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Abstract
We provide the experimental research on a novel type of all-dielectric magnetic structure designed to achieve an enhanced magneto-optical response. 1D grating fabricated via etching of bismuth substituted iron garnet film supports the excitation of optical guided modes, which are highly sensitive to the external magnetic field. A unique feature of proposed structure is the synergetic combination of high transparency, tunability, high Q-factor of the resonances and superior magneto-optical response that is two orders higher in magnitude than in the non-structured smooth iron-garnet film. The considered all-dielectric magnetic garnet structures have great potential in various fields including the magneto-optical modulation of light, biosensing and magnetometry.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Rapid development of nanostructured materials [1] combined with the magneto-optical response allowed to find various applications in different fields of science and technology, such as sensing [2–4], magnetometry [5,6], routing [7], informantion storage [8]. In such structures special selection of parameters result in resonant phenomena leading to a significant increase in the optical and magneto-optical effects and modulation of the polarization and intensity of the light.
One of the goals of current research is to investigate possible enhancement of magneto-optical effects, namely transverse magneto-optical Kerr effect (TMOKE) determined as the relative change of the reflected or transmitted light intensity in magnetized materials [9]. This effect is rather small in bulk mediums, nevertheless, nanostructuring can significantly increase its absolute value. Although some enhancement was observed in the magnetic diffraction gratings [10], the most promising nanostructures in these fields are magneto-plasmonic crystals, which are periodic gratings with magnetic material providing the excitation of surface plasmon polaritons (SPPs) at the metal/dielectric interface. The wave vector of SPP can be nonreciprocally changed by an external magnetic field leading to significant enhancement of magneto-optical effects [11–14]. However, the presence of metal components in plasmonic nanostructures provide considerable absorption losses making such structures non-transparent and the observed resonances broad and low-Q. Excitation of the optical resonances in dielectric nanostructures is more promising in the sense that they offer superior merits over metal-dielectric nanostructures. However the approaches in these schemes have several disadvantage of their own [15,16]. Recently performed theoretical studies showed the possibility to significantly improve the TMOKE response using subwavelength nanowire gratings [17] or focusing on finding bound in the continuum states in different magnetic structures [18,19]. But the most feasible in terms of fabrication and promising way is utilizing 1D all-dielectric resonant gratings with guided modes [19–21], however experimental results have not been demonstrated thus far.
For the first time, we perform the experimental observation of multifold TMOKE enhancement in all-dielectric resonant subwavelenth gratings with three major advantages. First, the gratings are fabricated via etching of the iron-garnet film - a highly transparent dielectric material (Im$(\varepsilon )\sim 0.002$) with superior magneto-optical response ($\varepsilon _{xz}\sim 0.01$). Secondly, the structures are designed to support propagating TM-polarized modes with the dispersion extremely sensitive to the external magnetic field, in contrast to localized Mie [15,22] or surface plasmon [13] modes. Third, due to the high refractive index of the garnet material, the excited mode energy is concentrated predominantly in the magneto-optical material itself. Therefore, this approach allows one to obtain high-Q resonances of TMOKE with the magnitude two orders higher than for a smooth magnetic film without any modes combined with high transparency of the structure ($T>80\%$).
2. Nano-fabrication of the gratings
The films of bismuth-substituted iron garnet (BIG – Bi$_{1.0}$Lu$_{2.0}$Ga$_{0.7}$Fe$_{4.3}$O$_{12}$) grown on gadolinium gallium garnet (GGG) substrate by liquid-phase-epitaxy were used in this study. 2 µm thick BIG film in the original wafer piece was reduced to $225$ nm thin film by wet etching in ortho-phosphoric acid ($85\%$ from Sigma-Aldrich) for about an hour. The acid was heated to $130^{\circ }C$ and stirred using a magnetic stirrer for uniform etching of the film. The thickness of the film was measured using variable angle spectroscopic ellipsometry. Nano-patterns were then fabricated using a $100$ KeV e-beam lithography system (VISTEC EBPG 5000+). A $250$ nm-thick ZEP positive e-beam resist was spin-coated on the substrate together with a $30$ nm-thick gold layer coating on top to suppress electrical charging of the dielectric garnet film during electron-beam exposure. 1D gratings were patterned on ZEP resist by uniform e-beam exposure at a dose of 150 µC/cm$^2$ under proximity effect correction (PEC). The gold layer was first removed by wet etching in a gold etchant solution and afterwards the resist was developed in an amyl acetate solution. The resist patterns were then transferred onto the BIG film by sputter-etching in an argon-ion milling system (Intlvac Nanoquest) with ion source parameters: beam voltage - $200$ V, accelerating voltage - $24$ V, beam current - $70$ mA and plasma forward power - $72$ Watt. The sample stage temperature was kept at $6^{\circ }$C throughout the etching duration. The resist was then removed using resist remover N-methyl-2-pyrrolidine (NMP) by heating at $80^{\circ }$C for about half an hour. Finally, the sample was wet-etched in phosphoric acid at $120^{\circ }$C for $\sim 1$ minute to smoothen the side walls of the structures.
The nano-fabrication was conducted to provide two different types of structures: with fully etched iron-garnet grating and with partially etched one. The height of the gratings in both cases is $h_1=225$ nm and the thickness of BIG layer left below the grating in partially etched structure is $h_2=75$ nm. Gratings were fabricated with different widths of an air gap $W$ and different periods of the structures $P$ (Fig. 1). In order to study how different grating parameters influence optical and magneto-optical properties of the structure, the following gratings were selected: $P=350, 400, 450, 500, 600$ nm, $W=200,300,400$ nm, $h_2=0$ or 75 nm.
Fig. 1. (a) Schematic representation of fabricated partially etched structure (for fully etched one $h_2=0$) and mode excitation; (b) Scanning electron microscope image of an 1D BIG partially etched grating. (c) Schematic representation of TMOKE enhancement via magnetic-field induced variation of mode propagation constant $\Delta \beta$.
3. Optical and magneto-optical resonances of the guided modes in 1D BIG gratings
The formation of 1D gratings in the film with the refractive index higher than the surrounding media ($n_{BIG}\sim 2.25$, $n_{GGG}\sim 1.95$) excites the guided modes propagating inside the BIG layer perpendicular to the slits (Fig. 1(a)) under the following excitation condition:
where $k_{0}=2 \pi /\lambda$ is the wave vector of the incident light, $\lambda$ is wavelength of incident light in free space, $\theta$ is the angle of incidence, $m$ is the diffraction order, $G=2 \pi /P$ is the reciprocal lattice vector value, $\beta _0=2 \pi n_{\beta _N}/\lambda$ is the wave vector of the guided mode, $n_{\beta _N}$ is a refractive index of the guided mode. In the fabricated structures both TM$_0$- and TE$_0$-polarized guided modes are efficiently excited by p- and s-polarized light respectively. We focus our attention on the TM-polarized mode excited by p-polarized light as it allows for the significant enhancement of the transverse magneto-optical Kerr effect.The characteristics of excited guided modes are well described by the theory of planar waveguides where the patterned iron-garnet is considered as a smooth film with corresponding effective refractive index. Thus, the dispersion equation for excited TE-modes ($\Sigma =0$) and TM-modes ($\Sigma =2$), which determine $n_{\beta _N}$ (and, therefore, $\beta$) as a function of the wavelength $\lambda$ and the thickness of the guiding layer $h=h_1+h_2$ (in the case of fully etched structure $h_2=0$), has the following form [23]:
Thus, the 1D grating in this case is used to achieve the phase matching conditions between the incident light and the waveguide mode through diffraction. On the other hand, the grating itself is medium for the mode propagation.
In the structures with subwavelength period, only zeroth propagating diffraction order exists. The effect of mode excitation can be clearly seen in the transmittance spectra (Fig. 2(a) and (b)). Q-factor of the resonances obtained in partially etched grating is about $Q=\lambda /\Delta \lambda =138$. This value is almost one order of magnitude larger that the one for the magneto-plasmonic structures reported previously [13]. Such a narrow resonance width makes partially etched structure highly sensitive to external changes induced, for example, by applying magnetic field.
Fig. 2. Wavelength vs. angle spectra of 1D all-dielectric partially etched grating ($P=500$ nm, $W=200$ nm, $h_2=75$ nm): transmittance (a,b) and TMOKE (c,d) obtained experimentally (a,c) and numerically (b,d) using rigorous coupled-wave analysis method.
Along with this, utilization of dielectric materials provides high transmittance of the gratings ($T\approx 70\%$) in the spectral area of interest, and the resonances manifest as the noticeable dips up to $\Delta T\approx 30\%$ in magnitude. Notice that due to the high Fresnel reflection from GGG substrate ($n_{GGG}=1.95$), demonstrated transmittance is close to its theoretical limit $T=80\%$.
Transverse magneto-optical Kerr effect (TMOKE) is determined as the relative change $\delta$ of the reflected or transmitted light intensity in the transverse orientation of sample magnetization ($\mathbf {M}$) with respect to the plane of the incident light ($\mathbf {M}$ is oriented along the external magnetic field $\mathbf {H}$ in Fig. 1(a)).
We study the modulation of the intensity of the light transmitted through the structure, the value of $\delta$ is defined as:
TMOKE originates from the magnetic-field induced modification of the boundary conditions for $\mathbf {D}$ vector [9]. The enhancement of this effect in resonant structures with guided modes arises due to the impact of transverse magnetization on the mode propagation constant. An additional term [9] $\Delta \beta$ in the dispersion equation (2) appears that is linear on magnetization: $\beta (\mathbf {M})=\beta +\Delta \beta (\mathbf {M}).$ Both the propagation constant $\beta$ and the additional magneto-optical term $\Delta \beta (\mathbf {M})$ have real and imaginary parts.
Let us first consider the case of low mode attenuation: $Im(\beta )\ll Re(\beta )$, so that $Im(\Delta \beta )\ll Re(\Delta \beta )$. Modification of the real part of the propagation constant $\Delta \beta (\mathbf {M})$ leads to a shift of the position of the resonance dip in spectra according to Eq. (1). This shift results in the modulation of the intensity of the transmitted and reflected light as schematically shown in Fig. 1(c) and produces S-shaped TMOKE response. Figure 1(c) also illustrates that the narrower the resonance is, the more prominent changes of the transmittance or reflectance are observed for the same $Re(\Delta \beta )$. Thus, high-Q modes excited in the considered structures provide a significant enhancement of TMOKE.
For the guided modes with higher losses: $Im(\beta )\sim Re(\beta )$, $Im(\Delta \beta ) \gg Re(\Delta \beta )$ the magneto-optical variation of the imaginary part of the propagation constant is more important. It results [16] in the simultaneous variation of the resonance depth and width as shown schematically in Fig. 1(c) and produces U-shaped TMOKE response. The relative variation of the transmittance or reflectance increase with the increase of $Im(\Delta \beta )/Im(\beta )$ ratio, so that all-dielectric nanogratings are superior compared to the magnetoplasmonic structures where the metals produce high $Im(\beta )$.
It is worth noting, that the magnetization of the structure does not affect the TE-polarized modes, and consequently, s-polarized incident light.
The experimental spectra of resonances associated with the guided modes both in transmittance and TMOKE spectra are in a good agreement with the numerical simulations performed using rigorous coupled-wave analysis (RCWA) method [24] shown in Fig. 2. Notice that the maxima of the TMOKE effect correspond to the slope of the resonance curve in transmittance rather than to its dip, so that it is possible to achieve simultaneously high transmittance $T\sim 60\%$ and TMOKE $\delta \sim 0.9\%$.
4. Comparison of fully and partially etched 1D BIG gratings
The important feature of the proposed structures is the possibility to excite the guided resonances even in the case of the fully etched gratings, in which the BIG columns are separated by the subwavelength air slits. Figure 3(c) and (f) show the distribution of $H_y$ component of electromagnetic field for TM$_0$-mode excited in both structures under illumination of the p-polarized light. Eventhough considerable part of the mode energy excited in the partially etched structure lies in the area of thin BIG film below the grating, the presence of gratings plays an important role in the process of mode propagation. It can be seen from Eq. (2) that $75$-nm thick smooth film alone does not support the TM$_0$-modes itself whereas the structured film does. Moreover, Fig. 3(c) and (f) show that even in the case when the guided layer itself is not continuous and contains the subwavelength air slits, the guided mode is excited with a rather good efficiency and has electromagnetic field only 1.5 times smaller magnitude.
Fig. 3. Transmittance (a,d) and TMOKE (b,e) spectra for partially (top pane) and fully (bottom pane) etched structures with the same period and air gap width of the grating ($P=600$ nm, $W=200$ nm) under the illumination of p-polarized incidence light. Electromagnetic field distribution ($Re(H_y)$ component) of TM$_0$-mode for partially (c) and fully (f) etched structures.
Closer comparison between two types of structures reveals that the fully etched one provides considerable scattering losses and the magnitude of the excited mode is lower (Fig. 3(c) and (f)). Thus, the waveguide mode propagation length in this structure is shorter than in partially etched one. This impacts into broadening of the resonances and lowering their Q-factor value ($Q=189$ in partially etched vs. $Q=85$ in fully etched ones).
Such difference also manifests the change in the shape of the TMOKE spectra (Fig. 3(b) and (e)): it is S-shaped in partially etched structure and U-shaped in the fully etched case. This means that the external magnetic field predominantly makes an impact on the real part of the propagation constant associated with the resonance position in partially etched structures, where the scattering and absorption losses are low (see Fig. 1(c)). In contrast to that, in fully etched structures the magnetic field impacts on the imaginary part of the propagation constant associated with all kinds of losses and is responsible for the resonance width and depth.
However, in both kind of the structures, the value of the TMOKE is almost two orders higher than in a smooth magnetic film without any modes.
5. Control of TMOKE resonance spectral position
The spectral position of the resonance can be controlled via its geometrical parameters. The height of the BIG grating and unetched smooth BIG sublayer, as well as the width of the air slits, determine the effective refractive index of the guiding layer $n_2$. The increase of the amount of BIG in the 1D grating leads to the increase of $n_2$ and results in the red-shift of the guided wave spectral position. For example, variation of the air slit width between the BIG grating columns changes the effective refractive index of the guiding layer: the larger the slit is, the lower $n_2$ the structure possesses. However, widening of the air slit (as well as reducing the thickness of the smooth sub-layer, see Fig. 3(b) and (e)) leads to the increase of scattering losses that results into deterioration, and in some cases – to the disappearance of the guided-wave associated resonances (see Fig. 4(b), where the TMOKE resonances for $W=200$ nm are well-pronounced, and for $W=400$ nm, disappear completely).
Fig. 4. Wavelength spectra of TMOKE for structures with different period of the gratings and the same width of the air gap ($W=200$ nm) (a); and for structures with different width of the air gap and same period ($P=600$ nm) (b). Measurements were obtained under the illumination of p-polarized light at the fixed angle of incidence $\theta =10$ degrees. The standard deviation is about $7 * 10^{-2} \%$.
Moreover, $n_2$ for the discussed structure could vary in the range $n_{GGG}=1.95<n_2<n_{BIG}=2.3$, so the resonance could be shifted for only about $25\%$ of the wavelength. Such moderate changes of the resonance position can be observed in Fig. 3(b) and (e) showing TMOKE for different $h_2$, and in Fig. 4(b), corresponding to different $W$. As the variations of the resonance position are low, this way of the guided-mode resonance control is not the optimal one.
Another possibility to control the resonance position is by the variation of the period $P$ of the structure (Fig. 4(a)), which, according to Eq. (1), could significantly change the resonance spectral position. Guided mode could be efficiently excited at any wavelength of the BIG transparency range $\lambda >500$ nm (Fig. 4(a)) in contrast to the BIG-based plasmonic structures, where the resonant wavelength is limited by the ratio of the BIG and metal permittivity (that results in the limitation $\lambda >700$ nm). This tunability and flexibility of resonance position of the proposed BIG gratings is important as variation of BIG magneto-optical activity [25,26] with the wavelength can be exploited to control the resonance position. This could be also seen in Fig. 4(a) where the long-wavelength TMOKE resonance has the lower magnitude compared to the short-wavelength resonance of the same grating.
Absolute values of TMOKE enhancement obtained (up to $\delta \approx 1\%$) are three orders of magnitude greater than that of a smooth $300$-nm-thick smooth BIG film ($\delta \approx 0.004\%$ measured at $780$ nm). In addition, TMOKE resonances possess a high Q-factor of $155$ and a width at half maximum of about $4$ nm. The obtained values are also an order of magnitude higher than those obtained in the study of plasmonic crystals reported previously [11–14] and are accompanied by significantly higher transparency and resonance quality factor.
6. Conclusion
Nanostructured all-dielectric gratings made of bismuth-substituted iron-garnet film were demonstrated to provide the effective excitation of waveguide modes leading to significant increase in TMOKE combined with high transmittance of the structure. The utilization of all-dielectric materials makes it possible to investigate changes in transmitted light and obtain high-Q resonances. Obtained values of Q-factor are hardly attainable using magneto-plasmonic gratings.
The ability to control the spectral position and amplitude of the resulting resonances by changing the parameters of the structures was experimentally demonstrated. One could tune the optical and magneto-optical resonance position to any desired wavelength by changing the BIG grating period.
Further tuning of the structure parameters, for example filling the air gaps with high-refractive index materials could improve the guiding properties of the structure and lead to the further amplification of the magneto-optical response.
High transparency of the structures and Q-factor of the resonances open up wide possibilities for application in the field of magneto-optical modulation of light. The advantages of the considered structures are also highly valuable for implementation in the field of biosensing and magnetometry.
Funding
Russian Science Foundation (18-72-00233).
Acknowledgments
The gratings were fabricated at the Nano-fabrication facility, Nanocenter, University of Minnesota and the microfabrication facility (MFF) at Michigan Tech. University. ML and DK gratefully acknowledge support from the Michigan Tech Henes Center for Quantum Phenomena.
Disclosures
The authors declare no conflicts of interest.
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