Optical tweezers manipulate microscopic objects with light by exchanging momentum and angular momentum between particle and light, generating optical forces and torques. Understanding and predicting them is essential for designing and interpreting experiments. Here, we focus on geometrical optics and optical forces and torques in this regime, and we employ neural networks to calculate them. Using an optically trapped spherical particle as a benchmark, we show that neural networks are faster and more accurate than the calculation with geometrical optics. We demonstrate the effectiveness of our approach in studying the dynamics of systems that are computationally “hard” for traditional computation.
Optical forces are often calculated by using geometrical optics to compute the exchange of momentum between particle and light beam. In geometrical optics, the light beam is represented by a certain number of rays. This sets a trade-off between calculation speed and accuracy. Here, we show that using neural networks allows overcoming this limitation, obtaining not only faster but also more accurate simulations. Then, we exploit our neural networks method to study the dynamics of ellipsoidal particles in a double trap, a system that would be computationally impossible otherwise.
Several models have been used to calculate optical forces since the beginning of optical trapping in the 1970´s to the Optical Tweezers (OT) in 1986 and are still under discussion these days. These models range from ray tracing geometrical optics to full electromagnetic Maxwell stress tensor formalisms, for very small particles in the Rayleigh regimen to tens of micron size particles in the Mie regime, where Mie resonances also appear. There is also a large effort to distinguish gradient vs scattering forces, which are clearly distinguished the geometrical optics frame, by reflected vs refracted beams, but not so easily distinguished in the full electromagnetic formalism. Moreover, Mie formalism was developed for an incident plane wave, which is far from the high numerical aperture (NA) beams used in OT. Even though there are models for high NA axial beams but most optical tweezers systems today use several OT points with inclined beams. Furthermore, the development of Bessel beams and other beams, also require a much more general calculation of the optical forces, as well as a theory for the forces in waveguides and photonic bandgap fibers in which is impossible to speak in terms of ray optics. One of the main difficult to calculate the optical forces in all these systems is the vector spherical wave decomposition of the incident beam. We develop a very general theory to perform this expansion for any beam which allowed us to calculate the forces for any beam and any particle size, and show a criteria to distinguish gradient from scattering forces, and the role of the Mie resonances in these cases. Dependence of the forces on the size of the particles is an important result for the development of optical chromatography. Experimental results in suspended microspheres allow us to compare the results with theory.
We will present the multi-modal photonic platform including Optical Tweezers, linear and non linear optics techniques in a single instrument to allow parallel information gathering during single cell processes. The platform includes the following techniques: multipoint Optical Tweezers; Laser cutting; multi/single photon fluorescence, Fluorescence Lifetime Imaging (FLIM); Förster Resonant Energy Transfer (FLIM-FRET); Fluorescence Correlation Spectroscopy (FCS); Raman; Second/Third Harmonic Generation (SHG/THG); Coherent AntiStokes Raman Scattering (CARS) and cascade CARS; Near field tip-enhancement and 1 and 2 photons Photoluminescence Excitation Spectroscopy (1-2 PLE). Next, we will discuss the issue of spherical wave vectors decomposition of any optical beam in the Fourier space without any approximation solving the problem of spherical Bessel functions cancellation in both sides of the expansion. This expansion is the necessary first step to perform optical forces, as well as optical signals intensities, of scattering/absorbing particles. The limit of Rayleigh regime is easily obtained.
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.
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 coordinate's 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.
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.
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.
In this work we developed a setup consisting of an Optical Tweezers equipped with linear and non-linear micro-spectroscopy system to add the capabilities of manipulation and analysing captured objects. Our setup includes a homemade confocal spectrometer using a monochromator equipped with a liquid nitrogen cooled CCD. The spectroscopic laser system included a cw and a femtosecond Ti:sapphire lasers that allowed us to perform Raman, hyper-Raman, hyper-Rayleigh and two photon Excited (TPE) luminescence in particles trapped with an Nd:YAG cw laser. We obtained Raman spectra of a single trapped polystyrene microsphere and a single trapped red blood cell to evaluate the performance of our system. We also observed hyper-Rayleigh and hyper-Raman peaks for SrTiO3 with 60s integration time only. This was possible because the repetition rate of the femtosecond Ti:sapphire lasers, on the order of 80 MHz, are much higher than the few kHz typical picosecond laser repetition rate used before in hyper- Raman experiment, which required acquisition times of order of few hours. We used this system to perform scanning microscopy and to acquire TPE luminescence spectra of captured single stained microsphere and cells conjugated with quantum dots of CdS and CdTe and hyper-Rayleigh spectra of a noncaptured ZnSe microparticle. 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.
Up to now optical spectroscopies have analyzed the scattered light or the heat generated by absorption as a function of the wavelength to get information about the samples. Among the light matter interaction phenomena one that has almost never been used for spectroscopy is the direct photon momenta transfer. Probably because the forces involved are very small, varying from hundreds of femto to tens of pico Newtons. However, the nowadays very popular Optical Tweezers can easily accomplish the task to measure the photon momenta transfer and may be the basis for the Optical Force Spectroscopy. We demonstrate its potential as such a tool by observing more than eight Mie resonance peaks of a single polystyrene microsphere, and showed the capability to selective couple the light to either the TE, TM or both microsphere modes depending of the beam size, the light polarization and the beam positioning. The Mie resonances can change the optical force values by 30-50%. Our results also clearly show how the beam polarization breaks the usually assumed azimuthal symmetry by Optical Tweezers theories. We also obtained the spectrum from the two photon excited luminescence using the Optical Tweezers to hold a single bead suspended and a femtosecond Ti:sapphire laser for the non-linear excitation. This spectrum shows the pair of peaks due to both TE and TM spherical cavity modes. We have been able to observe more than 14 Mie resonance peaks in the TPE luminescence. Our results are in good agreement with optical force calculations using Maxwell stress tensor and partial wave decomposition of the incident beam approximated to a 3th order gaussian beam.
Semiconductor nanocrystals composed by few hundred to a few thousand atoms also known as quantum dots have received substantial attention due to their size tunable narrow-emission spectra and several other advantages over organic molecules as fluorescent labels for biological applications, including resistence to photodegradation, improved brightness and only one laser excitation that enable the monitoring of several processes simultaneously. In this work we have synthesized and characterized thiol-capped CdTe and bioconjugated them to macrophages. We have mapped the fluoroscence intensity along the macrophage's body in our set up consisting of an optical tweezer plus a non-linear micro-spectroscopy system to perform scanning microscopy and observe spectra using two photon excited luminescence.
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.
We developed a set up consisting of an Optical Tweezers plus linear and non-linear micro-spectroscopy system to add the capabilities of manipulation and analysing the captured object. For the confocal micro-spectrometer we used a 30 cm monochromator equipped with a cooled back illuminated CCD. The spectroscopic laser system included a cw and a femtosecond Ti:sapphire lasers that allowed us to perfom raman, hyper-raman, hyper-rayleigh and two-photon excited (TPE) luminescence in trapped particles with an Nd:YAG cw laser. With the cw Ti:sapphire laser we obtained raman spectra of a single trapped polystyrene microsphere and red blood cells and silicon to evaluate the performance of our system. The femtosecond Ti:sapphire laser was used to observed hyper-rayleigh and hyper-raman peaks of SrTiO3 with 60s integration time only. In the past, hyper-raman measurements required integration times of few hours, but the huge intensity together with the 80 MHz repetition rate of the femtosecond laser decreased this time for the seconds range. The sensitiveness of our system also permitted to observe more than 14 Mie resonance peaks in the TPE luminescence of a single stained trapped microsphere, which agrees well with the calculations. This system opens up the possibility to perform spectroscopy in a living trapped micro-organism in any desired neighbourhood and dynamically observe the chemical reactions and/or mechanical properties change in real time.
Optical tweezers (OT) rely on the radiation pressure to trap and manipulate microscopic particles and living microorganisms. Because the optical forces vary from hundreds of femto to tens of pico Newtons, OT can be used as an ultra sensitive force measurement tool to study interactions involving very small forces. We use a double tweezers to perform ultra sensitive measurement of the force due to the scattering of light as a function of its wavelength, in other words, to perform a Force Spectroscopy. Our results show not only the Mie resonances but also a selective coupling to either the TE, TM or both microsphere modes using the light polarization and the beam positioning. Mie resonances have usually been observed by scattering measurements. Very few reports of levitation experiments observed these resonances directly through the force. The double tweezers system has the advantage and flexibility of a stable restorative force measurement system. The experimental results show excellent agreement with Gaussian shaped beam partial wave decomposition theory. The understanding of the optical scattering forces in dielectric microspheres under different incident beam conditions is important as they have been used as the natural force transducer for mechanical measurements. Our results show how careful one has to be when using optical force models for this purpose. The Mie resonances can change the force values by 30-50%. Also the results clearly show how the usually assumed azimuthal symmetry in the horizontal plane no longer holds because the beam polarization breaks this symmetry.
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