Method for generating dual-amplitude particle population gratings

Abstract

A method for generating a dual-amplitude particle population grating is disclosed. In this method, multiple light pulses are incident onto a dielectric crystal to obtain a dual-amplitude grating. The invention further analyzes the grating amplitude and phase shift, revealing that the grating amplitude exhibits a periodic change with increasing light pulse delay, while the phase shift changes linearly. When the light pulse delay is an integer multiple of T0, the generated dual-amplitude grating is unaffected by the light pulse delay. However, between two adjacent integer multiples of T0, i.e., when the light pulse delay is a non-integer multiple of T0, the dual-amplitude grating exhibits significant fluctuations, and the two amplitudes of the grating alternate between adjacent phases. The dual-amplitude particle population grating obtained by this method not only has significant application value in nonlinear optics research, but more importantly, it enables the generation of controllable dual-amplitude particle population gratings, significantly improving its applicability.

Description

Technical Field

[0001] This invention relates to the field of population grating generation technology, and more specifically, to a method for generating a dual-amplitude particle population grating. Background Technology

[0002] Particle population gratings are typically generated in a resonant crystal medium by two spatially overlapping coherent light pulses. These gratings have wide applications in various types of spectroscopy and nonlinear optics.

[0003] However, in the existing technology, the particle population grating generation method can only form a single pattern with a slit of a specific width, which results in the problem that the traditional particle population grating generation method has a narrow range of applications and poor applicability. Summary of the Invention

[0004] (I) Technical Issues

[0005] In summary, how to solve the problem of narrow applicability and poor applicability of traditional particle population grating generation methods has become an urgent problem to be solved by those skilled in the art.

[0006] (II) Technical Solution

[0007] This invention provides a method for generating a dual-amplitude particle population grating, the method comprising:

[0008] Step 1: Input the first optical pulse into the crystal medium to generate polarization oscillations in the crystal medium;

[0009] Step 2: Input a second optical pulse with the opposite direction to the first optical pulse into the crystal medium to generate a single-amplitude grating by interacting with polarization oscillations in the crystal medium;

[0010] Step 3: Input a third optical pulse into the crystal medium to generate a double-amplitude grating by interacting with the single-amplitude grating in the crystal medium.

[0011] Preferably, in the dual-amplitude particle population grating generation method provided by the present invention, in step three, the third optical pulse has the same incident direction as the first optical pulse.

[0012] Preferably, in the dual-amplitude particle population grating generation method provided by the present invention, in step three, the third optical pulse includes a steady-state optical pulse and an active optical pulse, wherein the steady-state optical pulse has the same incident direction as the second optical pulse, and the active optical pulse has the same incident direction as the first optical pulse.

[0013] Preferably, in the dual-amplitude particle population grating generation method provided by the present invention, the first light pulse, the second light pulse, and the third light pulse are all monopolar light pulses.

[0014] Preferably, in the dual-amplitude particle population grating generation method provided by the present invention, the time points of each light pulse are obtained, and the parameter T0 is obtained by normalization according to the electric field expression of the light pulse; the incident time of the third light pulse is adjusted so that the time difference between the third light pulse and the first light pulse is N*T0, where 5≤N<29.

[0015] Preferably, in the dual-amplitude particle population grating generation method provided by the present invention, the incident time of the third light pulse is adjusted, and the amplitude of the dual-amplitude grating is adjusted by adjusting the incident time of the third light pulse within a period of length T0.

[0016] Preferably, in the dual-amplitude particle population grating generation method provided by the present invention, the first light pulse, the second light pulse, and the third light pulse have the same shape and amplitude.

[0017] Preferably, in the dual-amplitude particle population grating generation method provided by the present invention, the first optical pulse and the second optical pulse do not overlap in the crystal medium.

[0018] (III) Beneficial Effects

[0019] This invention proposes a method for generating transient dual-amplitude particle population gratings by sequentially and coherently interacting non-overlapping monopole optical pulses with a resonant crystal medium, and evaluates the grating performance. This invention considers two typical optical pulse configurations: a three-pulse configuration and a four-pulse configuration, and obtains the corresponding optical pulse delay requirements for each. Analysis of the grating amplitude and phase shift shows that their behavior is highly dependent on the time delay between optical pulses. The grating amplitude exhibits a periodic change with increasing optical pulse delay, while the phase shift shifts linearly. We also note that when the optical pulse time delay is an integer multiple of T0, the generated dual-amplitude grating is almost unaffected by the optical pulse delay. However, between two adjacent integer multiples of T0, i.e., when the optical pulse delay is a non-integer multiple of T0, the dual-amplitude grating exhibits significant fluctuations, and the two amplitudes of the grating alternate between adjacent stages. The dual-amplitude particle population grating obtained by the method of this invention not only has great application value in nonlinear optics research, but more importantly, this invention can generate controllable dual-amplitude particle population gratings, which significantly improves its applicability. Attached Figure Description

[0020] Figure 1 This is a simplified structural diagram of the novel water-cooled laptop computer in an embodiment of the present invention;

[0021] Figure 2 Based on Figure 1 Optical pulse delay τ 13 Population grating pattern formed when T0 is an integer multiple of T0;

[0022] Figure 3 The optical pulse interval τ 13 Double-amplitude population grating pattern varying within a T0;

[0023] Figure 4 Let the amplitude values ​​of two vibrations change with time delay τ within a time interval T0. 13 A schematic diagram illustrating the changes;

[0024] Figure 5 The phase varies with the optical pulse delay τ 13 A graph showing the relationship between changes;

[0025] Figure 6 Based on Figure 1 Optical pulse delay τ 14 Population grating pattern formed when T0 is an integer multiple of T0;

[0026] Figure 7 The optical pulse interval τ 14 Double-amplitude population grating pattern varying within a T0;

[0027] Figure 8 For two amplitude values ​​within a time interval T0 and the optical pulse delay τ 14 Relationship diagram;

[0028] Figure 9 Phase and optical pulse delay τ 14 A diagram showing the relationships between them.

[0029] exist Figures 1 to 9 In the middle, τ ab Let be the time interval between two optical pulses, where a is the first optical pulse in the time interval and b is the second optical pulse in the time interval. Detailed Implementation

[0030] The embodiments of the present invention will be described in further detail below with reference to the accompanying drawings and examples. The following examples are for illustrative purposes only and should not be construed as limiting the scope of the invention.

[0031] In the description of this invention, unless otherwise stated, "a plurality of" means two or more; the terms "upper," "lower," "left," "right," "inner," "outer," "front end," "rear end," "head," "tail," etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings, and are only for the convenience of describing the invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation, and therefore should not be construed as a limitation of the invention. Furthermore, the terms "first," "second," "third," etc., are used for descriptive purposes only and should not be construed as indicating or implying relative importance.

[0032] In the description of this invention, it should be noted that, unless otherwise explicitly specified and limited, the terms "connected" and "linked" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral connection; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium. Those skilled in the art can understand the specific meaning of the above terms in this invention based on the specific circumstances.

[0033] When multiple non-overlapping light pulses interact with a resonant crystal medium in the time domain, one light pulse induces polarization oscillations. These oscillations are retained after the light pulse passes and interact with a second light pulse that has a time delay, thereby altering the overall population and forming a transient particle population grating in the crystal medium, similar to a coherent fringe structure. Furthermore, experiments have demonstrated that, in the case of resonant coherent light interacting with matter, the interaction between the polarization waves generated by one light pulse and another can rapidly create and eliminate the grating.

[0034] Please refer to Figure 1 , Figure 1 A schematic diagram of the optical pulse configuration for generating a transient particle population grating.

[0035] The excitation light pulses used in this invention (including the first light pulse, the second light pulse, and the third light pulse) are monopolar light pulses, and all of them have the same shape and amplitude. Multiple monopolar light pulses act on the resonant crystal medium in different directions.

[0036] exist Figure 1 Section a describes the optical pulse configuration scheme for generating a dual-amplitude grating when three optical pulses are applied. The first and second optical pulses are injected into the crystal medium sequentially in opposite (or opposite) directions, with a time interval τ between them. 13 Then, the third light pulse (the action light pulse) enters the crystal medium along the direction of the propagation of the first light pulse.

[0037] exist Figure 1Section b describes another optical pulse configuration scheme for generating a dual-amplitude grating under the action of three optical pulses. The first and second optical pulses are incident on the crystal medium sequentially in opposite directions, and the third optical pulse (steady-state optical pulse) is along the direction of the second optical pulse at τ. 23 After a certain time, the light is injected into the crystal medium. In this case, a double-amplitude grating will not be generated, so this light pulse configuration scheme will not be studied.

[0038] exist Figure 1 Section c describes a light pulse configuration scheme for generating a dual-amplitude grating under four-pulse action. Figure 1 In (c), a configuration of four optical pulses interacting with the crystal medium to generate a dual-amplitude grating is shown. Figure 1 In (c), the first and second optical pulses are incident on the crystal medium sequentially in opposite directions. The incident direction of the steady-state optical pulse is the same as that of the second optical pulse, and the time interval is τ. 23 The light pulse acts along the incident direction of the first light pulse at interval τ 14 It was then injected into the crystal medium, and a dual-amplitude grating was generated.

[0039] As can be seen from the above, the necessary conditions for generating a dual-amplitude grating are: the first optical pulse and the second optical pulse act on the crystal medium in different directions, and at the same time, there should be at least one third optical pulse (acting optical pulse) with the same direction as the first optical pulse.

[0040] The coherent interaction between an atomic system and a single-pole light pulse can be calculated using the following density matrix equation:

[0041]

[0042]

[0043] Where, ρ 12 These are the off-diagonal elements in the density matrix. Define w = ρ 22 -ρ 11 It represents the difference in particle population between the upper and lower energy levels in a two-level system, where ρ 22 ρ 11 These are all diagonal elements in the density matrix. E(t) is the electric field, w0 is the initial state of the atomic system without an electric field input (w0 = 1 for an absorbing crystal medium), and ω0 is the resonant transition frequency of the crystal medium, taken as ω0 = 2.69 × 10⁻⁶. 15 Hz, This is Planck's constant, and μ is the transition dipole moment of the atom, taken as μ = 5 × 10⁻⁶. -18 CGSE.

[0044] for Figure 1The principle of the dual-amplitude grating formed in segment a is as follows:

[0045] Two monopolar light pulses (the first light pulse and the second light pulse) propagate toward each other through the crystal medium from two opposite directions, ensuring that the two light pulses do not overlap within the crystal medium.

[0046] The first light pulse causes polarization oscillations, which can be considered the source of polarized waves. These polarized waves then interfere with the second light pulse. Since these two monopole light pulses enter the crystal medium from opposite directions, the arrival time delay of the light pulses along the incident direction within the crystal medium decreases linearly. Furthermore, the final population state at a certain location within the crystal medium changes periodically with the time interval between the first and second light pulses. This results in a periodic change in the particle swarm along the incident direction, forming a transient population grating, which is a single-amplitude grating. After the two light pulses, a third light pulse (the acting light pulse) enters the crystal medium along the propagation direction of the first light pulse, forming a double-amplitude grating.

[0047] The expressions for the electric fields of the three light pulses are as follows:

[0048]

[0049] Where, τ 13 τ is the time delay between the first and third light pulses, and τ is the time delay between the first two excitation light pulses. The pulse width of a single-pole light pulse is τ. p =7.37×10 -16 s, E0 with τ p Variations are made to keep the area of ​​the light pulse always equal to The time period is T = 2π / ω0, T0 = 1.5T, and the time delays mentioned are all normalized to T0.

[0050] The impact of parameter variations on grating imaging in the scheme of forming a dual-amplitude grating using three light pulses is analyzed as follows:

[0051] Please refer to Figure 2 , Figure 2 Based on Figure 1 Optical pulse delay τ 13 Population grating pattern formed when T0 is taken as an integer multiple.

[0052] Depend on Figure 2 From section a, we can see that when τ 13 When =2T0, the dual amplitude grating begins to appear.

[0053] Depend on Figure 2 From segment a to segment c, it can be seen that with time delay τ 13With the increase in amplitude, dual-amplitude gratings will gradually replace single-amplitude gratings.

[0054] Depend on Figure 2 From segment d, we can see that τ 13 It cannot be increased indefinitely. When it increases to 29 times T0, the double-amplitude grating will disappear and the single-amplitude grating will reappear.

[0055] It is important to note that, Figure 2 In segments a and b, at the junction of the double-amplitude grating and the single-amplitude grating (shaded area in the figure), a small range of irregular oscillations will appear. This is because the time interval between the first and third optical pulses is too small, causing the second and third optical pulses (the action pulses) to meet in the crystal medium and produce oscillations. This oscillation can be easily eliminated by selecting an appropriate time delay range between the first and action pulses.

[0056] Through the Figure 2 A comparison of segments a to c reveals that: when τ 13 When the value is an integer multiple of T0, the generated dual-amplitude grating will not change significantly.

[0057] Please refer to Figure 3 , Figure 3 The optical pulse interval τ 13 Double-amplitude population raster pattern varying within a T0.

[0058] Through the Figure 3 The analysis shows that when the time delay between the first optical pulse and the action optical pulse varies within a T0, its effect on the dual-amplitude grating is significant. For different time intervals between the first optical pulse and the action optical pulse, the amplitude of the grating will change significantly. Here, the two amplitudes of the dual-amplitude grating are named A1 and A2, respectively.

[0059] Please refer to Figure 4 , Figure 4 This is a schematic diagram showing the change of the amplitude values ​​of two vibrations with time delay within a time interval T0.

[0060] Within each T0, the two amplitudes of the dual-amplitude grating exhibit the same variation trajectory, with the two amplitudes A1 and A2 varying with the optical pulse delay τ within a T0. 13 An increase in will produce non-monotonic changes.

[0061] Please refer to Figure 5 , Figure 5 The phase varies with the optical pulse delay τ 13 The relationship diagram of the changes.

[0062] Depend on Figure 5As can be seen, the phase shift increases linearly with the increase of the time interval between the first optical pulse and the applied optical pulse. The phase shift referred to here is the relative phase shift, that is, the displacement of the grating phase relative to the first grating within one T0 period.

[0063] The impact of parameter variations on grating imaging in the four-pulse optical method for forming a dual-amplitude grating is analyzed as follows:

[0064] The four-pulse configuration is another way to generate a double-amplitude grating. This configuration differs from the three-pulse configuration in that the third pulse is split into two: one is an active pulse with the same incident direction as the first pulse, and the other is a steady-state pulse with the same incident direction as the second pulse. The steady-state pulse enters the crystal medium in the same direction as the second pulse. Subsequent active pulses will enter the crystal medium along the incident direction of the first pulse. The positions of the four pulses on the time axis are as follows: Figure 1 As shown in section c, its electric field expression can be written as:

[0065]

[0066] Where, τ 14 This is the time delay between the first and fourth optical pulses. Here, the time interval between the second and steady-state optical pulses is set to a constant, i.e., τ. 23 =2.5T0, the pulse width of a single-polar light pulse is τ p =7.37×10 -16 s, E0 with τ p Variations are made to keep the area of ​​the light pulse always equal to The time period is T = 2π / ω0, T0 = 1.5T, and the time delays are all normalized to T0.

[0067] Please refer to Figure 6 , Figure 6 Based on Figure 1 Optical pulse delay τ 14 Population grating pattern formed when T0 is taken as an integer multiple.

[0068] Similar to the case of three light pulses, the delay between light pulses must meet certain conditions to generate a double-amplitude grating.

[0069] Depend on Figure 6 From section a, we can see that when τ 14 At τ = 5T0, the double amplitude grating begins to appear, and then as τ... 14 With the increase of amplitude, dual-amplitude gratings will gradually replace single-amplitude gratings. When the time interval τ between the first and second optical pulses is selected appropriately, single-amplitude gratings will be completely replaced.

[0070] Depend on Figure 6 From segment d, it can be seen that when τ 14 When τ = 29T0, the dual-amplitude grating will disappear and the single-amplitude grating will reappear. Furthermore, as τ continues to increase... 14 The dual-amplitude grating will no longer appear.

[0071] Depend on Figure 6 As can be seen from segments a and b, irregular oscillations similar to those in the three-pulse configuration also occurred when the four-pulse configuration was used. This is because the fourth light pulse overlapped with the second and third light pulses. Similarly, this oscillation can be easily eliminated by appropriately selecting the time delay range between the first light pulse and the action light pulse.

[0072] Please refer to Figure 7 , Figure 7 The optical pulse interval τ 14 Double-amplitude population raster pattern varying within a T0.

[0073] When the time delay τ between the first light pulse and the acting light pulse 14 When the time delay is an integer multiple of T0, the resulting double-amplitude grating does not exhibit significant fluctuations with changes in time delay. However, when τ... 14 When the time delay is not a multiple of T0, the dual amplitude grating will exhibit different states as the time delay changes.

[0074] Please refer to Figure 8 , Figure 8 For two amplitude values ​​within a time interval T0 and the optical pulse delay τ 14 Relationship diagram.

[0075] Within a time interval T0, the two amplitudes of the grating change with the optical pulse delay as follows: Figure 8 As shown, although the two amplitudes will exhibit different trends within this range, in the next adjacent T0, the two amplitudes will repeat their original amplitude changes. That is, the amplitude of the grating will exhibit periodic changes as the time interval between the first light pulse and the applied light pulse increases.

[0076] Please refer to Figure 9 , Figure 9 Phase and optical pulse delay τ 14 A diagram showing the relationships between them.

[0077] The phase φ of the dual amplitude grating and the optical pulse delay τ 14 The relationship between them still exhibits a linear and monotonic change, such as Figure 9 As shown, this phenomenon is consistent with the phase change phenomenon described when three light pulses are applied.

[0078] Compared with traditional methods for generating particle population gratings, this invention can generate dual-amplitude gratings, and the generated dual-amplitude gratings are shape-controllable gratings. Based on the above analysis, the advantages of this invention are:

[0079] This invention proposes a method for generating transient dual-amplitude particle population gratings by sequentially and coherently interacting non-overlapping monopole optical pulses with a resonant crystal medium, and evaluates the grating performance. This invention considers two typical optical pulse configurations: a three-pulse configuration and a four-pulse configuration, and obtains the corresponding optical pulse delay requirements for each. Analysis of the grating amplitude and phase shift shows that their behavior is highly dependent on the time delay between optical pulses. The grating amplitude exhibits a periodic change with increasing optical pulse delay, while the phase shift shifts linearly. We also note that when the optical pulse time delay is an integer multiple of T0, the generated dual-amplitude grating is almost unaffected by the optical pulse delay. However, between two adjacent integer multiples of T0, i.e., when the optical pulse delay is a non-integer multiple of T0, the dual-amplitude grating exhibits significant fluctuations, and the two amplitudes of the grating alternate between adjacent stages. The dual-amplitude particle population grating obtained by the method of this invention not only has great application value in nonlinear optics research, but more importantly, this invention can generate controllable dual-amplitude particle population gratings, which significantly improves its applicability.

[0080] The embodiments of the present invention are given for illustrative and descriptive purposes only, and are not intended to be exhaustive or to limit the invention to the forms disclosed. Many modifications and variations will be apparent to those skilled in the art. The embodiments were chosen and described in order to better illustrate the principles and practical application of the invention, and to enable those skilled in the art to understand the invention and to design various embodiments with various modifications suitable for a particular purpose.

Claims

1. A method for generating a dual-amplitude particle population grating, characterized in that, The method comprises the following steps: Step one, inputting a first light pulse into a crystal medium to form a polarization oscillation in the crystal medium; Step two, inputting a second light pulse into the crystal medium, which is opposite to the direction of the first light pulse, to generate a single-amplitude grating by interacting with the polarization oscillation in the crystal medium; Step three, inputting a third light pulse into the crystal medium to generate a double-amplitude grating by interacting with the single-amplitude grating in the crystal medium; In the step three, the third light pulse has the same incident direction as the first light pulse; The first light pulse, the second light pulse and the third light pulse are all single-pole light pulses; The first light pulse and the second light pulse do not overlap in the crystal medium; The time point of each light pulse is obtained, and the parameter T0 is obtained by normalization according to the electric field expression of the light pulse; The incident time of the third light pulse is adjusted, and the time difference between the third light pulse and the first light pulse is N*T0, wherein 5≤N<29; The first light pulse, the second light pulse and the third light pulse have the same shape and amplitude.

2. The method according to claim 1, wherein In the step three, the third light pulse comprises a steady light pulse and an action light pulse, the incident direction of the steady light pulse is the same as that of the second light pulse, and the incident direction of the action light pulse is the same as that of the first light pulse.

3. The method according to claim 1, wherein The incident time of the third light pulse is adjusted, and the amplitude of the double-amplitude grating is adjusted by adjusting the incident time of the third light pulse within a period of T0.

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