The present invention relates in general to methods for measuring electric fields. The measurement of an electric field is usually carried out through methods based on capacitive systems, which have the advantage of simple construction but are limited in that they modify the electric field that is the object of the measurement, and in that, for constructive reasons, they do not allow the identification of the direction of the field itself. Moreover, the probes require being connected to a ground reference, which leads to a considerable distortion of the electric field, as the sensor distance increases from the ground point. Furthermore, often for security reasons, this configuration cannot be achieved. Recently some methods have been developed based on the Pockels, or electro-optic, effect, which have the advantage of being non-invasive and having very rapid response times. At the present time, the measurement of electric fields occurs through the use of sensors equipped with multiple sensing elements, thus multiple laser beams for optical interrogation and a non-local measurement of the field, or through successive measurements over time, according to the variation of the orientation of the sensing element or characteristics of the laser beam. Recently, methods have been developed wherein the sensing element is arranged on the fiber itself, but also in this case, the use of several sensing elements is necessary for measuring the directionality of the field.

Van der Valk et al, "Terahertz polarization imaging", Optics Letters, Optical Society of America, vol. 30, no. 20, 15 October 2005, describes a method for measuring the polarization state of a terahertz pulse. Such method comprises:

- generating a circularly polarized radiation beam;

sending the radiation beam through an isotropic nonlinear optical material, said nonlinear optical material being arranged in an observation region susceptible to be occupied by an electric field to be measured and being capable of exhibiting a variation of optical birefringence induced by the electric field;

- by means of an optical separation system comprising a non-polarizing beam splitter, a pair of half-wave plates and a pair of Wollaston prisms, separating the radiation beam emerging from the nonlinear optical material into four linearly polarized components; detecting the respective light intensities related to the four components of the radiation beam;

measuring fluctuations of the light intensities related to the four components of the radiation beam, induced by the electric field; and

- determining modulus and direction of the electric field based on the measured fluctuations related to the four components of the radiation beam.

An object of the present invention is to provide a method for the vector measurement of electric fields which allows a non-invasive and real-time measurement of an electric field, in particular a pulse field.

In view of such aim, the object of the invention is a method for measuring an electric field, comprising

a) generating a circularly polarized radiation beam;

b) sending the radiation beam through a uniaxial nonlinear optical material, said nonlinear optical material being arranged in an observation region susceptible to be occupied by an electric field to be measured, and capable of exhibiting a variation of optical birefringence induced by the electric field, wherein the radiation beam is propagated along the direction of the extraordinary optical axis of the nonlinear optical material;

c) by means of a pair of juxtaposed optical separating means arranged directly downstream of the nonlinear optical material, receiving respective parts of the radiation beam emerging from the nonlinear optical material and separating said parts of the radiation beam respectively into two components linearly polarized at 0° and 90°, and into two components linearly polarized at 45° and 135° with respect to a predetermined reference system;

d) detecting the respective light intensities related to the four components of the radiation beam;

e) measuring fluctuations of the light intensities related to the four components of the radiation beam, induced by the electric field; and

f) determining modulus and direction of the electric field based on the measured fluctuations related to the four components of the radiation beam. It is moreover the object of the invention an apparatus for measuring an electric field, comprising

a source configured to generate a radiation beam;

polarizing means configured to circularly polarize the radiation beam;

a uniaxial nonlinear optical material to be arranged in an observation region susceptible to be occupied by an electric field to be measured, said nonlinear optical material being configured to be traversed along an extraordinary optical axis by the radiation beam and capable of exhibiting a variation of optical birefringence induced by the electric field; a pair of juxtaposed optical separating means arranged directly downstream of the nonlinear optical material and configured to receive respective parts of the radiation beam emerging from the nonlinear optical material and separating said parts of the radiation beam respectively into two components linearly polarized at 0° and 90°, and into two components linearly polarized at 45° and 135° with respect to a predetermined reference system;

detecting means configured to detect the respective light intensities related to the four components of the radiation beam; and

an acquisition system configured to

measure fluctuations of the light intensities related to the four components of the radiation beam, induced by the electric field; and

determining modulus and direction of the electric field based on the measured fluctuations related to the four components of the radiation beam.

The proposed system allows real-time measurements of the modulus and direction of the electric field in a plane through the use of a single sensing element and a single beam of light radiation. Moreover, the measurements are free from any ground point or potential reference (floating measurement). The method being totally dielectric and, in the case of some embodiments, having fiber transmission, it does not present problems related to electrical safety.

The advantages of the proposed approach are therefore the almost total non-invasiveness of the measurement, the quality of the response to the electric field (very high linearity in a very wide measurement range), the rapidity of the instrument's response to fast variations up to a few tens of nanoseconds (due to the absence of moving elements). According to one embodiment, it is possible to configure the system so that it is insensitive to the variation of the temperature wherein the measurement is carried out.

Further features and advantages of the method and the apparatus according to the invention will become more apparent in the following detailed description, made with reference to the accompanying drawings, provided purely to be illustrative and non-limiting, wherein:

- figure 1 is a block diagram representing the optical part of a measuring apparatus according to the invention;

- figure 2 is a block diagram representing the detection and acquisition part of the apparatus of figure 1 ;

- figures 3 to 5 are graphs showing measurements of the electric field modulus made with the method according to the invention.

With reference to figure 1 , an apparatus for measuring an electric field comprises a source 10 configured to generate a beam of light radiation, in particular, laser. In the illustrated example, the beam generated by the source 10 is linearly polarized, for example vertically (90°) as indicated by the double vertical arrow PI in figure 1.

The laser beam is sent into a single-mode optical fiber that preserves the polarization and, through the use of a collimator (not shown), is carried to a polarization system.

In the illustrated example, the polarization system comprises a polarizer 20, which transforms the linear polarization of the beam at 90° into a linear polarization at 45°, as indicated by the double arrow P2, and a quarter-wave plate 30, which transforms the linear polarization of the beam into a circular polarization, P3.

The apparatus therefore comprises a non-linear optical material 40, which represents the sensing part of the apparatus. The non-linear optical material 40 is arranged in an observation region OR susceptible to be occupied by an electric field to be measured. The non-linear optical material 40 is configured to be traversed by the radiation beam along the extraordinary optical axis thereof. The non-linear optical material 40 is able to show a variation of optical birefringence induced by an electric field to be measured. In particular, the material 40 is a uniaxial material, arranged with its own extraordinary optical axis parallel to the direction of propagation of the beam, indicated by the arrow z. Such orientation allows the material 40 to be sensitive only to the external electric field vector, which lies on the plane perpendicular to the direction of propagation of the laser beam.

The nonlinear optical material 40 may be, for example, a z-cut barium borate crystal (BaB ₂ 0 ₄ ), i.e. processed in such a way that the extraordinary optical axis is perpendicular to one of its flat faces.

In the absence of an external electric field, at the emergence from the crystal 40, the polarization is still circular; in the presence of an external electric field, however, the output polarization becomes elliptic (arrow P4) due to the variation of birefringence induced by the external field.

The polarization state of the light emerging from the crystal 40 is analyzed by means of the measurement of the four Stokes parameters:

S ₀ = l .

5 ₂ = Ip sin 2ψ cos 2χ

5 ₃ = Ip sin 2χ,

where Ip, 2ψ and 2χ are the spherical coordinates of a vector within the Poincare unit sphere, (S _lt S ₂ , S ₃ ). I is the total intensity of the beam, and p is the degree of polarization,0≤ p < 1.

The apparatus therefore comprises a pair of juxtaposed optical elements 51 and 52, configured to receive respective parts of the radiation beam emerging from the nonlinear optical material 40 and to separate each of them into two linearly polarized parts, so as to obtain four components linearly polarized at 0°, 90°, 45° and 135° (arrows P5 in figure 1). In particular, one of the two optical elements, 51 , separates a part of the beam into two components linearly polarized at 0° and 90°, and the other element, 52, separates the other part of the beam into two components polarized at 45° and 135°. The optical elements 51, 52 may, for example, be two Wollaston prisms arranged so as to obtain an orthogonal separation of the beams. The four beams relating to the four polarization directions are collected in optical fiber and sent to four sensors 60, in particular four avalanche photodiodes (APD), configured to detect the respective light intensities of the four beams. Compared to classic photodiodes, these devices allow the transduced current to be amplified in order to detect light signals of low intensity.

With reference, to Figure 2, a resonant DC/DC converter 71 is used to provide a constant adequate supply voltage to the respective photodiode 60. The voltage level necessary for the operation of the sensor 60 is generated starting from a constant input voltage value ISV equal to 5 V, and, through the resonant converter 71, is raised to a value OSV adjustable from a minimum of 130 V to a maximum of 160 V. The output voltage value OSV is established via a user-adjustable GR reference. Such adjustment allows the level of the gain of the APD 60, variable from a minimum of 1 to a maximum of 50, to be determined. One of the main advantages of using a resonant converter with respect to a switching converter is shown by the fact that voltages with less harmonic content and lower conducted emissions are obtained. The residual ripple obtained in the case described is on the order of one part per million.

As such gain, at the same voltage, is a function of the temperature, an automatic adjustment system is provided, which, as a function of the temperature TM measured on the board, allows the set gain to remain constant at the variation of the ambient temperature within a range between 0 and 60 degrees Celsius.

The light signal is converted by the APD 60 into a current signal and subsequently, through a current/voltage converter (I/V) 72, into a voltage signal. In order to measure small fluctuations of light around a constant intensity value much higher than the fluctuations themselves, to increase the sensitivity of the measurement and to avoid saturation of the I/V converter 72, a compensator 73 of the constant light/current component is provided through a feedback system. Such method allows an equal and opposite current to be drained from the I/V converter 72 ensuring a perfect balance of the constant part. Such method also makes it possible to obtain a measurement, 74, of the constant current value, and therefore of the constant light intensity value, which is necessary for the polarimetric analysis.

The high frequency signal, corresponding to the fluctuations of light deriving from the application of an electric field to the non-linear material 40, is then transmitted to an analog filter 75 and then sent to a digital analog acquisition system 76. The filter 75 has a bandwidth of 75 Mhz in order to perform extremely rapid pulse measurements.

The acquisition system 76 is configured to measure the fluctuations of the light intensities related to the four components of the radiation beam, induced by the electric field.

The acquisition system 76 is also configured to determine the modulus and direction of the electric field based on the fluctuations measured relative to the four components of the radiation beam.

The measurement of the intensities of the four polarized components makes it in effect possible to obtain the Stokes parameters, which uniquely characterize the polarization emerging from the crystal 40. From the link between the Stokes parameters and the electro- optical properties of the crystal 40, it is possible to obtain the modulus and direction of the external electric field, which has altered the polarization state of the laser beam.

The use of optical fibers, both for sending and for receiving, allows only the sensing part of the apparatus to be brought into the measurement area OR, while the generation of the beam and all of the transduction, amplification and management of the signals may be managed separately, in an area even far away from the measurement area.

The geometric division of the beam allows much greater sensitivity than traditional polarimetry. In effect, the use of normal non-polarizing beam splitters leads to a significant depolarization of the beam emerging from the sensing element, which significantly degrades the measurement. Such solution also makes it possible to perform a polarimetry without any moving parts, thus guaranteeing the possibility of single-shot measurements.

Finally, the system described above allows continuous monitoring of the four signals and is thus able to 1) avoid having to perform direct monitoring from the source, 2) compensate for any defects in the division of the beams or in the circularity of the polarization of the beam at the entry of the crystal 40.

Measurements have been carried out, the results of which are shown in figures 3 to 5. Fig. 3 shows the result of measurements carried out in the laboratory by subjecting the system to fields on the order of hundreds of kV/m. The abscissa shows the time; the ordinate shows the measured voltage expressed in arbitrary units. Both the imposed field and the measured field are reported. The data are related to a single discharge event. Fig. 4 shows the rising ramp of the field measured by the system for the pulses of the previous case. The delay between the curve of the imposed field and the measured one is due to a systematic error in the measurement chain.

Fig. 5 shows the results of measurements carried out as in the configuration of Fig. 3 and 4 with increasing ranges from 200 kV/m to 1 MV/m. The graph shows in the abscissa the imposed field and in the ordinate the measured field. The values reported in the graph report the parameters of a linear fit.