CN111046588A - Chirp quasiperiodic structure superlattice material and design method thereof - Google Patents

Chirp quasiperiodic structure superlattice material and design method thereof Download PDF

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CN111046588A
CN111046588A CN201911387203.XA CN201911387203A CN111046588A CN 111046588 A CN111046588 A CN 111046588A CN 201911387203 A CN201911387203 A CN 201911387203A CN 111046588 A CN111046588 A CN 111046588A
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尹志军
崔国新
吴冰
许志城
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Nanjing Nanzhi Institute Of Advanced Optoelectronic Integration
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Abstract

The application discloses a chirp quasi-periodic structure superlattice material and a design method thereof. The phase matching of the peak-like reciprocal lattice vector requires that the ambient temperature and the input laser wavelength are narrow-band, otherwise the power stability and efficiency of frequency conversion of the peak-like reciprocal lattice vector fluctuate dramatically, and the phase matching puts high requirements on the conditions of practical use of the superlattice material with a periodic structure. The embodiment of the application introduces the chirp structure into the design of the quasi-periodic structure, and one or more inverted lattice vectors are widened and flattened through the chirp quasi-periodic structure, so that the bandwidths and the strengths of the inverted lattice vectors are simultaneously controllable, the frequency conversion bandwidth of the quasi-periodic superlattice is improved, the stability of the conversion efficiency is improved, and the harsh environmental requirements of the quasi-periodic material in practical application are reduced.

Description

Chirp quasiperiodic structure superlattice material and design method thereof
Technical Field
The application relates to the technical field of superlattice, in particular to a superlattice material with a chirped quasiperiodic structure and a design method thereof.
Background
Quasi-periodic structures are important structures for multiple quasi-phase matching. The concept of Quasi-Phase Matching (QPM) was proposed in 1962, which is nearly 60 years ago. Although the QPM theory was proposed very early, due to the difficulty in the preparation of periodically poled crystals, until the first 80 s of the last century, researchers introduced microstructures into dielectrics to develop Dielectric superlattices (Dielectric superlattices), and then experimentally explored QPM. Since the parameter to be periodically modulated is mainly the second-order nonlinear coefficient χ (2) in the dielectric Superlattice, the dielectric Superlattice is also called an Optical Superlattice. The optical superlattice substrate material is lithium niobate (LiNbO)3LN), lithium tantalate (LiTaO)3,LT)、KTiOPO4(KTP) and the like. One of the major applications of QPM is efficient laser Frequency conversion, including processes of Frequency doubling (SHG), Sum-Frequency-Generation (SFG), difference-Frequency (DFG), Optical Parametric Generation/Amplification/Oscillation (OPG/OPA/OPO), etc. At present, the laser frequency conversion technology has been developed as an important technology in the laser industry.
Since the nineties, optical superlattices of unconventional periodic structures began to be explored, with a new structure of interest being a quasi-periodic optical superlattice. The alignment period (quasi-period), a completely new structure that does not exist in nature, has generated a great deal of interest since the first discovery of quasicrystals in 1984. The skilled person first introduces a quasiperiodic structure into a dielectric superlattice, proposing the concept of a quasiperiodic optical superlattice. And then, the high-efficiency triple frequency of laser is realized for the first time in the optical superlattice of the Fibonacci sequence, and the application value of the quasi-periodic optical superlattice is verified experimentally. The quasi-periodic structure is a new structure between a periodic structure and a disordered structure, can provide a plurality of mutually independent reciprocal lattice vectors, can realize mutual coupling of a plurality of optical parameter processes, and has good application prospect in the field of laser frequency conversion. According to the quasiperiodic projection theory proposed by technicians, a one-dimensional quasiperiodic structure can be regarded as being obtained by projecting a two-dimensional periodic lattice to a straight line, so that the information of the projected lattice and the projected straight line is hidden in the quasiperiodic structure. According to the projection theory, the low-dimensional quasi-periodic structure can be regarded as being obtained by projecting the high-dimensional periodic structure, and the high-dimensional periodic lattice ' shows ' the implicit symmetry ' of the low-dimensional quasi-periodic lattice. For example, a one-dimensional quasi-periodic structure can be viewed as a two-dimensional square lattice projected onto a straight line, as shown in FIG. 1 below.
In FIG. 1, ξ is a projection straight line, the included angle between the x-axis and the y-axis is theta, a straight line perpendicular to the ξ axis is η axis, the length w of the projection window is the sum of the projections of the x-axis and the y-axis in the η axis direction, i.e., w = sin theta + cos theta, all points falling within the projection window are projected to the η axis from the origin
Figure 173103DEST_PATH_IMAGE001
The resulting sequence is the well-known Fibonacci sequence. This projection results in a two-component quasi-periodic structure. Two components A and B are projected from the longitudinal lattices and the transverse lattices respectively.
For dielectric superlattices such as lithium niobate (LiNbO)3LN) or lithium tantalate (LiTaO)3LT), it is generally assumed that component a and component B are each composed of a pair of positive and negative domains, wherein the positive domains are each 1 in length, as shown in fig. 2 below.
The reciprocal lattice vector of the quasi-periodic structure thus obtained satisfies:
Figure 870932DEST_PATH_IMAGE002
(1)
(1) wherein τ is a member of the structureThe ratio NA/NB of the number NA of elements A to the number NB of elements B is determined by τ alone, so τ is called the sequence parameter. In the quasi-periodic structure projected from the square lattice, τ satisfies τ = tan θ. D = τ DA+DBReferred to as the average structural parameter, DA、DBRespectively, the lengths of elements A, B. Since component a occurs τ times as many times as component B, D characterizes A, B the average length of the components and is referred to as the average structural parameter. And m and n are integers and represent the order of the reciprocal lattice vector. The Fourier coefficient of each reciprocal lattice vector satisfies:
Figure 216593DEST_PATH_IMAGE003
(2)
(2) in the formula
Figure 681073DEST_PATH_IMAGE004
. In the design process of the quasi-periodic structure, proper structure parameters are selected, so that the Fourier coefficient of the required two reciprocal lattice vectors is maximum.
When the quasi-periodic structure is projected from a square lattice, DA/DBIs constant value, has DB/DA= τ = tan θ. In a more general quasi-periodic structure, a one-dimensional quasi-periodic structure is projected from a two-dimensional rectangular lattice. At this time DA/DBIs an adjustable parameter, tau is still NA/NBBut no longer τ = tan θ. Since the general quasi-periodic structure is projected from a rectangular lattice, the expression of the sequence parameter τ can be easily derived. If the lengths of the horizontal lattice and the vertical lattice are dx and dy respectively, τ satisfies:
Figure 412268DEST_PATH_IMAGE005
(3)
another important new structure of optical superlattices other than the conventional periodic structures is the chirped optical superlattices (chirpgratings). Initial research on chirped and chirp-like structures based optical superlattices has focused on increasing the frequency doubling acceptance bandwidth, and another major use of chirped optical superlattices is pulse compression and pulse shaping techniques using chirped superlattices. The skilled person has conducted intensive studies on this technique and, with this technique, generated a blue pulse having a pulse width of less than 6 femtoseconds, which is the blue pulse having the shortest pulse width that can be generated at that time. In fact, besides the two main applications of the chirped superlattice, there are some other applications reported, such as the regulation of optical solitons in the chirped superlattice.
In practical applications, the phase mismatch of the nonlinear frequency conversion is matched and compensated by the reciprocal lattice vector generated by the spatial periodic modulation of the superlattice material in the fourier spectrum of the space. The fourier spectrum of a quasi-periodic structure is shown in fig. 3, where each individual spectral line is called the "reciprocal lattice vector", a vector of reciprocal space. Each reciprocal lattice vector can match a frequency conversion process, and a plurality of reciprocal lattice vectors can realize simultaneous matching of a plurality of frequency conversions in the same crystal, or realize frequency conversion of a plurality of wavelengths. The quasi-periodic structure of FIG. 3 is a one-dimensional quasi-periodic structure that extends from a horizontal grid length dx0=19.1 μm, length of longitudinal grid dy0A two-dimensional lattice of =17.5 μm is projected onto a straight line with a slope tan θ =0.414, and the lengths of the positive domains of both components are L =6 μm, and the total length L =10 mm.
A chirp (chirp) structure, also known as a non-uniform (non-uniform) structure, refers to a periodic non-constant polarization (PP) structure in a periodically poled crystal. The variation of the period with position may be linear or non-linear. In the chirped structure, the polarization period varies with position, but the amount of variation is generally small. A schematic diagram of a superlattice with such a chirped structure is shown in fig. 4 below:
the degree of chirp is exaggerated in fig. 4 to clearly reflect the pattern of chirp. Wherein the dark color part is in the shape of a superlattice positive domain, the light color part is in the shape of a superlattice negative domain, the positive and negative domains are alternately arranged along one direction, and the appearing length period is changed along with the position. The reciprocal lattice vector of a superlattice having such a structure is generally broadened, but the peak value is somewhat decreased.
Taking linear chirp as an example, first a parameter r describing the degree of chirp needs to be defined. In a superlattice comprising N periods, the chirp r is defined to satisfy:
Figure 221611DEST_PATH_IMAGE006
(4)
(4) in the formula, Λ (N), Λ (1) and Λ0The length of the last period, the length of the first period and the length of the central period of the superlattice are respectively. The period at each position x satisfies the following equation:
Figure 303837DEST_PATH_IMAGE007
(5)
when taking the center period Lambda of the superlattice0And when the total length of the superlattice is =2cm and the chirp degree r is different, the variation of the first-order reciprocal lattice vector intensity of the superlattice along with the phase mismatch is shown in the following figure 5:
phase mismatch is defined herein as
Figure 57160DEST_PATH_IMAGE008
. As shown in fig. 5 above, when the chirp degree r is zero, the reciprocal lattice vector is a standard sinc function pattern. When the chirp degree is larger and larger, the broadening degree of the reciprocal lattice vector is wider and wider, and the peak value is lower and lower. When the chirp degree r is 0.02, the broadening degree of the reciprocal lattice vectors is +/-130 rad, but the central intensity of the reciprocal lattice vectors is reduced to be lower than 20 percent of the original central intensity.
In the quasi-periodic inverse fourier spectrum in fig. 3, the shape of each reciprocal lattice vector is a sine function-like peak-like structure, like the shape of the reciprocal lattice vector of r =0 in fig. 5. Such a reciprocal lattice vector has a high peak value but a narrow width, and the peak intensity rapidly decreases as the degree of mismatch increases. In the process of in-place matching, once the matching temperature and wavelength deviate from the matching position of the reciprocal lattice vector, the matching strength will rapidly decrease or even the matching effect cannot be generated, so that the phenomena of conversion power decrease, power instability and the like caused by environmental factor change are easily generated in the actual use process. Especially in the process of level matching with multiple bit matching, because multiple matching processes are coupled or cascaded, the mismatch of one matching process can cause the failure of the whole conversion process, so that the sensitivity of multiple bit matching (level matching) is higher than that of single bit matching. For example, in a frequency doubling process, when the temperature of a 20mm long superlattice crystal changes by more than 0.1 ℃, the conversion efficiency may drop to less than 50% of the peak value, which causes instability of output frequency doubled light.
Disclosure of Invention
The application provides a superlattice material with a chirped quasiperiodic structure and a design method thereof, which are used for solving the problem that the superlattice material with the quasiperiodic structure in the prior art needs harsh condition requirements in actual use.
In a first aspect, the present application provides a method for designing a chirped quasi-periodic structure superlattice material, as shown in fig. 6, the method comprising:
step 101, projecting a longitudinal grid and a transverse grid to obtain a component A and a component B;
step 102, introducing chirp, and determining the length of the component A and the length of the component B;
103, determining a sequence parameter tau according to the length of the component A and the length of the component B;
104, determining the position of the reciprocal lattice vector of the chirp quasi-periodic structure according to the sequence yield tau, the length of the component A and the length of the component B;
and 105, determining the positions of any two reciprocal lattice vectors according to the positions of the reciprocal lattice vectors of the chirped quasi-periodic structure, and determining the superlattice material.
Further, the chirp is introduced, and the length of component a and the length of component B are determined using the following equations:
Figure 908441DEST_PATH_IMAGE009
wherein D isAIs the length of component A, DBAnd the length of component B is represented by dx (ξ) which is the length of the transverse grid after chirp, dy (ξ) which is the length of the longitudinal grid after chirp, and theta is the included angle between the projection straight line ξ and the x axis.
Further, according to the sequence yield tau, the length of the component A and the length of the component B, determining the position of the reciprocal lattice vector of the chirp quasi-periodic structure according to the following formula:
Figure 603865DEST_PATH_IMAGE010
wherein G is reciprocal lattice vector, m and n are integers, representing the order of reciprocal lattice vector, theta is the included angle between the projection straight line ξ and the x axis, dx (ξ) is the length of transverse lattice after chirp, and dy (ξ) is the length of longitudinal lattice after chirp.
In a second aspect, the present application provides a chirped quasi-periodic structure superlattice material, the periodic structure of which is determined by the following equation:
Figure 924119DEST_PATH_IMAGE011
wherein dx (ξ) is the length of the transverse lattice after chirp, dy (ξ) is the length of the longitudinal lattice after chirp, ξ is a projection straight line, theta is the included angle between the projection straight line ξ and the x axis, m and n are integers, the order of the reciprocal lattice vector is represented, and G is the reciprocal lattice vector.
As can be seen from the above embodiments, according to the chirped quasiperiodic structure superlattice material and the design method thereof provided by the present application, a quasiperiodic structure is an important structure for multiple quasiphase phase matching, and phase matching in multiple quasiphase nonlinear frequency conversion processes can be performed through the design of the quasiperiodic structure, so that multi-wavelength nonlinear frequency conversion of laser is achieved. The common quasi-periodic structure has a plurality of reciprocal lattice vectors in a Fourier reciprocal space, and each of the reciprocal lattice vectors has a shape of a peak with a narrow width. The phase matching of the peak-like reciprocal lattice vector requires that the ambient temperature and the input laser wavelength are narrow-band, otherwise the power stability and efficiency of frequency conversion of the peak-like reciprocal lattice vector fluctuate dramatically, and the phase matching puts high requirements on the conditions of practical use of the superlattice material with a periodic structure. The invention aims to introduce a chirp structure into the design of a quasi-periodic structure, and widen and flatten one or more reciprocal lattice vectors through the chirp quasi-periodic structure, so that the bandwidths and the strengths of the multiple reciprocal lattice vectors are controllable at the same time, the frequency conversion bandwidth of a quasi-periodic superlattice is improved, the stability of the conversion efficiency is improved, and the harsh environmental requirements of a quasi-periodic material in practical application are reduced.
Drawings
In order to more clearly explain the technical solution of the present application, the drawings needed to be used in the embodiments will be briefly described below, and it is obvious to those skilled in the art that other drawings can be obtained according to the drawings without any creative effort.
Fig. 1 is a diagram illustrating a two-dimensional periodic projection method for generating a one-dimensional quasi-periodic structure according to an embodiment of the present disclosure;
FIG. 2 is a diagram illustrating a quasi-periodic binary component according to an embodiment of the present disclosure;
FIG. 3 is a Fourier spectrum of a quasiperiodic space provided by an embodiment of the present application;
fig. 4 is a schematic diagram of a chirped superlattice according to an embodiment of the present application;
fig. 5 is a first order reciprocal lattice vector of a chirped structured superlattice according to an embodiment of the present application;
fig. 6 is a flow chart of a method for designing a chirped quasi-periodic structure superlattice material according to an embodiment of the present disclosure;
FIG. 7(a) shows an example of the present application in which only the lateral chirp r is takenxA fourier spectral pattern of the chirped quasi-periodic superlattice at = 0.05;
FIG. 7(b) shows an embodiment of the present application with only the longitudinal chirp ryA fourier spectral pattern of the chirped quasi-periodic superlattice at = 0.05;
fig. 8 is a diagram of a chirped quasiperiodic reciprocal lattice vector provided in an embodiment of the present application;
FIG. 9(a) is G provided in the examples of the present application1,1The frequency multiplication allowed spectrum of (1);
FIG. 9(b) is G provided in the examples of the present application2,1The allowable spectrum of (2).
Detailed Description
In order to make the objects, technical solutions and advantages of the present application more apparent, the technical solutions of the present application will be described in detail and completely with reference to the following specific embodiments of the present application and the accompanying drawings. It should be apparent that the described embodiments are only some of the embodiments of the present application, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present application. The technical solutions provided by the embodiments of the present application are described in detail below with reference to the accompanying drawings.
In a first aspect, the present application provides a method for designing a chirped quasi-periodic structure superlattice material, the method comprising:
according to the embodiment of the application, a chirp structure is introduced into a quasi-periodic structure by adopting a projection method, so that the combination of the functions of the chirp structure and the quasi-periodic structure is realized.
Specifically, the one-dimensional quasi-periodic structure can be regarded as being obtained by two-dimensional periodic lattice projection. And carrying out chirp processing on the two-dimensional periodic lattice, wherein the influence of chirp is hidden in the obtained quasi-periodic structure, so that the chirped quasi-periodic structure is obtained.
In the embodiment of the application, according to a projection method, a projection straight line ξ is taken as a superlattice front direction, dx and dy are respectively used for representing the transverse lattice length and the longitudinal lattice length of a two-dimensional lattice, after chirp is introduced, the transverse lattice length and the longitudinal lattice length are changed along with the position change of a projection straight line ξ, namely dx is converted into dx (ξ), dy is converted into dy (ξ), it is required to be noted that the parameters for describing the transverse lattice length change and the longitudinal lattice length change are transverse coordinates x and y, ξ is selected for the following derivation convenience, as seen in fig. 1, when the lattice length is described in a rectangular lattice, the oblique coordinate of the projection straight line ξ is selected to be equivalent to the longitudinal coordinate x and the transverse coordinate y, because the oblique coordinate can form a right-angle side and a hypotenuse of a right triangle, and therefore the lattice length can be changed according to a proportion.
The lattice length varies continuously with projected line ξ, and the resulting lattice, superlattice structure, is discrete.
Given the diagonal initial coordinates of the projected straight line ξ of the structure, the length of the first cell can be calculated so that the diagonal initial coordinates of the second cell can be obtained, then the length of the second cell can be calculated, and so on, so that a recursive approach can be used to obtain the desired structure of any length.
Projecting the longitudinal lattices and the transverse lattices to obtain a component A and a component B;
introducing chirp, and determining the length of the component A and the length of the component B;
specifically, the chirp is introduced, and the length of component a and the length of component B are determined using the following equations:
Figure 261559DEST_PATH_IMAGE009
（6）
wherein D isAIs the length of component A, DBAnd the length of component B is represented by dx (ξ) which is the length of the transverse grid after chirp, dy (ξ) which is the length of the longitudinal grid after chirp, and theta is the included angle between the projection straight line ξ and the x axis.
Since element A, B is projected from the vertical and horizontal lattices, respectively, the lattice length chirp affects the length of element A, B.
(6) Formula (a) illustrates that lateral chirp causes a change in the length of element B, while having no effect on the length of element a. Similarly, a longitudinal chirp will cause a change in the length of element a, but will have no effect on the length of element B.
Determining a sequence parameter tau according to the length of the component A and the length of the component B;
from the equation (3), the length of the lattice also has an influence on the parameter τ, i.e., the quasi-periodic sequence. The influence thereof can be represented by the formula (7):
Figure 921342DEST_PATH_IMAGE012
(7)
(7) the equation gives the variation of the sequence parameter τ with position. The sequence parameter tau in the chirped quasiperiod is not constant, but changes with position, which shows that the quasiperiod sequence of the chirped quasiperiod structure changes continuously in the whole crystal lattice, and the property is completely different from that of the traditional quasiperiod structure.
Determining the position of the reciprocal lattice vector of the chirp quasi-periodic structure according to the sequence yield tau, the length of the component A and the length of the component B;
specifically, according to the sequence yield tau, the length of the component A and the length of the component B, determining the position of the reciprocal lattice vector of the chirp quasi-periodic structure according to the following formula:
Figure 584405DEST_PATH_IMAGE010
(8)
wherein G is reciprocal lattice vector, m and n are integers, representing the order of reciprocal lattice vector, theta is the included angle between the projection straight line ξ and the x axis, dx (ξ) is the length of transverse lattice after chirp, and dy (ξ) is the length of longitudinal lattice after chirp.
Structural parameter D = τ DA+DBAnd (6) and (7) are substituted into (1) to obtain an expression of the reciprocal lattice vector position of the chirp quasi-periodic structure:
Figure 123446DEST_PATH_IMAGE013
Figure 264577DEST_PATH_IMAGE014
Figure 28134DEST_PATH_IMAGE015
Figure 612830DEST_PATH_IMAGE016
Figure 625785DEST_PATH_IMAGE017
when the chirp amount of the chirp quasi-period is 0, the chirp is evolved into a common quasi-period structure, which shows that the chirp quasi-period structure is a more extensive expression form of the quasi-period, and the length of the grid is taken as being not chirped, namely dx (ξ) = dx0And dy (ξ) = dy0Then use DA=dy0sin theta and DB=dx0cos θ, and can be returned to the conventional quasi-periodic expression from equation (8) by equation (3):
Figure 586919DEST_PATH_IMAGE018
。
and determining the positions of any two reciprocal lattice vectors according to the positions of the reciprocal lattice vectors of the chirped quasi-periodic structure, and determining the superlattice material.
By using the formula (8), the position and the shape of any two reciprocal lattice vectors can be changed in any form in a chirped quasi-periodic superlattice, so that a wide design dimension is provided for the design of the chirped superlattice structure. For example, the reciprocal lattice vector G of a quasiperiodic superlattice is requiredm1,n1In any form Gm1,n1(ξ) change while another reciprocal lattice vector Gm2,n2In any form Gm2,n2(ξ) by applying equation (8), only the following system of equations needs to be solved:
Figure 204982DEST_PATH_IMAGE019
(9)
(9) in the formula
Figure 960580DEST_PATH_IMAGE020
And
Figure 726411DEST_PATH_IMAGE021
is unknown quantity, and other are known quantities, and must have a solution according to a binary equation system
Figure 412607DEST_PATH_IMAGE022
(10)
This is the structural parameter of the chirped quasiperiod obtained from the desired reciprocal lattice vector.
The quasi-periodic superlattice as shown in fig. 3 is chirped according to the above design method. The basic parameters of which are constant according to the quasi-superlattice as shown in fig. 3. If only the length d of the transverse grid is takenxChirping to maintain longitudinal lattice length dyAll m =0 order, unchangedThe reciprocal lattice vector should not be broadened. Similarly, if only the longitudinal grid length d is takenyChirp to keep transverse lattice length dxWithout change, all the n =0 order reciprocal lattice vectors should not be broadened. FIGS. 7(a) and 7(b) show the case where only the lateral chirp r is takenx=0.05 and taking only the longitudinal chirp ryFourier spectral pattern of chirped quasi-periodic superlattice at = 0.05. The subscripts x and y herein represent the lateral and longitudinal directions, respectively, and the chirp r is defined as in the formula (4).
And the distance between the transverse grids and the longitudinal grids is chirped, so that any two reciprocal grid vectors can be controlled to change in any form along with the position. Arbitrarily selecting two reciprocal lattice vectors G1,1And G2,1And let G1,1Non-widening while G2,1Broadening to + -deltaGThen the two reciprocal lattice vectors vary with position as follows:
Figure 677718DEST_PATH_IMAGE023
(11)
introducing (11) into (10) to obtain structural parameters
Figure 119064DEST_PATH_IMAGE024
(12)
If the reciprocal lattice vector spread is taken
Figure 60606DEST_PATH_IMAGE025
And carrying out (12) to obtain the structural parameters of the chirped quasi-periodic superlattice. Fourier transform is performed on the chirped quasiperiodic structure, and the obtained reciprocal lattice vector is shown in fig. 8:
the inset in the upper right corner of FIG. 8 is the inverted graticule G2,1See that the structure is implemented at G1,1Without stretching G2,1Spread out to
Figure 347231DEST_PATH_IMAGE026
。
The chirped quasi-periodic superlattice may simultaneously implement two frequency doubling processes. The specific method of use will now be described in terms of a specific implementation of a chirped quasi-periodic superlattice for two frequency doubling processes.
The previously given parameters of the chirped quasiperiodic superlattice structure, the reciprocal lattice vector G thereof, are still used1,1Not widening, G2,1Broadening to +/-0.01 mu m-1. The original positions of the two reciprocal lattice vectors are respectively G1,1=0.441μm-1，G2,1=0.745μm-1. The nonlinear optical matrix material is LiTaO3The crystal is prepared from LiTaO at 180 deg.C3The Sellmeier equation of the crystal obtains that the frequency doubling wavelengths corresponding to the two reciprocal lattice vectors are 1334.4nm and 1103.9nm respectively. The two frequency doubling wavelengths are numerically simulated according to the coupled wave equation (the pump light is forced to be 30 MW/cm)2) The allowable spectrum of the frequency multiplication fundamental wave can be obtained:
as shown in FIGS. 9(a) and 9(b), G is not widened1,1Has a full width at half maximum (FWHM) of about 0.3nm, and a broadened G2,1Has a full width at half maximum (FWHM) of about 9nm and is G1,130 times the full width at half maximum. Since both wavelength and temperature deviations can be considered as some form of phase mismatch, and are equivalent, we can deduce the temperature bandwidth from the wavelength bandwidth. For the above process, the G is not broadened1,1The full width at half maximum of the wavelength of 0.3nm corresponds to the full width at half maximum at 2.4 ℃ and the broadened G2,1The full width at half maximum of the wavelength of 9nm corresponds to the full width at half maximum of the temperature of 88 ℃, and the visible temperature bandwidth is also widened considerably.
In a second aspect, the present application provides a chirped quasi-periodic structure superlattice material, the superlattice material being:
Figure 487356DEST_PATH_IMAGE027
wherein dx (ξ) is the length of the transverse lattice after chirp, dy (ξ) is the length of the longitudinal lattice after chirp, ξ is a projection straight line, theta is the included angle between the projection straight line ξ and the x axis, m and n are integers, the order of the reciprocal lattice vector is represented, and G is the reciprocal lattice vector.
As can be seen from the above embodiments, according to the chirped quasiperiodic structure superlattice material and the design method thereof provided by the present application, a quasiperiodic structure is an important structure for multiple quasiphase phase matching, and phase matching in multiple quasiphase nonlinear frequency conversion processes can be performed through the design of the quasiperiodic structure, so that multi-wavelength nonlinear frequency conversion of laser is achieved. The common quasi-periodic structure has a plurality of reciprocal lattice vectors in a Fourier reciprocal space, and each of the reciprocal lattice vectors has a shape of a peak with a narrow width. The phase matching of the peak-like reciprocal lattice vector requires that the ambient temperature and the input laser wavelength are narrow-band, otherwise the power stability and efficiency of frequency conversion of the peak-like reciprocal lattice vector fluctuate dramatically, and the phase matching puts high requirements on the conditions of practical use of the superlattice material with a periodic structure. The invention aims to introduce a chirp structure into the design of a quasi-periodic structure, and widen and flatten one or more reciprocal lattice vectors through the chirp quasi-periodic structure, so that the bandwidths and the strengths of the multiple reciprocal lattice vectors are controllable at the same time, the frequency conversion bandwidth of a quasi-periodic superlattice is improved, the stability of the conversion efficiency is improved, and the harsh environmental requirements of a quasi-periodic material in practical application are reduced.
Other embodiments of the present application will be apparent to those skilled in the art from consideration of the specification and practice of the application disclosed herein. This application is intended to cover any variations, uses, or adaptations of the invention following, in general, the principles of the application and including such departures from the present disclosure as come within known or customary practice within the art to which the invention pertains. It is intended that the specification and examples be considered as exemplary only, with a true scope and spirit of the application being indicated by the following claims.
It will be understood that the present application is not limited to the precise arrangements described above and shown in the drawings and that various modifications and changes may be made without departing from the scope thereof. The scope of the application is limited only by the appended claims.

Claims (4)

1. A design method of a superlattice material with a chirped quasi-periodic structure is characterized by comprising the following steps:
projecting the longitudinal lattices and the transverse lattices to obtain a component A and a component B;
introducing chirp, and determining the length of the component A and the length of the component B;
determining a sequence parameter tau according to the length of the component A and the length of the component B;
determining the position of the reciprocal lattice vector of the chirp quasi-periodic structure according to the sequence yield tau, the length of the component A and the length of the component B;
and determining the positions of any two reciprocal lattice vectors according to the positions of the reciprocal lattice vectors of the chirped quasi-periodic structure, and determining the superlattice material.
2. The method of claim 1 wherein said introducing chirp, determining the length of component a and the length of component B utilizes the following equation:
Figure DEST_PATH_IMAGE001
wherein D isAIs the length of component A, DBAnd the length of component B is represented by dx (ξ) which is the length of the transverse grid after chirp, dy (ξ) which is the length of the longitudinal grid after chirp, and theta is the included angle between the projection straight line ξ and the x axis.
3. The method of claim 1 wherein determining the reciprocal lattice vector position of the chirped quasiperiodic structure based on the sequence yield τ, the length of component a, and the length of component B is calculated according to the following equation:
Figure 182699DEST_PATH_IMAGE002
wherein G is reciprocal lattice vector, m and n are integers, representing the order of reciprocal lattice vector, theta is the included angle between the projection straight line ξ and the x axis, dx (ξ) is the length of transverse lattice after chirp, and dy (ξ) is the length of longitudinal lattice after chirp.
4. A chirped quasi-periodic structure superlattice material, wherein a periodic structure of said superlattice material is determined by the following equation:
Figure 905804DEST_PATH_IMAGE003
wherein dx (ξ) is the length of the transverse lattice after chirp, dy (ξ) is the length of the longitudinal lattice after chirp, ξ is a projection straight line, theta is the included angle between the projection straight line ξ and the x axis, m and n are integers, the order of the reciprocal lattice vector is represented, and G is the reciprocal lattice vector.
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Citations (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN1290982A (en) * 2000-10-11 2001-04-11 南京大学 Method for preparing super lattice quasi-period structure dielectric material and equipment
CN101741000A (en) * 2009-12-11 2010-06-16 南京大学 Yellow light laser using cascading superlattice as frequency changer crystal
CN106842379A (en) * 2017-04-14 2017-06-13 山东师范大学 A kind of method for designing of two-dimentional quasi-periodic optical superlattice structure

Patent Citations (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN1290982A (en) * 2000-10-11 2001-04-11 南京大学 Method for preparing super lattice quasi-period structure dielectric material and equipment
CN101741000A (en) * 2009-12-11 2010-06-16 南京大学 Yellow light laser using cascading superlattice as frequency changer crystal
CN106842379A (en) * 2017-04-14 2017-06-13 山东师范大学 A kind of method for designing of two-dimentional quasi-periodic optical superlattice structure

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