ANÁLISIS DE LA SENTENCIA CON CARACTER DE SUSPENDIA.

Building an optical trap for metal nanoparticles is in many ways identical to set- ting up a standard trap for micron-sized particles. We dedicate separate sections to the illumination and detection as these two topics become more challenging for nanoparticles. We start this section describing conventional optical tweezers that are the central part of our red-detuned tweezing experiments presented in Chapter 4. A dual beam trap has been suggested to be advantageous for metal nanoparticle trapping [13], thus we present our experiments with this trapping geometry here. Depending on the trapping geometry, we have to consider adequate objectives with the right choice of numerical aperture (NA), the types of lasers and the beam deliv- ery. We would like to stress that we trap the metal nanoparticles in 3 dimensions deep in the sample chamber to avoid proximity effects that distort the trap stiffness measurements. This is harder to achieve and different to 2D trapping where the confinement along the beam axis is accomplished by pushing the trapped sphere against the glass coverslip of the sample chamber [9].

f1 f1 f2 f2 conjugate plane lens 2 lens 1 mirror 1 mirror 2 co nju ga_te pla ne co nju ga_te pla ne sample

Figure 3.5: This is a detailed view of the beam steering mechanism provided by the relay

telescope. The two lenses image the beam steering mirror onto the back aperture of the objective. In that way we can move the laser focus in the sample plane without the beam walking off the entrance pupil of the back aperture of our trapping objective.

3.2.1 The single-beam trap: Optical tweezers

The standard optical tweezers is composed of a laser trapping the particle, a high NA objective to focus the trapping laser tightly, beam resizing optics to acquire a suitable laser beam diameter and beam steering optics such as mirrors coated appropriately to the applied laser wavelength. We provide a diagram of a generic tweezers setup in Fig. 3.4 including the key elements essential to control the position and form of a single laser beam. We implemented our tweezers setup around a basic microscope (Nikon Eclipse LV100) to benefit from the robustness and fine-steering of the microscope stage.

To optically tweeze a nanoparticle we require a strong trap stiffness, which means to focus a Gaussian laser beam as tightly as possible to achieve high intensity gra- dients in all directions in space (x-y-z). We chose an oil immersion microscope objective with a high numerical aperture and focussing abilities (Nikon CFI Plan Fluor, 100x oil, NA 1.3) for our experiment. The diameter of the trapping beam has to match the back aperture of the microscope objective in order to get the steep- est field gradient at the focus of the trap. For trapping metal nanoparticles this is particularly important as a slight decrease in trapping efficiency potentially renders trapping impossible. The input beam should neither be clipped nor underfill the back aperture. The lens systems of the beam expander and relay telescope serve to adjust the beam diameter according to our needs (see Fig 3.4). Depending on the laser output, the beam expander may be redundant. We found that using high refractive index immersion oil, not matched to the index of refraction of the glass coverslip, increased the trapping abilities along the beam axis according to [57].

The relay telescope is not always used for beam resizing as it serves yet another, more important purpose. Two lenses (lens 3 and lens 4 in Fig. 3.4), spaced the sum of their focal lengths apart, form the relay telescope. The objective back aperture

optical tweezers supercontinuum source dielectric mirror (IR) dielectric mirrors (VIS) dielectric mirror (IR) silver mirror dielectric mirror (IR)

visible band infra-red band

supercontinuum source dielectric mirror (VIS) hot mirrors dielectric mirror (VIS) silver mirror Semrock filter optical tweezers dielectric mirror (VIS)

Figure 3.6: We passed the broadband supercontinuum through a range of wavelength

specific reflection and filtering optics. Left - The combination of 3 dielectric mirrors (Thorlabs EO2, 400-750nm reflective) and 2 hot mirrors (Thorlabs, 750-1200nm reflective) filtered out the infrared part of the spectrum. Inserting a Semrock brightline filter allowed us to select 40nm out of the visible part of the spectrum, depending on the filter. Right - Combining 3 dielectric mirrors (Thorlabs EO3, 750-1100nm reflective) to reflect part of the infrared spectrum and 2 dielectric mirrors (Comar, 400-900nm reflective), specifically coated to filter out the remaining visible parts of the spectrum, helped us to select a band (900-1100nm) for our in infrared experiments.

and the steering mirror (mirror 1 Fig. 3.4) form optical conjugate planes. That way, the trapping beam can move in the sample plane without being displaced off the back aperture of the objective. The position of the beam at the conjugate planes remains fixed as these are imaged onto each other with the relay telescope. However, the position of the beam focus in the sample plane as well as the beam path change according to the movement of the steering mirror. Figure 3.5 shows a more detailed diagram of the beam path between the steering mirror and the sample plane through a relay telescope.

We chose appropriate anti-reflection coated lenses (visible 450-900nm, infrared 630-1100nm) for all experiments to minimise back reflection and power losses. Our laser source for the single-beam trap is a supercontinuum laser from Fianium, pro- viding a pulsed (10ps, 40MHz repetition rate) output covering the entire spectrum between 470nm-1750nm. We took specific narrow wavelength bands out of this broad spectrum by exploiting this one laser as a multi-line source. We selected the relevant wavelength bands with a combination of dielectric mirrors and Semrock brightline filters. The wavelength band for our infrared experiments was 200nm broad, whereas the selected visible bands were only 40nm wide. The latter provided just enough power after all filtering steps for optical trapping. The two diagrams in Fig. 3.6 show more details of the filtering beam path before entering the optical tweezers.

60nm Au sphere 1.1 m SiO sphereμ 2 fibre 1 Fgrad Fscat Fscat Fgrad fibre 2

Figure 3.7: Left - The two pictured objects have the same scattering cross section,

although the 60nm gold sphere is a lot smaller compared to the 1.1µm silica sphere. This sketch illustrates that metal nanoparticles have a much larger scattering cross section than their same-sized dielectric counterparts. Right- The dual beam fibre trap holds a particle at the point where the scattering forces Fscat of the two counter propagating laser beams balance out. The gradient force Fgrad of the Gaussian beam profile provides confinement orthogonal to the beam axis.

3.2.2 The dual beam trap: Fibre trap

Metal nanoparticles scatter more light than dielectric beads as a result of their larger scattering cross section (see Fig. 3.7). Consequently the scattering force Fscat

exerted on a metal particle in a laser beam is larger than the force upon dielectrics of the same size. In an optical tweezers configuration the scattering force destabilises trapping. Thus it has been suggested to design an optical trap taking advantage of the increased scattering force [13]. A dual beam trap takes advantage of the scattering force by holding a particle in the middle of two counter propagating beams. Stable trapping occurs at the position where the scattering force components of both beams along the optical axis cancel out. The confinement perpendicular to the propagation axis is realised by the gradient force Fgradpresent due the Gaussian

beam profile. Figure 3.7 shows a diagram of a dual beam fibre trap. Optical fibres deliver the trapping beams into the sample chamber.

We tested a dual beam fibre setup, which has been used successfully before in our group, for various studies on micron sized dielectric beads [58, 59]. We implemented the fibre trap in a standard microscope setup taking advantage of the imaging and illumination system of the microscope. A dual beam trap needs fewer optics and beam alignment compared to single beam tweezers. We chose a linearly polarised 1070nm fibre laser (IPG photonics VLM-5-1070-LP) for our experiment. The laser coupled through a microscope objective (Newport, 10x) into a single mode fibre suitable for this wavelength (Thorlabs, 6.6µm core size, single mode). A fibre launch stage (Elliot Scientific MDE510) turned out to be helpful for aligning the input beam and achieving better coupling efficiency. A single mode fibre coupler with a

fibre 2 guided 100nm Au spheres fibre 1 trapped 250nm Au sphere fibre 1 fibre 2

Figure 3.8: Left - The two fibres of the dual beam trap are not aligned on the same

axis which results in guiding of the 100nm gold spheres rather than trapping. Right- We achieved trapping of a 250nm gold sphere in the dual beam fibre trap.

50:50 split ratio divided the incoming fibre into two arms for the dual fibre trap (Thorlabs, FC1064-50B). The power output at both fibre ends was the same and could be adjusted by slightly bending one fibre.

The two opposing optical fibres are directly inserted into the sample chamber. We imaged the sample chamber in brightfield transmission microscopy, perpendicular to the fibre axes. We fixed one fibre on the glass coverslip of the bottom of the sample chamber. We used a spacer (adhesive sticker) of the same thickness as the fibre diameter so we were able to place a second glass coverslip on top to prevent the sample from evaporating. The spacer had two opposing gaps to insert the fibres. Attaching the second fibre to an x-y-z stage gave us full control of its positioning and its alignment with the fixed fibre. We experimented with 100nm and 250nm gold nanoparticles. We also added ethylene glycol to the nanoparticle buffer solution to delay the evaporation of the sample. This made the buffer solution more viscous, damping the particle motion even further which helped to achieve trapping.

The alignment of both fibres proved to be the critical part of the experiment. As the fibre output has a weakly diverging Gaussian profile, the beam will spread with propagation distance. Consequently the gradient across the profile decreases which results in less effective transverse trapping. Hence the gradient force is rather weak and the trapping of the particle is dominated by the scattering force. The slightest offset of the two fibres causes the scattering forces of the opposing beams not to be along the same axis and the weak transverse trapping is not able to hold the particle. The gold spheres are guided away from the trap site, along the beam from one fibre end to the other as shown in Figure 3.8 on the left side.

It was straightforward to achieve guiding of 100nm and 250nm gold spheres as pictured in Fig. 3.8. However, we only managed trapping of 250nm gold spheres occasionally and never for 100nm gold spheres. The gradient of the Gaussian fibre output was too weak to produce a strong enough gradient force to hold 100nm gold spheres. Once trapped, we were able to move the position of the 250nm gold

sphere between the fibres towards one or the other by varying the laser power in one of the fibres. In addition to positioning the fibres along the same axis, the angle towards each other had to be exactly 180◦ _{to create a trap site where the}

scattering forces would cancel out and the gradient force would be strong enough for transverse trapping. The particles entered the propagating laser beam transversely from all directions and accelerated along the axial beam propagation path. With no correctly aligned opposing beam they would speed up towards the other fibre and eventually fall out of the guiding beam as the gradient force weakened over distance. For micron-sized particles alignment is not as critical as the particles are larger. Their Brownian motion is too small to disturb trapping as substantially as it does for nanometer-sized particles and thus less force is needed to stably trap micron-sized spheres. The ratio of scattering and gradient force for micron-sized dielectrics is also completely different to the one for nanometre-sized metal particles. For micron-sized dielectrics, a slight misalignment of the fibres usually only degrades trapping a little resulting in a trap site off-axis. Additionally light is able to propagate through a dielectric particle which then acts as a lens and supports the gradient force for trapping.

Overall we found that this trapping geometry works in principle but poses chal- lenging technical issues. Designing a setup with nanometre-precise fibre alignment is necessary to achieve trapping for 100nm metal particles. Additionally the issue of sample evaporation need to be addressed. A sealed sample chamber, still allow- ing the movement of one fibre would certainly be beneficial. We suggest increasing the transverse gradient force by using lensed fibres in the future. Because of these difficulties we did not pursue the fibre trapping geometry any further. However, there have been investigations showing a dual beam trap created with two opposing objectives instead of optical fibres to work satisfactory [60]. This certainly solves the issue of week transverse gradient forces and adds additional gradient forces towards the common focus, though this setup is more complex than single beam tweezers.