Issue #8/2020

Using Zeeman Ring Laser to Measure Magnetic Field

**Yu. Yu. Kolbas, M. E. Grushin, A. A. Medvedev**Using Zeeman Ring Laser to Measure Magnetic Field

DOI: 10.22184/1993-7296.FRos.2020.14.8.664.672

This work is devoted to the construction of a precision magnetometer based on a Zeeman ring laser (ZRL). It is shown that the ZRL allows high-precision measurements of magnetic fields up to 10 Oe in a wide range of operating temperatures. Such a ZRL has a narrow directivity pattern, which is especially important when measuring the vertical component of the Earth’s magnetic field or the direction to the magnetic poles. The main reasons affecting the sensitivity of the ZRL to the magnetic field are revealed. Experimental results of the use of ZRL for measuring magnetic fields of various strengths are presented.

This work is devoted to the construction of a precision magnetometer based on a Zeeman ring laser (ZRL). It is shown that the ZRL allows high-precision measurements of magnetic fields up to 10 Oe in a wide range of operating temperatures. Such a ZRL has a narrow directivity pattern, which is especially important when measuring the vertical component of the Earth’s magnetic field or the direction to the magnetic poles. The main reasons affecting the sensitivity of the ZRL to the magnetic field are revealed. Experimental results of the use of ZRL for measuring magnetic fields of various strengths are presented.

Теги: magnetic drift ring laser zeeman effect zero bias кольцевой лазер магнитный дрейф нуля смещение нуля эффект зеемана

Using Zeeman Ring Laser to Measure Magnetic Field

Yu. Yu. Kolbas, M. E. Grushin, A. A. Medvedev

JSC “Research Institute “Polyus” n. a. M. F. Stelmakh, Moscow, Russia

This work is devoted to the construction of a precision magnetometer based on a Zeeman ring laser (ZRL). It is shown that the ZRL allows high-precision measurements of magnetic fields up to 10 Oe in a wide range of operating temperatures. Such a ZRL has a narrow directivity pattern, which is especially important when measuring the vertical component of the Earth’s magnetic field or the direction to the magnetic poles. The main reasons affecting the sensitivity of the ZRL to the magnetic field are revealed. Experimental results of the use of ZRL for measuring magnetic fields of various strengths are presented.

Key words: ring laser, Zeeman effect, zero bias, magnetic drift

Received on: 30.10.2020

Accepted on: 15.11.2020

Introduction

Magnetic field strength meters (magnetometers) are widely used in geology, geodesy, archeology [1, 2]. Fluxgate, proton, and quantum magnetometers are used to measure the magnetic field. Such devices provide measurement of magnetic fields of strength from 5 to 50 Oe and have a sensitivity in the range of 10–5–10–7 Oe.

One of the varieties of a quantum magnetic field meter is a Zeeman ring laser (ZRL). The principle of its operation is based on the Zeeman effect: frequency division of the gain circuit of a helium-neon gas laser into two – for left and right circularly polarized light. As a result of the pulling of waves to the maxima of the gain curves, a difference in the frequencies of counterpropagating waves propagating in opposite directions in the non-planar cavity of the ZRL arises [3].

This difference in frequencies of counterpropagating waves is called the magnetic component of the ZRL zero displacement. This is what we will use to measure the magnetic field strength.

The interest in studying the possibility of using precisely the ZRL as a magnetometer is due to the exceptional strength and resistance of these devices to mechanical shocks and vibrations, as well as to changes in the external temperature [4–6]. Very few devices are capable of operating at shocks with an amplitude of up to 100 g, vibrations up to an amplitude of 15 g, without any shock absorption, and at temperatures from –55 °C to 75 °C without heating or cooling. Moreover, the mass of a uniaxial ZRL with all the electronics does not exceed 1.5 kg.

1. Magnetic component of the ZRL zero bias

The magnetic component of the zero bias in the ZRL is called the component dependent on the magnetic field on the active medium, which can be isolated in the quasi-four-frequency mode of the ZRL generation (the mode with periodic switching of polarizations) or in the four-frequency mode, when two longitudinal modes of the ZRL cavity are simultaneously generated [4, 5].

As mentioned above, when a longitudinal magnetic field with strength H is applied to the active medium, due to the Zeeman effect, the emission line of active atoms splits by μ = g · μВ · Н, where g is the Lande factor, μB is the Bohr magneton. Due to the pulling effect, the Zeeman splitting leads to a frequency difference of counterpropagating waves, the magnetic component of the zero bias fm, which depends on the value of H and the relative detuning of the cavity Δλ from the gain maximum. When tuned to the maximum gain Δλ = 0, the frequency difference of counterpropagating waves, the magnetic component of the zero offset fm is equal to [3, 6]

, (1)

where ∆νk is the cavity bandwidth, is the excess of gain over losses, G is the gain per cavity pass, p is the loss per pass , Zi and Zr are the real and imaginary parts of the plasma dispersion function, respectively, μ is the value splitting of the Zeeman sublevels in a magnetic field, γab is the parameter of uniform line broadening, k is the wave number, and u is the average thermal velocity of atoms.

The cavity bandwidth is related to the cavity losses

, (2)

where c is the speed of light, L is the length of the cavity, p is the loss factor per pass.

In the Doppler limit with at the maximum of the gain curve in the linear approximation , we obtain [6]

, where . (3)

The magnitude of the magnetic sensitivity a, as follows from formula (3), is determined by the amplification G and the thermal velocity of motion of atoms u. With allowance for gain saturation where G > p, losses p play an important role.

For typical values of the parameters of a ring laser, a ≈ 1.7 kHz / Oe [6].

2. Arrangement of the magnetometer on the ZRL

Fig. 1 shows a drawing of a non-planar cavity ZRL [5], a functional diagram and a photograph of a quasi-four-frequency ZRL K‑5 manufactured by JSC NII “Polyus” n. a. M. F. Stelmakh is shown in Figs. 2 and 3, respectively.

The ZRL cavity has a non-planar contour formed by 4 mirrors. In this circuit, in each arm of the cavity, the rotation of the circular polarization of the light wave is reversed, therefore, when the field is applied in all directions, except for the one perpendicular to the base of the ZRL, no magnetic displacement of zero occurs. Of course, provided that the cavity is ideal and the gain in all arms is the same.

The operation of such ZRL and the separation of the magnetic component of the zero bias are described in detail in [4]. It is important for us that the frequency bias created by applying a magnetic field from the coils wound on the gas-discharge gaps allows us to accurately determine the change in the coefficient a during the operation of the ring laser, since the current in these coils is stabilized with an accuracy of no worse than 0.01%.

To isolate the magnetic component of the zero bias in the ZRL K‑5, alternating work on longitudinal modes with opposite polarization direction is used [4, 5]. At the stage of factory setting, by creating a reference external magnetic field at a temperature of 25 °C, the coefficient a0 is determined, as well as the corresponding dithering frequency A0. Further, at any temperature, the magnetic field strength is calculated by the formulas

. (4)

Here f + and f – are the bias of the ZRL zero on longitudinal modes with opposite polarization direction, A is the bias frequency.

It is obvious that, in addition to external magnetic fields in the ZRL, there is an internal magnetic field, which also causes the magnetic component of the zero displacement [6]. To measure it, before direct use, it is necessary to measure the magnetic field in the main and rotated at an angle of 180° to the ZRL positions. Since the internal magnetic field in this case will retain its value and direction, and the direction of the external will change to the opposite, it is easy to calculate the value of the internal magnetic field strength and then subtract it from the readings.

3. Sensitivity of the ZRL magnetometer

The sensitivity of the GCL is limited by the noise of the generation frequency of the GCL and the sampling frequency of the frequency meter used to measure the offset of the GCL zero at longitudinal modes with opposite polarizations f + and f –.

, (5)

where Df is the spectral density of fluctuations of the frequency difference of counter-propagating laser waves at zero frequency, с is the speed of light, L is the cavity perimeter, S is the area covered by the optical circuit, ω0 = 2πν0 is laser generation frequency, Δωcav. = 2πΔνcav. is the cavity bandwidth, is the Planck constant, P is the power of laser radiation inside the cavity, δ is the relative loss of light in the cavity for a circular passage.

For ZRL K‑5, L = 0,2 m, S = 0,0025 m 2, νо = 4,73 ∙ 1014 Hz, Δνcav = 5,6 ∙ 105 Hz, Р = 5 ∙ 10–2 W, T = 6 s, = 1,054 ∙ 10–34 J ∙ s, Dfg = 0,0012 Hz.

The discrete frequency meter [7, 8] is equal to 0.125 / t. For t = 6 s, this will be 0.02 Hz, for t = 60 s, respectively, 0.002 Hz, for t = 600 s it will be 0.0002 Hz.

Since the ZRL cavity has a non-planar contour, and only the magnetic field is sensitive, the direction of which is parallel to the axis of the cavity channel, the value of a in the direction perpendicular to the cavity base turns out to be significantly less than that given above in Section 1.

For ZRL K‑5, the angle α is 32°, which reduces the value of a by about 6 times, to 250 Hz / Oe.

Note that along the other two orthogonal directions parallel to the base, the influence of the magnetic field in four gaps turns out to be pairwise the same, but opposite in sign. Therefore, the ZRL has spatial selectivity and can work as a single-component magnetometer.

At a ≈ 250 Hz / Oe, the sensitivity threshold of the ZRL can be estimated at 7 · 10–7–7 · 10–5 Oe, depending on the measurement time, which corresponds to modern samples of quantum magnetometers.

4. Experimental results and their discussion

The ZRL K‑5 device was used in the experiment. Measurement procedures were carried out:

Measurements of the dependence of the magnetic component of the zero displacement of the ZRL in the GCC when an external magnetic field with a strength of up to 2.5 Oe is applied in three orthogonal directions and the calculation of the coefficient a along the sensitivity axis.

Measurement of the stability of the coefficient a in the temperature range from –55 to 75 °C when a magnetic field of 1 Oe is applied.

Measurement of the frequency-uncompensated bias relative error of the coefficient a in the temperature range from – 55 to 75 °C.

The measurement results are shown in Fig. 4–9. Analysis of Fig. 4–6 shows that the dependence of the magnetic component of the zero bias of the K‑5 ZRL on the magnetic field strength is linear. In this case, the ZRL demonstrates good selectivity to the direction of the magnetic field, which makes it possible to measure the projections of the magnetic field to each of the three directions in space separately. The mutual influence does not exceed 1.7% (see Table).

The functional dependences of the magnitude of the magnetic component of the ZRL zero bias and the bias frequency on temperature are practically the same (Fig. 7, 8). This makes it possible to compensate for both these dependences using formula (4). As follows from Fig. 9, the measurement error does not exceed 5% in the temperature range from –55 to 75 °С and 1.8% in the temperature range from –25 to 75 °C.

6. Conclusion

The Zeeman ring laser can be used as a single-component magnetometer. Its sensitivity is 7 · 10–7–7 · 10–5 Oe.

ZRL has a linear characteristic, its temperature error does not exceed 5% in the widest temperature range from –55 to +75 °C and 1.8% in the actual operating temperature range from –25 to 75 °C. ZRL has good spatial selectivity, the mutual influence of the axes does not exceed 1.7%.

Thus, a convenient magnetometer for operation in harsh conditions can be constructed based on a Zeeman ring laser.

About the authors

Kolbas Yuri Yurievich, Doctor of Technical Sciences, tigra-e@rambler.ru, JSC “Research Institute “Polyus” n. a. M. F. Stelmakh” (Moscow); specialist in the field of inertial navigation and laser gyroscopy.

SCOPUS id: 6504072429

Grushin Mikhail Evgenievich, Candidate of Physical and Mathematical Sciences, mihail.grushin1968@gmail.com, JSC “Research Institute “Polyus” n. a. M. F. Stelmakh” (Moscow); specialist in the field of physics of gas discharge, plasma chemistry, plasma medicine and inertial navigation and laser gyroscopy.

SCOPUS id: 6603354719

Medvedev Aleksey Aleksandrovich, alexdyn92@yandex.ru, JSC “Research Institute “Polyus” n. a. M. F. Stelmakh” (Moscow); specialist in the field of inertial navigation and laser gyroscopy.

ORCID id: 0000-0002-7308-1839

Yu. Yu. Kolbas, M. E. Grushin, A. A. Medvedev

JSC “Research Institute “Polyus” n. a. M. F. Stelmakh, Moscow, Russia

This work is devoted to the construction of a precision magnetometer based on a Zeeman ring laser (ZRL). It is shown that the ZRL allows high-precision measurements of magnetic fields up to 10 Oe in a wide range of operating temperatures. Such a ZRL has a narrow directivity pattern, which is especially important when measuring the vertical component of the Earth’s magnetic field or the direction to the magnetic poles. The main reasons affecting the sensitivity of the ZRL to the magnetic field are revealed. Experimental results of the use of ZRL for measuring magnetic fields of various strengths are presented.

Key words: ring laser, Zeeman effect, zero bias, magnetic drift

Received on: 30.10.2020

Accepted on: 15.11.2020

Introduction

Magnetic field strength meters (magnetometers) are widely used in geology, geodesy, archeology [1, 2]. Fluxgate, proton, and quantum magnetometers are used to measure the magnetic field. Such devices provide measurement of magnetic fields of strength from 5 to 50 Oe and have a sensitivity in the range of 10–5–10–7 Oe.

One of the varieties of a quantum magnetic field meter is a Zeeman ring laser (ZRL). The principle of its operation is based on the Zeeman effect: frequency division of the gain circuit of a helium-neon gas laser into two – for left and right circularly polarized light. As a result of the pulling of waves to the maxima of the gain curves, a difference in the frequencies of counterpropagating waves propagating in opposite directions in the non-planar cavity of the ZRL arises [3].

This difference in frequencies of counterpropagating waves is called the magnetic component of the ZRL zero displacement. This is what we will use to measure the magnetic field strength.

The interest in studying the possibility of using precisely the ZRL as a magnetometer is due to the exceptional strength and resistance of these devices to mechanical shocks and vibrations, as well as to changes in the external temperature [4–6]. Very few devices are capable of operating at shocks with an amplitude of up to 100 g, vibrations up to an amplitude of 15 g, without any shock absorption, and at temperatures from –55 °C to 75 °C without heating or cooling. Moreover, the mass of a uniaxial ZRL with all the electronics does not exceed 1.5 kg.

1. Magnetic component of the ZRL zero bias

The magnetic component of the zero bias in the ZRL is called the component dependent on the magnetic field on the active medium, which can be isolated in the quasi-four-frequency mode of the ZRL generation (the mode with periodic switching of polarizations) or in the four-frequency mode, when two longitudinal modes of the ZRL cavity are simultaneously generated [4, 5].

As mentioned above, when a longitudinal magnetic field with strength H is applied to the active medium, due to the Zeeman effect, the emission line of active atoms splits by μ = g · μВ · Н, where g is the Lande factor, μB is the Bohr magneton. Due to the pulling effect, the Zeeman splitting leads to a frequency difference of counterpropagating waves, the magnetic component of the zero bias fm, which depends on the value of H and the relative detuning of the cavity Δλ from the gain maximum. When tuned to the maximum gain Δλ = 0, the frequency difference of counterpropagating waves, the magnetic component of the zero offset fm is equal to [3, 6]

, (1)

where ∆νk is the cavity bandwidth, is the excess of gain over losses, G is the gain per cavity pass, p is the loss per pass , Zi and Zr are the real and imaginary parts of the plasma dispersion function, respectively, μ is the value splitting of the Zeeman sublevels in a magnetic field, γab is the parameter of uniform line broadening, k is the wave number, and u is the average thermal velocity of atoms.

The cavity bandwidth is related to the cavity losses

, (2)

where c is the speed of light, L is the length of the cavity, p is the loss factor per pass.

In the Doppler limit with at the maximum of the gain curve in the linear approximation , we obtain [6]

, where . (3)

The magnitude of the magnetic sensitivity a, as follows from formula (3), is determined by the amplification G and the thermal velocity of motion of atoms u. With allowance for gain saturation where G > p, losses p play an important role.

For typical values of the parameters of a ring laser, a ≈ 1.7 kHz / Oe [6].

2. Arrangement of the magnetometer on the ZRL

Fig. 1 shows a drawing of a non-planar cavity ZRL [5], a functional diagram and a photograph of a quasi-four-frequency ZRL K‑5 manufactured by JSC NII “Polyus” n. a. M. F. Stelmakh is shown in Figs. 2 and 3, respectively.

The ZRL cavity has a non-planar contour formed by 4 mirrors. In this circuit, in each arm of the cavity, the rotation of the circular polarization of the light wave is reversed, therefore, when the field is applied in all directions, except for the one perpendicular to the base of the ZRL, no magnetic displacement of zero occurs. Of course, provided that the cavity is ideal and the gain in all arms is the same.

The operation of such ZRL and the separation of the magnetic component of the zero bias are described in detail in [4]. It is important for us that the frequency bias created by applying a magnetic field from the coils wound on the gas-discharge gaps allows us to accurately determine the change in the coefficient a during the operation of the ring laser, since the current in these coils is stabilized with an accuracy of no worse than 0.01%.

To isolate the magnetic component of the zero bias in the ZRL K‑5, alternating work on longitudinal modes with opposite polarization direction is used [4, 5]. At the stage of factory setting, by creating a reference external magnetic field at a temperature of 25 °C, the coefficient a0 is determined, as well as the corresponding dithering frequency A0. Further, at any temperature, the magnetic field strength is calculated by the formulas

. (4)

Here f + and f – are the bias of the ZRL zero on longitudinal modes with opposite polarization direction, A is the bias frequency.

It is obvious that, in addition to external magnetic fields in the ZRL, there is an internal magnetic field, which also causes the magnetic component of the zero displacement [6]. To measure it, before direct use, it is necessary to measure the magnetic field in the main and rotated at an angle of 180° to the ZRL positions. Since the internal magnetic field in this case will retain its value and direction, and the direction of the external will change to the opposite, it is easy to calculate the value of the internal magnetic field strength and then subtract it from the readings.

3. Sensitivity of the ZRL magnetometer

The sensitivity of the GCL is limited by the noise of the generation frequency of the GCL and the sampling frequency of the frequency meter used to measure the offset of the GCL zero at longitudinal modes with opposite polarizations f + and f –.

, (5)

where Df is the spectral density of fluctuations of the frequency difference of counter-propagating laser waves at zero frequency, с is the speed of light, L is the cavity perimeter, S is the area covered by the optical circuit, ω0 = 2πν0 is laser generation frequency, Δωcav. = 2πΔνcav. is the cavity bandwidth, is the Planck constant, P is the power of laser radiation inside the cavity, δ is the relative loss of light in the cavity for a circular passage.

For ZRL K‑5, L = 0,2 m, S = 0,0025 m 2, νо = 4,73 ∙ 1014 Hz, Δνcav = 5,6 ∙ 105 Hz, Р = 5 ∙ 10–2 W, T = 6 s, = 1,054 ∙ 10–34 J ∙ s, Dfg = 0,0012 Hz.

The discrete frequency meter [7, 8] is equal to 0.125 / t. For t = 6 s, this will be 0.02 Hz, for t = 60 s, respectively, 0.002 Hz, for t = 600 s it will be 0.0002 Hz.

Since the ZRL cavity has a non-planar contour, and only the magnetic field is sensitive, the direction of which is parallel to the axis of the cavity channel, the value of a in the direction perpendicular to the cavity base turns out to be significantly less than that given above in Section 1.

For ZRL K‑5, the angle α is 32°, which reduces the value of a by about 6 times, to 250 Hz / Oe.

Note that along the other two orthogonal directions parallel to the base, the influence of the magnetic field in four gaps turns out to be pairwise the same, but opposite in sign. Therefore, the ZRL has spatial selectivity and can work as a single-component magnetometer.

At a ≈ 250 Hz / Oe, the sensitivity threshold of the ZRL can be estimated at 7 · 10–7–7 · 10–5 Oe, depending on the measurement time, which corresponds to modern samples of quantum magnetometers.

4. Experimental results and their discussion

The ZRL K‑5 device was used in the experiment. Measurement procedures were carried out:

Measurements of the dependence of the magnetic component of the zero displacement of the ZRL in the GCC when an external magnetic field with a strength of up to 2.5 Oe is applied in three orthogonal directions and the calculation of the coefficient a along the sensitivity axis.

Measurement of the stability of the coefficient a in the temperature range from –55 to 75 °C when a magnetic field of 1 Oe is applied.

Measurement of the frequency-uncompensated bias relative error of the coefficient a in the temperature range from – 55 to 75 °C.

The measurement results are shown in Fig. 4–9. Analysis of Fig. 4–6 shows that the dependence of the magnetic component of the zero bias of the K‑5 ZRL on the magnetic field strength is linear. In this case, the ZRL demonstrates good selectivity to the direction of the magnetic field, which makes it possible to measure the projections of the magnetic field to each of the three directions in space separately. The mutual influence does not exceed 1.7% (see Table).

The functional dependences of the magnitude of the magnetic component of the ZRL zero bias and the bias frequency on temperature are practically the same (Fig. 7, 8). This makes it possible to compensate for both these dependences using formula (4). As follows from Fig. 9, the measurement error does not exceed 5% in the temperature range from –55 to 75 °С and 1.8% in the temperature range from –25 to 75 °C.

6. Conclusion

The Zeeman ring laser can be used as a single-component magnetometer. Its sensitivity is 7 · 10–7–7 · 10–5 Oe.

ZRL has a linear characteristic, its temperature error does not exceed 5% in the widest temperature range from –55 to +75 °C and 1.8% in the actual operating temperature range from –25 to 75 °C. ZRL has good spatial selectivity, the mutual influence of the axes does not exceed 1.7%.

Thus, a convenient magnetometer for operation in harsh conditions can be constructed based on a Zeeman ring laser.

About the authors

Kolbas Yuri Yurievich, Doctor of Technical Sciences, tigra-e@rambler.ru, JSC “Research Institute “Polyus” n. a. M. F. Stelmakh” (Moscow); specialist in the field of inertial navigation and laser gyroscopy.

SCOPUS id: 6504072429

Grushin Mikhail Evgenievich, Candidate of Physical and Mathematical Sciences, mihail.grushin1968@gmail.com, JSC “Research Institute “Polyus” n. a. M. F. Stelmakh” (Moscow); specialist in the field of physics of gas discharge, plasma chemistry, plasma medicine and inertial navigation and laser gyroscopy.

SCOPUS id: 6603354719

Medvedev Aleksey Aleksandrovich, alexdyn92@yandex.ru, JSC “Research Institute “Polyus” n. a. M. F. Stelmakh” (Moscow); specialist in the field of inertial navigation and laser gyroscopy.

ORCID id: 0000-0002-7308-1839

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