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Abstract
We utilized a metal propionate solution to prepare polycrystalline bismuth-substituted yttrium iron garnets through the metal-organic decomposition process. After conducting thorough optimization, we successfully synthesized a garnet that exhibited a high magneto-optic response directly at the end of an optical fiber. A notable achievement of our work lies in the ability to restrict the size and position of the garnet to match the dimensions of the fiber's core. The functionalized fiber was integrated into a magneto-optical sensor setup, offering the flexibility to operate either in the Faraday rotation or magnetic circular dichroism mode.
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1. Introduction
In the electric power industry, magneto-optical fiber sensors have undergone significant development for current monitoring. These sensors leverage the Faraday rotation (FR, θF) phenomenon, which involves polarizing light propagating through a silica fiber coiled around a conductor [1–3]. Unlike electrical sensors, optical fiber detection systems are immune to strong electromagnetic fields and offer various advantages, including flexibility, high insulation, and compact size. The latter is crucial for spatially resolved measurements at the millimeter scale or below. However, silica's Verdet constant (V), denoted as θF = VHL (where L is the material's thickness and H is the applied magnetic field), is relatively low, necessitating materials with higher magneto-optical performance. One such material is bismuth-substituted yttrium iron garnet (Bi:YIG), which has been known for its efficient magneto-optical properties and has been utilized in various optical magnetic sensor setups [4–6]. By incorporating Bi:YIG at the end of an optical fiber, fibered magneto-optic sensors with a measurable range from 0.27 µT to 27 mT have been successfully fabricated [6]. The size of the prototype's sensing head typically ranges from 5 to 10 mm, depending on the configuration. Another promising all-fiber optical sensor is based on terbium-doped fiber with a 2 cm-long section and a Verdet constant of −24.5 rad/(Tm) at 1053 nm [7]. In both examples, the sensitive part's relatively larger size compared to the fiber itself necessitates careful mechanical alignment to ensure proper coupling with the optical fiber. In recent years, there has been growing interest in integrating magnetic nanoparticles into optical fibers due to their promising magneto-optical properties. For instance, cobalt ferrite (CoFe2O4) magnetic nanoparticles (∼10 nm) have been embedded within a TEOS (tetraethoxysilane) matrix in a suspended core fiber using the sol-gel deposition method under compressed air [8]. This approach shows potential for further enhancing the performance of magneto-optical sensors.
The operational principle of these magneto-optical fiber sensors draws inspiration from optical gyroscopes that employ non-reciprocal dephasing within a rotating Sagnac interferometer [9]. These magnetic sensors capitalize on the non-reciprocal dephasing phenomenon inherent in Faraday rotation induced by magnetic fields [10,11]. Although magnetic circular dichroism finds widespread use in material spectroscopy, its potential for sensing applications has been largely overlooked. However, magnetic circular dichroism can indeed serve as a valuable tool for magnetic sensing, introducing novel advantages for fiber-optic sensors. In particular, the effect of the magnetic field can significantly alter the polarization of light within a magnetic field-immersed silica fiber, despite the relatively small Verdet constant of silica. This expansion of influence beyond the sensor's head necessitates the inclusion of the fiber's contribution in measurements. Conversely, the magnetic circular dichroism of silica proves inconsequential, allowing for the neglect of its impact and ensuring precise spatial localization in magnetic field detection.
To address the challenges associated with sensor head size, we propose the utilization of bismuth-doped yttrium iron garnet as the magneto-optical material for fiber-optic magneto-optical sensors. This material choice effectively addresses issues related to sensor head dimensions and enables operation leveraging both Faraday rotation and magnetic circular dichroism effects.
2. Material
Several compelling factors underlie the selection of bismuth-substituted yttrium iron garnet as the preferred sensing material. Foremost, Bi: YIG stands out as an exceptionally efficient substance for magneto-optical applications within the UV-visible spectral range. Notably, among the diverse fabrication methods available – such as liquid phase epitaxy [12], pulsed laser deposition [13], sputtering, and sol-gel techniques [14,15] – the metal-organic decomposition (MOD) route offers notable advantages in terms of both simplicity and efficacy.
The MOD process commences with the creation of a low-viscosity liquid solution compatible with deposition techniques like spin-coating or dip-coating on various substrates like glass, silica, or GGG. Subsequent deposition and open-air pyrolysis eliminate the organic constituents, leaving behind an amorphous metal oxide film. This deposition/pyrolysis sequence can be iterated to increase material thickness. Ultimately, high-temperature annealing triggers crystallization, transforming the amorphous material into polycrystalline garnet.
Since the ultimate composition of the garnet hinges on the initial composition, annealing duration, and temperature, a meticulous optimization of these parameters is imperative to achieve optimal bismuth substitution and thereby govern the final magneto-optical properties. We performed this optimization task on garnet film [16] and we have established the following procedure that has been transposed to the preparation of the garnet on the fiber.
Bismuth (III) propionate, yttrium (III) propionate, and iron (III) propionate are synthesized through acid-based reactions. The collective concentration of metal chelates in propionic acid is capped at 1 M to forestall precursor crystallization. The solution is then applied via spin-coating onto silica plates. A pyrolysis phase of 40 minutes at 300°C is followed by annealing. Systematic variations of the initial composition, annealing duration, and annealing temperature have been undertaken to ascertain the optimal fabrication conditions. Evaluation of magneto-optical performance is correlated with X-ray diffraction-based structural characterization. Optimal results were observed for an initial composition corresponding to 1.3 bismuth substitution and annealing at 660°C for 10 hours [16]. Under saturation, this configuration yielded a Verdet constant of approximately −4°/µm and an ellipticity angle of roughly −2.5°/µm measured by ellipsometry at 532 nm (refer to Fig. 1) [17]. Notably, an excess of initial bismuth content can induce detrimental side reactions as bismuth ferrites (BiFeO3 and Bi2Fe4O9) compromising final performance.
Fig. 1. Hysteresis loops measured from the FR and the ellipticity angle at 532 nm for Bi1.3Y1.7Fe5O12.
We have harnessed this method to fabricate a polycrystalline garnet film directly onto an optical fiber's end. This is accomplished by immersing the fiber in the initial solution and subsequently undergoing the pyrolysis and annealing stages as previously elucidated, ultimately resulting in the production of a nanoscale film measuring 200 nm in thickness determined by Interferometric microscopy (Zygo NewView 6300). To enhance reflectivity and optimize the return of light within the fiber, a layer of gold is sputtered onto the garnet film. Additionally, the garnet layer can be confined to the dimensions of the fiber core. Following the immersion in the solution, light is introduced at the opposite end of the fiber. As the light exits, it interacts with the solution, leading to heating and drying. A simple rinse with ethanol serves to remove the unexposed solution, leaving behind an initial material residue in the fiber's core region. Subsequent pyrolysis and annealing steps result in the formation of a micrometric garnet that is centered on the core, as visually demonstrated in Fig. 2(a). The resulting self-centered Bi: YIG micro-crystal grown at the end of the optical fiber is depicted in Fig. 2, displaying scanning electron microscopy (SEM) images in (b, c) and microscopic interferometry in (d).
Fig. 2. (a) Scheme of the production of self-centered garnet at the fiber end, (b) SEM image of the fabricated Bi: YIG appearing between the two stress rods at the PANDA-type polarization maintaining single mode fiber end after gold deposition (c) SEM image, and (d) Interferometric microscopy image of the Bi: YIG microcrystal with 3 µm thick on the core of a single mode optical fiber with the initial composition a 1.3 substitution of bismuth. The deposition procedure was repeated 5 times before the annealing at 660 °C for 10 hours.
3. Setup and calculation
The sensor configuration is depicted in Fig. 3. A doubled Nd:YAG laser (VERDI) generates a continuous-wave light beam at 532 nm. By employing a neutral density filter, a half-waveplate, and a polarizer, we control the beam's intensity and polarization state. This configuration is designed to achieve linear polarization at a 45° angle with respect to the the photoelastic modulator (PEM) axes, which dynamically changes polarization states at a rapid rate of 50 kHz. Following the PEM modulation, the light is coupled into a single mode fiber and propagates to reach the Bi: YIG material positioned at the fiber's end. Upon reaching the Bi: YIG material, the light reflects on the gold layer directly sputtered onto the garnet. The backward propagation of light involves it passing back through both the Bi: YIG material and the fiber. In one configuration, the returning light is detected by a single photodiode, subsequently interfaced with a lock-in amplifier that is synchronized with the PEM modulation. Alternatively, in a second configuration, the two polarizations aligned with the neutral axes of the PEM are segregated via a Wollaston prism. These separated polarizations are then individually detected by two distinct photodiodes, both linked to separate digital lock-in amplifiers (Stanford SR810), synchronized with the PEM modulation.
We use the Jones formalism to compute the response of the sensor arrangement for both these configurations (see Supplement 1 for full details). The fiber is considered as a waveplate with a random dephasing, $\varphi $, and a random orientation, $\xi $. We take into account both the contributions of the Faraday rotation, ${\theta _F}$ and of the induced ellipticity angle, ${\eta _F}$, originating from the magnetic circular dichroism (MCD). The output signal is decomposed into continuous, $I(0 )$, first harmonic, $I(\omega )$ and second harmonic, $I({2\omega } )$, contributions regarding the modulation of the polarization induced by the PEM operating at a circular frequency $\omega $ with an amplitude of modulation of the phase ${\varphi _M}$. For the configuration without the polarizer the different contributions are given by the set of equations (1):
${I_0}$ is simply the intensity measured at zero magnetic field, ${J_1}({{\varphi_M}} )$ and ${J_2}({{\varphi_M}} )$ are respectively first and second order Bessel functions. These different quantities depend on the ellipticity angle and are independent of the Faraday rotation. The orientation of the fiber is set to make the $\xi $ parameter zero. It is then possible to retrieve the value of ${\eta _F}$, due to MCD, by combining the values of the first and second harmonics and choosing the amplitude of the modulation of the phase ${\varphi _{12}}$ such as: ${J_1}({{\varphi_{12}}} )= {J_2}({{\varphi_{12}}} ) .$ The ellipticity angle is then given by the Eq. (2):
For the second configuration involving the separation of the polarizations by a Wollaston polarizer, the intensities measured for the vertical, ${I_v}$, and for the horizontal polarization, ${I_h}$, are:
The sum of the two intensities leads back to the previous results for the configuration without the polarizer. The difference of the two intensities $\mathrm{\Delta }I(t )= {I_h}(t )- {I_v}(t )$, is now independent of ${\eta _{F\; }}$ and varies with the sine of $4{\theta _F}$ preferred for its variations for low values. The different harmonics for $\mathrm{\Delta }I(t )$ are:
In the calculation of Faraday rotation, akin to Eq. (2), adjusting the modulation amplitude of the PEM to ${\varphi _{12}}$ eliminates the unknown $\varphi $ dephasing. The resulting expression for the Faraday rotation is as follows:
The value of the dephasing introduced by the fiber is simply given by:
for ${\varphi _M} = {\varphi _{12}} = 2.5\; rad$, and ${J_1}({2.5\; rad} )= {J_2}({2.5\; rad} )= 0.4623$.Since the magneto-optical material can be directly deposited onto the fiber and can even be scaled down to match the core's dimensions, our primary aim is to maintain a compact footprint for the sensing segment. In our sensor arrangement, incoming light polarization is dynamically modulated through a photoelastic modulator.
Among the various detection approaches, the inline Sagnac interferometer offers notable benefits in terms of stability and sensitivity [10]. This setup relies on interferometric measurement of phase shifts experienced by two circular waves polarized in opposite directions as they traverse the magneto-optical medium. To implement the Sagnac configuration, the use of a quarter waveplate positioned just before the sensing section is necessary. However, the introduction of the quarter waveplate and the opto-mechanical apparatus required for its integration within the fiber-based circuit detracts from the advantage of maintaining a compact sensor. In the initial setup configuration, the dephasing angle φ introduced by the fiber is considered, rendering the quarter-wave plate unnecessary. The value of this angle can be calculated and compensated using Eq. (6). An example of a measured mean value for $\varphi $ of 0.27 radians is presented and detailed calculations are provided in Supplement 1.
4. Results
In pursuit of measuring the response within the context of the second configuration setup, we subject the optical fiber's end to a time-varying magnetic field via an electric coil, as depicted in Fig. 3. The modulation of this magnetic field is controlled by means of a current generator. For this particular evaluation, we opt for an arbitrary frequency of 23 Hz, selecting an amplitude that generates magnetic fields spanning the range of 2 mT to 100 µT. The MO response is gauged on a synthesized garnet layer measuring approximately 200 nm in thickness, positioned at the end of a 0.5-meter optical fiber. It is worth emphasizing that the time constant of the lock-in amplifiers, essential for precise parameter measurement, needs to be judiciously chosen. It should be extended enough to facilitate accurate integration of the 50 kHz modulated signal, yet concurrently short enough compared to the characteristic time of random phase variations denoted by $\varphi $. As a general practice, this constant is set below 1 ms.
The outcomes of these experiments are presented in Fig. 4. The Fourier spectrum of the FR measurements (as depicted in Fig. 4(a)) unveils distinct and well-defined peaks at 23 Hz, exhibiting amplitudes that fluctuate in accordance with the magnetic field's strength. The resultant FR values, plotted against the magnetic field, are illustrated in Fig. 4(b). Notably, these values clearly follow a linear law, as anticipated. Evidently, the detection of magnetic fields at the 100 µT level is easily attained in this setup.
Fig. 4. (a) Fourier spectrum of the FR response, (b) FR angle dependency on the amplitude of the magnetic field.
In contrast to the setup depicted in Fig. 3, the arrangement for the 1st configuration simplifies matters by omitting the inclusion of a half-wave plate, a Wollaston polarizer, and employs just a single detector. Similar to the previous scenario, the magnetic field at the optical fiber's end is modulated at a frequency of 23 Hz, with amplitudes ranging between 2 mT and 100 µT.
The findings of this setup are showcased in Fig. 5(a). The Fourier spectrum of the response concerning the ellipticity angle aptly displays a sharp peak at 23 Hz, aligning with our expectations. The same linear dependence of ellipticity angle on the amplitude of the applied magnetic field is observed in Fig. 5(b).
Fig. 5. (a) Fourier spectrum of the ellipticity angle response, (b) ellipticity angle dependency on the amplitude of the magnetic field.
In Supplement 1, we present the temporal variation of the measured ellipticity response, showcasing diverse shapes of amplitude modulation in the magnetic field. The modulation has a consistent 1 mT amplitude and operates at a frequency of 23 Hz, as illustrated in Fig. S4. Additionally, our investigation extends to the MO response measurements under the same configuration. The magnetic field spans from −200 mT to 200 mT, revealing the hysteresis loop associated with the Bi: YIG synthesized at the fiber end. This insightful hysteresis behavior is depicted in Fig. S5. Importantly, we highlight that the magnetic circular dichroism-based measurements exhibit sensitivity comparable to FR-based measurements. Notably, these measurements achieve this sensitivity with fewer optical components and a simplified detection scheme.
5. Conclusion
In this paper, we present a simple and low-cost procedure of functionalization of optical fiber by Bi: YIG microcrystals with 2-3 µm size self-centered on the fiber’s core. Furthermore, we built the experimental optical setup for magnetic field measurements in the range from 100 mT down to 50 µT for such fibered MO sensor head, operating as well on the Faraday rotation as on the magnetic circular dichroism (ellipticity angle). The last one can bring a new perspective of fiber magnetic field detection as far the sensitivity is comparable to the device based on FR, but with a much-simplified detection system.
Funding
Agence Nationale de la Recherche (ANR-10-EQPX-52, ANR-16-CE08-0014-01).
Acknowledgments
The authors acknowledge financial support from the French National Research Agency via the project FOGAMO [grant number: ANR-16-CE08-0014-01] and the project Equipex UNION [grant number: ANR-10-EQPX-52].
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
Supplemental document
See Supplement 1 for supporting content.
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