The pulse laser device and method of laser pulse are established based on kerr lens mode locking

文档序号:1760547 发布日期:2019-11-29 浏览:21次 中文

阅读说明:本技术 基于克尔透镜锁模建立激光脉冲的脉冲激光设备和方法 (The pulse laser device and method of laser pulse are established based on kerr lens mode locking ) 是由 O·普罗宁 F·克劳斯 J·布龙斯 于 2017-02-23 设计创作,主要内容包括:一种脉冲激光设备(100),其用于基于振荡器腔(10)中的循环光场的克尔透镜锁模来建立激光脉冲(1)、尤其孤子激光脉冲(1),该脉冲激光设备包括:至少两个谐振器镜(11,12,......),其跨越振荡器腔(10)的谐振器光路(2);至少一个克尔介质(21,22,23),其用于将自相位调制和自聚焦引入振荡器腔(10)中的循环光场;至少一个增益介质(31),其用于增强振荡器腔(10)中的循环光场;和调谐装置(40),其用于设置振荡器腔(10)的第一锁模状况和第二锁模状况,使得与第二锁模状况相比,在第一锁模状况下用于锁模的腔内阈值功率更低,其中,第一锁模状况适于启动或关停克尔透镜锁模,第二锁模状况适于持续的克尔透镜锁模,且循环光场的谐振器内部峰值功率在第二锁模状况下比在第一锁模状况下更高。此外,描述了一种操作该脉冲激光设备的方法。(A kind of pulse laser equipment (100), it is used to establish laser pulse (1), especially soliton laser pulse (1) based on the kerr lens mode locking of the circulation light field in oscillator chamber (10), the pulse laser equipment includes: at least two resonator mirrors (11,12, ...), cross over the resonator optical path (2) of oscillator chamber (10);At least one kerr medium (21,22,23) is used for the circulation light field being introduced into Self-phase modulation and self-focusing in oscillator chamber (10);At least one gain media (31), is used to enhance the circulation light field in oscillator chamber (10);With tuner (40), its first mode locking situation for being used to be arranged oscillator chamber (10) and the second mode locking situation, so that compared with the second mode locking situation, intracavitary threshold power under the first mode locking situation for mode locking is lower, wherein, first mode locking situation is suitable for starting or closing down kerr lens mode locking, and the second mode locking situation is suitable for lasting kerr lens mode locking, and the resonator inside peak power for recycling light field is higher than under the first mode locking situation under the second mode locking situation.In addition, describing a kind of method for operating the pulse laser equipment.)

1. it is saturating to be disposed for the Ke Er based on the circulation light field in oscillator chamber (10) for a kind of pulse laser equipment (100) Mirror mode locking establishes laser pulse (1), especially soliton laser pulse (1), and the pulse laser equipment (100) includes:

- at least two resonator mirrors (11,12 ...), the resonator optical path (2) of oscillator chamber (10) is crossed over,

At least one kerr medium (21,22,23) is disposed for Self-phase modulation and self-focusing introducing oscillator chamber (10) the circulation light field in, and

At least one gain media (31) is disposed for enhancing the circulation light field in oscillator chamber (10),

It is characterized in that,

Tuner (40) is disposed for that the first mode locking situation and the second mode locking situation of oscillator chamber (10) is arranged, makes It obtaining compared with the second mode locking situation, the intracavitary threshold power under the first mode locking situation for mode locking is lower, and

- the first mode locking situation is suitable for starting or closing down kerr lens mode locking, and the second mode locking situation is suitable for lasting kerr lens and locks Mould, wherein the resonator inside peak power for recycling light field is higher than under the first mode locking situation under the second mode locking situation.

2. pulse laser equipment according to claim 1, wherein

- the first mode locking situation is chosen to minimize for the intracavitary threshold power of mode locking.

3. pulse laser equipment according to any one of the preceding claims, wherein

The resonator inside peak power that-the second mode locking situation is chosen to circulation light field maximizes.

4. pulse laser equipment according to any one of the preceding claims, wherein

- the second mode locking situation is chosen to recycle the resonator inside peak power ratio of light field under the second mode locking situation the Height at least 20% under one mode locking situation.

5. pulse laser equipment according to any one of the preceding claims, wherein

At least one described gain media (31) include be provided separately at least one described kerr medium (21,22,23) it is thin Piece gain media.

6. pulse laser equipment according to any one of the preceding claims, wherein

At least one described kerr medium has at least one antireflective coating.

7. pulse laser equipment according to any one of the preceding claims, wherein

Tuner (40) includes translating device, the translating device be disposed for making at least one kerr medium (21, 22,23) arrangements of operations in oscillator chamber (10) changes between the first arrangements of operations and the second arrangements of operations, and

- the first mode locking situation is provided with the first arrangements of operations of at least one kerr medium (21,22,23), the second mode locking Situation is provided with the second arrangements of operations of at least one kerr medium (21,22,23).

8. pulse laser equipment according to claim 7, wherein

- the first and second arrangements of operations include at least one described kerr medium (21,22,23) along resonator optical path (2) First and second positions.

9. pulse laser equipment according to claim 7 or 8, wherein

At least one described kerr medium includes a pair of of kerr medium wedge (22,23), and the kerr medium wedge (22,23) is by cloth It sets for translating, the translation has the component perpendicular to resonator optical path (2), so that the pair of kerr medium wedge (22, 23) the total effective thickness passed through by circulation light field can be conditioned, and

- the first and second arrangements of operations include kerr medium wedge (22,23) along the radial direction relative to resonator optical path (2) The first and second positions.

10. pulse laser equipment according to claim 9, wherein

At least one of described kerr medium wedge (22,23) has at least one antireflective coating.

11. pulse laser equipment according to claim 9 or 10, wherein

The kerr medium wedge (22,23) has the angle of wedge, and the angle of wedge is chosen to work as in resonator optical path close to cloth scholar When this special angle is placed, reflection loss is minimized.

12. pulse laser equipment according to any one of claims 7-11, wherein

Translating device is disposed for changing behaviour by the movement without friction of at least one kerr medium (21,22,23) It arranges.

13. pulse laser equipment according to any one of the preceding claims, wherein the pulse laser equipment includes extremely Few two kerr mediums, wherein

Translating device is disposed for changing the arrangements of operations of at least one of kerr medium.

14. pulse laser equipment according to any one of the preceding claims, wherein

Tuner (40) is disposed for making at least one described kerr medium (21) and/or phase mismatch I type second harmonic The phase mismatch situation that (SHG) crystal (71) occur changes between first phase mismatch conditions and second phase mismatch conditions, At least one described kerr medium (21) and/or phase mismatch I type second harmonic occur (SHG) crystal (71) and are arranged in oscillator In the resonator optical path (2) of chamber (10) and it is disposed for adding second nonlinear in oscillator chamber (10), second phase is lost There is at least one described kerr medium (21) and/or SHG crystal (71) compared with first phase mismatch conditions more with situation Big phase mismatch, phase mismatch change between the first and second mismatch conditions, so that compared with first phase mismatch conditions, In It is total intracavitary non-linear lower in second phase mismatch conditions, and peak power and/or spectral bandwidth and/or pulse stability increase Add, and

- the first mode locking situation is provided with first phase mismatch conditions, and the second mode locking situation is provided with second phase mismatch conditions.

15. pulse laser equipment according to claim 14, wherein

Tuner is configured to: tuning at least one described Ke Er for the resonator optical path (2) relative to oscillator chamber (10) At least one of the temperature and incidence angle of medium (21) and/or SHG crystal (71).

16. pulse laser equipment according to any one of the preceding claims, wherein the pulse laser equipment is also wrapped It includes:

It operates regulating device (50), is disposed in the pump power and gain that adjust at least one gain media At least one, with when changing mode locking situation keep oscillator chamber (10) mode locking.

17. pulse laser equipment according to any one of the preceding claims, wherein the pulse laser equipment further includes

Detector means (51) are arranged for the kerr lens mode locking state of detection oscillator chamber (10), especially circulation light The resonator inside peak power of field.

18. pulse laser equipment according to claim 17, wherein the pulse laser equipment further include:

Control loop (52) is arranged for controlling tuner (40) according to detector means output.

19. pulse laser equipment according to any one of the preceding claims, wherein

Oscillator chamber (10) is suitable in the abnormal dispersion area dispersed with negative group delay at least 50MW, especially at least 500MW Intracavitary oscillator power operation, or generate dissipative solitons with positive group delay dispersion normal dispersion area in at least The intracavitary oscillator power of 5MW operates.

20. pulse laser equipment according to any one of the preceding claims, wherein

At least one described gain media (31) is suitable for providing soft aperture in oscillator chamber (10), and/or

Oscillator chamber (10) includes hard aperture (15).

21. a kind of method that operation has the pulse laser equipment of oscillator chamber (10), the pulse laser equipment include at least Two resonator mirrors cross over the resonator optical path (2) of oscillator chamber (10);At least one kerr medium (21,22,23), Be disposed for circulation light field Self-phase modulation and self-focusing being introduced into oscillator chamber (10);With at least one gain media (31), it is disposed for enhancing the circulation light field in oscillator chamber (10), which comprises

Based on the kerr lens mode locking of the circulation light field in oscillator chamber (10), laser pulse (1), especially soliton laser are established Pulse (1),

It is characterized in that, the described method comprises the following steps:

Using the first mode locking situation and the second mode locking situation of tuner (40) setting oscillator chamber (10), so that with second Mode locking situation is compared, and the intracavitary threshold power under the first mode locking situation for mode locking is lower, wherein

Kerr lens mode locking starts or closes down under the first mode locking situation, and provides lasting Ke Er under the second mode locking situation Lens mode locking, wherein recycle the resonator inside peak power of light field under the second mode locking situation ratio under the first mode locking situation It is higher.

22. according to the method for claim 21, wherein

Intracavitary threshold power for mode locking is minimized under the first mode locking situation.

23. the method according to any one of claim 21-22, wherein

The resonator inside peak power of circulation light field is maximized under the second mode locking situation.

24. the method according to any one of claim 21-23, wherein

The resonator inside peak power ratio that light field is recycled under the second mode locking situation is high at least under the first mode locking situation 20%.

25. the method according to any one of claim 21-24, wherein

The first mode locking situation of setting and the step of the second mode locking situation include: make at least one kerr medium (21,22, 23) arrangements of operations in oscillator chamber (10) changes between the first arrangements of operations and second of arrangements of operations.

26. according to the method for claim 25, wherein

Make the arrangements of operations of at least one kerr medium (21,22,23) the first arrangements of operations and the second arrangements of operations it Between the step of changing include: to translate at least one described kerr medium (21,22,23) along resonator optical path (2).

27. the method according to any one of claim 25-26, wherein

At least one described kerr medium (21,22,23) includes a pair of of kerr medium wedge (22,23), and

Make the arrangements of operations of at least one kerr medium (21,22,23) the first arrangements of operations and the second arrangements of operations it Between change the step of include: make kerr medium wedge (22,23) with perpendicular to the component of resonator optical path (2) translate, and adjust institute State total effective thickness that a pair of of kerr medium wedge (22,23) is passed through by circulation light field, wherein

- the first arrangements of operations and the second arrangements of operations include kerr medium wedge (22,23) along relative to resonator optical path (2) The first position and the second position of radial direction.

28. the method according to any one of claim 25-27, wherein

The step of changing the arrangements of operations of at least one kerr medium (21,22,23) includes at least one described Ke Er The movement without friction of medium (21,22,23).

29. the method according to any one of claim 25-28, wherein

- at least two kerr mediums are provided for the kerr lens mode locking of the circulation light field in oscillator chamber (10), and

The step of changing arrangements of operations includes at least one of mobile kerr medium.

30. the method according to any one of claim 21-29, wherein the method also includes:

Second nonlinear is added in oscillator chamber (10), wherein at least one described kerr medium (21) and/or phase misalignment (SHG) crystal occurs with I type second harmonic to be arranged in the resonator optical path (2) of oscillator chamber (10), wherein

The first mode locking situation of setting and the step of the second mode locking situation include: make at least one described kerr medium (21) and/or The phase mismatch situation of SHG crystal (71) changes between first phase mismatch conditions and second phase mismatch conditions, wherein with First phase mismatch conditions are compared, and second phase mismatch conditions have at least one described kerr medium (21) and/or SHG crystal (71) bigger phase mismatch, and

Change phase mismatch between the first and second mismatch conditions, so that compared with first phase mismatch conditions, It is total intracavitary non-linear lower in two phase mismatch conditions, and peak power and/or spectral bandwidth and/or pulse stability increase.

31. according to method described in claim 25 and 30, wherein

First phase mismatch conditions are provided when at least one described kerr medium (21,22,23) has the first arrangements of operations, Second phase mismatch conditions are provided when at least one described kerr medium (21,22,23) has the second arrangements of operations.

32. the method according to claim 30 or 31, wherein

Changing phase mismatch situation includes at least one described gram of resonator optical path (2) tuning relative to oscillator chamber (10) At least one of the temperature and incidence angle of that medium (21) and/or SHG crystal (71).

33. the method according to any one of claim 21-32, wherein the method also includes steps

At least one of pump power and the gain for adjusting at least one gain media, when changing arrangements of operations Keep oscillator chamber (10) mode locking.

34. the method according to any one of claim 21-33, wherein the method also includes steps

Kerr lens mode locking state is detected, the resonator inside peak power of light field is especially recycled.

35. according to the method for claim 34, wherein

Make the arrangements of operations of at least one kerr medium (21,22,23) the first mode locking situation and the second mode locking situation it Between change the step of include that tuner (40) are controlled according to detector means output.

36. the method according to any one of claim 21-35, wherein

Oscillator chamber (10) is in the abnormal dispersion area dispersed with negative group delay with the chamber of at least 50MW, especially at least 500MW Internal oscillator power operation, or at least 5MW's in the normal dispersion area with positive group delay dispersion for generating dissipative solitons Intracavitary oscillator power operation.

Technical field

The present invention relates to a kind of for establishing laser arteries and veins based on the kerr lens mode locking of the circulation light field in oscillator chamber The pulse laser equipment of punching, especially soliton laser pulse.Laser is established based on kerr lens mode locking in addition, the present invention relates to one kind The method of pulse, especially soliton laser pulse.Application of the invention can be used for such as laser physics, the measurement based on laser pulse Technology and field of spectroscopy.

Background technique

In the present specification, the following prior art of reference the technology of the present invention background:

[1] V.L.Kalashnikov etc., " Solid State Laser ", A.Al-Khursan, ed. (InTech, 2012), pp.146I84;

[2] F.Krausz etc., " J.Quantum Electron. " 28,2097-2122 (1992);

[3] O.Pronin etc., " Opt.Lett. " 36,4746-4748 (2011);

[4] J.Brons etc., " Opt.Lett. " 41,3567 (2016);

[5] J.Brons etc., " Opt.Lett. " 39,6442-6445 (2014);

[6] S.B.Mirov etc., " IEEE J.Sel.Top.Quantum Electron. " 21,292-310 (2015);

[7] M.Lettenberger etc., " Opt.Co mmun. " 131,295-300 (1996);

[8] V.Magni etc., " J.Opt.Soc.Am. " B 12,476-485 (1995);

[9] A.Penzkofer etc., " Opt.Quantum Electron. " 28,423-442 (1996);

[10] X.Han etc., " Opt.Express " 16,3686 (2008);

[11] R.DeSalvo etc., " Opt.Lett. " 17,28-30 (1992)

The periodic sequence of laser pulse can be established especially with orphan's kerr lens mode locking (KLM) oscillator.Orphan KLM The working principle summary of oscillator can be for example, see document [1].It is high-power kerr lens mode locking (KLM) oscillator, especially thin The start-up course of piece KLM oscillator usually requires external disturbance sustained wave (CW) stable state, to cause fluctuation, thus produces mode locking Pulse.If careful measure is not taken to be controlled, which easilys lead to tracavity optical component wear.Damage mechanism It needs to study, however, carrying out analysis using fast oscilloscope and photodiode can find oscillating to mode-lock operation turn from CW It when changing and is switched to when CW vibrates from mode-lock operation and strong high energy pulse occurs.

The illustrated examples of this characteristic of traditional KLM oscillator are shown in Fig. 7, it illustrates in starting mode-lock operation When with the violent pulse of high power/energy/intensity noise spike enhance.These powerful pulses are to cause optical damage most Possible cause.

It is well known that when clamping apparatus (usually true (such as SESAM) or virtual (such as KLM) saturable absorber) When being easily saturated, q switch or the spike unstability (document [2]) in passive mode-locking oscillator can inhibit.However, it means that The relevant reflectivity of power or transmission variation are had reached the maximum under the relatively low instantaneous power of fluctuation or pulse.Cause This can only make if the concept will be used to inhibit above-mentioned spike unstability with the relatively low KLM oscillator of output power With.

Another solution for avoiding this flash is using additional clamping apparatus, which mainly passes through Pulse flux rather than intensity are saturated, such as the semiconductor saturable absorbing mirror (SESAM) reported in document [3].In principle, Any passive mode-locking device with low saturation flux or saturation intensity is all helpful.However, the saturation of clamping apparatus The reduction of power limit again come self-oscillator maximum can be achieved peak power, and usually with high power mode locking oscillator Design object mutually conflicts.

For traditional KLM oscillator, shutting down program (stopping mode-lock operation) may be by same chaotic dangerous spike Unstability influences, as shown in Figure 8, wherein shows the oscillography of the measurement of the photodiode signal with oscillator output Device trace.Spike behavior when reducing gain can be clearly observed.

Summary of the invention

The object of the present invention is to provide a kind of improved pulse laser equipment and a kind of improved methods, for being based on Ke Er Lens mode locking establishes laser pulse, especially soliton laser pulse, so as to avoid the limitation of traditional technology.Particularly, the arteries and veins Impulse light device and this method should be able to optimize output parameter, such as power, bandwidth and the pulse duration of KLM oscillator, It avoids damaging optical element during pulse is established or shut down simultaneously.

These purposes are solved by a kind of pulse laser equipment for generating laser pulse and/or a kind of method respectively.

First general aspect according to the present invention, above-mentioned purpose are solved by a kind of pulse laser equipment, the pulse laser Equipment is for generating laser pulse, especially soliton laser arteries and veins based on the kerr lens mode locking of the circulation light field in oscillator chamber Punching.The pulse laser equipment (or: KLM oscillator) includes the resonator mirror of two or preferably more than two, the resonator Mirror crosses over the resonator optical path of oscillator chamber.Preferably, at least one of resonator mirror is for that will recycle the one of light field Divide the outer coupling mirror for being coupled out oscillator chamber.

At least one kerr medium is arranged in the optical path of oscillator chamber.In general, at least one described kerr medium is suitable for Self-phase modulation and self-focusing are introduced into the circulation light field in oscillator chamber, so as to cause the arteries and veins of resonance mode converter and circulation light field Rush the Mode Coupling of shape.The a part for being coupled out circulation light field leads to the pulse train of laser pulse.In addition, at least one increases Beneficial medium is arranged in the optical path of oscillator chamber.Gain media is suitable for enhancing the circulation light field in oscillator chamber.Preferably, described At least one gain media is suitable for providing soft aperture (gain region for forming the aperture KLM) in oscillator chamber.Alternately or additionally Ground, oscillator chamber may include the hard aperture for KLM filtering.

According to the present invention, pulse laser equipment further includes tuner, which is disposed for that oscillator is arranged The the first mode locking situation and the second mode locking situation of chamber.First mode locking situation is adapted to provide for the intracavitary threshold power for mode locking, should Intracavitary threshold power is lower than the situation under the second mode locking situation.First mode locking situation is suitable for starting or closing down kerr lens lock Mould, the second mode locking situation are suitable for lasting kerr lens mode locking, wherein recycle the resonator inside peak power of light field second It is higher than under the first mode locking situation under mode locking situation.

Threshold power is minimum sustained wave (CW) power in oscillator chamber, occurs to turn to mode-lock operation at the power Become.First mode locking situation (or: start or close down state) it is the mode locking situation that kerr lens mode locking starts or closes down.Second mode locking Situation (or: operating status) it is the mode locking situation that kerr lens mode locking persistently carries out, and have compared in the first arrangements of operations Higher intracavitary peak power, the shorter pulse duration compared in the first arrangements of operations, and/or have and the first operation The different pulse characteristic of the multiple-pulse generated in arrangement.Oscillator chamber is arranged to the first mode locking situation and is advantageouslyed allow for Starting terminates mode-lock operation, while the high power spike to avoid confusion and damage.Second mode locking situation is provided for increase The output power operating impulse laser equipment added.First and second mode locking situations are the fixed operation states of oscillator chamber, described Fixed operation state is particularly determined by the specification of oscillator chamber, such as intracavitary focal length and Ke Er and/or gain medium material. First and second mode locking situations by actual test or can use control cited below based on the numerical simulation of oscillator behavior It realizes in circuit.

Second general aspect according to the present invention, above-mentioned purpose generate laser by operating impulse laser equipment by a kind of The method of pulse solves, which includes oscillator chamber, has at least two resonator mirrors, the resonance Device mirror crosses over the resonator optical path of oscillator chamber;At least one kerr medium is disposed for Self-phase modulation and autohemagglutination Coke is introduced into the circulation light field in oscillator chamber;With at least one gain media, it is disposed for enhancing following in oscillator chamber Ring light field.Preferably, the method for the present invention is carried out by the pulse laser equipment of the first general aspect according to the present invention.

The method of the present invention includes generated based on the kerr lens mode locking of the circulation light field in oscillator chamber laser pulse, Especially soliton laser pulse, and change the mode locking situation of oscillator chamber between the first mode locking situation and the second mode locking situation Become.According to the present invention, lower than under the second mode locking situation under the first mode locking situation for the intracavitary threshold power of mode locking, and Starting or closing down for kerr lens mode locking provides under the first mode locking situation, the lasting kerr lens under increased output power Mode locking provides under the second mode locking situation.

Advantageously, it provides and is suitable for making it possible to inhibit in arteries and veins to the tuner of one of mode locking situation by oscillator chamber setting The chaotic oscillation of the deterioration during laser pulse in light field is established and is then established with increased output power in punching.From document [6] [10] it is found that kerr medium can lead to multiple-pulse operation, harmonic mode locking, output spectrum and pulse persistance along the translation of focus The change of time.However, compared with the traditional KLM oscillator of kerr medium for including translation, compared in the first arrangements of operations, Average power level and peak power level increase in the second arrangements of operations, so that starting and/or the stage of shutting down avoids Damage the other component of oscillator chamber or pulse laser equipment.

According to a preferred embodiment of the present invention, the first mode locking situation is selected such that the intracavitary threshold value for mode locking Minimum power.Threshold power is mean power in the minimum cavity for can be switched to mode-lock operation.Minimizing threshold power indicates the One mode locking situation is maximized the inhibition of chaotic oscillation and spike under the first mode locking situation.Preferably, the first mode locking Situation starts or closes down process without spike formula suitable for kerr lens mode locking.

According to another preferred embodiment of the invention, the second mode locking situation is selected such that in the resonator for recycling light field Portion's peak power maximizes.Advantageously, this allows pulse laser equipment to operate with peak power output.According in oscillator chamber Dispersion condition, in the abnormal dispersion area with negative group delay dispersion, intracavitary oscillator power can reach at least 50MW, especially At least 500MW, or can reach at least in the normal dispersion area dispersed with positive group delay for generating the chirp orphan to dissipate 5MW.The output peak power of pulse laser equipment correspondingly can reach for example, at least 5MW for abnormal dispersion area, or for different Normal dispersion area at least 0.5MW (unpressed).These export peak powers only representative example.According to applicable cases (for example, if If carrying out intracavitary experiment), it is possible to provide lower output peak power.

According to another preferred embodiment of the invention, the second mode locking situation is selected such that in the resonator for recycling light field Portion's peak power is higher by least 20% than under the first mode locking situation under the second mode locking situation.Advantageously, this allows pulse laser The new high power applications of equipment, the risk without influencing optical component.

Preferably, oscillator chamber includes single gain media, particularly preferably includes thin slice gain media, which increases Beneficial medium is provided separately at least one kerr medium and is positioned to contact with one in resonator mirror (for example, see document [4]).Thin slice gain media and kerr medium are separated into (this is for example different from document [6]) and are conducive at least one described in optimization The first arrangements of operations and the second arrangements of operations of kerr medium.

According to another preferred embodiment of the invention, there is at least one described kerr medium at least one antireflection to cover Layer.Advantageously, this increased resonator inside peak power for supporting to establish circulation light field under the second mode locking situation.

Another advantage according to the present invention can get a plurality of types of for the tuning of the first and second mode locking situations to be arranged Device, the tuner can be used for acting on oscillator chamber single operation parameter or multiple operating parameters.

According to the first preferred embodiment, tuner includes translating device, which includes at least one translation Platform, the translation stage are arranged in the optical path of oscillator chamber (first embodiment of the present invention).At least one described kerr medium with Translating device coupling.Provided that multiple kerr mediums, then it is therein at least one for starting kerr lens mode locking, and this gram You couple medium with a translation stage of translating device or multiple kerr mediums are coupled with corresponding multiple translation stages.Translation dress It sets and is suitable for changing the arrangements of operations of at least one kerr medium in oscillator chamber.At least one described kerr medium can be It is translated between first arrangements of operations and the second arrangements of operations.First mode locking situation is grasped with the first of at least one kerr medium Make arrangement to provide, the second mode locking situation is provided with the second arrangements of operations of at least one kerr medium.It is operated by changing Arrangement, the geometric position of optical path of at least one the described kerr medium along oscillator chamber, especially with a distance from resonator mirror, and/ Or the thickness at least one kerr medium being introduced in the optical path of oscillator chamber can be changed.In the first and second operations In arrangement, at least one described kerr medium has different influences to the mode locking process of oscillator chamber.

First embodiment according to the present invention, translating device are adapted to provide for the first and second arrangements of operations, so that for locking The intracavitary threshold power of mould is lower than under the second arrangements of operations under the first arrangements of operations.Described in the positioning of first arrangements of operations At least one kerr medium is suitable for starting or terminating mode-lock operation, while the high power spike to avoid confusion and damage.Second behaviour Make arrangement to provide for increased output power operating impulse laser equipment.First and second arrangements of operations are by oscillator chamber Specification determine fixation position.

Advantageously, may be used alone or in combination a variety of modifications used can be used for being arranged the first and second arrangements of operations.Root According to the first advantageous variant, the first and second arrangements of operations include at least one described kerr medium along the first of resonator optical path The second position and.Changing arrangements of operations includes that at least one described kerr medium is movable into and out intracavitary focus.Preferably, One arrangements of operations makes kerr medium be in intracavitary focal point, especially in the about +/- of the focal length of resonator mirror around intracavitary focus In the range of 2%.Focal length is limited by the focal length for providing the curved mirror of intracavitary focus (for example, see the mirror 12 and 13 of Fig. 1).Having Have the focus lamp (such as 12 and 13) of different focal length asymmetric focusing arrange in the case where, relevant focal length be two mirrors compared with Short focus.At least one described kerr medium is moved into the second arrangements of operations, so that intracavitary peak power increases.Translation distance Selected from focal length about 3% to 10% in the range of, for example, if focal length be 1 meter, distance is at 3 centimetres to 10 centimetres In range.In the case where the first arrangements of operations, by least one described kerr medium towards one in adjacent resonator mirror It is a to remove the distance from focus.The embodiment has the advantage that, because it can be used with the kerr medium of any type and shape, and Beam axis will not be changed.

According to the second advantageous variant, at least one described kerr medium includes a pair of of kerr medium wedge, the kerr medium Wedge is arranged to translate, which has the durection component perpendicular to resonator optical path, so that this follows kerr medium wedge Total effective thickness that ring light field is passed through can be by adjusting wedge into and out optical path.In this case, first and second Arrangements of operations includes first and second positions of the kerr medium wedge along the radial direction relative to resonator optical path.The embodiment There can be compact resonator design.

Preferably, at least one of kerr medium wedge has antireflective coating, to reduce intracavitary caused by reflecting Loss.It is particularly preferred that the angle of wedge of kerr medium wedge is selected to, so that when being placed on relative to optical path close to Brewster's angle When in optical path, reflection loss is minimized.

Another particularly preferred embodiment according to the present invention, arrangements of operations pass through the nothing of at least one kerr medium Vibration motion changes.Movement be it is vibrationless, from without vibrating or only inappreciable vibration, thus will not damage lock Mould.For this purpose, translating device preferably includes linear translation platform, such as the translation stage with servo motor driving.Advantageously, this is utilized Embodiment can avoid the disturbance of oscillator and changing unintentionally for mode locking situation.

According to the second preferred embodiment, tuning is disposed for making at least one described kerr medium and/or additional The phase mismatch situation that (SHG) crystal occurs for phase mismatch I type second harmonic is lost in first phase mismatch conditions and second phase With changing between situation, (SHG) crystalline substance occurs at least one described kerr medium and/or additional phase mismatch I type second harmonic Body is arranged in the resonator optical path of oscillator chamber so that for increasing second nonlinear in oscillator chamber, the second phase is lost There is compared with first phase mismatch conditions the bigger phase of at least one described kerr medium and/or SHG crystal with situation Mismatch (second embodiment of the present invention).Phase mismatch changes between the first and second mismatch conditions, so that and first phase Mismatch conditions are compared, total intracavitary non-linear lower under second phase mismatch conditions, and peak power and/or spectral bandwidth and/ Or pulse stability increases.As an example, phase mismatch can be zero or insignificant under first phase mismatch conditions (i.e. close to zero), and increase under second phase mismatch conditions.First mode locking situation has first phase mismatch conditions, the second lock Mould situation has second phase mismatch conditions.First and second phase mismatch situations are the fixed operation states of oscillator chamber, Especially determined by the specification of oscillator chamber, such as intracavitary focal length and Ke Er and/or gain medium material.Oscillator row can be used For numerical simulation, actual test or control loop the first and second phase mismatch situations are set.

Preferably, tuner is disposed for tuning at least one described gram relative to the resonator optical path of oscillator chamber At least one of the temperature and incidence angle of that medium and/or SHG crystal.In the first scenario, tuner includes crystal Register, such as the temperature control supporting table of at least one described kerr medium and/or SHG crystal, such as crystal conditioning oven.Second In the case of kind, tuner includes Crystal Rotation device, for example, at least one described kerr medium and/or SHG crystal can pivot Turn supporting table, to allow to rotate at least one described kerr medium and/or SHG crystal perpendicular to the axis of resonator optical path.

Advantageously for second embodiment, at least one described kerr medium and/or additional SHG crystal are in resonator It is introduced in optical path second nonlinear (or: cascade quadratic nonlinearity interaction).It in this case, can be for example such as bibliography [11] define like that non-linear in, so that the nonlinear phase shift due to caused by transmissive element is derived from total nonlinear refractive index, this is total Nonlinear refractive index is made of the sum of cube (Kerr) nonlinear refractive index and secondary (cascade) effectively nonlinear refractive index.Cause This, it is increased non-linear means that: due to the summation of effective nonlinear refractive index of elements all in oscillator chamber, to pass through The increase of each round-trip total nonlinear phase shift of oscillator chamber.Due to phase mismatch, the generation of second harmonic radiation can be low , so that the spectral losses of circulation mode locking light field occurred from second harmonic are negligible.Advantageously, in oscillator chamber from width The saturation and mode locking entry condition for spending modulation can be influenced by second nonlinear.

Another modification according to a second embodiment of the present invention, SHG crystal can realize by non-linear introducing oscillator chamber and gram Dual function in terms of your lens mode locking.Therefore, kerr medium can be by the phase mismatch I type two with above-mentioned SHG crystal feature Subharmonic occurs (SHG) crystal and provides, and the mode locking situation of the settable kerr medium of tuner of second embodiment of the invention.

The first and second embodiments of the invention can be combined, that is, translation can be passed through by starting or closing down state and operating status Any combination of device, crystal register crystal and/or rotating device is arranged.For example, first phase mismatch conditions can be At least one described kerr medium have the first arrangements of operations when provide, and second phase mismatch conditions can it is described at least one Kerr medium provides when having the second arrangements of operations.

If such as in pump power and gain by operation regulating device control at least one gain media At least one, then can get the further advantage of operational stability, so that oscillator chamber keeps mode locking, while make to operate cloth It sets and changes between the first and second arrangements of operations.

Advantageously, it is possible to provide detector means especially recycle the resonator of light field for detecting kerr lens mode locking situation Internal peak power, pulse duration and/or the pulse or multiple-pulse characteristic that recycle light field.Detector means allow to monitor Oscillator chamber operation, while change arrangements of operations between the first and second arrangements of operations.

According to another preferred embodiment of the invention, control loop is provided, control loop preferably includes detector means With operation regulating device.Advantageously, control loop permission controls translating device according to detector means output, and grasps changing Oscillator mode locking is kept while arrangement.

Detailed description of the invention

Below with reference to the accompanying drawings further details and advantages of the present invention are described, attached drawing is shown:

Fig. 1 is the schematic diagram of pulse laser equipment according to the preferred embodiment of the invention;

Fig. 2 is to provide the diagram of kerr medium wedge;

Fig. 3 is the graphical representation of the stability range of pulse laser equipment;

Fig. 4-6 is the further graphical representation for illustrating feature that laser pulse of the invention is established;

Fig. 7 and Fig. 8 is the diagram of the instable generation of spike for starting or closing down process of traditional KLM oscillator.

Specific embodiment

It is illustratively retouched below with reference to including the linear resonator of a kerr medium and an individual gain media State feature of the invention.The present invention is not limited to this embodiment, but can by multiple kerr mediums and/or multiple gain medias or Single public Ke Er and gain media are realized.The details of operation KLM oscillator is not described, because these details are from existing skill It is known in art.Particularly, the working principle that pulse laser equipment can refer to orphan's mode locking oscillator disclosed in document [3] carries out Operation.

Fig. 1 is shown according to the present invention for generating the schematic diagram of the pulse laser equipment 100 of laser pulse 1, and pulse swashs Light device 100 includes that there are four the oscillator chambers 10 and pump source 60 of resonator mirror 11,12,13 and 14, such as bis- pole cw for tool Pipe laser (such as cw diode laser of 940nm fiber coupling, with the pump power for being more than 100W).Resonator mirror 11,12,13 and 14 cross over optical path 2, and optical path 2 includes kerr medium 21, gain media 31, and optional SHG crystal 71 (is shown with dotted line Out) and hard aperture 15.One, such as resonator mirror 11 in resonator mirror, are outer coupling mirrors, and if using as shown in Figure 1 Body gain media, then another in resonator mirror, such as resonator mirror 14 are arranged for interior coupling from pump source 60 Pumped light.One reflecting region in resonator mirror can be used as aperture (hard aperture 15).Additionally, oscillator chamber 10 includes At least one introduces the device of dispersion (especially group delay dispersion), which is not shown, but can pass through one in resonance mirror (as dispersion mirror) Lai Shixian.

Kerr medium 21 includes such as sapphire plate, and sapphire plate is with a thickness of 1mm to 5mm, and relative to optical path 2 with cloth scholar This special angle arrangement.Kerr medium 21 is supported by the translating device of offer tuner 40, and translating device includes single translation stage, example Such as electronic supporting table or manually adjustable platform.Translating device 40 is suitable for for example flat for several centimetres of translation about 5 seconds to 10 seconds Move speed.According to application conditions, in particular according to the noise introduced by translating device 40, it is possible to provide faster or slower translation.Benefit With translating device 40, kerr medium 21 can be moved along optical path 2, with one be arranged in the first and second arrangements of operations, be used for Start mode locking and steadily run pulsed laser source 100, as described below.For this purpose, translating device 40 and operation regulating device 50 Coupling, operation regulating device 50 includes computer based control circuit, the arrangements of operations of kerr medium 21 is arranged.Gain is situated between Matter 31 may be disposed so that body gain material as shown in the figure, or be preferably arranged as thin slice gain media, such as Yb:YAG, with it is humorous One in vibration device mirror, such as resonator mirror 12 directly contacts, or contacts with additional refrative mirror.

Note that Fig. 1 is only the schematic diagram of pulse laser equipment 100.For example, actually can provide the resonator more than four Mirror.In addition, if using thin slice gain media, then pumped light is directed on laminated dielectric from individual pump chamber, therefore pumped light It is inconsistent with zlasing mode, and interior coupling mirror is not provided.According to a preferred embodiment of the present invention, pulse laser equipment 100 There can be the resonator of kerr lens mode locking thin slice oscillator disclosed in document [4] to be arranged.It is arranged about resonator, it is especially humorous The arrangement of vibration device mirror, gain media and kerr medium, is incorporated by reference into this specification for document [4].For the embodiment, arteries and veins Impulse light device 100 has linear oscillator chamber, has the relatively high -12.000fs introduced by dispersion mirror coating2's Intracavitary GDD.Gain is provided by Yb:YAG thin slice, and is coupled out 15% circulating power back and forth every time, and pulse recurrence rate is about 16MHz.A focus is provided by the focus arrangement structure that two radius of curvature form for the concave mirror of 2000mm, here, 5mm thickness Sapphire plate is as main kerr medium.Oscillator works in the air atmosphere of decompression.Pass through the slight movement of mirror pair, In Start mode locking in first arrangements of operations at 0mm.Avoid damage.Then kerr medium position is moved to distance starting position about The second arrangements of operations of 60mm, it is stopped until oscillator is shut down again herein.

According to another alternative solution, pulse laser equipment 100 can have kerr lens mode locking thin slice disclosed in document [5] (operating in normal atmosphere) is arranged in the resonator of oscillator.At this point, intracavitary GDD value is in -48.000fs2With -18.000fs2It Between change, and introduce radius of curvature be 900mm focusing section, the sapphire kerr medium including 1mm thickness.Output coupler passes Defeated 21% cycle pulse, intracavitary peak power are about 180MW.

The saturation degree modulated from amplitude can be influenced by second nonlinear, the also referred to as interaction of cascade quadratic nonlinearity, Especially influenced by the second harmonic of phase mismatch (see document [11]).By the way that phase mismatch I type second harmonic is occurred Crystal 71 (such as beta-barium borate (BBO) crystal or three lithium borates (LBO) crystal) is placed in oscillator optical path (of the invention Two embodiments), such as it is placed between mirror 11 and 12 or in another collapse branch of oscillator chamber, and from phase matched solution It is humorous, it can control the amount by the nonlinear phase shift of intracavitary pulse accumulation and the amount of self-focusing.I type phase mismatch can be filled by tuning 40 (being shown in broken lines) are set by using Crystal Rotation device progress angle tuning (such as BBO) and/or by using SHG crystal 71 crystal register carries out thermal tuning (such as LBO) to control.Nonlinear phase shift may be selected to be it is positive or negative so that autohemagglutination Burnt or self-defocusing is possible.Provided that crystal 71 occurs for second harmonic, then can save according to a first embodiment of the present invention Kerr medium translation.

Preferably, the temperature adjustment of SHG crystal 71 is provided.Crystal register is for example including furnace, the crystal temperature of 250 DEG C of setting Degree be used as the first mode locking situation, and be raised and lowered temperature be tuned to the second mode locking situation, wherein with the first mode locking situation It compares, phase mismatch increases.If realizing that of the invention second is implemented in the case where the translating device of not first embodiment Example then can avoid any moving assembly of tuner.

According to still another embodiment of the invention, such as the kerr medium 21 of Fig. 1 can be replaced wedge-shaped Ke Er as shown in Figure 2 Medium 22,23.Kerr medium 22,23 includes two for example sapphire wedge pieces, and wedge piece can be along with perpendicular to oscillation Direction (laser field of transmission is propagated) translation of the component of the optical path 2 of device chamber.Kerr medium 22,23 passes through two translation stage (Fig. 2 In be not shown) it is translated.Translatable wedge-shaped kerr medium can also with can along optical path translate common kerr medium combine.

Additionally, pulse laser equipment 100 includes detector means 51, such as photodiode, and detector means 51 are supervised Survey a part of the circulation light field in oscillator chamber 10.Preferably, the output signal of detector means 51 is provided to operation and adjusts Regulating device 50, operation regulating device 50 are coupled to have translating device 40, pumped source device 60 and gain media for providing At least one of 31 control loop 52.Using control loop 52, at least one in these components is controlled according to output signal It is a, to keep the mode-lock operation of pulse laser equipment 100.If can be simulated based on the predetermined value of chamber behavior or be surveyed based on experiment It tries not needing then to provide control loop 52 to adjust the first arrangements of operations and the second arrangements of operations of kerr medium 21.

Such as according to the distance between resonator mirror 12 and kerr medium 21 b1, may recognize that there are Gauss TEM00 modes Two stable regions.These available such as Ray Matrix methods calculate.For annular chamber, there is only a stable regions.Fig. 3 Show the mode radius in the sagittal and tangential face on the stable region of exemplary KLM oscillator (for example, as shown in Figure 1) Wa, s (curve A) and Wa, t (curve B).When (such as Fig. 3, shadow region) is operated oscillator chamber near stabilised edge, mention For kerr lens mode locking, wherein resonator mode is highly susceptible to the influence of the variation of any intracavitary focal length of lens.In general, Net round is considered beneficial to pulse establishment process to the high sensitivity (initial slope) of transient pulse power, and especially has Help self-starting modelocking laser [1].When oscillator self-starting or when needing external disturbance to start mode locking, the present invention can be with Two ways work.

The oscillator chamber 10 of pulse laser equipment 100 (such as according to Fig. 1) is by adjusting b1And b2And it is adjusted to stable side One in edge, in order to kerr lens mode locking.b1It is remained unchanged with the sum of b2, and the position of kerr medium 21 is for example with distance b2Characterization.The effect of caused kerr lens is that the power transmission of cavity mold is modulated at intracavitary aperture in kerr medium 21.This It has been calculated numerically and has been plotted in Fig. 4, Fig. 4 is particularly illustrated dependent on 21 position b of kerr medium2(referring to Fig. 1) The power associated transport in hard aperture 15 in transit chamber.Give initial slope and its value.

The difference (vertical intercept) that Fig. 4 shows saturation power is almost the factor 2 in the example shown.Saturation power is limited herein It is set to the power transmitted when poor (or more generally, round) reaches the half of its maximum value, also referred to as modulation depth Δ R. In practice, the exact shape of transmission or gain curve additionally depends on the total amount and property and gain saturatiuon degree in intracavitary aperture (referring to Fig. 4 in document [1]).However, in general, Fig. 4 shows saturation power and gain/transmission curve initial slope And total modulation depth Δ R (aperture is almost always more than one) can be influenced strongly by 21 position of kerr medium.

According to the present invention, using this characteristic behavior, so that kerr medium position (the second arrangements of operations) is optimized to For stable operation, and the peak power of laser pulse and/or spectral bandwidth are significantly higher than and are optimized for reliably starting and arteries and veins The case where rushing position (the first arrangements of operations) established and/or optimised kerr medium position (the second arrangements of operations) are in chamber Only allow single pulse during two-way time, and multiple pulses can be formed in starting position (the first arrangements of operations).Utilize second Kerr medium in arrangements of operations, wherein the peak power and/or bandwidth of cycle pulse are optimised, even if there is no damage, Oscillator may also refuse mode locking.This may be the weaker reason of instant power loss/gain modulation initial slope.Utilize The creative setting of one arrangements of operations, eliminates this difficulty.

First and second arrangements of operations of kerr medium 21 are set based on considered below.For described in starting at least one A kerr medium is initially positioned at the first arrangements of operations (" starting position "), wherein saturation power is relative to the second arrangements of operations (" running position ") reduces.First arrangements of operations of kerr medium 21 is preferably at intracavitary sustained wave needed for making to start mode locking (CW) at the smallest kerr medium position of mean power.Start kerr lens mode locking in the first arrangements of operations, to avoid pair The optical damage of intracavitary element.Once oscillator by mode locking, then at least one described kerr medium is translated into the second operation cloth It sets, wherein saturation power increases, and saturation power and possible modulation depth Δ R are optimised, to be used for higher peak power And/or bandwidth and/or pulse stability.

For an actual example, distance b1The first arrangements of operations, distance b are obtained when=120cm1Is obtained when=126cm Two arrangements of operations.During translation motion, it may be necessary to pump power or gain are adjusted using operation regulating device 50, to keep shaking Swing device mode locking.Gain is maintained at a value, may also lead to chaos power peak to avoid being transformed into orphan's oscillator Multiple-pulse state.The method being mentioned below can be used to adjust gain.Using translating device 40, kerr medium translation is without friction , for example do not interrupt mode locking pulse and cause spike with itself.

If there are more than one kerr mediums in oscillator chamber 10, some of which or whole may must be translated To realize desired effects.Each kerr medium can have the first arrangements of operations of their own, and kerr medium can once all It translates to ground or sequential order, to reach second arrangements of operations with optimum output power.There is provided multiple kerr mediums with There is advantage in terms of adjusting the bigger freedom degree of optimum operation condition of oscillator.

It, can be secondary non-thread using adjustable cascade is shown in the first arrangements of operations in order to which safely starting impulse is established Property this crystal so that increasing the intracavitary non-linear and saturation degree modulated from amplitude relative to the second arrangements of operations.This In two arrangements of operations, change phase mismatch so that total is intracavitary non-linear lower, and peak power and/or spectral bandwidth and/or Stability increases.The realization of the first and second arrangements of operations with cascade quadratic nonlinearity can be with previously mentioned two wedges Translation and/or one or more kerr mediums are combined along the translation of optical path.Use cascade quadratic nonlinearity interaction One advantage is, it is possible to provide every time by nonlinear phase shift very strong variation and oscillator reliable starting in temperature There is no any moving parts under the specific condition of tuning.

The starting of mode locking can be realized by any actively or passively means.Proactive method includes such as mechanical disturbance device, Such as manual pusher or piezoelectric actuator, with mobile one or more hysteroscopes or vibrator or active optic modulators, such as Acousto-optic or electrooptic modulator (pockels cell (Pockels cell)) or injection optics seed pulse.Starting can also be by following Mode is realized: such as synchronizing pumped middle modulation gain, or by periodically being consumed with another laser by stimulated emission Gain to the greatest extent, or gain is increased by intracavity beam attenuator or beam blocker or aperture suddenly.Passive means can pass through auxiliary Coupler is rotated by nonlinear polarization or is done using saturable absorber, such as SESAM or graphene or Nonlinear Multi Relate to filter (MAM) Lai Shixian.It is all these all but self-starting need not to be caused to configure.

One particular implementation of starting mode-lock operation may also include two wedge pieces 22 that moving charging works as kerr medium, 23 (as shown in Figure 2).By the way that wedge piece 22,23 is moved close to or far from (direction is indicated by horizontal black arrow), can adjust By the total effective thickness for the kerr medium that pulse is passed through.This will lead to the tunable saturation of amplitude modulation, be situated between similar to by Ke Er Matter is movable into and out intracavitary focus.Wedge piece 22,23 can be moved additionally along beam propagation axis, be used to start lock to realize The bigger saturation effect of mould.Wedge piece 22,23 can have antireflective coating or without coating, and have the very small angle of wedge, make Proper when being placed in optical path close to Brewster's angle, reflection loss is smaller.

It was found by the inventors that experiment instruction safely shuts down mode locking and extensive using reverse procedure in some configurations It is also likely to be beneficial for arriving CW oscillation again or shutting down laser completely.If some intracavitary elements be highly susceptible to thermal shock and Pumped/gain must slowly rise/fall, then this may be especially necessary.Peak restrained of the invention can answer as follows For shut-down process.

At least one described 21 initial alignment of kerr medium is in the second arrangements of operations, wherein saturation power is relative to One arrangements of operations increases, and oscillator is in the mode locking situation of the output parameter with optimization.In order to safely disconnect mode locking simultaneously Q switch/spike or q switch mode locking and the optical damage to oscillator unit, at least one described kerr medium 21 is avoided to be put down Move on to corresponding first arrangements of operations (" shutting down position "), wherein saturation power is optimized to realize that the lossless of mode locking is shut down.In When reaching the first arrangements of operations of at least one kerr medium 21, mode locking is interrupted, so that oscillator is switched to CW oscillation Or it shuts down completely.

The interruption of mode locking or shut down can be by mechanically disturbing cavity using acousto-optic or electrooptic modulator, by modulating or subtracting Small gain is realized by opening intracavitary aperture or beam blocking, or by increasing by the transmission rate of intracavity beam attenuator. Shutting down position may be overlapped with starting position, and if there are multiple kerr mediums in oscillator, each kerr medium can Can have their own shuts down position, this, which shuts down position, may need in a lump or arrive sequentially at.

In translation motion, it may be necessary to pump power or gain are adjusted, to keep oscillator mode locking and avoid being transformed into Multiple-pulse state, in multiple-pulse state, it is also possible to the damage of optical element occur.Equally, kerr medium translation is smooth enough, such as Mode locking pulse will not be interrupted in advance and/or q switch/spike or q is caused to switch mode locking.

Fig. 5 shows the peak power variation in the pulse laser equipment 100 of the setting of the resonator with document [4], In, first arrangements of operations of the kerr medium position from 0mm is displaced to the second arrangements of operations close to 60mm.Beyond optimum position Mode locking can be destroyed.Intracavitary peak power becomes 450MW from 200MW.

Fig. 6 is shown when kerr medium is displaced to the second arrangements of operations from the first arrangements of operations, exports the spectrum of pulse The variation of bandwidth.Pulse remains the Fourier limit.Changing for spectral bandwidth can be monitored by detector means 51 (referring to Fig. 1) Become, to optimize the second arrangements of operations.

The feature of the invention disclosed in above description, drawings and claims for realizing this in different embodiments For invention can individually, in combination or sub-portfolio it is meaningful.

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