An optical frequency tripling system based on cascaded second harmonic generation

Abstract

The present invention discloses an optical frequency tripling system based on cascaded second harmonic generation, which includes a first mirror, a second mirror, a third mirror, a pulse switch, a pump source, a Nd:YAG crystal, and a second-order polarization crystal; wherein, the first mirror is used to reflect the fundamental wave, the second harmonic wave, and the third harmonic wave; the second mirror is used to reflect the second harmonic wave; the fundamental wave emitted in the second direction is incident on the second-order polarization crystal, and the second harmonic wave is generated after being processed by the second-order polarization crystal; the second harmonic wave output by the second-order polarization crystal reaches the second mirror in the second direction, and the second mirror reflects the second harmonic wave to change the emission direction of the second harmonic wave to the first direction; in the second-order polarization crystal, when the phase mismatch between the fundamental wave and the second harmonic wave reaches |Δ 21 k| >> 1, the cubic nonlinear effect occurs to generate the third harmonic wave. The present invention realizes optical frequency tripling through a second-order polarization crystal, has a simple structure and is easy to implement, and can be widely applied in the field of lasers.

Description

Technical Field

[0001] The present invention relates to the field of lasers, and particularly to an optical frequency tripling system based on cascaded second harmonic generation. Background Art

[0002] Currently, fiber lasers are usually used in 3D printers. Among them, since ultraviolet lasers are expensive, it is difficult to popularize the application of ultraviolet lasers in 3D printing devices. Currently, the best way to obtain ultraviolet laser is to apply frequency conversion of laser radiation. Considering that the wavelength of infrared fiber lasers is 1.06 microns, it is necessary to up-convert the frequency of infrared fiber lasers to twice or triple frequency (frequency up-conversion: the conversion process where the output optical wave frequency is higher than the input wave frequency), to obtain ultraviolet light, blue light, green light, etc. with wavelengths of 300nm - 500nm, so as to realize the SLM forming of multi-component materials.

[0003] Currently, there are two common methods to achieve optical third harmonic conversion. The first is to use a medium with a cubic nonlinear response, and the incident pulse power density is at least dozens of GW / cm 2 (depending on the different nonlinear media used, from 10GW / cm 2 to 50GW / cm 2 ), which has a very high requirement for the power density of fiber lasers, and the achieved efficiency is about 40%. Moreover, in a medium with a cubic nonlinear response, the light beam will undergo strong self-focusing, resulting in the damage of the medium. The second is achieved by continuously generating second harmonics (SHG) in two crystals with a second-order nonlinear response, and then sum-frequency mixing with the fundamental wave. This optical third harmonic generation method has the highest efficiency at present, reaching 80%. However, it also has some disadvantages (the size is large enough, and the ratio of the fundamental wave intensity to the second harmonic wave intensity is very large), which makes the technical application inconvenient. Summary of the Invention

[0004] To solve at least one of the technical problems existing in the prior art to a certain extent, the purpose of the present invention is to provide an optical frequency tripling system based on cascaded second harmonic generation

[0005] The technical solution adopted by the present invention is as follows:

[0006] An optical frequency tripling system based on cascaded second harmonic generation includes a first mirror, a second mirror, a third mirror, a pulse switch, a pump source, a Nd:YAG crystal, and a second-order polarization crystal; wherein, the first mirror is used to reflect the fundamental wave, the second harmonic wave, and the third harmonic wave; the second mirror is used to reflect the second harmonic wave; the third mirror is used to reflect the fundamental wave and the second harmonic wave;

[0007] The pump source pumps the Nd:YAG crystal to generate a fundamental wave, which is emitted in a first direction and a second direction; wherein, the first direction and the second direction are opposite;

[0008] The fundamental wave emitted in the first direction passes through a pulse switch and then reaches a first mirror, and the first mirror emits the fundamental wave, causing the emission direction of the fundamental wave to turn to the second direction;

[0009] The fundamental wave emitted in the second direction is incident on a second harmonic generation crystal, and a second harmonic is generated through the processing of the second harmonic generation crystal; the second harmonic output by the second harmonic generation crystal reaches a second mirror in the second direction, and the second mirror reflects the second harmonic, causing the emission direction of the second harmonic to turn to the first direction;

[0010] In the second harmonic generation crystal, when the phase mismatch between the fundamental wave and the second harmonic reaches |Δ 21 k| >> 1, a cubic nonlinear effect occurs to generate a third harmonic; wherein, Δ 21 k represents the phase mismatch on the normalized length;

[0011] After being reflected by the first mirror, all the third harmonics are emitted in the second direction.

[0012] Further, along the emission direction of the fundamental wave, the length of the second harmonic generation crystal is 2 - 4 cm.

[0013] Further, the fundamental wave is an infrared laser with a wavelength of 1060 nm.

[0014] Further, the first mirror and the third mirror form a laser resonator, and the first mirror and the second mirror form a second harmonic resonator;

[0015] In the second direction, the fundamental wave output from the second harmonic generation crystal passes through the second mirror and then reaches the third mirror, and the third mirror reflects the fundamental wave, causing the emission direction of the fundamental wave to turn to the first direction;

[0016] Among them, the fundamental wave propagates back and forth between the first mirror and the third mirror to be enhanced.

[0017] Further, when the second harmonic generated by the second harmonic generation crystal continuously enters the second harmonic generation crystal, a cascaded second harmonic is generated.

[0018] Further, the second harmonic generation crystal is made of a second-order nonlinear material.

[0019] The beneficial effects of the present invention are as follows: By controlling the phase mismatch between the fundamental wave and the second harmonic, a cubic nonlinear response appears in the second harmonic generation crystal to generate a third harmonic, realizing optical frequency tripling. The system structure is simple and easy to implement. Brief Description of the Drawings

[0020] In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following provides an introduction to the drawings of the relevant technical solutions in the embodiments of the present invention or the prior art. It should be understood that the drawings in the following introduction are only for conveniently and clearly presenting some embodiments of the technical solutions of the present invention. For those skilled in the art, without creative efforts, other drawings can also be obtained based on these drawings.

[0021] Figure 1 is a schematic structural diagram of an optical frequency tripling system based on cascaded second harmonic generation in an embodiment of the present invention;

[0022] Figure 2 is a schematic diagram of the phase matching and mismatch schemes of various frequency conversion processes in an embodiment of the present invention. Detailed Embodiments

[0023] The following details the embodiments of the present invention. The examples of the embodiments are shown in the drawings, where the same or similar reference numerals represent the same or similar elements or elements with the same or similar functions throughout. The embodiments described below with reference to the drawings are exemplary and are only used to explain the present invention and should not be construed as a limitation of the present invention. For the step numbers in the following embodiments, they are only set for the convenience of elaboration and explanation, and no limitation is imposed on the order between the steps. The execution order of each step in the embodiments can be adaptively adjusted according to the understanding of those skilled in the art.

[0024] In the description of the present invention, it should be understood that for the orientation description, such as the orientation or positional relationship indicated by up, down, front, back, left, right, etc., is based on the orientation or positional relationship shown in the drawings. It is only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and thus should not be construed as a limitation of the present invention.

[0025] In the description of the present invention, the meaning of several is one or more, the meaning of multiple is more than two, greater than, less than, exceeding, etc. are understood as not including the present number, and above, below, within, etc. are understood as including the present number. If there is a description of first and second, it is only for the purpose of distinguishing technical features and should not be construed as indicating or implying relative importance or implicitly indicating the quantity of the indicated technical features or implicitly indicating the sequence of the indicated technical features.

[0026] In the description of the present invention, unless otherwise clearly defined, words such as setting, installing, connecting, etc. should be understood in a broad sense, and those skilled in the art can reasonably determine the specific meanings of the above words in the present invention in combination with the specific content of the technical solution.

[0027] The second-order polarization crystal of this embodiment is made of a second-order nonlinear material. When a laser acts on the second-order nonlinear material, in addition to generating light with the same frequency ω as the incident light (linear part), it also generates second-harmonic light with a frequency of 2ω and an electrostatic field with a frequency of 0 (nonlinear part). The generation of second-harmonic light is called the second-harmonic generation (SHG) effect. It is commonly used to represent the performance of second-order nonlinear materials.

[0028] The second-order polarization crystal of this embodiment has the function of polarizing the corresponding medium, which can be defined as: the response of the medium is proportional to the square of the incident electric field strength.

[0029] (1) Second-order susceptibility medium

[0030] Participate Figure 2 , in order to clarify the optical third-harmonic generation in the second-order susceptibility medium, we consider the following frequency conversion process, which is schematically described in Figure 2 a crystal with second-order (χ(2)) and cubic (χ(3)) susceptibilities.

[0031] When the incident light intensity is greater than a certain value, the cubic susceptibility in the non-centrosymmetric crystal (crystal with second-order susceptibility) comes into play. Note that considering the cubic susceptibility is only for explaining the frequency conversion process. The symbol ω represents the FW (fundamental wave) frequency. Below we consider three methods for generating the third-harmonic wave.

[0032] The first is to generate the second-harmonic light wave (ω + ω = 2ω, χ (2) ), and then, due to the second-order nonlinear response of the crystal, the third-harmonic (THG) is generated based on sum-frequency generation (SFG) (ω + 2ω = 3ω, χ (2) ). The second is to directly generate the third-harmonic wave by the cubic nonlinearity of the crystal χ (3) . Compared with the aforementioned second-harmonic generation method, this process requires a more energetic incident pulse. The third (proposed by the present invention) third-harmonic generation method is based on second-harmonic generation under large phase mismatch. Compared with the case where the third-harmonic generation occurs due to the cubic nonlinearity of the crystal itself, this process can occur at a lower incident wave intensity. This method is denoted as (ω → 3ω, ). In Figure 2 , we also describe another frequency conversion process (3ω = 2ω + 2ω - ω, χ (3) ), which can occur in a medium with cubic susceptibility.

[0033] Different frequency conversion processes require the self-phase matching and crystal susceptibility values at the corresponding frequencies. Therefore, and χ (3)The polarizabilities are different. Usually, only one of the multiple conversion processes can occur during phase matching. Therefore, the cascaded SHG used to achieve THG in the invention is different from the SFG process.

[0034] (2) Cubic nonlinear response, magnitude condition of the mismatched phase, and mathematical derivation of cascaded second harmonic generation:

[0035] The three-wave interaction in a medium with a second-order nonlinear response is governed by the following dimensionless Schrödinger equations for the slowly varying envelopes of wave packets with equally spaced frequencies:

[0036]

[0037]

[0038]

[0039] For this equation, if the pulse duration is large enough (greater than 1 picosecond) and the length of the crystal is about a few centimeters, we can neglect the group velocity dispersion of the wave packet.

[0040] Where \(A_1(z,t)\), \(A_2(z,t)\), \(A_3(z,t)\) are the complex amplitudes of the waves of the fundamental frequency wave (FF) (\(\omega\)), second harmonic wave (2\(\omega\)) and third harmonic wave (3\(\omega\)) respectively. The parameter \(\gamma\) is the multi-wave interaction coupling coefficient generated by the second-order nonlinear response of the corresponding frequency. Generally, for the generation of different frequencies, this possible coefficient is different. However, for simplicity, we choose the same \(\gamma\) value for all frequency conversion processes involved in the equation.

[0041] The parameter \(\Delta\) 21 \(k = k_2 - 2k_1\) characterizes the phase mismatch on the normalized length \(Z\) n \(= 1\) mm. \(k_1\) and \(k_2\) represent the dimensionless wave numbers of the fundamental frequency wave (FF) and the second harmonic wave. The parameter \(\Delta\) 31 \(k = k_3 - 3k_1\) characterizes the phase mismatch of \(Z\) under THG n The symbol \(k_3\) represents the dimensionless third harmonic (TH) wave number. The coordinate \(t\) is a time measured in units of the pulse duration \(\tau\) at the fundamental frequency wave (FF) p \(D\) j (\(j = 1,2,3\)) represents the dimensionless second-order dispersion (SOD) of the corresponding wave packet.

[0042] We discuss the terms involved in the system of equations (1). The term in the second equation (second-order susceptibility \(\chi^{(2)}(2\omega;\omega,\omega)\)) corresponds to the generation of the second harmonic wave for the process (\(\omega+\omega\rightarrow2\omega\)). The term in the first equation is responsible for the reverse process (\(2\omega\rightarrow\omega+\omega\)). The term (Second-order susceptibility χ(2)(3ω; ω, 2ω)) describes the process of achieving THG by SFG (ω + 2ω = 3ω).

[0043] Conversely, the term in the first equation (Second-order susceptibility χ (2) (3ω; 2ω, ω)) and the term in the second equation (Second-order susceptibility χ (2) (3ω; ω, 2ω)) correspond to the reverse (3ω - 2ω = ω) and (3ω - ω = 2ω), respectively. We have neglected the dispersion of the second-order susceptibility. Therefore, the parameters in the equations become the same.

[0044] At the input part of the medium, only the pulse at the fundamental frequency wave (FF) exists (only the fundamental frequency wave exists at the input part of the present invention):

[0045] A1(z = 0, t) = A 10 (t)

[0046] The other two waves do not exist

[0047] A2(z = 0, t) = A3(z = 0, t) = 0

[0048] They appear in the crystal (i.e., cascaded second harmonic generation and third harmonic generation occur in the second-order polarization crystal).

[0049] Cascaded second harmonic generation (SHG) occurs when there is a large phase mismatch between the fundamental frequency wave (FF) and the second harmonic wave, i.e., |Δ 21 k| >> 1. In this case, the complex amplitude A2 of the second harmonic is proportional to the term . It is part of the polarization of the crystal medium at the second harmonic frequency. Considering this fact, we see that a cubic nonlinear response appears in the third equation which gives rise to THG.

[0050] Specifically, there is a phase mismatch |Δ 21 k| >> 1 between the second harmonic light and the fundamental frequency light, i.e., |Δ 21 k| = |2k1 - k2| >> 1. From the wave vector formula k w = (ω / c)n w and k 2w = (2ω / c)n 2w , we get |n w - n 2w|>>c / 2w. According to the phase formula φ = wnL / c, when two light beams propagate a distance L in the same direction, different refractive indices n result in phase mismatch. Therefore, by controlling the angle between the optical axis of the anisotropic crystal (i.e., the second-order polarization crystal) and the light beam propagation direction, different refractive indices of the light beam in the crystal can be achieved, thereby achieving phase mismatch; of course, the crystal temperature can also be controlled to achieve phase mismatch.

[0051] This is a qualitative explanation of the physical mechanism of THG generation. Explicit equations can be derived using the multi-scale method. Their forms are as follows:

[0052]

[0053]

[0054]

[0055]

[0056] The initial conditions are as follows:

[0057]

[0058] Based on the above theoretical knowledge, this embodiment provides an optical frequency tripling system based on cascaded second harmonic generation, including a first mirror M1, a second mirror M2, a third mirror M3, a pulse switch QS, a pump source, a Nd:YAG crystal, and a second-order polarization crystal; wherein, the first mirror M1 is used to reflect the fundamental wave, the second harmonic, and the third harmonic; the second mirror M2 is used to reflect the second harmonic; the third mirror M3 is used to reflect the fundamental wave and the second harmonic.

[0059] Among them, the Nd:YAG crystal is used to generate laser. The pulse switch QS is used to control whether the laser pulse is on or off. The second-order polarization crystal is used to generate the second harmonic after the fundamental wave is incident on the crystal; the second harmonic is repeatedly incident on the crystal to generate cascaded second harmonics; appropriate phase mismatch occurs between the fundamental wave and the second harmonic inside, generating the third harmonic effect and generating the third harmonic.

[0060] See Figure 1 , the working principle and steps of this system are as follows:

[0061] S1. The pump source pump pumps the Nd:YAG crystal to generate an infrared laser of 1060 nm. An optical resonator is composed of the first mirror M1, the third mirror M3, and the entire internal structure. The resonator continuously reflects photons into the gain medium (Nd:YAG), emitting more photons of radiation and amplifying and enhancing the laser.

[0062] S2. The infrared laser serves as the fundamental wave and propagates along the optical path towards the lenses of the first mirror M1 and the third mirror M3. The light in the direction perpendicular to the optical path is lost in the form of heat.

[0063] S3. When propagating in the left direction (i.e., towards the first mirror M1), the pulse switch QS controls the length of the pulse interval. The first mirror M1 highly reflects the fundamental wave, second harmonic, and third harmonic. After all the waves propagate to the first mirror M1, they are reflected back into the resonant cavity for amplification and enhancement.

[0064] S4. When propagating in the right direction (i.e., towards the third mirror M3), the fundamental wave is incident on the second - order polarization crystal, generating a second harmonic that exits the crystal. The second harmonic is reflected back to the second - order polarization crystal by the second mirror M2, and the first mirror M1 on the left also reflects the second harmonic, causing the second harmonic generated by the second - order polarization crystal to continuously be incident on the second - order polarization crystal, i.e., cascaded second harmonic.

[0065] S5. The fundamental wave reciprocates and propagates between the first mirror M1 and the third mirror M3 for enhancement. When incident on the second - order polarization crystal, by controlling parameters such as the length of the second - order polarization crystal, the phase - mismatch amount between the fundamental wave and the second harmonic reaches |Δ 21 k| >> 1, and the cubic nonlinear effect occurs, generating a third harmonic that exits from the right end of the second - order polarization crystal.

[0066] In some alternative embodiments, phase - mismatch can also be achieved by controlling the temperature of the second - order polarization crystal to cause the cubic nonlinear effect.

[0067] S6. The third mirror M3 highly reflects the fundamental wave and the second harmonic, causing the third harmonic to finally exit from the third mirror M3.

[0068] In this embodiment, the cascaded second - harmonic effect can be understood as follows: If there is no phase - matching between the second harmonic and the fundamental wave, the frequencies of the waves will exchange their energies. The energy of the frequency - conversion efficiency (SHG) decreases. For a large phase - mismatch, the doubling energy and its intensity become very small: as described above, the complex amplitude A2 of the second harmonic is proportional to the term In addition, if we consider the sum - frequency generation process 3ω = 2ω+ω, then if the phase - matching condition is valid, we can obtain the generation of THG (third harmonic).

[0069] In summary, the traditional sum - frequency or difference - frequency technology based on phase - matching requires multiple nonlinear crystals; while this embodiment is based on phase - mismatch and cascaded harmonics, only a 2 - 4 cm second - order polarization crystal is needed to achieve optical - frequency tripling, with a simpler structure and easier implementation. In addition, the energy required for the second harmonic in this embodiment is much lower than that of the traditional scheme.

[0070] In the foregoing description of the present specification, the description referring to terms such as "one embodiment", "another embodiment" or "certain embodiments" means that the specific features, structures, materials or characteristics described in connection with the embodiment or example are included in at least one embodiment or example of the present invention. In the present specification, the schematic representation of the above terms does not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials or characteristics described may be combined in any one or more embodiments or examples in a suitable manner.

[0071] Although the embodiments of the present invention have been shown and described, those of ordinary skill in the art can understand that various changes, modifications, substitutions and variations can be made to these embodiments without departing from the principles and spirit of the present invention, and the scope of the present invention is defined by the claims and their equivalents.

[0072] The above is a specific description of the preferred embodiment of the present invention, but the present invention is not limited to the above embodiments. Those skilled in the art can also make various equivalent deformations or substitutions without departing from the spirit of the present invention, and these equivalent deformations or substitutions are all included in the scope defined by the claims of this application.

Claims

1. An optical frequency tripling system based on cascaded second harmonic generation, characterized in that, It includes a first mirror, a second mirror, a third mirror, a pulse switch, a pump source, a Nd:YAG crystal, and a second harmonic generation crystal; wherein, the first mirror is used to reflect the fundamental wave, the second harmonic, and the third harmonic; the second mirror is used to reflect the second harmonic; the third mirror is used to reflect the fundamental wave and the second harmonic; The pump source pumps the Nd:YAG crystal to generate a fundamental wave, and the fundamental wave is emitted in a first direction and a second direction; wherein, the first direction and the second direction are opposite; The fundamental wave emitted in the first direction passes through the pulse switch and then reaches the first mirror, and the first mirror emits the fundamental wave, changing the emission direction of the fundamental wave to the second direction; The fundamental wave emitted in the second direction is incident on the second harmonic generation crystal, and the second harmonic is generated after being processed by the second harmonic generation crystal; the second harmonic output by the second harmonic generation crystal reaches the second mirror in the second direction, and the second mirror reflects the second harmonic, changing the emission direction of the second harmonic to the first direction; In a second-order polarization crystal, when the phase mismatch between the fundamental wave and the second harmonic wave reaches |Δ 21 k| >> 1, a cubic nonlinear effect occurs and a third harmonic wave is generated; where Δ 21 k represents the phase mismatch over the normalized length; After being reflected by the first mirror, all the third harmonics are emitted in the second direction.

2. The optical frequency tripling system based on cascaded second harmonic generation according to claim 1, characterized in that, Along the emission direction of the fundamental wave, the length of the second harmonic generation crystal is 2 - 4 cm.

3. The optical frequency tripling system based on cascaded second harmonic generation according to claim 1, characterized in that, The fundamental wave is an infrared laser with a wavelength of 1060 nm.

4. The optical frequency tripling system based on cascaded second harmonic generation according to claim 1, characterized in that, The first mirror and the third mirror form a laser resonator, and the first mirror and the second mirror form a second harmonic resonator; In the second direction, the fundamental wave output from the second harmonic generation crystal passes through the second mirror and then reaches the third mirror, and the third mirror reflects the fundamental wave, changing the emission direction of the fundamental wave to the first direction; Wherein, the fundamental wave propagates back and forth between the first mirror and the third mirror to be enhanced.

5. The optical frequency tripling system based on cascaded second harmonic generation according to claim 1, characterized in that, When the second harmonic generated by the second harmonic generation crystal continuously enters the second harmonic generation crystal, cascaded second harmonics are generated.

6. The optical frequency tripling system based on cascaded second harmonic generation according to claim 1, characterized in that, The second harmonic generation crystal is made of a second-order nonlinear material.

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