JP4912387B2 - Nonlinear optical element - Google Patents

Description

  The present invention relates to a nonlinear optical device, and more particularly to a nonlinear optical device having a wavelength conversion function used in an optical communication system.

  Research and development of wavelength division multiplexing (WDM) communication technology has progressed as a technology for dramatically increasing the communication capacity by utilizing the current optical network. In WDM communication, if a plurality of optical signals having different wavelengths can be processed as light without being converted into electrical signals by an exchange, ultrahigh-speed signal processing can be performed.

Research on all-optical wavelength conversion technology necessary to realize this has also progressed, and representative methods include (1) a method using mutual gain modulation and cross phase modulation of a semiconductor optical amplifier, and (2). There has been proposed a method of utilizing sum frequency and difference frequency generation, which is a second order nonlinear effect of a nonlinear optical crystal. In the latter nonlinear optical crystal, the electric polarizability P of the crystal with respect to the electric field E of incident light is P = ε ₀ (χ ⁽¹⁾ E + χ ⁽²⁾ E ² + χ ⁽³⁾ E ³ +. Thus, a crystal such as LiNbO _{3 having} a large χ ⁽²⁾ component without central symmetry is often used. Here, ε ₀ is the dielectric constant in vacuum. In particular, a quasi-phase matching (QPM) method using a periodically poled structure that can effectively perform phase matching of propagating light in a nonlinear crystal is used to generate sum frequency and difference frequency with high efficiency. A LiNbO ₃ (QPM-LM) element having this periodically poled structure has been developed.

  As a feature of the wavelength conversion described above, in the method (1), it is necessary to input light (trigger light) having a wavelength equal to the wavelength of the conversion destination from the outside in advance, and light of any wavelength can be freely generated. I can't. On the other hand, the method (2) has a feature that it can generate even light of a wavelength that is not input, eliminates the need for a laser device that generates trigger light, and avoids a complicated device configuration.

  Therefore, the wavelength conversion of (2) will be taken up, and the following explanation will be made by taking as an example a cascade type difference frequency generation often used in the optical communication field (see FIG. 1). FIG. 1 is a diagram illustrating an example of wavelength conversion in WDM communication. The signal light 1 is composed of a plurality of wavelengths. In the cascade type wavelength conversion, the excitation light 2 is once converted into the SHG light 3, the SHG light 3 and the signal light 1 generate a difference frequency, and the converted light 4 is output. Therefore, the converted light 4 and the signal light 1 are output symmetrically with the excitation light 2 as the center. Here, although cascade type difference frequency generation is taken as an example, the same difference frequency generation is performed even if excitation light having the same wavelength as that of the SHG light 3 is independently incident from the outside.

  When the wavelength of the excitation light 2 is swept, it is considered that the wavelength of the SHG light 3 is also shifted, and the wavelength of the converted light 4 is also shifted accordingly. In practice, however, the signal light 1, the SHG light 3, and the converted light 4 are If the wavelength is not shifted so as to satisfy the quasi-phase matching condition (QPM condition) as shown, there arises a problem that the efficiency of the converted light is extremely lowered.

  In order to solve this problem, a multi-period QPM structure that is discrete but satisfies the QPM condition and can realize wavelength shift has been proposed (see Patent Document 1 and Non-Patent Document 1). With this structure, as shown in FIG. 2, the wavelength of the converted light 4 can be shifted discretely without reducing the conversion efficiency.

  In the following, a brief description of this principle and the problems that occur will be described.

FIG. 3 shows a configuration of a wavelength conversion device including a QPM-LN element. This apparatus includes a multiplexer 5 and a QPM-LN element 6 that synthesize signal light l (wavelength λ ₁ ) and pump light 2, and a demultiplexer that separates converted light 4 (wavelength λ ₂ ) and non-converted light 7. 8 is composed. The non-converted light 7 is completely converted into the SHG light (wavelength λ ₃ ) generated in the QPM-LN element 6 in addition to the signal light 1 and completely converted into the pumping light 2 and the converted light 4 that remain. It refers to the SHG light 3 remaining without being processed. In WDM communication, the wavelength of the signal light 1 are a plurality, one representative of them is the wavelength lambda _1. Even when the signal light 1 has a wavelength distribution, the WDM light can be collectively converted because the QPM condition has a large tolerance for the signal light wavelength.

  The QPM-LN element 6 shown in FIG. 3 is provided with an optical waveguide 9 for increasing the electric field strength of the signal light 1, the SHG light 3, and the converted light 4. Although wavelength conversion is realized even in a bulk QPM-LN element without the optical waveguide 9, the conversion efficiency is reduced because the electric field strength is reduced.

In a wavelength converter including a QPM-LN element, assuming that the wavelength of the signal light 1 is λ ₁ and the wavelength of the SHG light generated in the QPM-LN element 6 is λ ₃ , the wavelength λ ₂ that satisfies the following relational expression is converted: Light 4 can be output.

  When the second-order nonlinear constant of the QPM-LM element 6 is modulated as a function of the light propagation direction z as d (z), the power of the converted light 5 is

It is proportional to the quantity. Where j is the imaginary unit, L is the total element length, Δβ is the amount of phase mismatch

Is defined. Here, n _i (i = 1, 2, 3) is a refractive index with respect to the wavelength λ _i (i = 1, 2, 3). If the function d (z) is a function of the uniform period of the periodic lambda _0, using the Fourier coefficients d _m d (z) is

(M: integer). Using this, the conversion efficiency η to the converted light 4 is calculated.

The result is obtained. Here, η ₀ is the maximum value of the conversion efficiency realized by Δβ = 2πm / Λ ₀ . Since η ₀ is proportional to 1 / m ² , it is necessary to optimally design Λ ₀ under the condition that Λ ₀ is Δβ = 2π / Λ ₀ so that η ₀ is maximized. .

On the other hand, in the multi-period QPM-LN element, a phase term φ (z) having a period Λ _ph different from Λ ₀ is introduced into the function d (z), modulation is applied to d (z), and the phase matching condition is Δβ = 2π / Λ ₀ + 2πl / Λ _ph (l: integer). Thereby, although it is discrete, phase matching can be realized in a wider wavelength range (see Patent Document 1 and Non-Patent Document 1).

  Further, a possible value of the conversion efficiency η at a given integer value l is expressed as conversion efficiency η (l). If the conversion efficiency η (l) is constant for N l and the spectrum of SHG light becomes flat, the output of the converted light after wavelength shift becomes constant, which is important for wavelength conversion in WDM communication. It becomes a condition.

  In order to prevent the conversion efficiency η (l) from fluctuating with l,

The shape of φ (z) is changed while the phase function φ (z) satisfies the condition of φ (z) = φ (z + Λ _ph ) so as to minimize δ. As a result, it is possible to obtain a spectrum of SHG light in which N conversion efficiencies η (l) are aligned to a value very close to η _norm / N. Here, η _norm is the conversion efficiency realized in the case of a uniform period of period Λ ₀ .

Japanese Patent No. 3971660 M. Asobe, O. Tadanaga, H. Miyazawa, Y. Nishida, and H. Suzuki, “Multiple quasi-phase-matched device using continuous phase modulation of χ (2) grating and its application to variable wavelength converslon”, IEEE Journal of Quantum Electronics, 2005, Vol.41, pp.1540-1547

  However, the wavelength conversion using the multi-cycle QPM-LN element described above can achieve a certain conversion efficiency even at the wavelength between the peaks of the SHG light as shown in FIG. 4 in the phase matching curve under the QPM condition. There was a problem. That is, due to the conversion efficiency at the base between the peaks, in WDM communication, sum frequency generation (SFG) occurs between the other channel components of the signal light (circles) and the component of the converted light (circles). SFG light is generated in the meantime. Since the signal light wavelength is converted into the converted light wavelength region with the SFG light as the center, there is a problem in that it is superimposed on the converted light as crosstalk light.

  In WDM communication, when another signal light component is superimposed on a certain converted light component and crosstalk occurs, the SN ratio deteriorates. Therefore, the WDM signal is separated into one wave by a demultiplexer and each is sent to a different delivery destination. Causes a signal error in the signal.

  Furthermore, it is essential to increase the output as one of the improvement of the performance of the element, but this can be achieved by increasing the output of the pumping light or increasing the power density by reducing the waveguide diameter. If this is dealt with, extra light components existing between the aforementioned peaks will also increase, and crosstalk will also increase.

  The present invention has been made in view of such problems, and the object of the present invention is to significantly reduce the component of extra signal light superimposed on converted light when performing wavelength conversion in cascade-type difference frequency generation. An object of the present invention is to provide a non-linear optical element that can reduce the crosstalk to a minimum even when the output is increased.

In order to achieve such an object, the invention described in claim 1 is a nonlinear optical medium having a periodic structure with a fundamental period Λ ₀ in which the sign of a second-order nonlinear constant is periodically inverted with respect to the traveling direction of light. And a function that gives the phase change of the periodic structure is repeated for each period Λ _ph ,

Light having one or two of the three wavelengths λ ₁ , λ ₂ , and λ ₃ satisfying the above conditions is input, and light converted to a wavelength different from the input wavelength at any of the three wavelengths is output. In the non-linear optical element, the periodic structure of the non-linear optical element is that of the polarization inversion pair when two regions having second-order non-linear constants having different signs adjacent to each other are used as one inversion pair. The duty ratio, which is the ratio of the domain-inverted pair length including the area length of one code and the area of both codes, is a control function representing the duty ratio of all pairs of the nonlinear optical elements, A control function in which the duty ratio increases from the pair at both ends toward the pair at the center as a hyperbolic tangent function, and the refractive indices in the medium of the three wavelengths λ ₁ , λ ₂ , and λ ₃ are n ₁ , As n ₂ and n ₃ ,

The phase of the periodic structure optimized so that the peaks of a plurality of conversion efficiencies generated when the phase mismatch amount Δβ given by (2) matches 2π / Λ ₀ + 2πl / Λ _ph (l: integer) have the same value. It is set based on the function which gives a change.

  According to a second aspect of the present invention, in the nonlinear optical element according to the first aspect, when the total length of the nonlinear optical element is L and the traveling direction of light is the z direction, the control function is f ( z) is calculated using the parameter a

It is a hyperbolic tangent function given by

  According to a third aspect of the present invention, in the nonlinear optical element according to the first aspect, when the total length of the nonlinear optical element is L and the traveling direction of light is the z direction, the control function f ′ (Z) is calculated using the parameter a

It is a hyperbolic tangent function given by

The invention according to claim 4 includes a nonlinear optical medium having a periodic structure with a fundamental period Λ ₀ in which the sign of a second-order nonlinear constant is periodically inverted with respect to the traveling direction of light, and the period A nonlinear optical element in which the function that gives the phase change of the structure is repeated every period Λ _ph ,

Light having one or two of the three wavelengths λ ₁ , λ ₂ , and λ ₃ satisfying the above conditions is input, and light converted to a wavelength different from the input wavelength at any of the three wavelengths is output. In the nonlinear optical element, the periodic structure of the nonlinear optical element is a control function representing an average distribution of the second-order nonlinear constant of the entire nonlinear optical element, and one of the second-order nonlinear constants near both ends of the nonlinear optical element. A control function that is a hyperbolic tangent function that selectively reverses the sign of a part of the plurality of areas having the sign of ## EQU2 ## and reduces the frequency of sign inversion as it approaches the center of the nonlinear optical element. And the refractive indexes of the mediums of the three wavelengths λ ₁ , λ ₂ , and λ ₃ as n ₁ , n ₂ , and n ₃ , respectively,

Of the periodic structure optimized so that the peaks of the plurality of conversion efficiencies generated when the phase mismatch amount Δβ given by (2) matches 2π / Λ ₀ + 2πl / Λ _ph (l: integer) have the same value. It is set based on the function which gives a phase change.

  According to a fifth aspect of the present invention, in the nonlinear optical element according to the fourth aspect, when the total length of the nonlinear optical element is L and the traveling direction of light is the z direction, the control function is f ( z) is calculated using the parameter a

It is a hyperbolic tangent function given by

  According to a sixth aspect of the present invention, in the nonlinear optical element according to the fourth aspect, when the total length of the nonlinear optical element is L and the traveling direction of light is the z direction, the control function f ′ (Z) is calculated using the parameter a

It is a hyperbolic tangent function given by

  The invention described in claim 7 is the nonlinear optical element according to claim 3 or 6, wherein the parameter a is set so as to minimize a ripple value generated between the peaks.

The invention according to claim 8 is the nonlinear optical element according to any one of claims 1 to 7, wherein the nonlinear optical medium is LiNbO ₃ , KNbO ₃ , LiTaO ₃ , KTiOPO ₄ , LiNb _X Ta _{1. It is characterized by using -X} O ₃ (0 ≦ x ≦ 1) and a material in which at least one element selected from Mg, Zn, In, and Sc is added.

  According to the present invention, when wavelength conversion is performed in cascade-type difference frequency generation, the excess signal light component superimposed on the converted light is significantly reduced, and crosstalk is minimized even when the output increases. It becomes possible.

(Embodiment 1)
FIG. 5 shows a configuration of a wavelength conversion apparatus including a multi-period QPM-LN element 10 with a controlled duty ratio, which is a nonlinear optical element according to an embodiment of the present invention. The wavelength conversion device 11 includes a generation device for signal light 1 and a generation device for pumping light 2 that are input to the multi-cycle QPM-LN element 10.

  In the wavelength converter 11, the laser beams output from the plurality of light sources 12 have different wavelengths, and the modulator 13 superimposes different signals for each wavelength by the modulator 13. Thereafter, the light is multiplexed by the multiplexer 5 and transmitted to the optical waveguide 9 in the multi-period QPM-LM element 10 as the signal light 1 through the optical fiber 14. On the other hand, the pumping light 2 generated from the wavelength tunable light source 15 is passed through the optical amplifier 16 to increase the power in order to enhance the nonlinear optical effect, and then combined with the signal light 1 by the optical coupler 17 and input to the optical waveguide 9. Is done. When the signal light 1 and the excitation light 2 are input to the optical waveguide 9, wavelength conversion occurs in the optical waveguide 9, and the desired converted light 4 is extracted through the wavelength filter 18.

  Next, the structure of the multi-period QPM-LN element 10 will be described in detail. In the multi-period QPM-LN element 10, a domain of polarization directed in a certain direction and a domain of polarization adjacent in the opposite direction are considered as one pair, and the length of each pair is D. The ratio Δ / D between the pair length D and the occupancy region Δ of the unidirectional polarization domain in the pair (this is called the duty ratio) is controlled by a given function f (z) for all pairs. Think about it. That is, Δ / D = f (z) is set, and Δ / D is changed as a function of z (see FIG. 6). Here, z is a distance measured from one end (z = 0) of the element along the light traveling direction, and when the total length of the element is L, the other end is z = L.

  When the function f (z) takes a constant value such as f (z) = 1/2 when 0 ≦ z ≦ L, the change of f (z) becomes steep when z = 0 and z = L. Such a steep change causes generation of ripples between the peaks of the SHG light 3 as shown in FIG. 4 (that is, ripples due to the SFG of the ○ component and the ● component), and therefore, f (z) is changed to z = By using a function that gradually changes in the vicinity of 0 and z = L, the occurrence of ripples between peaks is reduced.

  As a function to be used, a prototype function (a) for comparison, f (z) = 1/2 (0 ≦ z ≦ L), a Gaussian function (b), a parabolic function (c), a sine wave The spectrum of the SHG light 3 was analyzed using the type function (d) and the hyperbolic tangent type function (e). The important points in this analysis are that f (z) of various functions are used, and the peak value η (l) (l = 1, 2,..., N (N = 5) of the SHG light 3 is used. )) Is flat so that

In other words, the phase function φ (z) is optimized so as to minimize δ.

  7A to 7E show the results of spectra flattened in the case of the functions (a) to (e). 7 (b) to (e), FIG. 7 (b) has a higher value around each peak than FIG. 7 (c) to (e). d) has a higher value than the center between peaks, that is, a ripple, as compared with FIG. That is, the following formula

The best results were obtained with the hyperbolic tangent function (e) given by Hereinafter, a detailed analysis is performed for the case of this hyperbolic tangent function (e). Here, a is a dimensionless amount parameter, and is hereinafter referred to as an apodized parameter. FIG. 8 shows how the function f (z) changes when the apodization parameter a is changed.

  FIG. 9A shows how the ripple value between the peaks of SHG light changes as a function of the apodized parameter in the case of the hyperbolic tangent function (e). In FIG. 9A, the ripple value is normalized by the peak value. FIG. 9A shows that the ripple value decreases as the apodization parameter a decreases. Since the hyperbolic tangent function (e) has a function form f (z) that matches the prototype (a) when a → ∞, the portion with a large apodization parameter a (a >> 1) and the small portion in FIG. Can be obtained the reduction rate of the ripple value when compared with the prototype (a). As shown in FIG. 9A, when the apodization parameter a is near 1, the ripple value is reduced by about 15 dB compared to the prototype (a).

  FIG. 9B shows the result of analyzing the conversion efficiency into the SHG light 3 at the QPM peak wavelength at the same time. The conversion efficiency decreases as the apodization parameter a decreases. This is because the hyperbolic tangent function f (z) shown in FIG. 8 decreases in amplitude as the apodization parameter a decreases, and the effective second-order nonlinear constant value having upward (or downward) polarization decreases. This is because the QPM effect is also weakened.

  Thus, when the apodization parameter a is reduced, the ripple value is reduced, but the conversion efficiency is also lowered.

  Next, in order to solve this dilemma, the amplitude of the hyperbolic tangent function f (z) is controlled, and a correction function f ′ (z) in which the maximum value of the amplitude is always constant (= ½). Is adopted. FIG. 10 shows the correction function f ′ (z) function. Here, the correction function f ′ (z) is expressed by the following equation:

Given in.

  FIG. 11 shows the conversion efficiency when the correction function f ′ (z) is used. The conversion efficiency decreases as the apodization parameter a decreases, but converges to a finite value and does not decrease further. This is because the correction function f ′ (z) asymptotically approaches a triangle as the apodization parameter a decreases, and even if a = 0, the correction function f ′ (z) has a finite half-value width and is upward ( This is because the distribution of the second-order nonlinear constant having polarization (or downward) also effectively remains in a finite region.

  Next, FIG. 12 shows a ripple value when the correction function f ′ (z) is used. The ripple value tends to decrease as the apodization parameter a decreases, but increases after reaching the lower limit in the vicinity of a = 0.85. This is because the deformation from the ideal function shape is increased by the correction. The ripple value at the optimum value (a = 0.85) can be reduced by about 10 dB compared to the case of the prototype function (a). This optimum value was also used in actual device design.

  Thus, the present invention can balance the conversion efficiency and the ripple value. The effect of the invention is that the distribution of the second-order nonlinear constant having upward (or downward) polarization gradually increases from both ends of the element toward the center and becomes maximum at the center. ) Or formula (3).

(Embodiment 2)
Another method for setting the periodic structure of the multi-period QPM-LN element 10 having the effect of balancing the conversion efficiency and the ripple value as in the first embodiment for controlling the duty ratio of the polarization inversion pair will be described.

  That is, the duty ratio of each pair is fixed, and instead, a large number of upward (or downward) polarization domains are inverted in opposite directions near both ends of the element, and the second-order nonlinear constant value in the vicinity is effectively changed. A method may be used in which the frequency of inversion is reduced near the center of the element, the second-order nonlinear constant value is increased, and the distribution of the second-order nonlinear constant follows Formula (2) or Formula (3). .

  FIG. 13A shows a structure of a multi-period QPM-LN element according to Embodiment 2 of the present invention. As shown in FIGS. 13 (a) and 13 (1), in a multi-cycle QPM-LN element with a fixed duty ratio (Δ / D = 1/2), an interval of a certain length as shown by a dotted line from the left end is provided. As shown in FIGS. 13 (a) and (2), a large number of polarization domains are inverted in the leftmost section, and the inversion frequency gradually decreases as it goes to the center, and after the center, the inversion frequency increases again. In addition, a large number of domain inversions occur in the right end section.

  FIG. 13B shows a spectrum diagram of the SHG phase matching curve of the multi-period QPM-LN element according to Embodiment 2 of the present invention. This spectrum diagram shows the multi-period QPM-LN element in which the domain inversion is performed so that the distribution of the second-order nonlinear constant of the multi-period QPM-LN element conforms to the equation (3), and a = 0.85 is set as the abolish parameter. It is calculated based on. It can be confirmed that the ripple between peaks is sufficiently reduced.

The nonlinear optical material of the multi-period QPM-LN element 10 includes LiNbO ₃ , KNbO ₃ , LiTaO ₃ , KTiOPO ₄ , LiNb _X Ta _1-X O ₃ (0 ≦ x ≦ 1), and Mg, Zn A material to which at least one element selected from In, Sc is added is preferable. Mg, Zn, In, and Sc are added to improve photodamage resistance. By using the above-mentioned nonlinear optical material, there is spontaneous polarization even at room temperature, and high controllability that can easily reverse the polarization by applying an electric field in the direction opposite to the polarization orientation can be obtained. Suitable for creating domain-inverted structures. In addition, since a complicated periodic domain-inverted structure can be accurately produced as designed, it is possible to produce devices with a high yield.

It is the figure which showed wavelength conversion in case the wavelength of excitation light and conversion light is fixed in wavelength conversion of the conventional cascade type | mold difference frequency generation. It is a figure explaining wavelength conversion when the wavelength of excitation light is varied using the conventional multi-period QPM-LN element, and the wavelength of converted light is also variable. It is a figure explaining the wavelength converter which has the conventional multiperiod QPM-LN element. It is the figure explaining the problem in the case of performing wavelength conversion using the conventional multiperiod QPM-LN element. It is a figure explaining the wavelength converter with which the nonlinear optical element of this invention is used. It is the figure explaining the control method of a duty ratio by the multi-period QPM-LN element by which the duty ratio was controlled which is the nonlinear optical element which concerns on one Embodiment of this invention. (A) is a prototype function, (b) is a Gaussian function, (c) is a parabolic type, with the periodic structure of a multi-period QPM-LN element, which is a nonlinear optical element of the present invention, as a duty ratio control function. It is a figure which shows the spectrum of SHG light when using a function, (d) uses a sine wave type function, (e) uses a hyperbolic tangent type function. It is a figure which shows the hyperbolic tangent function (Formula (2)) used as a duty ratio control function in the multi-period QPM-LN element which is the nonlinear optical element of the present invention. It is a figure which (a) generate | occur | produces when converting excitation light into SHG light using the multi-period QPM-LN element which is a nonlinear optical element of this invention, and (b) shows a conversion efficiency. It is a figure which shows the function (Formula (3)) which correct | amended the control function (Formula (2)) of a duty ratio in the multiperiod QPM-LN element which is a nonlinear optical element of this invention. It is a figure showing the conversion efficiency at the time of using the function (Formula (3)) correct | amended for control of the multiperiod QPM-LN element which is a nonlinear optical element of this invention. It is a figure which shows the ripple value at the time of using the function (Formula (3)) correct | amended for control of the multiperiod QPM-LN element which is a nonlinear optical element of this invention. (A) is a figure which shows the structure of the multi-period QPM-LN element which concerns on Embodiment 2 of this invention, (b) is the SHG phase matching of the multi-period QPM-LN element which concerns on Embodiment 2 of this invention. It is a spectrum figure of a curve.

Explanation of symbols

DESCRIPTION OF SYMBOLS 1 Signal light 2 Excitation light 3 SHG light 4 Conversion light 5 Multiplexer 6 QPM-LM element 7 Non-conversion light 8 Demultiplexer 9 Optical waveguide 10 Multiperiod QPM-LM element 11 Wavelength converter 12 Light source 13 Modulator 14 Light Fiber 15 Wavelength variable light source 16 Optical amplifier 17 Optical coupler 18 Wavelength filter

Claims (8)

A nonlinear optical medium having a periodic structure with a fundamental period Λ ₀ in which the sign of a second-order nonlinear constant is periodically inverted with respect to the traveling direction of light, and a function that gives a phase change of the periodic structure is a period Λ _ph A non-linear optical element repeated every time,

Light having one or two of the three wavelengths λ ₁ , λ ₂ , and λ ₃ satisfying the above conditions is input, and light converted to a wavelength different from the input wavelength at any of the three wavelengths is output. In the nonlinear optical element,
The periodic structure of the nonlinear optical element is:
When the two regions having the second-order nonlinear constants having different signs adjacent to each other of the nonlinear optical element are used as one polarization reversal pair, the length of one sign of the polarization reversal pair and the region of both signs are included. The duty ratio, which is the ratio of the polarization inversion pair length, is a control function representing the duty ratios of all the pairs of the nonlinear optical elements, and the duty ratio from the pair at both ends of the nonlinear optical elements toward the center pair. Is a hyperbolic tangent functionally increasing control function;
Assuming that the refractive indexes in the medium of the three wavelengths λ ₁ , λ ₂ , and λ ₃ are n ₁ , n ₂ , and n ₃ , respectively,

The phase of the periodic structure optimized so that the peaks of a plurality of conversion efficiencies generated when the phase mismatch amount Δβ given by (2) matches 2π / Λ ₀ + 2πl / Λ _ph (l: integer) have the same value. A nonlinear optical element characterized in that it is set based on a function that gives a change. When the total length of the nonlinear optical element is L and the traveling direction of light is the z direction, the control function f (z) is expressed by the following equation using the parameter a:

The nonlinear optical element according to claim 1, wherein the nonlinear optical element is a hyperbolic tangent function given by: When the total length of the nonlinear optical element is L and the traveling direction of light is the z direction, the control function f ′ (z) is expressed by the following equation using the parameter a:

The nonlinear optical element according to claim 1, wherein the nonlinear optical element is a hyperbolic tangent function given by: A nonlinear optical medium having a periodic structure with a fundamental period Λ ₀ in which the sign of a second-order nonlinear constant is periodically inverted with respect to the traveling direction of light, and a function that gives a phase change of the periodic structure is a period Λ _ph A non-linear optical element repeated every time,

Light having one or two of the three wavelengths λ ₁ , λ ₂ , and λ ₃ satisfying the above conditions is input, and light converted to a wavelength different from the input wavelength at any of the three wavelengths is output. In the nonlinear optical element,
The periodic structure of the nonlinear optical element is:
A control function representing an average distribution of second-order nonlinear constants of the whole nonlinear optical element, and a part of a plurality of areas having one sign of the second-order nonlinear constant near both ends of the nonlinear optical element And a control function that is a hyperbolic tangent function that reduces the frequency of sign inversion as it approaches the center of the nonlinear optical element,
Let n ₁ , n ₂ , and n _{3 be} the refractive indexes of the three wavelengths λ ₁ , λ ₂ , and λ ₃ , respectively.

Of the periodic structure optimized so that the peaks of the plurality of conversion efficiencies generated when the phase mismatch amount Δβ given by (2) matches 2π / Λ ₀ + 2πl / Λ _ph (l: integer) have the same value. A nonlinear optical element, which is set based on a function that gives a phase change. When the total length of the nonlinear optical element is L and the traveling direction of light is the z direction, the control function f (z) is expressed by the following equation using the parameter a:

The nonlinear optical element according to claim 4, wherein the nonlinear optical element is a hyperbolic tangent function given by: When the total length of the nonlinear optical element is L and the traveling direction of light is the z direction, the control function f ′ (z) is expressed by the following equation using the parameter a:

The nonlinear optical element according to claim 4, wherein the nonlinear optical element is a hyperbolic tangent function given by:   7. The nonlinear optical element according to claim 3, wherein the parameter a is set so as to minimize a ripple value generated between the peaks. The nonlinear optical medium is LiNbO ₃ , KNbO ₃ , LiTaO ₃ , KTiOPO ₄ , LiNb _x Ta _1-x O ₃ (0 ≦ x ≦ 1), and at least one selected from Mg, Zn, In, and Sc The nonlinear optical element according to claim 1, wherein a material to which any of the elements is added is used.

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