Measuring Systems and Devices

The present invention relates to measuring systems and devices, and in particular to such systems and devices that use resonance effects of electromagnetic radiation to perform sensitive measurements.

It is known, for example, to use an arrangement in which the resonance of a beam of electromagnetic radiation, such as a laser beam, is used to measure very small linear or rotational movements.

Systems that use resonance effects of electromagnetic radiation to make measurements exploit the fact that if a suitable electromagnetic radiation, e.g., laser, beam is trapped in an arrangement, such as a cavity or chamber, in which it is reflected back over itself, then if the length of the path that the beam traverses in the chamber is equal to a whole number of wavelengths of the beam, the beam will positively interfere with itself, i.e. resonance will occur, thereby leading to a significant increase in intensity of the beam (which can be detected, e.g., by allowing a portion of the beam to escape the resonance chamber and measuring when its intensity peaks) .

This is illustrated in Figure 1, which shows a linear resonance chamber arrangement, in which a laser beam 1 of wavelength λ resonates in a chamber 9 formed by two mirrors 2, 3, spaced nλ apart, where n is an integer. The resonance can be detected by a detector 4.

It is also known, for example, to use resonators that are in the form of a loop, as shown in Figure 2. In Figure 2, the laser source 1 is reflected around a loop resonance chamber 9 formed by the mirrors 5, 6, 7 and 8, which are spaced such that the total distance

around the loop is again nλ (where n is an integer) , such that resonance will occur.

In these resonator arrangements, any change in the size of the resonance cavity (i.e. in the distance within the cavity (i.e. between its boundaries or walls) that will be traversed by the laser beam) will, as is known in the art, change the frequency at which the cavity resonates . This is because the cavity will no longer have, e.g., a path length of nλ, but will now have a path length of, e.g., nλ _1λ where X ₁ is a different wavelength to λ. This property can be exploited to make sensitive measurements of linear movement or rotation, because any movement of one of the boundaries of the resonance cavity (e.g. the mirrors in Figures 1 and 2) will change the path length within the cavity and thereby the frequency that will resonate in the cavity. Therefore, by monitoring how the resonant frequency of the resonance cavity changes, such movement can be detected and measured. It is known to exploit these effects to, e.g., make sensitive measurements of vibration and rotation. For vibration measurements, an arrangement such as that shown in Figure 1 can be used, with, e.g., the boundary mirror 3 being mounted on the vibrating surface whose movement is to be measured. In this arrangement, as the surface on which the mirror 3 is mounted vibrates, the mirror 3 will move correspondingly, thereby changing the length of the resonate cavity 9, and accordingly the frequency that will resonate in the cavity 9. These changes in resonant frequency can be detected and used to determine the movement of the mirror 3 (and hence of the surface to which it is mounted) .

For rotational measurements, a loop arrangement such as that shown in Figure 2 can be used. If the loop is rotated (e.g. by mounting it on a rotating surface), then the effective path length of the loop will change

(because, e.g., the light must travel slightly further to the next mirror of the loop if the loop is rotating in the same direction as the light beam is travelling and vice-versa - as is known in the art, this is called the Sagnac effect) , and thus so will the resonant frequency of the loop . The change in resonant frequency can again be detected and used to give a measure of the rotation of the loop.

The above arrangements all use the fact that varying the physical path length or distance traversed by the (laser) beam within the resonance cavity will change the resonant frequency.

It is also known to detect changes in the resonant frequency of a resonance cavity or chamber caused by variations in the effective refractive index experienced by a beam as it traverses the cavity. For example, evanescent coupling of a sample to be detected into the resonant cavity can change the effective refractive index seen by the laser beam, and thereby the effective path length of the cavity as seen by the laser beam, such that the resonant frequency will change. This change in resonant frequency can be used to detect the presence of the sample. Changing the effective refractive index of the cavity in effect changes the speed at which the laser beam traverses the cavity and thus, again, the effective path length seen by the laser beam.

The Applicants believe that there remains scope for improvement to techniques for using changes in the resonant frequency of a resonance cavity or chamber to make measurements, particularly measurements of a sensitive nature.

According to a first aspect of the present invention, there is provided a method of making a measurement using an arrangement in which a beam of

electromagnetic radiation is or can be arranged to resonant within a resonance cavity, comprising: introducing a beam of electromagnetic radiation into the resonance cavity; passing the beam through a dispersive medium in the cavity; changing the effective refractive index experienced by the beam within the cavity; and determining the effect of the change in refractive index on the resonant frequency of the cavity.

According to a second aspect of the present invention, there is provided an apparatus for making a measurement, comprising: a resonance cavity into which a beam of electromagnetic radiation can be introduced, and in which a beam of electromagnetic radiation can be arranged to resonate; a dispersive medium in the cavity through which a beam of radiation in the cavity can be arranged to pass in use; means for changing the effective refractive index experienced by a beam of electromagnetic radiation within the cavity; and means for determining the effect of the change in refractive index on the resonant frequency of the cavity.

The present invention uses a resonant cavity to make measurements, as in the prior art systems. However, in the present invention, a dispersive medium through which the electromagnetic beam is passed is arranged in the cavity, together with means for or a step of changing the effective refractive index experienced by the beam in the cavity.

The Applicants have found that a small shift in the refractive index experienced by the beam in the resonant cavity can cause a relatively large shift in the

resonant frequency of the cavity. Thus changing the effective refractive index experienced by a beam in the resonant cavity can cause a relatively large (and thus detectable) shift in the resonant frequency. Moreover, including a dispersive medium in the cavity (i.e. a medium whose refractive index is frequency dependent (such that the refractive index experienced by the electromagnetic beam as it passes through the medium is dependent on the frequency of the beam) ) means that any changes in resonant frequency in the cavity are, in effect, amplified by the dispersive medium, since the change in resonant frequency will cause the refractive index experienced by the beam in the dispersive medium to change, thereby further shifting the resonant frequency. This increases the sensitivity of the system to refractive index and resonant frequency changes, and, combined with the fact that the resonant frequency can be measured to a relatively high accuracy (as compared, e.g., to measuring phase shifts) , means that, as will be explained further below, the present invention advantageously facilitates very sensitive measurements of a number of phenomena .

It is believed that the provision of a resonant cavity containing a dispersive medium may be new and advantageous in its own right .

Thus, according to a third aspect of the present invention, there is provided a method comprising: providing a resonance cavity in which a beam of electromagnetic radiation is or can be arranged to resonant; introducing a beam of electromagnetic radiation into the resonance cavity; passing the beam of electromagnetic radiation through a dispersive medium within the cavity; and

assessing the resonant frequency of, or changes in the resonant frequency of, the cavity.

According to a fourth aspect of the present invention, there is provided an apparatus comprising: a resonance cavity into which a beam of electromagnetic radiation can be introduced, and in which a beam of electromagnetic radiation can be arranged to resonate; a dispersive medium arranged within the resonance cavity such that it can be traversed by an electromagnetic radiation beam travelling within the cavity; and means for assessing the resonant frequency of, or changes in the resonant frequency of, the cavity. As will be appreciated by those skilled in the art, these aspects and embodiments of the invention can include any one or more or all of the preferred and optional features of the invention described herein, as appropriate. Thus, for example, the dispersive medium is preferably a medium whose refractive index may be varied in use (as will be discussed further below) .

The resonant cavity should be such that an appropriate electromagnetic radiation beam can be arranged to resonate within it, but can otherwise have any suitable construction. Thus, it could, for example, have a linear arrangement as shown in Figure 1, or be in the form of a closed loop, such as that shown in Figure 2.. The boundaries of the cavity can be formed in any appropriate manner, and should, e.g., be selected to be appropriate for the electromagnetic radiation in question. They could, e.g., comprise appropriate mirrors, as is known in the art.

The electromagnetic radiation beam may be of any suitable form and provided by any suitable source. As is known in the art, it will typically comprise a laser, although other electromagnetic radiation (e.g. light)

sources could be used (with an appropriate resonant cavity) , if desired.

In a preferred embodiment, the frequency and hence wavelength of the electromagnetic radiation beam can be varied in use. This facilitates determining any changes in resonant frequency of the resonant cavity (as will be explained further below) . Thus the radiation source, e.g., laser, is preferably such that the frequency of the radiation beam it emits can be varied in use . In a preferred embodiment, the apparatus of the present invention includes the radiation source, e.g., a laser.

The radiation beam should be such that it will or can resonate in the resonant cavity under the appropriate conditions. Thus, it should, for example, be coherent and preferably monochromatic with a pure polarisation.

The dispersive medium within the cavity can be any suitable such medium. It should, as is known in the art, comprise a medium whose refractive index is frequency dependent (i.e. dependent on the frequency of the electromagnetic beam that passes through it), i.e. a medium in which the phase velocity of the wave is a function of its frequency. The dispersive medium is preferably highly dispersive. As will be discussed further below, the dispersive medium is preferably a medium that will exhibit electromagnetically induced transparency (EIT) .

The entire resonance cavity could be filled with the dispersive medium. However, in a preferred embodiment, only a portion of the cavity contains the dispersive medium. For example, a block or unit of the dispersive medium could be placed in the cavity, with the cavity otherwise containing, e.g., air. The refractive index experienced by the electromagnetic radiation beam in the resonant cavity

can be changed in any desired and suitable manner. For example, a or the medium that the beam travels through in the cavity could be changed. This would then allow, e.g., the change in resonant frequency to be used to determine the change in refractive index caused by the new medium in the cavity (and hence, e.g., a property or properties of the medium to be assessed) . In such arrangements, the entire resonance cavity could be filled with the medium. However in a preferred embodiment, only a portion of the cavity contains the particular medium in question. For example, a block or unit of the medium could be placed in the cavity, with the cavity otherwise containing, e.g., air.

In such an arrangement, the dispersive medium could be in addition to the "refractive index changing" medium. However, in a preferred embodiment the medium that causes the change in refractive index is also dispersive (and may therefore comprise the dispersive medium as well) . In a particularly preferred embodiment, the radiation beam is arranged to pass through a medium in the cavity whose refractive index can be varied by external factors or influences. For example, it is known that certain materials ' refractive indexes will vary in the presence of a magnetic field. In such an arrangement, changes in the resonant frequency of the cavity can be used as a measure of the external, refractive index affecting factor or influence (e.g. magnetic field) experienced by the medium in the cavity (since any changes in the external factor or influence, e.g., magnetic field, will change the refractive index of the medium and hence the resonant frequency of the cavity) . Indeed, it is believed that a significant advantage of the present invention is that it facilitates very sensitive measurements of properties such as magnetic fields when arranged in this manner.

Thus, according to a fifth aspect of the present invention, there is provided a method of measuring a selected property, comprising: providing a resonance cavity in which a beam of electromagnetic radiation is or can be arranged to resonate; introducing a beam of electromagnetic radiation into the resonance cavity; passing the beam within the cavity through a medium whose refractive index is dependent upon the selected property to be measured; and assessing the resonant frequency of, or changes in the resonant frequency of, the cavity.

According to a sixth aspect of the present invention, there is provided an apparatus for measuring a selected property, comprising: a resonance cavity into which a beam of electromagnetic radiation can be introduced, and in which a beam of electromagnetic radiation can be arranged to resonate; a medium whose refractive index is dependent upon the selected property to be measured arranged within the resonance cavity such that it will be traversed by an electromagnetic radiation beam travelling within the cavity; and means for assessing the resonant frequency of, or changes in the resonant frequency of, the cavity.

As will be appreciated by those skilled in the art, these aspects and embodiments of the invention can include any one or more or all of the preferred and optional features of the invention described herein, as appropriate. Thus, for example, the medium whose refractive index is dependent upon the selected property to be measured is preferably dispersive. In these aspects and embodiments of the invention, a medium whose refractive index is sensitive to a

particular property, such as (the strength of) a field or other factor to which it is exposed, is included in the resonant cavity such that the radiation beam will pass through the medium when it resonates in the cavity. Thus, when the medium is exposed to the selected property to be measured, the resonant frequency of the cavity will then give a measure of the refractive index of the medium and hence of the property, e.g., field, to which it is exposed. If the medium is dispersive (as it preferably is) the effect of the refractive index change on the resonant frequency is in effect amplified by the dispersive nature of the medium, thereby providing greater measurement sensitivity.

The medium in the cavity whose refractive index will or can vary in dependence upon a selected property can be any suitable such medium. Most preferably the property in question is an external factor or influence to be measured, such as an environmental condition, such as a magnetic or other field, temperature, pressure, etc., and the medium is such that its refractive index is dependent upon the value of a property or parameter (e.g. strength or intensity) of the factor or influence (e.g. magnetic field) to which it is subjected.

In a particularly preferred embodiment of these arrangements and aspects of the invention, the material in the cavity is a material whose refractive index is or can be made sensitive to magnetic fields (or changes in magnetic field) (and the system is accordingly used to determine or measure magnetic fields (or changes in magnetic field) .

In a particularly preferred embodiment, the material in the cavity is a material that exhibits or can be arranged to exhibit electromagnetically induced transparencey (EIT) . (As is known in the art, when some materials are placed in a suitable excited state, such as by being excited by a laser, their refractive indices

become sensitive to changes in any magnetic field to which they are exposed. This is referred to as electromagnetically induced transparency.) Such a set-up can be used to provide a variable refractive index medium in the resonant cavity and thereby be used to measure the magnetic field to which the medium is exposed (e.g. via coherent population trapping in a magnetically susceptible medium).) Moreover, electromagnetically induced transparency is usually highly dispersive in effect, such that an "EIT" material will act as a (the) dispersive medium in the cavity as well.

Suitable materials for inclusion in the resonant cavity for this purpose include, for example, a rubidium gas cell, ruby or suitably doped glass or other material .

The Applicants have also recognised that another way in which the effective refractive index seen by the radiation beam as it traverses the cavity can be changed is due to the influence of a mass on the radiation beam in the cavity. As is known in the art, general relativity predicts that a mass will affect the speed of an electromagnetic beam that passes by it, i.e. it will, in effect, change the effective refractive index experienced by the radiation beam. These effects are too small to be noticed under everyday conditions, but the Applicants believe that the system of the present invention can be made, and will be, sufficiently sensitive to detect such effects. For example, if general relativity is correct, changes in mass close to the resonant cavity will affect the speed of travel of the beam through the cavity and hence the effective refractive index seen by the beam. Changes in the resonant frequency of the cavity could therefore be used to detect such changes in mass.

Similarly, general relativity also predicts that if a

radiation beam is made to pass by a rotating body, the rotating body will vary the speed of travel of, and hence effective refractive index seen by, the radiation beam depending on whether it is travelling with or against the direction of rotation. Thus, again, any changes in resonant frequency caused by such changes in effective refractive index could be used as a measure of the rotation, e.g., angular momentum, of the rotating body. Thus, the Applicants believe that the system of the present invention can, firstly, be used to test the above predictions of general relativity of the effect of a mass and/or a rotating body on a radiation beam, and, secondly, if the predictions are found to be true, to measure mass and/or angular momentum and changes therein.

Thus, according to a seventh aspect of the present invention, there is provided a method of detecting or measuring a mass or the rotation of a body, comprising: providing a resonance cavity in which a beam of electromagnetic radiation is or can be arranged to resonant; arranging the cavity relative to the mass or rotating body it is desired to detect or measure; introducing a beam of electromagnetic radiation into the resonance cavity; and assessing the resonant frequency of, or changes in the resonant frequency of, the cavity.

According to an eighth aspect of the present invention, there is provided an apparatus for detecting or measuring a mass or the rotation of a body, comprising: a resonance cavity into which a beam of electromagnetic radiation can be introduced, and in which a beam of electromagnetic radiation can be arranged to resonate;

means for arranging a mass or rotating body relative to the cavity; and means for assessing the resonant frequency of, or changes in the resonant frequency of, the cavity. As will be appreciated by those skilled in the art, these aspects and embodiments of the invention can include any one or more or all of the preferred and optional features of the invention described herein, as appropriate . In these aspects and embodiments of the invention, the orientation of the resonance cavity will, as discussed below, determine the type of signal and property that can be detected and measured. Thus, by appropriate arrangement of the resonant cavity, the effective refractive index experienced by the radiation beam in the cavity can be arranged to be dependent upon, e.g., the presence of a mass or the rotation of a rotating body. It should be noted in this regard that the mass may be internal or external to the cavity. In a preferred embodiment, the arrangement is such that the (light) radiation will or can travel vertically or perpendicularly (from the perspective of the mass) away from or toward the mass. This will allow the mass itself to be detected. In a particularly preferred such embodiment, a ring, preferably triangular, resonance cavity is used, with the mass to be detected or measured arranged at one end of an arm of the (triangular) ring. This arrangement means that radiation (light) travelling towards the mass is accelerated and radiation travelling away is decelerated, which effects can, as discussed above, be detected by changes in the resonant frequencies of the cavity. Where a variable refractive index medium is included in the cavity, the mass is preferably arranged at one end of the arm of the cavity that contains the variable refractive index medium.

To measure the, e.g., angular momentum, of a rotating body, for example, a loop resonance cavity- arrangement may be and preferably is used, with the rotating body being arranged inside the resonance loop (i.e. such that the resonance loop and the path of the radiation beam in the resonance cavity surrounds the rotating body) . This allows the rotating body to influence the effective refractive index seen by the radiation beam as it travels around the resonance loop. It should be noted here that the resonance loop itself (e.g. the mirrors forming it) need not, and indeed preferably does not, itself rotate in such an arrangement .

In the case of detecting the presence of a "mass", or measuring a mass or changes in mass, general relativity predicts that electromagnetic radiation such as light will, effectively, experience a different refractive index depending upon whether the radiation is travelling towards or away from the mass. Thus, an appropriately arranged linear resonant cavity can be and, again, preferably is, used, e.g., to detect changes in relative mass in the direction of the longitudinal axis of the cavity, for example as the cavity is moved over the surface of the earth (with the cavity being arranged to point vertically downwards towards the earth) .

In a particularly preferred embodiment of the above arrangements for determining and detecting mass, etc., a dispersive medium, such as those discussed above, and preferably a medium whose refractive index will vary depending upon, e.g., an external factor or field, is included within the resonant cavity. This has the advantage that the dispersive medium will effectively amplify any refractive index (and hence resonant frequency) changes due to the presence of a mass, etc., and therefore make the arrangement more sensitive to

this. This is because the presence of the dispersive medium increases the susceptibility of the arrangement to refractive index changes (i.e. changes the relative resonant frequency changes for a given refractive index change) .

The effect of the refractive index change on the resonant frequency of the cavity, and the resonant frequency of the cavity or any changes therein can be determined and assessed as desired. For example, in some applications it may be sufficient simply to determine that the resonant frequency has changed. This could be done, e.g., by detecting that resonance is no longer occurring (for example by detecting a loss of the resonance peak at the current frequency of the electromagnetic radiation, e.g., laser, beam).

However, in a preferred embodiment, the change or relative change, in resonant frequency, and/or the actual (e.g. new) resonant frequency, is determined. This could comprise, e.g., determining the relative change in resonant frequency, and/or determining an actual value for the resonant frequency of the resonance cavity.

The resonant frequency measurements can similarly be used to determine relative changes in the property, e.g., magnetic field, to be measured, or the absolute value of that property.

The resonant frequency or changes therein can be detected and determined as desired. For example, a portion of the radiation beam could be allowed to exit the cavity and its intensity monitored, to see, e.g., whether it is at a resonant peak or not.

In a particularly preferred embodiment, the frequency of the radiation beam can, as discussed above, be varied in use, and the arrangement is such that the frequency is varied until resonance is detected, at which point the new, or change in, resonant frequency

can be determined. This process is preferably carried out automatically, e.g. by using a feedback arrangement between the detector and radiation source to "tune" the radiation source to the new resonant frequency. It would be possible to use a single radiation beam in the resonate cavity and to detect the changes in resonant frequency using that beam alone.

However, in a particularly preferred embodiment, two radiation, e.g., laser, beams are used, a "probe" beam which is subjected to the (potentially) varying refractive index within the resonance cavity and whose frequency may, e.g., be varied in use to "tune" it to the cavity, and a reference beam that passes through the resonance cavity (or another resonance cavity) , but without being subjected to any varying refractive index. In effect, the reference beam is fixed to resonate at a given frequency, whereas the resonant frequency for the probe beam will vary in dependence upon the property which is being measured. Thus, in a particularly preferred embodiment, the resonant frequency of the cavity, and/or changes therein, is assessed by using a probe beam that is subjected to the refractive index change within the resonant cavity, and a reference beam that is not subjected to the refractive index change within the resonant cavity. This arrangement has the advantage that changes in the resonant frequency of the cavity as experienced by the probe beam can be (and indeed preferably are) detected by comparison of that beam with the reference beam. Most preferably such a comparison is carried out by detecting the beat frequency of the two beams after they have traversed the cavity (or their cavities) , or by measuring a shift of the probe resonant frequency relative to the resonant frequency of the reference beam using the intensity distribution leaving the cavity (or cavities) .

In these arrangements, the two radiation, e.g., laser, beams, could be provided by different sources and, e.g., have different frequencies, or they could, e.g., be provided by splitting the same, single source. Where a variable refractive index medium to be used with the present invention needs to be excited to a suitable state (for example as with the magnetic field sensitive, and/or EIT exhibiting, materials discussed above) , then that medium is preferably driven by, or using a portion of, the reference beam.

The resonant cavity or cavities can be set up in any appropriate manner in these arrangements . For example, in the case of a loop resonator arrangement, one beam could be arranged to travel clockwise around the loop, and the other beam arranged to travel counter-clockwise, with the probe beam further being arranged to, e.g., pass through the variable refractive index medium in the cavity (but the reference beam not doing so) . It would also be possible for the probe and reference beams to co-propagate (i.e. travel in the same direction) around the resonance loop.

In the case of a linear arrangement, both beams could, e.g., traverse the same cavity, but with only the probe beam passing through the, e.g., variable refractive index medium in the cavity.

In another arrangement, different cavities could be used for the probe and reference beams, with only the probe beam's cavity containing, e.g., the variable refractive index medium. In such an arrangement, the cavities may be identical save for the refractive index medium (i.e. such that they have the same base resonant frequency) or differ.

Which arrangement is used will depend, e.g., on whether the probe and reference beams have the same or differing frequencies.

Where a refractive index medium that needs to be, or that can be, driven by a drive beam to place it in a suitably excited state (as discussed above) is used then in a preferred embodiment, the intensity of the drive beam (e.g. of the reference beam when it is used for this purpose) can be varied, e.g. by using an intensity modulator. Such intensity modulation of the "drive" beam allows the sensitivity (susceptibility) of the variable refractive index material (i.e. the amount of refractive index change per unit of external, e.g., magnetic, field) to be varied or modulated. This can facilitate the detection of, e.g., magnetic fields, such as, for example, the detection of a constant (unvarying) background field. In a preferred embodiment, as well as the resonant cavity including a dispersive medium (and preferably a medium that will exhibit electromagnetically induced transparency) , the cavity also includes a device that will effect Fresnel drag on a beam in the cavity that is passed through it in use.

Fresnel drag is a property of a transparent or semi-transparent medium having a refractive index "n" in which motion of the medium tends to change the phase of light travelling in the medium by an amount that is proportional to the velocity of the medium.

The Applicants have recognised that the property of Fresnel drag can be exploited in arrangements in accordance with the present invention.

In particular, the Applicants have recognised that if a medium that can cause the effect of Fresnel drag is moved in a linear fashion as a beam of electromagnetic radiation is passed through it, then the effect of the medium (due to Fresnel drag) on the beam of electromagnetic radiation that is passed through the medium as it moves will be to induce a change of phase or phase shift in the beam. Moreover, the phase shift

will be proportional to the motion (velocity) of the medium. This accordingly means that a relative simple to construct and use phase shifting or modulating device can be constructed. Moreover, the device can be robust and need only contain one moving part .

The device can also be similarly used to introduce a frequency splitting of a radiation beam in the resonance cavity (e.g. ring resonator) arrangement.

It is believed that such arrangements may be new and advantageous in their own right. Thus, according to another aspect of the present invention, there is provided a device comprising: a medium that can effect Fresnel drag on a beam of electromagnetic radiation that is passed through it; and means for moving the medium linearly.

According to a further aspect of the present invention, there is provided a method comprising: passing a beam of electromagnetic radiation through a medium that can effect Fresnel drag on a beam of electromagnetic radiation that is passed through it; and moving the medium linearly whilst the beam is passing through the medium.

The present invention also accordingly extends to the use of Fresnel drag to phase shift and/or phase modulate a beam of electromagnetic radiation, and/or the use of Fresnel drag to introduce a frequency splitting in a beam of electromagnetic radiation.

In these embodiments and aspects of the invention, the medium that can or will cause Fresnel drag can be any suitable such medium, such as a suitable transparent or semi-transparent medium. It is preferably a suitable transparent medium. In a preferred embodiment, it is glass.

In a preferred embodiment the device is an optical device, but this is not essential as the aspects and

embodiments of the invention can be applied to all forms of electromagnetic radiation, as appropriate.

The medium may take any suitable form. It is preferably in the form of a block or slab of the medium, e.g. a rectangular block.

The Fresnel drag causing medium may be moved in a linear fashion in any suitable manner. It can preferably be moved in a reciprocating manner, i.e. such that it will move backwards and forwards . Most preferably it can be arranged to vibrate in a linearly reciprocating fashion. The medium is preferably moved (e.g. reciprocated) in a direction that is parallel to the direction of travel of the beam that is passing through it (and thus the system is preferably arranged such that the beam passes through the medium in a direction that is parallel to the direction of motion of the medium) .

In a preferred embodiment, a desired phase shift and/or frequency is determined, and the Fresnel drag device is moved accordingly in dependence upon the determined desired phase shift or frequency. For example, it is preferably vibrated at a frequency corresponding to .a desired frequency to be imposed on the beam of electromagnetic radiation, such as a desired "lock-in" frequency.

In a preferred embodiment, the medium is mounted on a stage or element that can be moved in the desired fashion (and that can thereby move the medium accordingly) . Such a stage or mount could, e.g., comprise a mechanical or electrically movable stage or mount. As discussed above, the stage or mount is preferably arrangeable to and preferably vibrates in a linear reciprocating fashion. This facilitates moving the medium at frequencies appropriate to apply, e.g., phase modulation and phase shifts to the laser beam. Thus, in a preferred embodiment, the medium that can

cause Fresnel drag is mounted on a, preferably linearly, vibrating stage or mount.

Thus, according to a further aspect of the present invention, there is provided a device comprising a transparent or semi-transparent medium through which a beam of electromagnetic radiation can be passed in use mounted on a stage that can be used to move the medium in a linear, preferably reciprocating, fashion.

In a particularly preferred embodiment, the medium that can exhibit Fresnel drag is mounted on a piezo-electric device (e.g. crystal). The device can preferably be activated to vibrate the medium back and forward in a linear reciprocating fashion. This facilitates moving the medium in such a manner as to achieve the desired Fresnel drag effects.

Thus, according to another aspect of the present invention, there is provided a device comprising a medium that will or can cause Fresnel drag on a beam of electromagnetic radiation that is passed through the medium mounted on a piezo-electric device that can be used to move the medium in a linear, preferably reciprocating, fashion.

As will be appreciated by those skilled in the art, the above aspects and embodiments of the invention can and preferably do include any one or more or all of the preferred and optional features of the invention described herein, as appropriate. Thus, for example, the medium that will or can cause Fresnel drag preferably comprises a glass or other suitably transparent or semi-transparent material block, and the stage (e.g. piezo-electric device) preferably is vibratable and vibrates, preferably in a linear reciprocating fashion.

The motion of the medium that will or can exhibit Fresnel drag can preferably be varied and controlled, preferably selectively, in use. In a preferred

embodiment, the frequency of motion (vibration) of the medium can be controlled (and set, e.g., to the desired frequency) .

The medium that will or can exhibit Fresnel drag may be directly mounted on its stage or mount (e.g. piezo-electric crystal) , but this is not essential and there may be, e.g., intermediate components, etc., if desired.

The Fresnel drag device in the resonant cavity, where present, is preferably used to enable a lock-in amplifier arrangement. In particular, the device is preferably arranged to vibrate at the desired "lock-in" frequency (e.g. by arranging the piezo-electric crystal device to which the glass or other block is mounted to vibrate at that frequency) . This then, in effect, gives a reference or carrier frequency that the system can lock to, as is known in the art. Then, if the EIT medium (e.g.) in the cavity is exposed to a magnetic field, that will cause the resonant frequency to shift from the "locked in" frequency, which shift can be detected, e.g., as an amplitude drop in the output signal. Such an arrangement can be used to detect very small changes in magnetic field, and thus to provide a system having enhanced sensitivity. Thus, in a particularly preferred embodiment, the resonant cavity also includes a medium that will or can be arranged to cause Fresnel drag to a beam of electromagnetic radiation within the cavity, which medium is preferably in the form of a device comprising a block of a transparent or semi-transparent medium, such as glass, mounted on a linearly reciprocable, preferably, vibrating, mount or stage, and preferably on a piezo-electric device.

It should be noted that the present invention uses frequency measurements, and, in particular, shifts in resonant frequency, to detect, e.g., changes in

refractive index within the resonant cavity. The use of frequency measurements and shifts, is advantageous, e.g., as compared to measuring and detecting phase shifts, because it facilitates more sensitive measurements .

This is because, firstly, a relatively small refractive index change or shift in the resonance cavity can cause a relatively large shift in resonant frequency, such that changes in refractive index can be detected with high sensitivity. Furthermore, frequencies can be measured, e.g., to an accuracy of about 10 ^"3 Hz, which corresponds to a frequency shift of a part in 10 ¹⁸ . The effect of this is that in the case of magnetic field measurements, for example, the present invention can provide a field sensitivity of about 10 ^"20 Tesla.

(This should be contrasted with systems that detect phase shifts, and thus rely on intensity based detection and are accordingly limited in sensitivity by low intensity detection problems, such as shot noise.)

The present invention can be used and has application wherever it is desired to make sensitive measurements of properties that can or will affect the refractive index experienced by the radiation beam in the resonance cavity. Thus, it could, e.g., be used as discussed above to detect the presence of or relative changes in mass . Such arrangements may have application in, e.g., geological surveying. It can also, e.g., be used to determine (changes in) the angular momentum of a moving body.

As discussed above, a particularly preferred application of the present invention is the detection and measurement of magnetic fields (in which case a suitably magnetic-field sensitive medium is included in the resonance cavity) . Such applications could be used to, e.g., measure magnetic field strengths, and to

detect and image currents. This may be useful for, e.g., geological applications, detecting undersea or underground cables, detecting submarines, etc.

In the case of current imaging, for example, a two-dimensional magnetic field map obtained using the present invention could be and preferably is reverse engineered (using, e.g., finite element analysis) to give the source of the magnetic field, i.e. the series of electrical currents that are generating the magnetic field.

The measurements made or to be made using the method or apparatus of the present invention could thus include, for example, detecting the presence or absence of a mass or field, detecting or determining relative changes in mass or a field, and/or determining absolute values of or relative changes in, selected properties.

It is envisaged that a particularly important application of the present invention may be in medical technology, and in particular in magneto-cardiology, i.e. detecting the magnetic fields induced by currents in the heart (and thereby imagining those currents) .

According to a ninth aspect of the present invention, there is provided an apparatus for use in magneto-cardiology, comprising: a resonance cavity into which a beam of electromagnetic radiation can be introduced, and in which a beam of electromagnetic radiation can be arranged to resonate ; a medium whose refractive index is dependent upon the magnetic field to which it is exposed arranged within the resonance cavity such that it will be traversed by an electromagnetic radiation beam travelling within the cavity; and means for assessing the resonant frequency of, or changes in the resonant frequency of, the cavity.

As will be appreciated by those skilled in the art, all of the above aspects and embodiments of the invention can include any one or more or all of the preferred and optional features of the invention described herein. Thus, for example, the medium within the cavity is preferably dispersive.

The methods in accordance with the present invention may be implemented at least partially using software e.g. computer programs. It will thus be seen that when viewed from further aspects the present invention provides computer software specifically adapted to carry out a method or the methods herein described when installed on data processing means, a computer program element comprising computer software code portions for performing a method or the methods herein described when the program element is run on data processing means, and a computer program comprising code means adapted to perform all the steps of a method or of the methods herein described when the program is run on a data processing system. The invention also extends to a computer software carrier comprising such software which when used to operate a measuring system comprising data processing means causes in conjunction with said data processing means said system to carry out the steps of the method of the present invention. Such a computer software carrier could be a physical storage medium such as a ROM chip, CD ROM or disk, or could be a signal such as an electronic signal over wires, an optical signal or a radio signal such as to a satellite or the like. It will further be appreciated that not all steps of the method of the invention need be carried out by computer software and thus from a further broad aspect the present invention provides computer software and such software installed on a computer software carrier for carrying out at least one of the steps of the methods set out herein.

The present invention may accordingly suitably be embodied as a computer program product for use with a computer system. Such an implementation may comprise a series of computer readable instructions either fixed on a tangible medium, such as a computer readable medium, for example, diskette, CD-ROM, ROM, or hard disk, or transmittable to a computer system, via a modem or other interface device, over either a tangible medium, including but not limited to optical or analogue communications lines, or intangibly using wireless techniques, including but not limited to microwave, infrared or other transmission techniques . The series of computer readable instructions embodies all or part of the functionality previously described herein. Those skilled in the art will appreciate that such computer readable instructions can be written in a number of programming languages for use with many computer architectures or operating systems. Further, such instructions may be stored using any memory technology, present or future, including but not limited to, semiconductor, magnetic, or optical, or transmitted using any communications technology, present or future, including but not limited to optical, infrared, or microwave . It is contemplated that such a computer program product may be distributed as a removable medium with accompanying printed or electronic documentation, for example, shrink-wrapped software, pre-loaded with a computer system, for example, on a system ROM or fixed disk, or distributed from a server or electronic bulletin board over a network, for example, the Internet or World Wide Web.

A number of preferred embodiments of the present invention will now be described by way of example only and with reference to the accompanying drawings, in which:

Figure 1 shows schematically a resonant cavity arrangement;

Figure 2 shows schematically a second resonant cavity arrangement in the form of a loop cavity; Figure 3 shows schematically a first embodiment of a resonance cavity arrangement that is in accordance with the present invention;

Figure 4 shows schematically a second embodiment of a resonance cavity arrangement that is in accordance with the present invention;

Figures 5, 6, 7, 8, 9, and 10 show schematically further embodiments of resonance cavity arrangements that are in accordance with the present invention.

Like reference numerals are used for like components throughout the Figures.

Figure 3 shows schematically a resonance cavity arrangement arranged in accordance with the present invention.

In the arrangement shown in Figure 3, a laser 10 acts as a source of electromagnetic radiation which is then split by means of a beam splitter and mirror arrangement 18 to direct it into two resonance cavities 11, 14, formed by mirrors 12, 13 and 15, 16, respectively. The laser radiation in the cavities 11, 14 is allowed to escape from the cavities to detectors 28 and 27, respectively. These detectors 27, 28 determine when the laser beam in each cavity is resonating in the cavity (e.g. by looking for a peak in its intensity) . The laser radiation in the cavities 11, 14 is also allowed to escape from the cavities and directed via beam splitter and mirror arrangement 18 to a detector 19. The detector 19 is arranged to determine the beat frequency of the combined beams (i.e. the beams from each cavity) when they are at resonance (i.e. at the resonant frequency of their respective cavities) .

A frequency modulator 20 is included in the path of the beam to the cavity 14 , for varying the frequency of that beam .

There is also arranged within the resonance cavity 14 a medium 17 which exhibits electromagnetically induced transparency and thus whose refractive index varies in dependence upon the strength of the magnetic field to which the medium 17 is exposed. The medium 17 could comprise, e.g., a rubidium gas cell, ruby or appropriately doped glass, which is exposed in use, e.g., to a drive laser beam (e.g. from the laser 10) to place it, as is known in the art, in a suitably excited state such that its refractive index will vary in dependence upon the magnetic field to which it is exposed.

In use of this arrangement, the laser 10 is set to the resonant frequency of the cavity 11 (and the beam 25 in that cavity accordingly acts as a reference beam) . The frequency modulator 20 is then used to vary the frequency of the laser beam 26 input to the cavity 14 (the "probe" beam) containing the magnetic field sensitive medium 17, until such time as resonance in the cavity 14 is detected by the detector 27. At that point the detector 19 can determine the beat frequency between the reference beam in the cavity 11 and the probe beam in the cavity 14 and thereby obtain a measure of the magnetic field to which the medium 17 is being exposed.

The medium 17 which exhibits electromagnetically induced transparency is highly dispersive. This means, as is known in the art, that its refractive index is frequency dependent. Thus the refractive index of the medium 17 is frequency dependent as well as being magnetic field dependent. This has the effect of amplifying the effect of any magnetic field shift on the resonant frequency of the cavity. A small change in magnetic field causes a small change in the frequency of

the atoms in the medium 17 but this causes a much larger change in the refractive index experienced by the probe beam and hence in the resonant frequency. The Applicants have found that this can lead to amplifications of up to 10 ⁷ .

Figure 4 shows a similar resonator arrangement to Figure 3, but which uses a loop resonance cavity 21 formed by mirrors 22, 23 and 24. In this arrangement, the probe laser beam 26 travels in a clockwise direction around the loop cavity 21 and passes through the variable refractive index and dispersive medium 17, and the reference beam 25 travels in a counter-clockwise direction around the loop cavity (and does not pass through the variable refractive index medium 17) . Other arrangements, such as the use of co-propagating laser beams would be possible.

Again, the resonant frequency within the cavity of the probe beam 26 will vary depending upon the magnetic field to which the medium 17 is exposed, which changes in resonant frequency can be detected by determining the beat frequency of the probe beam 26 and reference beam 25 using the detector 19.

Figure 5 shows a further embodiment of a resonance cavity arrangement that is in accordance with the present invention.

In this arrangement, there is again a laser source 10 whose beam is split to provide a drive (pump) beam 31 and a probe beam 32 which are directed into a loop resonance cavity 33 formed by mirrors 34, 35 and 36. The mirror 36 is mounted on a piezo-electric stage, so that its position can be varied in use, under the control of a driver 44.

In this embodiment, the drive beam 31 also serves as a reference beam (like the reference beam 25 in the arrangements of Figures 3 and 4) for the arrangement.

The loop resonance cavity 33 again includes a variable refractive index and dispersive medium 17 in the form of a rubidium gas cell that is suitably excited by the drive beam 31. Other arrangements for the variable refractive index medium 17, such as other optically active media, such as ruby or suitably doped glass would, as is known in the art, be possible.

Both the drive laser beam 31 and the probe laser beam 32 pass through the variable refractive index medium cell 17, but, as is known in the art, the variable refractive index applies only to the probe laser 32 via the mechanism, as is known in the art, of Electromagnetically Induced Transparency.

In this embodiment, the drive beam 31 and probe beam 32 are engaged to travel around the resonance loop 33 in counter-propagating directions, although the beams could also be co-propagating.

The rubidium cell 17 may optionally, as shown in Figure 5, be bounded by λ/4 plates 37, 38 which are arranged with opposite handedness to turn vertically polarised clockwise and anti-clockwise modes into circularly polarised beams of opposite handedness. This configuration will achieve maximum sensitivity to the magnetic field to which the rubidium cell 17 is exposed. (In the case of co-propagating pump and probe beams, the polarisation, if desired, should be established external to the resonance cavity 33.)

In use of this arrangement, the resonant cavity 33 is frequency locked to the drive (reference) laser beam 31 using the Pound Drever Hall method, using optical output detector 40, frequency modulator 20 and its driver 44, internal frequency modulator 45, the piezo-driven mounted mirror 36, mixer 43 and electrical filters 41 and 42, as is known in the art. Frequency shifts due, e.g., to a magnetic field, can then be detected by modulating the drive laser 31

intensity using an intensity modulator 48 (which is driven by a low frequency source 46) . Changing the intensity of the drive laser 31 in this manner modifies the susceptibility of the rubidium cell 17 to the effect a magnetic field (as will be discussed further below) .

The output signal via which frequency shifts can be detected and measured can be detected and measured via intensity detection at detector 47 via mixer 39 and beam splitter 49. Any detected intensity change indicates a frequency shift (since the cavity will no longer be resonant with the laser beam) . This detection is limited by the quality of the cavity. Other frequency shift detection and measurement arrangements would be possible. For example, the beat frequency (i.e. the frequency separation of the combined drive and probe beams) could be measured.

Figure 6 shows a further embodiment of the present invention that is similar to that shown in Figure 5, but which uses two different lasers as the (drive) pump laser and probe laser.

In this embodiment, the lasers are again arranged to resonate within a loop resonance cavity 33 formed by mirrors 34, 35 and 36 which contains a rubidium cell 17. However, in this case, the drive beam 31 is provided by a drive laser 50, and the probe beam 32 is provided by a separate, different probe laser 51.

Again, in this arrangement, Pound Drever Hall stabilisation using a frequency modulator 20, its driver 44, a detector 40, a piezo-electric driven mirror 36 and an internal frequency modulator 45, together with electrical filters 41 and 42 and a mixer 43 is used to lock the cavity to the frequency of the drive laser 50. (The driver laser 50 can be locked in addition to a rubidium transition, but this is not essential.) The probe laser 51 is then stabilised to the counter-propagating mode again using Pound Drever Hall

stabilisation using a high frequency source 56, a frequency modulator 59 and the signal mixer 39. A detector 57 and feedback electronics are used to control and alter the frequency of the probe laser 51 to keep it resonant within the cavity.

In this arrangement the drive laser 50 is stabilised to one mode of the resonant cavity 33, and the probe laser 51 is stabilised to the counter-propagating mode of the resonant cavity 33. The effect of this is that the beat signal derived by interfering the two laser beams when so stabilised will reflect the size of the magnetic field to which the rubidium cell 17 has been exposed, as is known in the art. In other words, in this arrangement, the lasers are varied in frequency until they both resonate within the cavity 33. Once both lasers are at resonant frequencies within the cavity 33, the laser beams are combined by means of a beam combining mirror arrangement 52 close to their sources, and the beat frequency detected via detection arrangement 53. As discussed above, the beam frequency gives a measure of the frequency difference between the two lasers, and hence of the frequency shift induced by the magnetic field to which the rubidium cell 17 has been exposed.

Again, the susceptibility of the arrangement to a magnetic field is determined by the intensity of the drive laser beam 31, and so a low frequency oscillator 58 and intensity modulator 54 that can be used to vary the intensity of the drive laser beam 31 so that an appropriate output signal can be recovered, are included in the arrangement .

The intensity modulator 54 is used to modulate the intensity of the drive (reference) beam 31. Such modulation of the drive beam modulates the intensity of the electromagnetic field experienced by the rubidium

cell 17 (since the drive beam "drives" the cell) and accordingly modulates the susceptibility of the rubidium cell 17 to a magnetic field (i.e. the amount of refractive index change in the rubidium cell 17 per unit of external (magnetic) field) . In this way, the intensity modulator 54 can be used to modulate the apparatus' susceptibility to an external field.

Such modulation of the apparatus ' susceptibility to an external field facilitates, for example, the detection of constant fields (i.e. that do not vary with time, such as the earth's magnetic field that is always present and cannot be switched off) , that might otherwise be undetectable. This is because the intensity modulation-induced changes in the refractive index susceptibility of the refractive index medium will only become apparent in the presence of an external field, thereby allowing, e.g., the determination that a constant but otherwise undetectable field is present. This arrangement can also be used to detect very small fields, by giving the "target" signal a marker that allows it to be extracted from an otherwise large background (using, e.g., a lock-in amplifier type arrangement) .

The intensity modulator 54 can also be used to determine the size of the signal relative to known frequency shifts (or high intensity measurements) .

The above embodiments are of arrangements which can be used to measure, for example, magnetic fields in a very sensitive manner. As discussed above, it is also believed that the present invention can be used to detect general relativistic frequency shifts, i.e. the effect of a mass or a rotating body on the resonant frequency of the resonance cavity.

Figure 7 shows a suitable arrangement of a resonance cavity in accordance with the present invention for determining, for example, the angular

momentum of a rotating body. In this embodiment, the same resonance cavity, laser source, detection, optical and electronic arrangement and layout as in Figure 6 above is used (and accordingly like components and operations are not described again here) , but in this case, a rotating body 61 is arranged within the loop resonance cavity 60 in which the two counter-propagating beams 62 and 63 are travelling.

General relativity predicts that the beams 62, 63 will in effect experience a different refractive index within the cavity depending upon whether they are travelling with or against the direction of rotation of the body 61. That will accordingly change the resonant frequency for the beams, depending upon their direction of travel within the cavity. Accordingly, in a similar manner to that discussed above, the difference in the resonant frequencies can be detected and used as a measure of, e.g., the angular momentum of the rotating body 61. It is, for example, believed that the system of the present invention could be used, e.g., to detect bodies of the order of 1 kg rotating at 50 m per seconds (at their outer circumference) .

Figure 8 shows a similar arrangement but that could be used, for example, to detect the presence of or changes in mass. This arrangement again uses the same basic set-up as the embodiment of Figure 6 (and Figure 7) (and so again, similar components and operations will not be described again) , but a mass 71 is arranged at one end of the arm of the resonant cavity 70 that contains the variable refractive index and dispersive medium 17.

General relativity predicts that a mass will have an effect on the relative speed of travel of a radiation beam depending upon whether the radiation beam is travelling towards or away from the mass. Accordingly, the resonant frequency of the cavity 70 shown in Figure

8 will depend upon the nature of and the presence of the mass 71 in the direction along the longitudinal axis of the (arm of the) resonance cavity 70. Changes in resonant frequency of the cavity 70 can therefore be used to detect, for example, relative changes in mass present in the direction perpendicular to the longitudinal axis of the (arm of the) cavity.

It should be noted here that although the embodiments of Figures 7 and 8 have been shown as using separate drive and probe lasers 50, 51, it would equally be possible to use a single laser whose beam is split, like in the embodiment shown in Figure 5. However, the use of two separate lasers is preferred, as that is the more sensitive arrangement. It should also be noted that, as will be appreciated by those skilled in the art, the arrangements and construction of the above and other arrangements of the present invention can be varied as desired. Thus, for example, rather than using, e.g., free-space optics and mirrors, optical fibres and fibre optic arrangements could be used for routing the laser beams, optical signals, etc.

Figure 9 shows schematically a ring resonator arrangement including an EIT cell 17 similar to the preceding embodiments, but in which the ring resonator

100 also includes a "Fresnel drag" device 101 within the cavity 100.

The basic set-up in Figure 9 is similar to that shown in the preceding embodiments . Thus , a laser beam from a laser 102 is split by a beam splitter 103 and travels in counter-propagating directions around the resonant cavity 100 formed by beam splitter 103 and mirrors 104 and 105. Again, a portion of the beam can escape to a detector 106. The "Fresnel drag" device 101 comprises a glass block or slab 107 mounted on a piezo-electric crystal

device which can be activated to cause the glass slab 107 to vibrate linearly in a direction 108 parallel to the direction of travel of the laser beams in the resonator 100. As shown in Figure 9, the laser beams travel through the glass slab 107. The motion of the glass slab 107 causes Fresnel drag on the laser beams which induces a phase shift in the beams. The phase shift is proportional to the velocity of glass slab 107 (and thus directionally dependent) .

The effect of this is that the laser light in the resonator 100 is phase shifted as it passes through the vibrating glass slab 107.

In this arrangement, the Fresnel drag device 101 can be used to provide a method of scanning the frequency difference between the two laser beams in the resonant cavity, and to provide a method of phase modulating the light in the resonant loop (cavity) differentially so that the effect of the EIT cell becomes clearer (as, e.g., a magnetic field will change the background level of the Fresnel dragged frequency shift: this can be extracted using a full wave rectifier and a lock-in amplifier with high resolution) (which can be used to enhance signal sensitivity, e.g., when sensing magnetic fields) .

The Fresnel drag device in the resonant cavity is preferably used to enable a lock-in amplifier arrangement. In particular, the device is preferably arranged to vibrate at the desired "lock-in" frequency (e.g. by arranging the piezo-electric crystal to which the glass or other block is mounted to vibrate at that frequency) . This then, in effect, gives a reference or carrier frequency that the system can lock to, as is known in the art. Then, if the EIT medium 17 in the cavity 100 is exposed to a magnetic field, that will use resonant frequency to shift from the "locked in"

frequency, which shift can be detected, e.g., as an amplitude drop in the output signal. Such an arrangement can be used to detect very small changes in magnetic field, and thus to provide a system having enhanced sensitivity.

Figure 10 shows an arrangement similar to Figure 9, but in this case optical fibres 120 are used to allow the EIT cell 17 to be arranged at a distance from the control apparatus so as to facilitate, e.g., remote sensing of a magnetic field. This embodiment also uses waveguide (fibre) circulators 121, to enable easier signal extraction.

It can be seen from the above that the present invention, in its preferred embodiments at least, provides a device that can be used to measure very sensitively changes in refractive index experienced by a laser beam in a resonant cavity, and accordingly parameters, such as magnetic fields or mass, that can affect the refractive index of materials. This is achieved in particular, by using frequency-based detection to determine shifts in resonant frequency of a resonant cavity.

The present invention can be used to detect, for example, both relative changes and absolute values of properties, such as magnetic fields. It has application, for example, in the imaging of currents, geological applications and magnetocardiology. It can also be used to detect the presence of or changes in mass and angular momentum and to test the principles of general relativity. In the case of current imaging, for example, a two-dimensional magnetic field map obtained using the present invention could be and preferably is reverse engineered (using, e.g., finite element analysis) to give the source of the magnetic field, i.e. the series of electrical currents that are generating the magnetic field.