizes 120 x 60 nm and thickness 30nm was produced by e-beam lithography on a BK7 glass coverslip. In each row of the array, the orientation of the rods was rotated by 15 degrees. Individual NPs and a typical spectrum of a single NP are shown in Fig. 2 ; these indicate the aspect ratio of the particles and give some indication of the shape variation between particles.
Fig. 2 SEM images of fabricated nanoparticles with several orientations (top, scale bar 100 nm) and the spectrum (bottom). The nanorods sample has nominal sizes of 120 x 60 nm, and the orientation of the rods rotates through 15 degrees in each row.
4. Experiment results
The sample described above was imaged with the PM-TLM microscope. The spatial resolution in TLM is defined by the focused spot size of the pump beam. In our microscope, the spot size was approximately 1 μm, so the x-y translation stage was moved in steps of 200 nm. The experimental results displayed in Fig. 3 are the amplitudes of Vω (top) and V 2 ω (bottom) acquired by the two identical LIAs. A quadrature relationship between Vω and V 2 ω with respect to the orientation of the nanorods (Eqs. (3)a and 3b) can be clearly observed.
Fig. 3 (Color online) Raw data recorded by the lock-in amplifiers, PM-TLM thermal intensity of the fundamental (top) and the second harmonic signals (bottom).
In order to obtain the particle orientation a small amount of data processing was required. We calibrated the Vω and V 2 ω signals by rotating a polarizer, which showed that the Vω signal is subject to offset when the components deviate from the ideal. The offset determined by the calibration was removed from the Vω signal, then Eq. (4) was used to obtain the orientation and dichroism on the brightest pixel in the NP. Figure 4(a) and 4(b) are the measured dichroism (arbitrary unit) and orientation (degrees), and Fig. 4(c) shows a quiver plot where the direction of the arrows indicates the particle orientation, with the length showing the dichroism. It can be seen that the orientations recovered agree well with expected values.
Fig. 4 (a) Plots of dichroism (arbitrary units) and (b) orientation (degrees) calculated from the data in Fig. 3. (c) Quiver plot representing the orientation (rotation) and dichroism (length).
5. Conclusion
In summary we have presented a simple modification to the thermal lens microscopy technique that allows us to measure nanoparticle orientation. Experimental results have been presented that demonstrate the practicality of the technique. Electrooptic modulators could be used in future which permit the use of higher modulation frequencies and different modulation waveforms to further improve the signal to noise ratio. The method should have considerable application for biological live cell imaging as it could provide similar information to fluorescent techniques but without the need for an unstable fluorescent label to be attached to the live cell. PM-TLM could also be modified to determine orientation in all three dimensions if a very high numerical aperture objective is used with a significant axial component of electrical field vector.
Acknowledgments
The authors gratefully acknowledge the financial support of the Engineering and Physical Sciences Research Council (EPSRC), the UK. We thank Dr. George Zorinyants, Cardiff University, for sample fabrication.
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