WO2007113274A1

WO2007113274A1 - Compensation device for thermal lens in a high-frequency femtosecond regenerating cavity

Info

Publication number: WO2007113274A1
Application number: PCT/EP2007/053150
Authority: WO
Inventors: Emmanuel Baubeau; Guillaume Matras
Original assignee: Thales
Priority date: 2006-03-31
Filing date: 2007-04-02
Publication date: 2007-10-11
Also published as: FR2899390B1; FR2899390A1

Abstract

The invention concerns a laser cavity which is a laser cavity of the type of high-frequency pumping femtosecond regenerative cavity, comprising a gain medium, such as a Ti:Sa crystal, and at least two cavity base mirrors. The invention is characterized in that its gain medium (12) is designed to be contacting or proximate one of its cavity base mirrors (11), which is a convex mirror of which the radius of curvature is a function of the desired stability range compatible with the thermal focus of the crystal.

Description

DEVICE FOR COMPENSATING THE THERMAL LENS IN A REGENERATIVE HIGH-CADENCE FEMTOSECOND CAVITY

The present invention relates to a device for compensating the thermal lens in a femtosecond regenerative cavity at high speed.

The production of laser sources of the femtosecond type amplified at a high rate (several kHz) and for example in Ti: Sa technology, faces a worsening of the phenomenon of the thermal focal point when the rate of repetition of the laser increases. This is particularly the case in regenerative amplifiers which generally constitute the first amplification stage of such sources.

One of the techniques used to overcome this problem is to cool the sapphire-titanium crystal at very low temperatures. This makes it possible to increase the thermal conductivity of the crystal and to reduce the index variation with the temperature, these two phenomena having the effect of reducing the thermal focal effect. However, this technique is relatively expensive (use of cryogenic techniques) and greatly increases the size and complexity of the laser. It also poses problems of insulation and maintenance of the crystal.

Reference will be made to the diagrams of the examples of FIGS. 1 and 2 to expose the characteristics of regenerative laser cavities to which the present invention relates. These cavities are generally of type "V" (Figure 1) or "Z"

(Figure 2). The similar elements of these two figures are assigned the same numerical references.

The cavity of FIG. 1 essentially comprises a plane mirror 1, two concave mirrors 2 and 3, a gain medium 4, an electro-optical system 5 (a Pockels cell, for example) and a polarizer 6. The mirrors 1 to 3 are arranged so that the axis 7 joining the centers of the mirrors 1 and 2 make an acute angle with the axis 8 joining the centers of the mirrors 2 and 3. The mirrors 1 and 3 are called "cavity bottom mirrors" . The system 5 and the device 6 are arranged on the axis 7, while the crystal 4 is disposed on the axis 8, near the neck ("waist" in English) of the beam propagating between the two concave mirrors 2 and 3. The crystal 4 is pumped longitudinally through the mirror 3, so that the overlap between the pump and the mode of the cavity is the best possible. The crystal is usually cut at the angle of Brewster.

The cavity of FIG. 2 essentially comprises, in addition to the first plane mirror 1 and two concave mirrors 2 and 3, a second plane mirror 9, a gain medium 4, an electro-optical system 5 and a polarizer 6. As in the case 1, the mirrors 1 to 3 are arranged so that the axis 7 joining the centers of the mirrors 1 and 2 makes an acute angle with the axis 8 joining the centers of the mirrors 2 and 3. In addition, the mirror 9 is arranged so that the axis 10 joining its center to the center of the mirror 2 makes an acute angle with the axis 8. In this configuration, the mirror 9 is the cavity bottom mirror. Thus, the axes 7, 8 and 10 form a "Z". The elements 4, 5 and 6 are arranged in the same way as in FIG. 1. The crystal 4 is also pumped longitudinally through the mirror 3.

Several criteria govern the operation of a regenerative cavity: o In one of the arms of the cavity, the beam is collimated (axis 7) and of fairly large diameter. The electro-optical device or devices (6) necessary for injecting and ejecting the pulse to be amplified into the cavity are inserted therein. The beam in the arm of the Pockels cell (5) must be slightly divergent and wide enough to guarantee its good functionality. o The energy extracted from the cavity is directly connected to the volume of the gain zone in the crystal (4). It is important that the mode on the crystal is as big as possible. o There must be the best possible overlap between the pump laser and the cavity mode inside the crystal. This condition imposes strong constraints on the choice of the pump laser and in particular its M ² factor.

In such cavities, there may be a parasitic phenomenon, it is the effect of thermal lens. When pumped, the crystal heats inhomogeneously and behaves like a lens. In a first approximation, the focal length of the thermal lens is given by the following formula [Thermal Lensing in Nd: Rod YAG, Koechner, Applied Optics, Nov 1970, Vol 9, N ⁰ I l]:

in this formula, r is the pump radius, P, the thermal power dissipated in

the crystal, - the index variation as a function of the temperature. The thermal lens is all the stronger (that is to say, its focal length is even shorter) than the pumping power is strong or the pumping radius is low.

This phenomenon is sensitive to the increase of the repetition rate of the pump laser. It is possible to reformulate the previous expression by introducing the pumping energy density Jp:

in this formula, τ is the repetition rate of the pump laser, Pp is the power of a pump pulse, and η is the efficiency between ^the pump energy and the energy available for amplification. The formula (1) then becomes:

^{/ Λ =} 7FT ^<3)

It thus appears that at constant pump energy density, that is to say at constant gain, the thermal focal length is inversely proportional to the laser repetition rate.

For example, to have the same gain at 10 kHz as at 1 kHz, either multiply the average power by 10 or reduce the pumping area by a factor of 10. In both cases, the thermal focal length is reduced by a factor ^of 10. At 10 kHz, the latter has a value less than 10 cm in optimal pumping conditions.

Conventionally, we always position the crystal in the "waist" of the cavity, but it is possible in some cases to move it to get a bigger mode on it. With the aid of optical calculation software, it is possible to trace the propagation of the beam in a conventional V-shaped recess (such as that of FIG. 1) composed of a crystal subjected to a thermal lens effect. This is illustrated by the examples of FIGS. 3 to 7. The cavities for which the propagation diagram has been drawn in FIGS. 3 and 4 are identical, the only difference being the position of the crystal with respect to the "waist". These two identical cavities are designed to be stable for long thermal focal lengths. The left arm (to the left of the M2 mirror) is intended to accommodate the Pockels cell. In order to magnify the mode on the crystal, one can move the crystal a few centimeters outside the waist of the cavity without altering the propagation of the intracavity beam as shown in Figure 4.

The cavities of which the propagation diagram has been drawn in FIGS. 5 to 7 are also identical with each other, with the sole difference of the position of the crystal with respect to the "waist" and refer to the diagram of FIG. 1. They are designed to short thermal focal lengths. In Figure 5, the waist is only 87μm. If one performs the same operation as in the cavity of FIG. 4, one increases the size of the waist, but the propagation of the beam is degraded very quickly: one focuses either on the cavity bottom mirror (figure 6), or in the arm that contains the Pockels cell (Figure 7). Conventional regenerative cavities therefore offer very little flexibility.

For short thermal focal lengths, one can not increase the mode size on the crystal without altering the propagation of the beam inside the cavity. The energy that can be extracted from these cavities is therefore limited.

Another important parameter of these cavities is their stability. In the reference [V. Magni "Resonators for solid-state lasers with wide-aperture fundamental mode and high alignment stability". Applied Optics, 25: 107-117, 1986], it is shown that a two-mirror cavity containing a bar subjected to a thermal lens effect, has two zones of stability of the same width and that the volume of the mode (at crystal level) has a stationary point insensitive to fluctuations in the thermal focal length. From this calculation, it is possible to extend the demonstration to a cavity in V or Z. The curve of FIG. 8 represents the evolution of the fundamental mode size on the crystal (mode radius at the crystal level) as a function of the inverse of the thermal focal length.

In this Figure 8, there are two symmetrical stability zones of width Δ respectively called "Zone 1" and "Zone 2"; w ₀ is the point where the cavity is the least sensitive to the fluctuations of the thermal focal length. Outside stability zones of width Δ, the laser effect in TEMoo mode can not exist (non-existent or degraded laser effect).

From these calculations, one can also extract an essential relation: the width of the stability zone Δ is inversely proportional to H ^> ₀ ^~ :

The larger W ₀ is, the greater the amplification volume, but the smaller the stability range. We must therefore seek a compromise.

The standard cavities all work in Zone 1 and are constructed in such a way that the cavity can be stable even without thermal focus. The relation (4) then implies a maximum mode size for a given thermal focal length.

In zone 2, the cavity is stable only in the presence of the thermal lens. This would theoretically allow for a larger mode, but so far no achievements have been made and no description of such a possibility has been published.

Another parameter to take into account for cavities of the aforementioned type is their sensitivity to misalignment. The sensitivity to misalignment of the cavity is defined in the above-reference Eilee as the inverse of the maximum angle applicable to the orientation ^of a mirror without shift mode outside the pumping area . It is measured in rad ^~ '.

FIG. 9 shows a typical curve of the sensitivity of a cavity bottom mirror as a function of the inverse of the thermal focal length. In zone 1, the sensitivity to misalignment remains low, while ^that in zone 2 the sensitivity tends rapidly towards ^infinity. In practice, it is therefore difficult to work in zone 2.

The present invention relates to a laser cavity in which one can increase the energy extracted consistently ^a regenerative amplifier in a simple and inexpensive way. The laser cavity according to the invention is a cavity of the femtosecond regenerative type with a high pumping rate, comprising a laser crystal and two cavity bottom mirrors, and is characterized in that its gain medium (12) is disposed at contact or near one of its cavity bottom mirrors (1 1), which is a convex mirror whose radius of curvature is a function of the desired stability range compatible with the thermal focal length of the crystal. Preferably, it is architecture "V" or "Z".

The laser cavity of the invention makes it possible to obtain a large amplification volume irrespective of the value of the thermal focal length involved, while maintaining a TEM 0 0 beam. As a corollary, this technique makes it possible to release the constraint on the parameter M ² of the pump laser. This invention is applicable to cavities provided with crystals of various types, in particular, but not limited to Ti: sapphire or ytterbium.

The present invention will be better understood on reading the detailed description of an embodiment, taken by way of nonlimiting example and illustrated by the appended drawing, in which: FIGS. 1 and 2, described above, are simplified schematics of laser cavities of the prior art, with "V" and "Z" architecture, respectively, FIGS. 3 to 7, also described above, are laser beam propagation diagrams in cavities of FIG. the prior art, FIG. 8, also described above, is a typical curve illustrating the stability of a regenerative cavity and represents the evolution of the fundamental mode radius on its crystal as a function of the inverse of the thermal focal length. , FIG. 9, also described above, is a typical curve illustrating the sensitivity to misalignment of a cavity bottom mirror, FIG. 10 is a diagram of an example of a laser cavity according to the invention, FIGS. 1 and 12 are laser beam propagation diagrams in a cavity according to the invention, FIG. 13 is a typical curve illustrating the evolution of the stability range for different radii of curvature of the convex mirror of a cavity according to the invention. the invention and giving the mode radius

TEMoo at the crystal according to the inverse of the thermal focal length, Figure 14 is a curve relating to a laser cavity according to the invention and giving both sensitivity to a misalignment of the cavity and the diameter of the mode TEMOO at the level of the laser crystal as a function of the inverse of its thermal focal length, and FIGS. 15 and 16 are simplified diagrams of examples of laser cavities according to the invention with a "Z" and "V" architecture , respectively. The principle of the invention is to position the crystal in the cavity bottom, just in front of a plane or convex mirror. The choice of the radius of curvature of this mirror makes it possible to tune the cavity according to the thermal focal length.

This principle makes it possible to obtain any size of mode, whatever the thermal focal length, while maintaining a wide mode and collimated in the arm of the Pockels cell. In addition, the crystal is, by construction, always located in a Rayleigh zone of the mode, i.e., an area in which the beam is collimated. Finally, the possibility of obtaining a cavity with a large mode makes it possible to release the stress on the parameter M ² of the pump laser and facilitates its realization.

FIG. 10 diagrammatically shows a cavity in "V" according to the invention. The cavity of FIG. 10 is similar to that of FIG. being that the concave mirror 3 is replaced by a convex mirror 1 1 and that the crystal 4 is replaced by a crystal 12 in contact with the mirror 1 1 or close to it.

To expose the design of the cavity of the invention, let us first assume that the cavity bottom mirror 1 1 is flat, and that the crystal 12 is devoid of thermal lens effect. The cavity is designed in such a way that it satisfies the criteria described above with reference to FIGS. 1 and 2 (collimation of the beam in the arm of the Pockcls cell and a large mode on the crystal). Then the radius of curvature of the mirror is adjusted to set the desired stability range compatible with the thermal focal length of the crystal. The optimum value of the radius of curvature is equal to the thermal focal length of the crystal: R optimum = J f Ih cπslai

First, we impose the diameter of the fundamental mode at the crystal at 300 .mu.m. Knowing that the two bottom mirrors of the cavity in "V" are planes by hypothesis (the mirror 1 is plane by construction, and the mirror 1 1 is first assumed to be plane), the known parameters are sufficient to determine the distances as well. that the adapted radius of curvature of the concave mirror 2. There is shown in Figure 1 1 the pattern of propagation of the laser beam in the cavity of Figure 10.

The crystal 12 is then placed in front of the plane mirror 11, then the mirror 11 is considered to be convex, and adapts its radius of curvature to impose the position of the stability range. The propagation diagram of the laser beam in the cavity then becomes that represented in FIG. 12.

To study the stability of the cavity thus obtained, reference will be made to the diagram of FIG. 13. This diagram shows the evolution of the stability zone No. 1 (as defined with reference to FIG. 8) for different radii of FIG. curvature. These radii of curvature R are respectively equal to 5, 10, 30 and infinity. Thus, by only playing on the radius of curvature of the cavity bottom mirror 1 1, the stability zone can be adjusted without altering the minimum mode radius W ₀ (equal to 150 μm in the example shown) and the width Δ from zone 1. In the same way, the sensitivity to a misalignment of the cavity can be determined, and for this purpose, reference will be made to the diagram of FIG.

The sensitivity curve can be divided into two parts: the first corresponds to a zone (marked "Zone 1" in the figure) where the sensitivity remains low and the second to a sensitivity that increases very rapidly. The first part of the sensitivity curve, which has a low sensitivity, matches 90% of the stability zone of the laser (as shown in Figure 13). The invention therefore allows the regenerative cavity to be adjusted without much difficulty.

In the context of short thermal focal lengths, the diameter of the fundamental mode that can be envisaged in conventional cavities is generally less than 200 μm, whereas in the example described here, there is a diameter of 300 μm (the radius W ₀ is 150 μm). The maximum M ² of the pump laser will therefore be 50% higher. In this case, it is possible to envisage using a pump laser with an M ² of 20 (instead of 13 in the case of pumping a conventional cavity). FIG. 15 shows the diagram of a regenerative cavity architecture variant in "Z" according to the invention. This cavity is similar to that of FIG. 2, the difference residing mainly in the fact that the plane mirror (9) of the configuration of FIG. 2 has been replaced by a convex mirror 13 and that the crystal (4) has been replaced by a crystal 14, disposed between the mirrors 3 and 13 and advantageously larger than the crystal 4. In addition, the pumping is done through the mirror 13. This configuration allows greater flexibility in the choice of the mode size on the crystal as a function of the radii of curvature of the two concave mirrors 2 and 3.

FIG. 16 illustrates an exemplary embodiment of a "V" regenerative cavity, to highlight the advantages of the invention. The cavity of FIG. 16 has the same configuration as that of FIG. 10, and the same elements are assigned the same reference numerals. The pumping frequency of the crystal 12 is here 5 kHz. Λ 5 kl Iz, the thermal focal length of the crystal is about 20 cm. The concave mirror 2 has a radius of curvature of -100 cm, and a convex M3 cavity bottom mirror with a radius of curvature of 20 cm. The distances are as follows: mirror 1-mirror 2 = 80 cm, mirror 2-mirror 1 1 = 55 cm. Crystal 12 has a length of 1, 5 cm. The mode diameter of this cavity is 450 μm. The power extracted from this cavity is 4 W for a pump power of 24 W. The minimum parameter M ² required to pump this cavity is 40, which corresponds to a Rayleigh area equal to half the length of the crystal. .

In conclusion, the invention makes it possible, without using cryogenic processes, to envisage regenerative cavities of much higher power than at present, while allowing a greater flexibility on the parameter M ² of the pump lasers used. .

Claims

A laser cavity of the femtosecond regenerative type with a high pumping rate, comprising a gain medium and two cavity bottom mirrors, characterized in that its gain medium (12) is disposed in contact with or near one of its cavity bottom mirrors (1 1), which is a convex mirror whose radius of curvature is a function of the desired stability range compatible with the thermal focal length of the crystal.

2. Laser cavity according to claim 1, characterized in that it has a "V" or "Z" architecture.

3. Laser cavity according to claim 1 or 2, characterized in that the gain medium is Ti: 8a.