Fiber-optic sensor and method

Abstract

A fiber optic sensor and related method are described, with the sensor including a cross-coupling element in the optical path between a polarizing element and a sensing element, but separated from the sensing element itself; with the cross-coupling element generating a defined cross-coupling between the two orthogonal polarization states of the fundamental mode of a polarization maintaining fiber guiding light from the light source to the sensing element thus introducing a wavelength-dependent or temperature-dependent sensor signal shift to balance wavelength-dependent or temperature-dependent signal shifts due to other elements of the sensor, particularly signal shifts due to the wavelength dependence of the Faraday effect or the electro-optic effect constant.

Claims

1. A fiber optic sensor comprising: a light source, a polarizing element, a detector, a polarization maintaining (PM) fiber, and a sensing element, wherein the fiber optic sensor further comprises a cross-coupling element in an optical path between the polarizing element and the sensing element, with the cross-coupling element generating a defined cross-coupling between the two orthogonal polarizations of the fundamental mode in the PM fiber, and wherein the cross-coupling element and the sensing element are separated along the optical path, and further wherein the cross-coupling element is designed such that shifts in a sensor signal introduced by the wavelength dependence of the cross-coupling element balance signal shifts introduced by the wavelength dependence of further sensor elements; wherein the shifts introduced by the wavelength dependence of further sensor elements include shifts introduced by wavelength dependence of any or all of: the Verdet constant, of retarders or Faraday rotators in the optical path, or of the sensing element.

2. The fiber optic sensor of claim 1, wherein the cross-coupling element and the sensing element are separated by at least one element selected from the group consisting of: at least a section of PM fiber, a retarder, a Faraday rotator, and combinations thereof.

3. The fiber optic sensor of claim 1, wherein the cross-coupling element is a separate element present in addition to the PM fiber.

4. The fiber optic sensor of claim 1, wherein the sensing element is sensitive to an external field selected from an electrical field, a magnetic field or a strain field.

5. The fiber optic sensor of claim 1, wherein the cross-coupling element is designed such that shifts in the sensor signal introduced by the wavelength dependence of the cross-coupling balance signal shifts introduced by the wavelength dependence of the Faraday effect or the electro-optic effect.

6. The fiber optic sensor of claim 1, wherein the cross-coupling element comprises an optical retarder or a Faraday rotator; or wherein the cross-coupling element comprises a retarder detuned from exact half-wave retardance or exact multiple-order half-wave retardance by a non-zero amount or phase (.sub.o); or wherein the cross-coupling element is a fiber retarder comprising a birefringent fiber, an elliptical core fiber or a microstructured birefringent fiber.

7. The fiber optic sensor of claim 1, wherein one of: a) the principal optical axes of the PM fiber and the principal optical axes of the cross-coupling element are rotated against each other by an orientation angle in the range of (4522.5); and b) wherein the cross-coupling element is a halfwave retarder with principal axes forming an orientation angle in the range of 15 or in a range of 90 15 with respect to the principal axes of the PM fiber, and with a half wave retardance (T.sub.0,.sub.0) equal to an integer multiple of 180 within 20 to achieve a sensor signal insensitive to temperature up to second order within a given temperature range.

8. The fiber optic sensor of claim 1, comprising a retarder adjusted to compensate for shifts in the sensor signal caused by temperature changes of the cross-coupling element or of other optical elements in the sensor.

9. The fiber optic sensor of claim 1, comprising a retarder adjusted to compensate for linearly temperature-dependent shifts in the sensor signal caused by temperature changes of any of the elements selected from the group consisting of: the cross-coupling element, the sensing element, and further optical elements in the fiber optic sensor.

10. The fiber optic sensor of claim 1, wherein a quadratically temperature-dependent contribution from the cross-coupling element to the sensor signal counteracts a quadratically temperature-dependent contribution from other elements, to the sensor signal.

11. The fiber optic sensor of claim 1, wherein one of: a) the cross-coupling element is temperature stabilized; and b) the cross-coupling element is located within a common housing with an opto-electronic module comprising at least an active or passive for modulating or biasing the differential phase of light waves.

12. The fiber optic sensor of claim 1, wherein one of: a) the sensing element comprises one of a sensing fiber to be looped around a conductor and to be in operation exposed to a magnetic field of a current I in the conductor, and b) an electro-optical crystal or an electro-optic fiber or a fiber connected to piezo-electric material.

13. The fiber optic sensor of claim 1, wherein one: of a) the sensing element is terminated with a reflective element, and b) the light source is not in thermal contact with active heating or cooling elements.

14. The fiber optic sensor of claim 1, wherein the optical path with the cross-coupling element comprises one of: a) an optical phase modulator between the polarizing element and the sensing element, and b) an optical beam splitter between the polarizing element and the sensing element.

15. A method of measuring a current, a magnetic field, a voltage, an electric field, or a strain field, the method comprising: providing a fiber optic sensor including a light source, a polarizing element, a light detector, a polarization maintaining (PM) fiber, and a sensing element, wherein the fiber optic sensor further comprises a cross-coupling element in an optical path between the polarizing element and the sensing element, generating polarized light using the light source with the polarizing element, passing the light through the polarization maintaining (PM) fiber into the sensing element and from the sensing element back to the light detector to determine a signal indicative of a phase shift in the light, and characterized by using the cross-coupling element located in the optical path between the polarizing element and the sensing element to balance signal shifts introduced by the wavelength dependence due to other sensor elements by shifts in a sensor signal introduced by the wavelength dependence of the cross-coupling element, wherein the shifts introduced by the wavelength dependence of further sensor elements include shifts introduced by wavelength dependence of any or all of: the Verdet constant, of retarders or Faraday rotators in the optical path, or of the sensing element.

16. The method of claim 15, further comprising tuning the cross-coupling between polarization states of the fundamental mode of the PM fiber by introducing in the cross-coupling element a phase shift of m.Math.180+(.sub.0) between the polarization states, wherein m is an integer including zero and (.sub.0) is not zero and is selected such that said cross-coupling balances a wavelength-dependent shift in a measured signal due to other sensor elements.

17. The method of claim 15, further comprising reducing the temperature dependence of the cross-coupling element by providing a thermally stable environment or by using an athermal cross-coupling element; or wherein the cross-coupling element is a half wave retarder with principal optical axes forming an orientation angle in the range of 15 or in a range of 9015 with respect to the principal optical axes of the PM fiber, and with a half wave retardance (T.sub.0, .sub.0) equal to an integer multiple of 180 within 20 to achieve a sensor signal insensitive to temperature up to second order within a given temperature range.

18. The method of claim 15, further comprising using a retarder adjusted to compensate for shifts in the sensor signal induced by temperature changes of the cross-coupling element or of other optical elements in the fiber optic sensor.

19. The method of claim 15, further comprising using a retarder adjusted to compensate for linearly temperature-dependent shifts in the sensor signal induced by temperature changes of any of the elements selected from the group consisting of: the cross-coupling element, the sensing element, further optical elements in the fiber optic sensor.

20. The method of claim 15, further comprising compensating, by a quadratically temperature-dependent shift in the sensor signal from the cross-coupling element, a quadratically temperature-dependent shift in the sensor signal from other elements.

21. The method of claim 15, further comprising using as the sensing element one of a sensing fiber to be looped around a conductor and in operation being exposed to a magnetic field of a current I in the conductor to measure a current or magnetic field or an electro-optical crystal or an electro-optic fiber or a fiber connected to piezo-electric material to measure a voltage or electric field.

22. A fiber-optic sensor, comprising: a light source, a polarizing element, a least two light detectors, a polarization maintaining (PM) fiber, at least three optical transmission channels and a sensing element; wherein the fiber-optic sensor further comprises a cross-coupling element in an optical path between the polarizing element and the sensing element, with the cross-coupling element generating a defined cross-coupling between the two orthogonal polarizations of the fundamental mode in the PM fiber, and wherein the cross-coupling element and the sensing element are separated along the optical path, and further wherein the cross-coupling element is designed such that shifts in a sensor signal introduced by the wavelength dependence of the cross-coupling balance signal shifts introduced by the wavelength dependence of further sensor elements; wherein one channel providing a forward channel for the light to the sensing element and two channels providing return detector channels for the light to the detectors, and an optical polarization splitter module for introducing a static bias optical phase shift between two different sets of light waves, having different velocities within said sensing element in the presence of a non-vanishing measurand field and for converting a total optical phase shift including the static bias optical phase shift and an optical phase shift induced by the measurand field into optical power changes of opposite signs (anti-phase) in the at least two detector channels, and PM fiber being connected directly or indirectly via at least one retarder or Faraday rotator element to the sensing element, wherein the measurand field is a voltage or electric field and the sensing element is responsive to the voltage or electric field and that the sensor is a medium or high-voltage sensor.

Description

BRIEF DESCRIPTION OF THE FIGURES

(1) FIG. 1 is a schematic diagram of a fiber optic sensor head connected to a PM fiber of a sensor in accordance with an example of the invention;

(2) FIG. 2A illustrates a cross-coupling by using a non-exact half-wavelength fiber retarder in a PM fiber;

(3) FIG. 2B illustrates the function of a cross-coupling element;

(4) FIGS. 3A and 3B illustrate examples of the invention as used in sensors of a reflective type with active phase modulation for signal detection;

(5) FIG. 4 is a numerical example of balancing signals shift due to shifts in the center wavelength of light by means of a polarization cross-coupling element;

(6) FIG. 5 is an example of the invention as used in sensors of a reflective type with passive optical elements for signal detection;

(7) FIG. 6 is another example of the invention as used in sensors of a reflective type with passive optical elements for signal detection and a Faraday rotator mirror as terminal of the sensing element;

(8) FIG. 7 shows an example of a temperature-insensitive cross-coupling element;

(9) FIG. 8 shows a cross-coupling element based on a Faraday rotator;

(10) FIGS. 9A and 9B illustrate a fiber-optic voltage sensor in accordance with two examples of the invention having an active phase modulation detection scheme and a detection scheme with passive (static) phase bias, respectively;

(11) FIG. 10 shows a typical normalized sensor signal versus temperature of a state-of-the-art fiber-optic current sensor;

(12) FIG. 11 shows a fiber retarder as an embodiment of the cross-coupling element; and

(13) FIG. 12 shows a calculated normalized sensor signal of a fiber-optic current sensor versus the temperature of the cross-coupling element (solid curve) and versus the common temperature of the sensing element and a fiber retarder at the entrance to the sensing fiber (dashed curve) as well as the combined temperature dependence (dotted curve).

DETAILED DESCRIPTION

(14) In FIG. 1 there is shown a general example of the present invention illustrating configurations of the sensor head 10-1 of a reflective fiber-optic current sensor 10 in a schematic manner. In this general example, a polarization maintaining (PM) fiber lead 11 transfers the light into and back from the sensor head which includes a sensing element 12 being in this example a sensing fiber 12 wound in one or more (N) loops around a conductor 13. Depending on the method of measuring the magneto-optic phase shift, either a superposition of light in both of the two orthogonal polarization states of the fundamental PM fiber mode or only light in one polarization state is injected into the sensing fiber element 12.

(15) Depending on the specific detection technique the linearly polarized light waves may be converted to circular waves before they enter the sensing fiber by using a retarder 14, which in the present example is a fiber-optic QWR (quarter-wave retarder), located at the transition from the PM fiber 11 to the sensing fiber 12. A reflector 15 terminates the sensing fiber 12 at one end. The reflector 15 can for example be a standard mirror (e.g. a reflective coating 15 on the fiber tip) or a Faraday rotator mirror 15. In certain sensors with rotator mirrors, the retarder 14 is omitted or implemented as a (detuned) half-wavelength retarder.

(16) In case where the sensor is a voltage sensor 90, the sensor head 10-1 as shown can be replaced by a different sensor head, in which the sensing fiber is replaced as the sensing element 12 for example by an electro-optic crystal to measure a voltage V applied over the length of the crystal, as detailed in FIG. 9 below.

(17) If a temperature compensation of the sensor 10 is desired, the retarder 14 can be detuned by an angle to (M.Math.180+90+) in case of a quarter-wave retarder or (M.Math.180+) in case of a half-wave retarder as described for example in the references [3, 5, 6].

(18) Also shown in FIG. 1 is an element 16 located in the example between two sections of the PM fiber 11. The element 16 is designed to cause a defined amount of cross-coupling between the two polarization states of the PM fiber 11.

(19) In the context of the present invention the term cross-coupling means that light which has propagated in one polarization state of the fundamental mode, e.g. LP.sub.01(x), before the cross-coupling element 16 is split onto both states, LP.sub.01(x) and LP.sub.01(y).

(20) It should be noted that this element 16 need not be located between sections of the PM fiber 11 to achieve such a cross-coupling, but instead can be located anywhere in the optical path between an initial linear polarizer and the sensing element 12 (though not directly coupled to its proximate end), for example between the linear polarizer and PM fiber 11, or between PM fiber 11 and retarder 14. In embodiments where a light source generates directly light with the desired polarization, such as specifically designed laser, such a light source is understood to include the initial polarizer.

(21) Details of an example of the cross-coupling element 16 and its function are illustrated in FIGS. 2A and 2B. In FIG. 2A the cross-coupling element 16 is shown as a non-achromatic fiber-optic retarder integrated within the PM fiber 11. Below the illustration of the fiber 11, there is shown a graph indicating the relative orientation of fast and slow axes of the fiber retarder 16 with respect to the principal axes of the PM fiber 11. The orientation and in particular the length (i.e. the differential phase retardance between the orthogonal polarization states) of the retarder 16 is designed to cause a controlled amount of polarization cross-coupling (or mode mixing) between the two orthogonal polarization states of the fundamental mode of the PM fiber 11, LP.sub.01(x) and LP.sub.01(y), as indicated in FIG. 2B for sensors using both orthogonal polarization states (upper half of FIG. 2B) or sensors using only one polarization state (lower half of FIG. 2B).

(22) The cross-coupling changes the scale factor (or sensitivity) of the sensor 10 in a defined manner. Since the retardance of the retarder 16 and thus the cross-coupling varies with wavelength, it can be used to compensate for variations in the Verdet constant and other sensor parameters which change when drifts in the wavelength of the light occur. The phase retardance of the retarder 16 at the center wavelength is set in this example to m.Math.180+(m=0, 1, 2, 3, . . . ), with m=0 being a possible choice when >0.

(23) It should be noted that if the retarder 16 were an exact zero-order or multiple order half-wave retarder (i.e. =0) there would be no additional cross coupling between the orthogonal modes of the PM fiber lead. As the retardance achieved with the cross-coupling element 16 varies with the actual wavelength in a known manner, can be set to compensate for a change in the sensor signal, in particular of its scale factor, due to the change of the Verdet constant with wavelength. The method can also compensate the wavelength dependence of other elements in the optical path, in particular of the retarder 14 at the entrance to the sensing fiber 12 as shown in FIG. 1 above.

(24) The compensation of the wavelength dependence as described above can be integrated in all fiber-optic current sensor configurations, in which a PM fiber lead transfers the light to the sensing fiber and/or from the sensing fiber. In the reflective sensor configurations of FIG. 1 the cross-coupling occurs both during the forward and return travel of the light.

(25) In the following, there is shown in greater detail, how the cross-coupling element 16 can be integrated into three distinct sensor configurations: a fiber-optic current sensor with non-reciprocal phase modulation for phase biasing (illustrated in FIG. 3), a fiber-optic current sensor with a quarter-wave retarder for passive phase biasing (FIG. 5), and a fiber-optic current sensor with a Faraday rotation mirror for passive phase biasing (FIG. 6).

(26) These designs differ in how the magneto-optical birefringence in the sensing fiber is detected and with the cross coupling element 16 being adapted accordingly.

(27) In a fiber-optic current sensor design with non-reciprocal phase modulation, as shown in FIG. 3A, light is injected, preferably from a low coherent light source 1 such as a superluminescent diode, after passing through an optical fiber, a fiber coupler 101 and an initial optical fiber polarizer 2, which reduces the emitted light into a single linear polarized state, injected at a 45 fiber splice 3 into both orthogonal polarization states of the PM fiber 11, which in turn are projected onto circular or close to circular light states in the sensing fiber 12 by a fiber-optic retarder 14. The two light states in the sensing fiber 12 acquire a magneto-optic phase delay due to the applied electrical current (Faraday effect). The phase delay is detected by means of a closed-loop detection circuit that includes an optical phase modulator 4 and a detector 5 linked to the optical path by the fiber coupler 101. The optical phase modulator 4 and the detector 5 are also electrically linked through a signal processor 6 for the closed loop detection. Alternatively, an open-loop detection circuit may be used.

(28) It should be understood that in these as in the following examples components cited can be replaced by components with identical or similar functionality. For example, the light source 1 mentioned can be replaced by other types of light sources 1, such as light emitting diodes (LEDs), edge-emitting LEDs, vertical-cavity surface-emitting lasers (VCSELs), doped-fiber light sources, or laser diodes. Similarly, the modulator 4 of FIG. 3A may be an integrated-optic birefringence modulator, such as a lithium niobate modulator, or a piezoelectric modulator. The latter modulates the differential phase of the orthogonal polarization states by modulating the optical length of a section of PM fiber 11 that is attached to the modulator.

(29) As described in the references cited, the quarter-wave retarder 14 can be detuned from exact quarter-wave retardance by to achieve an intrinsic temperature compensation of the sensor (also a higher order retarder can be used, such that the retardance of the quarter-wave retarder amounts in total to =M.Math.180+90+ where M=0, 1, 2, 3, . . . ), see for example references [3, 5, 6].

(30) In the case of no birefringence in the sensing fiber 12 apart from the magneto-optic birefringence, the current signal at small magneto-optic phase shifts of sensors according to FIGS. 3A, 3B is in good approximation proportional to
S(1).sup.MV(T,)NI/cos (T,)[1]

(31) Here, N is the number of loops of the sensing fiber coil 12, and I the current in the conductor 13. A change in sign indicates a phase shift of 180 between the current and the resulting signal. The Verdet constant V generally varies linearly with temperature T and is a function of wavelength . M and (T.sub.0, ) can be chosen so that the current signal becomes independent of temperature, as done in the references mentioned above. Here, T.sub.0 is a reference temperature, e.g. room temperature.

(32) In the prior art, the wavelength is commonly kept stable by working with a temperature-stabilized light source 1. If the wavelength shifts by (herein assuming /.sub.0<<1), the relative signal change S/S.sub.0 (with S.sub.0 being a central or an undisturbed signal) is given by
S/S.sub.0=(2tan (T,.sub.0)[M.Math.180+90+(T,.sub.0)])/.sub.0[2]

(33) wherein the first term, i.e. 2 /.sub.0, results from the wavelength dependence of the Verdet constant V, and the second term results from the wavelength dependence of the retarder 14 when assuming that the retardance of the retarders 14 varies inversely proportional to the wavelength and that the Verdet constant of the sensing fiber 12 shows quadratic dispersion as previously reported, see ref. [8]. In case of a different type of dispersion, the principle of this calculation is not altered, but the values given herein for have to be adapted.

(34) Eq. [2] has been derived from a description of the wave propagation in the optical circuit by means of the Jones matrix formalism, which is shown in general form in reference [15]. As noted, in the references cited above, M and (.sub.0) are chosen so that the overall current signal becomes nearly independent of temperature. For instance, with a temperature dependence of the Verdet constant of C.sub.Verdet=0.7.Math.10.sup.4 C..sup.1 in fused silica fiber and assuming a temperature coefficient of the retarder of C.sub.QW=2.4.Math.10.sup.4 C..sup.1 a quarter-wave retarder having M=0 and (.sub.0)=9.5 results in an essentially (linearly) temperature independent signal. This sensor of prior art however still yields, according to eq. [2], a relative (combined) wavelength dependence of S/S.sub.0=(20.29) /.sub.0=2.29 /.sub.0.

(35) This wavelength dependence can be balanced in accordance with the example shown by using a retarder as cross-coupling element 16 with retardance m.Math.180+() arranged in the optical path of the emitted light after the polarizer 2 but before the retarder 14. In the example, the cross-coupling retarder 16 is included in the opto-electronic module 10-2 which comprises most components of the sensor 10 with the exception of the components of the sensor head 10-1 and parts of the PM fiber 11. The opto-electronic module 10-2 and the sensor head 10-1 are optically connected through the PM fiber 11. The cross-coupling element 16 can be maintained at constant temperature separately or inside a housing of the opto-electronics module 10-2.

(36) The wavelength-dependence-compensating retarder 16 is essentially a zero or multiple order half-wave retarder (HWR) with a phase deviation () from perfect half-wave retardance. Using such a cross coupler 16 and assuming small magneto-optic phase shifts NVI (NVI<<1), the signal S is approximately proportional to
S(1).sup.M+mV()NI/[cos ()cos ()][3]

(37) The relative change S.sub.HWR in sensor signal at a wavelength change resulting from the extra retarder 16 can be written as
S.sub.HWR/S.sub.0=tan (.sub.0)[m.Math.180+(.sub.0)]/.sub.0[4]

(38) with .sub.0 being the nominal center wavelength of the sensor 10 and in particular S.sub.0=S(.sub.0). The integer m and the deviation or phase (.sub.0) from perfect half-wave retardance can be adjusted so that the term S.sub.HWR/S.sub.0 of eq. [4] balances the term S/S.sub.0 of eq. [2], i.e. the current signal becomes independent of wavelength.

(39) For instance, m=2 and (.sub.0)21 can be chosen to effectively compensate the wavelength dependence of the Verdet constant and of the quarter-wave retarder 14. In the above derivation it is assumed that the temperature of the compensating cross-coupling retarder 16 is kept constant or that its retardance is essentially independent of temperature. As mentioned and described below in more details, this can be for example achieved by placing the cross-coupling element 16 in a constant temperature environment.

(40) In embodiments, already (.sub.0)20 or (.sub.0)>20 (i.e. (.sub.0) being less negative than 20) can effect a partial (yet useful) compensation of the wavelength dependence of the Verdet constant and of the quarter-wave retarder 14.

(41) In a variant of these examples as shown in FIG. 3B, the phase modulator 4 of the type as shown (birefringence modulator) may be replaced by a y-type integrated optic phase modulator 41 with PM fiber pig tails as often used in fiber-optic gyroscopes and a polarization-maintaining fiber coupler 43 as described in more detail in references [19, 20]. In this example, the modulator 41 also acts as initial polarizer. The two light waves with parallel polarization directions emerging from the modulator are projected onto the orthogonal linear polarization states of the pm fiber 11 by a 90-fiber splice 42 and by the polarization-maintaining fiber coupler 43. The second arm of the modulator 41 includes an optical delay element 44.

(42) The half-wave retarder 16 is then preferably arranged in the PM fiber link 11 between the fiber coupler 43 and the sensing fiber coil 12. Alternatively, an appropriately adjusted half-wave retarder can be placed into each of the two fiber arms between the y-modulator 41 and the PM coupler 43.

(43) In this example, the cross-coupling element 16 is shown in a temperature-controlled housing 160 spatially separated from the other components. This arrangement can be regarded as an alternative to including the cross-coupling element 16 in the opto-electronic module 10-2.

(44) In FIG. 4 there is shown the variation of sensor signal S vs. wavelength of a compensated sensor together with the individual contributions from Verdet constant S(V()), the quarter wave retarder S(()) and the compensating cross-coupling retarder S(()). The signal variation without compensation (combined contribution from Verdet constant and quarter-wave retarder) corresponds to 3.5% for the wavelength span (20 nm) in FIG. 4. The residual signal variation after compensation is negligible.

(45) In a fiber-optic current sensor design with splitter and with passively generated phase bias as shown in FIG. 5, the same design for the sensor head 10-1 is used as in the previous embodiments (e.g. FIG. 1). Instead of closed-loop detection with an optical phase modulator 4, 41 as in the previous example of FIG. 3, a detection scheme with a passively generated phase bias is employed in this example, as described in detail in reference [16]. In such an arrangement, the sensor 10 includes again a light source 1 which preferentially generates non-polarised light to enter an optical path with an optical fiber, an initial linear polarizer 55a (in 45 orientation with respect to the axes of the PM fiber 11) attached via a spacer 53 made of glass to an integrated-optic splitter 54. The light exits the integrated-optic splitter 54 via a PM fiber 11 with a cross-coupling element 16. The light returning from sensing fiber 12 is split and then passes a quarter-wave retarder and appropriately oriented polarizers 55b, 55c. The retarder 56 introduces a 90-phase-bias between the returning light waves. The light is guided through two optical fibers to the respective detectors 5-1, 5-2, which can be photodiodes. The signals S.sub.1,2 at the two detectors 5-1 and 5-2 are given by
S.sub.1,21(1).sup.M cos sin 4NVI[5]

(46) Dividing the difference of the two signals by their sum gives a signal that is independent of the light source power and is proportional to
S(1).sup.MV(T,)NI cos (T,)[6]

(47) Here, it is assumed that 4NVI<<1. The fiber quarter-wave retarder 14 at the near end of the sensing fiber 12 is again used to achieve a temperature independent current signal, i.e. the retarder deviates by an appropriate amount from perfect quarter-wave retardance, see also reference [16]. It should be noted that the retarder 56 and spacer 53 can also be interchanged such that the phase bias is introduced in front of the sensor head 10-1.

(48) As in the previously described embodiments, another fiber retarder 16 is inserted as cross-coupling element 16 in the PM fiber lead 11 of the sensing coil 12 to achieve a wavelength-independent current signal. With the introduction of the additional retarder 16 the current signal is approximately proportional to (when again assuming that the sensing fiber is free of any non-magneto-optic birefringence)
S(1).sup.M+mV()NI cos ()cos ()[7]

(49) Analogously to the previous case, (.sub.0) and N can be chosen such that the individual contributions to the overall wavelength dependence of the current signal compensate each other. The retardance of the quarter-wave retarder can be set to M=0 and (.sub.0)=9.5 to balance the temperature dependence of the Verdet constant (assuming that the sensing fiber is free of linear birefringence). The relative wavelength dependence of the sensor signal amounts to
S/S.sub.0=/.sub.0(2+[M.Math.180+(.sub.0)] tan (.sub.0)+[m.Math.180+(.sub.0)] tan (.sub.0))[8]

(50) In the given example, the half-wave retarder 16 can be set to N=2 and (.sub.0)=21 to compensate the variations of the sensor signal with wavelength due to the combined contributions from the Verdet constant and the quarter-wave retarder: S/S.sub.0=(20.29) /.sub.0=2.29 /.sub.0. Note that the absolute value of (.sub.0) is the same as for the sensor designs with non-reciprocal phase modulation (FIG. 3A, FIG. 3B) but the sign is opposite. With the values above, the individual signal contributions are again as those shown in FIG. 4.

(51) In embodiments, already (.sub.0)+20 or (.sub.0)<+20 (i.e. (.sub.0) being smaller than +20) can effect a partial (yet useful) compensation of the wavelength dependence of the Verdet constant and of the quarter-wave retarder 14.

(52) In another embodiment as illustrated in FIG. 6 the sensor coil 12 is terminated by a Faraday polarization rotator mirror 15 for phase biasing (see also references [17, 18] for further details). The Faraday rotator 15 biases the current induced magneto-optical phase shift by 90, i.e. this rotator 15 corresponds to a single pass polarization rotation angle of 22.5 (or equivalently a single pass differential phase shift of 45 for left and right circular light waves).

(53) Hence, light from the light source 1 is guided through an optical fiber into a combined polarizing splitter 24 and into the PM fiber 11 with an integrated cross-coupling element 16. On the return after being reflected and phase-shifted by the rotation mirror 15, the signals at the two detectors 5-1, 5-2 are equivalent to the signals in the previous configuration and are given by:
S.sub.1,2[1sin(4NVI+4)].[9]

(54) The term (T, ) is the deviation of the single pass rotation angle of the Faraday rotator from 22.5. Dividing the difference of the two signals by their sum again gives a signal that is independent of the light source power (with the assumption 4NVI<<1):
SV(T,)NI cos 4(T,)[10]

(55) The half- or quarter-wave retarder 14 in some sensor designs between the PM fiber 11 and the sensing fiber 12 (see also FIG. 1) is set to zero for the sake of simplicity (M=0 and =0). By including an extra retarder as cross-coupling element 16 in the PM fiber link 11 to achieve the disclosed controlled, wavelength-dependent polarization cross-coupling, the current signal is as well proportional to cos.sup.2(). Proper adjustment of N and enables compensation of the wavelength dependence of the current signal, including a compensation of the wavelength dependence of the Faraday rotator 15 and the sensing fiber 12.

(56) The compensation for wavelength dependency is not limited to the wavelength-dependent contributions from the Verdet constant of the sensing fiber 12 and contributions from the retarder 14. It can also compensate other contributions, such as those of the embedded linear birefringence in a spun, highly birefringent sensing fiber 12 or of the bend-induced linear birefringence in a sensing fiber 12 with low intrinsic birefringence. Hence, the value of has to be appropriately adapted, if the cross-coupling element 16 is also to compensate for those elements.

(57) In the above variants it was assumed that the cross-coupling element 16 is kept at constant temperature by a temperature stabilization environment 160. Particularly, in the sensor according to FIG. 3A or FIG. 3B, the extra retarder 16 is preferably part of the opto-electronic module 10-2. At this location, a stable temperature of the cross-coupling element 16 can be achieved, for example by means of a thermoelectric cooler/heater (not shown).

(58) In addition or alternatively, the temperature of the cross-coupling element 16 can be measured and the temperature-dependence of the cross-coupling element 16 can be corrected at a signal processing stage. Small or negligible temperature dependence of the element 16 can also be achieved through the use of a fiber with low temperature dependence of the differential phase shift such as polarization-maintaining fibers with birefringence determined by their geometrical structure, e.g. elliptical core or micro-structured fibers. Such fibers are known to show a relatively weak temperature dependence in comparison to fibers with stress induced birefringence.

(59) A compensation of the temperature-dependence of element 16 can also be achieved, if both the cross-coupling element 16 in the PM fiber link and the retarder 14 at the beginning of sensing fiber 12 are subject to the same ambient temperature. In such a case the additional temperature contribution stemming from the cross-coupling element 16 can be balanced by an extra contribution from the retarder element 14 to the overall temperature dependence of the signal. Taking again a configuration as in FIG. 3 as an example, the relative signal change due to a temperature change T of the cross-coupling element 16 amounts to S/S.sub.o=tan (T.sub.0,.sub.0) [N.Math.180+(T.sub.0,.sub.0)]C.sub.HWT, wherein the constant C.sub.HW describes the relative change of the retardance with temperature. Both retarders 14, 16, i.e. m, M, , and , can be adjusted so that the overall temperature dependence as well as the overall wavelength dependence vanishes. In more detail, the parameters have to be chosen so that not only dS/d=0 (or small) is fulfilled (as in the examples above), but also dS/dT=0 (or small), which in the example of FIG. 3A results in:
0=2tan (T.sub.0,.sub.0)[M.Math.180+90+(T.sub.0,.sub.0)]tan (T.sub.0,.sub.0)[m.Math.180+(T.sub.0,.sub.0)][11]
and
0=C.sub.Verdet+C.sub.QW tan (T.sub.0,.sub.0)[M.Math.180+90+(T.sub.0,.sub.0)]+C.sub.HW tan (T.sub.0,.sub.0)[m.Math.180+(T.sub.0,.sub.0)][12]

(60) As a further alternative or in addition to other thermal stabilization methods as described above, it is possible to prepare the cross-coupling element 16 as an athermal retarder. This can be achieved as illustrated in FIG. 7. Here, the cross coupling element 16 consists of two sections of PM fiber: a fiber section 16-1 of length l.sub.1 with small temperature dependence (e.g. an elliptical-core fiber) and a section of length l.sub.2 with larger temperature dependence (e.g. a Panda fiber). The two fiber sections 16-1, 16-2 are joined with a 90-offset in the orientation of their principal axes. As a result the birefringent phase changes due to temperature changes add with opposite sign and tend to cancel each other. Assuming for simplicity that the birefringence n (and beat length) of both fiber sections is the same but the temperature coefficients differ by a factor of 5, the combined phase retardance of the two fiber sections will be independent of temperature if the length ratio is chosen as: l.sub.1:l.sub.2=5:1. The length l.sub.1 must be chosen as l.sub.1=(5/4).sub.0/(2n) in order to achieve the desired total retardance of at reference center wavelength .sub.0.

(61) It should be noted that the above described methods and components for reducing the temperature dependence of the sensor 10 can be used separately or in isolation from each other or in combination with each other.

(62) While only reflective sensor configurations are considered in the above examples, the invention also applies to Sagnac-type fiber optic current sensors, see for example reference [3] and other types of non-reflective fiber-optic current sensors that contain a PM fiber lead to transmit light from or to the sensing fiber. In a Sagnac-type current sensor according to reference [3], at least one appropriately adjusted cross-coupling element can be included into each of the PM fiber leads of the sensor. As a result of the application of the half-wave retarders, part of the light travels with a polarization orthogonal to the launched polarization direction in between the retarders. Thereby, the sensitivity of the sensor can be controlled in a wavelength dependent manner, since the cross-coupled light experiences a Faraday phase shift of opposite sign.

(63) In the detailed embodiments disclosed in this document, a 45 degree angle between the axes of the PM fiber 11 and the axes of the retarder 16 is assumed. It is preferred that the tolerances of this angle (i.e. orientation angle ) remain within (4510) or at least within (4522.5). However, it is to be understood that an angle different from 45 can also be chosen intentionally. In this case the retardance of cross-coupling element 16 must be adapted accordingly in order to achieve again full compensation of effects of source wavelength shifts on the sensor signal sensitivity.

(64) In the examples shown, the cross-coupling retarder 16 is integrated between two parts of the PM fiber 11, which is in most cases the preferred location. However, it is also possible to place the cross-coupling retarder 16 between the phase modulator 4 and the PM fiber 11, between the 45-splice 3 and the phase modulator 4, or between beam splitter 54 and the PM fiber 11 or even integrate it into the beam splitter 54. On the other hand, it is possible to position the cross-coupling element 16 just before the components of the sensor head, e.g. between distal end of the PM fiber 11 and any additional retarder such as retarder 14.

(65) Depending on the sensor embodiment, the cross-coupling element is preferred to be in a common housing with the phase modulator 4 or the beam splitter 54.

(66) In another embodiment as illustrated by FIG. 8, a Faraday rotator can be used as cross-coupling element 16. A Faraday rotator 16 comprises a magneto-optic crystal 161 and a permanent magnet 162 exerting a magnetic field on the crystal 161. A fiber-coupled Faraday rotator 16 typically comprises in addition lenses 163 to couple the light into and out of the PM fiber 11. The crystal 161 rotates incoming linear light polarization states by an angle defined by the type and length of the crystal 161 and by the magnetic field of the permanent magnet 162.

(67) To achieve wavelength compensation, the Faraday rotator 16 can be set for example to a single-pass rotation angle of i*90+ at the wavelength .sub.0, wherein i is any integer including zero and a bias rotation angle. Due to the wavelength dependence of the magneto-optic effect in the crystal, is wavelength dependent, e.g. .sup.2. With 0, this Faraday rotator 16 generates a wavelength dependent cross coupling between the two polarizations of the PM fiber as described previously. Accordingly, i and can be chosen to balance all wavelength dependent contributions to the sensor signal similar to the case of retarder described in detail before.

(68) The invention can also be used with sensors that work with orthogonal linear polarizations in the sensing medium rather than circular polarizations and that employ detection schemes according to FIG. 3A, 3B and FIG. 5. Patent publication WO 2008/077255A1 (cited as reference [21]) discloses for example, how the detection schemes according to FIGS. 3A, 3B with active phase modulators can be adapted for sensing elements that work with orthogonal linear polarizations, see also Ref. [22, 23]. Even though not explicitly mentioned in Ref. [21], the adaptation is also valid for detection schemes with passive phase biasing, such as described above with reference to FIG. 5.

(69) As mentioned above when referring to FIG. 1, aspects of the invention include the use of a cross-coupling element 16 in an optical voltage or electric field sensor 90. A first example of such a sensor is shown in FIG. 9A. The general arrangement and previously known components are described in further detail for example in reference [21]. As in FIG. 3A, the detection system includes a light source 1, a fiber coupler 101, a polarizer 2, a polarizer 3, an active phase modulator 4, a detector 5 and a signal processor 6. Two light waves with orthogonal polarization directions are again injected in a PM fiber 11 and sent towards the sensing element 12. For voltage measurements, the sensing element 12 of FIG. 9A includes a rod shaped electro-optic crystal 12, such as e.g. a Bi.sub.3Ge.sub.4O.sub.12 (BGO) crystal to measure a voltage applied over the length of the crystal 12. Instead of a bulk electro-optic crystal a crystalline electro-optic fiber (e.g. also of Bi.sub.3Ge.sub.4O.sub.12) [24] or an electrically poled fiber, as described for example in reference [25], can be used, as well.

(70) A Faraday polarization rotator 14 rotates the two orthogonal light waves emerging from PM fiber 11 by 45 before they enter the electro-optic crystal 12. The polarization directions after the Faraday rotator 14 coincide with the electro-optic axes of the crystal 12. The light is reflected at the far end of the crystal 12 by the reflector 15. The two orthogonal light waves experience a differential electro-optic phase shift in the crystal 12 that is proportional to the applied voltage. The Faraday rotator 14 rotates the returning light waves by another 45 so that the total roundtrip polarization rotation corresponds to 90 like in the current sensor of FIG. 3A. (The polarization rotation is needed so that the roundtrip group delay of the orthogonal polarization states in PM fiber 11 is zero and the two waves are again coherent when they interfere at the polarizer. Moreover, the modulation concept assumes swapped polarization states on the return path.)

(71) The cross-coupling element 16 in the PM fiber is added again to compensate for wavelengths shifts of the light source. Assuming the cross-coupling element 16 is a detuned half-wave retarder, and the detuning angle or detuning phase shift (.sub.o) is now adjusted so that the cross-coupling element 16 balances the wavelength dependence of the electro-optic effect. Other than the Faraday effect (Verdet constant) the electro-optic effect varies in proportion to the inverse of the wavelength (rather than the inverse of the square of the wavelength). As a result the proper value of (.sub.o) in case of the electro-optic effect is only half the value of (.sub.o) in case of the Faraday effect. Moreover, (.sub.o) can be chosen such that it compensates for the wavelength dependence of Faraday rotator 14 (and possibly further components) in addition to compensation for the wavelength dependence of the electro-optic effect.

(72) A second example of a voltage sensor 90 is shown in FIG. 9B. The sensing element 12 includes a rod shaped electro-optic Bi.sub.3Ge.sub.4O.sub.12 (BGO) crystal 12 to measure a voltage applied over the length of the crystal 12. Instead of a bulk electro-optic crystal 12 an electro-optic fiber 12 may be used such as a crystalline fiber [24] or an electrically poled fiber, as described for example in reference [25].

(73) A Faraday polarization rotator 14 rotates the two orthogonal light waves emerging from PM fiber 11 by 45 before they enter the electro-optic crystal 12. The polarization directions after the Faraday rotator 14 coincide with the electro-optic axes of the crystal 12. The light is reflected at the far end of the crystal 12 by means of reflector 15. The two orthogonal light waves experience a differential electro-optic phase shift in the crystal 12 that is proportional to the applied voltage. The Faraday rotator 14 rotates the returning light waves by another 45 so that the total roundtrip polarization rotation corresponds to 90.

(74) In the example of FIG. 9B a detection scheme with a passively generated phase bias is employed, as described in detail in reference [16] and with reference to FIG. 5 above. In such an arrangement, the sensor 90 includes again a light source 1 which preferentially generates non-polarized light to enter an optical path with an optical fiber, an initial linear polarizer 55a (in 45 orientation with respect to the axes of the PM fiber 11) attached via a spacer 53 made of glass to an integrated-optic splitter 54. The light exits the integrated-optic splitter 54 via a PM fiber 11 with an optional cross-coupling element 16. The light returning from the sensor head 10-1 is split and then passes a quarter-wave retarder 56 and appropriately oriented polarizers 55b, 55c. The retarder 56 introduces a 90-phase-bias between the returning light waves. The light is guided through two optical fibers to the respective detectors 5-1, 5-2, which can be photodiodes. It should be noted that the retarder 56 and spacer 53 can also be interchanged, i.e. with the spacer element in front of the polarizers 55b and 55c such that the phase bias is introduced prior to entering the sensor head 10-1. In the example of FIG. 9B the initial linear polarizer 55a (in 45 orientation with respect to the axes of the PM fiber 11) the spacer 53, the 13 integrated-optic splitter 54, the quarter-wave retarder 56 and the polarizers 55b, 55c are shown as an single integrated passive optical module, herein referred to as integrated optical polarization splitter module 50.

(75) It should be further noted that the compensation provided by the cross-coupling element 16 is optional for operation of the sensor of FIG. 9B. Hence in a variant of the example of FIG. 9B the cross-coupling element 16 and its temperature stabilizing environment 160 can be omitted, in particular when the light source is itself temperature stabilized.

(76) There is a variety of options how to install a voltage sensor of this kind in high voltage power transmission systems. In air-insulated substations the sensing element may be mounted in an insulator with gas [26] or dry insulation [27]. The insulator may be installed as a free-standing insulator or hanging from a power line. In gas-insulated switchgear it may be installed in ways as disclosed in [28] and [29]. Furthermore, the sensing element may be part of a capacitive voltage divider and measure only a fraction of the line voltage [30]. It should be noted that instead of the integrated-optic splitter (54) with waveguides as shown in FIGS. 5, 9B, a splitter of the same functionality can be made using bulk components, e.g. using beam splitter cubes and/or prisms.

(77) The method of the present invention can be applied for compensation of wavelength shift also in other sensor configurations, for example those disclosed in Ref. [21]. In particular, the sensing element 12 may represent an optical voltage sensor based on the piezo-electric effect in materials such as quartz. The quartz element(s) strain(s) a PM sensing fiber in the presence of an applied voltage and as a result introduce(s) again a voltage-dependent phase shift between the orthogonal polarization states of the sensing fiber (see ref. [21] for further details). The PM sensing fiber may also in a similar manner act as a sensor for strains or forces of other origin.

(78) Note that the Faraday rotator 14 of FIG. 9 has a function different from the Faraday rotator of FIG. 8, which acts as a cross-coupling element 16 and different from the Faraday rotator 15 of FIG. 6, which acts as a phase biasing element.

(79) The light source may already emit light with a sufficiently high degree of linear polarization due to inherent polarization means or an integrated polarizer. In this case, at least parts of the functionality of the polarizers 2, 41, 55a, 24 as shown in FIGS. 3A, 3B, 5, and 9 can be incorporated into the light source. This requires all fiber components between source 1 and sensor element 12 to be polarization-maintaining.

(80) In the following, the further aspect of the invention is discussed in detail. For the fiber-optic current sensor configurations similar to FIGS. 3A, 3B but not including the shown cross-coupling element 16, the current signal is in good approximation proportional to the expression given in equation [1], with the two temperature dependent contributions from V(T,) and (T,). The linear temperature dependence results in a relative change S/S.sub.0 of the sensor signal (with S.sub.0 being a central or undisturbed signal) given by equation [13]:
S/S.sub.0=T.Math.(C.sub.Verdet+C.sub.QW.Math.[M.Math.180+90+(T.sub.0,.sub.0)].Math.tan [(T.sub.0,.sub.0)])[13]
wherein T=temperature change of the cross-coupling element 16, C.sub.Verdet=temperature dependence of the Verdet constant, C.sub.QW=temperature coefficient of the retarder, M=0, 1, 2, 3, . . . , =detuning from quarter-wave retardance, T.sub.0=reference temperature, and .sub.0=reference wavelength. With the example parameters selected herein to be M=0, C.sub.Verdet=0.710.sup.4 C..sup.1 and C.sub.QW=2.410.sup.4 C..sup.1, the linear term of the temperature dependence substantially vanishes by setting (T.sub.0,.sub.0)=9.5.

(81) However, a parabolic, i.e. quadratic, term remains which can be found from the equation [13] by Taylor series expansion as follows:
S/S.sub.0=0.5.Math.T.sup.2.Math.(tan.sup.2 [(T.sub.0,.sub.0)]+sec.sup.2 [(T.sub.0,.sub.0)]).Math.(C.sub.QW.Math.[M.Math.180+90+(T.sub.0,.sub.0)]).sup.2[14]

(82) With the numerical example parameters from above, the quadratic contribution to S/S.sub.0 amounts approximately to 9.Math.10.sup.8 C..sup.2, i.e. to 0.033% at 60 C. above or below the reference temperature T.sub.0. In real sensor systems the quadratic signal contribution may exceed this value as shown in FIG. 10, where it reaches about 0.1% at the extreme temperatures.

(83) This quadratic temperature dependence can be compensated for according to the further aspect of the invention. A cross-coupling element 16 providing a defined temperature dependent cross-coupling is inserted into the optical circuit of a fiber-optical sensor, such as fiber-optical current sensor 10 as shown in FIGS. 1, 3A, 3B, 5, and 6 or a fiber-optical-voltage sensor 90 as shown in FIGS. 9A and 9B. The cross-coupling element is e.g. placed between the polarizing element 2, 41, 55a, 24a and the sensing element 12 so that the cross-coupling is separated from the sensing element 12 by at least a retarder 14, a Faraday rotator 14, or a section of polarization maintaining fiber 11. The disclosed invention can be applied to different embodiments of fiber-optic sensors, of which some are described in more detail herein with respect to their design and working principle. As the cross-coupling element 16 is preferably exposed to a temperature as similar as possible to the temperature of the sensing element 12, a configuration with element 16 being spatially close to the sensing element 12, e.g. by sharing a common housing with the sensing element 12, is preferred. In other less favourable embodiments the element 16 can be a part of the opto-electronic module 10-2, as indicated in FIG. 3A.

(84) Temperature-dependent contributions to the signal candepending on the sensor designoriginate from the temperature dependence of the magneto-optic effect in the sensing element 12 (given by the temperature dependence of the Verdet constant), of the electro-optic effect of the sensing element 12, e.g. given by the temperature dependence of the Pockels effect, of the piezo-electric effect of a piezo-electrical material attached to the sensing element, of the intrinsic birefringence in the sensing element 12 such as in a spun highly-birefringent optical fiber, of bend-induced birefringence in the sensing fiber 12, of the working point of the sensor, e.g. in a sensor configuration where the working point is adjusted by a Faraday rotator mirror 15 (FIG. 6), of a fiber retarder at the entrance to the sensing fiber 14, of a Faraday rotator 14 at the entrance of the sensing element 12 (FIGS. 9a and 9b), of mechanical stress exerted on the sensing fiber, or of combinations thereof.

(85) For further description, the embodiment of a fiber-optical current sensor 10 using an optical phase modulator 4 between the polarizing element 2 and the cross coupling element 16 as in FIG. 3A is considered in more detail. Nevertheless, the invention can be equally applied to different embodiments of fiber-optic sensors, in particular to embodiments with an optical splitter 54 between the polarizing element 55 and the cross coupling element 16, with the following mathematical expressions and quantitative values being subject to proper modification. Furthermore, it is assumed that the linear temperature variation due to the Verdet constant in the sensing fiber 12 is counteracted by the temperature dependence introduced by the fiber retarder 14 (see equation [13]), i.e. in the numerical example above (T.sub.0, .sub.0) is set to 9.5. In this case, the quadratic contribution to be compensated by the temperature dependent cross-coupling of element 16 amounts to 910.sup.8 C..sup.2. In this embodiment, the cross-coupling element 16 is represented by an optical retarder 16, preferably a fiber-based retarder 16 built from a short section of polarization maintaining fiber, with its principal axes aligned under an orientation angle of with respect to the incoming light polarization. For example, the retarder 16 can be inserted into the polarization maintaining fiber section 11 as depicted in FIG. 11. Preferably, all polarization maintaining fiber sections 11 have a length so that the relative phase delay exceeds the coherence length of the light source utilized. With the retardation of the cross-coupling element 16 denoted by , the signal can be approximately calculated to be
SV(T,).Math.NI/(cos [(T,)].Math.{cos.sup.2 [2]+cos [(T,)].Math.sin.sup.2 2})[15]

(86) Note that by setting =45, this expression coincides with the expression given in equation [3].

(87) Accordingly, by setting the retardance (T.sub.0,.sub.0) (i.e. half wave retardance or generally retardance of the cross-coupling element 16) to an integer multiple of 180, the cross coupling element 16 does not introduce a linear temperature dependence. Under the assumption of a vanishing second order temperature dependence of the Verdet constant, the overall second-order temperature dependence then becomes:
S/S.sub.0=0.5.Math.T.sup.2.Math.{(tan.sup.2 [(T.sub.0,.sub.0)]+sec.sup.2 [(T.sub.0,.sub.0)]).Math.(C.sub.QW.Math.[M.Math.180+90+(T.sub.0,.sub.0)]).sup.2+(C.sub.HW.Math.(T.sub.0,.sub.0)).sup.2.Math.cos [(T.sub.0,.sub.0)].Math.sin.sup.2 [2]/(cos.sup.2 [2]+cos [(T.sub.0,.sub.0)].Math.sin.sup.2 [2])}[16]

(88) Accordingly, by setting the retardance (T.sub.0,.sub.0) of the cross-coupling element 16 to an odd multiple of 180, the quadratic temperature-dependent contribution from the cross-coupling element 16 to the sensor signal counteracts the quadratic temperature-dependent contribution from the retarder 14 to the sensor signal. Proper choice of orientation angle(s) depending on the temperature variation of retardance (T.sub.0,.sub.0)=m.Math.180 (with m being an odd integer) given by C.sub.HW.Math.(T.sub.0,.sub.0)results in a vanishing quadratic temperature variation, i.e. together with the temperature compensation by the detuned quarter-wave retarder 14, the sensor signal becomes independent of temperature up to third order variations in temperature. Overall, the parabolic=quadratic coefficient introduced by the cross-coupling element 16 can be tuned by choice of the orientation angle , the order of the retarder m, and the quantity C.sub.HW. The quantity C.sub.HW is given by the temperature dependence of the birefringence of the optical fiber used for the fiber retarder 16 and can accordingly be tuned by the choice of the proper type of linear birefringent optical fiber. Typical choices include elliptical core fiber, panda or bow-tie fiber, elliptical cladding fiber, and microstructured birefringent fiber. With the numerical parameters from above and assuming C.sub.HW=C.sub.QW, setting m=3 and orientation angles =5.25 removes the second order temperature dependence of the sensor. This is illustrated in FIG. 12, where the calculated residual quadratic temperature dependence of retarder 14 and sensing element 12 indicated by the dashed curve is counteracted by the calculated temperature dependence of the cross-coupling element 16 indicated by the solid curve such that the combined temperature dependence of the normalized current signal becomes independent of temperature (dotted curve).

(89) As seen from expression [16], other choices of retardance (T.sub.0,.sub.0) and orientation angle of the cross-coupling element 16 yield a different temperature dependence of the cross-coupling element 16 that in the general case can also be optimized to compensate a (residual) linear temperature dependence, e.g. of further components of the fiber-optical sensor. In particular, in fiber-optic voltage sensors 90, an overall temperature dependence resulting from the temperature dependence of the electro-optical effect in the sensing element 12 and of the Faraday rotator 14 can be compensated for.

(90) In further embodiments of the invention, a first cross-coupling element can be used to compensate the overall wavelength dependence of the sensor and a second cross-coupling element can be used to compensate a residual temperature dependence of the sensor, in particular a quadratic temperature dependence. In such a configuration (not shown), the second cross-coupling element resides close to the sensing element 12, in particular in a common housing with the sensing element 12, in order to be exposed to the same or a similar temperature as the sensing element 12; whereas the first-cross coupling preferably shares a common housing with the opto-electronic module 10-2 or with at least parts of the opto-electronic module 10-2. In configurations where parts of the opto-electronic module 10-2 and the sensing element 12 share a common housing, also first and second cross-coupling element can share a common housing.

(91) Throughout this application, tan x=sin x/cos x, and sec x=1/cos x, with x being any variable which may also be written in parentheses [x]; and multiplication can be denoted by dot .Math. or simply by empty space between variables.

(92) While there are shown and described presently preferred embodiments of the invention, it is to be understood that the invention is not limited thereto but may be otherwise variously embodied and practiced within the scope of the following claims. In particular, embodiments or features relating to the sensor are also disclosed for the method and vice versa.

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LIST OF REFERENCE SIGNS

(125) light source 1

(126) fiber coupler 101

(127) optical fiber polarizer 2

(128) polarizing splitter 24

(129) 45 fiber splice 3

(130) optical phase modulator 4

(131) y-type optical phase modulator, polarizer 41

(132) 90 fiber splice 42

(133) polarization maintaining fiber coupler 43

(134) optical delay element 44

(135) detector 5, 5-1, 5-2

(136) integrated optical polarization splitter module 50

(137) spacer 53

(138) splitter 54

(139) polarizer 55a

(140) polarizer 55b

(141) polarizer 55c

(142) quarter-wave retarder 56

(143) signal processor 6

(144) fiber-optical current sensor 10

(145) sensor head 10-1

(146) opto-electronic module 10-2

(147) polarization maintaining fiber 11

(148) sensing element (fiber, crystal) 12

(149) conductor 13

(150) optical retarder 14

(151) Faraday polarization rotator 14

(152) reflector 15

(153) Faraday polarization rotator mirror 15

(154) cross-coupling element (retarder, Faraday rotator) 16

(155) fiber sections 16-1, 16-2

(156) temperature stabilized environment 160

(157) magneto-optic material 161

(158) magnet 162

(159) lens(es) 163

(160) optical voltage sensor 90