The present disclosure relates to the field of optics and photonics, and more specifically to an optical manipulation device that may be used for example for trapping or moving micro or nanoparticles.
The disclosure can be of interest in any field where neutral particles have to be trapped and/or manipulated as for instance in atomic physics, nonlinear physics, biology and medicine, etc.
This section is intended to introduce the reader to various aspects of art, which may be related to various aspects of the present invention that are described and/or claimed below. This discussion is believed to be helpful in providing the reader with background information to facilitate a better understanding of the various aspects of the present invention. Accordingly, it should be understood that these statements are to be read in this light, and not as admissions of prior art.
Photonic condensed optical beams, or photonic “nanojets” generally relate to the generation of a transverse beam width smaller than the diffraction limit and to propagation over several wavelengths without significant divergence. The structured field of nanojets may induce specific optical forces providing the possibility for micro or nanoparticles manipulation along the nanojet EM (for “ElectroMagnetic”) field trajectories.
Since optical manipulation devices (like optical tweezers) are a powerful non-invasive tool in biological and medical application, the study of micro or nanoparticles manipulation based on the nanojet has stimulated researchers' interest. However, the previous works regarding nanojet-induced optical forces focused on trapping particles along an axis of symmetry of the device used to generate the nanojet.
Recently, the asymmetric dielectric system creating a curved photonic jet (“photonic hook”) was introduced to generate the optical forces for moving particles in a curved trajectory as disclosed for instance in the article by A. S. Ang, A. Karabchevsky, I. V. Minin, O. V. Minin, S. V. Sukhov and A. S. Shalin: “‘Photonic Hook’ based optomechanical nanoparticle manipulator”, Scient. Rep., 2018. It was demonstrated that a particle could go around a glass obstacle or be stably trapped near glass and gold obstacles, which allows new applications in optical manipulation of micro or nanoparticles.
There is thus a need for a new type of optical manipulation device providing more flexible nanoparticle manipulation, in particular through the generation of curved jet beams.
A particular aspect of the present disclosure relates to a device configured for radiating a focused electromagnetic beam in a dielectric host medium having a first refractive index n1, when an incoming electromagnetic wave illuminates a first face of the device, named illumination face. Such a device comprises:
The focused electromagnetic beam results from a combination of at least two beams among the first, second and third jet beams. The device is configured for having a direction of propagation of the focused electromagnetic beam being tilted in respect of a direction of propagation of the incoming electromagnetic wave.
Thus, the present disclosure proposes a new and inventive solution for trapping or moving micro or nanoparticles.
More particularly, when the device comprised in the claimed optical manipulation apparatus is illuminated by the incoming electromagnetic wave, the resulting focused electromagnetic beam (or resulting jet beam) is generated in a direction that is tilted in respect of the direction of propagation of the incoming electromagnetic wave. In that case, the electromagnetic field lines of the outgoing focused electromagnetic beam present a curvature allowing the micro or nanoparticles to be trapped or moved, even around or behind objects present in the vicinity of the radiating face of the device from which the focused electromagnetic beam comes out of the device. This allows for a more flexible manipulation of the micro or nanoparticles.
According to one embodiment, the direction of propagation of the focused electromagnetic beam is tilted in respect of a direction of propagation of the incoming electromagnetic wave as a function of at least part of:
According to one embodiment, the focused electromagnetic beam results from a combination of the first, second and third jet beams.
According to one embodiment, n3≥√{square root over (n1n2)}, W1=W2 and H1≥HA, with HA a height, along the Z-axis and relative to the illumination face, of the intersection point of the first and second jet beams.
According to one embodiment, n3<√{square root over (n1n2)} and W2>W1.
According to one embodiment, n3<√{square root over (n1n2)}, W2<W1 and H1≥HA, with HA the height, along the Z-axis and relative to the illumination face, of an intersection point of the first and second jet beams.
According to one embodiment, n3>√{square root over (n1n2)}, W2<W1 and H1 is targeted to be equal to HA−λ/2, with HA the height, along the Z-axis and relative to the illumination face, of an intersection point of the first and second jet beams.
According to one embodiment, the height HA fulfils
and ΘB2 being respectively radiation tilt angles of the first and second jet beams in respect of the direction of propagation of the incoming electromagnetic wave.
Thus, the device is configured for having the focused electromagnetic beam tilted in respect of the direction of propagation of the incoming electromagnetic wave e.g. when the incoming electromagnetic wave presents a normal incidence relative to the illumination face of the device.
According to one embodiment, ΘB1 and ΘB2 are targeted to be respectively equal to
and to
where angles α1 and α2 are respectively the base angles of the first and second contact areas relative to the X-axis, and where ΘTIR1 and ΘTIR2 are respectively limit angles of refraction associated with the first and third contact areas.
Thus, the device is configured for having the focused electromagnetic beam tilted in respect of the direction of propagation of the incoming electromagnetic wave e.g. when the first and second parts have nonvertical contact areas relative to the illumination face.
According to one embodiment,
According to one embodiment, the equivalent wavelength in the host medium, λ, of the incoming electromagnetic wave belongs to the visible light spectrum. For instance, the equivalent wavelength in the host medium of the incoming electromagnetic wave belongs to the range going from 390 nm to 700 nm.
According to one embodiment, at least one of the first and second materials belongs to the group comprising: glass, plastic, a polymer material, oxides and nitrides.
Another particular aspect of the present disclosure relates to an optical manipulation system comprising a device as described above (in any of the disclosed embodiments) and an electromagnetic source configured for generating the incoming electromagnetic wave.
Another particular aspect of the present disclosure relates to the use of a device as described above (in any of the disclosed embodiments) or of an optical manipulation system as described above (in any of the disclosed embodiments) for trapping or moving micro or nanoparticles in the dielectric host medium.
Other features and advantages of embodiments shall appear from the following description, given by way of indicative and non-exhaustive examples and from the appended drawings, of which:
The components in the figures are not necessarily to scale, emphasis instead being placed upon illustrating the principles of the invention.
In all of the figures of the present document, the same numerical reference signs designate similar elements and steps.
The present disclosure relates to a technique for generating optical forces through jet beams which field lines exhibit curvatures allowing micro or nanoparticles to be trapped or moved e.g. around obstacles. This is achieved through the use of a device comprising two or more parts of dielectric materials with different refractive indexes. The refractive indexes of the constitutive parts are higher than the surrounding host medium in which the micro or nanoparticles are trapped or moved. The constitutive parts are configured in such a way that at least two of the jet beams, originating from different contact areas (associated with different parts) of the device, recombine and contribute to the formation of a focused electromagnetic beam which direction of propagation is deflected in respect of a direction of propagation of an incoming electromagnetic wave illuminating the device.
Numerical simulations show that the deflection of a generated focused jet beam can be controlled by the parameters of the device in view of the surrounding host medium.
The device 100 is configured to be in contact with a dielectric host medium 103 having a first refractive index n1 and in which the micro or nanoparticles are intended to be trapped or moved by a focused electromagnetic beam radiated by the device 100 when an incoming electromagnetic wave IEM radiated by an electromagnetic source 100s illuminates at least one face of the device 100, named illumination face 100i. More particularly:
For instance, the first and second materials belong to the group comprising glass, plastic, a polymer material, oxides and nitrides.
The first part 101 and the second part 102 are located side by side along the X-axis with W1+W2 greater than the equivalent wavelength in the host medium, λ, of the incoming electromagnetic wave IEM radiated by the electromagnetic source 100s. The first part 101 and second part 102 extend along the Z-axis (the Z-axis is orthogonal to X-axis and thus to the illumination face 100i in the chosen coordinate system) from the illumination face 100i up to another face of the device 100, named radiating face 100r, opposite to the illumination face 100i. The first part 101 and second part 102 have respectively a first height H1 and a second height H2 along the Z-axis.
In the embodiment of
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However, in other embodiments, the direction of propagation of the incoming electromagnetic wave IEM may be tilted relative to the Z-axis as discussed below in relation with
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However, in other embodiments, some prismatic structures (with arbitrary base angles) can also be used for the device 100 as discussed below in relation with
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More particularly, when the incoming electromagnetic wave IEM presents an oblique angle of incidence (i.e. the angle of incidence of the incoming electromagnetic wave IEM relative to a normal of the illumination face 100i), the incoming electromagnetic wave IEM illuminates the illumination face 100i, but also at least another lateral face of the device 100. Whatever the considered slant angles of incidence, the first contact area 100e1, the second contact area 100e2 and the third contact area 100e3 contribute respectively to the radiation of the first jet beam NJ1, of the second jet beam NJ2 and of the third jet beam NJ3. Such jet beams are obtained from the superposition of a plurality of contributions resulting from the diffraction or refraction of the incoming electromagnetic wave IEM by the different faces or contact areas (e.g. between parts) of the device 100. Thus, in any case the first contact area 100e1 contributes to the radiation of the first jet beam Nil, the second contact area 100e2 contributes to the radiation of the second jet beam NJ2 and the third contact area 100e3 contributes to the radiation of the third jet beam NJ3.
Back to
According to the present disclosure, the materials and size of the first part 101 and of the second part 102 can be optimized in order to manage the positions of the jet hot spots, EM powers, directions and angles of deviation of the three jet beams NJ1, NJ2 and NJ3. As a result, the device 100 behaves as if it was radiating a focused electromagnetic beam resulting from the combination of at least two beams among said first jet beam NJ1, second jet beam NJ2 and third jet beam NJ3. The device 100 can thus be configured for having a direction of propagation of the focused electromagnetic beam being tilted in respect of a direction of propagation of the incoming electromagnetic wave as a function of at least part of:
In this Section, a set of equations is provided for estimating example optimal combinations of materials and dimensions of the blocks for having a jet beam shift (i.e. having a tilt angle relative to the direction of propagation of the incoming electromagnetic wave) and deviation. As shown below, the hot spot position and the direction of beam deviation are sensitive to the sizes of constitutive parts. For devices with dimensions larger than a few wavelengths, the Fresnel diffraction phenomenon may have a huge impact.
Generally, the beam-forming phenomenon appears on a contact area between two materials of different refractive indexes, and is associated with this contact area (e.g. contact area 100e1, 100e2 or 100e3 of the device 100 of
More particularly, the jet beam radiation angle can be derived in relation to the Snell's law. For instance, in the case of the first contact area 100e1 of the device 100, when in contact with the dielectric host medium 103, the radiation angle of the first jet beam NJ1 associated with the first contact area 100e1 is determined using the approximate formula:
where
is the corresponding critical angle of refraction under the assumption that n2>n1.
It can be noted that in general, the point of intersection of two jet beams radiated from opposite sides of an element determines the focal length of that element behaving as a microlens. In a first approximation, in the case of a single material element, the focal length of the microlens can be characterized as the function of the width and index ratio of the materials inside and outside the lens. The radiated electromagnetic beam will be directed along the symmetry axis of the element and the focal length of the resulting microlens can be estimated as:
where
and W1 is the width of the element.
Back to
where
is the corresponding limit angle of refraction.
Accordingly, the third jet beam NJ3 associated with the third contact area 101e3 is refracted at the angle ΘB3 with:
where
is the corresponding limit angle of refraction.
The length and intensity of the three jet beams NJ1, NJ2 and NJ3, are generally different. The maximal intensity and minimal length correspond to the beam with highest ratio between the refractive indexes, which corresponds to the first jet beam NJ1 refracted at the angle ΘB1 when n2>n3>n1.
The behavior of the focused electromagnetic beam radiated by the device 100 may be explained when determining the points of intersection of the three jet beams NJ1, NJ2 and NJ3 radiated respectively at the angles ΘB1, ΘB2 and ΘB3.
The point A of intersection of the first NJ1 and second NJ2 jet beams has the coordinates (WA, HA) in the XoZ coordinate system of
Defining ΘB4 as the angle of deviation of the focal point A from the axis of symmetry 101 as of the first part 101 with width W1,
In the same way, the first jet beam NJ1 and third jet beam NJ3 intersect at point B with the coordinates (WB, HB), where:
Defining ΘB5 as the angle of deviation of the focal point B from the axis of a symmetry of the device 100 (i.e. the Z-axis in
The second NJ2 and third NJ3 jet beams intersect only if n3 is above a critical value, i.e. if n3≥√{square root over (n1n2)}. In this case the coordinates of the point C are determined as:
In this case, defining ΘB6 as the angle of deviation of the focal point C from the axis of symmetry 102 as of the second part 102 with width W2,
The particular case where the three jet beams NJ1, NJ2 and NJ3 intersect at the same point for fixed refractive indexes of the two parts 101, 102 and of the host medium 103 can be obtained as the result of variation of the widths W1, W2 of the two parts 101, 102. In order to get an intersection of the three jet beams NJ1, NJ2 and NJ3 at one point, the ratio W1/W2 has to be equal to:
In this case, all three jet beams NJ1, NJ2 and NJ3 contribute to the total generated focused electromagnetic beam radiated by the device 100. Thus, the intensity of the generated focused electromagnetic beam is maximal.
The dependencies of the deviation angles ΘB4-B6 on the refractive index n3 for the fixed value n2=1.8 and W1=W2 are presented in
Based on the identified properties of the device 100 depicted in
The following numerical simulations have been performed assuming that H1=H2=H, W1=W2, and W=W1+W2 is greater than the equivalent wavelength in the host medium, λ, of the incoming electromagnetic wave IEM. However, as indicated in relation with
Under the present assumptions, it can be shown that the hot spots positions of the generated jet beams are almost independent from the height H of the device 100 for n3<√{square root over (n1n2)} as illustrated e.g. in
For n3>√{square root over (n1n2)} and starting from H1≈HA, a shift of the hot spot toward increasing X coordinates is observed. The power density distribution along the X-axis for n3=1.6 is presented in
The equivalent wavelength in the host medium 2 of the incoming electromagnetic wave influences the hot spots positions of the generated jet beams.
Thus, in some embodiments of the present disclosure, the device 100 is configured such as n3≥√{square root over (n1n1)}, W1=W2 and H1≥HA, with HA the Z coordinate of the intersection point of the first jet beam NJ1 and of the second jet beam NJ2 (i.e. the height, along the Z-axis and relative to the illumination face 100i, of the intersection point of the first NJ1 and second NJ2 jet beams). This allows obtaining a tilt of the direction of the generated focused electromagnetic beam which is obtained from a combination of at least two beams among the first jet beam NJ1, the second jet beam NJ2 and the third jet beam NJ3 in respect of the direction of propagation of the incoming electromagnetic wave IEM.
This part of the description deals with the influence of the width W1 and W2 of the first part 101 and of the second part 102 of the device 100.
The influence of the width W2 of the second part 102, having the refractive index n3, on the parameters of the generated jet beams is analyzed assuming a fixed width W1 of the first part 101 that has the refractive index n2 (n2>n3>n1).
More particularly, for n3<√{square root over (n1n2)}, two jet beams emerge in the proximity of the radiating face 100r of the device 100 when W2>W1 as illustrated in
The power density distribution along the X-axis at different widths W2 of the second part 102 of the device 100 is presented in
Alternatively, when n3>√{square root over (n1n2)}, two additional jet beams are obtained (e.g. as in the configuration of
Thus, in some embodiments of the present disclosure, the device 100 is configured such that n3<√{square root over (n1n2)}, and W2>W1, independently of the heights H1 and H2 of the first part 101 and of the second part 102 of the device 100 (as long as the condition |H2−H1|≤λ/4 is fulfilled). Such parameters allow obtaining a tilt of the direction of the generated focused electromagnetic beam (that results from a combination of at least two beams among the first jet beam NJ1, the second jet beam NJ2 and the third jet beam NJ3) in respect of the direction of propagation of the incoming electromagnetic wave IEM radiated by the electromagnetic source 100s.
There is also an influence of the width W1 of the first part 101 having the refractive index n2, on the parameters of the generated jet beams assuming a fixed width W2 of the second part 102 that has the refractive index n3 (n2>n3>n1).
In fact, a similar behavior can be observed as in the previous case discussed above where W2 was varying for a fixed value of W1. However, in the present case, the side jet beams (or secondary lobes) are deviated toward the angles ΘB4 (for the side jet beams on the left side when looking at the figures) and ΘB6 (for the side jet beams on the right side when looking at the figures). As mentioned above, in accordance with equation (11) the generated focused electromagnetic beam can be intensified based on some particular dimensions of the device 100. For the values of the parameters of the system as chosen in
Thus, in some embodiments of the present disclosure, the device 100 is configured such that n3<√{square root over (n1n2)}, W2<W1, and H1≥HA (still with |H2−H1|≤λ/4). Such parameters allow obtaining a tilt of the direction of the generated focused electromagnetic beam (that results from a combination of at least two beams among the first jet beam NJ1, the second jet beam NJ2 and the third jet beam NJ3) in respect of the direction of propagation of the incoming electromagnetic wave IEM.
With the sizes W1>W2, the deviation to the right (when looking at the figures) is observed for n3<√{square root over (n1n2)} (e.g. as in the configuration of
Thus, in some embodiments of the present disclosure, the device 100 is configured such that n3>√{square root over (n1n2)}, W2<W1, and H1 is targeted to be equal to HA−λ/2 (still with |H2−H1|≤λ/4). Such parameters allow obtaining a tilt of the direction of the generated focused electromagnetic beam (that results from a combination of at least two beams among the first jet beam NJ1, the second jet beam NJ2 and the third jet beam NJ3) in respect of the direction of propagation of the incoming electromagnetic wave IEM.
Examination of power density distributions obtained for different oblique angles of incidence, a, (i.e. the angle of incidence of the incoming electromagnetic wave IEM relative to a normal of the illumination face 100i) shows that the tilt of the direction of the generated focused electromagnetic beam in respect of the normal to the radiating face 100r is sensitive to the height of the device 100.
For example, when the device 100 is in contact with a dielectric host medium 103 such that n1=1, n2=1.8, n3=1.6, W1=1000 nm, W2=700 nm, H1=H2=H=300 nm and α=10°, the tilt angle γ of deviation of the generated focused electromagnetic beam from the normal incidence is equal to 14.49° and remains constant for all wavelengths of incident waves in the theoretical hypothesis of non-dispersive materials. The slight dispersion in the case of α=10° is observed for H=550 nm. Moreover, the angle γ is approximately equal to 17.54°. The dispersion of the system rises with the height H. The comparison of
One can note that the present simulations have been performed for H=H1=H2, however, as discussed above, the conclusion remains the same as long as |H2−H1|≤λ/4.
According to the embodiment of
It can be shown that for the device 100′ with the base angles αj greater than 90°−ΘBj, with j equal to 1, 2 or 3, the corresponding jet beam radiation angle can be determined using the approximate formula:
where the angles θ′TIRj are the critical angles of refraction from the nonvertical edges, or contact areas 100′e1, 100′e2 and 100′e3.
To get the approximate formula for θ′TIRj, the changing of the position of the contact areas compared to the configuration of the device 100 of
These expressions can then be injected into the equations (4)-(11) for having a description of the behavior of the jet beams associated with the contact areas 100′e1, 100′e2 and 100′e3 of the device 100′.
To consider the effect of the first part 101′ and of the second part 102′ with nonvertical contact areas 100′e1, 100′e2 and 100′e3, simulation results are discussed below that show the influence of the height H1=H2=H of the first part 101′ and of the second part 102′ on the generated jet beams when the total width W′=W′1+W′2 is such that W′>λ with W′1=W′2. It is seen that the hot spot position is almost independent from the height H′ of the device 100′ that is in contact with the dielectric host medium 103 when n3<√{square root over (n1n2)} (see
More particularly,
As can be seen in
More particularly, the optical forces acting on arbitrary micro or nanoparticles can be obtained by approximating the particle by an electric dipole.
This method applies for Rayleigh particles (particles much smaller than the incident wavelength) as detailed for instance in the article by P. Chaumet and M. Nieto-Vesperinas: “Time-averaged total force on a dipolar sphere in an electromagnetic field,” Opt. Lett. 25, 1065-1067 (2000).
Using the dipole approximation for the subwavelength radius of the sphere, the force can be obtained as:
where
is the particle's complex polarizability,
is the refractive index of the material of the particle, nm is the refractive index of the medium outside the particle and a is the radius of the particle.
The forces produced by the deviated jet beams in the presence or not of obstacles 1800 have been simulated using Comsol software and based on the dipolar approximation for gold particles with a radius of 0.03 μm and a dielectric permittivity ε=−11.208+1.31184i. Further, those forces have been simulated on one hand for a single material device 1710 having a refractive index n, and for the dual-material device 100 of
In
Referring to
Thus, such double-material device 100, 100′ according to the disclosure (in any of its embodiments discussed above) can be used as an elementary part of an optical manipulation apparatus (e.g. an optical tweezer) 1700 for trapping or moving micro or nanoparticles in the dielectric host medium 103. For instance, the equivalent wavelength in the host medium, λ, of the incoming electromagnetic wave IEM belongs to the visible light spectrum (e.g. the wavelength in the host medium 2 lays between 400 nm and 700 nm, or equivalently the frequency of the incoming IEM wave lays between 430 THz to 790 THz). Thus, devices with nano-scale dimensions can be obtained for forming visible light wave patterns. In other embodiments, the frequency of the incoming IEM wave belongs to the group comprising:
radio waves, i.e. between 30 Hz to 300 GHz;
microwaves, i.e. 1 GHz to 100 GHz;
terahertz radiations, i.e. 100 GHz to 30 THz;
infrared, i.e. 300 GHz to 430 THz; and
ultraviolet, i.e. 790 THz to 30 PHz.
In those embodiments, the size of the device 100, 100′ is thus scaled according to the wavelength of the incoming IEM wave in order to achieve the tilt of the generated focused electromagnetic beam.
In some embodiments, an optical manipulation system comprises the optical manipulation apparatus 1700 and the electromagnetic source 100s for radiating the incoming electromagnetic wave IEM that illuminates the illumination face 100i of the device 100, 100′ (in any of its embodiments discussed above).
Number | Date | Country | Kind |
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18213584.8 | Dec 2018 | EP | regional |
Filing Document | Filing Date | Country | Kind |
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PCT/EP2019/084526 | 12/10/2019 | WO | 00 |