Wendel L. Moreira

Double optical tweezers for ultrasensitive force spectroscopy in microsphere Mie scattering

We used a double tweezers setup to perform ultrasensitive force spectroscopy and observe the forces due to light scattering in a single isolated particle. We demonstrate how to selectively couple the light to the transverse electric (TE), transverse magnetic (TM), or both TE and TM microsphere modes by means of the beam polarization and positioning, and to observe correspondent morphology-dependent resonances (MDR). The results show how the usually assumed azimuthal symmetry in the horizontal plane no longer holds because of the symmetry break caused by the beam polarization. Also, the MDR resonances can change the force values by more than 30–50%.

Expansion of arbitrary electromagnetic fields in terms of vector spherical wave functions

Since 1908, when Mie reported analytical expressions for the fields scattered by a spherical particle upon incidence of plane-waves, generalizing his analysis for the case of an arbitrary incident wave has been an open question because of the cancellation of the prefactor radial spherical Bessel function. This cancellation was obtained before by our own group for a highly focused beam centered in the objective. In this work, however, we show for the first time how these terms can be canceled out for any arbitrary incident field that satisfies Maxwells equations, and obtain analytical expressions for the beam shape coefficients. We show several examples on how to use our method to obtain analytical beam shape coefficients for: Bessel beams, general hollow waveguide modes and specific geometries such as cylindrical and rectangular. Our method uses the vector potential, which shows the interesting characteristic of being gauge invariant. These results are highly relevant for speeding up numerical calculation of light scattering applications such as the radiation forces acting on spherical particles placed in an arbitrary electromagnetic field, as in an optical tweezers system.

Exact partial wave expansion of optical beams with respect to arbitrary origin

Partial wave decomposition of incident beams is the first task to be performed to impose boundary conditions at the particle interface in the calculation of the scattering of spherical particles. The coordinates origin must be in the center of the particle and not at high symmetry positions of the beam. This can be a quite complicated problem, especially when a full vectorial diffraction description of the electromagnetic fields and highly focused laser beams are required where the paraxial limit fails. Traditional approximation techniques have been used to proceed forward and to obtain numerical results. The main fault relies on a radial dependence of the beam shape coefficients, which limits the validity of such approximations. Here we prove that the radial dependence will emerge from the solid angle integration in this way obtaining an exact, closed expression, without any approximation, for the beam shape coefficients, for an arbitrary beam shape, origin and polarization, the special case of a Gaussian beam is presented.

Nonlinear microspectroscopy in an optical tweezers system: application to cells marked with quantum dots

In this work we used our set up consisting of an optical tweezers plus non-linear micro-spectroscopy system to perform scanning microscopy and observe spectra using two photon excited (TPE) luminescence of captured single cells conjugated with quantum dots of CdS and CdTe. The CdS nanocrystals are obtained by our group via colloidal synthesis in aqueous medium with final pH = 7 using sodium polyphosphate as the stabilizing agent. In a second step the surface of CdS particles is functionalized with linking agents such as Glutaraldehyde. The CdTe quantum dots are functionalized in the its proper synthesis using mercaptoacetic acid (AMA). We used a femtosecond Ti:sapphire laser to excite the hyper Rayleigh or TPE luminescence in particles trapped with an Nd:YAG cw laser and a 30 cm monochromator equipped with a cooled back illuminated CCD to select the spectral region for imaging. With this system we obtained hyper Rayleigh and TPE luminescence images of macrophages and other samples. The results obtained show the potential presented by this system and fluorescent labels to perform spectroscopy in a living trapped microorganism in any neighbourhood and dynamically observe the chemical reactions changes in real time.

Raman, Hyper-Raman, Hyper-Rayleigh and Two-Photon Excited Luminescence Microspectroscopy in an Optical Tweezers System

Single beam optical tweezers have been used as a tool to manipulate biological material at cellular level, as well as to measure mechanical properties such as forces at femtonewton scale and stiffness or elasticity of membranes and single DNA macromolecule [1-3]. We used the optical tweezers to study disease related to the mechanical properties of individual red blood cells [4] and we demonstrated the importance of using spectroscopic techniques while manipulating particles and living cells. The ability of performing spectroscopy in a living microorganism optically trapped in any desired neighborhood means that we could dynamically observe the chemical reactions and/or mechanical properties change in real time. Therefore, we decided to set up an Optical Tweezers plus a Raman system like the one described in reference [5, 6]. We present a homemade set-up confocal spectrometer using a Spectra Pro 300 i Acton Research Corporation 30 cm triple grating monochromator equipped with a Princeton Instruments liquid cooled back illuminated CCD using a femtosecond Ti:sapphire laser, Spectra Physics Tsunami. Previous works used only cw lasers. In our system we have the possibility of using the Tsunami and/or a cw Ti:sapphire laser, Spectra Physics model 3900S. The use of a femtosecond laser with or without a cw laser opens up a great number of different applications and spectroscopies, as discussed below. The drawback of a femtosecond laser is the intrinsic broad linewidth associated with time-frequency Fourier transform 2 1 ≥ ∆ ∆ τ ν . If the issue is a great spectral resolution we can use the narrow cw laser line or narrow down the femtosecond laserline with an intracavity slit. It is also possible to narrow the femtosecond laser line with an external band pass filter but loosing the power out of the filter range. With the cw laser we used two supernotch filter to reject the laser line from the monochromator. The linewidth of a 100 femtosecond pulse, however, is larger than the 350 cm of the supernotch filter, which leads to a leakage of the laser line out of the supernotch filter spectral range. Nonetheless, because the leaking power was low, it was still possible to observe the Raman lines superimposed to the tail of the Gaussian laser line leakage. Only using the band pass filter it was possible to avoid this leakage. Figure 1 shows the obtained Raman spectra for a trapped polystyrene sphere, a red blood cell and a ZnSe sample. One possible application for the pulsed laser is the excitation of the luminescence by two photon absorption (TPA). Two photon optical processes only happen when two photons meet at the same time and at the same spot, which happens much more frequently for a pulsed laser (photons at the same time) and at the laser focus (photons at the same spot). The TPA allow the simultaneously observation of the Raman, at the infrared region, and the luminescence, at the visible region. Figure 2 shows the TPA excited luminescence of ZnSe. The systems that use the absorption of two photons or more are confocal by itself, because at the right pump power, the signal is generated only at the spot size of the exciting laser. This makes the signal collection optics not so 164 Microsc Microanal 9(Suppl 2), 2003 Copyright 2003 Microscopy Society of America DOI: 10.1017/S1431927603440373

Exact theory of optical forces of Mie scatterers exposed to high numerical aperture beams examined with 3D photonic force measurements

One very important contribution of the Optical Tweezers technique is its ability to extract the missing mechanical measurements in the world of microorganisms and cells that could be correlated to biochemical information. A microsphere displacement is the preferential force transducer for this kind of measurement. However, the typical conditions used in Optical Tweezers with very high numerical aperture beams and microspheres with diameters up to ten wavelengths, requires a full vectorial description of the incident beam in partial waves with the origin of coordinate system at the center of the microsphere and not at the focus of the beam. Using the Angular Spectrum Representation of the incident beam and an analytical expression for integrals involving associated Legendre Polynomials, Bessel functions and plane waves we have been able to obtain a closed expression, without any approximation, for the beam shape coefficients of any orthogonally incident beam. The theoretical prediction of the theory agrees well with the experimental results performed on a 3D positioned dual trap in an upright standard optical microscope, thus obtaining the whole optical force curves as a function of the microsphere center for different wavelengths.

Optical tweezers 3D photonic force spectroscopy

Since optical tweezers trapped microspheres can be used as an ultrasensitive force measurements technique, the knowledge of its theoretical description is of utmost importance. However, even the description of the incident electromagnetic fields under very tight focusing, typical of the optical trap, is not yet a closed problem. Therefore it is important to experimentally obtain whole accurate curves of the force as a function of wavelength, polarization and incident beam 3D position with respect to the center of the microsphere. Theoretical models for optical forces such as the Generalized Lorenz-Mie theory, can then be applied to the precisely evaluated experimental results. Using a dual trap in an upright standard optical microscope, one to keep the particle at the equilibrium position and the other to disturb it we have been able to obtain these force curves as a function of x, y and z position, incident beam polarization and also wavelength. Further investigation of optical forces was conducted for wavelengths in and out Mie resonances of the dielectric microspherical cavities for both TM and TE modes.

Double optical tweezers for 3D photonic force measurements of Mie scatterers

The ability to observe quantitatively mechanical events in real time of biological phenomena is an important contribution of the Optical Tweezers technique for life sciences. The measurements of any mechanical property involves force measurements, usually performed using a microsphere as the force transducer. This makes the understanding of the photonic force theory critical. Only very sensitive and precise experimental 3D photonic force measurements for any particle size will be able to discriminate between different theoretical models. In particular it is important to obtain the whole photonic force curve as a function of the beam position instead of isolate particular points. We used a dual trap in an upright standard optical microscope, one to keep the particle at the equilibrium position and the other to disturb it. With this system we have been able to obtain these force curves as a function of x, y and z position, incident beam polarization and wavelength. We investigated the optical forces for wavelengths in and out of Mie resonances of dielectric microspherical cavities for both TM and TE modes and compared the experimental results with the calculations performed with different models for the optical force.

Exact Partial Wave Expansion for an Arbitrary Optical Beams

Optical tweezers have become an important tool for biological manipulations and cell mechanical properties measurements [1]. These measurements use the displacement from equilibrium position of a microsphere as the force transducer. Therefore, the calibration procedure requires the use of good models for the optical force in microspheres. Geometrical optics has been used when the particle dimensions are much greater than the light wavelength, and Rayleigh scattering theory for the opposite. However, when the particles are of the same order of the wavelength these approximations are no longer valid. Mie resonances are typical of this size regime. Classical Mie scattering theory was developed for plane waves and cannot explain the measurements obtained using a focus beam as we have in optical tweezers. In this case, it is necessary to decompose the incident beam in plane waves relative to the center of the microsphere. As the beam focus is no longer at the origin of the coordinate system all the beam azimuthal symmetry is lost. This can be a complicated problem, especially when a full vectorial diffraction description of the electromagnetic fields and highly focused laser beams are required. All sorts of approximations and tricks have been used to proceed forward to obtain numerical results [2].

Multilayers of PbTe quantum dots embedded in SiO/sub 2/

In the present work, PbTe quantum dots embedded in a dielectric host (SiO/sub 2/) were fabricated. The structural and optical properties of the multilayers were studied.