Method and device for measuring light radiation pressure

A device for measuring a light radiation pressure is provided which includes a torsion balance, a laser, a convex lens, and a line array detector. The laser is configured to emit a first laser beam. The convex lens is located on an optical path of the first laser beam and configured to focus the first laser beam to a surface of the reflector. The line array detector is configured to detect a reflected first laser beam reflected by the reflector. The disclosure also provides a method for measuring the light radiation pressure using the device.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is related to commonly-assigned application entitled, “TORSION BALANCE AND METHOD FOR MAKING THE SAME”, concurrently filed Ser. No. 17/147,769. The entire contents of which are incorporated herein by reference.

FIELD

The present application relates to the field of precision instruments, and in particular, to a device and a method for measuring light radiation pressure.

BACKGROUND

The measurement of light radiation pressure is particularly important, but the magnitude of the light radiation pressure is quite small, and it is difficult to measure it with ordinary force measuring devices. At present, the main methods for measuring the light radiation pressure are mostly improved on the basis of Lebedev's experimental device. Under the action of light radiation pressure, the existing torsion balance is twisted, and the light radiation pressure is derived by measuring the rotation angle. The light radiation pressure can be direct measured by the pressure observer (pressure ceramic). The method for measuring the light radiation pressure by the pressure observer (pressure ceramic) includes the following steps: the pressure is applied to a measuring instrument, the electric signal of the measuring instrument is changed accordingly; and the electric signal is amplified, and the relationship between the voltage and the measured pressure is finally obtained. However, the accuracy and sensitivity of the above-mentioned device and method are quite low, and they are not suitable for measuring light radiation pressure.

Therefore, there is room for improvement in the art.

DETAILED DESCRIPTION

FIG.1shows an embodiment of a device10for measuring light radiation pressure. The device10includes a torsion balance100, a laser200, a convex lens300, and a line array detector400. The laser200is used to emit a first laser beam, and the first laser beam is focused by the convex lens300to form a focused first laser beam. The focused first laser beam irradiates the torsion balance100, and then is reflected by the torsion balance100to form a reflected first laser beam. The line array detector400is used to receive the reflected first laser beam.

Referring toFIG.2andFIG.3, the torsion balance100includes a suspended carbon nanotube101and a reflector102hung on the carbon nanotube101. The reflector102includes a film1021, a first reflecting layer1022a, and a second reflecting layer1022b. The film1021includes at least two layers of two-dimensional materials stacked with each other. The film1021has a first surface10211and a second surface10212opposite to the first surface10211. The first reflecting layer1022ais located on the first surface10211, and the second reflecting layer1022bis located on the second surface10212.

The carbon nanotube101can be selected from a single-walled carbon nanotube or a multi-walled carbon nanotube, or the carbon nanotube101can be prepared by removing the outer wall of a multi-walled carbon nanotube, so that the outer surface of the carbon nanotube can be super clean, which can facilitate the suspension and fixation of the reflector102onto the surface of the carbon nanotube101. The diameter of the carbon nanotube101is not limited. The smaller the diameter of the carbon nanotube101, the higher the sensitivity and accuracy of the torsion balance100. In one embodiment, the diameter of the carbon nanotube101is less than 10 nanometers. The suspended length of the carbon nanotube101is not limited. The longer the suspended lengths of the carbon nanotube101, the higher the accuracy of the torsion balance100. In one embodiment, the carbon nanotube101is a single-walled carbon nanotube with a diameter of about 7 nanometers and a suspended length of about 300 micrometers. Since the diameter of a single carbon nanotube is in nanometer scale, using the single carbon nanotube as a twisting wire of the torsion balance100can improve the sensitivity and accuracy of the torsion balance100.

The film1021can be a “free-standing” film. The term “free-standing” includes, but is not limited to, a structure that does not have to be supported by a substrate and can sustain the weight of itself when it is hoisted by a portion thereof without any significant damage to its structural integrity. A shape of the film1021is not limited, specifically, it can be regular or irregular shape, such as rectangle, circle, or triangle. The film1021can be an axisymmetric shaped film, and the carbon nanotube101is located on the symmetry axis of the film1021. In one embodiment, the film1021is a rectangle shaped film with a width of about 80 μm and a length of about 120 μm.

The film1021includes at least two layers of two-dimensional materials stacked one after another. The two-dimensional material layer has a continuous surface with a certain area. The two-dimensional material can be carbon nanotube film, graphene, boron nitride, molybdenum disulfide, tungsten disulfide or any combination thereof. The types of the two-dimensional materials in the film1021can be the same or different. On one hand, increasing the thickness of the first reflecting layer1022aand/or the second reflecting layer1022bcan make the surface of the reflector102flat and then increase the reflectivity of the incident light, especially when the film1021only includes carbon nanotube films and the carbon nanotube films include a plurality of micropores. On the other hand, the increase in the thickness of the first reflecting layer1022aand/or the second reflecting layer1022bwill inevitably reduce the sensitivity and accuracy of the torsion balance100.

In one embodiment, the carbon nanotube film coexists with other two-dimensional materials, such as graphene, boron nitride, molybdenum disulfide, or tungsten disulfide, and serves as a supporter for the other two-dimensional materials.

The carbon nanotube film includes a plurality of carbon nanotubes combined by van der Waals attractive force therebetween. The carbon nanotubes in the carbon nanotube film can be orderly aligned or disorderly aligned. The disorderly aligned carbon nanotubes are carbon nanotubes arranged along many different directions, such that the number of carbon nanotubes arranged along each different direction can be almost the same (e.g. uniformly disordered); and/or entangled with each other. The orderly aligned carbon nanotubes are carbon nanotubes arranged in a consistently systematic manner, e.g., most of the carbon nanotubes are arranged approximately along a same direction or have two or more sections within each of which the most of the carbon nanotubes are arranged approximately along a same direction (different sections can have different directions). The carbon nanotube film can be a drawn carbon nanotube film, a flocculated carbon nanotube film, or a pressed carbon nanotube film.

In one embodiment, the carbon nanotube layer includes at least one drawn carbon nanotube film. A film can be drawn from a carbon nanotube array, to form a drawn carbon nanotube film. The drawn carbon nanotube film includes a plurality of successive and oriented carbon nanotubes joined end-to-end by van der Waals attractive force therebetween. A plurality of carbon nanotubes in the drawn carbon nanotube film are arranged substantially parallel to a surface of the drawn carbon nanotube film. The drawn carbon nanotube film is a free-standing film. Each drawn carbon nanotube film includes a plurality of successively oriented carbon nanotube segments joined end-to-end by van der Waals attractive force therebetween. Each carbon nanotube segment includes a plurality of carbon nanotubes substantially parallel to each other, and combined by van der Waals attractive force therebetween. When the film1021includes a plurality of drawn carbon nanotube films stacked one after another, an angle between the aligned directions of the carbon nanotubes in at least two drawn carbon nanotube films can be in a range from about 0 degrees to about 90 degrees.

In another embodiment, the carbon nanotube layer can include at least one pressed carbon nanotube film. The pressed carbon nanotube film can be a free-standing carbon nanotube film. The carbon nanotubes in the pressed carbon nanotube film can be substantially arranged along a same direction or substantially arranged along different directions. The carbon nanotubes in the pressed carbon nanotube film can rest upon each other. Adjacent carbon nanotubes are attracted to each other and combined by van der Waals attractive force. The pressed carbon nanotube film has excellent durability, and can be fashioned into desired shapes with a low risk to the integrity of the pressed carbon nanotube film. An angle between a primary alignment direction of the carbon nanotubes and a surface of the pressed carbon nanotube film is in a range from about 0 degrees to about 15 degrees. The greater the pressure applied, the smaller the angle formed. When the carbon nanotubes in the pressed carbon nanotube film are substantially arranged along different directions, the carbon nanotube structure can be isotropic. When pressed in different directions, the carbon nanotubes are arranged in preferred orientations in different directions. When pressed in the same direction, the carbon nanotubes are arranged in a preferred orientation along a fixed direction. In addition, when the pressing direction is perpendicular to the surface of the carbon nanotube array, the carbon nanotubes can be arranged in disorder.

The area of the pressed carbon nanotube film can be basically the same as the area of the carbon nanotube array. The thickness of the pressed carbon nanotube film is related to the height of the carbon nanotube array and the pressure. It can be understood that the greater the height of the carbon nanotube array, the greater the thickness of the pressed carbon nanotube film; and the smaller the pressure applied, the greater the thickness of the pressed carbon nanotube film.

In another embodiment, the carbon nanotube layer can include at least one flocculated carbon nanotube film formed by a flocculating method. The flocculated carbon nanotube film can include a plurality of long, curved, disordered carbon nanotubes entangled with each other. The length of the carbon nanotube can be greater than 10 micrometers. The carbon nanotubes can be randomly arranged and curved in the flocculated carbon nanotube film. The carbon nanotubes can be substantially uniformly distributed in the flocculated carbon nanotube film. The adjacent carbon nanotubes are acted upon by the van der Waals attractive force therebetween, thereby forming an entangled structure with micropores defined therein. The size of the micropores can be less than 10 micrometers. Due to the carbon nanotubes in the flocculated carbon nanotube film being entangled with each other, the flocculated carbon nanotube film has excellent durability, and can be fashioned into desired shapes with a low risk to the integrity of flocculated carbon nanotube film. The flocculated carbon nanotube film can be a free-standing structure due to the carbon nanotubes being entangled and adhered together by van der Waals attractive force therebetween.

Since the thickness of the single-layer two-dimensional materials is very thin, the thickness of the film1021can be greatly reduced, and accordingly the thickness of the reflector102of the torsion balance100can be reduced, thereby improving the sensitivity and accuracy of the torsion balance100.

Increasing the number of layers of the two-dimensional material may increase the mass and thickness of the reflector102, resulting in a larger moment of inertia of the reflector102, which is unhelpful for improving the sensitivity and accuracy of the torsion balance100. In addition, the reflector102is not easy to be fixed and suspended on the carbon nanotube101and may cause the twisting wire of the carbon nanotube101to break when there are too many layers of two-dimensional materials. Therefore, the number of layers of the two-dimensional material should not be too many, which can be greater than 2 and less than 10. In one embodiment, the number is greater than 2 and less than 5.

The film1021can be a carbon nanotube-graphene composite film, which includes a first drawn carbon nanotube film, a second drawn carbon nanotube film, and a single layered graphene film sandwiched between the first drawn carbon nanotube film and the second drawn carbon nanotube film. An angle between the extending direction of the carbon nanotubes in the first drawn carbon nanotube film and the extending direction of the carbon nanotubes in the second drawn carbon nanotube film can be about 90 degrees. The single layered graphene film is a two-dimensional planar hexagonal dense array structure composed of sp2 hybridized carbon atoms. The single layered graphene film can be prepared by mechanical exfoliation or chemical vapor deposition (CVD). The first drawn carbon nanotube film, the second drawn carbon nanotube film, and the single layered graphene film can be overlapped each other. The term ‘overlap’ means that when the graphene film is disposed on a surface of the carbon nanotube film, the graphene film can completely cover the carbon nanotube film; and when the carbon nanotube film is disposed on a surface of the graphene film, the carbon nanotube film can completely cover the graphene film as well. Additionally, the carbon atoms of the single layered graphene film can be sp3hybridized to the carbon atoms of the drawn carbon nanotube film, so that the graphene film is stably fixed to the surface of the carbon nanotube film.

The film1021can be selected from carbon nanotubes, graphene or other two-dimensional materials. The torque can be improved by selecting a film1021with low density, light weight, and a large surface area, then the sensitivity and accuracy of the torsion balance100is improved, so that the torsion balance100can be used for measuring micro-force and micro-torque.

The first reflecting layer1022ais located on the first surface10211of the film1021, and the second reflecting layer1022bis located on the second surface10212of the film1021. The first reflecting layer1022aand the second reflecting layer1022bcan be formed by evaporation, sputtering, or the like. The first reflecting layer1022aand the second reflecting layer1022bform a reflecting layer1022. If the reflecting layer1022is only formed on one surface of the film1021, the film1021may tend to curl after the reflecting layer1022is formed. Therefore, it is necessary to form reflecting layers1022on both the first surface10211and the second surface10212.

The first reflecting layer1022aand the second reflecting layer1022bcan be made of a material having small density and high reflectivity. Specifically, the material of the first reflecting layer1022aand the second reflecting layer1022bis metal material, such as aluminum, silver, copper, chromium, platinum, or the like. The metal material can be formed on the surface of the film1021by a chemical method such as chemical vapor deposition (CVD), or by a physical method such as vacuum evaporation or magnetron sputtering.

The thickness of the first reflecting layer1022aand the second reflecting layer1022bshould not be too small or too large. If the thicknesses of the first reflecting layer1022aand the second reflecting layer1022bis too small, the reflectivity of the incident laser beam at the reflector102will decreases; however, if the thickness of the first reflecting layer1022aand the second reflecting layer1022bis too large, the mess of the reflector102increases and the sensitivity of the torsion balance100decreases. Specifically, the thickness of the first reflecting layer1022acan be in a range of 5 nm to 20 nm, and the thickness of the second reflecting layer1022bcan be in a range of 5 nm to 20 nm. In one embodiment, both the first reflecting layer1022aand the second reflecting layer1022bare aluminum layers with a thickness of about 10 nm.

In one embodiment, the reflecting layer has a smooth surface at molecular level, with which the deflection angle of the film1021can be accurately determined, thereby improving the sensitivity and accuracy of the torsion balance100. The molecular level surface can be achieved by controlling the forming conditions of the reflecting layer.

The film1021can be directly contacted with the carbon nanotube101, or the film1021can be contacted with the carbon nanotube101through the reflecting layer between the film1021and the carbon nanotube101.

It can be understood that in the process of preparing the torsion balance100, the thin film1021can be firstly fixed to the carbon nanotube101, and then the reflecting layers are formed on the surface of the thin film1021. In this method, the carbon nanotube101is directly contacted with the film1021, so that the reflecting layer can coat and fix the carbon nanotube101and the film1021together. Alternatively, the reflecting layer1022can also be formed on the surface of the film1021first, and then the film1021is suspended and fixed on the carbon nanotube101, so that the single carbon nanotube101is directly contacted with the reflecting layer.

Referring toFIG.4, the torsion balance100can further include a substrate103as a fixing element for fixing and supporting the carbon nanotube101. A space1031is defined on a surface of the substrate103, and the single carbon nanotube101can be arranged across the space1031.

Specifically, the carbon nanotube101includes a first end1011, a second end1012opposite to the first end1011, and a middle portion1013located between the first end1011and the second end1012. The first end1011and the second end1012respectively contact with the surface of the substrate103and are fixed on the surface of the substrate103. The middle portion1013of the carbon nanotube101is suspended on the space1031, and the film1021hung on the surface of the suspended carbon nanotube.

The material and size of the substrate103are not limited and can be selected according to practical application.

The space1031should have a certain depth and a certain width, so as to provide sufficient space for the rotation of the film1021when the film1021rotates around the carbon nanotube101under a micro force. The size of the space1031is not limited and can be selected according to practical applications. Specifically, the space1031can be a through hole or a blind hole. The shape of the through hole or the blind hole is not limited, and it can be a regular hole or an irregular hole, for example, a circular hole, a square hole, or so on.

The film1021is fixed on the surface of the carbon nanotube101. The position of the film1021is not limited to the space1031. For example, the film1021can be located inside the space1031or outside the space1031.

In one embodiment, the space1031is a through hole formed on the surface of the substrate103, and the through hole is a square hole with two side lengths of 300 μm.

FIG.5is an optical microscope photo of the torsion balance100in one embodiment of the present disclosure. Since the diameter of the carbon nanotubes is about 7 nanometers, the carbon nanotubes cannot be shown inFIG.5.

The working principle of the torsion balance100is as follows:

providing a laser beam emitted to the surface of the reflector, the laser beam is reflected at the reflector and received by the detector at a first position;

applying a micro force to the surface of the reflector to deflect the reflector, the laser beam is received by the detector at a second position; and

calculating the magnitude of the micro force according to the first position and the second position.

It can be seen that the value of the micro force is calculated based on the position of the reflected light spot before deflecting the reflector and the position of the reflected light spot after deflecting the reflector.

The laser200is used to emit a first laser beam. The type of the laser200is not limited any device capable of emitting laser beam can be used in this disclosure.

The convex lens300is located on an optical path of the first laser beam and is used to focus the first laser beam to the surface of the reflector102. The type of the convex lens300is not limited, any lens with focusing function can be used in this disclosure.

The line array detector400is configured to receive the reflected light of the reflector102and detect the position of light received reflected light spot. The line array detector400is located on the optical path of reflected light.

Referring toFIG.6, the device10can further include an optical microscope500for observing the torsion balance100. The optical microscope500can be used to observe whether the reflector102of the torsion balance100is deflected, and to observe and measure the length of the arm of the reflector102under a micro force, which is convenient for calculating the light radiation pressure. The position of the optical microscope500is not limited, as long as the torsion balance100can be observed by the optical microscope500. In one embodiment, the optical microscope500is set opposite to the torsion balance100, and the center point of the torsion balance100is on the axis of the optical microscope500.

FIG.7is a schematic photo of the device for measuring light radiation pressure according to one embodiment. The torsion balance100can be placed in a vacuum chamber, which can avoid the influence of the fluctuation of the external air flow on the light radiation pressure. The vacuum chamber includes a quartz window, the light passing through the convex lens300. The light from the convex lens300passes through the quartz window and then enters the surface of the reflector102. It should be noted the torsion balance100cannot be clearly shown inFIG.7because the torsion balance100is only in micrometer scale.

A method for measuring light radiation pressure using the device10is provided according to one embodiment. The method includes, at least the following blocks:

S1, emitting a first laser beam by the laser200, wherein the light radiation pressure of the first laser beam is known and defined as F1, the first laser beam is focused by the convex lens300and then irradiates to a surface of the reflector102, the reflector102is deflected under the first laser beam, and the first laser beam is reflected at the reflector102to form a first reflected beam, and the first reflected beam is received by the line array detector400at a first position x1;

S2, emitting a second laser beam by the laser200, wherein the light radiation pressure of the second laser beam is unknown and defined as F2, the second laser beam is focused by the convex lens300and then irradiates to the surface of the reflector102, the reflector102is deflected under the second laser beam, and the second laser beam is reflected at the reflector102to form a second reflected beam, and the second reflected beam is received by the line array detector400at a second position x2;

S3, calculating the deflection angle Δθ between the second reflected beam and the first reflected beam according to the first position x1and the second position x2:

wherein D is the distance from the reflector102to the line array detector400;

S4, calculating the light radiation pressure of the second laser beam F2according to the torsion Hooke's law:×Δα=ΔF×L, wherein κ is the torsional stiffness of the carbon nanotube101; Δα is the angle of the second deflection of the reflector102compared to the first deflection of the reflector102,

Δα=Δ⁢θ2;
ΔF is the light radiation pressure difference between the second laser beam and the first laser beam, ΔF=F2−F1; and L is the length of the arm.

In the step S1, the position of the spot of the first reflected beam is received and recorded as x1by the line array detector400. The reflector102twists and swings slightly around an balance position at a natural frequency when the first laser beam irradiates the reflector102, and the spot of the first reflected beam moves back and forth around the first position x1on the line array detector400. In one embodiment, the line array detector400continuously acquires a plurality of data at intervals of 1 millisecond (ms), and then calculates the average value of these data to obtain the first position x1

In the step S2, the position of the spot of the second reflected beam is received and recorded as x2by the line array detector400. The method of obtaining the second position x2can be the same as the method in the step S1.

In the step S3, the deflection angle Δθ is in radians.

In the step S4, the length of the arm L can be measured by imaging software of the optical microscope500in a computer.

The torsional stiffness κ of the carbon nanotube101can be calculated by the following formula:
=I×ω2,

Wherein I is the moment of inertia of the torsion balance100, assuming that the length of the reflector102is a, the width of the reflector102is b, the thickness of the reflector102is h, and the density of the reflecting layer is p, then the moment of inertia is

Wherein ω is the natural frequency of swing of the carbon nanotube101. The carbon nanotube101and the reflector102swing at the same natural frequency. The reflector102twists and swings slightly around the balance position at the natural frequency when the first laser beam irradiates the reflector102, and the spot of the first reflected beam moves back and forth around the first position x1on the line array detector400at the same natural frequency. The line array detector400can continuously acquire a plurality of data at intervals of 1 ms, then the relationship between the position of the center of the spot of the first reflected beam and time can be obtained, and then the natural frequency ω can be obtained by Fourier transform.

Furthermore, in order to reduce the measurement error, the balance position of the reflector102can be changed by changing the power of the laser200, and the natural frequency ω can be measured several times at different balance positions to obtain an average torsional stiffness κ.

If the torsional stiffness κ, the angle Δα, and the arm length L are known, the light radiation pressure difference between the second laser beam and the first laser beam ΔF can be easily calculated, and then the light radiation pressure of the second laser beam can be calculated.

In one embodiment, laser beams with power currents of 10 mA, 15 mA, 20 mA, and 25 mA are used to irradiate the reflector102, respectively. Photos obtained by an optical microscope are shown inFIG.8. The reflector102is deflected under laser irradiation, and the greater the power of the laser, the greater the deflection angle of the reflector102, as shown inFIG.8. It can be seen that the torsion balance100used in this embodiment can respond to the light radiation pressure and twist under the light radiation pressure.

In another embodiment, the power currents of the laser beams are reduced to nanoampere (nA) level. Specifically, laser beams with power currents of 41 nA, 42 nA, 43 nA, 44 nA, 45 nA, 46 nA, 47 nA, 48 nA, 49 nA, and 50 nA are used to irradiate the reflector102respectively. The laser power, the light radiation pressure obtained by laser power, the position of the reflected spot, the theoretical deflection angle, and the actual deflection angle are shown in the following table:

It can be seen from the above table that the actual deflection angle of the reflector102is much smaller than the theoretical deflection angle, which is mainly due to various losses in actual operation, such as the reflection of light by the quartz window of the vacuum cavity, the reflectivity of the surface of the mirror102is relatively small, and so on. In actual operation, the light radiation pressure received by the reflector102is much smaller than the theoretical light radiation pressure calculated in the above table, indicating that the device10is also sensitive to forces that are two orders of magnitude smaller than fN.

Referring toFIG.9, the actual deflection angle of the reflector102is linearly related to the theoretical light radiation pressure, and the regression sum of squares R2is close to 1.

It is also possible to use multiple laser beams with known power to irradiate the reflector102, then the line array detector400can obtain multiple deflection angles, and then obtain the relationship between the actual deflection angle and the theoretical light radiation pressure. Thereafter, when the reflector102is irradiated with laser beams with known power, the light radiation pressure with unknown power can be obtained according the actual deflection angle of the reflector102and the relationship between the actual deflection angle and the theoretical light radiation pressure.

The single carbon nanotube has a nanosized diameter, and the two-dimensional nanomaterial is light in weight and large in surface area, so the two-dimensional nanomaterial has a small moment of inertia. The present disclosure uses a single carbon nanotube as the twisting wire of the torsion balance and uses two-dimensional nanomaterials as the reflector of the torsion balance, which can make the torsion balance have extremely high sensitivity and accuracy, so that device using the torsion balance can realize fN-level light radiation pressure resolution, and can even achieve light radiation pressure resolution two orders of magnitude smaller than fN.