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Abstract
The enhancement of magneto-optical (MO) effects in planar devices is commonly obtained through the combination of a plasmonic resonance and a MO material, or through the microstructuration of such materials. However, the devices often suffer from weak optical signal, or require fastidious lithography processes. We present a much simpler device made of a photoresist 1D grating processed on a MO composite planar waveguide. This latter is formed by magnetic nanoparticles embedded in a silica matrix. Such all-dielectric device produces much higher Q-factor resonances, which finally result in giant MO intensity effects. Their magnitude combined with the ability of the device to be processed on large scale and various substrates, are very promising for a wide range of sensing applications.
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1. Introduction
Magneto-Optical (MO) [1] effects are described by a modulation of the intensity, the phase or the polarization of light, reflected or transmitted through a magnetized MO material. The transverse magneto-optical Kerr effect (TMOKE) describes the intensity modulation effect, through the influence of a magnetic field $\overrightarrow {B}$ applied perpendicularly to the incident plane. Due to the magnetic field configuration, this effect exists only for TM-polarization (its electric field components lies in the incident plane), and for oblique incidences. Thus, the TMOKE $\delta$ is defined as the relative change of the intensity $I$ of the transmitted (or reflected) light upon magnetization $M$ reversal [2]:
Due to its magnetic field dependance, the TMOKE can be used to improve the sensitivity of optical sensors [3–6]. Thus, suitable devices based on such effect are currently highly desirable for several applications like integrated biosensing, non-destructive testing or fast spatial light modulation. However, the TMOKE response of continuous magnetic films such as nickel or cobalt is of the order of 0.1% [1], and its detection is challenging, what limits its practical applications. Thus, the enhancement of this effect is currently taking lots of attention, and different approaches have been implemented to reach this objective. In each case, the principle is to combine a MO material with a resonant device in order to enhance light-matter interaction.
Concerning planar devices, most of these structures are magneto-plasmonic with a combination of the MO activity with surface or localized plasmon resonances [7]. Among the magneto-plasmonic structures implemented to enhance the TMOKE signal, one can cite Au/Co heterostructures processed as 2D membranes or coupled to a multi-layer resonator [8–11], 2D Mie Ni nanoantennas [12], or 1D Au grating deposited on top of a magnetic film, generally Bi-substituted Yttrium Iron Garnet (Bi:YIG ) [2,13–17]. In this latter case, the incident light is resonantly coupled through the grating to the TM waveguide plasmon polariton mode which propagation constant is modulated by the transverse magnetic field. The spectral position of the maximum of the transmitted (or reflected) light is thus highly sensitive to the magnetic field leading to an enhanced MO effect. Thereby, Pohl et al. [16] experimentally reached a TMOKE signal up to 13% with a transmittance of 6%. Furthermore, such devices which support hybrid dielectric/plasmonic modes are suitable for polarization rotation enhancement because they can ensure a phase matching between TE and TM modes [18]. However, magneto-plasmonic devices often suffer from a low optical response (transmittance or reflectance) because of the large absorption of the metal, limiting hence the resonances Q-factor [19,20]. Even if Kaihara et al. [21] have proposed a trilayer dielectric/metallic configuration which increases the propagation distance of surface plasmon mode, the most relevant way to reduce the losses is to work with all-dielectric resonant structures. In this vein, large enhancements of MO effects were theoretically demonstrated through magneto-photonic metasurfaces of 2D array of Bi:YIG nanodisks [19,22], or through 1D all-dielectric MO gratings [23,24]. Nevertheless, few experimental demonstrations exist because of the difficulty to process YIG-type materials on photonic substrates, and to pattern them at the sub-micron scale [25,26]. One can nonetheless cite the recent enhancement of both Faraday and Kerr effects with a 1D Si$_{3}$N$_{4}$ impregnated with a MO nanocomposite [27], or the TMOKE enhancement up to 1% with a grating patterned at the surface of a BIG layer [20,28]. In these two examples, the device behaves as a guided-mode resonance (GMR) grating [29,30], with a resonant coupling of the incident light to the guided modes of the dielectric waveguide leading to a dip in the transmittance spectrum. But, in both cases, the fabrication process of the device is not straightforward with the requirements of fastidious lithography processes, not suitable for large scale or mass production.
We propose, in this work, another type of GMR device made of a 1D photoresist grating on top of a MO composite layer made of CoFe$_{2}$O$_{4}$ nanoparticles embedded in a silica matrix. This all-dielectric structure is easily realized through liquid phase coatings of the sol-gel MO composite and the photoresist at low temperature, followed by a classical photolithographic step to form the grating. It has shown its ability to enhance longitudinal Kerr effect [31], but it is much more suitable for TMOKE enhancement because of the high Q-factor of its TM resonance. In the following section, a theoretical analysis of the TMOKE enhancement mechanism in such structure is presented with the support of numerical simulations. Experimental details about the realization of the device, the measurements set-up and the simulation tools are gathered in the materials and methods section. Measurements of TMOKE in transmission and reflection modes are then presented, compared to the simulations and to already published works.
2. TMOKE enhancement analysis
The optical and MO behavior have been simulated with a homemade RCWA (Rigorous Coupled Waves Analysis) code, taking into account the whole permittivity tensor [32]. This code has previously been employed to calculate intensity as well as polarization rotation magneto-induced effects in resonant devices [24]. The Fourier modal method (FMM) or RCWA is the most suitable numerical method to solve Maxwell’s equations and analyze the interaction of electromagnetic waves with periodic diffractive structures. The simulated TMOKE signal is defined as in Eq. (1).
The structure under consideration is illustrated in Fig. 1(a). It consists of a photoresist (PR) grating (n$_{PR}$ =1.59), with height and width equal to 300 nm and 400 nm respectively, on top of a MO thin film. An example of a 3D image for the PR grating’s topography, obtained by AFM measurements, is illustrated in Fig. 1(b). One can notice from this figure the uniformity and the rectangular profile of the grating.
Fig. 1. (a) Schematic representation of the structure geometry, the incidence conditions and the magnetic field configuration for TMOKE. (b) 3D image of the photoresist grating’s topography obtained by AFM measurements. (c) Simulated distribution of the magnetic field intensity $|H_z|$ of TM-polarized incident light in the $xy$ plane, for AOI=2$^\circ$ at the coupling wavelength ($\lambda _{0}=1550$ nm).
The MO film is formed by magnetic nanoparticles embedded in a silica matrix by a sol-gel process and deposited on a glass substrate (n$_s$ = 1.51). For a nanoparticles volume fraction of 26%, the refractive index of this composite film is n$_{f}$ = 1.64. Considering the coupling equation: $\beta =2\pi sin($AOI$)/ \lambda _{0}+2m\pi / \Lambda$ ($\beta$ the propagation constant, $\lambda _{0}$ the wavelength, AOI the angle of incidence, $m$ the diffraction order and $\Lambda$ the grating period), and in order to obtain a resonant transmittance dip around 1550 nm for angles close to normal incidence, $\Lambda$ the period of the grating has been fixed to 1000 nm.
Thus, at 1550 nm, a coupling of the incident light to the waveguide mode takes place as illustrated in Fig. 1(c) for an AOI=2$^{\circ }$. This field map evidences the main confinement of the light in the MO film waveguide, and a minor part in the substrate. Very little field is confined in the PR grating. Such coupling of the incident light to a waveguide mode results as a dip in the far-field transmittance or a peak for the reflectance [30].
In such devices, the enhancement of TMOKE is based on the phase shift induced by a transverse magnetic field on the TM waveguide mode propagation constant, leading to a shift of the transmittance or reflectance spectra. Indeed, in a planar MO waveguide, a transverse magnetic field induces intra-modes coupling that produces a modification of the TM propagation constant ($\beta$) upon magnetization reversal, as illustrated by the dispersion equation of TM guided-mode subjected to a transverse magnetic field [33]:
Thus, the optimization of TMOKE in the structure under consideration has been carried out through numerical simulations in order to follow these two requirements. Concerning the optical resonance quality, it has been studied for different MO film thicknesses ($t_{MO}$). Figure 2(a) illustrates a calculated 2D diagram of the transmittance (T) as a function of the wavelength and the MO film thickness ($t_{MO}$), for TM polarization ($x$ direction referring to Fig. 1(a)) at an AOI = 2$^\circ$. The behavior of the resonance wavelength, as a function of $t_{MO}$ is explained by the propagation equation of guided-modes in dielectric planar waveguides. Hence, as seen in Fig. 2(a), a guided-mode does not always exist: a sufficient thickness of guiding layer is necessary and it is named cut-off thickness.
Fig. 2. (a) Calculated 2D diagram of the transmittance at AOI=2$^\circ$ and for TM polarization, as a function of the wavelength and the MO film thickness, for the structure of Fig. 1(a). (b) TM propagation constant shift upon magnetization reversal, in a MO waveguide illustrated in inset with the following parameters : $\epsilon _c=1.77$, $\epsilon _s=2.28$, $\epsilon _f=2.7$ and $\epsilon _{MO}=-0.0064$. Calculated (c) transmittance and (d) TMOKE spectra for different MO film thicknesses, for the structure of Fig. 1(a). $\epsilon _{MO}$ was fixed to a value of -0.0064+i0.0044. Inset (c) calculated Q-factor as a function of the MO film thickness.
Moreover, one can see in Fig. 2(a-c) that by increasing the thickness, the Full-Width Half Maximum (FWHM) of the transmittance resonance increases while its amplitude decreases. Indeed, near the cut-off value, for $t_{MO}=380$ nm, the FWHM of the transmittance resonance is very small ($\Delta \lambda =$ 0.5 nm) resulting in a very high Q-factor ($Q=\lambda /\Delta \lambda$ ) [20] equal to 3000 at $\lambda =1545$ nm (see inset Fig. 2(c)). Such value, which benefits from the optical quality of the MO film [35], is two orders of magnitude higher than that demonstrated previously with a magneto-plasmonic structure [36], and one order higher than that achieved through an all-dielectric GMR structure based on a BIG grating [20]. The increase of the FWHM with the thickness and the decrease of the resonance magnitude are linked to the electromagnetic field distribution of TM mode inside the MO film. It is well known that, for a planar waveguide, the quantity of mode field (see Fig. 1(c)) confined in the film depends on thickness. If $t_{MO}$ is higher, the mode field is more confined in the MO film which is absorbing, and less in the substrate. Thus, the light absorption increases leading to resonances with larger FWHM and weaker amplitudes. Hence, as illustrated in Fig. 2(c), in order to increase the Q-factor of the resonance, it is more favorable to work with $t_{MO}$ close to cut-off value.
Concerning the field induced modification of the TM mode propagation constant ($\Delta \beta _{\pm M}$), it has been calculated using Eq. (2) and reported in Fig. 2(b) as a function of the thickness for a MO planar waveguide without any grating (see inset Fig. 2(b)). To take into account that the grating exists in the real device, the permittivity of the cladding layer has been obtained through an effective medium approximation between air and PR ($\epsilon _c=1.77$). As demonstrated a long time ago by Auracher et al. [37], $\Delta \beta$ increases with the thickness to rapidly reach a maximum value not so far from the cut-off.
Finally, the two requirements about the resonance Q-factor and shift $\Delta \beta$ lead to a MO film thickness close to the cut-off value. As a confirmation, the calculated TMOKE, reported in Fig. 2(d) for several thickness values, is maximum for the thickness close to the cut-off, with a TMOKE value up to 11% associated to a transmittance of 62%. When the thickness increases, the TMOKE then decreases.
3. Materials and methods
The PR grating was prepared by a classical photolithographic process using a periodic quartz-supported chromium amplitude mask. In order to insure the presence of the TM mode with the given waveguide parameters, the PR grating is not dug to the bottom and a thin layer of thickness 130 nm is kept since its refractive index is close to that of the MO waveguide.
The MO material is a composite consisting of cobalt ferrite ($CoFe_{2}O_4$) nanoparticles embedded in a silica matrix by the sol-gel process [38]. The MO waveguide was prepared by depositing a layer of the MO composite on a glass substrate by dip coating, then thermally treated at $90^\circ$C for one hour.
An important feature of the MO composite is that the whole permittivity tensor can be tuned by modifying the volume fraction of nanoparticles ($\phi$) inside the MO sol-gel [31]. The tensor permittivity terms for the MO composite, are given for $\phi =26\%$. This MO composite can be deposited on a large scale substrate with a thermal treatment of $100^\circ$C. Moreover, it can be employed to impregnate 1D [27], 2D [39] and 3D micro/nano-structured templates [40]. It was used as well for the fabrication of integrated MO converters [41].
At $\lambda =1550$ nm, the diagonal elements of the permittivity tensor of the PR, the substrate and the MO film are 2.5281, 2.2801 and $2.6896-i0.0144$ respectively. The off-diagonal element of the MO composite’s tensor permittivity is $i\epsilon _{MO}$ where $\epsilon _{MO}=-0.0064+i0.0044$ at $\lambda =1550$ nm.
The TMOKE measurement setup consists of a tunable laser DL pro TOPTICA photonics [1490 nm; 1630 nm] followed by a polarizer and a rotating sample’s support. This latter is placed in the air gap of an electromagnet generating a magnetic field oriented perpendicularly to the incident plane. The amplitude of the magnetic field can be varied in the range of [−900 mT; +900 mT] through a 4 quadrant linear amplifier HUBERT 1110-16-QE. The reflected or transmitted light through the sample is then analyzed by a photodetector. The reflected light is directed towards the photodetector by a mirror placed before the sample.
The TMOKE measurements consist of varying continuously the magnetic field for a fixed wavelength, and the intensity of the light is measured as a function of the magnetic field by the photodetector. As a result, an intensity hysteresis loop (see inset Fig. 3(b)) is obtained for each wavelength. The TMOKE is deduced from opposite saturated intensity values using Eq. (1) and then plotted as a function of the wavelength.
Fig. 3. (a) Measured transmittance for TM polarization (b) Measured TMOKE in transmission at AOI=2$^\circ$ and 4$^\circ$. Inset (b): measured intensity loop at $\lambda =1533.6$ nm for AOI=2$^\circ$. (c), (d): calculated transmittance and TMOKE spectra. Inset (d): calculated TMOKE spectrum for a single MO film at AOI=4$^\circ$.
The transmittance of the resonant structure is referred to the MO film transmittance and it is measured through a NIRQuest spectrometer, using a Laser-Driven Light Source (LDLS$^{TM}$).
4. Experimental results
Figure 3 illustrates the experimental values (a-b) and the numerical ones (c-d) of the transmittance and the TMOKE signal for AOI=$2^\circ$ and $4^\circ$, for the GMR structure illustrated in Fig. 1(a).
One can see in Fig. 3(a-c) dips in transmittance spectra down to 80% (measurements) and 65% (simulations) for the two AOI, revealing the guided-mode resonance [30]. The measured Q-factor reaches values of 283 for AOI=2$^\circ$ and 234 for AOI=4$^\circ$. These values could be higher as demonstrated by the simulations (Q=689 for AOI=2$^\circ$ and 833 for AOI=4$^\circ$), but the 2 nm spectral resolution of the used spectrometer in this configuration limits the accuracy of these measurements.
As seen in Fig. 3(b-d), the TMOKE signal is higher for AOI=4$^\circ$ and its spectrum is more asymmetric, compared to AOI=2$^\circ$. The measured TMOKE reaches 9.5% as highest value at $\lambda =1567.5$ nm for AOI=4$^\circ$, with a transmittance higher than 80%. These measurements are in good agreement with the simulations, and the small spectral shift can be related to the imperfections of the fabricated structure. The inset of Fig. 3(d) shows that the TMOKE signal for a single MO composite film is very small (maximum 0.001%), what evidences a four-order of magnitude enhancement of the TMOKE in transmission with the all-dielectric structure under consideration.
Simultaneously to the transmittance dip, the GMR structure produces a resonant peak of intensity in reflection [30]. Thus, the TMOKE signal has also been studied in reflection, for different AOI. Figure 4(a-c) illustrates respectively the measurements of the reflected intensity spectra and the simulations of the TM reflectance for different AOI (2$^\circ$, 4$^\circ$ and 5.5$^\circ$). One can see in Fig. 4(a) peaks in the reflected intensity spectra, which can be equivalent to 5% of reflectance as demonstrated in Fig. 4(c). These curves also evidence that by increasing the AOI, the resonances become narrower, with a Q-factor which varies from 770 at AOI=2$^\circ$ to 935 at AOI=5.5$^\circ$. This behavior is related to the fact that by increasing the AOI, in other words the coupling wavelength, the propagation constant of the TM guided-mode slightly decreases. Hence, the propagation constant is getting closer to the cut-off value resulting in narrower resonances as explained in the previous section. Concerning the values of the Q-factor, they are really substantial for a device employing a magnetic material [20,36]. Indeed, the MO composite, as other MO materials, absorbs the light, but as the structure is an all-dielectric one, there is no other contribution like metal loss, which may even more limit the Q-factor.
Fig. 4. (a) Measured reflected light intensity (b) Measured TMOKE in reflection for TM polarization and for different AOI. Simulated (c) reflectance and (d) TMOKE spectra. The dashed curves on (d) illustrate the dispersion of the real (black) and imaginary (gray) parts of the MO term $\epsilon _{MO}$ for cobalt ferrite nanoparticles with a concentration of 26%.
The measured and simulated TMOKE spectra are reported in Fig. 4(b-d). As seen on this figure, the TMOKE signal increases with the AOI and reaches a maximum value equal to 18.5% at $\lambda =1591$ nm (measured) and 42% at $\lambda =1609$ nm (simulated). One can mention that the TMOKE spectra is gradually asymmetric by increasing the AOI as for the TMOKE in transmission (Fig. 3(b-d)). A very good agreement between the simulations and the measurements can be mentioned concerning the spectral behavior of TMOKE resonances. However, due to fabrication and measurements imperfections, the simulated TMOKE signals are higher than the measured ones. One can also notice that the TMOKE in reflection is higher than in transmission (9.5%), contrary to MP structures [16]. The TMOKE signal in reflection for a single MO film is around 0.01%, hence a four-order of magnitude enhancement of this effect was achieved also in reflection through the all-dielectric GMR structure.
The angular evolution of the spectral behavior of the TMOKE signal in reflection and in transmission, can be interpreted through several aspects. Firstly, as mentioned before, the reflectance and transmittance resonances are narrower (higher Q-factor) for higher AOI, increasing thus the TMOKE signal. Indeed, a shift of a narrow resonance gives rise to a higher TMOKE response than the same shift of a broad resonance. Secondly, the dispersion of MO term $\epsilon _{MO}$ (dashed curves in Fig. 4(d)) plays a role in the increase of the TMOKE signal with the AOI as well as its asymmetric behavior. Indeed, as it was explained by Voronov et al. [20], the TMOKE signal results from the real and imaginary parts of $\epsilon _{MO}$. The TMOKE response resulting from Re($\epsilon _{MO}$) is described by a change in the propagation constant upon magnetization reversal (Eq. (2)), resulting in a spectral shift of the transmittance dip, giving a TMOKE signal with symmetric shape (two opposite peaks). However, the TMOKE signal resulting from Im($\epsilon _{MO}$) is described by a change in the extinction coefficient of the magnetic film upon magnetization reversal, resulting in a variation in the transmittance dip amplitude, giving a TMOKE signal with asymmetric shape (one peak).
Hence, the presented TMOKE signal (Fig. 3(b-d) and Fig. 4(b-d)) is the sum of these two contributions resulting from Re($\epsilon _{MO}$) and Im($\epsilon _{MO}$). Moreover, as seen in Fig. 4(d), the real part of $\epsilon _{MO}$ decreases with the wavelength, however the imaginary part increases. As a result, by increasing the AOI thus the wavelength resonance, the TMOKE amplitude increases and loses its symmetric shape.
In Table 1, the TMOKE values demonstrated in this work, are compared to others selected in the literature and obtained with all-dielectric or magneto-plasmonic structures. As seen in this table, the achieved values in this work (9.5% and 18.5%) are several times higher than those obtained by Frolov et al. [42] through a structure formed by multilayer Au/Ni/Au nanowires, or than those demonstrated by Barsukova et al. [12] through nickel nanodisks. Moreover, the demonstrated values are highly competitive with the values obtained by Pohl et al. [16], who experimentally demonstrated a TMOKE signal of 13% but accompanied with low transmittance (6%). Furthermore, the reached TMOKE value in reflection is higher than that demonstrated by Ignatyeva et al. [10] and Regatos et al. [4], who experimentally demonstrated values of 10% (with reflectance R=10%) and 15% (with R close to zero) respectively, through structures formed by multilayers of gold and cobalt. The MO term ($\epsilon _{MO}$) of this latter is in two or three orders of magnitude higher than that of the MO composite (see Table 1). However, the advantage of these structures is their sensitivity to the dielectric medium, hence they are promising for biosensing applications [43]. Finally, to the best of our knowledge, maximum TMOKE value equal to 1% in transmission was demonstrated experimentally through all-dielectric structure [20]. Therefore, the TMOKE values demonstrated in this work are far beyond, especially concerning the TMOKE in reflection which can achieve values up to 42% (predicted by the simulations). They are mainly related to the high quality of the TM resonance of the device. Combined with a non-sophisticated elaboration process suitable for large scale, the magnitude of these TMOKE effects makes the devices very promising for the realization of high sensitive and low cost MO sensors even on non-conventional substrates.
Table 1. Comparison of the TMOKE values demonstrated with different structures. Di and MP are abbreviations for All-Dielectric and Magneto-Plasmonic structures, respectively. NPs is abbreviation for Nanoparticles.
5. Conclusion
Large values of the TMOKE signal (up to 18.5% in reflection and 9.5% in transmission) accompanied with high optical responses, were experimentally demonstrated through an all-dielectric device made of a 1D photoresist grating deposited on top of a MO composite film. This latter is formed by cobalt ferrite nanoparticles embedded in a silica matrix by a sol-gel process. The large quality factor of the TM resonances plays a main role on these values (Q=935 in reflection and Q=234 in transmission). The simulated values are even higher, since a 42% TMOKE signal was achieved in reflection (Q = 3000). By increasing the incident angle, the TMOKE signal increases and its spectrum is gradually asymmetric. Such increase is linked firstly to the decrement of the FWHM with the angle of incident (higher Q-factor), and secondly to the dispersion of the MO term which is also responsible for the asymmetric shape of the TMOKE spectrum. Moreover, to maximize the TMOKE values, the MO film thickness should be close to the cut-off value in order to have the minimum transmittance resonance width. Based on these results and on its high transparency, the device is promising for applications such as integrated biosensors, fast spatial light modulators, spintronic properties evaluators and non-destructive testing. For example, the device can be easily adapted for non-destructive sensors dedicated to MO imaging of defects on aircraft cabins, or on the inner face of pipelines. Moreover, its simplicity to be processed even on large scale substrates is also convenient for mass production and thus low cost devices.
Funding
Agence Nationale de la Recherche (ANR-16-CE09-0017).
Disclosures
The authors declare no conflicts of interest.
Data availability
The data that support the findings of this study are available within the article.
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