Structure and method for reducing transmission loss based on parallel silver nanowires

Abstract

The invention belongs to the technical field of excitation and transmission application of surface plasmons, and relates to a structure and method for reducing transmission loss based on parallel silver nanowires. The substrate is provided with at least one pair of parallel silver nanowires, the diameter of the silver nanowires is 400-800nm, the length of the silver nanowires is 10-20 microns, and the parallel spacing or gap of the silver nanowire pair is 5-50nm; the method comprises the following steps: step 1, preparing a large-size silver nanowire; 2, accurately moving the single silver nanowire on the substrate prepared in the step 1 by using a micro-control method, and constructing a parallel silver nanowire structure; and 3, exciting the parallel silver nanowires to generate SPPs by using an optical fiber coupling method, and measuring the transmission loss of the SPPs. The influence of mode coupling between the two parallel single silver nanowires in the parallel silver nanowire structure on electric field distribution is utilized, radiation leakage of energy to the substrate is restrained, and the transmission loss of SPPs is remarkably reduced.

Description

Technical Field

[0001] The present invention belongs to the technical field of excitation and transmission application of surface plasmons, and relates to a structure and method for reducing transmission loss based on parallel silver nanowires. Background Art

[0002] When light waves (electromagnetic waves) are incident on the interface between metal and dielectric, they can couple and excite the collective oscillation of free electrons on the metal surface. In metal nanoparticles, the collective oscillation of free electrons is limited by the size of the particle structure. This type of oscillation is called localized surface plasmon (LSPs); surface plasmons excited at the interface between metal nanowires (films) and dielectrics can be remotely transmitted along the interface, which is called propagating surface plasmon polaritons (SPPs). It is a non-radiative electromagnetic mode with unique properties that break through the optical diffraction limit. It is crucial to the development of on-chip optoelectronic integrated devices and has great application potential in ultra-sensitive detection, optical sensing, information processing, etc.

[0003] Silver nanowires (Ag NWs) are a quasi-one-dimensional surface plasmon waveguide structure, which is often used as a basic component of nanophotonic devices. Usually, the diameter of silver nanowires is tens to hundreds of nanometers, and the length can range from hundreds of nanometers to hundreds of microns. Silver nanowires have shown potential application value in many fields due to their unique physical and chemical properties. There are many methods for preparing silver nanowires, including chemical synthesis, physical vapor deposition, etc. Compared with silver nanowires prepared by physical methods, silver nanowires prepared by chemical methods have a five-fold twin structure with a regular morphology and a smooth surface. Therefore, the energy loss caused by surface defect scattering will be significantly reduced, which is an ideal material for SPPs waveguides. Based on the regulation of SPPs transmitted on silver nanowires, nanophotonic devices with different functions can be realized, including SPPs routers, logic gates, nanolasers, splitters, etc. These photonic devices are compatible with dielectric optical waveguides, and are widely used in nano-integrated photonic devices and circuits.

[0004] However, due to the strong field confinement characteristics of SPPs, the large Ohmic loss of the metal nanowires themselves, coupled with the radiation loss of SPPs into the surrounding medium, the energy loss of SPPs during nanowire transmission is still very large. Previous studies have mainly focused on reducing the energy loss during transmission by introducing dielectric layers, two-dimensional materials or gain materials between silver nanowires and substrates. These methods require additional dielectric layer structures, which complicates the manufacturing process of nanophotonic devices and is not conducive to the regulation of light fields.

[0005] Therefore, how to construct a simple waveguide structure to reduce the energy loss of SPPs during transmission on silver nanowires has become an urgent problem to be solved in the development of integrated photonic circuits and devices. Summary of the invention

[0006] The technical solution adopted by the present invention to solve the technical problem is: a structure based on parallel silver nanowires to reduce surface plasmon transmission loss, the structure is that at least one pair of mutually parallel silver nanowires is arranged on a substrate, the substrate generally has multiple nanowires, and the density of nanowire distribution can be artificially controlled; the diameter of the silver nanowire is 400-800nm, the length of the silver nanowire is 10-20μm, and the parallel spacing or gap of the silver nanowire pair is 5-50nm; the number of silver nanowires can be adjusted according to the concentration of the prepared solution; the parallel nanowire structure constructed by two silver nanowires has lower surface plasmon transmission loss than that of a single silver nanowire.

[0007] Preferably, the parallel spacing or gap between the silver nanowire pairs is 10 to 20 nm.

[0008] Preferably, the length and diameter of the two silver nanowires in the silver nanowire pair are close to each other.

[0009] Preferably, the substrate includes: a SiO2 / Si substrate, a common silicon substrate or a glass substrate.

[0010] The present invention also discloses a method for reducing transmission loss based on parallel silver nanowires, the method is used to prepare the above-mentioned structure for reducing transmission loss based on parallel silver nanowires, and the method comprises the following steps:

[0011] Step 1, preparing large-sized silver nanowires;

[0012] Step 2: Using a micromanipulation method to precisely move the single silver nanowire on the substrate prepared in step 1 to construct a parallel silver nanowire structure;

[0013] Step 3: Use the fiber coupling method to excite the parallel silver nanowires to generate SPPs and measure the transmission loss.

[0014] Preferably, in step 1, preparing large-sized silver nanowires comprises the following steps:

[0015] Step 1-1: Dissolve silver nitrate and PVP in ethylene glycol separately and stir until the reaction is complete to form a clear transparent liquid;

[0016] Step 1-2: inject ethylene glycol solution into a three-necked flask and heat it, use a syringe to draw the two precursor solutions prepared in step 1-1 respectively, and inject the solutions into the three-necked flask at a uniform speed for reaction, and stop the reaction when the solution turns milky white; take a small amount of the solution and inject it into the three-necked flask, and repeat the above reaction process twice to prepare large-sized nanowires;

[0017] Step 1-3: After the reaction solution in step 1-2 is cooled, the solution is washed twice with acetone and anhydrous ethanol respectively to obtain large-sized silver nanowires.

[0018] More preferably, in step 1-1, 0.25 g of AgNO3 and 0.20 g of PVP are used for every 10 ml of ethylene glycol, and the stirring time is 50 to 80 minutes;

[0019] In the step 1-2, the heating temperature is 150-180° C., the optimum temperature is 165° C., and the reaction time is 40-60 minutes.

[0020] Preferably, in step 2, the micromanipulation method comprises the following steps:

[0021] Step 2-1: preparing a fiber taper structure;

[0022] Step 2-2: Fix the fiber cone structure obtained in step 2-1 through a three-dimensional adjustment frame and form a certain inclination angle with the SiO2 / Si substrate or ordinary silicon substrate, disperse the silver nanowire solution on the SiO2 / Si substrate and set it on a rotating displacement stage, select two suitable adjacent single silver nanowires under a microscope, select nanowires with appropriate size and orientation (the size can be judged by color), adjust the position of the light cone and slowly push the two single silver nanowires to form a parallel silver nanowire structure; the angle adjustment of the silver nanowire and the fiber cone can be completed by the rotating displacement stage at the bottom. The optimal gap distance between the two silver nanowires is 10 to 20nm.

[0023] More preferably, in step 2-1, the tip diameter of the optical fiber cone is 0.5 to 3 μm.

[0024] More preferably, the three-dimensional adjustment frame is a support frame that can be adjusted in the three directions of X, Y, and Z, and is used to fix the rear part of the optical fiber cone. The three-dimensional adjustment frame is provided with three studs whose rotation axes are parallel to the X, Y, and Z directions, respectively. The three-dimensional adjustment frame is driven by the rotation of the studs to generate micro-displacements in the X, Y, and Z directions accordingly.

[0025] The rotary translation stage is a support platform that can rotate in the X, Y directions and in the horizontal plane, and is used to support and place the silver nanowires. The rotary translation stage is provided with two screws whose rotation axes are parallel to the X and Y directions respectively, and an angle adjustment screw whose rotation axis is located in the horizontal plane. The rotary translation stage is driven to generate a micro displacement in the X and Y directions by the rotation of the screws, and the rotary translation stage is driven to rotate in the horizontal plane by the rotation of the angle adjustment screw.

[0026] The base of the three-dimensional adjustment frame, the base of the rotary displacement stage and the base of the optical microscope are fixedly connected.

[0027] Preferably, the specific steps of step 3 are as follows:

[0028] Step 3-1: Prepare a fiber taper structure;

[0029] Step 3-2: Fix the optical fiber on a three-dimensional adjustment frame, and adjust the direction of the optical fiber cone along the axial direction of the silver nanowire under a microscope. Couple the laser into the optical fiber to excite the SPPs on the parallel silver nanowires, move the relative position of the optical fiber cone and the parallel silver nanowire structure, record the scattered light intensity at the end of the parallel silver nanowire structure at different positions, and obtain the transmission loss of SPPs on the parallel silver nanowires; the laser power, excitation optical fiber cone, and parallel silver nanowires used in the experiment are the same, and the angle between the excitation optical fiber cone and the silver nanowires is the same.

[0030] The beneficial effects of the present invention are:

[0031] 1. The present invention constructs a parallel metal nanowire structure so that the interaction between the two metal nanowires affects the field distribution of the surface plasmon, so that the radiation leakage of the surface plasmon to the substrate during the transmission process is suppressed, thereby significantly reducing the transmission loss of the surface plasmon.

[0032] 2. The present invention first prepares silver nanowires, then uses a micromanipulation method to construct a parallel silver nanowire composite structure, and finally uses a near-field coupling method to excite the surface plasmons in the composite structure and measure its transmission loss. On the one hand, the present invention can use the fiber-assisted manipulation method to assemble parallel silver nanowire structures of any size, which has the advantages of simple operation, accuracy, and flexibility; on the other hand, it better maintains the localization of the light field of the surface plasmon, which is conducive to the construction of sub-wavelength-scale nanophotonic devices.

[0033] 3. The present invention is achieved by precisely adjusting the relative position and angle of two single silver nanowires, so the assembly method of the present invention has the advantages of simple operation, accuracy, flexibility, etc.

[0034] Parallel silver nanowire structures can be prepared by micromachining technology. The silver nanowires prepared by this top-down etching method are polycrystalline structures with rough surfaces, and the transmission loss of their surface plasmons is large. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] Figure 1 This is an electron microscope image of synthesized silver nanowires based on a structure and method for reducing transmission loss of parallel silver nanowires according to the present invention;

[0036] Figure 2 Schematic diagram of the platform structure of the present invention using micromanipulation method to assemble parallel silver nanowire structures;

[0037] Figure 3 It is a schematic diagram of the process of assembling a parallel silver nanowire structure with a tapered optical fiber according to the present invention;

[0038] Figure 4 are optical microscope images of parallel silver nanowires and a single nanowire of the present invention;

[0039] Figure 5 This is a diagram of the experimental process of exciting SPPs and measuring transmission loss using the fiber coupling method of the present invention;

[0040] Figure 6 is a graph showing the variation of the surface plasmon scattered light intensity at the ends of the parallel silver nanowires and a single nanowire with the transmission distance;

[0041] Figure 7 It is a graph showing the change of transmission loss of the parallel silver nanowires and the single nanowire with the transmission distance of the present invention. DETAILED DESCRIPTION

[0042] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the relevant technologies in the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0043] refer to Figures 1 to 7 The structure of reducing transmission loss based on parallel silver nanowires in this embodiment is that at least one pair of silver nanowires parallel to each other is provided on the substrate, the diameter of the silver nanowire is 400-800nm, the length of the silver nanowire is 10-20μm, and the parallel spacing or gap between the silver nanowire pairs is 5-50nm; the number of silver nanowires can be adjusted according to the concentration of the prepared solution; when two silver nanowires are placed in parallel, the transmission loss is lower than that of a single silver nanowire. The length and diameter of the two silver nanowires of the silver nanowire pair are close respectively; and the positions of the two silver nanowires are close. The substrate includes: SiO2 / Si.

[0044] The method for reducing transmission loss based on parallel silver nanowire structure is as follows:

[0045] Step 1, preparing large-sized silver nanowires;

[0046] Step 2: Using a micromanipulation method to precisely move the single silver nanowire on the substrate prepared in step 1 to construct a parallel silver nanowire structure;

[0047] Step 3: Use the fiber coupling method to excite the parallel silver nanowires to generate SPPs and measure the transmission loss.

[0048] Example

[0049] The method of reducing transmission loss based on parallel silver nanowire structure in this embodiment includes first preparing silver nanowires, then assembling the parallel silver nanowire structure by micromanipulation method, and finally using fiber coupling method to excite the parallel silver nanowires to generate SPPs and measure the transmission loss.

[0050] In this embodiment, the diameter of the silver nanowires is 400-800 nm, and the length is 10-20 μm. The sizes of the two silver nanowires can be selected arbitrarily.

[0051] In this embodiment, the method for preparing large-sized silver nanowires includes the following steps:

[0052] Step A1, dissolve silver nitrate and PVP in ethylene glycol respectively and stir until the reaction is complete to form a clear transparent liquid;

[0053] Step A2: inject ethylene glycol solution into a three-necked flask and heat it, use a syringe to draw the two precursor solutions in step A1, and inject the solutions into the three-necked flask at a uniform speed for reaction, and stop the reaction when a creamy yellow flocculent appears in the solution.

[0054] Step A3: After the reaction solution is cooled, the solution is washed multiple times with acetone and anhydrous ethanol respectively to obtain large-sized silver nanowires.

[0055] In step A1, 0.25 g of AgNO3 and 0.2 g of PVP were added per 10 ml of ethylene glycol, and the stirring time was 40 minutes.

[0056] In step A2, the heating temperature is 170° C. and the reaction time is 60 minutes.

[0057] In this embodiment, the method of assembling a parallel silver nanowire structure using an optical fiber-assisted manipulation method includes the following steps:

[0058] Step B1, preparing an optical fiber taper structure;

[0059] Step B2, fix the optical fiber cone structure in step B1 through a three-dimensional adjustment frame and form a certain inclination angle with the SiO2 / Si substrate, disperse the silver nanowire solution on the SiO2 / Si substrate and select two suitable adjacent single silver nanowires under a microscope, adjust the position of the light cone and slowly push the two single silver nanowires to form a parallel silver nanowire structure.

[0060] In step B1, the diameter of the tip of the optical fiber taper is 2 μm.

[0061] In step B2, the positions of the two silver nanowires can be adjusted by the rotation stage at the bottom.

[0062] When a large number of photonic devices based on parallel nanowire structures need to be prepared, two silver nanowires can be placed in parallel in the grooves through nanogrooving to achieve rapid batch preparation of multiple groups of silver nanowire pairs, thereby achieving low-loss light transmission of nanodevices and limiting the light field to a relatively small area in the lateral direction.

[0063] In this embodiment, the fiber coupling method excites parallel silver nanowires to generate SPPs and measures the transmission loss, including the following steps:

[0064] Step C1, preparing an optical fiber taper structure;

[0065] Step C2, fix the optical fiber on a three-dimensional adjustment frame, keep the direction of the optical fiber cone parallel to the silver nanowire under a microscope, couple a 633nm laser into the optical fiber to excite the SPPs on the parallel silver nanowires, move the relative position of the optical fiber cone and the parallel silver nanowire structure, record the end scattered light intensity of the parallel silver nanowire structure, and calculate the transmission loss of SPPs on the parallel silver nanowires.

[0066] In step C1, the cone tip diameter of the optical fiber cone is 1.5 μm.

[0067] In step C2, the laser power, excitation fiber cone, and parallel silver nanowires used in the experiment are the same, and the contact mode and angle between the excitation fiber cone and the silver nanowires are the same.

[0068] Comparative Example

[0069] This comparative example uses a fiber coupling method to excite a single silver nanowire to generate SPPs and measure the transmission loss, which is used to compare the transmission losses of different structures.

[0070] In this comparative example, the diameter of the silver nanowire is 600 nm and the length is 16 μm.

[0071] The method of using a fiber coupling method to excite a single silver nanowire to generate SPPs and measure transmission loss comprises the following steps:

[0072] Step D1, preparing an optical fiber taper structure;

[0073] Step D2, fix the optical fiber on a three-dimensional adjustment frame, keep the direction of the optical fiber cone parallel to the silver nanowire under the microscope, couple a 633nm laser into the optical fiber to excite the SPPs on a single silver nanowire, move the relative position of the optical fiber cone and the single silver nanowire, record the scattered light intensity at the end of the silver nanowire, and calculate the transmission loss of the SPPs on the single silver nanowire.

[0074] In step D1, the diameter of the tip of the optical fiber taper is 1.5 μm.

[0075] In step D2, the laser power, the excitation fiber cone, and the single silver nanowire used in the experiment are all the same, and the angle between the excitation fiber cone and the silver nanowire is the same.

[0076] The following is a detailed description of the embodiments and comparative examples with reference to the accompanying drawings:

[0077] Figure 1 This is a scanning electron microscope image of synthesized silver nanowires. The scale is 2 microns, and the white ones are nanowires. From the image, we can see that the surface of the nanowires prepared in the laboratory is very smooth.

[0078] Figure 2 This is a schematic diagram of a device for assembling a parallel silver nanowire structure using optical fibers. The optical fiber is fixed on a three-dimensional adjustment frame to push the nanowires, and the rotation stage is used to adjust the angle between the optical fiber cone and the two silver nanowires.

[0079] Figure 3 This is a schematic diagram of the process of assembling parallel silver nanowire structures with tapered optical fibers. By controlling the position of the tapered optical fiber, the single nanowires are pushed closer to each other. The size of the two single silver nanowires can be freely selected, which has good flexibility and operability.

[0080] Figure 4 These are optical microscope images of the two structures, with a scale of 2 micrometers. The diameter of the two nanowire branches of the parallel silver nanowire structure is about 500nm, and the length is about 13μm. They are similar in size and parallel in direction. The diameter of the single silver nanowire used for comparison is about 600nm, and the length is about 16μm.

[0081] Figure 5 It is an experimental process of exciting SPPs and measuring transmission loss using the fiber coupling method. Laser (633nm) excites SPPs at different positions of the nanowire through a tapered fiber. SPPs are transmitted along the nanowire and finally scattered as photons at the end of the nanowire.

[0082] Figure 6The transmission loss of parallel silver nanowires was measured using the fiber coupling method. As the SPPs transmission distance increases, the scattered light intensity at the end of the silver nanowire decays exponentially. The measured transmission length of the parallel silver nanowires is ~6.7μm, while the transmission length of a single silver nanowire of similar diameter is

[0083] ~6.0μm. The transmission length of SPPs on the parallel silver nanowire structure is extended. Generally speaking, the thicker the diameter of a single nanowire, the smaller the corresponding loss. Although the parallel nanowires of this embodiment have a thinner diameter, the loss is still smaller than that of a single thick nanowire. This shows the superiority of the parallel nanowire structure of the present invention.

[0084] Figure 7 It is the variation of surface plasmon transmission loss corresponding to the two structures with transmission distance.

[0085] The transmission loss of parallel silver nanowires is 0.58dB / μm, while the transmission loss of a single silver nanowire of similar diameter reaches 0.77dB / μm. The experimental results further prove that the transmission loss of SPPs in parallel silver nanowire structure is significantly reduced.

[0086] In summary, the present invention places two metal nanowires in parallel and fully utilizes the influence of the interaction between the metal nanowires on the surface plasmon field distribution, so that the radiation leakage of the surface plasmon to the substrate during the transmission process is suppressed, thereby significantly reducing the transmission loss of the surface plasmon. Therefore, the present invention has broad application prospects in constructing a simple metal waveguide structure to reduce the transmission loss of SPPs and improve the practical application of surface plasmon photonic devices.

[0087] It should be emphasized that the above are only preferred embodiments of the present invention and do not impose any form of limitation on the present invention. Any simple modifications made to the above embodiments based on the technical essence of the present invention, including the use of other methods to prepare parallel metal nanowire structures and changes in the size of the nanowires, even if they are different from the size of the parallel nanowires in the present invention, also fall within the scope of protection of the present invention. Other equivalent changes and modifications still fall within the scope of the technical solution of the present invention.

Claims

1. A structure for reducing transmission loss based on parallel silver nanowires, characterized in that: The structure is that at least one pair of silver nanowires parallel to each other is arranged on a substrate, the diameter of the silver nanowire is 400-800nm, the length of the silver nanowire is 10-20μm, and the parallel spacing or gap between the silver nanowire pairs is 5-50nm; The surface of the silver nanowire is smooth.

2. The structure for reducing transmission loss based on parallel silver nanowires according to claim 1, characterized in that: The length and diameter of the two silver nanowires in the silver nanowire pair are close to each other.

3. The structure for reducing transmission loss based on parallel silver nanowires according to claim 1, characterized in that: The substrate includes: a SiO2 / Si substrate, a common silicon substrate or a glass substrate.

4. A method for reducing transmission loss based on parallel silver nanowires, characterized in that: The method is used to prepare the structure based on parallel silver nanowires to reduce transmission loss as claimed in any one of claims 1 to 3, and the method comprises the following steps: Step 1, preparing large-sized silver nanowires; Step 2: Using a micromanipulation method to precisely move the single silver nanowire on the substrate prepared in step 1 to construct a parallel silver nanowire structure; Step 3: Use the fiber coupling method to excite the parallel silver nanowires to generate SPPs and measure the transmission loss.

5. The method for reducing transmission loss based on parallel silver nanowires according to claim 4, characterized in that: In step 1, the preparation of large-sized silver nanowires comprises the following steps: Step 1-1: Dissolve silver nitrate and PVP in ethylene glycol separately and stir until the reaction is complete to form a clear transparent liquid; Step 1-2: Heat the ethylene glycol solution, take the solution prepared in step 1-1, and uniformly inject the solution into the ethylene glycol solution for reaction, and stop the reaction after the solution appears milky yellow flocs; Step 1-3: After the reaction solution in step 1-2 is cooled, the solution is washed twice with acetone and anhydrous ethanol respectively to obtain large-sized silver nanowires.

6. The method for reducing transmission loss based on parallel silver nanowires according to claim 5, characterized in that: In the step 1-1, every 10 ml of ethylene glycol corresponds to 0.25 g of AgNO3 and 0.20 g of PVP, and the stirring time is 50 to 80 minutes.

7. The method for reducing transmission loss based on parallel silver nanowires according to claim 4, characterized in that: In step 2, the micromanipulation method comprises the following steps: Step 2-1: preparing a fiber taper structure; Step 2-2: Fix the optical fiber cone structure obtained in step 2-1 through a three-dimensional adjustment frame and form an inclination angle with the substrate, disperse the silver nanowire solution on a SiO2 / Si substrate or an ordinary silicon substrate and set it on a rotating translation stage, select two adjacent single silver nanowires under a microscope, adjust the position of the light cone, and slowly push the two single silver nanowires to form a parallel silver nanowire structure.

8. The method for reducing transmission loss based on parallel silver nanowires according to claim 7, characterized in that: In the step 2-1, the tip diameter of the optical fiber cone is 0.5 to 3 μm.

9. The method for reducing transmission loss based on parallel silver nanowires according to claim 7, characterized in that: The three-dimensional adjustment frame is a support frame that can be adjusted in the three directions of X, Y, and Z, and is used to fix the rear part of the optical fiber cone. The three-dimensional adjustment frame is provided with three studs whose rotation axes are parallel to the X, Y, and Z directions respectively. The three-dimensional adjustment frame is driven by the rotation of the studs to generate micro displacements in the X, Y, and Z directions accordingly. The rotary displacement stage is a support platform that can rotate in the X, Y directions and in the horizontal plane, and is used to support and place the silver nanowires. The rotary displacement stage is provided with two screws whose rotation axes are parallel to the X and Y directions respectively, and an angle adjustment screw whose rotation axis is located in the horizontal plane. The rotary displacement stage is driven to generate a micro displacement in the X and Y directions by the rotation of the screws, and the rotary displacement stage is driven to rotate in the horizontal plane by the rotation of the angle adjustment screw. The base of the three-dimensional adjustment frame, the base of the rotary displacement stage and the base of the optical microscope are fixedly connected.

10. The method for reducing transmission loss based on parallel silver nanowires according to claim 4, characterized in that: The specific steps of step 3 are as follows: Step 3-1: Prepare a fiber taper structure; Step 3-2: Couple the laser into the optical fiber to excite the SPPs on the parallel silver nanowires, keep the direction of the optical fiber cone nearly parallel to the silver nanowire structure, accurately move the optical fiber, adjust the relative position of the optical fiber cone and the parallel silver nanowire structure, collect the scattered light at the end of the parallel silver nanowire structure, and calculate the transmission loss of SPPs on the parallel silver nanowires by comparing the scattered light intensity at different positions.

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