Method for generating polarization-adjustable extreme ultraviolet light source

Abstract

The invention discloses a method for generating an extreme ultraviolet light source with adjustable polarization, and relates to the technical field of ultrafast lasers. The method comprises the following steps: preparing different electronic states of a triple symmetric molecule; interacting a linearly polarized incident laser with different electronic states of the triple symmetric molecule to generate higher harmonics, adjusting the angle between the polarization direction of the linearly polarized incident laser and the molecular axis until the distribution of ellipticities of different electronic states with an arrangement angle is obtained, selecting a harmonic stage required for generating extreme ultraviolet light sources with different ellipticities, wherein the harmonic ellipticities in the harmonic stage change with the arrangement angle; synthesizing the spectrum of two harmonic components in the harmonic stage into attosecond pulses, and obtaining extreme ultraviolet light sources with different ellipticities after the synthesis; the extreme ultraviolet light source generated by the invention has adjustable polarization and a short pulse width.

Description

Technical Field

[0001] The invention relates to the technical field of ultrafast lasers, in particular to a method for generating a polarization-adjustable extreme ultraviolet light source. Background Art

[0002] Extreme ultraviolet light sources have broad application prospects in the fields of ultrafast dynamics detection and biological spectroscopy. High-order harmonics, with their good coherence, have become the preferred solution for obtaining short-pulse light sources in the extreme ultraviolet band. In the past, most studies focused on generating linearly polarized attosecond pulses, but circular or elliptical attosecond pulses with additional degrees of freedom will further broaden their scope of application. For example, circularly polarized attosecond pulses can be used to study ultrafast magnetic processes, such as spin dynamics in magnetic materials. In addition, it can also be used to study nonlinear dichroic effects in strong-field double ionization processes. Therefore, as an extreme ultraviolet light source with additional degrees of freedom, circularly polarized attosecond pulses have important application prospects in the fields of ultrafast dynamics detection and magnetic research, and are worthy of further research and development.

[0003] At present, the schemes for generating circularly polarized attosecond pulses can be mainly divided into three categories: 1) using two circularly polarized laser fields with opposite rotation directions; 2) using an elliptically polarized laser field in combination with an electrostatic field or a terahertz field; 3) using a two-color circularly polarized driving field. In the process of generating high-order harmonics, there are two defects: 1) the laser driving pulses used are all elliptically polarized, and the electron recovery rate decreases with the increase of the elliptically polarized driving field. The intensity of the radiated attosecond pulses is very weak and the pulse width is wide; 2) the operation of realizing polarization control of attosecond pulses is relatively complicated, and the driving field needs to be controlled accordingly, which is not stable enough. Summary of the invention

[0004] In order to solve the problems existing in the prior art, the purpose of the present invention is to provide a method for generating an extreme ultraviolet light source with adjustable polarization. The present invention adopts a linearly polarized incident laser to generate high-order harmonics after interacting with different electronic states of a triple-symmetric molecule, and obtains an extreme ultraviolet light source after corresponding processing. The generated extreme ultraviolet light source has adjustable polarization and short pulse width.

[0005] To achieve the above object, the technical solution adopted by the present invention is: a method for generating a polarization-adjustable extreme ultraviolet light source, comprising the following steps:

[0006] Step 1, preparing different electronic states of triple symmetric molecules;

[0007] Step 2, the linearly polarized incident laser interacts with different electronic states of the triply symmetric molecule to generate higher harmonics, the angle between the polarization direction of the linearly polarized incident laser and the molecular axis is adjusted until the distribution of the ellipticity of different electronic states with the arrangement angle is obtained, and the harmonic stage required to generate the extreme ultraviolet light source with different ellipticity is selected, and the harmonic ellipticity in the harmonic stage changes with the arrangement angle;

[0008] Step 3: synthesize the spectra of the two harmonic components in the harmonic stage into attosecond pulses, and obtain extreme ultraviolet light sources with different ellipticities after synthesis.

[0009] As a further improvement of the present invention, the step 1 is specifically as follows:

[0010] Using hydrogen trivalent ions As a triple symmetric molecule, the time-dependent Schrödinger equation TDSE is solved using imaginary time propagation to obtain the ground state and the first and second excited states:

[0011] ;

[0012] in, is the wave function, is the Hamiltonian;

[0013] By superimposing the first and second excited states, an excited state with non-zero electron angular momentum is obtained, which is called a circulating state. The ground state and the circulating state have different electron angular momentums and are used to interact with linearly polarized incident lasers to generate different harmonic signals.

[0014] As a further improvement of the present invention, in step 2, the ellipsometric ratio of the generated high-order harmonics is:

[0015] ;

[0016] in, is the left-handed component, is the right-hand component, , , The dipole acceleration The two vertical components of are transformed from Fourier transform:

[0017] ;

[0018] in, is the wave function, is the molecular potential energy, is the electric field strength.

[0019] As a further improvement of the present invention, in step 3, attosecond pulses are obtained by performing inverse Fourier transform on the spectrum, and the transformation formula is:

[0020] ;

[0021] in, is the harmonic order, is the angular frequency of the incident laser.

[0022] The beneficial effects of the present invention are:

[0023] The present invention adopts linearly polarized incident laser to generate high-order harmonics when interacting with different electronic states of triple symmetric molecules, and polarization-adjustable attosecond pulses can be obtained after processing; the polarization of the extreme ultraviolet light source generated by the present invention is adjustable, and the generated pulse width is shorter. BRIEF DESCRIPTION OF THE DRAWINGS

[0024] Figure 1 This is a flow chart of a method according to an embodiment of the present invention;

[0025] Figure 2 A schematic diagram of the method principle of an embodiment of the present invention;

[0026] Figure 3 The ground state and the circulating state in the embodiment of the present invention are arranged at different angles. Schematic diagram of the harmonic ellipticity corresponding to different harmonic orders;

[0027] Figure 4 It is a time-frequency analysis diagram corresponding to different harmonic stages of the ground state and the circulating state at different arrangement angles in an embodiment of the present invention;

[0028] Figure 5 is the attosecond pulse with different ellipticity in the embodiment of the present invention. Schematic diagram of the electric field distribution on a plane. DETAILED DESCRIPTION

[0029] The embodiments of the present invention are described in detail below with reference to the accompanying drawings.

[0030] Example

[0031] like Figure 1 As shown, a method for generating a polarization-adjustable extreme ultraviolet light source comprises the following steps:

[0032] S1. Preparation of different electronic states of triple symmetric molecules;

[0033] S2, the linearly polarized incident laser interacts with different electronic states of the triply symmetric molecule to generate higher harmonics, the angle between the polarization direction of the linearly polarized incident laser and the molecular axis is adjusted until the distribution of the ellipticity of different electronic states with the arrangement angle is obtained, and the harmonic stage required to generate the extreme ultraviolet light source with different ellipticity is selected, and the harmonic ellipticity in the harmonic stage changes with the arrangement angle;

[0034] S3. The harmonic spectra of the two harmonic components in the harmonic stage are synthesized into attosecond pulses using an inverse Fourier transform formula, and after the synthesis, extreme ultraviolet light sources with different ellipticities are obtained.

[0035] In step S1, due to the trivalent hydrogen ion It is a three-fold symmetric molecule, easy to arrange, and has a ground state and a circulating state with similar structure, so hydrogen trivalent ions are preferred. The ground state and the first and second excited states are obtained by solving the Schrödinger equation TDSE using imaginary time propagation, and the formula is: is the wave function, It is a Hamiltonian. By further superimposing the first and second excited states, an excited state with non-zero electron angular momentum, namely, a circulating state, can be obtained. The ground state and the circulating state differ in the electron angular momentum, so as to facilitate the subsequent interaction with the linearly polarized incident laser to generate different harmonic signals.

[0036] In step S2, the ellipsometric ratio of the generated harmonics is , is the left-handed component, is the right-hand component, , , The dipole acceleration The two vertical components of are transformed from Fourier transform: is the wave function, is the molecular potential energy, is the electric field strength.

[0037] The angle (arrangement angle) between the linearly polarized incident laser and the molecular axis has a significant ellipticity in the range of 0°-180°, and the ellipticity is modulated as the arrangement angle changes. In the ground state, two polarization controls can be realized, from positive ellipticity to negative ellipticity, and then to positive ellipticity. In the circulation state, three polarization controls can be realized, from negative ellipticity to positive ellipticity, then to negative ellipticity, and finally to positive ellipticity. Randomly select the ground state arrangement angle 30°, 60°, 120°, the annular arrangement angle At different harmonic stages of 25°, 30° and 45°, the ellipticity changes significantly.

[0038] In step S3, the harmonic spectrum is subjected to inverse Fourier transform to obtain attosecond pulses. The transformation formula is: , is the harmonic order, is the angular frequency of the incident laser.

[0039] The present embodiment is further described below with reference to a specific case:

[0040] like Figure 2 As shown, only considering The plane of is parallel to the pulse polarization. Figure 2 (a) in the equation is the ground state where the electron angular momentum is zero. Figure 2 (b) is an excited state (circulation state) in which the electron angular momentum is not zero. Both are also three-fold symmetric structures. Get different arrangement angles .

[0041] The linearly polarized incident laser propagates inward along the z plane, and its polarization direction is The generated harmonics can be divided into components in the x and y directions. The ellipticity of harmonics of different orders can be obtained. In the range of arrangement angles of 0°-180°, high-order harmonics have significant changes in ellipticity. By selecting the harmonic stages of different arrangement angles when the ellipticity is positive, zero, or negative, attosecond pulses with positive, zero, or negative ellipticity can be obtained.

[0042] In this embodiment, the electric field of the incident linearly polarized laser is , is the amplitude of the incident laser, and its peak intensities for the ground state and the circulating state are and . Wavelength of incident linearly polarized laser , pulse width T=12T0, T0 is the light period of the incident laser, and the trapezoidal envelope is selected.

[0043] According to the ellipticity calculation formula, different ellipticities corresponding to different harmonic orders of two electronic states at different arrangement angles are obtained, such as Figure 3 shown. Figure 3 (a) in the figure shows that In the ground state, the ellipticity changes from positive ellipticity to negative ellipticity and then to positive ellipticity as the arrangement angle changes, and is modulated twice within a cycle of 120°. Figure 3 (b) in the figure shows that In the circulation state, the ellipticity changes from negative ellipticity to positive ellipticity, then to negative ellipticity, and finally to positive ellipticity as the arrangement angle changes, and is modulated three times in a cycle of 120°. Figure 3 In the ellipticity distribution, three harmonic phase regions with negative, zero and positive ellipticity were randomly selected. In the ground state, the harmonic phases were 110-132 times at an arrangement angle of 60°, 80-90 times at 30°, and 40-49 times at 120°. In the circulation state, the harmonic phases were 58-67 times at an arrangement angle of 25°, 29-35 times at 30°, and 57-68 times at 45°.

[0044] exist Figure 4According to the different harmonic orders selected above, the inverse Fourier transform formula is used to synthesize attosecond pulse chains. Figure 4 It can be seen that the pulse width of the maximum peak of the attosecond pulse generated in the harmonic stage ranges from 43as to 190as. Therefore, in the ground state and the circulating state, as the arrangement angle is different, the pulse width of the attosecond pulse generated by the selected harmonic order is shorter.

[0045] Figure 5 The synthesized attosecond pulses are given in The electric field distribution in the plane, the ellipticity of the extreme ultraviolet light source synthesized in the harmonic stage in the ground state is -0.219, 0, 0.607, and the ellipticity in the circulating state is -0.304, 0, 0.438. Therefore, the polarization of the generated extreme ultraviolet light source can be controlled by selecting different harmonic stages with different arrangement angles.

[0046] The above-mentioned embodiments only express the specific implementation of the present invention, and the description thereof is relatively specific and detailed, but it cannot be understood as limiting the scope of the present invention. It should be pointed out that, for ordinary technicians in this field, several variations and improvements can be made without departing from the concept of the present invention, which all belong to the protection scope of the present invention.

Claims

1. A method for generating a polarization-adjustable extreme ultraviolet light source, characterized in that: The following steps are involved: Step 1, preparing different electronic states of triple symmetric molecules; Step 2, the linearly polarized incident laser interacts with different electronic states of the triply symmetric molecule to generate higher harmonics, the angle between the polarization direction of the linearly polarized incident laser and the molecular axis is adjusted until the distribution of the ellipticity of different electronic states with the arrangement angle is obtained, and the harmonic stage required to generate the extreme ultraviolet light source with different ellipticity is selected, and the harmonic ellipticity in the harmonic stage changes with the arrangement angle; Step 3: synthesize the spectra of the two harmonic components in the harmonic stage into attosecond pulses, and obtain extreme ultraviolet light sources with different ellipticities after synthesis.

2. The method for generating a polarization-adjustable extreme ultraviolet light source according to claim 1, characterized in that: The step 1 is specifically as follows: Using hydrogen trivalent ions As a triple symmetric molecule, the time-dependent Schrödinger equation TDSE is solved using imaginary time propagation to obtain the ground state and the first and second excited states: ； in, is the wave function, is the Hamiltonian; By superimposing the first and second excited states, an excited state with non-zero electron angular momentum is obtained, which is called a circulating state. The ground state and the circulating state have different electron angular momentums and are used to interact with linearly polarized incident lasers to generate different harmonic signals.

3. The method for generating a polarization-adjustable extreme ultraviolet light source according to claim 1, characterized in that: In step 2, the ellipsometric ratio of the generated high-order harmonics is: ； in, is the left-handed component, is the right-hand component, , , The dipole acceleration The two vertical components of are transformed from Fourier transform: ； in, is the wave function, is the molecular potential energy, is the electric field strength.

4. The method for generating a polarization-adjustable extreme ultraviolet light source according to claim 1, characterized in that: In step 3, attosecond pulses are obtained by inverse Fourier transforming the spectrum. The transformation formula is: ； in, is the harmonic order, is the angular frequency of the incident laser.

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