CN113866992B - Spherical harmonic cone lens for generating non-diffraction light beams in terahertz wave band - Google Patents
Spherical harmonic cone lens for generating non-diffraction light beams in terahertz wave band Download PDFInfo
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- CN113866992B CN113866992B CN202111060608.XA CN202111060608A CN113866992B CN 113866992 B CN113866992 B CN 113866992B CN 202111060608 A CN202111060608 A CN 202111060608A CN 113866992 B CN113866992 B CN 113866992B
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- G02B27/00—Optical systems or apparatus not provided for by any of the groups G02B1/00 - G02B26/00, G02B30/00
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Abstract
The invention discloses a spherical harmonic cone lens for generating a non-diffraction light beam in a terahertz waveband, which is an axicon lens with bulges on two oblique edges; the two end points of the bulge are overlapped with the two end points of the bevel edge, the shape of the bulge is determined based on a probability density function, and the probability density function is the square of a spherical harmonic function. According to the spherical harmonic cone lens for generating the non-diffraction light beam in the terahertz waveband, the bulges with certain special shapes are added on the two inclined edges of the axicon lens in an extending mode, and compared with the existing axicon lens with a fixed inclined angle, the non-diffraction distance of the light beam generated when the terahertz Gaussian light beam passes through the special lens can be increased, and the longer length of a non-diffraction area is obtained; therefore, during terahertz imaging, clear images of objects can be obtained within the non-diffraction distance of the wave beams, so that the terahertz imaging system has longer focal depth, large longitudinal measurement range and high transverse resolution.
Description
Technical Field
The invention belongs to the field of optics, and particularly relates to a spherical harmonic cone lens for generating a non-diffraction light beam in a terahertz waveband.
Background
Terahertz (THz) waves refer to electromagnetic waves with the frequency of 0.1-10 THz and the wavelength of 30 um-3 mm, and refer to the electromagnetic waves with the frequency of 0.3-3 THz in some places, and the THz waves are located between infrared waves and microwaves in an electromagnetic spectrum. Nature possesses a large amount of terahertz radiation, for example, the thermal radiation of most objects is terahertz waves. Due to the development of ultrafast optoelectronics and semiconductor technology, terahertz wave bands are provided with suitable terahertz emission and detection technologies. The long wave direction of the terahertz wave band is developed from the field of traditional electromagnetism, and the short wave direction is developed from the field of optics. In the field of electromagnetism, terahertz radiation is also called millimeter waves and submillimeter waves, and development mainly depends on the electronics technology; in the field of spectroscopy, which is known as far infrared radiation, development has relied primarily on photonics techniques.
Terahertz imaging has wide application prospects in the fields of safety inspection, nondestructive testing, medical diagnosis and the like. The terahertz imaging technology is to irradiate a measured object with THz rays, obtain information of a sample through transmission or reflection of an object, and then image. Terahertz imaging can be classified into terahertz pulse imaging and continuous terahertz wave imaging according to the manner of generation and detection of terahertz waves. According to the traditional terahertz pulse imaging technology, the recording of time domain waveforms mainly depends on the mechanical movement of delay lines, the system structure is complex, the building is difficult, the power of an emission source is low, the imaging time is too long, the cost of a femtosecond laser is high, and the imaging cost of the system is too high. In the traditional terahertz imaging technology, a Gaussian beam is applied to be incident on a sample, a focused Gaussian imaging system can only clearly image an object near a focus, and the terahertz imaging system based on the Gaussian beam is difficult to have both longer depth of field and higher transverse resolution. Therefore, in recent years, the development of terahertz non-diffracted beams provides an effective solution to this problem.
When light travels in a certain direction in vacuum, the light encounters an obstacle and a diffraction phenomenon occurs, which is called diffraction. The method has great influence on the traditional light wave field, and after a general collimated single light beam propagates Rayleigh distance in free space, the light beam starts to generate obvious diffraction diffusion. The diffraction-free beam is an important discovery of modern physical optics, has excellent propagation characteristics, is far away from the propagation distance, has intensity and size which are greatly different from those of a Gaussian beam, and can realize a large measurement range and high resolution. The non-diffraction light beam can be applied to a plurality of fields such as optical communication, laser machining, precision machining and the like. The non-diffraction beam can obtain a clear image of an object in the non-diffraction distance of the beam, so that the focal depth of two-dimensional imaging is improved.
The Bessel beam is a typical diffraction-free beam, and has the advantages of no diffraction, small central light spot, constant light intensity distribution and high concentration of light intensity in the process of propagation. Methods for generating Bessel beams include the circular seam method, the axicon method, and the computer holography method. In terahertz wave band, axicon lens is widely used due to advantages of simple structure, high conversion efficiency and the like. The non-diffraction distance of the Bessel light is inversely proportional to the base angle of the axicon, and the smaller the base angle of the axicon is, the longer the non-diffraction distance of the light beam is. However, the axicon with a smaller base angle has higher requirements on processing technology and higher cost, and when the angle of the axicon is too small, errors are easy to generate in the processing process. And thus a less angled axicon is generally not selected. When the axicon is angled, its non-diffractive distance is also limited, but in some applications a longer non-diffractive distance is required.
Disclosure of Invention
In view of the above defects or improvement requirements of the prior art, the present invention provides a spherical harmonic conic lens capable of generating a non-diffracted beam in a terahertz band, thereby solving the technical problem of limited non-diffracted length generated by the conventional axicon lens.
In order to achieve the above object, according to a first aspect of the present invention, there is provided a spherical harmonic axicon lens for generating a non-diffracted beam in a terahertz waveband, the spherical harmonic axicon lens being an axicon lens having protrusions on both inclined sides;
the two end points of the bulge are overlapped with the two end points of the bevel edge, the shape of the bulge is determined based on a probability density function, and the probability density function is the square of a spherical harmonic function.
Preferably, in a rectangular coordinate system, the expression of the probability density function is:
wherein l is the number of angular quanta, m is the number of magnetic quanta,
preferably, in a polar coordinate system, the expression of the probability density function is:
wherein theta is an altitude angle,
is the azimuth, l is the number of angular quanta, m is the number of magnetic quanta, Pl mIn order to be a function of legendre,
preferably, l ═ m.
Preferably, 1. ltoreq. m.ltoreq.20.
Preferably, the bottom surface of the spherical harmonic cone lens is 2mm thick.
Preferably, the spherical harmonic axicon is made by 3D printing.
According to a second aspect of the present invention, there is provided a terahertz imaging system comprising the spherical harmonic cone lens for generating a non-diffracted beam in a terahertz waveband as described in the first aspect.
In general, compared with the prior art, the above technical solution contemplated by the present invention can achieve the following beneficial effects:
1. according to the spherical harmonic cone lens for generating the non-diffraction light beam in the terahertz waveband, the bulges with certain special shapes are added on the two inclined edges of the axicon lens in an extending mode, and compared with the existing axicon lens with a fixed inclined angle, the non-diffraction distance of the light beam generated when the terahertz Gaussian light beam passes through the special lens can be increased, and the longer length of a non-diffraction area is obtained; therefore, during terahertz imaging, clear images of objects can be obtained within the non-diffraction distance of the wave beams, so that the terahertz imaging system has longer focal depth, large longitudinal measurement range and high transverse resolution, and has unique advantages in some application occasions.
2. According to the spherical harmonic cone lens for generating the non-diffraction light beam in the terahertz waveband, when the number of the angular quantum and the number of the magnetic quantum are both 9, 10 or 11, the non-diffraction distance of the light beam generated when the terahertz Gaussian light beam passes through the special lens is 3 times of that of the axicon with the fixed angle, the length of a non-diffraction area which is about 3 times of that of the axicon with the fixed inclination angle is obtained, and the optimal terahertz imaging effect can be achieved.
3. The spherical harmonic cone lens capable of generating the non-diffraction light beam in the terahertz wave band is manufactured by adopting a 3D printing technology, an advanced material additive manufacturing technology is used, the production speed is high, the manufacturing cost is low, and the product structure is accurate.
Drawings
FIG. 1 is a schematic diagram of a spherical harmonic cone lens structure for generating a non-diffracted light beam in a terahertz wave band, provided by the invention;
FIG. 2 is a three-dimensional schematic diagram of a spherical harmonic cone lens for generating a non-diffracted beam in a terahertz waveband according to the present invention;
FIG. 3 is an intensity distribution diagram of a non-diffracted light beam generated by the spherical harmonic cone lens for generating the non-diffracted light beam in a terahertz waveband at the xoz plane, provided by the invention;
fig. 4 is a central light intensity curve of the non-diffracted light beam generated by the spherical harmonic cone lens for generating the non-diffracted light beam in the terahertz wave band in the z direction.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention. In addition, the technical features involved in the embodiments of the present invention described below may be combined with each other as long as they do not conflict with each other.
The embodiment of the invention provides a spherical harmonic cone lens for generating a non-diffraction light beam in a terahertz waveband, as shown in fig. 1, the spherical harmonic cone lens is an axicon lens with bulges on two oblique edges;
the two end points of the bulge are overlapped with the two end points of the bevel edge, the shape of the bulge is determined based on a probability density function, and the probability density function is the square of a spherical harmonic function.
Specifically, the axicon lens and the protrusion are both made of a LY1101 material having the same refractive index.
Under a polar coordinate system, the expression of the probability density function is as follows:
wherein theta is an altitude angle,
is the azimuth angle, l is the number of angular quanta, m is the number of magnetic quanta, Pl mIn order to be a function of legendre,
preferably, the expression of the probability density function is:
wherein l is the number of angular quanta, m is the number of magnetic quanta,
preferably, l ═ m.
Preferably, 1. ltoreq. m.ltoreq.20.
Preferably, the bottom surface of the spherical harmonic cone lens is 2mm thick.
Preferably, the spherical harmonic axicon is made by 3D printing.
The design steps of the spherical harmonic cone lens for generating the non-diffraction light beam in the terahertz waveband provided by the invention are as follows:
1. determining the wavelength lambda of the used terahertz Gaussian beam; determining the beam waist radius omega of the terahertz Gaussian beam according to the propagation dynamics of the terahertz Gaussian beam in the experiment0. When the spherical harmonic cone lens is manufactured by 3D printing, it is also necessary to determine the refractive index n of the material for 3D printing at the terahertz wavelength λ.
2. Determining the inclination angle gamma and the radius size r of the basic axicon lens; and calculating the edge length b of the basic axicon lens according to the radius dimension r and the inclination angle gamma of the axicon lens,
3. designing special models, i.e. probability density functions, based on the edges of the cross-section of the basic axicon lens
On two oblique edges of the axicon, the end points of the first oblique edge and the second oblique edge are used as a new coordinate system, and spherical harmonics are added on the extension of the axicon
Square of (probability density function) trend-type convex model:
wherein l is the number of angular quanta, m is the number of magnetic quanta, theta is the height angle,
is the azimuth angle. N is a radical oflmA constant value associated with l and m,
as can be seen from the characteristics of spherical harmonics, there are (2l +1) different eigenfunctions
Different angle quantum numbers and spherical harmonic models are different, and the formed convex trend is different. Preferably, l ═ m, that is:
in this model, the range of the elevation angle θ is (0, π/2), and the azimuth angle is
The range is (0,2 π), i.e., the two-dimensional model rotates. The probability density function is a three-dimensional model formed by rotating one circle of the two-dimensional graph related to the elevation angle.
And converting the function from a polar coordinate system to a rectangular coordinate system.
x＝Wcos(θ)；
y＝Wsin(θ)；
Substituting the above formula to obtain an expression in the rectangular coordinate system as follows:
since l ═ m, i.e.:
from this, it can be seen that the coefficient N is changed2 mmThis only scales the model ratio column and does not change the convex trend. Increase in the extension of axiconThe protrusions are formed by increasing the probability density function curve trend outside the oblique edges of the axicon by taking the oblique edges of the axicon as an x axis, taking the intersection point of the two oblique edges as a coordinate origin and taking a normal perpendicular to the oblique edges as a y axis.
4. Since the actual minimum thickness of the lens cannot be 0, the base thickness h of the special lens element is added as shown in fig. 1-2.
5. And manufacturing the designed special terahertz lens element by using a 3D printer.
The spherical harmonic cone lens for generating a non-diffracted beam in the terahertz waveband provided by the invention is further explained by using a specific example.
Determining the wavelength λ of the terahertz gaussian beam used in the design of the terahertz special spherical harmonic cone lens to be 3mm (it is understood that the lens is equally applicable to other terahertz gaussian beam wavelengths); determining the beam waist radius of the terahertz Gaussian beam to be omega according to the propagation dynamics of the terahertz Gaussian beam in the experiment025 mm; determining that a refractive index n of a material for 3D printing is 1.6 when a terahertz wavelength is lambda is 3 mm; determining a basic axicon lens inclination angle gamma of 15 degrees for the transform design; the basic axicon lens for the transform design was sized to be 3 inches with a radius length r of 38.1 mm; the edge length b of the basic axicon lens is calculated according to the radius dimension r of the basic axicon lens being 38.1mm and the base angle gamma being 15 degrees,
establishing a new rectangular coordinate system by taking the intersection point of two inclined edges of the basic axicon lens as the origin of coordinates, taking the inclined edge of the axicon as an x axis, and taking a normal perpendicular to the inclined edge as a y axis, and establishing a probability density function (namely the square of a spherical harmonic function) on the rectangular coordinate system:
the selected spherical harmonic model structure is l ═ m, and the expression of the above formula in the rectangular coordinate system is as follows:
the coefficient N is due to the fact that the length of the bottom edge is 3 inches and the bottom angle is 15 degrees2 mm38.1/cos (15 deg.), so that the probability density function can create a coincident extension bump on the pyramid hypotenuse, i.e.:
the value of m was gradually increased from 1 to 20, for a total of 20 simulations, and longer diffraction-free distances were produced at values of m between 9 and 13. Compared with simulation results, when l is 9, the diffraction-free distance is longest. When m is less than 8, substantially no diffraction-free light beam is generated and spread to both sides.
When l ═ m ═ 9:
the base angle γ is 15 ° of axicon extension, where the bump of the established spherical harmonic yields the longest diffraction-free distance. In the modeling, a cartesian coordinate system is used, and the expression of the formula is represented by a spherical coordinate system, so that the formula is converted into a cartesian coordinate system:
namely:
x ranges from 0 to 39.444mm, increasing the convexity of the trend of the probability density function curve outside the oblique edges of the axicon, as shown in figure 1.
The practical minimum thickness of the lens cannot be 0, and the bottom thickness h of the additional special lens element is 2 mm; and a 3D printer is used for manufacturing the designed special terahertz lens element.
A Gaussian beam obtained through FDTD (finite difference time domain) simulation calculation passes through the special conical lens to generate a special non-diffraction beam, the two-dimensional intensity distribution is shown in figure 3, z is the propagation direction, the central light intensity curve of the special non-diffraction beam propagated in the z direction is shown in figure 4, and the non-diffraction distance of the beam can be obtained by taking the full width at half maximum FWHM of the central light intensity curve;
the embodiment of the invention provides a terahertz imaging system which comprises a spherical harmonic cone lens capable of generating a non-diffraction beam in a terahertz waveband.
It will be understood by those skilled in the art that the foregoing is only a preferred embodiment of the present invention, and is not intended to limit the invention, and that any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the scope of the present invention.
Claims (6)
1. The spherical harmonic cone lens is characterized in that the spherical harmonic cone lens is an axicon lens with bulges on two oblique sides;
the two end points of the bulge are overlapped with the two end points of the bevel edge, the shape of the bulge is determined based on a probability density function, and the probability density function is the square of a spherical harmonic function;
under a rectangular coordinate system, the expression of the probability density function is as follows:
wherein l is the number of angular quanta, m is the number of magnetic quanta,
under a polar coordinate system, the expression of the probability density function is as follows:
wherein theta is an altitude angle,
is the azimuth, l is the number of angular quanta, m is the number of magnetic quanta, Pl mIn order to be a function of legendre,
2. the spherical harmonic axicon for generating a non-diffracted beam in the terahertz wavelength band as defined in claim 1, wherein l is m.
3. The spherical harmonic axicon lens for generating a non-diffracted beam in the terahertz wave band as defined in claim 2, wherein m is 1. ltoreq. m.ltoreq.20.
4. The spherical harmonic cone lens for generating a non-diffracted beam in the terahertz waveband of claim 1, wherein the bottom surface of the spherical harmonic cone lens is 2mm thick.
5. The spherical harmonic axicon lens for producing a non-diffracted beam in the terahertz waveband of claim 1, wherein the spherical harmonic axicon lens is made by 3D printing.
6. A terahertz imaging system is characterized by comprising the spherical harmonic cone lens for generating a non-diffraction light beam in the terahertz wave band according to any one of claims 1 to 5.
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| JPH01191801A (en) * | 1988-01-28 | 1989-08-01 | Sumitomo Electric Ind Ltd | Condenser lens |
| JP2009082958A (en) * | 2007-09-28 | 2009-04-23 | Sunx Ltd | Laser beam machining apparatus and axicon lens |
| CA2668095A1 (en) * | 2009-06-02 | 2010-12-02 | Algonquin College | Axicon lens array |
| DE102014213775B4 (en) * | 2014-07-15 | 2018-02-15 | Innolas Solutions Gmbh | Method and device for laser-based processing of flat, crystalline substrates, in particular of semiconductor substrates |
| KR20170019855A (en) * | 2015-08-13 | 2017-02-22 | 한국기계연구원 | Multi-Angle Axicon Lens for Increased Laser Processing Efficiency of Bessel Beam |
| CN105891916B (en) * | 2016-06-26 | 2018-08-14 | 上海嘉强自动化技术有限公司 | A kind of aspherical mirror based on axicon lens Yu focus lamp characteristic |
| CA3170860A1 (en) * | 2020-02-21 | 2021-08-26 | Tornado Spectral Systems Inc. | Optical spectroscopy probe configurations for focusing light to a portion of a sample |
| CN112540055B (en) * | 2020-11-20 | 2021-12-03 | 华中科技大学 | Terahertz laminated imaging method and system with Bessel beam as probe |
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