Method and system for tomography imaging of mid-infrared near field in medium and light field reconstruction algorithm

Abstract

The invention belongs to the technical field of ultrafast nonlinear optics, and particularly relates to a method and a system for tomography imaging of an intermediate infrared near field in a medium and a light field reconstruction algorithm. According to the method, a focused intermediate infrared pulse light beam is used for exciting a detection object, and a near infrared pulse light beam is coaxially focused on the detection object; enabling the detection object to generate high-order sideband harmonic radiation, and recording sideband harmonic spectrum and light field information; moving the detection object in a plane perpendicular to the near-infrared pulse light beam, and performing surface scanning on the detection object to obtain an image of a mid-infrared near field of the detection object; the radius of the near-infrared pulse light beam focused to the focusing light spot reaches the diffraction limit. Compared with the prior art, the problems that in the prior art, due to physical property limitation of a probe, the detection depth of a block dielectric material is small, and a near-field light field in the dielectric material cannot be detected are solved, and multi-dimensional measurement of polarization, depth distribution and phase of a mid-infrared light field is achieved.

Description

Technical Field

[0001] The present invention belongs to the field of ultrafast nonlinear optics technology, and specifically relates to a method and system for mid-infrared near-field tomographic imaging in a medium and a light field reconstruction algorithm. Background Art

[0002] Near-field optics is a branch of optics that studies and manipulates light-matter interactions and the coupling between light fields and micro-nanostructures at scales smaller than the wavelength of light. Imaging and manipulating optical structures and devices at the nanoscale are crucial for studying and understanding materials and devices at the nanoscale.

[0003] Near-field optics is important for several reasons. First, it allows us to image and manipulate structures and devices smaller than half the wavelength of light, providing a key tool for nanoscale research. Second, near-field optics can overcome the diffraction limit of traditional optical microscopy, providing higher spatial resolution. This is crucial for the development of nanophotonic devices such as nanoantennas, waveguides, and resonators, which have important applications in communications, sensing, and nanoscale imaging.

[0004] At present, commonly used technologies for detecting the near-field distribution of light fields include scanning near-field optical microscopy (SNOM), electron energy loss spectroscopy (EELS) and cathodoluminescence scanning electron microscopy (CLSEM). SNOM technology is based on the development of scanning tunneling microscopy (STM) [Physical Review Letters, 1982, 49 (1): 57.] and atomic force microscopy (AFM) [Physical Review Letters, 1986, 56 (9): 930.], and is an imaging device used to break through the optical resolution. SNOM can overcome the diffraction limit resolution of optical imaging, and can not only achieve nanoscale resolution imaging, but also be used to explore the spectral characteristics of materials and structures. EELS technology and CLSEM technology are based on the development of transmission electron microscopy (TEM) [Patent: US22677137A] and scanning electron microscopy (SEM) [Zeitschrift für Technische Physik, 1935, 16: 467.]. Both use the high spatial resolution provided by the electron beam to achieve nanoscale spatial resolution. The former measures the distribution of the local near field by the loss of electron energy because the electron energy is sensitive to the local electric field, while the latter uses the cathode luminescence effect generated by the coupling of the incident high-energy electron external field and the nanostructure mode to detect the mode electric field distribution of the structure.

[0005] However, due to the limitations of the physical properties of the probes used, the above methods are unable to deeply detect the near-field distribution of the mode electric field in bulk dielectric materials. The SNOM method usually uses a nanometer-scale metal needle tip as a probe, which can only detect the electric field distribution within 100nm below the surface at most. As for EELS technology and CLSEM technology, since the detection depth of the electron beam as a probe in the material is extremely short, it can usually only penetrate and detect the electric field mode distribution in dielectric materials with nanometer thickness. At the same time, the application of the above technologies is usually limited to the near-infrared and visible light bands, and there are few applications for mid-infrared near-field detection. Summary of the Invention

[0006] The purpose of the present invention is to solve at least one of the above problems and to provide a method and system for mid-infrared near-field tomographic imaging in a medium and a light field reconstruction algorithm, so as to solve the problem in the prior art that the detection depth of bulk dielectric materials is shallow and the near-field light field inside the dielectric material cannot be detected due to the limitations of the physical properties of the probe. This solution realizes multi-dimensional measurement of the polarization, depth distribution and phase of the mid-infrared light field.

[0007] The purpose of the present invention is achieved through the following technical solutions:

[0008] The first aspect of the present invention discloses a method for mid-infrared near-field tomographic imaging in a medium, which comprises exciting a detection object with a focused mid-infrared pulse beam, and coaxially focusing a near-infrared pulse beam on the detection object, causing the detection object to generate high-order sideband harmonic radiation (corresponding to English: high-order sideband generation or high-order sideband radiation, i.e., it is a high-order sideband harmonic), recording the sideband harmonic spectrum and light field information; moving the detection object in a plane perpendicular to the near-infrared pulse beam, performing a surface scan on the detection object, and obtaining a mid-infrared near-field imaging of the detection object;

[0009] The detection object includes a dielectric material and an optical microstructure carried on the surface of the dielectric material;

[0010] The near-infrared pulse light beam is focused until the radius of the focused light spot reaches the diffraction limit.

[0011] Preferably, one or more of the following are included:

[0012] (i) The wavelength of the mid-infrared pulse beam is 5-20 μm, the corresponding photon energy is 0.248-0.062 eV, the pulse length is 100 fs-10 ps, ​​the peak field strength is 0-10 MV / cm, and the diameter of the focused spot of the mid-infrared pulse beam on the detection object is 10-100 μm;

[0013] (ii) the wavelength of the near-infrared pulse beam is 300-1500 nm, corresponding to a photon energy of 4.13-0.83 eV, a pulse length of 50-500 fs, a pulse energy of 5 nJ-10 μJ, and a diameter of a focused spot of the near-infrared pulse beam on the detection object is 300-1500 nm;

[0014] (iii) the optical microstructure is made of metal or the same material as the dielectric material, and the dielectric material includes silicon dioxide, silicon, and lithium niobate;

[0015] (iv) The frequency of the high-order sideband harmonic radiation satisfies ω HSE =mω NIR +nω MIR , where: ω is the frequency, subscript HSE is the higher-order sideband harmonic radiation, subscript NIR is the near-infrared pulse beam, subscript MIR is the mid-infrared pulse beam, m is a positive integer, and n is an integer.

[0016] Preferably, the method:

[0017] Polarization resolution is achieved by scanning the linear polarization state of the near-infrared pulse beam;

[0018] By expanding the spectral bandwidth of the near-infrared pulse beam, adjacent sideband harmonic spectra overlap to form spectral interference, thus achieving phase resolution.

[0019] Tomography is achieved by fitting the imaging data of sideband harmonic spectra of different orders.

[0020] A second aspect of the present invention discloses a system for mid-infrared near-field tomographic imaging in a medium, which is used to implement any of the above methods, comprising: a near-infrared detection light source, a mid-infrared excitation light source, a first dichroic lens, a first wide-spectrum objective lens, a multi-dimensional displacement platform, a second wide-spectrum objective lens, a first lens, and a spectrometer;

[0021] The near-infrared pulse beam is emitted by a near-infrared detection light source, and the mid-infrared pulse beam is emitted by a mid-infrared excitation light source; the detection object is set on a multi-dimensional displacement platform;

[0022] After the near-infrared pulse beam and the mid-infrared pulse beam are coaxially combined by the first dichroic lens, they are coaxially focused on the detection object through the first wide-spectrum objective lens. The high-order sideband harmonic radiation generated by the detection object is collected by the second wide-spectrum objective lens and focused by the first lens into the spectrometer.

[0023] Preferably, the near-infrared detection light source is arranged through a combination of a half-wave plate and a polarizer to achieve continuous control of the light field energy and polarization state of the near-infrared pulse light beam; the mid-infrared excitation light source is arranged through a polarizer or a combination of polarizers to achieve control of the light field intensity and polarization state of the mid-infrared pulse light beam.

[0024] Preferably, the first dichroic lens is a wide-spectrum indium tin oxide coated lens or a metal reflective lens with a central through hole; the first wide-spectrum objective lens is a reflective objective lens with a numerical aperture of 0.28; and the second wide-spectrum objective lens is a transmissive or reflective objective lens with a numerical aperture of 0.40.

[0025] Preferably, the near-infrared pulse beam and the mid-infrared pulse beam are emitted by the same femtosecond laser pulse as a seed light source;

[0026] The femtosecond laser pulse is split into two sub-beams by the first near-infrared beam splitter, wherein the fourth sub-beam with high light intensity passes through a mid-infrared excitation light source to obtain a mid-infrared pulse beam, and the third sub-beam with weak light intensity passes through a near-infrared detection light source to obtain a near-infrared pulse beam.

[0027] Preferably, in the near-infrared detection light source: the third sub-beam is incident on a solid material or gas plasma to form a supercontinuum beam, and then the dispersion and central wavelength of the dispersion compensation device are adjusted through a prism, and then the bandwidth is adjusted through a color filter to obtain a near-infrared pulse beam.

[0028] Preferably, in the mid-infrared excitation light source: the fourth sub-beam is then split into a second sub-beam with strong light intensity and a first sub-beam with weak light intensity by a second near-infrared beam splitter; the first sub-beam is incident on the second dichroic lens after adjusting the beam energy by a half-wave plate and a polarizer; the second sub-beam is generated as a wavelength-shifted offset beam by a femtosecond laser wavelength adjustment device, and then the beam energy is adjusted by a half-wave plate and a polarizer before being incident on the second dichroic lens; the beams coaxially merged by the second dichroic lens are focused on a nonlinear crystal for difference frequency to form a mid-infrared pulse beam.

[0029] Preferably, the mid-infrared excitation light source further includes: a first time-delay displacement platform provided with a beam reflecting lens, wherein the first time-delay displacement platform is arranged on the optical path of the first sub-beam and adjusts the optical path of the first sub-beam by mechanical movement.

[0030] The third aspect of the present invention discloses a light field reconstruction algorithm for reconstructing mid-infrared near-field data obtained in any of the above methods.

[0031] The (m,n)th order sideband harmonic intensity generated by m near-infrared photons and n mid-infrared photons is shown in formula (1):

[0032]

[0033] In formula (1), x and y represent the spatial coordinates of the detection spot in the xy plane, z represents the depth from the surface into the dielectric material, H is the total thickness of the dielectric material at the plane position (x, y), and E is MIR (x, y, z) represents the electric field intensity of the mid-infrared light field at the spatial position (x, y, z);

[0034] In formula (1), g m,n (z) is determined by the properties of the dielectric material and the near-infrared detection light field, as shown in formula (2):

[0035]

[0036] In formula (2), χ m,n is the optical susceptibility constant of the dielectric material during the generation of high-order sideband harmonics, E0 represents the intensity of the incident near-infrared detection light field, S pr (z) is the distribution coefficient of the standing wave electromagnetic field formed at z after the near-infrared light is reflected inside the dielectric material, U m,n (z) is the coefficient of the (m,n)th order sideband harmonic electromagnetic field generated at z that transmits out of the sample; where S pr The (z) function depends on the refractive index of the material and substrate at near-infrared wavelengths, U m,n The (z) function depends on the refractive index of the material and substrate at the (m,n)th order sideband harmonic wavelength, that is, S pr (z), U m,n (z) Determined by the properties of the dielectric material;

[0037] Define the fitting error function of the (x, y) position in the plane as shown in formula (3):

[0038]

[0039] In equation (3), the summation on the right side of the equation covers the selected solid sideband harmonic orders, is the experimentally measured intensity of the sideband harmonics (m,n) at the position (x,y) in the plane, is the intensity of the sideband harmonics (m,n) at the position (x,y) in the plane simulated theoretically;

[0040] As shown in formula (4):

[0041]

[0042] In formula (4), β m,nis an intensity normalization constant related only to the sideband harmonic order (m,n), which is used to directly compare the sideband harmonic intensities measured experimentally and calculated by the model;

[0043] The first step of the reconstruction algorithm is to fit the cross-sectional data of the experimentally measured detection object to obtain the intensity normalization constant β corresponding to different sideband harmonic orders (m, n) m,n ; Use the Broyden-Fletcher-Goldfarb-Shanno algorithm to find the β that minimizes the error function J(x,y) m,n and E under this section MIR (x,y,z);

[0044] The second step of the reconstruction algorithm: fixing the intensity normalization constant β m,n , the three-dimensional spatial distribution E of the mid-infrared near field is fitted by the Broyden-Fletcher-Goldfarb-Shanno algorithm MIR (x,y,z).

[0045] The working principle of the present invention is:

[0046] The present invention mainly utilizes the high-order sideband harmonic process of the strong mid-infrared excitation light field (MIR) and the weak near-infrared detection light field (NIR) in the dielectric material. In the high-order sideband harmonic process, when these two lights are combined in the dielectric material, many new frequencies are generated. These new frequencies are also called sideband harmonic radiation (HSE). The sideband harmonic radiation frequency satisfies ω HSE =mω NIR +nω MIR , m is a positive integer, n is an integer, and for centro-inversion symmetric materials, m+n is an odd integer. (Considering the specific near-infrared light field intensity in this scheme, typically only m ≤ 2 near-infrared photons participate. For the generation condition of m = 1, n is an even integer, while for the generation condition of m = 2, n is an odd integer.)

[0047] First, because the intensity of high-order sideband harmonic radiation (HSE) is very sensitive to the intensity of the mid-infrared light field, the mid-infrared near-field intensity at different positions in different planes of the sample can be directly measured by the intensity of the HSE beam. The spatial resolution of HSE measurements is determined by the smaller spot diameter of the two lights in the medium. By tightly focusing the near-infrared detection spot to the diffraction limit, sub-micron spatial resolution can be provided during the measurement process. By scanning the sample position in the xy plane, spatial imaging of the mid-infrared near field can be achieved.

[0048] Second, because the intensity of the high-order sideband harmonic radiation is sensitive to the angle between the linear polarization of the near-infrared probe beam and the polarization direction of the mid-infrared near-field, near-field imaging can be measured by polarizing the near-infrared probe beam along the x- and y-directions of the sample, obtaining imaging results for different polarization components of the mid-infrared near-field.

[0049] Third, by analyzing the imaging results of different frequency components of high-order sideband harmonic radiation, the light field distribution at different depths in the near field of the mid-infrared light field in the dielectric material can be reconstructed. Here, the different frequency components of the high-order sideband harmonics can be the sideband harmonic radiation at a fixed near-infrared detection light field frequency (ω NIR ) under different order (n) conditions, or it can be the same order harmonic scanning near-infrared light field frequency (ω NIR )get.

[0050] Fourth, by fixing the near-infrared detection light frequency (ω NIR ) under the condition of making the high-order sideband harmonic spectra of different orders (n) overlap with each other, realizing the detection of mid-infrared near-field phase changes in dielectric materials. Here, the overlap of different order harmonic spectra can be controlled by controlling the near-infrared detection light field bandwidth Δω NIR to achieve.

[0051] Compared with the prior art, the present invention has the following beneficial effects:

[0052] 1) The present invention provides a high-resolution imaging method for the near-field distribution of mid-infrared light fields inside dielectric materials.

[0053] 2) The present invention has the ability to sensitively detect the intensity, polarization, depth distribution and phase of the mid-infrared light field. BRIEF DESCRIPTION OF THE DRAWINGS

[0054] Figure 1 A schematic diagram of the partial structure of a device for mid-infrared near-field tomography imaging in a medium;

[0055] Figure 2 Schematic diagram of the structure of a device for mid-infrared near-field tomography imaging in a medium;

[0056] Figure 3 This is a schematic diagram of the principle of the solid high-order sideband harmonic process;

[0057] Figure 4 Schematic diagram of the structure of the near-infrared detection light source and the mid-infrared excitation light source;

[0058] Figure 5 This is a microscope photo of the arrayed gold nanoantenna structure in Example 1;

[0059] Figure 6is the spectrum of the (1,2)-order sideband harmonics generated in the silicon substrate in Example 1;

[0060] Figure 7 Graph showing the variation of the (1,2)-order sideband harmonic intensity with the linear polarization direction of the near-infrared pulse beam in Example 1;

[0061] Figure 8 The mid-infrared near-field distribution inside the silicon substrate around a single gold nanoantenna structure measured in the experiment in Example 1, wherein (a) shows the mid-infrared near-field image polarized in the x-direction, and (b) shows the mid-infrared near-field image polarized in the y-direction;

[0062] Figure 9 The mid-infrared near-field distribution inside the silicon substrate around a single gold nanoantenna structure theoretically simulated in Example 1, wherein (a) shows the mid-infrared near-field image polarized in the x-direction, and (b) shows the mid-infrared near-field image polarized in the y-direction;

[0063] Figure 10 This is a microscope photograph of the silicon pillar structure in Example 2;

[0064] Figure 11 This is a spectrum of solid high-order sideband harmonics generated in the silicon pillar in Example 2;

[0065] Figure 12 The spatial resolution measurement results of the device in Example 2, where (a) is the (1, 2) order harmonic result and (b) is the (2, 1) order harmonic result;

[0066] Figure 13 is the variation law of the (2,1)-order sideband harmonic intensity with the polarization angle θ of the near-infrared pulse beam in Example 2;

[0067] Figure 14 The light intensity distribution of the mid-infrared near field in the silicon pillar of the (2,1)-order sideband harmonic imaging experimentally measured in Example 2, where (a) is the component polarized along the x-direction and (b) is the component polarized along the y-direction;

[0068] Figure 15 The light intensity distribution of the mid-infrared near field in the silicon pillar of the (2,1)-order sideband harmonic imaging theoretically simulated in Example 2, where (a) is the component polarized along the x-direction, and (b) is the component polarized along the y-direction;

[0069] Figure 16 The imaging results and reconstruction fitting results of different orders in Example 3;

[0070] Figure 17 The sideband harmonic intensities of different orders (m, n) at the cross section at x=0 in Example 3, and the fitting results obtained by the reconstruction algorithm;

[0071] Figure 18 3D mid-infrared near-field distribution diagram of the silicon pillar in Example 3, where (a) is the theoretical simulation result and (b) is the reconstructed near-field distribution based on the experimental results;

[0072] Figure 19 The mid-infrared near-field intensity distribution along the y=0 section obtained by theoretical simulation and experimental reconstruction in Example 3, where (a) is the theoretically simulated near-field distribution and (b) is the near-field distribution obtained by experimental reconstruction;

[0073] Figure 20 Schematic diagram of the phenomenon of adjacent sideband harmonic order spectral overlap and quantum channel interference caused by expanding the near-infrared detection beam bandwidth in Example 3;

[0074] Figure 21 Graphs showing the experimentally measured and theoretically simulated spectral interference at different spatial locations in Example 3, where (a) shows the imaging intensity and phase distribution in the xy plane, (b) shows the experimentally measured evolution of the spectral interference along paths (i) and (ii), and (c) shows the theoretically simulated evolution of the spectral interference along paths (i) and (ii).

[0075] Figure 22 for Figure 21 The mid-infrared near-field phase results along paths (i) and (ii) obtained from experimental measurements and theoretical simulations;

[0076] Reference numerals: 1-mid-infrared pulse beam; 2-optical microstructure; 3-dielectric material; 4-near-infrared pulse beam; 5-high-order sideband harmonic radiation; 6-first terahertz polarizer; 7-second terahertz polarizer; 8-first near-infrared half-wave plate; 9-first polarizer; 10-second time-delay displacement platform; 11-first dichroic lens; 12-first wide-spectrum objective lens; 13-second wide-spectrum objective lens; 14-first lens; 16-femtosecond laser pulse; 17-first near-infrared beam splitter; 18-second near-infrared beam splitter; 1 9-first sub-beam; 20-second sub-beam; 21-third sub-beam; 22-second near-infrared half-wave plate; 23-second polarizer; 24-offset beam; 25-third half-wave plate; 26-third polarizer; 27-second dichroic lens; 28-second lens; 29-nonlinear crystal; 30-silicon wafer; 31-off-axis parabolic mirror; 32-first time-delay displacement platform; 33-third lens; 34-solid material; 35-supercontinuum beam; 36-prism dispersion compensation device; 37-slit; 38-color filter. DETAILED DESCRIPTION

[0077] The present invention will be described in detail below with reference to the accompanying drawings and specific embodiments.

[0078] In the following description, unless otherwise specified, the reagents used are conventional commercial products, and the methods used are well known in the art.

[0079] Figure 1 A partial schematic diagram of the core detection area of ​​the polarization- and phase-resolved mid-infrared near-field tomography imaging device is shown. The device excites an optical microstructure 2 supported by a dielectric material 3 (serving as a substrate) via a focused, intense mid-infrared pulse beam 1 (mid-infrared excitation light). The optical microstructure 2 is supported by a dielectric material 3 (serving as a substrate). (The dielectric material 3 and the optical microstructure 2 are collectively referred to as the detection target.) The optical microstructure 2 is made of metal or the same material as the dielectric material 3. The excitation of the mid-infrared pulse beam 1 creates a mid-infrared light field pattern distribution within the optical microstructure 2 and the dielectric material 3. Furthermore, a weaker near-infrared pulse beam 4 (near-infrared probe light) is tightly focused on the optical microstructure 2 and the dielectric material 3, with the focused spot radius reaching the diffraction limit. Through the high-order sideband harmonic generation process, high-order sideband harmonic radiation 5, covering the infrared to visible wavelength range, is emitted from the area illuminated by the tightly focused near-infrared pulse beam 4. This high-order sideband harmonic radiation 5 is then fed into a spectrometer via a collection optical path, where the light field information is recorded. To achieve near-field distribution imaging of the mid-infrared light field in the xy plane, a multi-dimensional displacement platform with at least two-dimensional displacement function is used to move the detection object in the xy plane, so that the focused spot of the near-infrared pulse beam 4 scans the sample surface and records the sideband harmonic spectrum.

[0080] Figure 2 A schematic diagram of the structure of the mid-infrared near-field tomography imaging device is shown. The mid-infrared pulse beam 1 of the device is generated by a mid-infrared excitation light source. The mid-infrared pulse beam 1 passes through a pair of terahertz polarizers (a first terahertz polarizer 6 and a second terahertz polarizer 7, arranged sequentially along the optical path) to control the intensity of the excitation light field. The second terahertz polarizer 7 directly determines the polarization direction of the mid-infrared excitation light field, while the angle between the first terahertz polarizer 6 and the second terahertz polarizer 7 determines the intensity of the excitation light field.

[0081] On the other hand, a near-infrared pulsed light beam 4 is generated by a near-infrared detection light source device. This near-infrared pulsed light beam 4 continuously controls the energy, linear polarization direction, and optical path of the detection light field through a first near-infrared half-wave plate 8, a first polarizer 9, and a second time-delay displacement platform 10, which are sequentially arranged along the optical path. The combination of the first near-infrared half-wave plate 8 and the first polarizer 9 continuously controls the intensity and linear polarization direction of the detection light. The second time-delay displacement platform 10 is equipped with a series of beam reflectors. By mechanically moving the beam reflectors, the optical path of the near-infrared pulsed light beam 4 is adjusted to be equal to that of the mid-infrared pulsed light beam 1, ultimately ensuring that the near-infrared pulsed light beam 4 and the mid-infrared pulsed light beam 1 arrive at the sample surface simultaneously.

[0082] The mid-infrared pulse beam 1 and the near-infrared pulse beam 4 are then coaxially combined by the first dichroic lens 11. Here, the mid-infrared pulse beam 1 is reflected by the first dichroic lens 11, while the near-infrared pulse beam 4 passes through the first dichroic lens 11 from behind. The dichroic lens can be a wide-spectrum indium tin oxide (ITO)-coated lens or a metal reflective lens with a central through-hole. The coaxially combined beams are then coaxially focused on the optical microstructure 2 and the dielectric material 3 by the first wide-spectrum objective lens 12. The wide-spectrum objective lens can be a reflective objective lens or a transmissive objective lens. The numerical aperture of the first wide-spectrum objective lens 12 is 0.28. The optical microstructure 2 is supported on the dielectric material 3 and mounted together on a multi-dimensional displacement platform. The multi-dimensional displacement platform has three-dimensional (xyz) translation and in-plane rotation (θ) degrees of freedom.

[0083] After the mid-infrared pulse beam 1 and the near-infrared pulse beam 4 are focused, the high-order sideband harmonic radiation 5 generated within the optical microstructure 2 and / or dielectric material 3 is collected by a second broadband objective lens 13, which has a numerical aperture of 0.40. The high-order sideband harmonic radiation 5 is then focused by a first lens 14 and enters the spectrometer, where its spectral information is recorded.

[0084] In this device, the mid-infrared excitation light source can be generated by two femtosecond laser pulses 16 of different frequencies in a nonlinear crystal 29 (such as GaSe, AgGaS2, etc.) through a nonlinear difference frequency process, or it can be generated by a large light source device including a free electron laser. The near-infrared detection light source needs to have wide spectrum and wavelength tunability. It can be generated by a near-infrared supercontinuum spectrum of femtosecond laser pulses 16 in a solid material 34 or gas plasma, or by using a femtosecond laser wavelength adjustment device such as an optical parametric amplifier (OPA). The two pulsed lasers need to be synchronized in repetition rate and time delay by the same femtosecond laser as the seed light source.

[0085] The high-order sideband harmonic generation process inside the dielectric material 3 can be described by the high-order mixing process of two beams of different frequencies. For the (m,n)th order sideband harmonic generation process, there are m near-infrared photons and n mid-infrared excitation photons Participation, that is m is a positive integer, n is an integer, and for centroinversion symmetric materials, m + n is an odd number. Considering the intensity of the near-infrared light field in this device, typically only m ≤ 2 near-infrared photons participate. Therefore, for the generation condition of m = 1, n is an even integer, while for the generation condition of m = 2, n is an odd integer. Figure 3 Schematic diagrams of sideband harmonic generation in the above two cases are shown.

[0086] In this device, imaging of the mid-infrared near-field light within dielectric material 3 is achieved by scanning in the xy plane. The multi-dimensional displacement stage used for scanning has a travel range of 65 mm and an accuracy of 5 nm. The polarization direction of the near-infrared excitation light field can be changed by rotating the sample in the θ direction within the plane.

[0087] Example 1

[0088] This embodiment provides an imaging device for detecting the mid-infrared near-field distribution and polarization state inside the dielectric material 3 around the metal nanostructure.

[0089] The overall structure of the imaging device is as follows Figure 2 As shown, Figure 4 The method for generating a mid-infrared pulse beam 1 and a near-infrared pulse beam 4 is further specifically illustrated. Both beams are generated by the same femtosecond laser, which generates femtosecond laser pulses 16 with an energy of 1 mJ, a pulse duration of 170 fs, a wavelength of 1030 nm, and a repetition rate of 5 kHz. The femtosecond laser beam is first split by a first near-infrared beam splitter 17 into a fourth sub-beam with a higher intensity and a third sub-beam 21 with a lower intensity. The fourth and third sub-beams 21 are then input into a mid-infrared excitation light source and a near-infrared detection light source for processing, respectively. After the fourth sub-beam is input into the mid-infrared excitation light source, it is further split by a second near-infrared beam splitter 18 into a second sub-beam 20 with a higher intensity and a first sub-beam 19 with a lower intensity. The beam energies of the third sub-beam 21, the second sub-beam 20, and the first sub-beam 19 are 15%, 83%, and 2%, respectively (as a proportion of the energy of the femtosecond laser pulse 16).

[0090] To generate the mid-infrared pulse beam 1, the first sub-beam 19 passes through a combination of a second near-infrared half-wave plate 22 and a second polarizer 23, enabling continuous adjustment of the beam's energy. The second sub-beam 20 is then fed into an optical parametric amplifier (OPA), generating a wavelength-shifted offset beam 24 with a pulse energy of 50 μJ and a wavelength of 1118 nm. The offset beam 24 then passes through a combination of a third half-wave plate 25 and a third polarizer 26, enabling continuous adjustment of the beam's energy. The adjusted first sub-beam 19 and offset beam 24 are then coaxially combined by a second dichroic lens 27 and focused by a second lens 28 onto a nonlinear crystal 29, generating the mid-infrared pulse beam 1 through a difference frequency process. Here, nonlinear crystal 29 is a 1 mm thick GaSe crystal. The generated mid-infrared pulse beam 1 then passes through a silicon wafer 30 at the Brewster angle to filter out the near-infrared pulse beam 4, before being collimated by an off-axis parabolic mirror 31. In the mid-infrared excitation light source, before the first sub-beam 19 enters the second near-infrared half-wave plate 22, it also passes through a first delay displacement platform 32 provided with a plurality of beam reflecting lenses. The first delay displacement platform 32 can adjust the optical path of the first sub-beam 19 so that the two beams input into the nonlinear crystal 29 can achieve temporal and spatial overlap in the pulse.

[0091] To generate the near-infrared pulse beam 4, the third sub-beam 21 is focused by a third lens 33 onto a 5 mm thick YAG crystal (solid material 34), generating a supercontinuum beam 35, which is then collimated by another third lens 33. The supercontinuum beam 35 is then fed into a prism dispersion compensation device 36 to adjust the dispersion of the beam pulses. This device also includes an adjustable slit 37, which further adjusts the central wavelength of the beam. After being processed by the prism dispersion compensation device 36, the beam is further fed into a color filter 38 for bandwidth adjustment, resulting in the near-infrared pulse beam 4.

[0092] In this embodiment, the optical microstructure 2 in the detection object is a gold nanoantenna structure arranged in an array. Figure 5 As shown, the structure is 2.80μm long, 0.95μm wide, and 90nm thick. The spacing between structures in the x and y directions is 7.00μm. The gold nanoantenna array is grown on a 140nm thick silicon film (dielectric material 3), which is grown on a 500μm thick optical glass by magnetron sputtering. The entire gold nanoantenna array is prepared by micro-nano processing technology. When the mid-infrared light pulse beam excites the antenna array, a transient plasmon electric field is generated around the gold nanostructure, and the electric field penetrates deep into the silicon substrate. When the near-infrared detection pulse light is incident on the silicon substrate area, the high-order sideband harmonic signal intensity represents the near-field intensity of the mid-infrared light field in the silicon substrate.

[0093] Figure 6 The optical spectrum of the (1st, 2nd) sideband harmonics generated in a silicon substrate by two optical beams is presented. In this set of measurements, the mid-infrared excitation light has a wavelength of 13μm and a peak field intensity of 1.0MV / cm, while the near-infrared probe light has a wavelength of 967nm and a pulse energy of 5nJ, focused to a spot diameter of 1μm on the sample. As a result, the (1st, 2nd) sideband harmonic spectrum is generated at a frequency of 842nm (356THz). Figure 7 The figure shows the (1st, 2nd) order harmonic spectrum intensity diagram obtained by scanning the angle between the polarization direction of the near-infrared pulse beam 4 and the polarization direction of the mid-infrared pulse beam 1 while keeping the polarization direction of the mid-infrared pulse beam 1 fixed. The polarization direction of the near-infrared pulse beam 4 can be changed by the first near-infrared half-wave plate 8 and the first polarizer 9. The figure shows that when the angle θ between the polarization direction of the near-infrared pulse beam 4 and the polarization direction of the mid-infrared pulse beam 1 is 0° or 180°, the harmonic intensity is maximum. Conversely, when the angle θ is 90° or 270°, the harmonic intensity is minimum. This gives the device the ability to detect the polarization direction of the mid-infrared light field.

[0094] Figure 8 Figure 2 shows the experimental results of scanning the mid-infrared near-field distribution inside the silicon substrate around a single gold nanoantenna structure. The scanning is achieved by moving the probe object in the xy plane using a mechanical translation stage (multi-dimensional displacement platform). Figure 8 The left figure (a) shows the imaging result of the mid-infrared near field with the polarization direction in the x direction. Figure 8 The right figure (b) shows the mid-infrared near-field imaging results with polarization direction y. The experimental results can be well compared with the simulation calculations (such as Figure 9 The spatial and polarization distributions of the mid-infrared near-field after excitation of the obtained gold nanoantenna are consistent.

[0095] Example 2

[0096] This embodiment provides an imaging device for detecting the mid-infrared near-field intensity and polarization state inside a silicon cylinder with a thickness of micrometer level.

[0097] This embodiment adopts the same device architecture as that of embodiment 1 ( Figure 2 ) and light source generation method ( Figure 4 ).

[0098] The detection object of this embodiment is the mid-infrared near-field distribution inside a silicon cylinder with a thickness of 0.5 μm and a diameter of 5.1 μm. Figure 10 An optical microscope image of a silicon cylinder grown on a fused silica substrate is shown. The silicon cylinder is fabricated using photolithography. Figure 11The high-order sideband harmonic spectrum under the co-excitation of mid-infrared pulse beam 1 and near-infrared pulse beam 4 is shown. The wavelength of near-infrared pulse beam 4 is 967nm, the pulse energy is 5nJ, and the spot diameter focused on the sample is 30μm. The wavelength of mid-infrared pulse beam 1 is 14μm, and the peak field intensity is 6.3MV / cm. The sideband harmonic spectrum contains multiple sideband harmonic peaks, which include two groups of harmonic components: (1) The light frequency satisfies ω NIR +nω MIR , n is an even integer; (2) the optical frequency satisfies 2ω NIR +nω MIR , n is an odd integer. The spectrum covers the range of 410-860nm (350-720THz).

[0099] Figure 12 The spatial resolution of the device is demonstrated by scanning the harmonic intensity of the silicon film boundary with different harmonic orders ((1,2) and (2,1)). When the harmonic order is (1,2) (left image (a)), the device has a spatial resolution of 1.35μm, while when the harmonic order is (2,1) (right image (b)), the device has a spatial resolution of 0.92μm. The nonlinear process of the near-infrared pulse beam 4 helps improve the spatial resolution of the device.

[0100] Figure 13 Figure 3 shows how the (2nd, 1st)-order sideband harmonic intensity changes when the polarization direction of near-infrared pulse beam 4 is rotated. The linear polarization direction of near-infrared pulse beam 4 can be adjusted by rotating the first near-infrared half-wave plate 8 and the first polarizer 9. When the angle θ between the near-infrared pulse beam 4 and the mid-infrared pulse beam 1 is 0° or 180°, the harmonic intensity is maximum. Conversely, when the angle θ is 90° or 270°, the harmonic intensity is minimum. Figure 13 The results show that the imaging device has the ability to detect the polarization direction of the mid-infrared light field inside the medium.

[0101] Figure 14 The device shows the imaging measurement results of the mid-infrared near-field distribution inside a silicon cylinder. A mid-infrared pulse beam 1 excites the silicon cylinder with linear polarization along the x-direction. The sideband harmonics of order (2,1) are selected. Figure 14 (a) shows the intensity distribution of the mid-infrared near-field polarization component along the x-direction, which is measured by rotating the near-infrared pulse beam 4 polarization to θ of 0° or 180°. Figure 14 (b) shows the intensity distribution of the mid-infrared near-field polarization component along the y direction, which is measured by rotating the polarization of the near-infrared pulse beam 4 to θ of 0° or 180°. Figure 15 The distribution results of different polarization components of the mid-infrared light field inside the silicon cylinder obtained by theoretical simulation are presented, verifying Figure 14 The experimental measurement results obtained.

[0102] Example 3

[0103] This embodiment provides an imaging device for detecting the mid-infrared near-field three-dimensional tomographic distribution and phase state inside a silicon cylinder with a thickness of micron level.

[0104] This embodiment adopts the same device architecture as that of embodiment 1 ( Figure 2 ) and light source generation method ( Figure 4 ).

[0105] The detection object of this embodiment is the mid-infrared near-field distribution inside a silicon cylinder with a thickness of 1.5 μm and a diameter of 5.6 μm.

[0106] Figure 16 The image shows the x-polarization component of the mid-infrared near-field distribution inside the same silicon cylinder, obtained by scanning different sideband harmonic orders ((1,2), (1,4), (2,-3), (2,-1), (2,1), and (2,3)). The different patterns obtained with different orders are mainly due to the different phase matching during the generation of higher-order sideband harmonics and the different penetration depths of light of different wavelengths.

[0107] Here, we can design a light field reconstruction algorithm to obtain the light field distribution of the mid-infrared near field inside the silicon cylindrical medium at different depths from the surface. The following will introduce the details of the reconstruction algorithm. According to the microscopic mechanism of the solid sideband harmonic generation process, the intensity of the (m,n)th order sideband harmonic generated by m near-infrared photons and n mid-infrared photons is

[0108]

[0109] Where x and y represent the spatial coordinates of the detection spot in the xy plane, z represents the depth from the surface into the dielectric material 3, H is the total thickness of the dielectric material 3 at the plane position (x, y), and E MIR (x, y, z) represents the electric field intensity of the mid-infrared light field at the spatial position (x, y, z).

[0110] In formula (1), g m,n (z) is a detection "gate function" determined by the properties of the dielectric material 3 and the near-infrared detection light field:

[0111]

[0112] Here, χ m,n is the optical susceptibility constant of dielectric material 3 during the generation of high-order sideband harmonics, E0 represents the intensity of the incident near-infrared detection light field, S pr(z) is the distribution coefficient of the standing wave electromagnetic field formed at z after the near-infrared light is reflected inside the dielectric material 3, U m,n (z) is the coefficient of the (m,n)th order sideband harmonic electromagnetic field generated at z that transmits out of the sample; where S pr The (z) function depends on the refractive index of the material and substrate at near-infrared wavelengths, U m,n The (z) function depends on the refractive index of the material and substrate at the (m,n)th order sideband harmonic wavelength, that is, S pr (z), U m,n (z) is determined by the properties of dielectric material 3.

[0113] Furthermore, the fitting error function of the (x, y) position in the plane is defined as

[0114]

[0115] where the sum on the right side of the equation covers the chosen solid sideband harmonic order, corresponding to m near-infrared photons and n mid-infrared photons, is the experimentally measured intensity of the sideband harmonics (m,n) at the in-plane position (x,y), and the intensity calculated by the model is Then it is given by formula (4)

[0116]

[0117] Here β m,n is an intensity normalization constant that is only related to the sideband harmonic order (m,n), and is used to directly compare the sideband harmonic intensities measured experimentally and calculated by the model.

[0118] In order to facilitate the reconstruction algorithm, the depth (z) distribution of the mid-infrared electric field at each (x0, y0) position can be decomposed using a polynomial: In this way, the reconstruction of the electric field depth distribution is transformed into solving the polynomial coefficient α at each position. j (x,y).

[0119] In the first step of the reconstruction algorithm, we first measure the experimental pattern (such as Figure 16 The high-intensity cross-sectional data (such as a cross-sectional data at position y = y0) are fitted to determine the intensity normalization constant β corresponding to different sideband harmonic orders (m, n) m,n The reconstruction algorithm uses the Broyden-Fletcher-Goldfarb-Shanno algorithm to find E that minimizes the error function J(x,y). MIR (x,y0,z) and β m,n . Figure 17The experimentally measured sideband harmonic intensities of different orders (m, n) of the cross section at x=0 and the fitting results obtained by the reconstruction algorithm are shown.

[0120] In the second step, the obtained normalization constant β is m,n Fixed, still using the Broyden-Fletcher-Goldfarb-Shanno algorithm to fit the three-dimensional spatial distribution E of the mid-infrared near field MIR (x,y,z). Figure 18 The comparison between the reconstructed three-dimensional near-field distribution and the theoretical simulation results is shown. Figure 19 Furthermore, the comparison between the cross-sectional light field distribution reconstructed by experimental data and the theoretical simulation results is shown.

[0121] Furthermore, the phase of the mid-infrared near-field inside the silicon pillar can be measured through spectral overlap of adjacent sideband harmonic orders and quantum channel interferometry. Figure 20 The schematic diagram shows the spectral overlap region formed by high-order sideband harmonics and the interference of quantum channels. The spectral overlap between adjacent sideband harmonic orders can be achieved by expanding the near-infrared detection light spectrum. In the device, this can be achieved by adjusting the width of the slit 37 in the prism dispersion compensation device 36 or by selecting filters 38 with different bandwidths. In the spectral overlap region, the condition for the constructive enhancement of the sideband harmonic intensity is Where m is the number of participating near-infrared photons, Δφ is the frequency ω1 and frequency ω2 within the bandwidth of the near-infrared pulse beam 4 = ω1 + 2ω MIR The phase difference between is the mid-infrared near-field phase at the coordinate (x, y), and l is an integer. Here, we can further assume that the dispersion of near-infrared light is a relatively simple group-delay dispersion, that is, Where D2 is the dispersion intensity. Further, taking the (2,n)-order sideband harmonic with m=2 as an example, the frequency of constructive interference must meet the condition:

[0122]

[0123] From formula (5), we can see that: (1) the infrared near-field phase Fixed, (2,n)-order sideband harmonics coherent phase frequency As l takes different integer values, it appears alternately in the spectrum; (2) When the imaging system scans different spatial positions (x, y) and the mid-infrared near-field phase changes, the coherent constructive frequency will also move accordingly, and when When the half-wave phase (π) is changed, the coherent constructive frequency of integer l will move to the spectrum position of l±1. It can be seen that the measurement method of this device is effective for the phase of the mid-infrared near field. sensitive.

[0124] Figure 21 The experimental measurements and theoretical simulations show how the spectral interference along imaging paths (i) and (ii) varies with spatial position. According to the theoretical simulations, the phase of the mid-infrared near-field shifts by half a wave (π) along paths (i) and (ii). Accordingly, the spectral interference fringes obtained from both experimental and theoretical observations shift by Δl = ±1. Accordingly, the experimental measurements allow the phase of the mid-infrared near-field at different spatial positions to be directly extracted. Figure 22 A comparison of the spatially varying phase extracted from the measurements and the theoretical simulation results is shown.

[0125] The above description of the embodiments is intended to facilitate understanding and use of the invention by those skilled in the art. It will be apparent that those skilled in the art can readily make various modifications to these embodiments and apply the general principles described herein to other embodiments without requiring inventive effort. Therefore, the present invention is not limited to the above-described embodiments. Improvements and modifications made by those skilled in the art based on the disclosure of the present invention, without departing from the scope of the present invention, should be within the scope of protection of the present invention.

Claims

1. A method for mid-infrared near-field tomography imaging in a medium, characterized in that: The detection object is excited by a focused mid-infrared pulse beam, and the detection object is coaxially focused with a near-infrared pulse beam, causing the detection object to generate high-order sideband harmonic radiation, and the sideband harmonic spectrum and light field information are recorded; the detection object is moved in a plane perpendicular to the near-infrared pulse beam, and the detection object is scanned to obtain a mid-infrared near-field imaging of the detection object; The detection object includes a dielectric material and an optical microstructure carried on the surface of the dielectric material; The near-infrared pulse light beam is focused until the radius of the focused light spot reaches the diffraction limit.

2. The method for mid-infrared near-field tomography imaging in a medium according to claim 1, characterized in that: Include one or more of the following: (i) The wavelength of the mid-infrared pulse beam is 5-20 μm, the corresponding photon energy is 0.248-0.062 eV, the pulse length is 100 fs-10 ps, ​​the peak field strength is 0-10 MV / cm, and the diameter of the focused spot of the mid-infrared pulse beam on the detection object is 10-100 μm; (ii) the wavelength of the near-infrared pulse beam is 300-1500 nm, corresponding to a photon energy of 4.13-0.83 eV, a pulse length of 50-500 fs, a pulse energy of 5 nJ-10 μJ, and a diameter of a focused spot of the near-infrared pulse beam on the detection object is 300-1500 nm; (iii) the optical microstructure is made of metal or the same material as the dielectric material, and the dielectric material includes silicon dioxide, silicon, and lithium niobate; (iv) The frequency of the high-order sideband harmonic radiation satisfies ω HSE =mω NIR +nω MIR , where: ω is the frequency, subscript HSE is the higher-order sideband harmonic radiation, subscript NIR is the near-infrared pulse beam, subscript MIR is the mid-infrared pulse beam, m is a positive integer, and n is an integer.

3. The method for mid-infrared near-field tomography imaging in a medium according to claim 1, characterized in that: The method described: Polarization resolution is achieved by scanning the linear polarization state of the near-infrared pulse beam; By expanding the spectral bandwidth of the near-infrared pulse beam, adjacent sideband harmonic spectra overlap to form spectral interference, thus achieving phase resolution. Tomography is achieved by fitting the imaging data of sideband harmonic spectra of different orders.

4. A system for mid-infrared near-field tomographic imaging in a medium, characterized in that: Used to implement the method according to any one of claims 1 to 3, comprising: a near-infrared detection light source, a mid-infrared excitation light source, a first dichroic lens (11), a first wide-spectrum objective lens (12), a multi-dimensional displacement platform, a second wide-spectrum objective lens (13), a first lens (14) and a spectrometer; The near-infrared pulse beam (4) is emitted by a near-infrared detection light source, and the mid-infrared pulse beam (1) is emitted by a mid-infrared excitation light source; the detection object is set on a multi-dimensional displacement platform; After the near-infrared pulse beam (4) and the mid-infrared pulse beam (1) are coaxially combined by a first dichroic lens (11), they are coaxially focused on a detection object by a first wide-spectrum objective lens (12); the high-order sideband harmonic radiation (5) generated by the detection object is collected by a second wide-spectrum objective lens (13) and focused by a first lens (14) into a spectrometer.

5. The system for mid-infrared near-field tomography imaging in a medium according to claim 4, characterized in that: The near-infrared detection light source is provided by a combination of a half-wave plate and a polarizer to achieve continuous control of the light field energy and polarization state of the near-infrared pulse light beam (4); the mid-infrared excitation light source is provided by a polarizer or a combination of polarizers to achieve control of the light field intensity and polarization state of the mid-infrared pulse light beam (1).

6. The system for mid-infrared near-field tomography imaging in a medium according to claim 4, characterized in that: The first dichroic lens (11) is a wide-spectrum indium tin oxide coated lens or a metal reflective lens with a central through hole; the first wide-spectrum objective lens (12) is a reflective objective lens with a numerical aperture of 0.28; and the second wide-spectrum objective lens (13) is a transmissive or reflective objective lens with a numerical aperture of 0.

40.

7. The system for mid-infrared near-field tomography imaging in a medium according to claim 4, characterized in that: The near-infrared pulse beam (4) and the mid-infrared pulse beam (1) are emitted by a same femtosecond laser pulse (16) as a seed light source; The femtosecond laser pulse (16) is split into two sub-beams by a first near-infrared beam splitter (17), wherein a fourth sub-beam with a strong light intensity is passed through a mid-infrared excitation light source to obtain a mid-infrared pulse beam (1), and a third sub-beam with a weak light intensity (21) is passed through a near-infrared detection light source to obtain a near-infrared pulse beam (4).

8. The system for mid-infrared near-field tomography imaging in a medium according to claim 7, characterized in that: In the near-infrared detection light source, a third sub-beam (21) is incident on a solid material (34) or a gas plasma to form a supercontinuum beam (35), and then the dispersion and central wavelength of the dispersion compensation device (36) are adjusted by a prism, and the bandwidth is adjusted by a color filter (38) to obtain a near-infrared pulse beam (4).

9. The system for mid-infrared near-field tomography imaging in a medium according to claim 7, characterized in that: In the mid-infrared excitation light source, the fourth sub-beam is further split into a second sub-beam (20) with high light intensity and a first sub-beam (19) with low light intensity by a second near-infrared beam splitter (18); the first sub-beam (19) is incident on a second dichroic lens (27) after adjusting the beam energy by a half-wave plate and a polarizing plate; the second sub-beam (20) is incident on a second dichroic lens (27) after generating a wavelength-shifted offset beam (24) by a femtosecond laser wavelength adjustment device, and then is incident on a second dichroic lens (27) after adjusting the beam energy by a half-wave plate and a polarizing plate; the beam coaxially combined by the second dichroic lens (27) is focused on a nonlinear crystal (29) for frequency difference, thereby forming a mid-infrared pulse beam (1).

10. A light field reconstruction algorithm, characterized in that: for reconstructing mid-infrared near-field data obtained by the method according to any one of claims 1 to 3, The (m,n)th order sideband harmonic intensity generated by m near-infrared photons and n mid-infrared photons is shown in formula (1): In formula (1), x and y represent the spatial coordinates of the detection spot in the xy plane, z represents the depth from the surface into the dielectric material, H is the total thickness of the dielectric material at the plane position (x, y), and E is MIR (x, y, z) represents the electric field intensity of the mid-infrared light field at the spatial position (x, y, z); In formula (1), g m,n (z) is determined by the properties of the dielectric material and the near-infrared detection light field, as shown in formula (2): In formula (2), χ m,n is the optical susceptibility constant of the dielectric material during the generation of high-order sideband harmonics, E0 represents the intensity of the incident near-infrared detection light field, S pr (z) is the distribution coefficient of the standing wave electromagnetic field formed at z after the near-infrared light is reflected inside the dielectric material, U m,n (z) is the coefficient of the (m,n)th order sideband harmonic electromagnetic field generated at z being transmitted out of the sample; Define the fitting error function of the (x, y) position in the plane as shown in formula (3): In equation (3), the summation on the right side of the equation covers the selected solid sideband harmonic orders, is the experimentally measured intensity of the sideband harmonics (m,n) at the position (x,y) in the plane, is the intensity of the sideband harmonics (m,n) at the position (x,y) in the plane simulated theoretically; As shown in formula (4): In formula (4), β m,n is an intensity normalization constant related only to the sideband harmonic order (m,n), which is used to directly compare the sideband harmonic intensities measured experimentally and calculated by the model; The first step of the reconstruction algorithm is to fit the cross-sectional data of the experimentally measured detection object to obtain the intensity normalization constant β corresponding to different sideband harmonic orders (m, n) m,n ; Use the Broyden-Fletcher-Goldfarb-Shanno algorithm to find the β that minimizes the error function J(x,y) m,n and E under this section MIR (x,y,z); The second step of the reconstruction algorithm: fixing the intensity normalization constant β m,n , the three-dimensional spatial distribution E of the mid-infrared near field is fitted by the Broyden-Fletcher-Goldfarb-Shanno algorithm MIR (x,y,z).

Images