Optical remote magnetometry

Introduction to remote optical magnetometry using a molecule and polarimetry

An important study entitled "Remote Atmospheric Optical Magnetometry" (Johnson, L. et al 2014)  describes how it is possible to conduct remote magnetometry using the oxygen molecule. The study will be described further below.

How magnetometry with molecules works

Pumping or excitation leads to molecule polarization

Certain atoms or molecules demonstrate a behavior that can be close to magnetic, meaning paramagnetic ("para" being synonymous to "next to"). Paramagnetic atoms or molecules are those that have unpaired electrons. The oxygen molecule (O2) is paramagnetic, as it has two unpaired electrons. 

The electrons, protons and neutrons which compose atoms and molecules have spins which act like tiny magnets, meaning magnetic dipoles. In the oxygen molecule, all spins cancel out with the exception of the spins of the two unpaired outer electrons. Therefore, these two spins are fundamental for determining the behavior of the oxygen molecule as a magnet or magnetic dipole, and figuratively-speaking, the direction to which this magnetic dipole will point. We could refer metaphorically to a fictional magnetic axis or a quantization axis of the molecule pointing to a specific direction. 

It must be noted that molecules rotate. In the case of the oxygen molecule, shown in Figure 4 (two oxygen atoms in blue), the rotation of the molecule which is characterized by a rotational angular momentum N (Figure 4) is generating a magnetic field. The electronic spin S, couples with N, yielding a large magnetic moment, and giving J, the total angular momentum (Figure 4). This is equivalent to a quantization axis and determines the direction to which the molecule will point.

Figure 4: Schematic representation of the oxygen molecule. Vector J represents the total angular momentum, which is related to the behavior of the molecule as a magnetic dipole. (Image from NASA/Caltech presentation - p.9).

These interactions determine the energetic levels of the unpaired electrons of the oxygen molecule and the corresponding electron transitions. Oxygen is a magnetic dipole whose rotation is affected by specific electron transitions. We are referring to magnetic dipole transitions and to rotation, as well as to rotational energetic levels. These are studied in magnetic dipole rotation spectroscopy.

Similarly to a compass which points to the direction of the Earth’s magnetic field, oxygen molecules will also point to the direction of the magnetic field in which they are found, under one condition: that the magnetic field is stronger than their thermal motion. This motion is generally strong enough to randomize the direction they point to. 

Oxygen molecule polarization leads to medium magnetization: a "magnetization current density" or a "magnetization current" is generated

When we irradiate an oxygen molecule with an electromagnetic wave which has a wavelength of 762 nm, we will energetically pump, or in other words, excite an outer unpaired electron, thereby changing its energetic level and also its spin state, including the direction of the spin. As the electron spins influence the axis of the molecule (quantitation axis), the latter will rotate and point to a new direction.

The oxygen (quantization) axes will be aligned, like tiny magnets which align their poles. In this manner, we are inducing molecule polarization; as a result, the medium will be polarized. As tiny magnets aligned in the same direction are equivalent to a strong magnet, the medium will behave as one. We are generating a "magnetization current density" or a "magnetization current". As a result, a net magnetization (https://en.wikipedia.org/wiki/Magnetization) will be grown and the medium will be magnetized. 

The polarized oxygen molecules of a medium are deflected by a magnetic field: a probe wave transversing the medium has its polarization rotated

What will occur if an electromagnetic wave transverses an oxygen medium, such as the atmosphere, which has been pumped to induce the 762 nm transition that leads to molecular rotation and alignment? The wave will be subjected to an influence that will result in the rotation of its polarization. The rotation will be proportional to the strength of the magnetic field in which the oxygen molecules reside. Specific instruments called polarimeters can measure the degree of rotation of polarization of a wave and calculate the strength of the transversed magnetic field.

Remote magnetometry: pumping of oxygen leads to magnetization current and subsequent electromagnetic wakefield generation

Brief description: "Molecular spins" get polarized and relaxed in regular intervals. Magnetization constitutes a magnetic current which generates an electric field. Electromagnetic wakefield co-propagates with pump wave modifying its polarization.

In optical magnetometers, most often we use a pump wave for excitation, and a probe wave for measurement of polarization rotation in order to calculate the magnetic field strength. In the remote magnetometry study by Johnson, L. et al (2014), the pump electromagnetic wave suffices. The authors use pulses of a pump wave of 762 nm which induces oxygen excitation, and specifically 100-picosecond pulses, which are considered optimal for magnetometry.

During the duration of the pump pulse, the molecules will be aligning themselves, meaning that there will be medium polarization, while in the interpulse interval they will be relaxing themselves. During the pumping interval, they will be absorbing energy, while during the relaxing interval they will be emitting energy or in other words they will be "ringing". During the pumping interval, the molecules will be precessing in accordance with the pumping frequency of 762 nm, while during the relaxation interval, the molecules will be precessing at the Larmor frequency indicated by the magnetic field of the location they are found at. During pumping, we will be generating a magnetization current density (magnetization current) which is linked to a magnetization field, while in the interpulse interval this will be decaying (cf. free-induction-decay regime). 

The magnetization current which corresponds to the polarization of oxygen will generate a response electric field. It is notable that this field will have rotated polarization. As a result, a response electric wakefield and magnetic wakefield will be generated, which will constitute an electromagnetic wakefield. This will be propagating, and specifically co-propagating with the pump pulse while influencing it. This will constitute a signal that can be processed for magnetometry. As shown in Figure 5, for the duration of a pulse (red rectangle), the wakefield (green) is increasing, while following the end of the pulse, the wakefield is decaying (exponentially).

In the study conducted by Johnson, L. et al (2014), the authors concluded that by processing the signal, the rotation of the polarization (wakefield) can be measured. Then, if for instance the rotation of polarization (wakefield) is found to be different between two distinct locations in the passage of the electromagnetic wave, that will mean that a magnetic source (e.g. magnetic object) is present in one location. The corresponding magnetic strength in that location can be calculated.

Figure 5: Pump pulse train and induced polarization rotated wakefields (as shown in Figure 5 of Johnson, L. et al (2014). Electromagnetic wave pulses (x-polarized) are shown in red while the induced electric wakefield x-component is indicated in green. As mentioned in the study Figure 5 legend, the wakefield and magnetization current have a similar polarization and temporal form. (The wakefield y-component, the magnetization current and the rotated signal are not shown for simplicity).