Gaussian beam photothermal single particle microscopy

Abstract

We explore the intuitive lensing picture of laser-heated nanoparticles occurring in single particle photothermal (PT) microscopy. The effective focal length of the thermal lens (TL) is derived from a ray-optics treatment and used to transform the probing focused Gaussian beam with ABCD Gaussian matrix optics. The relative PT signal is obtained from the relative beam-waist change far from the TL. The analytical expression is semiquantitative, capable of describing the entire phenomenology of single particle PT microscopy, and shows that the signal is the product of the point-spread functions of the involved lasers times a linear function of the axial coordinate. The presented particularly simple and intuitive Gaussian beam lensing picture compares favorably to the experimental results for 60 nm gold nanoparticles and provides the prescription for optimum setup calibration.

Imaging nano-objects by linear and nonlinear optical absorption microscopies

“…The size of the PHI signal depends on the magnitude of the thermal lens created by heat transfer from the nano-object to the environment. [9,23,48,124,[140][141][142] This depends on the heat capacity, thermal resistivity and change in refractive index with temperature ( ) of the environment. [47,48,124] This places restrictions on the types of samples that can be used for these measurements.…”

“…[5,18] In these experiments heat transfer from the particle to the surroundings creates a nano-lens that affects the propagation of the probe beam, and changes the intensity of the probe at the detector. [9, [140][141][142] The signal in PHI depends the linear absorption of the sample, in contrast to TAM which depends on the non-linear susceptibility. Because PHI relies on efficient heat transfer to the surroundings, it is typically not used to study fluorescent nanoparticles with high quantum yields.…”

Mie and potential scattering by a refractive 1/r inhomogeneity: Electromagnetic scattering by an infinite Coulomb-like scatterer

“…Since also particles must be assumed as finite wave-packets, this situation resembles the correct and arguably even more complicated treatment of Coulomb scattering in quantum mechanics [14]. For strongly focused beams with kω $ 1 in the optical domain, the rich lensing phenomenology of PT microscopy is recovered, including the sensitive dependence on the axial placement of the beam waist [6][7][8][9]. The behavior of the sum of scattering and interference, depicted as solid black lines in Fig.…”

“…(4) for radii larger than the particle radius R 5 λ. This is the situation commonly encountered in photothermal single particle microscopy [4][5][6][7][8][9]. Using Eq.…”

“…This analog was explicated in classical and wave-mechanics. Specifically, the situation of focused beam scattering [3] was of technical importance, as it closely approximates the situation encountered in photothermal single particle microscopy [4][5][6][7][8][9]. In contrast, here the plane-wave scattering behavior for the same idealized refractive index inhomogeneity is studied, as depicted in Fig.…”