Third-order nonlinear coefficient measuring method based on Airy beam

Abstract

The invention discloses a three-order nonlinear coefficient measurement method based on Airy beams, relates to the field of three-order nonlinear coefficient measurement of thin-layer optical materials, and aims to solve the problem that in the prior art, single measurement, high precision and low damage cannot be met at the same time. A cubic phase mask and a sample behind the cubic phase mask are irradiated through parallel Gaussian light, an Airy beam image is collected after Fourier transform and image amplification, and the third-order nonlinear coefficient of the material can be calculated through displacement and light field parameters of the Airy beam. The method is applicable to thin-layer samples, high in measurement precision, capable of directly determining specific coefficient values and symbols through single measurement, applicable to light damage sensitive materials, simple in measurement device and low in data processing difficulty. The invention provides a more robust and less invasive alternative for characterizing the nonlinear response in a thin sample.

Description

Technical Field

[0001] This invention relates to the field of third-order nonlinear coefficient measurement technology for optical materials, specifically a method for measuring third-order nonlinear coefficients based on Airy beams. Background Technology

[0002] The third-order nonlinear effect of optical materials has great application value and plays an important role in practical functions such as all-optical switching devices, optical routing, and optical communication. The measurement and research of the third-order nonlinear effect is particularly crucial, especially its coefficient (usually referring to the nonlinear refractive index coefficient). The third-order nonlinear coefficient (also known as the Kerr coefficient) directly reflects the strength of the Kerr nonlinear effect of a medium. Researchers can make reasonable selections based on the magnitude of the nonlinear coefficient of different media in the development of related application devices. Therefore, simple, fast, accurate and effective measurement of the third-order nonlinear coefficient is of great significance.

[0003] Commonly used methods for measuring third-order nonlinear coefficients include the Z-scan method, the nonlinear elliptic polarization method, the interferometry method, and the wave mixing method. These existing methods have the following drawbacks:

[0004] Z-scan method relies on high-intensity laser and requires multiple measurements on a moving sample, which can be damaging to thin or easily damaged samples (such as living biological tissues).

[0005] Nonlinear elliptic polarization method and wave mixing method have low measurement accuracy;

[0006] Interferometry and wave mixing methods cannot directly determine the sign of the third-order nonlinear refractive index;

[0007] Z-scan, nonlinear elliptic polarization, and interferometry all require multiple measurements and cannot be used to measure light-damage sensitive materials. It should be noted that although Z-scan involves a single irradiation, the sample is continuously irradiated by the light field during its movement, resulting in repeated damage. In particular, the damage is greater when the sample moves to the focal point of the light field. Therefore, Z-scan is also considered as multiple measurements.

[0008] In 2008, Song Yinglin et al. proposed a 4f phase coherent imaging method based on a Michelson interferometer to measure nonlinear refractive index. Although it can effectively measure third-order nonlinearity, the structure is complex, the beam stability requirement is high, and the data processing is relatively complicated.

[0009] In recent years, nonlinear response measurement methods based on Airy beams have emerged. However, these methods rely on the significant acceleration of the Airy beam's propagation (i.e., propagation along a distinctly curved trajectory) in thicker nonlinear media (e.g., 1-3 cm thick). In thin nonlinear media (micrometers and below), the accelerated propagation of the Airy beam is difficult to demonstrate over extremely short propagation distances. Furthermore, setting even greater acceleration to force propagation through thin samples leads to beam distortion. This hinders the use of self-accelerating Airy beams in nonlinear measurements of thin samples. Summary of the Invention

[0010] The technical problem this invention aims to solve is to overcome the shortcomings of existing methods and provide a method for measuring the third-order nonlinear coefficient based on an Airy beam. This method involves placing the thin-layer sample to be measured near a cubic phase mask and irradiating it with a relatively wide Gaussian beam. When the intensity of the Gaussian light field is sufficiently large and its shape is wide enough to be approximated by a parabolic surface, the nonlinear effect in the thin-layer medium can manifest as a frequency-domain second-order phase modulation of the Airy beam, resulting in a significant displacement of the Airy beam in real space. By measuring the displacement value of the Airy beam and the peak intensity of the incident Gaussian beam, the Kerr nonlinear coefficient of the thin medium can be directly determined, effectively solving the problems in the prior art.

[0011] Specifically, this invention discloses a method for measuring third-order nonlinear coefficients based on Airy beams. The technical solution includes placing the sample to be tested behind a cubic phase mask and illuminating the cubic phase mask with a parallel Gaussian light source. After the light passing through the cubic phase mask and the sample to be tested undergoes a Fourier transform, a two-dimensional Airy beam is obtained, and the morphology of the two-dimensional Airy beam is collected.

[0012] At this point, the third-order nonlinear coefficient of the sample under test The calculation formula is:

[0013]

[0014] in, The angle between the Airy beams (usually) ), The beam wave vector within the sample to be tested. The thickness of the sample being measured. The value describes the width of the spectral Gaussian beam. The value determines the acceleration that generates the Airy beam. This represents the displacement of the peak power position of the Airy beam due to frequency-domain phase modulation. The peak intensity of the incident Gaussian beam is given.

[0015] This method is applicable to thin-layer samples, is simple to operate, has high measurement accuracy, requires only a single measurement, is suitable for photodamage-sensitive materials, and has a simple device structure and simple data processing.

[0016] As a preferred embodiment of the present invention, the peak intensity of the Gaussian beam... The method for determining it is as follows:

[0017] When there is no sample to be tested, the average power of the Gaussian beam behind the cubic phase mask is measured using a power meter and recorded as power. The Gaussian light intensity image at this moment is recorded as image A, and the peak light intensity of the Gaussian beam incident on the sample is determined. The operation is repeated multiple times, and the maximum peak light intensity of the Gaussian beam corresponding to different incident powers is recorded. Make a record.

[0018] As a preferred embodiment of the present invention, the displacement of the Airy beam at the initial distance The method for determining it is as follows:

[0019] The sample to be tested is placed behind a cubic phase mask, and the two-dimensional Airy beam morphology generated under extremely low incident power (microwatt level) that cannot excite nonlinear effects is collected. The position L of the peak intensity of the Airy beam at this time is recorded and denoted as the origin.

[0020] Gaussian beams with different peak intensities were incident on the sample under test, and Airy beam patterns at different peak intensities were collected.

[0021] Record the location of the peak intensity of the obtained Airy beam pattern and calculate the difference between it and the location L. Then, determine the displacement of the Airy beam under Gaussian incident light with different peak intensities. .

[0022] As a preferred embodiment of the present invention, the Fourier transform is performed by a first spherical lens, and a second spherical lens is further disposed behind the first spherical lens to magnify the two-dimensional Airy beam shape.

[0023] As a preferred embodiment of the present invention, the third-order nonlinear coefficients The method for determining positive and negative signs is as follows:

[0024] After performing incident measurements and acquiring the morphology of the two-dimensional Airy beam, the sample position is fixed, and the position of the second spherical lens is adjusted along the optical axis in a direction away from the first spherical lens. The transmission process is reconstructed by superimposing the intensity patterns of the acquired Airy beam to obtain a transmission map. Then, by comparing the differences between the velocity direction and acceleration direction of the incident Airy beam in the transmission map, the third-order nonlinear coefficients are obtained. The negative and positive signs.

[0025] This method can quickly obtain the sign of the third-order nonlinear coefficients in a single measurement.

[0026] As a preferred technical solution of the present invention, the method for obtaining the parallel Gaussian light source is to illuminate the Gaussian beam emitted by the light source onto a 4f system, and then expand the Gaussian beam by the 4f system.

[0027] As a preferred embodiment of the present invention, the morphology of the two-dimensional Airy beam is acquired by a CCD camera, and the CCD camera is electrically connected to a computer with a display screen, which can transmit the acquired morphology of the two-dimensional Airy beam to the computer.

[0028] Compared with existing technologies, the advantages of this invention are as follows: This invention places the thin-layer sample to be measured behind a cubic phase mask and illuminates the cubic phase mask with a parallel Gaussian light source. The light penetrating the sample undergoes a Fourier transform to obtain a two-dimensional Airy beam. The third-order nonlinear coefficients are directly calculated using a formula, and their signs are obtained by reconstructing the transmission map. This method utilizes an Airy beam to measure third-order nonlinear coefficients, is applicable to thin-layer samples, and offers high measurement accuracy (error less than 1%). It can directly determine the specific coefficient value and sign in a single measurement, is suitable for photodamage-sensitive materials, and features a simple measurement device and low data processing difficulty. This invention provides a more robust and less invasive alternative for characterizing nonlinear responses in thin samples, and adjusting the Airy beam parameters can improve the accuracy of this method for different nonlinear intensities. Attached Figure Description

[0029] Figure 1 This is a schematic diagram of the measurement system of the present invention;

[0030] Figure 2 This is a comparison diagram of the Gaussian beam expansion process and the parabolic shape of the present invention;

[0031] Figure 3 This is a diagram showing the nonlinear displacement of the Airy beam under different incident light intensities according to the present invention.

[0032] Figure 4 This is a comparison chart showing the measurement accuracy of different incident Gaussian beam widths in this invention;

[0033] Figure 5 This is a schematic diagram illustrating how the third-order nonlinear coefficient is determined in this invention.

[0034] In the figure: 1. Light source; 2. First lens; 3. Second lens; 4. Cubic phase mask; 5. Thin sample under test; 6. First spherical lens; 7. Second spherical lens; 8. CCD camera. Detailed Implementation

[0035] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0036] Example 1

[0037] like Figure 1 As shown, this invention first discloses a third-order nonlinear coefficient measurement system based on Airy beams, including a light source 1. A 4f system, consisting of a first lens 2 and a second lens 3, is located at the rear end of the light source 1. The 4f system expands the Gaussian beam generated by the light source 1. By adjusting the 4f system, the expanded parallel Gaussian beam can be approximated as a parabolic intensity distribution. At the rear end of the 4f system are a cubic phase mask element 4, a first spherical lens 6, a second spherical lens 7, and a CCD camera 8. The thin-layer sample 5 to be measured is placed between the cubic phase mask element 4 and the first spherical lens 6. The CCD camera 8 is electrically connected to a computer with a display, and the computer can acquire the images collected by the CCD camera 8.

[0038] The present invention also discloses a measurement method based on the above-mentioned third-order nonlinear coefficient measurement system based on Airy beam. The technical solution adopted is that the Gaussian beam generated by the light source 1 is expanded into parallel Gaussian beam by the 4f system and then illuminates the cubic phase mask element 4. After the beam passes through the cubic phase mask element 4, it undergoes Fourier transform by the first spherical lens 6 to obtain a two-dimensional Airy beam. Then, it is magnified by the second spherical lens 7 and the magnified two-dimensional Airy beam is acquired by the CCD camera 8.

[0039] It should be emphasized that for high peak intensities, the Gaussian beam in the thin-layer medium only experiences self-phase modulation caused by Kerr nonlinearity, and there is no need to consider diffraction effects or other higher-order nonlinear effects. In this embodiment, the intensity of the third-order nonlinear effect of the medium is controlled solely by the intensity of the incident Gaussian beam.

[0040] The expression for a Gaussian light field can be written as: Where E is the amplitude of the Gaussian light field, and a represents its beam waist size. From this expression, it can be seen that the width of the Gaussian beam is controlled by the value of a; different values ​​of a result in Gaussian beams as shown below. Figure 2 As shown. In particular, when the value of a is very small (<0.005 / k), the Gaussian beam is wide enough that its shape profile can be approximated as parabolic. In this case, the Kerr self-phase modulation induced by the Gaussian beam in the medium has an effect of approximating the second-order phase modulation of the spectrum for the generated Airy beam. Therefore, after Fourier transform by the second spherical lens 6, the Airy beam will be displaced in real space.

[0041] The method for measuring third-order nonlinear coefficients includes the following steps:

[0042] Step 1: With the measurement system unloaded (without the sample being tested), start the measurement system and use a power meter to measure the average power of the Gaussian beam behind the cubic phase mask 4 (the detection position of the sample being tested) and record it as the power. The Gaussian light intensity image at this time is recorded as image A. The peak light intensity of the Gaussian beam incident on the sample is determined when the third-order nonlinear coefficient of the sample is measured. The peak light intensity of the Gaussian beam is measured sequentially at three incident powers of 0.5 W, 1.5 W, and 2.5 W, and the maximum peak light intensity is recorded each time. ;

[0043] Step 2: Place the thin-layer sample 5 to be tested at the sample detection position, adjust the power of the light source 1 to emit a Gaussian beam with an incident power on the order of microwatts that cannot excite nonlinear effects, collect the two-dimensional Airy beam morphology generated at the current power, and record the position L of the peak light intensity of the Airy beam at this time, which is recorded as the origin.

[0044] Adjust the power of light source 1, respectively (Corresponding to 0.5W incident power) (Corresponding to 1.5 W incident power) A Gaussian beam with peak intensity (corresponding to 2.5 W incident power) was incident on the thin-layer sample 5 under test, and Airy beam patterns at different peak intensities were acquired, as shown below. Figure 3 As shown;

[0045] Record the location of the peak intensity of the obtained Airy beam pattern and calculate the difference between it and the location L. Then, determine the displacement of the Airy beam under different peak intensity incident conditions. ;

[0046] Step 3, based on the Airy beam at different Gaussian incident intensities The corresponding displacement Given known parameters such as the thickness of the thin-layer sample 5, the acceleration of the Airy beam, and the width of the Gaussian beam, the third-order nonlinear coefficient can be obtained through calculation formulas. The formula is as follows:

[0047]

[0048] in, The angle between the Airy beams (usually) ), The beam wave vector within the sample to be tested. The thickness of the thin-layer sample 5 being measured is... The value determines the acceleration of the generated Airy beam;

[0049] The third-order nonlinear coefficient of the tested thin-layer sample 5 can be obtained through the calculation formula. ;

[0050] To verify the accuracy of the calculation results, the actual third-order nonlinear coefficient of the tested thin-layer sample 5 was used. Assuming Calculation results and ( The difference between the two values ​​is the measurement error. .Change Take the value and calculate the corresponding value multiple times. The value is calculated and the error is determined. The result is as follows: Figure 4 As shown, the measurement error is visible. This is achieved by assuming actual third-order nonlinear coefficients. The method of verifying accuracy by subtracting the calculated value from the assumed value is a common method in this field and belongs to the prior art.

[0051] Specifically, as mentioned earlier, this formula only applies when the value of 'a' is sufficiently small (i.e., the Gaussian beam is very wide, as shown in the case of a = 0.001 / k in the figure), in which case the measurement error... Very small (<1%), such as Figure 4 As shown. If the Gaussian beam width is insufficient (as in the case of a=0.01 / k in the figure), and is not enough to approximate a parabolic shape, then the nonlinear coefficient measured by this method will have a large error (2~18%).

[0052] Step 4: Determine the third-order nonlinear coefficients symbols,

[0053] In a measurement under high-intensity incident light, after recording the morphology of the two-dimensional Airy beam, the sample is kept stationary, and the position of the second spherical lens 7 is adjusted along the optical axis towards the CCD camera 8. During this process, the CCD camera 8 continuously acquires images of the Airy beam. By superimposing the recorded intensity patterns of the Airy beam, its transmission process is reconstructed to obtain a transmission map, such as... Figure 5 As shown;

[0054] If the incident velocity direction is the same as the acceleration direction of the Airy beam, the corresponding third-order nonlinear coefficient Positive (self-focusing);

[0055] If the incident velocity direction is not the same as the acceleration direction of the Airy beam, the corresponding third-order nonlinear coefficient It is negative (self-defocusing).

[0056] The placement and connection methods of the measurement system involved in this invention are conventional methods used by those skilled in the art, and can be learned through a limited number of experiments, and are common knowledge.

[0057] Components not described in detail in this article are existing technologies.

[0058] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A method for measuring third-order nonlinear coefficients based on Airy beams, characterized in that: The sample to be tested is placed behind the cubic phase mask (4), and the cubic phase mask (4) is illuminated by a parallel Gaussian light source. After the light passing through the cubic phase mask (4) and the sample to be tested undergoes Fourier transform, a two-dimensional Airy beam is obtained, and the morphology of the two-dimensional Airy beam is collected. At this point, the third-order nonlinear coefficient of the sample under test The calculation formula is: in, The angle between the Airy beams (usually) ), The wave vector of the beam in the medium. The thickness of the sample being measured. The value describes the width of the spectral Gaussian beam. The value determines the acceleration that generates the Airy beam. Let be the displacement of the Airy beam at the initial distance. denoted as the peak intensity of the Gaussian beam.

2. The method for measuring third-order nonlinear coefficients based on Airy beams according to claim 1, characterized in that, The peak intensity of the Gaussian beam The method for determining it is as follows: When there is no sample to be tested, the average power of the Gaussian beam behind the cubic phase mask (4) is measured using a power meter and recorded as power. The Gaussian light intensity image at this time is recorded as image A, and the peak light intensity of the Gaussian beam incident on the sample is determined. After repeated multiple times, the maximum peak light intensity of the Gaussian beam under different incident powers is recorded. .

3. The method for measuring third-order nonlinear coefficients based on Airy beams according to claim 2, characterized in that, The displacement of the Airy beam at the initial distance The method for determining it is as follows: The sample to be tested is placed behind the cubic phase mask (4), and the two-dimensional Airy beam morphology generated under the incident power that cannot excite nonlinear effects is collected. The position L of the peak intensity of the Airy beam at this time is recorded as the origin. Gaussian beams with different peak intensities were incident on the sample under test, and Airy beam patterns at different peak intensities were collected. Record the location of the peak intensity of the obtained Airy beam pattern and calculate the difference between it and the location L. Then, determine the displacement of the Airy beam under different Gaussian peak intensities. .

4. The method for measuring third-order nonlinear coefficients based on Airy beams according to claim 1, characterized in that: The Fourier transform is performed through a first spherical lens (6), and a second spherical lens (7) is provided behind the first spherical lens (6) to magnify the two-dimensional Airy beam shape.

5. The method for measuring third-order nonlinear coefficients based on Airy beams according to claim 4, characterized in that, Third-order nonlinear coefficients The method for determining positive and negative signs is as follows: After performing incident measurements and acquiring the morphology of the two-dimensional Airy beam, the sample position is fixed, and the position of the second spherical lens (7) is adjusted along the optical axis in a direction away from the first spherical lens (6). During this process, images of the Airy beam are continuously acquired, and its transmission process is reconstructed by superimposing the intensity patterns of the acquired Airy beam to obtain a transmission map. Then, by comparing the similarities and differences between the velocity direction and acceleration direction of the incident Airy beam in the transmission map, the third-order nonlinear coefficients are obtained. The negative and positive signs.

6. The method for measuring third-order nonlinear coefficients based on Airy beams according to claim 1, characterized in that: The parallel Gaussian light source is obtained by irradiating the Gaussian beam emitted by the light source (1) onto the 4f system, and then expanding the Gaussian beam by the 4f system.

7. The method for measuring third-order nonlinear coefficients based on Airy beams according to any one of claims 1-5, characterized in that: The morphology of a two-dimensional Airy beam is acquired using a CCD camera, which is electrically connected to a computer with a display screen, and the acquired morphology of the two-dimensional Airy beam is transmitted to the computer.

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