Phase matching method and device for optical nonlinear frequency conversion

Abstract

The present invention discloses a phase matching method and device for optical nonlinear frequency conversion. The method comprises the following steps: multiple light fields are incident along the X-axis onto a periodically poled lithium niobate crystal whose optical axis and positive and negative domain polarization directions are both along the Z-axis; an electric field is applied to the front and rear sides of the periodically poled lithium niobate crystal in the Y-axis direction to rotate the polarization of the light field, so that the light field forms a sine or cosine oscillation form in the X-Z plane projection to provide a reciprocal lattice vector, which is used to compensate for momentum mismatch in the process of second-order nonlinear optical effects to achieve phase matching; the device does not need to rotate multiple layers of two-dimensional optical materials one by one, and can adjust the compensated reciprocal lattice vector to achieve rapid tuning.

Description

Technical Field

[0001] The present invention relates to phase matching of light, and in particular to a phase matching method and device for optical nonlinear frequency conversion. Background Art

[0002] Optical nonlinear frequency conversion, such as frequency doubling and optical parametric amplification, is widely used in industries such as industry and defense. Phase matching is often required to compensate for momentum mismatch, otherwise the conversion efficiency is extremely low. Commonly used methods include birefringence phase matching (BPM) and quasi-phase matching (QPM).

[0003] Quasi-phase matching was first proposed by Bloembergen in 1962. Its initial form used a periodically inverted domain structure to compensate for the three-wave phase mismatch. In the 1980s, Min Naiben and others expanded the periodically arranged domain structure into the concept of a dielectric superlattice, proposed the theory of multiple quasi-phase matching for quasi-periodic superlattices, and used quasi-periodic superlattices to achieve red, green, and blue laser generation. Later, fan-shaped, arc-shaped, two-dimensional array, and even three-dimensional superlattice structures were proposed and implemented. However, whether it is BPM or QPM, once the design scheme is determined, the compensation reciprocal lattice vector cannot be changed and can only be tuned over a small range by temperature, resulting in slow tuning speed.

[0004] As optical devices trend toward miniaturization and integration, new phase matching methods, such as coupled phase matching, mode phase matching, and natural phase matching, have emerged to accommodate the phase matching of nonlinear waveguide devices. Recently, twist phase matching has been proposed by rotating the principal axis of nonlinear materials, a method known as twist phase matching. For example, this can be achieved by rotating the two-dimensional material boron nitride (rBN), and by rotating liquid crystals. However, rotating the two-dimensional material requires rotating multiple layers of optically processed two-dimensional material one by one, which is very labor-intensive. Furthermore, the nonlinear coefficient of liquid crystals is not high, and their damage threshold is very low, making it difficult to achieve high conversion power. Summary of the Invention

[0005] Purpose of the invention: The purpose of the present invention is to achieve a phase matching method for optical nonlinear frequency conversion that can adjust the compensation reciprocal lattice vector without rotating multiple layers of two-dimensional optical materials one by one, thereby realizing rapid tuning.

[0006] Technical solution: The phase matching method for optical nonlinear frequency conversion described in the present invention injects multiple light fields along the X-axis into a periodically poled lithium niobate crystal whose optical axis and positive and negative domain polarization directions are all along the Z-axis; one of the light fields is polarized by the periodically poled lithium niobate crystal, so that the light field forms a sine or cosine oscillation form in the XZ plane projection to provide a reciprocal lattice vector, which is used to compensate for the momentum mismatch in the process of second-order nonlinear optical effect to achieve phase matching.

[0007] Preferably, the applied electric field strength of the periodically poled lithium niobate crystal is calculated according to the following formula:

[0008]

[0009] Among them, γ 51 is the electro-optic tensor element, λ is the wavelength of the light to be rotated, n o is the refractive index of ordinary light, n e is the refractive index of the extraordinary light, and K is the wave vector mismatch to be compensated.

[0010] Preferably, the wave vector mismatch is calculated according to the following formula during the nonlinear three-wave coupling process:

[0011]

[0012] Among them, λ p ,λ s and λ i are the wavelengths of pump light, signal light, and idler light, respectively, and n p 、n s and n i represent the refractive indices of pump light, signal light, and idler light, respectively;

[0013] During the nonlinear dual-wave coupling process, the following formula is used to calculate

[0014]

[0015] Wherein, λ1 and λ2 represent the wavelengths of the frequency-doubled light and the fundamental light, respectively, and n1 and n2 represent the refractive indices of the frequency-doubled light and the fundamental light, respectively.

[0016] Preferably, the polarization-rotated light forms a sine or cosine oscillation form in the XZ plane projection as follows:

[0017] The complex amplitudes of the light field to be rotated in the Y and Z directions satisfy the following equations:

[0018]

[0019] Δβ=(β Z -β Y )-G

[0020] Among them, A Y and A Z They represent the complex amplitudes of the light field in the Y and Z directions, respectively, and x is the X-axis coordinate of the position of the light field; β Y and β Z are the wave vectors in the Y and Z directions, respectively, and are determined according to the following formulas:

[0021]

[0022] G is the wave vector of periodically poled lithium niobate crystal compensation, which is determined by the following formula

[0023]

[0024] when When the complex amplitude of the light field in the Y and Z directions satisfies the following formula

[0025]

[0026] According to the above formula, find A Z The second derivative of x and A Y Substituting the first-order derivative formula for x into the equation, we get

[0027]

[0028] The general solution of the above formula is

[0029] A Z =C(e iKx ±e -iKx )

[0030] Where C is a constant;

[0031] The polarization-rotated light field projected on the XZ plane satisfies the sine or cosine oscillation form defined by the above formula.

[0032] The phase matching device described in the present invention using any of the above methods includes lithium niobate, which is arranged in a strip shape on a silicon dioxide substrate, and positive and negative electrodes are provided on both sides of the length direction of the lithium niobate; the length direction of the lithium niobate adopts a periodic positive and negative domain alternating structure.

[0033] Preferably, the motor adopts transparent ITO electrodes.

[0034] Preferably, the period of the alternating positive and negative domain structure of lithium niobate is Λ.

[0035] Preferably, the lithium niobate is produced into a periodic positive and negative domain alternating structure by room temperature electric field polarization.

[0036] Beneficial effects: Compared with the prior art, the present invention has the following significant effects: the present invention adopts a phase matching method of rotating polarization state to realize second-order nonlinear optical frequency conversion, rotates the lithium niobate main axis through the electro-optical effect, and then realizes the rotation of polarized light. There is no need to rotate multiple layers of two-dimensional optical materials one by one, the operation is simple, and the compensating reciprocal lattice vector can be adjusted to achieve fast tuning. BRIEF DESCRIPTION OF THE DRAWINGS

[0037] Figure 1 Schematic diagram of periodically poled lithium niobate crystal and rotated polarized light;

[0038] Figure 2 Projection view of periodically poled lithium niobate crystal and rotated polarized light in the XZ plane;

[0039] Figure 3 Schematic diagram of the optical axis deflection after an electric field is applied to the positive and negative domains of a periodically poled lithium niobate crystal;

[0040] Figure 4 This is a schematic diagram of the front view of the optical axis deflection after an electric field is applied to the positive and negative domains of a periodically poled lithium niobate crystal;

[0041] Figure 5 A schematic structural diagram of a phase matching device provided by the present invention;

[0042] Figure 6 is the relationship between the compensated wave vector mismatch and the applied electric field strength;

[0043] Figure 7 is the relationship between temperature and wave vector mismatch. DETAILED DESCRIPTION

[0044] The present invention discloses a phase matching method for optical nonlinear frequency conversion, which injects multiple light fields along the X-axis into a periodically poled lithium niobate crystal whose optical axis and positive and negative domain polarization directions are all along the Z-axis; the periodically poled lithium niobate crystal is used to perform polarization rotation on one of the light fields, so that the light field forms a sine or cosine oscillation form in the XZ plane projection to provide a reciprocal lattice vector, which is used to compensate for the momentum mismatch in the process of second-order nonlinear optical effect to achieve phase matching.

[0045] In order to simplify the description, periodically poled lithium niobate crystals will be referred to as PPLN in the following text.

[0046] The length direction of the PPLN is along the X-axis direction. The PPLN adopts a structure with alternating positive and negative domains. The polarization directions of the positive and negative domains and the optical axis of the PPLN are parallel to the Z-axis direction. There are multiple light fields transmitted along the X-axis direction in the PPLN. By applying an electric field in the Y-direction, the PPLN rotates the polarization of one of the light fields.

[0047] like Figure 1As shown, Figure 1 For ease of demonstration, the upper part is the transmitted light field, and the lower part is the PPLN. The light color in the PPLN is the positive domain 4, and the dark color is the negative domain 5. For the frequency doubling process, E2 is set as the fundamental light field, and E1 is set as the frequency doubling light field. The PPLN rotates the polarization of E1 so that its polarization is formed along the X-axis as shown in the figure. Figure 1 The polarization form of the rotation shown in FIG, and the polarization direction of the E2 light field is always parallel to the Z axis; at this time, as shown in FIG. Figure 2 As shown, the projection of the rotating E1 field on the XZ plane forms a sine or cosine oscillation, providing a reciprocal lattice vector that compensates for the momentum mismatch from E2 doubling to E1. In addition, for the more general nonlinear three-wave coupling process, PPLN rotates the polarization of one of the light fields while the polarization states of the other two light fields remain unchanged, similar to the frequency doubling process, compensating for the momentum mismatch of three-wave coupling.

[0048] Consider only two domains, one positive and one negative, in PPLN, where the positive domain 4 is in front and the negative domain 5 is in the back. There are electrodes 3 on the sides of the domains, that is, there are electrodes 3 on the front and back sides in the Y direction, and positive and negative voltages are applied respectively. After applying the electric field, according to the electro-optical principle of lithium niobate, the main axis generates the following Figure 3 The rotation shown in the figure is opposite to the rotation direction of the positive and negative domains. The rotation angle of the positive domain 4 is recorded as -θ, and the rotation angle of the negative domain 5 is recorded as +θ. θ is calculated according to the following formula

[0049]

[0050] where γ 51 is the electro-optic tensor element, E is the external electric field intensity, n o and n e are the refractive indices of ordinary and extraordinary light, respectively.

[0051] like Figure 4 As shown, linearly polarized light E A Entering the positive domain 4 along the X axis, E A The polarization direction is along the Z axis. Under the action of the electric field, the optical axis of the positive domain 4 rotates to become the A1 axis. When the thickness of the positive domain 4 satisfies the following formula, the positive domain 4 is equivalent to a half-wave plate.

[0052]

[0053] Among them, L c is the thickness of a single PPLN domain, λ A For E A wavelength.

[0054] After L c After the length of the positive domain 4, E A Become E which is symmetrical with A1 B , that is, it rotates by -2θ degrees.

[0055] Under the action of the electric field, the optical axis of the negative domain 5 rotates to become the A2 axis. When the thickness of the negative domain 5 satisfies (2), the negative domain 5 is also equivalent to a half-wave plate. c After the negative domain length of 5, E B Become E which is symmetrical with A2 C , that is, rotated 6θ degrees relative to E A Rotated 4θ degrees. And so on, because the angle θ is very small, the total effect is Figure 1 The effect of continuous rotation is shown, eventually rotating 360 degrees and more.

[0056] The complex amplitude of the light field in the Z and Y directions in the above process is described as:

[0057]

[0058] Δβ=(β Z -β Y )-G (5)

[0059] Among them, A Y and A Z They represent the complex amplitudes of the light field in the Y and Z directions, respectively, and x is the X-axis coordinate of the position of the light field; β Y and β Z are the wave vectors in the Y and Z directions, respectively.

[0060] K is calculated according to the following formula

[0061]

[0062] And G is the wave vector of PPLN compensation:

[0063]

[0064] When Λ=2L c When Δβ=0, (3) and (4) become:

[0065]

[0066] After taking the second derivative of (8) with respect to x and substituting (9) into it, we obtain:

[0067]

[0068] The general solution of the above formula is:

[0069] A Z =C(e iKx ±e -iKx ) (11)

[0070] That is, the sine or cosine function, where C is a constant; taking the sine function as an example, (11) can be written as

[0071] A Z =Csin(Kx) (12)

[0072] According to the periodicity of the sine function, A Z It has a modulation frequency of ±K, or in other words, a reciprocal lattice vector of ±K.

[0073] For the nonlinear three-wave coupling process, due to the existence of dispersion The wave vector mismatch, where λ p ,λ s and λ i are the wavelengths of pump light, signal light, and idler light, respectively, and n p 、n s and n i Represent the refractive index of pump light, signal light and idler light respectively; Specially, the frequency doubling process belongs to λ s =λ i =2λ p The degenerate process of wave vector mismatch is expressed as Here, λ1 and λ2 represent the wavelengths of the frequency-doubled light and the fundamental light, respectively, and n1 and n2 represent the refractive indices of the frequency-doubled light and the fundamental light, respectively. To compensate for this wave vector mismatch, the polarization rotation method described above is used to set K = ΔK, that is, to compensate for the wave vector mismatch by the reciprocal lattice vector.

[0074] The present invention will be further described below with reference to examples.

[0075] like Figure 5 As shown, the specific structure of PPLN is a strip waveguide made of a ridge-type thin-film lithium niobate 2 on a silicon dioxide substrate 1. The cross-section of the waveguide is 1μm×1μm, and transparent ITO electrodes 3 are plated on both sides of the waveguide. The Z axis of the thin-film lithium niobate 2, that is, the optical axis, is vertically upward, and a domain structure with a period of Λ is produced by room temperature electric field polarization.

[0076] The frequency doubling process adopts λ2=1064nm→λ1=532nm, that is, the incident fundamental wave is linearly polarized light with a wavelength of 1064nm, and its polarization direction is parallel to the Y axis, and the polarization direction of the frequency doubling light is along the Z axis. The frequency doubling process is Class I phase matching, and at a certain temperature, it has a critical BPM matching point.

[0077] However, when the temperature is not suitable, there is a phase mismatch, which is compensated according to the above polarization rotation method. Specifically, according to formula (6), λ = 1064 nm, n o =2.228875,n e =2.147638,γ 51=32pm / V, the relationship between the compensated K and the applied electric field can be calculated as follows: Figure 6 As shown, the wave vector mismatch of about ±6000 can be compensated by the method of the present invention.

[0078] According to Figure 7 The relationship between temperature and phase mismatch is that at 20 degrees Celsius to 40 degrees Celsius, the wave vector mismatch is about 5000. According to the above calculation results, it can be seen that the range of wave vector mismatch in this case is within the range that can be compensated by the method of the present invention; therefore, the method of the present invention can be used to perform wave vector compensation on the frequency doubling process with certain temperature fluctuations.

[0079] In addition, if the nonlinear process is a parametric process, the wavelength tuning of the parameter can also be achieved through the method of the present invention.

Claims

1. A phase matching method for optical nonlinear frequency conversion, characterized by: Multiple light fields are incident along the X-axis onto a periodically poled lithium niobate crystal whose optical axis and positive and negative domain polarization directions are all along the Z-axis. An electric field is applied to the front and rear sides of the periodically poled lithium niobate crystal in the Y-axis direction to rotate the polarization of the light field, causing the light field to form a sine or cosine oscillation in the XZ plane projection to provide a reciprocal lattice vector, which is used to compensate for the momentum mismatch in the second-order nonlinear optical effect process to achieve phase matching. The complex amplitudes of the light field to be rotated in the Y and Z directions satisfy the following equations: Δβ=(β Z -b Y )-G Among them, K is the inverted lattice vector; A Y and A Z They represent the complex amplitudes of the light field in the Y and Z directions, respectively, and x is the X-axis coordinate of the position of the light field; β Y and β Z are the wave vectors in the Y and Z directions, respectively, and are determined according to the following formulas: G is the wave vector of periodically poled lithium niobate crystal compensation, which is determined by the following formula when When the complex amplitude of the light field in the Y and Z directions satisfies the following formula According to the above formula, find A Z The second derivative of x and A Y Substituting the first-order derivative formula for x into the equation, we get The general solution of the above formula is TO Z =C(e iKx ±e -iKx ) Where C is a constant; The polarization-rotated light field projected on the XZ plane satisfies the sine or cosine oscillation form defined by the above formula.

2. The phase matching method for optical nonlinear frequency conversion according to claim 1, characterized in that: The applied electric field strength of the periodically poled lithium niobate crystal is calculated according to the following formula Among them, γ 51 is the electro-optic tensor element, λ is the wavelength of the light to be rotated, n o is the refractive index of ordinary light, n e is the refractive index of extraordinary light, and K is the reciprocal lattice vector.

3. The phase matching method for optical nonlinear frequency conversion according to claim 2, characterized in that: The reciprocal lattice vector is equal to the wave vector mismatch, which is calculated according to the following formula in the nonlinear three-wave coupling process. Among them, λ p ,λ s and λ i are the wavelengths of pump light, signal light, and idler light, respectively, and n p 、n s and n i represent the refractive indices of pump light, signal light, and idler light, respectively; During the nonlinear dual-wave coupling process, the following formula is used to calculate Wherein, λ1 and λ2 represent the wavelengths of the frequency-doubled light and the fundamental light, respectively, and n1 and n2 represent the refractive indices of the frequency-doubled light and the fundamental light, respectively.

4. The phase matching method for optical nonlinear frequency conversion according to claim 1, characterized in that: The polarization-rotated light satisfies the sinusoidal oscillation form defined by the following formula in the XZ plane projection: THE Z =Cin(Kx).

5. A phase matching device using the method of any one of claims 1 to 4, comprising lithium niobate, characterized in that: A long thin-film lithium niobate (2) is produced on a silicon dioxide substrate (1), and positive and negative electrodes (3) are provided on both sides of the thin-film lithium niobate (2) in the length direction; the thin-film lithium niobate (2) adopts a periodic positive and negative domain alternating structure in the length direction.

6. The phase matching device according to claim 5, characterized in that: The electrode (3) is a transparent ITO electrode.

7. The phase matching device according to claim 5, characterized in that: The period of the alternating positive and negative domain structure of the thin film lithium niobate (2) is Λ.

8. The phase matching device according to claim 5, wherein: The thin film lithium niobate (2) is produced into a periodic positive and negative domain alternating structure through room temperature electric field polarization.

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