Beam generation device and beam generation method

Abstract

One aspect of the present invention pertains to a beam generation device provided with: a radiator that radiates a beam which has an intensity distribution, in a plane perpendicular to the propagation direction, represented by a Gaussian function; a primary reflecting mirror that reflects the beam to provide a third-order phase distribution to the beam; and a secondary mirror that reflects the beam to which the phase distribution has been provided by the primary mirror. The secondary mirror, by the reflection of the beam, converts the amplitude phase distribution of the beam in a focal plane of the secondary mirror to a result of Fourier transformation of the amplitude phase distribution of the beam in the focal plane before the reflection of the beam by the secondary mirror.

Description

Beam generating device and beam generating method

[0001] The present invention relates to a beam generating device and a beam generating method.

[0002] In recent years, there has been growing interest in using Airy beams in technical fields that use beams, such as communications technology.

[0003] Dajun Zhang, et al. "Generation of Broadband THz Airy Beams Applying 3D Printing Technique." 2019 13th European Conference on Antennas and Propagation (EuCAP). IEEE, 2019. Nikolaos K. Efremidis, et al. "Airy beams and accelerating waves: an overview of recent advances." Optica 6.5 (2019): 686-701.

[0004] Until now, Airy beams have been generated by transmitting a Gaussian beam through a phase modulating lens (PML) and a Fourier transform lens (FTL). However, when transmitting through the phase modulating lens and the Fourier transform lens, absorption by the phase modulating lens and the Fourier transform lens occurs, and therefore the energy of the Airy beam may be smaller than the energy of a Gaussian beam. In other words, the energy of the beam may be attenuated when the Airy beam is generated due to absorption by the phase modulating lens and the Fourier transform lens.

[0005] In view of the above circumstances, an object of the present invention is to provide a technique for reducing the energy loss of electromagnetic waves that occurs when generating an Airy beam.

[0006] One aspect of the present invention is a beam generating device comprising: a radiator that emits a beam whose intensity distribution in a plane perpendicular to the propagation direction is expressed by a Gaussian function; a primary reflecting mirror that reflects the beam to give the beam a third-order phase distribution; and a secondary reflecting mirror that reflects the beam with the phase distribution given by the primary reflecting mirror, wherein the secondary reflecting mirror, by reflecting the beam, converts the amplitude and phase distribution of the beam in the focal plane of the secondary reflecting mirror into the result of a Fourier transform of the amplitude and phase distribution of the beam in the focal plane before reflection of the beam by the secondary reflecting mirror.

[0007] A beam generation method using a beam generating device comprising: a radiator that radiates a beam whose intensity distribution in a plane perpendicular to the propagation direction is expressed by a Gaussian function; a primary reflecting mirror that reflects the beam to give the beam a third-order phase distribution; and a secondary reflecting mirror that reflects the beam to which the phase distribution has been given by the primary reflecting mirror, wherein the secondary reflecting mirror, by reflecting the beam, converts the amplitude and phase distribution of the beam in the focal plane of the secondary reflecting mirror into a Fourier transform result for the amplitude and phase distribution of the beam in the focal plane before reflection of the beam by the secondary reflecting mirror, the beam generation method comprising a radiation step of causing the radiator to radiate the beam.

[0008] The present invention makes it possible to reduce the loss of energy of electromagnetic waves that occurs in generating Airy beams.

[0009] 1 is an explanatory diagram for explaining a beam generating device of an embodiment. A diagram showing a first arrangement example in an embodiment. A diagram showing an example of a result of projecting a radiator, a primary reflecting mirror, and a secondary reflecting mirror onto a plane perpendicular to the optical axis in the first arrangement example of an embodiment. A diagram showing a second arrangement example in an embodiment. A diagram showing an example of a result of projecting a radiator, a primary reflecting mirror, and a secondary reflecting mirror onto a plane perpendicular to the optical axis in the second arrangement example of an embodiment. A diagram showing a third arrangement example in an embodiment. A diagram showing an example of a result of projecting a radiator, a primary reflecting mirror, and a secondary reflecting mirror onto a plane perpendicular to the optical axis in the third arrangement example of an embodiment. A diagram showing an example of a more specific hardware configuration of a beam generating device of an embodiment. A diagram showing an example of a processing flow executed by a control unit in an embodiment. An explanatory diagram used for mathematically explaining the second arrangement example and the third arrangement example.

[0010] 1 is an explanatory diagram illustrating a beam generating device 1 according to an embodiment. The beam generating device 1 is a device that generates an Airy beam. The beam generating device 1 includes a control unit 11 including a processor 91 such as a CPU (Central Processing Unit) and a memory 92, which are connected via a bus, a radiator 12, a primary reflecting mirror 13, and a secondary reflecting mirror 14.

[0011] The control unit 11 controls the operation of the radiator 12. The radiator 12 radiates a Gaussian beam under the control of the control unit 11. A Gaussian beam is a beam whose intensity distribution in a plane perpendicular to the propagation direction is expressed by a Gaussian function. The beam may be in any frequency band as long as it is an electromagnetic wave. Therefore, the beam may be, for example, radio waves, terahertz waves, near-infrared rays, light, or X-rays. The Gaussian beam radiated by the radiator 12 may or may not be a plane wave. Beam L1 in FIG. 1 shows an example of a Gaussian beam radiated by the radiator 12.

[0012] The primary reflecting mirror 13 reflects a beam, imparting a third-order phase distribution to the beam. That is, when a Gaussian beam is incident on the primary reflecting mirror 13, the primary reflecting mirror 13 emits a reflected beam in which a third-order phase distribution has been imparted to the incident wave. The beam L2 in FIG. 1 is the wave of the beam L1 reflected by the primary reflecting mirror 13. Note that the provision of a third-order phase distribution means that the phase at each position indicated by the distribution of phases, whose differential coefficient in the in-plane direction is expressed as a quadratic function of the position in the in-plane direction, is imparted according to the position at which the incident wave is incident. Because the differential coefficient is expressed as a quadratic function, the phase distribution is expressed as a cubic function.

[0013] Therefore, the phase that the primary reflecting mirror 13 gives to the incident wave is expressed by, for example, the following equation (1): １ Axis and Y １ X stretched between the axis１ Y １ Let X be the face. １ Axis and Y １ The origin of the axis is X １ Y １ The intersection of the surface and the optical axis of the primary reflecting mirror 13 is determined by x １ That X １ represents the coordinate of the axis, and y １ That Y １ represents the coordinate of the axis. In equation (1), b is a predetermined constant.

[0014]

[0015] Note that X' in FIG. １ Axis is X １ is parallel to the Y' axis １ Axis and Y １ It is parallel to the axis.

[0016] The secondary reflecting mirror 14 reflects the beam that has been given a third-order phase distribution by the primary reflecting mirror 13. By reflecting the beam, the secondary reflecting mirror 14 converts the amplitude and phase distribution of the beam in the focal plane of the secondary reflecting mirror 14 into the result of a Fourier transform of the amplitude and phase distribution of the beam on the focal plane before reflection of the beam by the secondary reflecting mirror 14. Beam L3 in FIG. 1 is the wave of beam L2 reflected by the secondary reflecting mirror 14.

[0017] The Gaussian beam emitted by radiator 12 is reflected by primary reflecting mirror 13 and then by secondary reflecting mirror 14, resulting in an Airy beam. Therefore, in the example of Fig. 1, beam L1 is a Gaussian beam and beam L3 is an Airy beam. Thus, the beams after Fourier transformation by secondary reflecting mirror 14 are Airy beams.

[0018] The primary reflector 13 may be any reflector that imparts a third-order phase distribution to the incident wave, such as a reflective phase plate such as a metasurface that imparts a third-order phase distribution to the incident wave. The primary reflector 13 may impart the phase expressed by the above formula (1) to the incident wave by using, for example, a path difference that occurs on the diameter of a metal conductor used in a general parabolic antenna.

[0019] The secondary reflecting mirror 14 may be any reflecting mirror as long as the reflected wave is the result of a Fourier transform of the incident wave. Therefore, the secondary reflecting mirror 14 may be, for example, a reflective phase plate such as a metasurface that performs a Fourier transform on the incident wave by reflection. The phase that a phase plate that performs a Fourier transform on an incident electromagnetic wave imparts to the incident electromagnetic wave is, for example, a phase expressed by the following equation (2). The electromagnetic wave to which the phase of equation (2) has been imparted is the result of the Fourier transform of the electromagnetic wave before the phase of equation (2) has been imparted.

[0020]

[0021] The planes perpendicular to the optical axis of the secondary reflecting mirror 14 are perpendicular to each other. ２ Axis and Y ２ X stretched between the axis ２ Y ２ Let X be the face. ２ Axis and Y ２ The origin of the axis is X ２ Y ２ The intersection of the surface and the optical axis of the secondary reflecting mirror 14 is x ２ That X ２ represents the coordinate of the axis, and y ２ That Y ２ represents the coordinate of the axis. ０ is the wave number of the beam emitted by the radiator 12. f is the focal length of the secondary reflector 14.

[0022] The secondary reflector 14 may be a type that imparts the phase expressed by the above equation (2) to the incident wave by using a path difference that occurs on the diameter of a metal conductor used in a typical parabolic antenna, for example.

[0023] Note that X' in FIG. ２ Axis is X ２ is parallel to the Y' axis ２ Axis and Y ２ It is parallel to the axis.

[0024] <Regarding the arrangement of radiator 12, primary reflecting mirror 13, and secondary reflecting mirror 14> Radiator 12 may be located in any position as long as it can emit a Gaussian beam that is incident approximately perpendicularly on primary reflecting mirror 13. Therefore, radiator 12 may be located in a position where it can emit a beam such that the beam is incident approximately perpendicularly on primary reflecting mirror 13, for example, from a position between primary reflecting mirror 13 and secondary reflecting mirror 14.

[0025] An arrangement in which a beam is incident on primary reflecting mirror 13 approximately perpendicularly from a position between primary reflecting mirror 13 and secondary reflecting mirror 14 may be, for example, an arrangement in which radiator 12 itself is positioned between primary reflecting mirror 13 and secondary reflecting mirror 14 and the beam is radiated toward primary reflecting mirror 13. However, the arrangement of radiator 12, primary reflecting mirror 13, and secondary reflecting mirror 14 does not necessarily have to be an arrangement in which radiator 12 itself is positioned between primary reflecting mirror 13 and secondary reflecting mirror 14.

[0026] For example, the radiator 12 may not be present between the primary reflector 13 and the secondary reflector 14, and a reflector may be positioned between the primary reflector 13 and the secondary reflector 14 instead of the radiator 12, and the beam emitted by the radiator 12 may be reflected by the reflector, causing the beam to enter the primary reflector 13 approximately perpendicularly.

[0027] The secondary reflecting mirror 14 may be located in any position as long as it can reflect the reflected wave from the primary reflecting mirror 13. For example, the secondary reflecting mirror 14 may be located at a position where the distance in the optical axis direction between the optical center of the primary reflecting mirror 13 and the optical center of the secondary reflecting mirror 14 is the same or approximately the same as the focal length of the secondary reflecting mirror 14. The secondary reflecting mirror 14 may be located at a position where the optical axis coincides with or approximately coincides with the optical axis of the primary reflecting mirror 13. The secondary reflecting mirror 14 may be located at a position where there is an offset between the optical axis of the secondary reflecting mirror 14 and the optical axis of the primary reflecting mirror 13.

[0028] An example of the arrangement of radiator 12, primary reflector 13, and secondary reflector 14 will be described with reference to the drawings.

[0029] 2 is a diagram showing a first example (hereinafter referred to as "first arrangement example") of the arrangement of radiator 12, primary reflecting mirror 13, and secondary reflecting mirror 14 in an embodiment. In the example of Fig. 2, radiator 12 is supported by secondary reflecting mirror 14 at a position where it radiates a Gaussian beam from a position between primary reflecting mirror 13 and secondary reflecting mirror 14 towards primary reflecting mirror 13 so that the beam is incident on primary reflecting mirror 13 approximately perpendicularly.

[0030] In the first arrangement example, the optical axis of the primary reflecting mirror 13 coincides with the optical axis of the secondary reflecting mirror 14. In the first arrangement example, the distance between the optical center of the primary reflecting mirror 13 and the optical center of the secondary reflecting mirror 14 is the same as the focal length of the secondary reflecting mirror 14.

[0031] 2 also shows an example of the spatial distribution of the intensity of the Airy beam generated in the first arrangement example. Graph G101 shows the intensity distribution of the Airy beam on the primary reflecting mirror 13, and the intensity distribution of the Airy beam on the optical axis Z of the secondary reflecting mirror 14. ０ A predetermined axis X perpendicular to ０ 2 shows an example of the intensity distribution in a direction parallel to the axis of the primary reflector 13. FIG. 2 shows that the main lobe and part of the side lobe of the Airy beam exist at the position of the rear surface of the primary reflector 13 as seen from the secondary reflector 14.

[0032] In the first arrangement example, the optical axis of the secondary reflecting mirror 14 and the optical axis of the primary reflecting mirror 13 coincide with each other, so the optical axis Z is also the optical axis of the primary reflecting mirror 13. ０ The positive direction is the direction from the secondary reflecting mirror 14 toward the primary reflecting mirror 13 .

[0033] As shown in FIG. 2, in the first arrangement example, the radiator 12 is aligned along the optical axis Z ０ The radiator 12 is located above the primary reflecting mirror 13 and is capable of radiating a beam toward the primary reflecting mirror 13. Therefore, the first arrangement example satisfies the condition that the radiator 12 is located at a position where it radiates a beam so that the beam is incident on the primary reflecting mirror 13 approximately perpendicularly.

[0034] Figure 3 shows an example of the result of projecting the radiator 12, primary reflector 13, and secondary reflector 14 onto a plane perpendicular to the optical axis in the first arrangement example of the embodiment. That is, Figure 3 shows an image 121 of the radiator 12, an image 131 of the primary reflector 13, and an image 141 of the secondary reflector 14 projected onto a plane perpendicular to the optical axis for the radiator 12, primary reflector 13, and secondary reflector 14 of the first arrangement example. Figure 3 shows that the image 141 of the secondary reflector 14 encompasses the image 131 of the primary reflector 13, and that the image 131 of the primary reflector 13 encompasses the image 121 of the radiator 12. Figure 3 also shows that the images of the radiator 12, primary reflector 13, and secondary reflector 14 are all rotationally symmetric and have the same center.

[0035] 4 is a diagram showing a second example of the arrangement of the radiator 12, the primary reflecting mirror 13, and the secondary reflecting mirror 14 in the embodiment (hereinafter referred to as the "second arrangement example"). In the second arrangement example, the optical axis Z of the secondary reflecting mirror 14 is ２ and the optical axis Z of the primary reflecting mirror 13 １ 4 shows the optical axis Z of the secondary reflecting mirror 14. ２ and the optical axis Z of the primary reflecting mirror 13 １ This indicates that the distance between the first and second electrodes (hereinafter referred to as the "offset length") is a non-zero distance D1.

[0036] As shown in FIG. 4, in the second arrangement example, the radiator 12 is aligned with the optical axis Z of the primary reflecting mirror 13. １ The radiator 12 is located above the primary reflecting mirror 13 and is positioned to radiate a beam toward the primary reflecting mirror 13. Therefore, the second arrangement example also satisfies the condition that the radiator 12 is positioned to radiate a beam so that the beam is incident on the primary reflecting mirror 13 approximately perpendicularly.

[0037] 4 shows an example of the intensity distribution of the Airy beam generated in the second arrangement example as an image G102. The image G102 is taken along the optical axis Z of the rear surface of the primary reflecting mirror 13 as seen from the secondary reflecting mirror 14. １ The position of the optical axis Z １ Origin of direction O ｚ１ The direction of the primary reflecting mirror 13 as seen from the secondary reflecting mirror 14 is defined as the optical axis Z １ As the positive direction of the optical axis Z １ Origin O above ｚ１ For each point in the positive direction as seen from the Airy beam,ｑ１ The intensity change in the axial direction is shown. ｑ１ The axis is the optical axis Z １ is perpendicular to the optical axis Z １ Optical axis Z as seen from ２ is parallel to the offset direction.

[0038] FIG. 4 shows the optical axis Z of the secondary reflecting mirror 14. ２ and the optical axis Z of the primary reflecting mirror 13 １ are parallel but not coincident, which indicates that the primary reflecting mirror 13 is not present on the paths of the main lobe and side lobes of the Airy beam. Therefore, in the case of the second arrangement example, the degree of attenuation of the energy of the main lobe and side lobes of the Airy beam by the primary reflecting mirror 13 is smaller than in the first arrangement example illustrated in FIG.

[0039] Figure 5 shows an example of the result of projecting radiator 12, primary reflector 13, and secondary reflector 14 onto a plane perpendicular to the optical axis in the second arrangement example of the embodiment. Figure 5 shows image 121 of radiator 12, image 131 of primary reflector 13, and image 141 of secondary reflector 14 projected onto a plane perpendicular to the optical axis for radiator 12, primary reflector 13, and secondary reflector 14 of the second arrangement example. Figure 5 shows that image 141 of secondary reflector 14 encompasses image 131 of primary reflector 13, and image 131 of primary reflector 13 encompasses image 121 of radiator 12.

[0040] Figure 5 also shows that the images of radiator 12, primary reflector 13, and secondary reflector 14 are all rotationally symmetric images, but unlike the example in Figure 3, the center of radiator 12 and the center of primary reflector 13 coincide, but the center C1 of secondary reflector 14 does not coincide with the center of radiator 12 or the center of primary reflector 13.

[0041] 6 is a diagram showing a third example of the arrangement of the radiator 12, the primary reflecting mirror 13, and the secondary reflecting mirror 14 in the embodiment (hereinafter referred to as the "third arrangement example"). In the third arrangement example, the optical axis Z of the secondary reflecting mirror 14 ２ and the optical axis Z of the primary reflecting mirror 13 １ 6 shows that the offset length is a non-zero distance D2.

[0042] As shown in FIG. 6, in the second arrangement example, the radiator 12 is aligned with the optical axis Z of the primary reflecting mirror 13. １ The radiator 12 is located above the primary reflecting mirror 13 and is positioned to radiate a beam toward the primary reflecting mirror 13. Therefore, the third arrangement example also satisfies the condition that the radiator 12 is positioned to radiate a beam so that the beam is incident on the primary reflecting mirror 13 approximately perpendicularly.

[0043] 6 shows an example of the intensity distribution of the Airy beam generated in the third arrangement example as an image G103. The image G103 is taken along the optical axis Z of the rear surface of the primary reflecting mirror 13 as seen from the secondary reflecting mirror 14. １ The position of the optical axis Z １ Origin of direction O ｚ１ The direction of the primary reflecting mirror 13 as seen from the secondary reflecting mirror 14 is defined as the optical axis Z １ As the positive direction of the optical axis Z １ Origin O above ｚ１ For each point in the positive direction as seen from the Airy beam, ｑ１ The intensity change in the axial direction is shown. ｑ１ The axis is the optical axis Z １ is perpendicular to the optical axis Z １ Optical axis Z as seen from ２ is parallel to the offset direction.

[0044] FIG. 6 shows the optical axis Z of the secondary reflecting mirror 14. ２ and the optical axis Z of the primary reflecting mirror 13 １ are parallel but not coincident, which indicates that the primary reflecting mirror 13 exists on the path of the side lobes of the Airy beam but does not exist on the path of the main lobe of the Airy beam. Therefore, in the case of the third arrangement example, the degree of attenuation of the energy of the main lobe of the Airy beam by the primary reflecting mirror 13 is greater than in the second arrangement example shown in Figure 4, but less than in the first arrangement example shown in Figure 2.

[0045] Figure 7 shows an example of the result of projecting radiator 12, primary reflector 13, and secondary reflector 14 onto a plane perpendicular to the optical axis in the third arrangement example of the embodiment. Figure 7 shows image 121 of radiator 12, image 131 of primary reflector 13, and image 141 of secondary reflector 14 projected onto a plane perpendicular to the optical axis for radiator 12, primary reflector 13, and secondary reflector 14 of the third arrangement example. Figure 7 shows that image 141 of secondary reflector 14 encompasses image 131 of primary reflector 13, and image 131 of primary reflector 13 encompasses image 121 of radiator 12.

[0046] Figure 7 also shows that the images of radiator 12, primary reflector 13, and secondary reflector 14 are all rotationally symmetric images, but unlike the example in Figure 3, the center of radiator 12 and the center of primary reflector 13 coincide, but the center C1 of secondary reflector 14 does not coincide with the center of radiator 12 or the center of primary reflector 13.

[0047] <Effects of Beam Generator 1> In the beam generator 1, an Airy beam is generated without the Gaussian beam passing through a phase modulate lens (PML) and a Fourier transform lens (FTL). Therefore, regardless of the arrangement of the radiator 12, primary reflecting mirror 13, and secondary reflecting mirror 14 in the first to third arrangement examples, etc., the loss caused by the generation of an Airy beam by the beam generator 1 is smaller than that caused by the generation of an Airy beam using a PML and an FTL.

[0048] 8 is a diagram showing an example of a more specific hardware configuration of the beam generation device 1 in the embodiment. The beam generation device 1 includes a control unit 11 including a processor 91 such as a CPU (Central Processing Unit) and a memory 92 connected by a bus, and executes a program. By executing the program, the beam generation device 1 functions as a device or system including the control unit 11, a radiator 12, a primary reflecting mirror 13, a secondary reflecting mirror 14, an interface unit 15, and a storage unit 16.

[0049] More specifically, the processor 91 reads out a program stored in the storage unit 16 and stores the read out program in the memory 92. When the processor 91 executes the program stored in the memory 92, the beam generating device 1 functions as a device including the control unit 11, the radiator 12, the primary reflecting mirror 13, the secondary reflecting mirror 14, the interface unit 15, and the storage unit 16.

[0050] The control unit 11 controls the operation of each functional unit included in the beam generating device 1. The control unit 11 acquires data to be transmitted by the Airy beam from an external device, for example, via the interface unit 15. The control unit 11 controls, for example, the operation of the radiator 12. The control unit 11 controls the operation of the radiator 12, for example, causing the radiator 12 to radiate a Gaussian beam.

[0051] The control unit 11 controls the operation of the radiator 12 so that the data to be transmitted is transmitted by an Airy beam, and emits a Gaussian beam that transmits the data to be transmitted. The control unit 11 acquires, for example, information stored in the memory unit 16. Specifically, the process of acquiring the information stored in the memory unit 16 is reading.

[0052] The interface unit 15 includes a communication interface for connecting the beam generating device 1 to an external device. The interface unit 15 communicates with the external device via wired or wireless communication. The external device is, for example, a device that transmits data to be transmitted by an Airy beam. In such a case, the interface unit 15 acquires the data to be transmitted by communicating with the device that transmits the data to be transmitted.

[0053] The interface unit 15 may be configured to include input devices such as a mouse, a keyboard, a touch panel, etc. The interface unit 15 may be configured as an interface that connects these input devices to the beam generating device 1. In this way, the interface unit 15 accepts input of various information to the beam generating device 1 via the input device, either wired or wireless. Note that data to be transmitted does not necessarily need to be input to a communication interface, but may also be input to an input device.

[0054] The interface unit 15 outputs, for example, various types of information. The interface unit 15 includes a display device such as a CRT (Cathode Ray Tube) display, a liquid crystal display, or an organic EL (Electro-Luminescence) display. The interface unit 15 may be configured as an interface that connects these display devices to the beam generating device 1. The interface unit 15 outputs, for example, information input to the interface unit 15.

[0055] The storage unit 16 is configured using a computer-readable storage medium device (non-transitory computer-readable recording medium) such as a magnetic hard disk drive or a semiconductor storage device. The storage unit 16 stores various information related to the beam generating device 1. The storage unit 16 stores, for example, a computer program for generating an Airy beam for data transmission, which controls the radiator 12. The storage unit 16 stores, for example, various information generated by the operation of the control unit 11. The storage unit 16 stores, for example, information acquired by the interface unit 15.

[0056] 9 is a diagram showing an example of the flow of processing executed by the control unit 11 in the embodiment. The control unit 11 controls the operation of the radiator 12 and causes the radiator 12 to radiate a beam (step S101).

[0057] The beam generating device 1 configured in this manner generates an Airy beam by reflection without transmitting a Gaussian beam through a lens, thereby reducing the energy loss of the electromagnetic wave that occurs when generating an Airy beam.

[0058] (Variations) Regarding the size of the primary reflecting mirror 13 and the secondary reflecting mirror 14 in a plane perpendicular to the optical axis direction, the size of the secondary reflecting mirror 14 may be equal to or larger than the size of the primary reflecting mirror 13. When the size of the secondary reflecting mirror 14 is equal to or larger than the size of the primary reflecting mirror 13, the energy loss in generating the Airy beam is smaller than when the size of the secondary reflecting mirror 14 is smaller than the size of the primary reflecting mirror 13. This is because when the size of the secondary reflecting mirror 14 is smaller than the size of the primary reflecting mirror 13, the size of the secondary reflecting mirror 14 may be smaller than the size of the wavefront of the electromagnetic wave emitted from the primary reflecting mirror 13. In such cases, there may be electromagnetic waves that cannot enter the secondary reflecting mirror 14, resulting in greater energy loss in generating the Airy beam than in other cases.

[0059] For simplicity of explanation, the control unit 11 has been described above using an example in which the beam generating device 1 includes the control unit 11. However, the control unit 11 does not necessarily have to be included in the beam generating device 1 as long as it is capable of controlling the beam generating device 1. Therefore, the control unit 11 may be included in, for example, an external device that controls the beam generating device 1.

[0060] The beam generating device 1 may be implemented using a plurality of information processing devices communicably connected via a network. In this case, the processes executed by the control unit 11 may be distributed among the plurality of information processing devices.

[0061] Note that all or part of the functions of the control unit 11, the radiator 12, the interface unit 15, and the storage unit 16 may be realized using hardware such as an ASIC (Application Specific Integrated Circuit), a PLD (Programmable Logic Device), or an FPGA (Field Programmable Gate Array). The program may be recorded on a computer-readable recording medium. Examples of computer-readable recording media include portable media such as flexible disks, magneto-optical disks, ROMs, and CD-ROMs, and storage devices such as hard disks built into a computer system. The program may be transmitted via a telecommunications line.

[0062] <Mathematical Explanation of Transformation> A mathematical explanation will be given for the second and third arrangement examples. For simplicity, the following explanation will be given by replacing the primary reflecting mirror 13 and the secondary reflecting mirror 14 with lenses, and by replacing the reflections by the primary reflecting mirror 13 and the secondary reflecting mirror 14 with transmissions.

[0063] Fig. 10 is an explanatory diagram used for mathematically explaining the second and third arrangement examples, showing a radiator 12, a phase modulating lens (PML) 13a that imparts a third-order phase distribution to an incident wave, and a Fourier transform lens (FTL) 14a.

[0064] The phase modulation lens 13a is a replacement for the primary reflecting mirror 13, and generates a wave to which a third-order phase distribution is imparted to the incident wave. However, the phase modulation lens 13a differs from the primary reflecting mirror 13 in that the wave to which a third-order phase distribution is imparted to the incident wave is a transmitted wave, not a reflected wave.

[0065] The Fourier transform lens 14a is a replacement for the secondary reflecting mirror 14, and generates a beam whose intensity distribution in a plane perpendicular to the propagation direction is the result of a Fourier transform of the intensity distribution of the incident wave. However, the Fourier transform lens 14a differs from the secondary reflecting mirror 14 in that the beam whose intensity distribution in a plane perpendicular to the propagation direction is the result of a Fourier transform of the intensity distribution of the incident wave is a transmitted wave rather than a reflected wave.

[0066] The optical axis of the phase modulation lens 13a and the optical axis of the Fourier transform lens 14a are parallel to each other but do not coincide with each other, i.e., there is an offset between the optical axis of the phase modulation lens 13a and the optical axis of the Fourier transform lens 14a.

[0067] For simplicity of explanation, the following description will be given assuming that the axis parallel to the optical axis of the Fourier transform lens 14a is the Z axis, and that the axis perpendicular to the Z axis and parallel to the offset direction of the optical axis of the phase modulation lens 13a and the optical axis of the Fourier transform lens 14a is the X axis. The positive direction of the Z axis is the direction from the secondary reflecting mirror 14 toward the primary reflecting mirror 13. The origin of the X and Z axes is the back focal point P1 of the Fourier transform lens 14a.

[0068] When the paraxial Helmholtz equation is solved using the waveform of the following equation (3) as the initial waveform, the following equation (4) is obtained. Note that γ is a predetermined constant that defines the pulse width of the Airy beam. The smaller γ is, the larger the pulse width of the Airy beam. α is a truncation factor, which is a predetermined constant that depends on the width of the Gaussian beam incident on the phase modulation lens 13a. The smaller the value of α, the larger the width of the Gaussian beam. v is a predetermined constant that determines the amount of offset between the optical axis of the phase modulation lens 13a and the optical axis of the Fourier transform lens 14a. Ai(.) represents the Airy function.

[0069]

[0070]

[0071]

[0072]

[0073] F2 represents the complex amplitude of the Airy beam relative to the X and Z axes. ０ The result of Fourier transform is expressed by the following equation (7).

[0074]

[0075] Equation (7) is approximated to the following equation (8) under Fresnel approximation (hereinafter referred to as "first approximation").

[0076]

[0077] Using the relationship in equation (9) below, the result of shifting the trajectory of the main lobe of the Airy beam in the X-axis direction by the amount given by equation (10) below is expressed by equation (11) below. Note that k represents a wave number in a wave number space based on the back focal plane P1 of the Fourier transform lens 14a. Note that the wave number space based on the back focal plane P1 means that wave numbers are used to represent spatial coordinates.

[0078]

[0079]

[0080]

[0081] Equation (11) is equivalent to the following equation (12).

[0082]

[0083] Equations (11) and (12) hold when x = 0 and z = 0, regardless of v. Therefore, the trajectory of the main lobe of the Airy beam passes through the origin regardless of the position of the phase modulation lens 13a. As mentioned above, the origin is the focal point of the Fourier transform lens 14a.

[0084] When v is positive, the locus expressed by equation (11) or equation (12) is approximately identical to the locus of the main lobe of the Airy beam in the case of arrangement example 2. When v is negative, the locus expressed by equation (11) or equation (12) is approximately identical to the locus of the main lobe of the Airy beam in the case of arrangement example 2.

[0085] The value of F1 is a value that does not depend on Z under first approximation. Furthermore, since F2 is a phase term, it does not affect the intensity of the Airy beam. Furthermore, the third term in parentheses in the following equation (13) approximates to 0 when α is sufficiently smaller than 1.

[0086]

[0087] Therefore, the only term that changes with a change in Z (i.e., representing the propagation of the beam) is the term expressed by the following equation (14).

[0088]

[0089] The maximum value of equation (14) is given at a point where the value in the parentheses of equation (14) is approximately equal to 0. In other words, the maximum value of the term in equation (14) is given at a point (x, z) that satisfies the following equation (15).

[0090]

[0091] Therefore, the trajectory of the main lobe is approximately expressed by the following equation (16).

[0092]

[0093] <More Specific Description of Airy Beam Generation> The generation of an Airy beam will be described more specifically using mathematical expressions.

[0094] When the initial waveform of an Airy beam is expressed by the following equation (17), its Fourier transform is expressed by the following equation (18).

[0095]

[0096]

[0097] Here, if the following equation (19) is satisfied, then equation (18) is a Gaussian with a third-order phase term.

[0098]

[0099] Since electromagnetic waves obey the reciprocity theorem, an Airy beam is generated by giving a Gaussian beam a third-order phase distribution and then performing a Fourier transform.

[0100] Although an embodiment of the present invention has been described above in detail with reference to the drawings, the specific configuration is not limited to this embodiment, and includes designs within the scope of the gist of the present invention.

[0101] REFERENCE SIGNS LIST 1... Beam generating device, 11... Control unit, 12... Radiator, 13... Primary reflecting mirror, 14... Secondary reflecting mirror, 15... Interface unit, 16... Storage unit, 13a... Phase modulation lens, 14a... Fourier transform lens, 91... Processor, 92... Memory

Claims

1. A beam generating device comprising: a radiator that radiates a beam whose intensity distribution in a plane perpendicular to the propagation direction is expressed by a Gaussian function; a primary reflecting mirror that gives the beam a third-order phase distribution by reflecting the beam; and a secondary reflecting mirror that reflects the beam with the phase distribution given to it by the primary reflecting mirror, wherein the secondary reflecting mirror, by reflecting the beam, converts the amplitude and phase distribution of the beam in the focal plane of the secondary reflecting mirror into the result of a Fourier transform of the amplitude and phase distribution of the beam in the focal plane before the reflection of the beam by the secondary reflecting mirror.

2. The beam generating device according to claim 1, wherein the optical axis of the primary reflector and the optical axis of the secondary reflector do not coincide.

3. The beam generating device according to claim 2, wherein the beam after the Fourier transform is an Airy beam, and the primary reflecting mirror is not on the path of a main lobe and a side lobe of the Airy beam.

4. The beam generating device according to claim 2, wherein the beam after the Fourier transform is an Airy beam, and the primary reflecting mirror is not on the path of a main lobe of the Airy beam but is on the path of a side lobe.

5. A beam generating method using a beam generating device comprising: a radiator that radiates a beam whose intensity distribution in a plane perpendicular to the propagation direction is expressed by a Gaussian function; a primary reflecting mirror that gives the beam a third-order phase distribution by reflecting the beam; and a secondary reflecting mirror that reflects the beam with the phase distribution given to it by the primary reflecting mirror, wherein the secondary reflecting mirror converts the amplitude and phase distribution of the beam in the focal plane of the secondary reflecting mirror by reflecting the beam into a result of a Fourier transform of the amplitude and phase distribution of the beam in the focal plane before reflection of the beam by the secondary reflecting mirror, the beam generating method comprising: a radiation step of causing the radiator to radiate the beam.

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