CN115437191A - Method for realizing quasi-phase matching multi-band broadband frequency multiplication - Google Patents

Abstract

The invention discloses a method for realizing quasi-phase matching multiband broadband frequency multiplication, which belongs to the technical field of optical elements, wherein crystals with a quasi-periodic structure and complementary duty ratios are used in the method, so that broadband frequency multiplication output of different wavebands is realized; the crystal material is a polarized lithium niobate crystal, the structure of the crystal is formed by nesting two unit domains A and B with different domain lengths, the nesting sequence of the unit domains is ABBA, and the numerical ratio of A to B \30052lengthis calculated by an algorithm; the invention can realize broadband frequency multiplication output of three wave bands in a quasi-periodic structure device with complementary duty ratio of 10 ℃ of temperature gradient and 60 ℃ of initial temperature under the condition of meeting Type-I (e + e → o) Type quasi-phase matching; meanwhile, the relation between the temperature gradient and the bandwidth and the relation between the temperature gradient and the conversion efficiency are analyzed, and the output bandwidth can be adjusted by adjusting the temperature gradient. The research realizes frequency doubling conversion full coverage of common optical communication wave bands, and has important significance for development of all-optical communication.

Description

Method for realizing quasi-phase matching multi-band broadband frequency multiplication

Technical Field

The invention belongs to the technical field of optical elements, and particularly relates to a method for realizing quasi-phase matching multi-band broadband frequency multiplication.

Background

At present, along with the rapid development of nonlinear optics, light waves generated by utilizing various nonlinear effects such as frequency doubling and sum frequency are greatly applied in actual life. In the second-order nonlinear phenomenon, due to the existence of material dispersion, the existence of phase mismatch amount in a series of nonlinear effects such as frequency multiplication and sum frequency is caused, only the phase mismatch is eliminated, the energy can be transferred from fundamental wave to harmonic wave only by the series of second-order nonlinear effects such as frequency multiplication and sum frequency, and the phase matching between interaction waves is a necessary condition for obtaining high conversion efficiency. For frequency doubling as an example, the phase matching must be such that the refractive indices of the fundamental and second harmonics are equal. Although the birefringence phase matching technique using the crystal birefringence phenomenon can achieve complete phase matching, the technique can be used only in the vicinity of one wavelength in a certain crystal to achieve wavelength conversion, and the bandwidth for achieving wavelength conversion is also small. The birefringence phase matching can achieve high conversion efficiency, but has high dependence on nonlinear materials, and the phase matching can be achieved only in a specific wave band for a specific nonlinear material. There are also high requirements on the angle of incidence, and these factors limit the practical application of birefringence phase matching. In contrast, quasi-phase matching (QPM) has many advantages. The quasi-phase matching technology can greatly improve the efficiency of nonlinear frequency conversion by periodically changing the polarization intensity of a nonlinear material and compensating the phase difference generated by the dispersion effect of the material by modulating the second-order polarizability of a nonlinear medium.

In quasi-phase matching, the refractive index of the nonlinear crystal changes with temperature. The change makes the matching condition of quasi-phase matching become more rigorous, and in order to ensure the quasi-phase matching process with higher conversion efficiency, QPM frequency conversion needs to be carried out in a constant temperature environment. However, in the process of broadband frequency multiplication, the change is favorable, an optical superlattice can be placed in an environment with a temperature change gradient, and the energy of all fundamental waves meeting the QPM condition in the temperature gradient is continuously coupled in the superlattice, so that the output of broadband frequency multiplication is realized. In 2019, a. Arie et al achieved second harmonic output with a bandwidth 5.4 times the fixed phase matching temperature in a 50mm long Lithium Borate (LBO) crystal by using a temperature gradient of 18 ℃. In 2013, heanhua, huangqin et al propose a new design scheme for generating a laser light source based on a broadband mid-infrared difference frequency with equal period PPLN crystal gradual change type temperature control. Theoretical research results show that under the condition of fixed pumping light wavelength, the quasi-phase matching (QPM) wavelength receiving bandwidth of the idler light/signal light increases along with the increase of the temperature gradient at two ends of the crystal, but the difference frequency conversion efficiency is reduced.

The search of the prior art finds that the technology based on quasi-phase matching broadband frequency multiplication is mature and has obvious advantages, but the following defects still exist: 1. in the quasi-phase matching broadband frequency multiplication generation, the prior art realizes broadband frequency multiplication in one wave band and cannot cover a plurality of wave bands; 2. in the generation of quasi-phase matching broadband frequency multiplication, the increase of the bandwidth sacrifices a large amount of conversion efficiency, and the prior art cannot realize the adjustment of the bandwidth and the conversion efficiency.

Disclosure of Invention

The invention aims to: in order to overcome the defects in the prior art, the invention provides a method for realizing quasi-phase matching multiband broadband frequency multiplication, in the method, a lithium niobate crystal with a specific quasi-periodic structure is adopted and designed as a complementary duty ratio quasi-periodic crystal structure model, and broadband frequency multiplication output of three wave bands of 0.85 mu m, 1.31 mu m and 1.55 mu m is realized by applying temperature gradient. Meanwhile, the relation between the temperature gradient and the bandwidth and the conversion efficiency is analyzed, and the output bandwidth can be adjusted by adjusting the temperature gradient.

The technical scheme is as follows: in a first aspect, the present invention provides a method for generating multi-band broadband frequency multiplication by quasi-phase matching, wherein the method uses a crystal with a complementary duty ratio quasi-periodic structure, and utilizes Type-I (e + e → o) quasi-phase matching to realize broadband frequency multiplication output for three different bands, namely 0.85 μm and 1.31 μm and 1.55 μm, by controlling temperature, and the method comprises the following steps:

step 1: providing a quasi-periodic crystal structure model based on quasi-phase matching multiband broadband frequency multiplication;

and 2, step: giving initial conditions, and determining specific parameters of a quasi-periodic crystal structure of a complementary duty ratio;

and step 3: the temperature is controlled by aligning with a periodic crystal structure, multiband broadband frequency doubling output is realized in a quasi-periodic device with the temperature gradient of 10 ℃ and the initial temperature of 60 ℃, and multiband broadband frequency doubling corresponding to the output under different temperature gradients is obtained;

and 4, step 4: analyzing the multi-band broadband frequency multiplication correspondingly output under different temperature gradients to obtain the relationship between the temperature gradient bandwidth and the conversion efficiency; and the temperature gradient of the crystal is adjusted through the relationship between the temperature gradient bandwidth and the conversion efficiency, so that the adjustment of the output bandwidth is realized.

In a further embodiment, in step 1, the material of the crystal is 5mol% magnesium oxide-doped lithium niobate crystal (5 mol% mgo ln), the crystal is in a rectangular parallelepiped shape, the upper and lower surfaces are parallel and are polished, the crystal is formed by nesting two a and B unit domains with different domain lengths in the light wave propagation direction, the crystal comprises four unit domains in one period, the order of nesting the unit domains is ABBA, and the spontaneous polarization direction of each unit domain is arranged from top to bottom in sequence.

In a further embodiment, the ratio of a to B \30052longin step 1 is lA: lB = 1.

In a further embodiment, in the step 2, an initial wavelength and a temperature are given, a coherence length required for realizing Type-I (e + e → o) quasi-phase matching under the condition is determined by using a Sellmeier equation, twice of the coherence length is taken as a period length of the quasi-periodic structure, and \30052lengthof a and B domains is determined by proportion, and the period number of the structure is determined according to the calculated period length.

In a further embodiment, in step 2, the calculation formula of the coherence length Lc is:

wherein λ is a fundamental wavelength of light, n _ω Refractive index of fundamental frequency light in crystal, n _2ω Is the refractive index of the frequency doubled light in the crystal.

In a further embodiment, in said step 2, the total length of the quasi-periodic structure crystals is 6.5mm.

In a further embodiment, in step 3, the frequency multiplication efficiency is calculated by the following formula:

in the formula I _ω Representing the intensity of the fundamental wave, c the speed of light in vacuum, epsilon ₀ Denotes the dielectric constant in vacuum, λ denotes the fundamental wavelength, n _ω And n _2ω Respectively representing the refractive indices of the fundamental and second harmonics in the crystal, d ₃₃ The maximum nonlinear coefficient in the z direction is represented, L represents the total length of the crystal, Δ k (λ) represents the phase mismatch amount, d (z) represents the polarization direction distribution of a single domain unit, and changes along with the change of the z value; when d (z) =1, the polarization direction is upward, when d (z) = -1, the polarization direction is downward;

wherein, the calculation formula of Δ k (λ) is:

in a further embodiment, in step 3, a relative effective nonlinear coefficient dreff (λ) is further introduced as:

the conversion efficiency is measured by introducing a normalized value of dreff (lambda).

Has the advantages that: compared with the prior art, the invention has the following advantages:

based on the principle of quasi-phase matching technology, the invention can simultaneously realize broadband frequency multiplication output of a plurality of wave bands in a quasi-periodic crystal structure with complementary duty ratio by applying temperature gradient; under the condition of meeting Type-I (e + e → o) Type quasi-phase matching, in a complementary duty ratio quasi-periodic device with the temperature gradient of 10 ℃ and the initial temperature of 60 ℃, broadband frequency multiplication output of three wave bands is realized; meanwhile, the temperature gradient can be adjusted to realize the adjustment of the output bandwidth by analyzing the relationship between the temperature gradient and the bandwidth and the conversion efficiency. The research realizes frequency doubling conversion full coverage of common optical communication wave bands, and has important significance for development of all-optical communication.

Drawings

FIG. 1 is a schematic diagram of a complementary duty cycle quasi-periodic poled lithium niobate crystal structure provided by an embodiment of the present invention;

FIG. 2 is a graph of complementary duty cycle quasiperiodic structure crystal length versus temperature provided by an embodiment of the present invention;

FIG. 3 is a graph of normalized conversion efficiency spectrum of multiband broadband frequency multiplication for a complementary duty cycle device under Type-I (e + e → o) quasi-phase matching and temperature gradient according to an embodiment of the present invention;

fig. 4 is a graph of the multi-band broadband frequency-doubled normalized conversion efficiency spectrum of the complementary duty cycle device provided by the embodiment of the invention under different temperature gradients.

Detailed Description

In order to more fully understand the technical contents of the present invention, the technical solutions of the present invention will be further described and illustrated with reference to specific embodiments, but not limited thereto.

The method for realizing the quasi-phase matching multiband broadband frequency multiplication provided by the embodiment of the invention uses a crystal with a quasi-periodic structure, the crystal material is a polarized lithium niobate crystal, the crystal structure is formed by nesting two unit domains A and B with different domain lengths, four unit domains are contained in one period, and the nesting sequence of the unit domains is ABBA. The method can realize broadband frequency multiplication output of three wave bands in a complementary duty ratio quasi-periodic device with the temperature gradient of 10 ℃ and the initial temperature of 60 ℃ under the conditions of meeting Type-I (e + e → o) Type quasi-phase matching and meeting Type-I (e + e → o) Type quasi-phase matching; meanwhile, the temperature gradient can be adjusted to realize the adjustment of the output bandwidth by analyzing the relationship between the temperature gradient and the bandwidth and the conversion efficiency. The research realizes frequency doubling conversion full coverage of common optical communication wave bands, and has important significance for development of all-optical communication. The specific implementation steps are as follows:

step 1: giving a quasiperiodic crystal structure model for realizing broadband frequency multiplication based on quasi-phase matching temperature gradient:

the crystal material adopted by the quasi-periodic structure is a 5mol% magnesium oxide-doped lithium niobate crystal (5 mol% MgO. lA to B \30052longratio lA: lB =1, which is the optimal value obtained by algorithm optimization.

And 2, step: given initial conditions, determining specific parameters of the quasi-periodic structure:

given an initial wavelength and temperature, the Sellmeier equation is used to determine the coherence length required to achieve Type-I (e + e → o) quasi-phase matching under this condition. The coherence length Lc is given by the following equation:

wherein λ is the wavelength of fundamental light, n _ω Refractive index of fundamental frequency light in crystal, n _2ω Is the refractive index of the frequency doubled light in the crystal.

The refractive index n is obtained by the Sellmeier equation:

wherein λ is the wavelength of the fundamental light and f is the temperature parameter, the coefficients a of o-light and e-light when the crystal is 5% _i 、b _i Shown in table 1.

TABLE 1 The MgO-doped LN Crystal Sellmeier equation parameter Table 5%

	n e	n o
			a 1	5.756	5.653
a 2	0.0983	0.1185
			a 3	0.2020	0.2091
a 4	189.32	89.61
			a 5	12.52	10.85
a 6	1.32×10 -2	1.97×10 -2
			b 1	2.860×10 -6	7.941×10 -7
b 2	4.700×10 -8	3.134×10 -8
			b 3	6.113×10 -8	-4.641×10 -9
b 4	1.516×10 -4	-2.188×10 -6

The temperature parameter f is obtained by the following formula:

f(T)＝(T-24.5)(T+570.82)

where T is temperature in degrees Celsius.

Taking twice of the coherence length as the period length of the quasi-periodic structure, determining the length of the A domain and the B domain by proportion, wherein the total length of the quasi-periodic structure crystal is 6.5mm, and determining the period number of the structure according to the calculated period length.

And step 3: by the quasi-periodic crystal structure, multi-band broadband frequency multiplication output is realized in a quasi-periodic device with the temperature gradient of 10 ℃ and the initial temperature of 60 ℃; by the structure, high-efficiency multi-wavelength frequency doubling conversion can be realized, and the frequency doubling efficiency eta is obtained by the following formula:

in the formula I _ω Denotes the fundamental light intensity, c denotes the speed of light in vacuum, ε ₀ Denotes the dielectric constant in vacuum, λ denotes the fundamental wavelength, n _ω And n _2ω Respectively representing the refractive index of fundamental and second harmonic in the crystal，d ₃₃ The maximum nonlinear coefficient in the z direction is represented, L represents the total length of the crystal, Δ k (λ) represents the phase mismatch amount, d (z) represents the polarization direction distribution of a single domain unit and changes along with the change of the z value; when d (z) =1, the polarization direction is upward, and when d (z) = -1, the polarization direction is downward;

wherein, the calculation formula of Δ k (λ) is:

introducing a relative effective nonlinear coefficient dreff (λ) to be expressed as:

in the invention, a normalized value of dreff (lambda) is introduced to measure the conversion efficiency.

And 4, step 4: analyzing the relation between the temperature gradient bandwidth and the conversion efficiency, and adjusting the output bandwidth by adjusting the temperature gradient;

the specific parameters are set as follows: the quasi-periodic structure of the present invention selects 5% MgO-doped lithium niobate crystals as frequency-doubled crystals, and with Type-I (e + e → o) Type quasi-phase matching, the period length of the quasi-periodic structure is set to 6.5 μm, the temperature gradient Δ T =10 ℃, the initial temperature T ₀ =60 ℃, total length of about 6.5mm. As shown in fig. 2, under the above conditions, the temperature increases linearly over a complementary duty cycle crystal of 6.5mm overall length, with a maximum temperature of 70 ℃.

As shown in fig. 3 (a), when at the initial temperature T ₀ Type-I (e + e → o) QPM produces three broadband frequency doubled fundamental frequency bands in a complementary duty cycle device of total length 6.5mm at a temperature gradient of 60 ℃ and temperature gradient Δ T =10 ℃. Fig. 3 (b), (c), and (d) show details of normalized conversion efficiency spectra of three bands, respectively. Compared with multi-wavelength frequency multiplication at fixed temperature, the bandwidth of multi-band broadband frequency multiplication under temperature gradient is obviously improved. Next, we analyzed the differencesUnder the temperature gradient, the multi-band broadband octave bandwidth is related to the change of the conversion efficiency. As shown in FIGS. 4 (a) and (c), the parameters and initial temperature T of the complementary duty cycle device ₀ With the temperature gradient Δ T =5 ℃ and Δ T =20 ℃, we model the normalized conversion efficiency spectrum of multi-band broadband frequency doubling, respectively. At a temperature gradient Δ T =5 ℃, the bandwidths of the three frequency doubling bands are all significantly reduced, as shown in fig. 4 (b), the bandwidth of the band C is only 13.3nm, which is shortened by nearly one time compared to Δ T =10 ℃; when the temperature gradient Δ T =20 ℃, the bandwidths of the three frequency doubling bands are all obviously increased, as shown in fig. 4 (d), the bandwidth of the band C is 53.1nm, which is more than doubled than the bandwidth of Δ T =10 ℃. But it is easy to see that, compared with Δ T =10 ℃ and Δ T =5 ℃, the maximum conversion efficiency of the three bands is significantly improved, which is about 142% of that of the three bands; whereas at =20 ℃, there is a significant drop in conversion efficiency, about 69.7% of it. Therefore, as the temperature gradient increases, the bandwidth of multi-band broadband frequency doubling increases with a decrease in conversion efficiency. In practical applications, we can select a suitable temperature gradient according to specific bandwidth and conversion efficiency requirements. In general, in a complementary duty ratio device under a temperature gradient, the temperature sensitivity of a Type-I (e + e → o) QPM can be utilized to realize broadband frequency multiplication output of multiple bands, and meanwhile, the adjustment of the output bandwidth can be realized by adjusting the temperature gradient.

In summary, a method for realizing quasi-phase matching multiband broadband frequency multiplication is provided, starting from the principle of the quasi-phase matching technology, by applying a temperature gradient, broadband frequency multiplication output of a plurality of wave bands can be simultaneously realized on a quasi-periodic crystal structure with complementary duty ratio; under the condition of meeting Type-I (e + e → o) Type quasi-phase matching and the condition of meeting Type-I (e + e → o) Type quasi-phase matching, in a complementary duty ratio quasi-periodic device with the temperature gradient of 10 ℃ and the initial temperature of 60 ℃, broadband frequency multiplication output of three wave bands is realized; meanwhile, the temperature gradient can be adjusted to realize the adjustment of the output bandwidth by analyzing the relationship between the temperature gradient and the bandwidth and the conversion efficiency. The research realizes frequency doubling conversion full coverage of common optical communication wave bands, and has important significance for development of all-optical communication.

The above description is only a preferred embodiment of the present invention, and it should be noted that, for those skilled in the art, several modifications and variations can be made without departing from the technical principle of the present invention, and these modifications and variations should also be regarded as the protection scope of the present invention.

Claims (8)

1. A method for realizing quasi-phase matching multiband broadband frequency multiplication generation is characterized in that a crystal with a complementary duty ratio quasi-periodic structure is used in the method, type-I (e + e → o) quasi-phase matching is utilized, and broadband frequency multiplication output of three different wavebands of 0.85 mu m and 1.31 mu m and 1.55 mu m is realized by controlling temperature, and the method comprises the following steps:

step 1: providing a quasi-periodic crystal structure model based on quasi-phase matching multiband broadband frequency multiplication;

step 2: giving initial conditions, and determining specific parameters of a quasi-periodic crystal structure with a complementary duty ratio;

and step 3: the temperature is controlled by aligning with a periodic crystal structure, multiband broadband frequency doubling output is realized in a quasi-periodic device with the temperature gradient of 10 ℃ and the initial temperature of 60 ℃, and multiband broadband frequency doubling corresponding to the output under different temperature gradients is obtained;

and 4, step 4: analyzing the multi-band broadband frequency multiplication correspondingly output under different temperature gradients to obtain the relationship between the temperature gradient bandwidth and the conversion efficiency; and the temperature gradient of the crystal is adjusted through the relationship between the temperature gradient bandwidth and the conversion efficiency, so that the adjustment of the output bandwidth is realized.

2. The method for realizing quasi-phase matching multiband broadband frequency multiplication according to claim 1, wherein in the step 1, the material of the crystal is 5mol% magnesium oxide doped lithium niobate crystal (5 mol% mgo.

3. The method of claim 2, wherein the ratio of A to B \ 30052length in step 1 is lA: lB = 1.

4. The method for generating multi-band broadband frequency multiplication realizing quasi-phase matching according to claim 1, wherein in the step 2, an initial condition is given to an initial wavelength and temperature, a coherence length required for realizing Type-I (e + e → o) quasi-phase matching under the condition is determined by using a Sellmeier equation, twice of the coherence length is taken as a period length of the quasi-periodic structure, \30052lengthof A and B domains is determined through proportion, and the period number of the structure is determined according to the calculated period length.

5. The method according to claim 4, wherein in step 2, the calculation formula of the coherence length Lc is:

wherein λ is a fundamental wavelength of light, n _ω Refractive index of fundamental frequency light in crystal, n _2ω Is the refractive index of the frequency doubled light in the crystal.

6. The method of claim 1, wherein in step 2, the total length of the quasi-periodic structure crystal is 6.5mm.

7. The method according to claim 1, wherein in step 3, the frequency multiplication efficiency is calculated by the following formula:

in the formula I _ω Denotes the fundamental light intensity, c denotes the speed of light in vacuum, ε ₀ Denotes the dielectric constant in vacuum, λ denotes the fundamental wavelength, n _ω And n _2ω Respectively representing the refractive indices of the fundamental and second harmonics in the crystal, d ₃₃ The maximum nonlinear coefficient in the z direction is represented, L represents the total length of the crystal, Δ k (λ) represents the phase mismatch amount, d (z) represents the polarization direction distribution of a single domain unit, and changes along with the change of the z value; when d (z) =1, the polarization direction is upward, and when d (z) = -1, the polarization direction is downward;

wherein, the calculation formula of Δ k (λ) is:

8. the method according to claim 6, wherein in step 3, a relative effective nonlinear coefficient dreff (λ) is further introduced as:

the conversion efficiency is measured by introducing a normalized value of dreff (lambda).

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