Frequency Domain Detection by Heterodyne Holography

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Photothermal Heterodyne Holography

In the precedent section we have shown that digital holography is a powerful 3D imaging tool, based on interferences between a signal of the optical field of interest and a reference beam. Combined with the heterodyne technique it offers the frequency investigation of phenomena modulated at any frequency by correctly detuning the heterodyne beating frequency.
Here, we present the technique of photothermal heterodyne holography which is able to achieve three dimensional imaging of absorbing nanoobjects submitted to a modulated photothermal excitation. Heated nanoobjects induce a temperature modulation and a small refractive index variation (typically 10−3 to 10−5 K−1) in the surrounding medium. This relatively large heated region scatters light towards the camera where it interferes with the phase-shifted reference beam. The beating frequency of the setup is tuned at the frequency of the photothermal excitation which permits to detect principally the heated objects. Photothermal excitation is a well established technique for the sensitive detection of absorbing objects. A modulated optical beam is sent on the sample, creating a localised  heating, which in turn induces a variety of phenomena including e.g. infrared emission, thermal expansion, or refractive index changes (Rosencwaig et al. 1985). When detected with good sensitivity, these phenomena can deliver information on the optical absorption of the sample. Recently, these techniques have been adapted to the detection of metal nanoparticles (Boyer et al. 2002) or nanotubes (Berciaud et al. 2007), specially in the context of biological studies (Lasne et al. 2006). Relying on absorption, which scales as the volume of the particle, is clearly an advantage for the detection of very small particles in comparison to scattering, which varies as the square of the particle volume.
This section presents the experimental setup of photothermal heterodyne holography. The principle of the detection of exclusively the photothermal signal is explained. Furthermore we analyse qualitatively the origin of the detected photothermal signal and prove that the photothermal signal is indeed proportional to the induced temperature in the nanoobject. This makes our method a novel technique to probe the temperature in metal nanoobjects.

Experimental Setup of Photothermal DHH

Figure 2.7 depicts the setup of photothermal holography. It is based on the off-axis setup of heterodyne holography as shown in Fig. 2.4. The holographic arms use a single mode laser emitting at λ2 = 785 nm. The photothermal excitation is delivered by a 2 W, continuous multimode solid state laser at λ = 532 nm, which is sine-modulated in amplitude by a third acousto-optical modulator, AOM3. Unlike AOMs 1 and 2, it serves as a heating power modulator by using a 80 MHz carrier, modulated in amplitude at FHeat. This beam is directed into the objective by a dichroïc beamsplitter (at 532 nm). The polarization of the heating beam can be adjusted by a combination of a half wave plate and a polarizing beam splitter. Thus, a polarization along each axis of the sample plane can be achieved.
An adjustable beam expander slightly uncollimates the beam to illuminate a 2−200 μm diameter region of the sample. At high laser power, an additional notch filter ensures that no heating light reaches the camera. This excitation, when hitting a point-like object in a homogeneous medium, creates a spherical region in which the temperature is modulated. A local modulation of the refractive index appears in this heated region due to photothermal effects, and is investigated by synchronizing the setup to FV ar = FHeat, resulting into a beating frequency of Δf = 1/4fCCD+FHeat. The reconstruction procedure of the hologram follows the 4-step method explained in Ch. 2.3.3.

Frequency Domain Detection by Heterodyne Holography

We have seen that heterodyne holography allows a dynamically shifted beating frequency which enables the imaging of the entire frequency domain of the system under study. Here, we will describe a method based on heterodyne holography that scans the frequency sidebands by systematically detuning one of the beams. This technique has been successfully applied to the frequency resolved temperature imaging of an integrated circuit. Furthermore, we used this detection method to study the frequency domain of Brownian movement of gold nanorods in an aqueous solution.
Joud et al. demonstrated recently that sideband digital holography can be used to quantitative measure the oscillation amplitude of vibrating objects (Joud et al. 2009). The authors used heterodyne holography to selectively detect the frequency sidebands of the light scattered by the object, shifted by n times the vibration frequency. First, we present our results of the temperature mapping of an integrated circuit. This study was chosen as a primary validation of the detection concept on an uncomplicated micro-system. In view of this work, we are interested mainly in the study of metal nanoobjects. Regarding our main scope, i.e. the application to plasmonics, we performed some measurements of the frequency domain of nanorods moving in an aqueous solution in the Brownian regime. The result of the heterodyne detection in this case reflects well the expected behaviour of the signal as a function of frequency.

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Application 1: Frequency-Resolved Temperature Imaging of Integrated Circuits

The scanning heterodyne imaging method is applied to image the temperature of an integrated circuit and to map its frequency domain content. An integrated circuit is supplied with a modulated current resulting into a temperature modulation. The frequency content for this modulation is detected using an object beam and a reference beam, frequencyshifted to create a beating of the interference pattern. The experimental setup will be characterized in the frequency domain. We will present and discuss the obtained frequency domain spectra of the temperature.
High frequencies and integration densities make temperature and thermal management a crucial aspect of integrated circuit design. Methods able to acquire temperature maps at submicron scales are well explored, since they are essential in order to validate thermal models and improve microelectronic devices. Infra-red imaging is a powerful tool, but its optical resolution is limited to a few micrometers. Thermoreflectance (Farzaneh et al. 2009) offers the advantage of being a non-invasive optical technique capable of determining temperature variations with good spatial resolutions in the visible or near UV range.

Table of contents :

Introduction
1 Plasmonics and Optical Antennas 
1.1 A Short Introduction to Plasmonics
1.1.1 Surface Plasmon Polaritons
1.1.2 Localized Surface Plasmons
1.1.3 Single Particle Plasmon Resonances – The Quasi-Static Approximation
1.1.4 Theoretical Considerations beyond the Quasi-Static Limit: Retardation Effects
1.2 Optical Antennas
1.2.1 Properties of Optical Antennas
1.2.2 Nanoantenna Geometries
1.2.3 Applications of Optical Antennas – State of the Art
1.3 Conclusion
2 Digital Heterodyne Holography 
2.1 Historical Overview
2.2 Principles of Holography
2.2.1 Off-Axis Holography
2.3 Digital Holography
2.3.1 Numerical Holographic Reconstruction
2.3.2 Phase Shifting Holography
2.3.3 Digital Heterodyne Off-Axis Holography
2.3.4 Experimental Setup of DHH
2.4 Photothermal Heterodyne Holography
2.4.1 Experimental Setup of Photothermal DHH
2.5 Frequency Domain Detection by Heterodyne Holography
2.5.1 Application 1: Frequency-Resolved Temperature Imaging of Integrated Circuits
2.5.2 Application 2: Frequency Detection in the Brownian Regime of Gold Nanorods
2.5.3 Conclusion on Frequency Detection
2.6 Conclusion on Digital Heterodyne Holography
3 The Nanostructures under Study 
3.1 Design of the Nanostructures
3.1.1 Nanostructure Fabrication
3.2 Spectroscopy of Single Nanoobjects
3.3 FEM Simulation of Plasmonic Nanoobjects
3.3.1 Scattering in the Far-Field
3.3.2 Scattering in the Near-Field
3.3.3 Tests for Validation
3.4 Conclusion
4 Validation of Experimental Techniques on Elementary Nanoobjects 
4.1 Single Nanodisks
4.1.1 Light Scattering by a Single Disk
4.1.2 Near-Field of Single Disks
4.1.3 Holography of Single Disks
4.1.4 Conclusion on the Scattering Behaviour of Single Disks
4.2 Coupling of Two Nanodisks
4.2.1 Introduction to the Study of Two Coupled Disks
4.2.2 Plasmon Hybridization Model
4.2.3 Scattering Spectra of Two Coupled Disks
4.2.4 Study of Different Modes Excited in Two Coupled Disks
4.2.5 Conclusion on Two Coupled Nanodisks
4.3 Two Coupled Nanorods
4.3.1 Light Scattering of Coupled Rods
4.3.2 Near-Field of Single and Coupled Rods
4.3.3 3D Far-Field Images of Light Scattered by Coupled Rods
4.3.4 Conclusion on Coupled Rods
4.4 Conclusion
5 Extensive Study of Plasmonic Nanostructures 
5.1 Probing the Coupling of Nanodisk Chains by Spectroscopy
5.1.1 Longitudinal and Transverse Modes in Nanodisk Chains
5.1.2 Far-Field Scattering Revealing Near-Field Coupling in Nanodisk Chains
5.2 Far- and Near-Field Maps of Scattered Light by Nanodisk Chains
5.2.1 The Influence of the Chain Length on the Far-Field Maps
5.2.2 TE Wave and TM Wave Excitation
5.2.3 Imaging of Longitudinal and Transverse Modes in a Chain
5.2.4 Influence of the Exciting Wavelength
5.2.5 Probing the Coupling of Nanodisk Chains by Holography
5.2.6 Imaging of Directional Scattering
5.2.7 Conclusion on the Far- and Near-Field Maps of Nanodisk Chains .
5.3 Probing the Plasmonic Coupling of Disks by Heating
5.3.1 Comparison of Holographic and Photothermal Images
5.3.2 Photothermal Imaging of Nanostructures – An Analytical Analysis of the Photothermal Signal
5.3.3 Photothermal Signal and Absorption Cross Section
5.3.4 Photothermal Holography Reveals Coupling of Nanodisk Chains .
5.3.5 Conclusion on Photothermal Imaging of Nanodisk Chains
5.4 Coupled Triangles
5.5 Conclusion on the Application of Holography to Plasmonics
Conclusions and Prospects
A FEM Simulation Parameters – Fresnel Coefficients 
A.1 Excitation Field in Reflection
A.2 Excitation Field in Transmission
B Square-Wave Function in Matlab 
Bibliography 

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