WO2008129492A2

WO2008129492A2 - Method and device for determining a phase relation between optical fields and radiofrequency or microwave fields

Info

Publication number: WO2008129492A2
Application number: PCT/IB2008/051503
Authority: WO
Inventors: Gabriele Ferrari
Original assignee: Gabriele Ferrari
Priority date: 2007-04-19
Filing date: 2008-04-18
Publication date: 2008-10-30
Also published as: ITFI20070096A1; WO2008129492A3

Abstract

A method and device for establishing a direct phase relation between an optical field and a radiofrequency field starting from a continuous wave optical radiation of frequency vL, wherein; - a first optical beam of the given radiation of frequency vL, which is initially single longitudinal mode and continuous wave, is phase modulated at a modulation radiofrequency vRF in order to generate a set of frequency components close to vL, separated in frequency from vL by an integer multiple of vRF; - the modulated optical beam is propagated through a device for an additional spectral broadening; - a second continuous wave optical radiation is generated, in a phase and frequency relation with said first continuous optical radiation of frequency vL, having a given frequency vD different from vL and within the spectral range covered by said modulated optical beam propagating trough the spectral broadening medium; - the frequency vRF of the said modulating signal is controlled so that one of the said optical frequency components distant from vL an integer multiple of vRF has a constant and defined frequency shift from the frequency vD of the said second continuous radiation.

Description

T I TLE

METHOD AND DEVICE FOR DETERMINING A PHASE RELATION BETWEEN OPTICAL FIELDS AND RADIOFREQUENCY OR MICROWAVE FIELDS

DESCRIPTION Field of the invention

The invention generally concerns a method and device for generating optical fields (wavelength comprised between 5 nanometers and 50 micrometers) coherent in phase with radiofrequency or microwave fields (frequency between 1 kHz and 1000 GHz) , or vice versa, to generate radiofrequency and microwave fields coherent in phase with optical fields, by modulating in phase a continuous wave laser field and the frequency stabilization of the generated optical frequency components. Background of the invention

In recent years the effectiveness was proven of pulsed mode-locked lasers to establish a phase relation between optical and radiofrequency (RF) fields (for instance see bibliography reference [I]). This technology has important applications since it allows for synthesizing optical frequencies starting from frequency calibrated RF, for applications in high resolutions spectroscopy and metrology. Moreover, it allows for generating RF reflecting the frequency stability of optical oscillators. This last application opens the possibility to realize optical clocks having improved stability and accuracy with respect to the present RF standards.

The use of pulsed mode-locked laser to establish a coherent phase relation between optical and RF fields can be classified in terms of the following aspects. The emission spectrum of the mode-locked laser is composed by a set of frequency components characterized by two frequencies, the repetition rate v_r and the CEO (Carrier Envelope Offset) VQ, and an integer number that identifies each frequency component V₁ according to the relation

V₁ = V₀ + I * V_r To measure the optical frequency v_L of a continuous wave (CW) laser with respect to a radiofrequency reference RF, the frequencies v_r and VQ are stabilized with respect to said reference RF, and one measures the minimum frequency difference between v_L and the set of frequency components of the pulsed laser through a measurement of the beatnote of v_L and the pulsed field measured on a photodetector .

Given the value of the beatnote, and the that of the index i (determined through the measurement of the wavelength of the laser) , it is possible to determine the optical frequency of v_L.

It is clear that by modifying v_r and VQ it is possible to synthesize all the optical frequencies within the spectral region covered by the pulsed laser, which may be spectrally broadened using photonic crystal fibers or other self-phase matching methods.

In addition, by stabilizing a precise frequency component of the pulsed laser with respect to a CW and highly stable laser it is possible to generate a RF field reflecting the stability of the optical oscillator.

The present state of the art is represented by titanium sapphire lasers (Ti: Sa) with Kerr-lens mode- locking, optically pumped by frequency doubled diode- pumped solid state Nd: YAG or Nd: YVO₄ lasers. In most cases the Ti: Sa lasers are spectrally broadened through photonic crystal fibers. These systems are commercially available (see for instance model FC8004 on the web site www.menlosystems.com), they have a volume in the range of one cubic meter and their employ requires qualified staff. Their cost is in the range of Euro 250.000.

The use of pulsed mode-locked lasers to generate a phase relation between optical and RF fields requires a setup composed by at least the following sources: -the optical pump for the mode-locked laser, -the mode-locked laser,

-the CW laser, which is single longitudinal mode. Each of the these systems has its own specificity and weak points, making the complete setup complex and reducing its reliability. Besides the high cost, complexity and limited reliability, this technology is not mature for outdoor applications, where transportability is required.

There is therefore a need for a simpler system, possibly based on a single laser, to realize compact, reliable, low cost and low power clocks, for space applications, with reference also to the clocks onboard of the GPS, Galileo or similar satellites. The consequent improvement in the stability with respect to present RF clocks would reduce the uncertainty of the signals sent by the satellites, with a clear improvement of the potentiality in the navigation system. Summary of the invention

An object of the present invention is to provide a reliable technique to generate a phase relation between optical and RF fields, which is simpler and cheaper than that using pulsed mode-locked lasers. The new method gives a solution to many problems associated to systems based on mode-locked lasers and can be implemented with available commercial devices which are relatively simple and low cost. The new method can be used for synthesizing RF fields starting from a given optical frequency or for synthesizing an optical frequency starting from a RF. A device realized according to the present invention can be employed to generate RF fields, applications of time and frequency metrology, and to realize RF and microwave oscillators reflecting the stability properties typical of optical oscillators.

The invention, the features of which are defined in the appended claims, provides for an alternative to the more complex systems based on self-referenced (or phase stabilized) mode-locked lasers in all the applications where they are employed.

Essentially, the invention consists in a method for establishing a phase relation between optical and radiofrequency or microwave fields, and for coherently generating ultra-short pulses of light starting from a continuous wave optical radiation such that the optical phase between adjacent pulses is stabilized and eventually set to zero.

In the present description, for radiofrequency field or signal it is intended an electro-magnetic field with frequency in the range comprised between 1 kHz and 1000 GHz (= 1 THz) . Even if at the higher frequencies of this range it would be conventionally more appropriate to use the term "microwave" or "TeraHertz radiation", for the sake of simplicity, the term radiofrequency or the acronym RF are intended hereafter (and also in the annexed claims) as covering the whole spectral range just mentioned. The initial radiation, which derives from a single longitudinal-mode laser of a given frequency v_Lr is modulated in phase at a radiofrequency of frequency v_RF, so as to generate a set of optical frequency components close to v_Lr distant from v_L of an integer multiple of v_RF. The phase modulated beam can then undergo an additional stage of spectral broadening by means of an appropriate device.

Simultaneously, starting from the same laser of frequency v_Lr it is generated another optical field of frequency v_D of which the relative phase noise is identical to that of v_Lr and such that its frequency lies within the spectral range of the phase modulated field, possibly broadened, generated as described above. By acting on the RF generator, the frequency v_RF is stabilized so that one of the frequency components of the phase modulated field corresponds, or at least has a constant and defined offset, with respect to the frequency field v_D. In this way it is possible to establish a well defined phase relation between the RF field and the continuous wave optical field, besides generating ultra- short optical pulses such that the relative phase between adjacent pulses is constant in time, and possibly zero.

Starting from the technique of use of a the device known as "optical frequency comb generator" (OFCG, see also [2]) for the absolute measurement of optical frequency differences (see also [3]), the invention finds an efficient implementation both for the absolute measurement of optical frequencies and, more generally, for the generation of ultra-short optical pulses in which the relative phase among adjacent pulses is stabilized or possibly made null. Ultra-short optical pulses are generated by means of an OFCG through a phase modulation at frequency v_RF of the initially given CW field of frequency v_Lr such that the spectrum of the modulated radiation contains the frequency component v_L. On the other hand, since the phase modulation of the optical field occurs at a constant frequency v_RF, pulses are produced with a repetition rate v_RF. Similarly to the spectrum of mode-locked lasers, the emission spectrum of the radiation generated by the device is composed of a set of frequency components characterized by two frequencies, the repetition frequency v_RF and the carrier envelope offset v₀, and one integer number i which identifies each component according to the relation:

V₁ = V₀ + i * v_RF

According to the method and the embodiments of device according to the present invention, given v_L, for each radiofrequency v_RF the carrier envelope offset frequency v₀ is determined according to the relation:

Vo = v_L- - integer part of (v_L / v_RF) * v_RF, Thus, the spectrum of frequency components generated with the method and device proposed by the invention is characterized by only one free parameter v_RF, with respect to the two free parameters VQ and v_r which determine the spectrum of frequency components of a mode-locked laser. This represents per se a substantial simplification.

According to the present invention, different techniques belonging to the following fields are involved: - phase modulation of optical fields; optical mirrors with dispersion compensation (chirped mirrors); temporal compression of ultra-short optical pulses; - stabilization of optical cavities with respect to radiofrequency fields;

- zero group velocity dispersion optical fibers; - highly nonlinear optical fibers;

- nonlinear generation of optical frequencies;

- phase stabilization among CW and monochromatic optical fields; in order to stabilize for instance a radiofrequency v_RF with respect to an optical frequency v_L or, vice versa, stabilize v_L with respect to v_RFl to fulfill the relation: v_L = N * v_RF where N is an integer number in the range from 100 (one hundred) to 1.000.000.000 (one billion), or to fulfill the relation: v_L = (N + d) * v_RF where N is an integer number in the range from 100

(one hundred) to 1.000.000.000 (one billion), and d is a real number in the range between 0 (zero) and 1 (one) . N, and possibly d if different from zero or one, are fixed or known in each particular application, and can be chosen by the user while remaining compliant with the specifications and/or technical limits of the embodiment of the device. Generally, the invention is useful for generating identical ultra-short pulses, that is with the same phase between adjacent pulses, for applications in the study of molecular dynamics like DNA, RNA, PNA and other biologic molecules and polymers: here the optical response of sample exposed to the radiation produced according to the invention is employed for analyzing, modifying or identifying the sample; in telecommunication applications the frequency components produced according to the invention can be used as frequency reference for the individual channels exploited for transmitting data, voice and images with particular reference to communication through optical fibers. According to a subsidiary object of the present invention, the parameters of the cavity of a OFCG phase modulator device can be optimized in order to get rid of the limitations induced by the phase noise, in particular by choosing an appropriate length of the cavity comprised between 1 cm and 1 km, and choosing the modulation frequency of the phase modulator equal to an integer number multiple of the free spectral range of the cavity

(the frequency separation of the resonances of the cavity) . The integer number can be comprised between one and one million.

Brief description of the drawings

Further characteristic and advantages of the invention will become apparent from the following description of embodiments thereof, made purely by way of example and not limitative, with reference to the attached drawings in which :

- figure 1 is a scheme of the principle of operation in a first embodiment of the invention; - figure 2 is a scheme of the principle of operation in a second embodiment of the invention;

- figure 3 is a scheme of the principle of operation in a third embodiment of the invention;

- figure 4 is a schematic diagram of an improved OFCG device according a further embodiment of the invention; and

- figure 5 is a schematic diagram of a OFCG device according to an embodiment alternative to that of figure 4. Detailed description of the preferred embodiments

With reference to the functional scheme of figure 1, the essential components of a generator of stabilized optical pulses produced with a radiofrequency rate according to the invention are, according to the numerals in the figure, the following:

1) continuous wave and single longitudinal-mode laser source of frequency v_L;

2) optical beam splitter of the radiation generated in D;

3) phase modulator of the field at frequency v_L and modulation frequency v_RF generated by 9) ; 4) non-linear optical element for further broadening the spectrum of the modulated radiation (such as a photonic crystal fiber, see for instance [4]);

5) optical beam splitter for the modulated and broadened radiation; 6) optical detector for measuring the frequency of the beatnote between the optical radiation generated in 7) and a frequency component of the modulated and broadened radiation produced in 3) or 4);

7) optical device for generating an optical radiation v_D such that the ratio v_L/v_D is predetermined;

8) detector of the phase of the radiofrequency generated by 6) ;

9) radiofrequency oscillator controlled by the signal produced by 8) for generating said signal of radiofrequency v_RF applied to the modulator 3) .

The continuous wave laser source 1) can be a laser diode stabilized on an extended cavity, or a laser diode DFB or DBR, or a solid state laser such as a Nd:YAG (also with monolithic cavity) , or a dye laser, or a gas laser, or an optical fiber laser. This laser source can be stabilized in frequency with respect to an atomic or molecular transition which is directly accessible close to v_Lr or close to the frequency 2*v_Lr or close to the frequency 3/2*vi, or close to the frequency v_D by using part of the radiation generated in I)₁ or close to a generic frequency component present in the spectrum of the radiation in E. This laser source can be composed of the above mentioned laser and an optical amplifier for increasing its power.

The phase modulation producing device 3 in figure 1 is driven by a generator 9 producing radiofrequency or micro- wave at frequency v_RF. These phase modulators typically generate pulses with spectral width in the range of 5 THz (5*10¹² Hz) . This spectral width is not sufficient to attain the required goal. A possible solution to this limitation is discussed in [3], and is represented by optical interval frequency dividers, but this solution is not feasible in a commercial device to be used frequently and in the long term. This is the reason why so far OFCG were used only for measuring the frequency difference between optical fields. In order to circumvent the limitation arising from the relatively small spectral width of the modulated radiation, it is possible to employ alternative techniques such as the following: a) using dispersion compensated mirrors (chirped mirrors) for the cavity containing the electro-optic modulator; in order to obtain a reduction of the dispersion in the cavity, the mirrors that define the same are two or more, and at least one of these mirrors is of the dispersion compensaion type; b) propagating the radiation coming from the phase modulator 3 into a nonlinear fiber 4 which has low group velocity dispersion and/or high non-linearity in order to enlarge the spectrum of the modulated beam (for instance see [4]); this choice allows for generating frequency components close to the frequency 2 * v_L when the frequency converter 7 is a frequency doubler, or close to 3/2 * Vi when the frequency converter 7 is a frequency multiplier by a factor 3/2 (see [5]).

With the method according to the invention, it is possible to achieve a substantial simplification for a device capable to synthesize radiofrequency or micro-wave radiation from an optical field or, vice versa, optical radiation from a radiofrequency or micro-wave field. Indeed, according to the present state of the art, the synthesizers with similar properties require ultra-fast, mode-locked and phase stabilized (see [I]) lasers, the device including at least the three following elements: a pump laser source for operating a mode-locked laser, the mode-locked laser, a continuous wave laser. On the other hand, the device realized according to the present invention includes the continuous wave laser 1, the pulse generator device starting from the continuous wave laser, and the frequency converter for continuous wave radiation such a frequency doubler or a 3/2 frequency multiplier. The reduction to a single laser necessary for implementing the synthesizer represents a substantial progress in terms of simplification of the setup which results in an improvement of the reliability of the system, reduced costs of installation and operation and reduced overall volume and power consumption, aspect which are critical towards the application in space.

According to an embodiment, the device according to the invention is further characterized by the fact that the radiofrequency signal, phase coherent with respect to the optical field, is generated by a radiofrequency generator (element 9 in figure 1) . On the other hand, when mode-locked lasers are used according to the known art, the radiofrequency is generated by a photo-detector intercepting part of the optical pulsed field produced by the laser (see [6]).

With respect to the usual OFCG devices, the device according to the invention can introduce an additional spectral broadening, for instance by using photonic crystal fibers. In this way it becomes possible to generate frequency components close to a harmonically (like 2* Vi) , or sub-harmonically generated (for instance 3/2*Vi) light starting from the primary frequency v_L, to close the loop and establish the phase relation between optical and radiofrequency or microwave fields, so as to permit the absolute measurement of optical frequencies.

So far, OFCG were employed only to measure optical frequency differences and not the absolute value of a generic optical frequency. Even if it was proposed to perform absolute optical frequency measurements combining

OFCG and OFID (Optical Frequency Interval Dividers, see

[3]), this approach requires a large number of OFID with consequent increase in the number of the required laser sources. Furthermore, to the best of the applicant's knowledge, the practical achievement of this method was never demonstrated.

Figure 2 represents the scheme of an alternative embodiment of a device according to the invention, functionally analogous to the device presented in figure 1. According to this embodiment, it is reduced even further the sensitivity to the phase noise of the source 9. The numbering of the elements from 1 to 9 in the fundamental scheme of figure 1 is maintained in figure 2.

The embodiment shown in figure 2 includes a beam splitter 20 downstream of the phase modulator 3 which sends part of the radiation to an optical detector 21. This detector is sensitive to the amplitude modulation of the optical field at frequency v_RF and sends the measured signal to the frequency generator 9. In this configuration the generator 9 substantially delivers to the modulator 3 the same radiofrequency delivered by the detector 21 with an additional phase determined by the detector 8. This embodiment allows to realize a self-oscillating optical device which simplifies and further diminishes the problems related to the phase noise of the radiofrequency source, which is one of the elements considered as a limitation in the application of OFCG for the absolute measure of optical frequencies.

Figure 3 represents the scheme of another alternative embodiment of a device according to the invention, substantially analogous to the device presented in the figures 1 and 2. Also in this case, the numerals 1 - 9 refer to the same components as in the previous figures.

The source 1 can be stabilized in frequency with respect to a device 11 for detecting the resonance condition with respect to an atom or molecular transition. The element 11 can also contain additional devices for nonlinear frequency conversion and generation.

As shown, the arrangement of figure 3 may comprise the following additional elements:

12) optical amplifier for the radiation generated in 1; 13) optical amplifier for the radiation generated in 4;

14) temporal compressor for the optical pulses, composed of dispersive prisms, and/or diffraction gratings, and/or compensation dispersion mirrors (chirped mirrors) ;

15) device for introducing a frequency shift of the radiation incident on 6 and coming from 7, by an amount in the range from 1 Hz to 100 GHz; such a device can be installed also upstream of the device 7, so that it acts on the fundamental radiation coming from the beam splitter 2;

16) continuous wave reference laser;

17) optical detector for measuring the beatnote between the optical field of the reference 16 and one or some of the frequency components of the optical field E generated in 4;

18) detector of the phase of the radiofrequency field generated in 17 and stabilization circuit of the phase by acting on the frequency v_L generated by 1;

19) laser whose frequency is to be measured;

22) optical detector for measuring the frequency of the beatnote between the optical field produced in 19 and at least one frequency component of the phase modulated field.

The optical amplifier 12 can be a semiconductor optical amplifier such as a tapered amplifier, or a solid state amplifier, or a fiber amplifier. This amplifier amplifies the continuous radiation produced by the source 1 so as to improve the efficiency of the nonlinear processes that may occur in the phase modulator 3 and in the spectral broadening device 4. Similarly, also the amplifier 13 may be a semiconductor optical amplifier such as a tapered amplifier, or a solid state amplifier, or a fiber amplifier. This amplifier amplifies the pulsed radiation coming from 3 so as to improve the efficiency of the spectral broadening in 4.

The temporal compressor of the pulses 14 reduces the temporal duration of each pulse coming from the modulator 3 such that the pulse peak intensity is maximized and hence the spectral broadening in 4 is optimized. The device 15 for introducing a frequency shift of the radiation incident on 6 and coming from 7 can be an acousto-optic modulator. It simplifies the process of stabilization of v_RF on the basis of the beatnote measured in 6. The continuous wave reference laser 16 operates at a frequency different from the source 1 and it can be frequency stabilized with respect to an atomic or molecular transition, with a wavelength comprised in the spectral range covered by the pulses generated in 4. Such a laser 16 can have a frequency stability better than the source 1, hence it can be used as a reference to stabilize the relative frequency of the source 1 at the same level of 16. To attain this goal, a portion of the radiation of the laser 16 and a portion of the pulsed radiation are detected on the detector 17, in order to detect the beatnote between the fields from the laser 16 and one of the frequency components present in the modulated radiation. The frequency of the source 1 is corrected on the basis of the signal generated in 17 and elaborated in the detector 18, such that the beatnote maintains a stable value .

The device described above can then be used for measuring the frequency of a generic continuous laser 19 through the measurement of the beatnote between the field from 19 and the phase modulated field according to the method described in [1] . According to a different aspect of the present invention, it is possible to stabilize, or set to zero, the phase between adjacent ultra-short optical pulses generated coherently starting from a continuous wave radiation . For generating optical pulses with the same phase, such that the pulse-to-pulse relative phase is zero, the field v_D can be generated by using a frequency doubler, in which case v_D=2*v_Lr or a frequency multiplier by a factor 3/2 (according to [5]), in which case

The phase detector 8 acts on the RF generator 9 in such a way that one of the frequency components of the phase modulated beam in F has exactly the same frequency of v_D. The following relation is then fulfilled: v_D-v_L= v_L = nl v_RF with nl integer, when the device 7 is a frequency doubler, or

with n2 integer, when the device 7 is a frequency multiplier by a factor 3/2, so that v_L = 2 * n2 * v_RF. In both cases the following results are achieved:

- a frequency v_RF is generated which is a sub-multiple of the optical radiation v_L;

- the spectrum generated in 4 is composed of an group of frequency components V₁ = i * v_RF with i integer, where the equivalent of the carrier envelope offset frequency VQ of the traditional mode-locked lasers is null.

It follows from the above that the phase of the electrical field of adjacent pulses is constant in time.

It is worth mentioning that the condition where the frequency components present in the spectrum of the radiation E in figure 1 are of the type: V₁ = i * v_RF with vo = 0, represents a simplification of the system, but not a necessary condition. Indeed, by fixing in an appropriate way the beatnote frequency measured in 6, or possibly using a frequency shifter 15, it is possible to obtain a set of frequency components of the type :

V₁ = I * V_RF + V₀.

In the use of OFGC another critical technical aspect consists in the length stabilization of the optical cavity containing the electro-optic modulator (see [2]) . With respect to this point, the invention also provides for an efficient method for stabilizing the optical cavities of OFCG devices. This method thus allows to realize optical cavities solving the limitations typically associated to the optical cavities of OFCG, in particular those concerning the group velocity dispersion, the problems associated to the phase noise of the radiofrequency source driving the electro-optic modulator of the OFCG, and the stabilization of the length of the optical cavity of the OFCG containing the electro-optic modulator.

It is known that in the processes of phase modulation at high modulation index, the phase noise on the generated frequency components more distant from the frequency v_L is proportional to the phase noise of the RF source driving the phase modulator, multiplied by the squared of the index of modulation. This result is obtained assuming an initial white noise, constant independently from the considered spectral interval. Considering that by using an OFCG device the modulation index is very high, it is generally believed that broadening the spectrum beyond 10 THz the generated signal has a phase noise larger than the intensity of the individual frequency components; this makes the device useless in measurements of beatnotes with other optical fields. This phenomenon is known as "phase collapse". However, using OFCG devices, the optical photons coupled into the modulation cavity remain therein during a finite time in the range of T = 2*L*F/c (assuming that the optical cavity is linear, L is the length of the cavity, F the finesse and c the speed of light) . Consequently, the injected RF noise with a fast evolution with respect to T give a contribution with zero average, and only components with slow evolution with respect to T give an appreciable contribution. In other terms, the optical cavity acts as a low pass filter for the RF or microwave phase noise with a cutoff frequency in the range of 1/ (2π*T) , in particular by choosing an appropriate length of the cavity in the range between 1 cm and 1 km, and choosing a modulation frequency sent to the electro- optic modulator equal to an integer multiple of the free spectral range V_FSR (the separation between the optical resonances of the cavity) . This integer number can also be between one and one million. In this way it is possible to increase T maintaining v_RF constant, improving the rejection, of the system with respect to the phase noise of the radiofrequency source 9.

In figure 4 there are sketched the fundamental components of an OFCG, such as the electro-optic modulator 43 and the mirrors 40 of the optical cavity containing the modulator. In order to maximize the efficiency of the OFCG, that is to maximize the spectral width of the generated pulses, it is required that a resonance condition is maintained between the modulation frequency v_RF and V_FSR (v_RF integer multiple of V_FSR) . While v_RF can have a great stability, V_FSR depends essentially on the length of the optical cavity and the instability of the length directly reflects on the instability of V_FSR, this resulting in a reduction of efficiency of the OFCG. So far, this aspect was treated only by improving the passive stability of the cavity.

According to the invention, it is proposed to use a device for the active stabilization of the cavity length.

The stabilizing device is sketched in figure 4. A beam splitter 45 sends part of the pulsed radiation coming from the OFCG to a spectrometer 46. An electronic device 47 elaborates the spectrum signal from 46 and generates a correction signal for the cavity length. Namely, the optical length of the cavity is finely tuned via a voltage generated by the device 47 and applied to piezo-electric actuators supporting and driving at least some of the cavity mirrors 40, or applying a voltage to one of the electrodes 42 of the eletro-optic modulator 43. The resonance condition, that is v_RF integer multiple of V_FSR, optimizing the efficiency of the OFCG, is then obtained when the optical length of the cavity is constant, and is equal to the value that maximizes the spectral length measured in 46.

A simplification of the stabilization system consists in replacing the spectrometer (element 46 in figure 4) with a device measuring the optical power transferred in a spectral range not containing the frequency v_L.

A possible implementation of this device is represented in figure 5 and it consists in the employ of an optical wavelength dispersive element 48, such as a diffraction grating or a prism, intercepting the radiation selected by the beamsplitter 45. The dispersive element separates the spectral components generated by the OFCG in at least two components.

Possible choices of spectral ranges are the spectral range containing v_L, the spectral range not containing v_L and with frequency larger than v_L, the spectral range not containing v_L and with frequency smaller than v_L.

In figure 5 there is illustrated a possible implementation in which the dispersive element is a diffraction grating. The optical power in the spectral interval not containing v_L and with frequency larger than Vi is detected by the photodetector 51, the optical power in the spectral interval not containing v_L and with frequency smaller than v_L is detected by the photodetector 50, the optical power in the spectral interval containing Vi is intercepted by the mirror 52 and sent to the photodetector 49. An optical device 47 receives the signal generated in the detectors 49, 50 and 51, and on the basis thereof it acts on the optical path of the cavity formed by the mirrors 40, through the piezolelectric transducers 41 or one of the electrodes 42 of the electro-optic crystal 43, in order to maintain the optical path in the cavity constant at the value maximizing the efficiency of the OFCG. BIBLIOGRAPHY

1. Review of Scientific Instruments Vol. 72, no. 10 October 2001, pp. 3749-3771, "Optical frequency synthesis based on mode-locked lasers", Cundiff et al .

2. IEEE J. Quan. Elec, vol.29, no.10, October 1993, pp. 2693-2701, "Wide-Span Optical Frequency Comb Generator for Accurate Optical Frequency Difference Measurement", Ohtsu et al . 3. Optics Letters, Vol. 23, No. 17, settembre

1998, pp. 1387-1389, "Accuracy of optical frequency comb generators and optical frequency interval divider chains", T. Udem et al .

4. Optics Letters, Vol. 25., No. 1, January 2000, pp. 25-27, "Visible continuum generation in air-silica microstructure optical fibers with anomalous dispersion at 800 nm", J. K. Ranka et al .

5. WO2006033133A2 "Method and device for multiplicating optical frequencies by a factor 1.5", G. Ferrari

6. US2004/0021056A1 "Method and device for producing radio frequency waves", Haensch et al .

Claims

1. A method for establishing a direct phase relation between an optical field and a radiofrequency field starting from a continuous wave optical radiation of frequency v_Lr including the steps of; phase modulating a first optical beam of the given radiation of frequency v_Lr which is initially single longitudinal mode and continuous wave, at a modulation radiofrequency v_RF in order to generate a set of frequency components close to v_Lr separated in frequency from v_L by an integer multiple of v_RF;

- propagating the modulated optical beam through a device for an additional spectral broadening;

- generating a second continuous wave optical radiation, in a phase and frequency relation with said first contnuous optical radiation of frequency v_Lr having a given frequency v_D different from v_L and within the spectral range covered by said modulated optical beam propagating trough the spectral broadening medium; - controlling the frequency v_RF of the said modulating signal so that one of the said optical frequency components distant from v_L an integer multiple of v_RF has a constant and defined frequency shift from the frequency v_D of the said second continuous radiation.

2. The method according to claim 1, whrein ultrashort optical pulses are generated with a constant or zero relative phase between adjacent pulses.

3. The method according to claim 1, wherein said frequency v_D is chosen between the values v_D = 2 * v_L and v_D = 3/2 * v_L.

4. The method according to any of the previous claims, wherein for each frequency component of frequency v_RF, the carrier envelope offset frequency v₀, defined as vo = Vi- integer part of (v_L/v_RF) *v_RF is null or has a known and constant value.

5. The method according to any of the previous claims, wherein said radiofrequency v_RF is stabilized with respect to said optical frequency v_L or vice versa, so as to satisfy the relation:

Vi = N * v_RF in which N is an integer comprised between 100 e 1.000.000.000.

6. The method according to claim 5, wherein the following relation is fulfilled: v_L = (N + d) * v_RF in which d is a known and constant number.

7. A device for generating optical pulses starting from an optical radiation of frequency v_Ll at a radiofrequency rate v_RF stabilized with respect to v_Ll comprising:

- a laser source (1) of a first continuous wave and single longitudinal mode optical radiation of frequency v_L;

- a beam splitter (2) separating a portion of said first single mode optical radiation in a first and a second beam;

- at least one electro-optic phase modulator (3) and a nonlinear optical device (4) for the spectral broadening of the generated optical pulses arranged along the path of said first beam;

- a device (7) for generating a second continuous wave and single longitudinal mode optical radiation of frequency v_D in a known ratio with the frequency v_Lr along a second propagation path of said second beam towards an optical detector (6) receiving said second continuous wave and single longitudinal mode optical radiation of frequency v_D and the modulated beam propagating along the first path, for determining the frequency difference between the radiation with known frequency v_D and one of the frequency components of the modulated and spectrally broadened beam, by means of the measurement of the radiofrequency beatnote signal; a phase detector (8) of the radiofrequency signal generated by said optical detector (6); and - a radiofrequency generator (9) controlled by the signal produced by said phase detector (8), for producing a radiofrequency v_RF signal sent to a modulation input of the phase modulator (3) of said first optical beam.

8. The device according to claim 7, wherein the laser source of said first continuous wave and single longitudinal model radiation (1) of frequency v_L is stabilized in frequency with respect to an atomic or molecular transition.

9. The device according to claim 7 or 8, wherein the device generator (7) of an optical radiation continuous wave and single longitudinal mode of frequency v_D is a frequency doubler.

10. The device according to claim 7 or 8, wherein the device generator (7) of an optical radiation continuous wave and single longitudinal mode of frequency v_D is a frequency multiplier by a factor 3/2.

11. The device according to any of the claims 7 to 10, wherein the nonlinear optical device (4) for the spectral broadening of the pulses comprises a nonlinear optical fiber.

12. The device according to any of the claims 7 to 10, wherein the nonlinear optical device (4) for the spectral broadening of the pulses comprises a nonlinear photonic crystal fiber.

13. The device according to any of the claims 7 to 12, wherein the continuous wave radiation generated by the laser source (1) is amplified by an optical amplifier (12) .

14. The device according to any of the claims 7 to 13, wherein the modulated optical radiation coming from said modulator (3) is amplified by an optical amplifier (13).

15. The device according to any of the claims 7 to 13, wherein the modulated optical radiation coming from the modulator (3) passes through a pulse temporal compressor (14) .

16. The device according to any of the claims 7 to 15, wherein the continuous wave radiation incident on the optical detector (6), propagating along the path C, is frequency shifted by a frequency shifting device (15).

17. The device according to any of the claims 7 to 16, wherein the laser source (1) is frequency stabilized with respect to a reference laser.

18. The device according to claim 17, wherein the laser source (1) is frequency stabilized with respect to a reference laser (16) by means of the measurement of the frequency of the beatnote, on a photodetector (17), between the radiation generated by the reference laser (16) and a frequency component of the radiation generated in the optical device (4), and the determination by means of a detector (18) of a correction signal of the frequency of the source (1), on the basis of the measured frequency of the beatnote.

19. The device according to any of the claims from 7 to 18, wherein said electro-optic phase modulator (3) is at least partly based on optical fibers.

20. A device for generating a radiofrequency or microwave electric field in which the radiofrequency is coherent in phase with a frequency v_RF generated according to any of the claims 7 to 19.

21. The device according to claim 7, in which said beamsplitter (2) sends part of the modulated radiation generated by the modulator (3) towards an optical detector

(21), said detector (21) being sensitive to the amplitude modulation of the intercepted optical signal and sending a proportional electric signal to said generator (9), which in turn sends to said modulator (3) a frequency signal equivalent to that received from said detector (21), with a phase determined by the signal coming from the detector (8) .

22. A device for the active stabilization of an optical cavity containing an electro-optic modulation crystal in an OFCG, receiving on one input a continuous wave optical radiation of frequency v_L and on a second input a modulation signal at radiofrequency v_RFr for producing a pulsed optical radiation with rate at said radiofrequency v_RFl based on the spectral analysis of the generated pulsed radiation.

23. The device according to claim 22 comprising: - an optical cavity, defined by a set of mirrors (40) defining a cavity containing said electro-optic modulation crystal (43) , receiving said beam of continuous wave optical radiation and said modulating signal at a radiofrequency v_RF applied to one of the electrodes (42) capacitively coupled to said crystal (43) to generate on the output said modulated optical radiation pulsed with a rate of said radiofrequency v_RF; - a beam splitter (45) arranged along the propagation path of said optical radiation pulsed with a rate of said radiofrequency v_RF;

- an optical spectrum analyzer (46); - electronic means (47) for the elaboration of the data produced by said optical spectrum analyzer (46);

- actuator means controlled by said control signals, for maximizing the spectral width of the optical pulses with a rate v_RF produced by the OFCG.

24. The device according to claim 23, wherein said actuator means are piezo electrical devices for the translation of one or more mirrors (40) defining the primary cavity containing said electro-optic modulation crystal (43) .

25. The device according to claim 23, wherein said actuator means are electrodes (42) capacitively coupled to said crystal (43) of the electro-optic modulator.

26. The device according to claim 22, wherein said optical spectrum analyzer is functionally replaced by an optical dispersive element (48), and at least three optical detectors (49, 50, 51) intercepting respectively: a first beam containing the frequency component v_Lr a second beam containing the frequency component larger than Vi but not Vi, a third beam containing the frequency component smaller than v_L but not v_Lr and generating signals corresponding to the input to said electronic devices (47) .

27. A method for generating an electric field at radiofrequency or microwave in which the electric field generated is phase coherent with the radiofrequency generated according to claim 1.