The invention relates to a laser oscillator system for generating pulsed laser radiation, a nonlinear polarization rotation device, a use of a nonlinear polarization rotation device for mode-locking a laser oscillator, and a method for mode-locking a laser oscillator.

Mode-locked laser oscillators play a crucial role in modem industry and research. They offer the possibility of generating short laser pulses with high peak powers. Mode-locking the laser oscillator relates to a technique, which induces a fixed phase relationship between the longitudinal modes of the resonator cavity of the laser oscillator such that a constructive interference of the longitudinal resonator modes can cause the laser light to be produced as a train of short pulses. The laser is then mode-locked, which is often also referred to as phase-locked.

By mode-locking a laser oscillator system having a few mW of output power can reach peak powers of many MW. However, the realization of mode-locking and its technical implementation is still rather challenging. Conventional mode-locking techniques suffer from a pronounced alignment sensitivity, a low modulation depth of the mode-locking and a very limited capability of adjusting the laser oscillator system to a different average power and/or peak power of the pulsed laser radiation. Thus, conventional mode-locking techniques require a large effort for adapting the mode-locking when modifying the laser oscillator system with regard to the average power and/or peak power at which the laser oscillator shall operate.

In many mode-locked oscillators pulse energies are very low and the laser pulses are amplified only afterward, i.e. after outcoupling of the laser oscillator, because the repetition rates (pulses per second) are very high. Their average power is usually below 1 W. Furthermore, conventionally known fiber lasers are limited because of large nonlinear effects accumulated during propagation of laser radiation in the fiber medium. A method for passive mode-locking well-known in prior art is the usage of a saturable absorber. A saturable absorber introduces intensity-dependent losses.

Also the use of nonlinear polarization rotation for model-locking is known in prior art and was first described and demonstrated by Dahlstrdm in the publication:

Dahlstrdm, L: Passive mode-locking and Q-switching of high power lasers by means of the optical Kerr effect. In: Optics Communications 5 (1972), Nr. 3, S. 157-162.

According to the technique described in this publication, nonlinear polarization rotation is applied inside the resonator cavity, wherein the laser radiation passes the nonlinear medium once in each direction. This technique requires a large polarization rotation per pass for achieving a nonlinear polarization rotation being sufficient for mode-locking.

It is, thus, desirable to provide a laser oscillator system and a technique for modelocking a laser oscillator system overcoming the disadvantages of the above- mentioned techniques.

This problem is solved by a laser oscillator system for generating pulsed laser radiation, a nonlinear polarization rotation device, a use of a nonlinear polarization rotation device for mode-locking a laser oscillator, and a method for mode-locking a laser oscillator having the features of the respective independent claim. Optional embodiments and features are provided in the dependent claims and the description.

In one aspect, a laser oscillator system for generating pulsed laser radiation is provided. The laser oscillator system comprises a resonator cavity and a nonlinear polarization rotation device arranged in a beam path of the resonator cavity. The nonlinear polarization rotation comprises a multipass arrangement having a Kerr medium arranged at least partly within the multipass arrangement, wherein the multipass arrangement is adapted such that the laser radiation carries out multiple roundtrips in the multipass arrangement and multiple passes through the Kerr medium when coupled into the multipass arrangement. The laser oscillator system is adapted to enable mode locking based on an intensity-dependent nonlinear polarization rotation of the laser radiation cumulated in the multiple passes through the Kerr medium.

In another aspect, a nonlinear polarization rotation device for rotating the polarization state of a laser radiation is provided. The nonlinear polarization rotation device comprises a first polarization modification arrangement adapted to change a linear polarization state of the laser radiation to an elliptical polarization state. The nonlinear polarization rotation device further comprises a multipass arrangement having a solid Kerr medium arranged at least partly within the multipass arrangement, wherein the multipass arrangement is adapted such that the laser radiation carries out multiple roundtrips in the multipass arrangement and multiple passes through the solid Kerr medium when coupled into the multipass arrangement. In addition, the nonlinear polarization rotation device comprises a second polarization modification arrangement adapted to change the elliptical polarization state of the laser radiation coupled out of the multipass arrangement at least partly to a linear polarization state.

In yet another aspect, a use of a nonlinear polarization rotation device for modelocking a laser oscillator system is provided, wherein the nonlinear polarization rotation device is arranged within the resonator cavity of the laser oscillator system. The use comprises a first polarization modification arrangement adapted to change a linear polarization state of a laser radiation in the resonator cavity to an elliptical polarization state, a multipass arrangement having a Kerr medium arranged at least partly within the multipass arrangement, wherein the multipass arrangement is adapted such that the laser radiation having the elliptical polarization state carries out multiple roundtrips in the multipass arrangement and multiple passes through the Kerr medium when coupled into the multipass arrangement. The nonlinear polarization rotation device further comprises a second polarization modification arrangement adapted to change the elliptical polarization state of the laser radiation coupled out of the multipass arrangement at least partly to a linear polarization state. According to the provided use the mode-locking is enabled based on an intensity-dependent nonlinear polarization rotation of the laser radiation cumulated in the multiple passes through the Kerr medium.

In yet another aspect, a method for mode-locking a laser oscillator system is provided. The method comprises providing a laser radiation having a linear polarization state within a resonator cavity of the laser oscillator system. The method further comprises changing the polarization state of the laser radiation to an elliptical polarization state, and propagating the laser radiation having the elliptical polarization state for multiple roundtrips through a multipass arrangement and for multiple passes through a Kerr medium arranged at least partly within the multipass arrangement such that the laser radiation experiences an intensitydependent rotation of the polarization state cumulated over multiple passes through the Kerr medium. Moreover, the method comprises changing the polarization state of the laser radiation having the elliptical polarization state at least partly to a linear polarization state after propagating for the multiple passes through the Kerr medium. The method further comprises isolating a part of the laser radiation affected by the intensity-dependent rotation of the polarization state based on its polarization state, and adjusting the laser oscillator system to resonate the isolated part of the laser radiation.

A laser oscillator system is a laser system consisting of or comprising a laser oscillator. The laser oscillator system may further comprise additional components, as for example a pump laser and/or a power supply.

The term “laser radiation” is used in the present disclosure for any kind of optical electromagnetic radiation and in particular for coherent electromagnetic radiation. The same applies, mutatis mutandis, to the term “laser pulse” indicating a pulsed form of laser radiation. Pulsed laser radiation may be a laser radiation provided as a train of pulses or single isolated pulses. The pulsed laser radiation may also be provided as a burst of laser pulses. The pulse duration of the laser pulses may for instance be 1 ps or less and optionally as short as 100 fs or less. The laser oscillator system may apply mode-locking in order to provide the pulsed laser radiation. Values for pulse durations provided throughout the disclosure are specified as full width at half-maximum (FWHM) assuming a Gaussian pulse shape, if not specified otherwise. Laser radiation and pulsed laser radiation may be used as synonyms throughout the present disclosure.

A nonlinear polarization rotation device is an optical device, which allows rotating the polarization of laser radiation, in particular pulsed laser radiation, coupled into the nonlinear polarization rotation device. After rotating the polarization of the laser radiation coupled into the nonlinear polarization rotation device, the laser radiation may be coupled out from the nonlinear polarization rotation device. “Nonlinear” means that the process of nonlinear polarization rotation depends on the intensity of the laser radiation. Furthermore, the nonlinear polarization rotation may depend on the polarization of the laser radiation. Laser radiation having an elliptical polarization may be particularly suitable or required for experiencing a nonlinear polarization rotation. Hence, an increased intensity may result in an increased efficiency of the polarization rotation. The magnitude of the nonlinear polarization rotation experienced by the laser radiation may follow a sinusoidal function with respect of the intensity of the laser radiation, which may lead to the magnitude of the nonlinear polarization rotation having at least one minimum and/or at least one maximum at specific intensities of the laser radiation. For instance, the efficiency of the nonlinear polarization rotation may be directly proportional to the intensity of the laser radiation. Due to the dependence of the nonlinear polarization rotation process from the intensity of the laser radiation, short laser pulses are favored, as they exhibit a more efficient nonlinear polarization rotation due to their higher peak power and peak intensity as compared to longer laser pulses and continuous laser radiation. The nonlinear polarization rotation device being arranged in the beam path of the resonator cavity means that the laser radiation resonantly propagating in the resonator cavity will propagate at least once through the nonlinear polarization rotation device in each roundtrip through the resonator cavity.

A multipass arrangement is an arrangement of optical elements which deflects a laser radiation coupled into the multipass arrangement in such a way that it propagates several times in the multipass arrangement before the laser radiation is coupled out of the multipass arrangement. The redirection of the laser radiation optionally takes place by reflections of the laser radiation, so that the laser radiation changes its propagation direction in the multipass arrangement. In contrast to arrangements which guide the laser radiation by means of optical fibers through total internal reflection, the propagation of the laser radiation in the multipass arrangement may take place in free space without a mode of the laser radiation being restricted by an optical fiber at any point along the optical path of the laser beam or laser pulse. The central axis of the multipass arrangement may be a central axis of the mode volume of the multipass arrangement. The central axis may at least partly coincide with an optical axis of a first mirror and/or a second mirror of the multipass arrangement. The central axis does not necessarily have to be a straight line, but may comprise one or more kinks, for instance when the multipass arrangement comprises one or more intermediate mirrors for reflecting the laser radiation on a propagation between the first mirror and the second mirror. The distance of a first mirror from a second mirror of the multipass arrangement may be a separation distance between the first and the second mirror measured along the central axis, in particular between a respective center point of the reflective surface of said mirrors. The multipass arrangement may be configured as or comprises a Herriott cell, a White cell and/or a Pfund cell. The multipass arrangement may have a central axis, which is folded by one or more further mirrors. The first and/or the second mirror of the multipass arrangement may have a flat or a convex shape, wherein the other mirror, respectively, has a concave shape. In other words, the multipass arrangement may have a convex- concave or concave-flat configuration.

The roundtrips of the laser radiation in the multipass arrangements may each have very similar optical paths through the multipass arrangement. In particular, in every or most of the roundtrips the laser radiation may be deflected by the same optical elements of the multipass arrangement, in particular a first mirror and a second mirror of the multipass arrangement. For instance, the first roundtrip may include an incoupling and/or the last roundtrip may include an outcoupling of the laser radiation into I out of the multipass arrangement. Thus, according to some embodiments the first and/or the last roundtrip may deviate from the other roundtrips with respect to the optical elements deflecting the laser radiation. In some embodiments, a roundtrip does not exactly revert the optical path of the laser radiation propagating in the multipass arrangement but after completing one entire roundtrip, the laser radiation may hit the respective optical element, i.e. the first mirror and/or the second mirror, at a position strongly deviating from the position at the beginning of the roundtrip. In particular, the laser radiation propagates in the multipass arrangement on an individual optical path in each roundtrip, wherein the individual optical paths may not overlap with each other. The first mirror and/or the second mirror may have a hole for incoupling and/or outcoupling the laser radiation into and out of the multipass arrangement, respectively.

The Kerr medium is a medium being optically transparent for the laser radiation, wherein the optical Kerr effect occurs when laser radiation, in particular pulsed laser radiation having a high peak intensity, propagates through the Kerr medium. The Kerr effect is also conventionally known as quadratic electro-optic effect. The Kerr medium exhibits a change in the refractive index of the Kerr medium’s material in response to an applied electric field, i.e. in response to the electric field of the laser radiation propagating through the Kerr medium. The change in refractive index is directly proportional to the square of the applied electric field and, thus, is proportional to the intensity of the laser radiation propagating through the Kerr medium. The Kerr effect provides a nonlinear polarization rotation of the laser radiation propagating through the Kerr medium which depends on the intensity of the laser radiation and may depend on the polarization of the laser radiation. For instance, laser radiation having an elliptic polarization state may be suitable for experiencing a nonlinear polarization rotation. Hence, the Kerr medium provides the used intensity-dependence of the nonlinear polarization rotation of the laser radiation propagating through the Kerr element.

The nonlinear polarization rotation being intensity-dependent means that the laser radiation experiences a different angle of polarization rotation depending on the intensity of the laser radiation. In particular, parts of the laser radiation having a higher intensity experience a larger angle of nonlinear polarization rotation than parts having a lower intensity. The polarization rotation being accumulated in the multiple passes of the laser radiation through the Kerr medium means that the total angle of nonlinear polarization rotation, which the laser radiation exhibits, corresponds to the sum of nonlinear polarization rotation angles exhibited in the individual passes through the Kerr medium. The laser radiation may have a peak power being lower than the critical power for self-focusing in the Kerr medium, which may prevent undesired effects of filamentation and/or damaging the Kerr medium. Alternatively, the laser radiation may have a peak power exceeding the critical power of the Kerr medium providing a high magnitude of nonlinear polarization rotation in the Kerr medium. In the latter case, the interaction length of the Kerr medium may be limited such as to avoid a laser induced damage of the Kerr medium.

A pass of the laser radiation through the Kerr medium represents a propagation of the laser radiation through the Kerr medium. In some embodiments, each roundtrip of the laser radiation in the multipass arrangement may include two passes through the Kerr medium, for instance one pass in a first direction and one pass in a second direction being opposite to the first direction. In other embodiments, each roundtrip may include only one pass through the Kerr medium. For instance, the optical path of the roundtrip may be configured such that the laser radiation passes through the Kerr medium only in one direction but does not pass through the Kerr medium in a second direction. In some embodiments, the resonator cavity may be configured such that the pass of light is not reverted in a roundtrip, such as a ring resonator, in which case only one pass of the laser radiation through the Kerr medium may occur per roundtrip in the resonator cavity. In yet other embodiments, each roundtrip may include more than one pass, in particular two passes, through the Kerr medium. According to yet other embodiments, some roundtrips may not include a pass through the Kerr medium. For instance, the device may be arranged such that in some roundtrips, such as directly after coupling the laser radiation into the multipass arrangement and/or directly before coupling the laser radiation out of the multipass arrangement, no pass through the Kerr medium is included.

The disclosure provides the advantage that it may be adapted to a very wide range of energy levels of the laser radiation. Consequently, the technique for mode-locking according to the disclosure may be applied in laser oscillators of a wide range of average powers and/or peak powers without the need of significant technical modifications. This bears and advantage over the conventional techniques, such as Kerr lens mode locking, at which an adaptation to a different average power and/or peak power level requires significant technical modifications of the oscillator layout and the replacement of optical components. In addition, the disclosure provides the advantage that the suggested mode-locking based on nonlinear polarization rotation allows achieving a high modulation depth which may facilitate achieving laser pulses having a very short pulse length, such as a pulse length of 100 fs or less (FWHM assuming a Gaussian profile of the temporal envelope) potentially going beyond the gain emission bandwidth limit. Further, the disclosure provides the advantage that it is not restricted with regard to the wavelength range of the laser radiation, for which it may be used.

Due to the ability to offer nonlinear polarization rotation at moderate peak powers within the resonator cavity, the disclosures allows using polarization rotation mode locking in free-space solid-state oscillators, i.e. , laser oscillators having a solid bulk gain medium.

Moreover, the disclosure provides the advantage that mode locking conditions of for a laser oscillator may be adapted by adjusting a propagation of the laser radiation through the Kerr medium. This may include adjusting the number of passes of the laser radiation through the Kerr medium together with the multipass cell configuration.

Moreover, the disclosure provides the advantage that the nonlinear polarization rotation device and an oscillator comprising such exhibits a moderate alignmentsensitivity. This bears the advantage that the stability is increased as compared to conventional mode-locking techniques, as slight deviations from perfect alignment, which may occur during laser operation, may not have a dramatic effect on the stability and efficiency of the laser oscillator. In addition, it bears the advantage that the modulation depth may be varied by simply adjusting one or more individual optical components, such as rotating the Kerr element in order to adjust the effective optical thickness and of the Kerr medium within the multipass arrangement and, hence, the propagation length of the laser radiation through the Kerr medium in each pass.

Furthermore, the disclosure provides the advantage that the nonlinear polarization device and the mode-locking of a laser oscillator may be realized without the need of cost-intensive optical components. The nonlinear polarization rotation device may be set up based on conventional optical elements, such as metal coated or dielectric mirrors and optionally dispersive mirrors. Also, for the Kerr medium a cheap and abundantly available material may be chosen having a moderate Kerr nonlinearity, as the total nonlinear polarization rotation angle may be obtained by accumulating over multiple passes through the Kerr medium.

The nonlinear polarization rotation device may further comprise a first polarization modification arrangement adapted to change a polarization state of the laser radiation. Such as a linear polarization state, to an elliptical polarization state before coupling the laser radiation into the multipass arrangement. The nonlinear polarization rotation device may further comprise a second polarization modification arrangement adapted to change the elliptical polarization state of the laser radiation coupled out of the multipass arrangement at least partly to a linear polarization state. In other words, the nonlinear polarization rotation device may be adapted to modify the polarization state of the laser radiation from linear to elliptical before or at the incoupling into the multipass arrangement and to at least partly modify the polarization state back to linear (or at least less elliptic) after or at the outcoupling from the multipass arrangement. This allows providing specific predetermined conditions of the polarization state of the laser radiation propagating through the Kerr medium and, hence, to apply a specific and predetermined polarization rotation to the laser radiation depending on the intensity of the laser radiation. Moreover, the polarization modification arrangements may allow adjusting a modulation depth provided by the nonlinear polarization rotation, which may facilitate adjusting the mode-locking condition.

The first polarization modification arrangement may comprise a first quarter-wave- plate and optionally may comprise a first linear polarizer. Likewise, the second polarization modification arrangement may comprise a second quarter-wave-plate and may optionally comprise a second linear polarizer. The first polarization modification arrangement may be arranged before the incoupling of the laser radiation into the multipass arrangement, wherein the quarter-wave-plate is arranged after the polarizer. This may ensure to first set a predetermined linear polarization state with the linear polarizer and afterwards to modify the polarization state in a specific manner to elliptic. The laser radiation having the elliptic polarization state is then propagated through the multipass arrangement and the Kerr medium. At or after outcoupling from the multipass arrangement, the laser radiation propagates first through the quarter-wave-plate and then through the linear polarized of the second polarization modification arrangement. This allows to modify the polarization state of the laser radiation back to linear and then to select a specific polarization angle of linear polarization transmitted by the linear polarizer. By setting the angle between the two linear polarizers to a specific predetermined angle allows enabling a transmission of the nonlinear polarization rotation device only for such laser radiation experiencing a suitable polarization between the first and the second polarization modification arrangement. For instance, the first and the second linear polarizers may be arranged such that the angle of their polarization directions is about 90°. This corresponds to the nonlinear polarization rotation device being transparent only for laser radiation having an intensity resulting in the predetermined polarization rotation. Consequently, adjusting the nonlinear polarization rotation device and in particular an angle between the two linear polarizers and the two quarter-wave-plates accordingly allows mode-locking the laser oscillator, i.e. allowing only this part of the laser radiation the resonant propagation in the resonator cavity, which exhibits the highest intensity.

The nonlinear polarization rotation device and/or the laser oscillator system may comprise further optical components and/or be adjusted for isolating the part of the laser radiation having the highest intensity, i.e. the part experiencing the most efficient nonlinear polarization rotation. For isolating the highest intensity part, the first and the second quarter-wave-plate may be arranged such that their fast axes are arranged perpendicular to each other. This configuration may allow that the highest intensity part of the laser radiation has a linear polarization after the second wave plate, which is perpendicular to the initial linear polarization state of the laser radiation impinging on the first wave plate. Thus, by having the second polarizer arranged at a polarization angle perpendicular to the polarization angle of the first polarized, the highest intensity part of the laser radiation may be isolated in an efficient manner.

The efficiency of nonlinear polarization rotation may depend on the input polarization and in particular on an angle [3 between the linear input polarization of the laser radiation and the fast axis of the first quarter wave plate 12b. High efficiencies of the nonlinear polarization rotation may be achieved in particular with a polarization state of the input laser radiation having only a slight ellipticity, i.e. a polarization state which deviates only in a very limited manner from a linear polarization state. For instance, for achieving a high efficiency of the nonlinear polarization rotation, an angle [3 between the linear polarization of the input laser radiation and the fast axis of the first quarter wave plate 12b may be chosen to be in the range from 1 ° to 10°, and optionally in the range from 5° to 7°. The nonlinear polarization rotation may at least theoretically reach efficiencies of 70% and more.

The Kerr medium may comprise a solid Kerr medium. The solid Kerr medium may comprise or consists for instance of one or more of the following materials: fused silica, sapphire, crystalline quartz, Silicon, Germanium, CaF2, and MgF2. The Kerr medium may be chosen to offer a sufficient optical transparency in the wavelength range of the laser radiation to be generated and/or amplified in the laser oscillator. Due to the multipass arrangement providing multiple passes through the Kerr medium, it is not necessary to provide a Kerr medium having a particularly high nonlinear susceptibility. Instead, materials having a moderate nonlinear susceptibility, such as the above-mentioned materials, may be chosen, which may be significantly cheaper than other materials having a high nonlinear susceptibility.

Alternatively or additionally the Kerr medium may comprise a gaseous Kerr medium, which may comprise or consist of at least one of the following elements: Argon, Xenon, Krypton, Neon, Helium, Nitrogen, and Air. For instance, the multipass arrangement may be configured as, comprise or be comprised in a pressure chamber containing the gaseous Kerr medium. Optionally, the atmospheric air may be used as a Kerr medium. The gaseous Kerr medium may have a lower nonlinear susceptibility as some solid materials which may be used as a Kerr medium. However, using a gaseous Kerr medium may facilitate providing a longer inter action length of the laser radiation with the Kerr medium as may be realizable with a solid Kerr medium. For instance, the entire multipass arrangement may be filled with a gaseous Kerr medium. Consequently, each pass of the laser radiation through the Kerr medium may extend over the entire propagation length of the laser radiation of a half or full roundtrip. The multipass arrangement may be arranged such that the laser radiation coupled into the multipass arrangement carries out at least five roundtrips in the multipass arrangement. This allows providing a significant propagation length while keeping the spatial dimensions of the nonlinear polarization rotation device small. Moreover, at least five roundtrips enable multiple passes of the laser radiation through the Kerr medium arranged in the multipass arrangement. In particular, the number of passes of the laser radiation through the Kerr medium may be equal to the number of roundtrips in the multipass arrangement or twice the number of roundtrips. For instance, the multipass arrangement may be configured such that the laser radiation carries out at least five roundtrips in the multipass arrangement and at least ten passes through the Kerr medium during the five roundtrips.

The laser oscillator system may further comprise an active medium arranged within the resonator cavity, wherein the active medium is a solid active medium. The solid active medium may be a conventionally used active medium and may be arranged in the resonator cavity according to any conventionally known manner. For instance, the active medium may be arranged as a solid crystal element in a central section of the resonator cavity. Unlike in a fiber laser, the solid gain medium may be arranged in a resonator cavity not being formed of an optical fiber. Alternatively or additionally, the laser oscillator system may be configured as a conventional disk laser or thin-disk laser having an active medium formed as a disk. The disk may be arranged at one of the mirrors of the resonator cavity. Hence, the laser oscillator system is configured as a thin-disk laser oscillator system or a solid-state laser oscillator system. In case of a thin-disk laser, the active medium may have a thickness of 1 mm or less or even of 200 pm or less. The active medium may be made of or comprise at least one of the following laser media: Titanium sapphire, Yb:YAG, Yb:KGW, Yb:CALGO, Yb:glass, Cr:ZnS/ZnSe. Laser oscillators having a solid active medium may offer the advantage that they support the generation of ultrashort laser pulses having a pulse duration of 100 fs or less or even 10 fs or less in combination with mode-locking based on nonlinear polarization rotation. Moreover, the combination of solid-state laser oscillator systems with nonlinear polarization rotation may allow providing a robust and stable laser oscillator system having a low complexity and offering a high degree of scalability with regard to the average power and peak power range. The laser oscillator system may be configured as a femtosecond laser oscillator system and adapted to emit pulsed laser radiation having a pulse duration of 1 ps or less and optionally 100 fs or less. The laser oscillator system may have and/or support an intra-cavity peak power of at least 1 MW, optionally of at least 10 MW and optionally of at least 100 MW or more.

The nonlinear polarization rotation device and/or the resonator may comprise one or more dispersive mirrors providing a negative optical dispersion to the laser radiation when reflected off said mirror. In particular, the dispersive mirrors may be arranged in the multipass arrangement. Accordingly, the one or more dispersive mirrors form part of the multipass arrangement. This may allow at least partly compensating and/or pre-compensating a positive optical dispersion affecting the laser radiation when propagating through the Kerr medium and/or through other optical components in the resonator cavity. The dispersive mirrors may provide a suitable dispersion control allowing the laser oscillator providing short laser pulses, for instance laser pulses having a pulse duration of 100 fs or less or even 10 fs or less, optionally without the need of further temporal compression after outcoupling of the laser oscillator. Alternatively, the resonator may comprise one or more dispersive mirrors providing a positive optical dispersion.

The nonlinear polarization rotation device may exhibit a total optical dispersion being positive, negative or zero. Zero dispersion may be beneficial for implementing the nonlinear polarization rotation device into a laser oscillator while keeping the effect of the nonlinear polarization rotation device on the dispersion of the laser oscillator low. A total dispersion of the nonlinear polarization rotation device being positive may be favorable for example when the laser oscillator comprises a dispersion control offering a surplus of negative dispersion or if the emission of chirped laser pulses is desired. A negative dispersion of the nonlinear polarization rotation device may be beneficial for (pre-)compensating at least a part of positive dispersion of other optical elements in the laser resonator or outside the laser resonator.

The laser oscillator system may be configured to have a tunable beam path of the laser radiation through the multipass arrangement and to allow adjusting a mode locking condition by tuning the beam path of the laser radiation through the multipass arrangement. This allows adjusting the mode locking condition for the laser oscillator system in a flexible and efficient manner. Moreover, this allows adjusting a pulse duration of pulsed laser radiation emitted by the laser oscillator system in a facilitated and efficient manner. Hence, this provides the advantage that a high flexibility of the laser oscillator system can be provided at a low technical complexity. The laser oscillator system may be configured to have a tunable beam path of the laser radiation through the multipass arrangement to tune a number of the multiple passes through the Kerr medium. This may allow adjusting the amount of polarization rotation and, hence, the mode locking condition in an efficient manner.

The method for mode locking a laser oscillator may further comprise adjusting a mode locking condition by varying a beam path of the laser radiation through the multipass arrangement. The beam path of the laser radiation may be varied such that a number of the multiple passes of the laser radiation through the Kerr medium is varied. This allows adjusting the amount of polarization rotation exhibited by the laser radiation propagating through the nonlinear polarization rotation device. The beam path of the laser radiation may be varied such that a number of the multiple roundtrips of the laser radiation through the multipass arrangement is varied. Accordingly, the method for mode locking a laser oscillator may further comprise adjusting a mode locking condition by varying the Kerr medium. Hence, this may allow adjusting the mode locking condition for the laser oscillator in an efficient and facilitated manner.

Varying the Kerr medium may include varying a propagation length of the laser radiation through the Kerr medium in at least one of the multiple passes of the laser radiation through the Kerr medium, wherein varying the Kerr medium may include varying a type and/or a pressure of a gaseous Kerr medium of the Kerr medium. Moreover, the method may further comprise tuning a pulse duration of the laser radiation emitted by the laser oscillator by adjusting the mode locking condition. This provides a large degree of flexibility for adjusting the mode locking condition.

It is understood by a person skilled in the art that the above-described features and the features in the following description and figures are not only disclosed in the explicitly disclosed embodiments and combinations, but that also other technically feasible combinations as well as the isolated features are comprised by the disclosure. In the following, several optional embodiments and specific examples are described with reference to the figures for illustrating the disclosure without limiting the disclosure to the described embodiments.

Figure 1 schematically depicts a nonlinear polarization rotation device according to an optional embodiment.

Figure 2 schematically shows a more detailed view of multipass arrangement of the nonlinear polarization rotation device of Figure 1 .

Figure 3 illustrates in an exemplary manner the quarter-wave-plate of the respective polarization modification arrangement.

Figure 4 illustrates a laser oscillator system using a nonlinear polarization rotation device arranged in a resonator cavity for passively mode-locking the laser oscillator system.

Figure 5 shows in a graph the dependence of the relative power of the part of the laser radiation having the highest intensity, in dependence of the pulse energy. Figure 6 schematically depicts a method according to an optional embodiment for mode locking a laser oscillator.

In the drawings the same reference signs are used for corresponding or similar features in different drawings.

Figure 1 schematically depicts a nonlinear polarization rotation device 10 to be implemented in a laser oscillator system for mode-locking the laser oscillator system. The nonlinear polarization rotation device 10 comprises a first polarization modification arrangement 12 and a second polarization rotation arrangement 14, which may be arranged such as to have a common optical axis. Moreover, the nonlinear polarization rotation device 10 comprises a multipass arrangement 16 having a first mirror 16a and a second mirror 16b. A Kerr medium 18 is arranged inside the multipass arrangement 16. The first mirror 16a and the second mirror 16b are adapted as concavely curved mirrors and form the multipass arrangement 16 in a Herriott cell configuration. However, according to other embodiments the first mirror 16a and the second mirror 16b may form a convex-concave or a concave-flat configuration. The multipass arrangement 16 ensures that laser radiation 1000, which may be a pulsed laser radiation, coupled into the multipass arrangement 16 carries out multiple roundtrips through the multipass arrangement, wherein each roundtrip includes a reflection of the laser radiation 1000 off the first mirror 16a and off the second mirror 16b, as schematically indicated as beam path by the dashed lines 1002. In other words, in each roundtrip the laser radiation 1000 travels back and forth through the multipass arrangement 16. The multipass arrangement 16 is configured to ensure at least five roundtrips of the laser radiation 1000 coupled into the multipass arrangement 16.

A Kerr medium 18 is arranged within the multipass arrangement 16, wherein according to the presented embodiment, the Kerr element 18 is provided as a solid Kerr element 18. The Kerr element 18 is arranged in a central area of the multipass arrangement 16 such that the laser radiation 1000 passes twice through the Kerr element 18 in each roundtrip in the multipass arrangement. Thus, for five roundtrips carried out in the multipass arrangement, the laser radiation 1000 passes ten times through the Kerr medium 18.

Each pass of the laser radiation 1000 through the Kerr medium 18 results in an intensity dependent rotation of the polarization state of the laser radiation 1000. Hence, during its propagation through the multipass arrangement 16 the laser radiation 1000 experiences a rotation of its polarization state, which is accumulated in the multiple passes through the Kerr medium 18. The total rotation angle of the polarization state of the laser radiation 1000 equals the sum of rotation angles experienced in each pass through the Kerr medium 18.

The Kerr medium 18 is a medium having a nonlinear susceptibility offering a rotation of the polarization angle of a laser radiation propagating through the Kerr medium 18 due to the optical Kerr effect. As the total polarization rotation is accumulated over multiple passes through the Kerr medium, there is no need for using a Kerr medium 18 having a particularly high nonlinear susceptibility. Instead, robust and cheap materials may be used as Kerr medium 18 offering a moderate nonlinear susceptibility. For instance, fused silica and/or crystalline quartz may be used as a Kerr medium 18.

The first polarization modification arrangement 12 ensures that the laser radiation 1000 exhibits a specific predetermined polarization state when coupled into the multipass arrangement 16. For this purpose, the first polarization modification arrangement 12 comprises a linear polarizer 12a set to a first polarization angle, which ensures that the laser radiation is linearly polarized with the first polarization angle. The first polarization modification arrangement 12 further comprises a quarter-wave-plate 12b which modifies the polarization state of the laser radiation 1000 to an elliptical polarization, which is then coupled into the multipass arrangement 16. The nonlinear polarization rotation in the multiple passes through the Kerr medium 18 will then affect the elliptically polarized laser radiation 1000 with an intensity-dependent polarization rotation. After completing the multiple passes through the multipass arrangement 16, the laser radiation is coupled out and propagates through the second polarization modification arrangement 14. The second polarization modification arrangement 14 firstly comprises a quarter-wave- plate 14b and secondly a linear polarizer 14a. The quarter-wave-plate 14b may be arranged such that its fast axis is arranged perpendicular to the fast axis of the first quarter-wave-plate 14a. Due to the nonlinear polarization rotation occurring in the Kerr element 18 for laser radiation 1000 having a sufficiently high peak intensity, the polarization angle of the laser radiation impinging on the linear polarizer 14a of the second polarization modification arrangement 12 will be different from the first polarization angle defined by the first polarizer 12a of the first polarization modification arrangement 12. The higher the (peak) intensity of the laser radiation 1000 in the Kerr medium 18, the more pronounced the nonlinear polarization rotation will be. Hence, by adjusting the difference of the first polarization angle of the first linear polarizer 12a and the second polarization angle of the second linear polarizer 14a, the nonlinear polarization device may be adjusted to be transparent only or mostly to that part of the laser radiation 1000 having a particular intensity. For transmitting the laser radiation having the highest peak intensity, the maximum angular difference between the first and the second polarization angle resulting in the partial transmission of laser radiation 1000 may be chosen. This ensures, that the part of the laser radiation 1000 having the highest peak intensity exhibits the highest transmission, while less intense parts of the laser radiation 1000 are blocked or transmitted with a lower efficiency. This intensity-dependent nonlinear polarization rotation may be exploited in a resonator cavity for mode-locking the laser oscillator system. Hence, the nonlinear polarization rotation device 10 may be configured, such that only the part of the laser radiation 1000 having the highest intensity obtains a polarization rotation angel ensuring the highest transmission through the nonlinear polarization rotation device 10.

Figure 2 schematically shows a more detailed view of the multipass arrangement 16 of the nonlinear polarization rotation device 10 of Figure 1. The laser radiation 1000 may be a pulsed laser radiation. The multipass arrangement 16 has the first mirror 16a and the second mirror 16b arranged on a central axis 1004 of the multipass arrangement 16 forming a Herriott cell. The first mirror 16a and the second mirror 16b are formed as spherical concave mirrors having a radius of curvature (ROC) of for instance 50 mm each. Both mirrors are arranged concentrically and perpendicular to the central axis 1004. The multipass arrangement 16 is adapted such that the laser radiation 1000 carries out multiple roundtrips between the first mirror 16a and the second mirror 16b when coupled into the multipass arrangement 16, as indicated by the light paths 1002. A distance 1006 of the first mirror 16a from the second mirror 16b along the central axis 1000 of the multipass arrangement may be for instance 100 mm or less.

The Kerr medium 18 is arranged at least partly within the multipass arrangement 16 such that the laser radiation 1000 coupled into the multipass arrangement 16 passes through the Kerr medium 18 in at least several of the multiple roundtrips.

In order to obtain short laser pulses after coupling the laser radiation 1000 out of the multipass arrangement 16 and/or for pre-compensating at least some of the optical dispersion originating in other optical components of a resonator cavity, the optical dispersion of the multipass arrangement 16 and the nonlinear polarization rotation device 10 is to be considered. For this purpose, the first mirror 16a and/or the second mirror 16b may be provided as dispersive mirrors applying a negative optical dispersion to the laser radiation 1000 when reflected off the respective mirror 16a, 16b. This allows compensating at least partly a positive material dispersion originating in the Kerr medium 18 and/or of other optical components outside the multipass arrangement 16, such as other optical elements in the laser oscillator.

Figure 3 illustrates in an exemplary manner the quarter-wave-plate 14a and 14b, respectively, exhibiting birefringence and, thus, having a fast axis 1008 and a slow axis 1010. The fast axis 1008 exhibits a lower refractive index than the fast axis 1010. Thus, for laser radiation 1000 having a linear polarization direction 1012 being tilted by an angle of I3> with respect to the fast axis 1008, a part of the laser radiation 1000 will experience the higher refractive index of the slow axis 1010 and, thus, be retarded with respect to the other part experiencing the lower refractive index of the fast axis 1008. Due to the thickness of the quarter-wave- plate corresponding to the quarter of a central wavelength of the laser radiation 1000, the polarization state of the laser radiation 1000 will be modified to an elliptic and optionally to a circular polarization state.

Figure 4 illustrates a laser oscillator system 20 using a nonlinear polarization rotation device 10 arranged in its resonator cavity 22 for passively mode-locking the laser oscillator system 20. The resonator cavity 22 is formed by a first cavity mirror 24 and a second cavity mirror 26, wherein the second cavity mirror 26 is adapted as an outcoupler and an aperture 36 is located in front of the first cavity mirror. The laser oscillator system 20 is configured as a thin-disk laser system having an active medium 28 in the shape of a thin disk attached to a further plane mirror 29 forming part of the resonator cavity 22. However, the passive modelocking using the nonlinear rotation polarization device 10 may be applied in the same or a similar manner to other types of laser oscillator systems having a different solid state active medium.

The optional mirrors 30 and 32 are curved mirrors focusing the laser radiation 1000 in the laser cavity 22 onto an optional further Kerr lens element 34. This may allow combining the nonlinear polarization rotation mode-locking using the nonlinear polarization rotation device 10 with an additional conventional Kerr lens mode locking. However, this is optional. Other embodiments may be mode-locked solely by using nonlinear polarization rotation. The nonlinear polarization rotation device 10 may be configured according to the optional embodiment shown in Figure 1 .

In the following, an optional embodiment of a laser oscillator system 20 having a configuration as shown in Figure 4 will be explained in detail together with measurements for characterizing the laser oscillator system 20 applying passive mode-locking by nonlinear polarization rotation. The laser oscillator system 20 has a nonlinear polarization rotation device 10, which comprises two quarter-wave-plates 12b and 14b and a multipass arrangement 16 with an included Kerr element 18 in between them. A Wollaston Polarizer may be installed to separate the s- and p-polarized components of the laser radiation 1000 after the nonlinear polarization rotation process for measuring the energy contained in both parts of the laser radiation 1000. This may not be required for a regular mode-locking and a regular operation of the laser oscillator system 20 but may merely serve for characterizing the nonlinear polarization rotation. The pulse energies of the laser radiation 1000 applied to the nonlinear polarization rotation device were varied between 0,1 and 0,9 pJ, resulting in a total accumulated nonlinear phase of approximately 5 - 36 rad. The accumulated B- integral and nonlinear phase may result in a substantial spectral broadening of the laser radiation. However, although also the nonlinear polarization rotation is a nonlinear optical effect, it may be regarded independently of the B-integral and a possible spectral broadening. As described in the publication

Khodakovskiy, N. G. et al.: Generation offew-cycle laser pulses with high temporal contrast via nonlinear elliptical polarization rotation in a hollow _bre compressor. In: Laser Physics Letters 16 (2019), Nr. 9, S. 095001. the efficiency of nonlinear polarization rotation may mainly depend on the input polarization and in particular on the angle [3 between the linear input polarization of the laser radiation and the fast axis of the first quarter wave plate 12b. High efficiencies of the nonlinear polarization rotation may be achieved in particular with a slightly elliptical polarization state, which deviates only in a very limited manner from a linear polarization state. For instance, for achieving a high efficiency of the nonlinear polarization rotation, an angle [3 between the linear polarization of the input laser radiation and the fast axis of the first quarter wave plate 12b in the range from 1° to 10° may be chosen, and optionally in the range from 5° to 7°. The nonlinear polarization rotation may at least theoretically reach efficiencies of 70% and more. Several different operation modes of the laser oscillator system 20 have been tested, which are structured in the same way and only differ in the input polarization angle, which is defined by the angle (3, which describes the angle between the linear input polarization of the laser radiation 1000, and the fast axis 1008 of the first quarter-wave plate 12b (see Figure 3). The linear polarized laser radiation 1000 (p-polarized) at the input of the nonlinear polarization device 10 is turned into an elliptic polarization state by the first quarter-wave plate 12b. The laser radiation 1000 passes through the multipass arrangement 16 where the intensity-dependent polarization rotation takes place in the Kerr medium 18. With higher intensities, the angle of polarization rotation increases, while lower intensities hardly rotate the polarization at all. Thus, the low intensity components of the laser radiation 1000 being unaffected or affected only in a weak manner by the nonlinear polarization rotation, are rotated back to the initial polarization direction by the second quarter-wave plate 14b, as the fast axis of the second quarter-wave-plate 14b is rotated by 90° with respect to the fast axis of the first quarter-wave plate 12b. However, the high-intensity part of the laser radiation 1000 experiences a significant polarization rotation accumulated over the multiple passes through the Kerr medium 18 and, hence, its polarization will not be entirely rotated back by the second quarter-wave-plate 14b. In other words, the orientation of the elliptical polarization of the part of the laser radiation 1000 having a higher intensities, will turn due to nonlinear polarization rotation in the multipass arrangement 16. Thus, their polarization state does not only consist of p-polarized light, like the input, but there will be an s-component as well. The s- and p- contents of the laser radiation 1000 are filtered by the Wollaston polarizer. As a result, the s - component after the Wollaston polarizer consists of the high intensity parts of the pulsed laser radiation 1000, while the remaining part of the laser radiation 1000 having a lower intensity exhibits a p-polarization. Consequently, the nonlinear polarization rotation may be used for isolating the part of the laser radiation having the highest intensity and, thus, may be applied in the resonator cavity 22 for mode-locking the laser oscillator system 20. Figure 5 shows in a graph the dependence of the relative power (vertical axis, in arbitrary units) of the isolated s-polarized part of the laser radiation 1000, i.e. the part that experienced the largest nonlinear polarization rotation and, thus, has the highest intensity, in dependence of the pulse energy in Nanojoules (horizontal axis). As can be seen, the power of the s-polarized light, relative to the total power, changes as the pulse energy is increased, which illustrates the efficiency of the nonlinear polarization rotation process of the laser radiation 10000 in the nonlinear polarization rotation device 10.

The behavior of power modulation changes if angle (3, which indicates an angle between the polarization direction of the laser radiation impinging on the first quarter-wave-plate 14 and the fast axis 1008 of the first quarter-wave-plate 12b, is changed and, thus, the elliptical polarization state after the first quarter-wave-plate 14b is changed. The comparison of several efficiency curves with different input polarizations, i.e. for different angles (3, shows a clear difference in modulation depth. The efficiency of laser radiation 1000 having an input polarization angle [3 of 5°, which results in a thin polarization ellipse with [3 = 5° (graph 5000) after the first quarter-wave-plate 14b, saturates at very high B-integrals, while the modulation depth, i.e. the ratio between efficiently polarization rotated part of the laser radiation and the total laser radiation 1000, exceeds 70%. For a more circular polarization achieved with an angle [3 of 20° ([3 = 20°, graph 5002), a modulation depth of only 20% is achieved. Furthermore, the maximum is reached at smaller pulse energies. As expected the graph for (3 = 15° (graph 5004) is in between the graphs 5000 and 5002.

This demonstrates that nonlinear polarization rotation using a Kerr medium 18 inside a multipass arrangement 16 offers a modulation depth which is well suited for mode-locking a laser oscillator system 20.

Figure 6 schematically depicts a method 600 for mode-locking a laser oscillator 20 according to an optional embodiment. The method 600 comprises in a step 602 providing a laser radiation 1000 having a linear polarization state within a resonator cavity 22 of the laser oscillator 20. In a step 604 the method 600 comprises changing the polarization state of the laser radiation 1000 to an elliptical polarization state. In a step 606 the method 600 comprises propagating the laser radiation 1000 having the elliptical polarization state for multiple roundtrips through a multipass arrangement 16 and for multiple passes through a Kerr medium 18 arranged at least partly within the multipass arrangement 16 such that the laser radiation 1000 experiences an intensity-dependent rotation of the polarization state cumulated over multiple passes through the Kerr medium 18. In a step 608 the method 600 comprises changing the polarization state of the laser radiation 1000 having the elliptical polarization state at least partly to a linear polarization state after propagating for the multiple passes through the Kerr medium 18. In a step 610 the method 600 comprises isolating a part of the laser radiation 1000 affected by the intensity-dependent rotation of the polarization state based on its polarization state. In a step 612 the method 600 comprises adjusting the laser oscillator system 20 to resonate the isolated part of the laser radiation 1000.

The method 600 may comprise a further step 614 of adjusting a mode locking condition by varying a beam path of the laser radiation 1000 through the multipass arrangement, wherein the beam path of the laser radiation 1000 may be varied such that a number of the multiple passes of the laser radiation 1000 through the Kerr medium 18 is varied. The beam path of the laser radiation 1000 may be varied such that a number of the multiple roundtrips of the laser radiation 1000 through the multipass arrangement 16 is varied.

The method 600 may further comprise in a step 616 adjusting a mode locking condition by varying the Kerr medium 18, wherein varying the Kerr medium 18 may include varying a propagation length of the laser radiation 1000 through the Kerr medium 18 in at least one of the multiple passes of the laser radiation through the Kerr medium 18. Varying the Kerr medium 18 may include varying a type and/or a pressure of a gaseous Kerr medium of the Kerr medium 18. The method may further comprise in a step 618 tuning a pulse duration of the laser radiation emitted by the laser oscillator (20) by adjusting the mode locking condition.

List of reference signs

10 nonlinear polarization rotation device

12 first polarization modification arrangement

12a first linear polarizer

12b first quarter-wave-plate

14 second polarization modification arrangement

14a second linear polarizer

14b second quarter-wave-plate

16 multipass arrangement

16a first mirror

16b second mirror

18 Kerr medium

20 laser oscillator system

22 resonator cavity

24 first end mirror

26 second end mirror

28 active medium

29 plane mirror

30 curved mirror

32 curved mirror

34 Kerr lens element

36 Aperture

600 method for mode locking a laser oscillator

602 - 618 method steps

1000 laser radiation

1002 paths in the multipass arrangement

1004 axis of multipass arrangement

1006 distance between first and second mirror of multipass arrangement

1008 fast axis of quarter-wave-plate

1010 slow axis of quarter-wave-plate

1012 angle of linear polarization

5000-5004 graphs indicating the modulation depth