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Abstract
Optical pulling is an attractive concept due to the counterintuitive feature, the profound mechanism underneath and promising applications. In recent ten years, optical pulling of micro-nano objects have been fully demonstrated. However, optical pulling of a macroscopic object is challenging. Herein, laser pulling of a macroscopic object is presented in rarefied gas. The pulling force is originated from the Kundsen force when a gauss laser beam irradiates a macroscopic structure composed of the absorptive bulk cross-linked graphene material and a SiO2 layer. A torsional pendulum device qualitatively presents the laser pulling phenomenon. A gravity pendulum device was used to further measure the pulling force that is more than three orders of magnitudes larger than the radiation pressure. This work expands the scope of optical pulling from microscale to macroscale and provides an effective technique approach for macroscopic optical manipulations.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Optical manipulations utilizing photon momentum and photon energy is a fascinating topic for both the public and scientists. Four hundred years ago, in 1619, Kepler began to discuss the possible effect of optical force on the direction of the comet’s tail. More than 200 years later, the radiation pressure was explained by Maxwell’s theory. In the past decades, various optical manipulations including levitation [1], pushing [2] and rotation [3] have been achieved in vacuum, gaseous medium and liquid [4,5], where the optical tweezers [6,7] and laser cooling of atom gas [8,9] are typical scenarios of optical manipulations.
About 10 years ago, optical pulling force (i.e. optical tractor beam) emerged [10–12] as an attractive and popular concept, not only because the counterintuitive feature but also the profound mechanism underneath and promising applications. In the recent several years, a variety of optical pulling schemes have been proposed mainly based on the physics of momentum transfer and energy transfer. On the one hand, as for the momentum transfer path, Bessel beams were proposed to pull elongated objects [13] and core–shell structures [14,15]. Fernandes et. al. reported an optical pulling using chiral light [16]. Enhancement of optical pulling force was reported using optically bound structures [17]. Optical pulling in a periodic photonic crystal background was reported, which was originated from the self-induced backaction of the object to the self-collimation mode [18]. Long-range optical pulling of nanoparticle based on Bessel beam was achieve by simultaneously using several novel and compatible mechanisms [19]. Optical pulling mechanism via engineering the topology of light momentum in the background was also reported [20]. Besides, optical pulling can be also realized using the fluidic drag force and metamaterials (the so called “meta-tweezers”) that have provided numerous opportunities in compact multifunctional optical manipulations, such as trapping, transporting, sorting and imaging [21,22]. On the other hand, optical pulling based on photon energy transfer also appear with the assistance of surrounding medium including gas and liquid, in which the photophoresis induced optical pulling is a significant scheme. Photophoretic force discovered by Ehrenhaft has been widely used in optical manipulation [4,23,24]. When an absorptive object is irradiated by inhomogeneous light, asymmetrical temperature distribution is created, and then hot side will give a larger recoiling force than the cold side originated from the thermal motion of medium molecules. In rough comparison, the Photophoretic force imparted by the gas molecules is c/3υ times greater than the radiation pressure originated from the photon momentum transfer, where c is the speed of light and υ is the gas molecular velocity [25]. Shvedov et. al. achieved long-range polarization-controlled laser pulling of gold-coated hollow glass spheres [26]. Zhang et. al. demonstrated a new principle of the laser-induced hammer-hit vibration of a micron-sized black sphere in liquid glycerol [27]. Lu et. al. reported light-induced pulling and pushing of micro gold plate by the synergic effect of optical force and photophoretic force [28]. Up to now, based on the physics of momentum transfer and energy transfer, various optical pulling of small objects at the micro-nano scale have been demonstrated. However, optical pulling of a macroscopic object is challenging and is rarely reported.
The aforesaid photophoretic force is essentially originated from the thermally non-equilibrium molecule motion in the environmental medium. Actually, this kind of molecule behavior is also capable to drive a macroscopic object, which is usually called Knudsen force. For instance, in 2021, Azadi et al. reported the light-driven pushing of a macroscopic polymer film based on Kundsen force [1]. The author wonders if the Kundsen force can be used to perform macroscopic light-driven pulling.
In this work, a macroscopic structure composited of a cross-linked graphene (CLG) front layer and a SiO2 back layer was designed. When a gauss laser beam irradiates the back layer in rarely gaseous environment (5 Pa), macroscopic laser pulling occurs, which is due to the photo-thermal Knudsen force. A lightweight torsional pendulum device qualitatively presents the laser pulling phenomenon, and a gravity pendulum device was used to measure the pulling force.
2. Experimental setup
2.1 Preparation of the lightweight torsional pendulum and the CLG-SiO2 sample
The arm of the torsional pendulum is made of a PET sheet with size of 50 mm × 10 mm × 0.1 mm. A CLG flake with size of about 5 mm × 3 mm × 0.5 mm was taken off a cylindrical bulk CLG material (inset of Fig. 1(D)) provided by a commercial corporation XFNANO. The CLG material with density of ∼17 mg/cm3 has a mass of anomalous micron-scale internal pores, in which the graphene sheets form the pore walls (Fig. S1). The CLG flake was sticked on the front side of a 0.17 mm thick glass sheet (mainly made of SiO2) by using a 1 µm thick optical transparent tape, forming a macroscale CLG-SiO2 sample (Fig. 1(C) and (D)). The CLG-SiO2 sample was sticked on the end of the pendulum arm by also using the 1 µm thick optical transparent tape (Fig. 1(C), (D) and (E)). At last, a polyester suspension line with diameter of 0.5 mm was used to suspend freely the pendulum arm from a holder (Fig. 1(F)).
Fig. 1. Mechanism of macroscopic laser pulling and experimental facility of the torsional pendulum. (A) Mechanism of macroscopic laser pushing of the bulk CLG material based on Kundsen force. (B) Mechanism of macroscopic laser pulling based on Kundsen force, and the yellow layer indicate an optical transparent material with low thermal conductivity. (C) Schematic diagram of the torsional pendulum device, and the CLG-SiO2 sample is fixed in the end of the pendulum arm. (D) Photograph of the front side of torsional pendulum and the inset shows the cylindrical bulk CLG material. (E) Photograph of the back side of torsional pendulum. (F and G) The whole torsional pendulum device in the vacuum chamber.
2.2 Preparation of the gravity pendulum and the CLG-SiO2 sample
The arm of the gravity pendulum is made of a copper sheet with size of 50 mm × 0.5 mm × 0.18 mm. A cross-linked graphene flake with size of about 4 mm × 3 mm × 0.5 mm was taken off the cylindrical bulk cross-linked graphene (CLG) (inset of Fig. 1(D)). Preparation method of the CLG-SiO2 sample is the same as that in the torsional pendulum. Then the CLG-SiO2 sample was sticked on the bottom of the gravity pendulum arm by using the 1 µm thick optical transparent tape (Fig. 5(A-C)). A 50 nm thick Au nanofilm was deposited in a part of region of the back side of the SiO2 sheet by an ion sputter (KYKY SBC-12) (Fig. 4(A) and Fig. 5(B)), which was used as a mirror to reflect the detection light. The deposition current was 10 mA and the deposition time was 200 s. At last, the gravity pendulum was suspended freely from a copper wire with diameter of 0.06 mm (Fig. 5(A)).
2.3 Characterization
The reflectivity and transmissivity of the CLG material were measured by using a spectrograph (Ocean Optics USB4000) combined with an optical microscope (Olympus, BX51). The laser powers claimed in this work were all measured by a light power meter (Thorlabs PM100A). The photos and videos were obtained by a smartphone (OPPO K9).
2.4 Laser pulling experiment
A small ion sputter (KYKY SBC-12) provided the vacuum chamber and the vacuum-pumping system. The gauss laser beams with wavelength of 360 nm (CNI, MSL-FN), 488 nm (Coherent Sapphire) and 532 nm (OXlasers) were used to implement laser pulling, respectively and all the beams are unfocused. The laser beams were all vertically incident on the material surfaces and the laser powers irradiated on the materials are given in the main text.
3. Results
3.1 Design of the macroscopic laser pulling based on the Kundsen force
When a bulk CLG material is irradiated by a laser beam (Fig. 1(A)) in rarely gaseous environment, laser pushing phenomenon can be achieved [29]. This kind of laser pushing originates from the Kundsen force due to the asymmetric temperature distribution (Fig. 1(A)) and the corresponding asymmetric molecular thermal motion. Generally, the side close to the light source possess high temperature for the bulk CLG material, thus the direction of motion is along with the direction of laser propagation (Fig. 1(A)). Based on this, the author infers that if the temperature distribution of the material is able to be inverted, macroscopic laser pulling will be potentially achieved. A possible approach is to add an optical transparent layer (i. e. yellow layer in Fig. 1(B)) with low thermal conductivity to the back side of the bulk CLG material, in which case, the back transparent layer close to the light source might have lower temperature than the CLG material on the front side (Fig. 1(B)), which might generate laser pulling in rarely gas. Obviously, SiO2 is an appropriate option as the back optical transparent layer. As shown in Fig. 1(C), a double layer structure composited of a CLG front layer and a SiO2 back layer was designed, which is called CLG-SiO2 sample in the following parts. Meanwhile, a sensitive torsional pendulum device was designed to observe the laser pulling phenomenon. The size of the bulk CLG flake is about 5 mm × 3 mm × 0.5 mm. The reflectivity of the CLG flake is about 8% at the visible light band (Fig. S2(A)) and transmissivity is negligible (Fig. S2(B)), and thus the light absorption is about 92%. The thickness of the back SiO2 layer is 0.17 mm and the arm of the torsional pendulum is made of a PET sheet with thickness of 0.1 mm. In order to obtain an observable rotation angle of the torsional pendulum, the soft polyester fiber was chosen as the material of suspension line with diameter of 0.5 mm. Other geometrical details of the torsional pendulum is given in Fig. 1(C-F) and the preparation method is shown in the Materials and Methods part. The whole mass of the suspended torsional pendulum as shown in Fig. 1(F) is 39 mg.
3.2 Macroscopic laser pulling experiments with different laser wavelength and different laser power
The macroscopic laser pulling experiments were implemented in a vacuum chamber (Fig. 1(G)) and the internal air pressure is 5 Pa. As shown in Fig. 2(A), without laser irradiation, the torsional pendulum is motionless. Afterwards, a continuous gauss laser beam with wavelength of 532 nm is incident on the back SiO2 layer of the CLG-SiO2 sample from the right to the left (green arrow shown in Fig. 2(B)), where the laser power irradiated on the material is 60 mW and the light is unfocused. In this case, counterclockwise rotation of the torsional pendulum is observed and the macroscopic CLG-SiO2 sample is pulled towards the light source (Fig. 2(B) and (C)), and the dynamic laser pulling process is shown in Visualization 1. In the experiments, the spatial position of the light source is fixed. Therefore, with the rotation of the torsional pendulum, the CLG-SiO2 sample will gradually deviate from the path of laser propagation, which gradually decreases the laser pulling force. As shown in Fig. 2(C), the rotation angle has a maximum value due to the decreasing of laser pulling force and the increasing of the torsional restoring force from the suspension line. Besides, it is confirmed that gauss beams with wavelengths of 488 nm and 360 nm are also capable to achieve macroscopic laser pulling (Fig. 2(D-I), Visualization 2 and Visualization 3), where the laser powers irradiated on the materials are 85 mW and 13 mW, respectively. It is needed to be explained that the rotation angle in Fig. 2(I) is comparatively small due to the limited maximum power (13 mW) of the 355 nm light source we used. Besides, experiment indicated that this kind of macroscopic laser pulling is very weak and negligible at normal pressure (Visualization 4), because in this case the molecular collisions are intense and the Kundsen force is negligible [30]. Actually, it is found that the macroscopic laser pulling happens when the air pressure is in the range from several Pascal to tens of Pascal, which agrees with the features of Kundsen force qualitatively.
Fig. 2. Macroscopic laser pulling with different laser wavelength. (A-C) Dynamic laser pulling of the torsional pendulum with wavelength of 532 nm. (B-F) Dynamic laser pulling of the torsional pendulum with wavelength of 488 nm. (G-I) Dynamic laser pulling of the torsional pendulum with wavelength of 360 nm. The arrows in B, E and H show the direction of laser propagation. The black dotted lines in C, F and I show the initial positions of the torsional pendulum without laser pulling.
Furthermore, the relationship between the laser power and the rotation angle of torsional pendulum was qualitatively investigated by using the laser beam with wavelength of 488 nm. As shown in Fig. 3(A-F), the maximum rotation angle of the torsional pendulum increases from 1° to 8.3° when the laser power irradiated on the material increases from 17 mW to 85 mW. The dynamic laser pulling processes are shown in Visualization 5, Visualization 6, Visualization 7, Visualization 8, and Visualization 2. The experiments display a positive correlation between the incident laser energy and the amplitude of pulling force. It is because the enhanced laser energy leads to greater temperature difference between the front side and the back side and thus generate larger recoiling force due to the thermal motion of the gas molecules.
Fig. 3. Macroscopic laser pulling with different laser powers. (A-F) Maximum rotation angles of the torsional pendulum with different pulling laser power (irradiated on the materials) of 0 mW, 17 mW, 34 mW, 51 mW, 68 mW and 85 mW, respectively. The laser wavelength is 488 nm. The black dotted lines in B-F show the initial positions of the torsional pendulum without laser pulling.
3.3 Measurement of the laser pulling force
In the torsional pendulum experiments, the macroscopic laser pulling is significant and visible to the naked eyes. However, the pulling force is unable to be analyzed more quantitatively due to the possibly complicated torsional rigidity parameter of the polyester suspension line. We also tested other suspension line material such as a super fine copper wire (diameter = 0.06 mm) with stable torsional rigidity at room temperature, however, the copper wire always deviated from the direction of gravity on account of the small length of the torsional pendulum arm, which makes the quantitative analysis of rotation invalid. In order to measure the pulling force more accurately, a gravity pendulum device was used in the following parts.
The principle diagram of the pulling force measurement using a gravity pendulum is shown in Fig. 4. As shown in Fig. 4(A), the pendulum arm made of a copper sheet hangs from a copper wire. The CLG-SiO2 sample is fixed in the bottom of the pendulum arm and the gauss laser beam with wavelength of 488 nm is incident on the back SiO2 layer form right to left to carry out laser pulling. A 50 nm thick Au nanofilm is deposited on the surface of SiO2 layer that is served as a mirror to reflect the detection light (360 nm) to the optical screen. Once the laser pulling happens with a small deflection angle θ, the displacement Δh of the reflected laser spot on the screen can be measured. According to the mechanical analysis of a rigid body, the torque is 0 for the steady state, thus the laser pulling force is decided by the following Eq. (1),
where Fgravity is the gravity of the pendulum, Lg is the distance from the center of mass (point C in Fig. 4(B)) to the junction (point O), and Lp is the distance from the point of action of the laser pulling force (point E) to the junction. Herein, Lg is approximately equal to 0.42 •Lp.Fig. 4. Measurement principle of the laser pulling force. (A) Schematic diagram of the experimental facilities by using a gravity pendulum. (B) Mechanical equilibrium analysis of the gravity pendulum under laser pulling, where the gravity pendulum is regarded as a rigid body that rotates around O-axis.
The real experimental facility of the gravity pendulum is shown in Fig. 5(A-C). The size of the pendulum arm is 50 mm × 5 mm × 0.18 mm. The dimeter of copper wire is only 0.06 mm, which is conducive to reduce the frictional resistance. The whole mass of the gravity pendulum as shown in Fig. 5(A) is 225 mg. The distance between the pendulum and the optical screen (D) is 3 m. The macroscopic laser pulling experiment is implemented in the same vacuum chamber as that in Fig. 1(G) with internal air pressure of 5 Pa (Fig. 5(A)). In order to reduce the interference of external light as much as possible, the weak red light illumination was adopted in the laboratory (Fig. 5(D) and (E)). As shown in Fig. 5(D), before the pulling laser (488 nm) works, the detection laser (360 nm) with power of 13 mW is incident on the Au nanofilm mirror and then the reflected laser spot falls on the optical screen at the position of 12.3 cm (inset of Fig. 5(D)). When the 488 nm gauss laser beam with power of 85 mW irradiates on the back SiO2 layer of the CLG-SiO2 sample as shown in Fig. 5(E), the reflected laser spot with wavelength of 360 nm shifts up to the position of 12.05 cm on the optical screen (inset of Fig. 5(E)). Therefore, Δh is approximately 2.5 mm and the corresponding laser pulling force is calculated to be 0.8 µN according to Eq. (1). It should be noted that, in this case, the radiation pressure applied to the sample is only about 0.28 nN under irradiation of the same 488 nm laser beam with power of 85 mW, which can be calculated by the equation F = P/c, where F is the radiation pressure and P is the laser power. Therefore, the laser pulling force here is more than three orders of magnitudes larger than the radiation pressure indicating great value in macroscopic optical manipulations.
Fig. 5. Experimental facilities and results of the laser pulling force measurement by using the gravity pendulum. (A-C) Size and material details of the gravity pendulum device. (D) Photograph of the gravity pendulum without laser pulling. The detection light with wavelength of 360 nm is incident on the Au nanofilm mirror on the back side of the gravity pendulum and the top-right inset shows the corresponding reflected detection (360 nm) laser spot on the optical screen. (E) Photograph of the gravity pendulum under laser pulling with wavelength of 488 nm. The top-right inset shows the reflected detection (360 nm) laser spot on the optical screen.
4. Discussion
The laser pulling presented in this paper is originated from the Kundsen force due to thermal nonequilibrium of a macroscopic object in rarefied gas environment. Generally, the Kundsen force is strongly associated with the gas pressure (or the mean free path of gas molecules) and the surface temperature difference of the object. (1) Firstly, the effect of gas pressure on Kundsen force can be analysed by using the Knudsen number (Kn = λ/L), where λ is the mean free path of gas molecules and L is the length of an object in the gaseous environment. Many literatures have reported that the force reaches the maximum when Kn is approximately equal to 0.1 [30]. In the case of a very large Kn compared to 0.1, namely a relatively large λ (low gas pressure), the Kundsen force is negligible, because the number of gas molecule is too small. In the case of a very small Kn compared to 0.1, the Kundsen force is also negligible, because the effect of thermal nonequilibrium is inapparent due to violent molecular collisions on both sides of the object. In other words, the amplitude of Kundsen force will show a bell-shape curve with a peak value (namely, firstly increases then decreases) as the gas pressure increases [31]. In our previous paper [32] related to laser propulsion, we have experimentally observed the bell-shape characteristic of the Kundsen force. In that paper, we found that, as for a graphene sponge material with size of ∼ 5 mm, the peak value of Kundsen force appears at the air pressure of ∼ 5 Pa and the corresponding Kn is about 0.2 ∼ 0.3. Similarly, in this work, the most remarkable laser pulling effect due to Kundsen force can be also obtained at the air pressure of ∼ 5 Pa. If the air pressure is smaller or larger than ∼ 5 Pa, the pulling force will decrease. (2) Secondly, the surface temperature difference of the object is also an important factor. Increasing the temperature difference generally leads to larger Kundsen force due to more inhomogeneous molecular collisions on different surfaces of the object.
According to results reported in literatures, up to now, there is not a united analytic formula to directly calculate the Kundsen force for arbitrary gas pressures and temperatures [30,31]. Only when the air pressure is extremely low, especially for the case of Kn > 10, the Kundsen force can be estimated by an analytic formula. By using such an analytic formula, as shown in the supplement file, the laser-induced Kundsen force is roughly estimated to be about 1.5 ∼ 4.7 µN that agrees with the above measuring result (0.8 µN) in the same order of magnitude.
In the case of laser pulling, raising the incident laser power is capable to promote the pulling force. Because the increased laser energy results in greater surface temperature difference of the object and thus a larger Knudsen force. An approximately linear relation between the measured pulling force and the laser power (10 mW ∼85 mW) is observed (Fig. S3). However, the incident laser energy density should not exceeds the ablative threshold of the materials, otherwise the laser pulling will be unrepeatable. Besides, if the volume of gaseous medium is fixed, for instance, an airtight chamber is used like the case of this work, changing the environmental temperature leads to the alterable λ and Kn, which will also affect the laser pulling force in a complicated way that can’t be described by a united analytic formula as stated above.
In this work, the torsional pendulum device was used to qualitatively present the laser pulling phenomenon. In fact, by designing more appropriate material and structure of the torsional pendulum equipments, a precise measurement of the laser pulling force can be also achieved. Herein, the measuring laser pulling force (0.8 µN) is more than three orders of magnitudes larger than the radiation pressure (0.28 nN) under the same irradiation condition, which is an important result. The light-driven manipulation based on radiation pressure is originated from the direct momentum transfer from the photon to object and the force is weak generally. When applying the radiation pressure to a macroscopic object, like the light sail propulsion, the surface area must be very large. Even so, macroscopical light pulling has not been reported to our knowledge. In this work, another laser pulling concept based on Knudsen force is proposed, where the pulling force can be increased dramatically with the help of molecular collision induced by laser. This result supplies a new way of macroscopical light manipulation with great advantages in the flexibility of control and the magnitude of driving force. From a practical point of view, a long-distance laser pulling of a macroscopical sail in a rarefied gas environment such as the near space and Mars is very promising and worth exploring.
5. Conclusions
In summary, we present the laser pulling of a macroscopic object in rarefied gas. The pulling force is originated from the Kundsen force when a gauss laser beam irradiates a macroscopic structure composed of the absorptive bulk cross-linked graphene material and a SiO2 layer. A torsional pendulum device was used to qualitatively present the laser pulling phenomenon in the rarely gaseous environment with universality in spite of incident laser energy and wavelength. A gravity pendulum device was used to further measure the pulling force, which is about 0.8 µN for the incident laser power of 85 mW and is more than three orders of magnitudes larger than the radiation pressure. This work expands the scope of optical pulling from microscale to macroscale, which has great potentials in macroscale optical manipulations.
Funding
Natural Science Foundation of Shandong Province (ZR2021QF003); National Natural Science Foundation of China (12174211); Research Start-up Fund of QUST (1203043003591).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
Supplemental document
See Supplement 1 for supporting content.
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