Optical resonator arrangement and a method for adjusting a round-trip time in a resonator

Abstract

In a resonator arrangement (1) including a resonator (2), an interferometer (9) is arranged inside the resonator (2) and includes at least a first and a second interferometer leg (9a, 9b). The two interferometer legs (9a, 9b) have optical path lengths (L1, L2) that differ from each other. According to the invention a splitting ratio is variably adjustable, with which the interferometer (9) splits radiation (8) circulating in the resonator (2) into the first and second interferometer legs (9a, 9b).

Claims

1. An optical resonator arrangement comprising a resonator and an interferometer having at least a first and a second interferometer leg arranged within the resonator, the first interferometer leg has a first optical path length and the second interferometer leg has a second optical path length other than the first optical path length, and a splitting ratio, with which the interferometer splits radiation circulating in the resonator into the first and second interferometer legs, is variably adjustable, wherein the resonator arrangement is configured to change a repetition rate of the resonator and a carrier envelope offset frequency by changing the splitting ratio of the radiation circulating in the resonator into the first and second interferometer legs, such that in a frequency domain, a comb of frequencies of the radiation circulating in the resonator contracts or expands by a uniform factor about a fixed point.

2. The resonator arrangement according to claim 1, wherein the resonator arrangement comprises an actuator for adjusting the splitting ratio, the actuator having a control bandwidth of at least 10 kHz.

3. The resonator arrangement according to claim 2, wherein the resonator arrangement comprises a measurement apparatus configured to measure a shift of the resonant lines obtained by the actuator.

4. The resonator arrangement according to claim 1, wherein the interferometer comprises at least one optical element having at least one of a polarization dependent propagation time shift and a phase shift.

5. The resonator arrangement according to claim 4, wherein the at least one optical element causes a phase shift of an integer or half-integral multiple of 2 for a target wavelength (.sub.z).

6. The resonator arrangement according to claim 1, wherein the interferometer includes one or more of the following optical elements: a polarization filter, a polarization adjuster, a plate, a n plate with n2, a /2 plate, a /4 plate, an electro-optical modulator and a variably adjustable liquid crystal.

7. The resonator arrangement according to claim 4, wherein at least two optical elements with polarization dependent phase shift are present in the resonator, and the splitting ratio of the radiation circulating in the resonator for the first and second interferometer legs is adjustable by adjusting an orientation of the two optical elements relative to each other and/or by differently influencing the polarization of the radiation passing through the two optical elements.

8. The resonator arrangement according to claim 1, wherein in the resonator is arranged a laser medium or an amplifier medium and/or a mode coupling element for the radiation circulating in the resonator, and the laser medium and the amplifier medium, respectively, are configured to be pumped.

9. The resonator arrangement according to claim 1, wherein the transmission of the resonator for the radiation circulating therein remains constant or substantially constant upon a variation of the splitting ratio of the radiation for the first and second interferometer legs.

10. The resonator arrangement according to claim 1, wherein the mode spacing of the resonator is an integer multiple of the mode spacing of radiation incident in the resonator, or the mode spacings of the resonator and incident radiation are related to each other by a rational ratio.

11. The resonator arrangement according to claim 1, wherein the resonator arrangement is configured to filter and/or amplify optical radiation, a nonlinear optical element is arranged within the resonator of the resonator arrangement and the nonlinear optical element is selected to generate the second or higher harmonic of the radiation circulating in the resonator, to generate radiation by means of sum frequency generation or difference frequency generation or to generate or amplify radiation by means of optical-parametric processes.

12. A fiber laser, a frequency comb generator, an active or passive mode coupled laser having a mode coupling element, or an injection stabilized laser, each comprising an optical resonator arrangement according to claim 1.

13. A method for adjusting a repetition rate (f.sub.rep) of a resonator or a round-trip time (i) of radiation or pulses circulating in a resonator, the method comprising splitting, by an interferometer positioned within the resonator, pulses circulating in the resonator into a first pulse portion that passes through a first interferometer leg having a first optical path length and into a second pulse portion that passes through a second interferometer leg having a second optical path length, causing the first and second pulse portions to interfere with each other after passing through the interferometer, the method further comprising varying the splitting ratio, with which the interferometer splits the pulses circulating in the resonator into the first and second pulse portions, so that the resonator changes a repetition rate and a carrier envelope offset frequency, such that in a frequency domain, a comb of frequencies of the radiation circulating in the resonator contracts or expands by a uniform factor about a fixed point.

14. The method according to claim 13, wherein upon varying the splitting ratio, the group round-trip time () of the pulses circulating in the resonator is varied without changing a phase round-trip time of a carrier wave in the resonator.

15. The method according to claim 13, wherein round-trip losses of pulses circulating in the resonator are not or substantially not changed when varying the splitting ratio, with which the interferometer splits the pulses circulating in the resonator into the first and second pulse portions.

16. The method according to claim 13, wherein the interferometer comprises at least one optical element with polarization dependent phase shifting, and wherein the splitting ratio, with which the interferometer splits the pulses circulating in the resonator into the first and second pulse portions, is varied by rotating the optical element around an optical axis of the resonator or by changing the polarization at this optical element.

17. The method according to claim 16, wherein the optical element causes a polarization dependent phase shift of m.Math.0.5.Math. for a given target wavelength (.sub.z), where m is a integer.

18. The method according to claim 13, wherein the variation of the splitting ratio, with which the pulses circulating in the resonator are split into the first and second pulse portions, is accomplished by varying a polarization dependent phase and/or a polarization angle of the pulses at an inlet of the interferometer.

19. The method according to claim 18, wherein the phase is changed by an angle or the polarization is changed by an angle , and wherein the group delay in the resonator caused by a change of the group velocity of the pulses is .sub.g, wherein a conversion factor of .sub.g/ or .sub.g/(2.Math.) is greater than 1.

20. The resonator arrangement according to claim 2, wherein the control bandwidth is at least 100 kHz.

21. The resonator arrangement according to claim 20, wherein the control bandwidth is at least 1000 kHz.

22. The resonator arrangement according to claim 3, wherein the measurement apparatus is configured to measure at least one of a repetition rate (f.sub.rep) of the resonator and a carrier envelope offset frequency (f) of a frequency comb generated or received by the resonator.

23. The resonator arrangement according to claim 4, wherein the at least one optical element is a birefringent optical element.

24. The resonator arrangement according to claim 5, wherein the at least one optical element is an integer or half-integral wave plate.

25. The resonator arrangement according to claim 11, wherein the nonlinear optical element is a gas jet or a crystal.

26. The method according to claim 15, wherein the pulses are the carrier wave.

27. The method according to claim 16, wherein the at least one optical element is a birefringent element.

28. The method according to claim 17, wherein m is an even number.

29. The method according to claim 19, wherein the conversion factor is greater than or equal to n or an integer multiple of n.

30. An optical resonator arrangement comprising a resonator, an interferometer having at a first and a second interferometer leg arranged within the resonator, the first interferometer leg has a first optical path length and the second interferometer leg has a second optical path length other than the first optical path length, a splitting ratio, with which the interferometer splits radiation circulating in the resonator into the first and second interferometer legs, is variably adjustable, and an actuator configured to variably adjust the splitting ratio during operation of the optical resonator arrangement, wherein the resonator arrangement is configured to change a repetition rate of the resonator and a carrier envelope offset frequency by changing the splitting ratio of the radiation circulating in the resonator into the first and second interferometer legs, such that in a frequency domain, a comb of frequencies of the radiation circulating in the resonator contracts or expands by a uniform factor about a fixed point.

31. An optical resonator arrangement comprising a resonator and an interferometer having at least a first and a second interferometer arranged within the resonator, the first interferometer leg has a first optical path length and the second interferometer leg has a second optical path length other than the first optical path length, and a splitting ratio, with which the interferometer splits radiation circulating in the resonator into the first and second interferometer legs, is variably adjustable, wherein during the operation of the optical resonator arrangement, the first optical path length and the second optical path length are both kept constant.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) In the following, advantageous embodiments of the present invention are illustrated in more detail by referring to the drawings. In particular in the drawings:

(2) FIG. 1a shows two subsequent laser pulses of a burst of pulses and the carrier wave associated therewith, wherein the horizontal axis represents the time and the vertical axis represents the electric field,

(3) FIG. 1b illustrates the frequency comb associated with the laser pulses of FIG. 1a, wherein the horizontal axis represents the frequency and the vertical axis represents the intensity of the respective frequency,

(4) FIG. 2 illustrates a first embodiment of the resonator arrangement including a ring resonator,

(5) FIG. 3 is a second embodiment of the resonator arrangement including a linear resonator,

(6) FIG. 4 is a schematic illustration of an interferometer in the resonator arrangement,

(7) FIG. 5a shows a frequency comb corresponding to FIG. 1b having a repetition rate f.sub.rep,

(8) FIG. 5b illustrates a second frequency comb having a changed repetition rate insert,

(9) FIG. 6 illustrates an embodiment of the splitting actuator of the interferometer,

(10) FIG. 7 shows a second embodiment of an interferometer,

(11) FIG. 8 shows a third embodiment of an interferometer,

(12) FIG. 9 shows a forth embodiment of an interferometer,

(13) FIG. 10 illustrates an embodiment of a polarization actuator and

(14) FIG. 11 illustrates an embodiment of a filter resonator or gain resonator.

DETAILED DESCRIPTION OF THE INVENTION

(15) Throughout the figures like components are denoted by the same reference signs.

(16) FIG. 2 schematically shows a resonator arrangement 1 according to the present invention comprising a resonator 2 configured here as a ring resonator. The resonator 2 comprises two curved mirrors 3, 4 as well as two planar deflection mirrors 5, 6. A laser medium 7, e.g. a laser crystal such as Ti:Sa, is arranged between the two curved mirrors 3, 4, in particular, at the location of the focus defined by the concave curvature of the two mirrors 3, 4. One of the curved mirrors 3 is semi-transparent and is thus used as an incoupling mirror for coupling pump light P into the resonator 2. One of the planar mirrors 6 is also semi-transparent to the radiation 8 circulating on the folded axis of the resonator 2 and is thus used as an outcoupling mirror for coupling the laser radiation out from the resonator 2. The radiation 8 circulates in the resonator 2 in the form of one or a plurality of exemplarily shown pulses 110 (cf. also FIG. 1a). Through the optical path length between the mirrors 3 to 6, the resonator is configured for being resonant to the carrier wave 120 having the frequency f.sub.c.

(17) In the interior of the ring resonator 2, an interferometer 9 is provided. The configuration of this interferometer and its importance for the present invention will be explained in more detail hereinbelow. In addition, the resonator 2 comprises, according to this embodiment, a mode coupler M, e.g. a Kerr-lens mode coupler (KLM), a semiconductor-based saturable absorber or a nonlinear optical loop.

(18) Outside the resonator 2, the resonator arrangement 1 comprises, in the optical path of the radiation 8, a beam splitter 10, which directs a portion of the laser radiation 8 onto a measuring apparatus 11. The measuring apparatus 11 is configured to detect one or a plurality of the characteristics of the radiation 8 leaving the resonator 2, e.g., the pulse repetition frequency or (synonymous) repetition rate at which laser pulses 110 leave the resonator 2, the precise position of a specific mode f.sub.c of a frequency comb leaving the resonator 2 and/or a (mean) output power of the resonator 2.

(19) For this purpose, the measuring apparatus 11 may also comprise a suitable group consisting of a plurality of measuring means or sensors, e.g. a photodiode.

(20) Via a data line 12, a measuring signal is transmitted from the measuring apparatus 11 to an evaluation and control unit 13, which may, e.g., be a control electronics, a computer or a CPU. The evaluation and control unit is suitably configured and/or programmed for generating information from the measuring signal and for determining deviations of the measuring signal from predetermined, possibly programmable target and threshold values. The evaluation and control unit subsequently accesses, via a suitable control line 14, an actuator or control element 15 that acts on the interferometer 9. The actuator 15 is configured for changing or adjusting the splitting ratio at which the radiation 8 circulating in the resonator 2 is distributed to various legs of the interferometer 9.

(21) FIG. 3 shows a second embodiment of a resonator arrangement 1 comprising, in this case, a linear resonator 2. One of the resonator end mirrors is a planar mirror 16. This mirror 16 may be configured as a semi-transparent outcoupling mirror of the resonator 2. The other resonator end mirror, however, is, in this embodiment, a mode coupler M in the form of a nonlinear optical loop mirror (Nonlinear Optical Loop Mirror, NOLM) 17, which is here configured as an amplifying loop mirror (Nonlinear Amplifying Optical Loop Mirror, NALM). The NALM includes an optical fiber 18 whose two ends are united in a beam splitter or coupler 19. The coupler 19 couples the NALM to a linear part of the resonator 2. In the NALM, i.e., in the loop mirror 17, an amplifying section 21, i.e. an area of the fiber 18 doped with suitable impurity atoms, is provided, said doped area being excited via a pump coupler 20 through an optical pump light source 22. The linear part of the resonator, i.e., the part between the planar end mirror 16 and the loop mirror 17, has arranged therein an interferometer 9 according to the present invention.

(22) Instead of the amplifying nonlinear loop mirror 17, the linear resonator 2 of FIG. 3 may also comprise a further planar end mirror or some other kind of optical back reflection element, e.g., a Bragg grating, a fiber Bragg grating or a possibly non-amplifying, optical linear or nonlinear loop mirror. In addition, the path of the radiation 8 between the two resonator end mirrors 16, 17 may be folded, e.g. V-, Z- or W-shaped, so as to obtain a more compact resonator arrangement 1. Also, such folded resonator arrangements are regarded as linear resonators within the meaning of the present invention as long as radiation propagates in the so-called linear section in both directions, i.e., back and forth.

(23) At this point, reference should be made to the fact that any form of the resonator arrangement 1 according to the present invention may optionally be provided with an active laser medium 7 (as exemplarily shown in FIGS. 2 and 3) or may not be provided with an active laser medium, i.e. it may be configured as a cold resonator.

(24) The resonator arrangement 1 according to FIG. 3 comprises, just like the embodiment according to FIG. 2, the elements 10 to 15, i.e. a beam splitter 10, a measuring apparatus 11, an evaluation and control unit 13, data and control lines 12, 14 as well as an actuator or control element 15 configured for adjusting and changing the splitting ratio at which the radiation 8 is distributed into two or more legs of the interferometer 9. It is only for the sake of clarity that these components are not shown in FIG. 3.

(25) FIG. 4 shows in the form of a schematic diagram a first embodiment of an interferometer 9 in the resonator arrangement 1 according to the present invention. The radiation 8 enters the interferometer 9 at an inlet 23, whereas the radiation leaves the interferometer 9 at an outlet 24. The interferometer 9 additionally comprises a first beam splitter 25 splitting the incident radiation 8 into a first portion 8a along a first interferometer leg 9a and a second beam portion 8b passing through a second interferometer leg 9b.

(26) A mirror 26, 27 is provided in each of the two interferometer legs 9a, 9b. It directs the radiation 8a, 8b in the respective interferometer legs 9a, 9b onto a second beam splitter 28 at which the radiation or pulse portions 8a, 8b from the two interferometer legs 9a, 9b interfere with each other before the light leaves the interferometer 9 at the outlet 24.

(27) An important aspect for the present invention is that the first interferometer leg 9a has an optical path length L.sub.g1 that is different from the optical path length L.sub.g2 of the second interferometer leg 9b. Each of the optical path lengths L.sub.g1, L.sub.g2 is here defined as the integral over the product of the geometric length and the refraction index for the respective interferometer legs 9a and 9b. Within the framework of the present invention, it is important to differentiate between group velocity and phase velocity, and the optical path length can therefore be indicated for the group center of a pulse (index g) as well as for the phase of the carrier wave (index ph). When calculating the integral, the respective refraction indices take effect. What is important for the present invention is, first of all, the diversity of the group wavelengths along the interferometer legs. Even if the geometric path length is identical, as shown in FIG. 4, the optical path lengths L.sub.g1, L.sub.g2 may differ from each other, if one of the two interferometer legs 9a, 9b has provided therein, at least sectionwise, a material whose index of refraction differs from that of the material provided in the other interferometer leg 9a, 9b.

(28) A configuration which is not mandatory but definitely advantageous for various cases of use is of such a nature that the magnitude of the difference between the two optical (phase) path lengths L.sub.ph1, L.sub.ph2 corresponds precisely to the wavelength or to an integer multiple, n, of a carrier wave 120 with which the resonator is operated. The optical path lengths L.sub.ph1, L.sub.ph2 on the two interferometer legs 9a, 9b are preferably constant during operation of the resonator arrangement 1.

(29) According to the present invention, the splitting ratio, with which the first beam splitter 25 splits the incoming radiation 8 into a first beam portion 8a and a second beam portion 8b, is variably adjustable, each of said beam portions 8a, 8b passing then through the interferometer 9 along a respective one of the two interferometer legs 9a, 9b. The portion 8a in the first interferometer leg 9a is here continuously variable, e.g. between 0% and 100%, but may also be adjusted within smaller ranges, such as from 0% to 1%, 0% to 5% or from 47% to 53% or 40% to 60%. An expedient selection orients itself according to the range to be achieved in the change of the group round-trip time as well as according to the desired optical bandwidth of the interferometer. Shorter pulses typically need a larger bandwidth. The complementary, second beam portion 8b is then transmitted from the beam splitter 25 into the second interferometer leg 9b. In the case of a very simple embodiment, the splitting ratio can be changed by manually adjusting the beam splitter 25. According to a more convenient embodiment, an actuator or control element 15 is provided, as shown in FIGS. 2 and 3, which is capable of acting on the beam splitter 25 and/or the beam splitter 28 automatically, i.e., without any additional action on the part of a user, so as to change the splitting ratio with respect to the two interferometer legs 9a, 9b.

(30) For the special case in which the magnitude of the path length difference L.sub.ph1L.sub.ph2 between the two interferometer legs 9a, 9b corresponds to an integer multiple, n.sub.c, with n1, of a carrier frequency f.sub.c resonant in the resonator 2, FIGS. 5a and 5b show what the invention is able to accomplish. FIG. 5a shows here again the same frequency comb that has already been shown in FIG. 1b with a spacing f.sub.rep between neighboring, overall equidistant modes that corresponds to the pulse repetition rate (repetition rate) of the resonator 2 and a carrier-envelope-offset frequency (CEO frequency) f.sub.o. The frequency comb reaches its intensity maximum at the frequency f.sub.c. In the variant schematically shown here, the interferometer 9 is adjusted such that the carrier having the frequency f.sub.c (and the wavelength .sub.c=c/f.sub.c) positively interferes at the outlet of the interferometer 9. FIG. 5a is obtained e.g. in the case of a splitting ratio A=a:b, where a stands for the portion of the radiation in the first interferometer leg 9a, whereas b stands for the portion of radiation in the second interferometer leg 9b.

(31) In the case discussed here, the optical path length L.sub.g1 in the first interferometer leg 9a is less than the optical path length L.sub.g2 in the second interferometer leg 9b. In the method according to the present invention, i.e. when the resonator arrangement 1 is in operation, the splitting ratio A is now changed, e.g. such that a second splitting ratio A=a:b=(a+x):(bx) is obtained. In other words, the beam splitter 25 is modified manually or automatically by the actuator 15 such that a larger portion of the radiation 8 is transmitted to the first, shorter interferometer leg 9a. Here, the two optical path lengths L.sub.g1, L.sub.g2 remain constant, so that the light still positively interferes at the outlet of the interferometer 9, but the change in the splitting ratio has the effect that a larger portion of the radiation 8 will have a shorter group round-trip time in the resonator 2 than before. It follows that the mean group round-trip time of the radiation 8 in the resonator 2 will decrease and the repetition rate of the resonator 2 will consequently increase such that a new, larger value f.sub.rep is obtained. This can be seen in FIG. 5b that illustrates the resulting frequency comb having the new mode spacing f.sub.rep.

(32) At the fixed point, i.e. the resonant frequency f.sub.c, the intensity maximum of the frequency comb still occurs, and the resonance point f.sub.c has not been shifted. However, around this fixed point f.sub.c, the other modes have been spread in a fan-shaped or concertina-like manner. This also had the effect that the offset frequency f.sub.0 changed. In the present embodiment, the repetition rate of the resonator 2 was even changed to such an extent that the former offset frequency f.sub.0 was so to speak shifted beyond the zero line, so that a new line of the resonator now defines the new offset frequency f.sub.0.

(33) It goes without saying that the resonator arrangement 1 works in a corresponding manner in the reverse direction. If, starting from the splitting ratio A (cf. FIG. 5a), a larger portion of the circulating radiation 8 were transmitted to the second, longer interferometer leg 9b, the mean group round-trip time would increase, so that, starting from FIG. 5a, the repetition rate f.sub.rep would therefore decrease. The frequency comb contracts so to speak around the fixed point f.sub.c.

(34) Also contemplated may be configurations, in the case of which the resonator 2, after a change of the splitting ratio, is no longer resonant for the carrier frequency f.sub.c, but for a new resonant frequency. In this case, the whole frequency comb would spread or contract around a fixed point f.sub.fix that is different from the carrier frequency f.sub.c.

(35) FIG. 6 shows a first possibility of macroscopically realizing the interferometer 9, and in particular, the beam splitters thereof. Each of the two beam splitters 25, 28 according to FIG. 4 is here configured as a combination of a polarization beam splitter 29 and a polarization beam splitter 30. The polarization beam splitter 30 may be a birefringent element, more specifically a rotatable half wave plate 30, which, controlled by the actuator 15, can be rotated. A change in the rotational position of the half wave plate 30 causes a change of the splitting ratio of the incident radiation 8 with respect to the two beam portions 8a, 8b for the two interferometer legs 9a, 9b.

(36) FIG. 7 shows a second embodiment of an interferometer, which is much more robust than the first variant. Also, the interferometer 9 according to FIG. 7 has an inlet 23 and an outlet 24 having provided between them a first and a second polarizer 31, 32 and between these polarizers a birefringent element 33, which is here an integer wave plate with n, where n1, with a variably adjustable orientation. The polarizers 31, 32 are optional in the case of this embodiment, since, when used in the resonator 2, some other polarizing or polarization-selective element is typically already present. In addition, the polarization can be predetermined from outside in some cases, e.g. through the polarization of an incoupled radiation. The advantage of a polarizing element within the resonator is to be seen in that a double mode state of the resonator and the polarization mode splitting that may result therefrom can be avoided.

(37) The n wave plate 33 splits at its surface the incoming radiation 8 into a first beam portion 8a along the ordinary axis and into a second beam portion 8b along the extraordinary axis of the birefringent crystal. At the exit face of the wave plate 33, the two beam portions 8a, 8b are again positively superimposed, the path lengths difference L.sub.ph1L.sub.ph2 being an integer multiple of a wavelength of the fixed point frequency f.sub.fix. The two paths of the ordinary and extraordinary beam portions 8a, 8b are here geometrically superimposed, i.e., they are geometrically identical. They, however, differ from one another with respect to their index of refraction and consequently with respect to their optical path lengths L2, L2. This is schematically indicated in FIG. 7. The two legs 9a, 9b of the interferometer 9 thus extend in the axial direction of the resonator 2 between the two surfaces of the birefringent element 33.

(38) A change in the splitting ratio and consequently in the mean group round-trip velocity and thus finally in the repetition rate of the resonator 2, is accomplished by rotating the wave plate 33. When the embodiment comprises an actuator 15, the latter may thus act on the wave plate 33 in the form of a rotary actuator.

(39) The greater the difference between the two interferometer legs 9a, 9b is, i.e., the greater the magnitude of the difference L.sub.ph1L.sub.ph2 is, the higher the dependence of the mean group round-trip delay on the splitting ratio of the two beam portions 8a, 8b will be. It follows that, in the case of the implementation through a wave plate 33, a higher order n of the wave plate 33 allows the achievement of a higher angular sensitivity, i.e. a greater change in the repetition rate of the resonator 2 on the basis of the same rotation of the wave plate 33. The highest angular sensitivity is achieved around the angles +/45, i.e., when the beam portions in both interferometer legs are approximately identical. However, an excessively high order n of the integer n wave plate will also lead to a high wavelength dependency of the transmission and/or of the intended line shift, whereby the bandwidth of the resonator arrangement 1 will be limited.

(40) FIG. 8 shows an alternative embodiment of the interferometer 9. The single birefringent element has here been replaced by two birefringent elements 34, 35, which are again arranged between the (optional) polarizers 31, 32. Each of the two birefringent elements 34, 35 consists of an integer wave plate 34, 35 for the same wavelength .sub.z of the resonant frequency f.sub.z. According to a preferred variant, the wave plates 34, 35 have orders n and n which do not differ from one another or which differ from one another only to a minor extent (e.g. |nn|=0). Again, according to a preferred variant, these wave plates are oriented relative to one another such that they are substantially opposed to one another, i.e. arranged at an angle of approx. 90 to one another. At least one of the two wave plates, e.g. the second wave plate 35, has a variable orientation, and the incident polarization is, expediently, at approx. 45 to the optical axes of the wave plates. In this arrangement, the adjustable birefringent element 35 is used like the element 33 in FIG. 7, whereas the fixed birefringent element 34 compensates the double refraction of the adjustable element 35 at the normal position of the latter. In this way, a high optical transmission bandwidth of the arrangement is achieved.

(41) In a more complex representation, the arrangement schematically shown in FIG. 8 can be described as a four-leg interferometer. The path lengths L1+L1, L1+L2, L2+L1 and L2+L2 of this four-leg interferometer having the legs 9aa, 9ab, 9ba and 9bb, which are also here geometrically identical, are shown in FIG. 8. For the sake of clarity, the components of the second interferometer legs 9b, 9b are shown slightly displaced to the side relative to the components of the first interferometer legs 9a, 9a. In contrast to the variant according to FIG. 7, the embodiment of the interferometer 9 according to FIG. 8 has the advantage that, at the rotation-sensitive normal position, all beam portions are guided in the two interferometer legs with lengths L1+L2 and L2+L1, respectively. In the case of a small difference between the wave plate orders n and n, in particular for n=n, this means that the transmission of the interferometer 9 is not wavelength dependent or that the wavelength-dependent losses are less than without the compensating wave plate. If there is a deviation from the normal position, small intensity components additionally contribute in the other two legs, whereas the portion in the original legs remains unchanged in the first order. This has the effect that, even for small angular deflections of the wave plates relative to one another, especially for angles that are less than 10 or less than 1, the wavelength-dependent losses are less than without the compensating wave plate. The selection of the order n and the orientation of the axis of the compensating wave plate also allow an adjustment of the broadbandedness of the transmission and/or of the targeted resonance line detuning. The compensation in its entirety has the effect that a high bandwidth is maintained, even if a comparatively high order of the individual wave plates should be chosen, e.g. n=n=5. In particular, it is thus possible to accomplish a high control sensitivity of the carrier-envelope-offset frequency f.sub.o, without substantially influencing the spectral optical bandwidth of the interferometer and thus the spectral width of the frequency comb generated or received by the resonator.

(42) The compensation also makes sense in the event that the frequency f.sub.z, for which the interferometer is adjusted to be resonant, lies outside the frequency range of the circulating radiation. For a target frequency f.sub.z close to the carrier frequency f.sub.c, a fixed point frequency f.sub.fixf.sub.z is obtained like in the case of the arrangement having no compensating wave plate. If the target frequency f.sub.z is chosen such that it is clearly different from f.sub.c, the compensated setup exhibits the tendency that the fixed point f.sub.fix no longer coincides with the target frequency f.sub.z. In the preferred variant described here, f.sub.fix is shifted away from f.sub.c relative to f.sub.z. This means that the target frequency f.sub.z, for which the interferometer is adjusted to be resonant, can be chosen closer to f.sub.c than an aimed-at fixed point frequency f.sub.fix. It will here be expedient to choose the target frequency f.sub.z close enough to the carrier frequency f.sub.c for making the transmission losses compatible with the desired case of use. Hence, a suitably chosen target frequency f.sub.z provides a large range for adjusting the fixed point frequency f.sub.fix.

(43) The arrangement shown in FIG. 8 can be modified in an evident manner, e.g. insofar as the compensation of the double refraction of the element 35 is achieved not only by one further birefringent element 34, but by a plurality of birefringent elements, e.g. by two birefringent elements in a symmetric mode of arrangement before and behind the element 35. The birefringent element 34, which is only provided in this modified symmetric version, is shown by a broken line in FIG. 8. Furthermore, not only the orientation of the wave plate 34 or the circulating radiation polarization existing at the wave plate 34 may be adjustable but also the orientation of the additional birefringent elements or the respective circulating radiation polarization existing there.

(44) FIG. 9 shows an alternative or extended embodiment of a rotatable wave plate (e.g. 33, 35) of the interferometer 9 in FIGS. 7 and 8. This wave plate 33 may now have either a fixed orientation, e.g. at 45, or, as before, a variable orientation. The arrangement comprises a first and a second polarization adjuster 36, 37 arranged around the birefringent element 33. The two polarization adjusters 36, 37 and/or the wave plate 33 are accessible by the actuator 15 and can variably be adjusted thereby. The polarization adjuster 36, 37 may here especially be adjusted, e.g. rotated, for changing the polarization of the radiation 8 arriving at the wave plate 33. To this end, the polarization adjusters 36, 37 may be realized, e.g., as an adjustable half wave plate, as a combination of wave plates and of an electro-optical modulator, a Faraday rotator, a liquid crystal element or with ferroelectric crystals. In FIG. 9 again it is indicated that the two interferometer legs 9a, 9b are located between the two surfaces of the birefringent elements 33 and are positioned geometrically above each other. Again the offset between the two interferometer legs 9a, 9b in FIG. 9 is introduced for superior intelligibility only. Depending on the targeted range, one of the two polarization adjusters may be omitted or may be replaced with a polarizer.

(45) FIG. 10 illustrates how each of the polarization adjusters 36, 37 is constructed in detail. Specifically, each of the polarization adjusters 36, 37 includes a first /4 plate 38 and a second /4 plate 39, where is preferably the wavelength .sub.c of the circulating radiation. A variably adjustable phase shifter 40 is positioned between the two /4 plates 38, 39, for instance an adjustable birefringent element, such as an electro-optic modulator (EOM), a controllable liquid crystal, a ferroelectric crystal and/or a thermally adjustable or pressure adjustable or strain adjustable birefringent element. It may be contemplated to influence the birefringence thermally and electrically at the same time. In particular, two or more crystals may be used, ideally having axes rotated by 90 with respect to each other in order to adjust the birefringence. In this case, the thermal adjustment may also be accomplished by a temperature difference between the two or more crystals.

(46) Depending on the type of the phase shifter 40 used, additional global phase delays and group delays may occur here, which superimpose onto the remaining effects. They may be used for a specific adjustment of the high-frequency fixed point f.sub.fix. For example, in an electro-optical crystal, the magnitude of the stress dependent global phase or group delay may be affected by the alignment of the crystal axes and the electric fields with respect to the optical beam. It may be advantageous for the polarization adjusters 36, 37 to use a common element, for instance by folding and/or reflection of the optical path.

(47) It is illustrated in the dashed lines that a /2 plate 41, 42 for a specific target wavelength, preferably .sub.c, is optionally inserted between the first /4 plate 38 and the phase shifter 40 and/or between the second /4 plate 39 and the phase shifter 40. By rotating this /2 plate 41, 42, the orientation of the birefringence is varied at a point at which the radiation is circularly polarized. In this way, the phase of the radiation 8 may thus be varied without concurrently causing a group delay .sub.g.

(48) It is a particular feature of the present invention that it is possible to initiate the group delay with a type of optical leverage effect, which may advantageously be used, for instance, when using electro-optic modulators. In order to change the round-trip time by one optical period T.sub.c=1/f.sub.c in a resonator 2 the optical path in the resonator 2 has to be varied by one wavelength. This variation corresponds to a phase shift of 2 in the free beam domain, which may be caused, for instance, by means of a movable mirror or by means of an electro-optic phase modulator, for which typically the group delay is approximately equal to the phase delay. According to the present invention, the optical path length is used instead of a direct change of the path by blending over between two parts of an interferometer 9. For example, the blend-over process may be accomplished by adjusting the polarization angle in front of a polarization beam splitter or in front of a birefringent element. For a difference in path of the interferometer legs 9a, 9b of |L.sub.g|L.sub.g2|=n*, the change in the optical path length is L.sub.g=n*/2*cos(2)=))n*/2*sin(2(45)). The change in path length L.sub.g is equivalent to a differential group delay of the pulses 110 of .sub.g=2/*L.sub.g. If a change of the phase shift between two polarization directions is used for rotating the polarization according to FIG. 10, then one obtains a rotation of polarization of =/2, which in turn causes a change of the optical path length of L.sub.g=n*/2*sin() and which becomes a linear dependency L.sub.g=n**/2 for small . Compared to a direct variation of the path length with L.sub.g=*/(2), here one obtains a magnification of the effect of n*. This advantage also holds true when the arrangement is used as actuator for the carrier envelope frequency.

(49) Of particular interest are realizations of the interferometer 9, in which a variation of the group round-trip time is achieved without a concurrent, or at least without a significant, influence on the transmission of the interferometer 9. In all the previously explained embodiments, there is no or substantially no influence on the transmission of the carrier frequency f.sub.c upon a variation of the splitting ratio and thus of the mean group delay of the pulses 110. Depending on the adaptation of the bandwidth of the interferometer, also the variation of the transmission with respect to the entire circulating light may be maintained at a low or negligible level.

(50) However, additional arrangements may be contemplated, in which the transmission of the interferometer is not constant. Such a situation may be encountered, when the path difference between the interferometer legs is not an integer multiple of a carrier wave .sub.c. For example, with a path difference of (n+1/2)*.sub.c and a following polarizer, a configuration may be achieved that is still advantageous, in which the transmission for the carrier frequency f.sub.c in an appropriate basic state is approximately 1 and varies only quadratically with the deviation from the basic state, while the group round-trip time varies linearly with this deviation.

(51) The resonator arrangement 1 of the present invention may not only be used with free beam resonators, for instance in solid state lasers or lasers of a different type, but also in fiber lasers. It is contemplated to implement the resonator arrangement 1 or at least the interferometer 9 microscopically by means of waveguides.

(52) For example, the present invention is appropriate for the amplification or filtering of optical radiation as well as for the generation of frequency combs and ultra-short pulses, respectively, in particular, with a variable adjustability and/or stabilization of a certain mode f.sub.c, a given repetition rate or a predefined offset frequency f.sub.0.

(53) FIG. 11 illustrates an embodiment, in which the resonator 2 of the present invention is used as a filtering and/or amplifying resonator. The resonator configured in this example as a ring resonator having 4 mirrors 3, 4, 5, 6, receives at an inlet 43 an optical radiation 111 that preferably includes two or more different spectral components. The interferometer 9 is located within the resonator 2 so that the position of the resonances (modes) of the resonator may be adjusted by means of the interferometer 9. By means of the resonator 2, portions or the entirety of the incident radiation 111 are amplified and thus circulate as modified radiation 110 within the resonator 2 of the resonator arrangement 1. Optionally, a nonlinear optical element 45 is located in the resonator 2, which further modifies the resonator internal radiation 110 and, in particular, changes its frequency by sum frequency blending and/or difference frequency blending. The nonlinear optical element 45 may alternatively be appropriately configured for sum frequency blending and difference frequency blending or may be selected for generating or amplifying light by means of an optically parametric process or for generating radiation at the second harmonic (SHG) or at higher harmonics of the fundamental wave or carrier wave 120. By means of the generation of higher harmonics, UV light for EUV light may be generated, for example. To this end, the nonlinear optical element 45 may be, for example, a gas jet or a nonlinear optical crystal. The possibly modified resonator internal radiation is coupled out of the resonator 2 (as exiting radiation 112) at an outlet 44. The geometric configuration of the resonator 2 is of illustrative nature. For example, also a linear resonator 2 may be used or inlet and outlet 43, 44 may be combined.

(54) Based on the illustrated embodiments the resonator arrangement 1 of the present invention may be modified in many ways for this purpose. In particular, it may be contemplated that in the interferometer 9 not only one first and one second interferometer legs 9a, 9b are provided, but more than two legs may be provided, wherein the splitting ratio is variably adjustable into two or more of the plurality of interferometer legs. This may be realized, for instance, when in one or both of the interferometer legs 9a, 9b in the interferometer 9 according to FIG. 4, a further interferometer is integrated, whose configurations again corresponds to the configuration according to FIG. 4 and which may, for instance, be realized in one of the variants illustrated in FIGS. 6 to 10. FIG. 9 itself is an example for such an interleaved interferometer 9. As already described above, not all wave plates have to be centred around the same wavelength (for example .sub.c), thereby providing the potential for influencing the fixed point. Moreover, it is evident that a reflection or deflection of the optical path enables an optimized and component saving configuration. It should be appreciated again that instead of birefringence any other effect may be used, which causes a polarization dependent shift of propagation time or phase.

(55) When used in frequency comb applications, the resonator of the present invention replaces the conventional laser source. Accordingly, the generated radiation may be varied in its characteristics by means of nonlinear steps, in particular by spectral broadening, frequency doubling or multiplying, difference frequency generation, sum frequency generation or Raman shift.