1. Introduction

Broad potential for manipulating the flow of light has attracted attention to artificial periodic dielectric structures – photonic crystals (PCs) [1,2]. Spectra of PCs exhibit photonic (or directional) band gaps where electromagnetic wave propagation is forbidden [3,4]. Such phenomena as pseudogaps and complete band gaps [5], superprism phenomenon [6,7], localized surface states [2,8,9], selective switching of stop bands [10] and hypersonic modulation of light [11] are demonstrated for PCs with various designs. Magnetophotonic crystals (MPCs) – PCs with magnetic constituents – are shown to have unique optical and magneto-optical (MO) properties [12]. For MPCs there exists an additional degree of freedom to operate the photonic band structure, diffraction patterns, and the state of polarization of light [13–19]; i.e., their characteristics can be influenced by the external magnetic field. It is shown that MPCs enhance responses of known magneto-optical (MO) materials. In fact, the large enhancement of the Faraday rotation is demonstrated in one-dimensional (1D) MPCs composed of a magnetic garnet thin film sandwiched between dielectric Bragg mirrors [8,13,20]. The enhanced Faraday rotation can also be seen at the edges of PBGs appearing in multilayered magnetic structures [12,21]. All-garnet 1D MPCs fabricated by pulsed laser deposition are demonstrated and shown to exhibit good functional performance in the visible spectral range [16,17]. Bragg grating magnetic photonic crystal waveguides are shown to enhance polarization rotation [22]. Recently, analytical treatment has been demonstrated for birefringent 1D MPCs; the photonic band structure, Bloch states, mode coupling and energy band splitting are studied [23,24]. Surface state peculiarities in photonic structures composed of adjoining (interfacing) magnetic and nonmagnetic photonic crystals are shown to enhance Faraday (Kerr) rotation [25], which is experimentally demonstrated in Ref [26]. Moreover Faraday rotation in the finite MPCs appears to be a nonlinear function of the total thickness of magnetic material and can be interpreted as the nonlinear Verdet law [27]. Magneto-optical microcavity in 2D photonic crystals evanescently coupled to waveguides is proposed for three-port circulators [28,29]. Large and fast MO response of MPCs controllable by external magnetic fields has already found applications [20,30].

Thin opal films are considered one of the constituent elements of MPCs [12]. Opals, which are close-packed dielectric structures composed of amorphous SiO₂ spheres, are well-known representative of 3D PCs [31]. Their angle- and polarization-resolved spectra are studied in detail [32–35]. Introduction of a magnetic point, line or planar defect into the opal structure is of interest because light can be trapped within such defects; therefore enhancements of the linear and nonlinear MO effects in these structures are expected. Such structure, based on thin opal film with incorporated bismuth-substituted yttrium iron garnet (Bi:YIG) planar defect, has been recently discussed theoretically in Ref [36]. It was shown that in a 3D case light polarization rotation has more complicated underlying physics in comparison with its 1D counterpart. At the same time 3D structures demand high-quality opal films and the exact choice of magneto-optical layer parameters. In particular, thickness should be estimated numerically since simple analytical expression of 1D case appears to be inapplicable. This is one of the reasons why previously reported results on 3D heterostructures were not successful and no resonances were found [37]. It is worth mentioning that an 1D PC/Bi:YIG/opal multilayer has been reported [38], however its MO response was found to be weak because of structural asymmetry.

In this work we demonstrate magneto-optics of opal/Bi:YIG/opal heterostructures. We discuss their structural features which influence optical and MO responses. It was found that the opal surface triggered the 2D periodicity of the Bi:YIG layer when sputtering Bi:YIG on top of opals (by analogy with the fabrication approach considered in Ref [39].). Light diffraction from such a 2D grating of Bi:YIG appeared in angle-resolved spectra as an additional stop band. This resulted in a dramatic change and a reverse of the MO response in the Kerr geometry. Enhancement of Faraday rotation was observed for wavelengths of the Fabry-Perot resonance. This was possible due to correct selection of thickness of the Bi:YIG layer and opal films’ perfection; that both provided the high quality factor microcavity.

2. Samples and experiment

Oblique deposition (OD), which is an improved version of the vertical deposition method [40], was used for fabrication of thin opal films. The OD approach was to deposit opal films onto substrates introduced obliquely into the colloidal suspension of SiO₂ spheres. In this case all forces acting on spheres worked so that the crystallographic structure of films was not distorted, and the film thickness was constant over wide surface areas (up to several millimeters). Note that opal films grown by vertical deposition have twinned fcc structure accompanied with various cracks, dislocations, and boundaries between twins [35,41]. On the contrary, the opal films fabricated using OD have more homogeneous fcc structure.

To fabricate opal/Bi:YIG/opal heterostructures, the steps were as follows. Quartz substrates were etched in the 1:3 mixtures of H₂SO₄ and H₂O₂, to make their surfaces hydrophilic. Colloidal 0.05 wt.% water suspension of monodisperse SiO₂ spheres with a diameter of D = 290 nm [42] were prepared. The substrate was set into a holder and dipped obliquely into the suspension. The whole setup was placed into a humidity chamber. The atmosphere with a humidity of 80% and a temperature of 80 °C was found to be optimal for self-assembling SiO₂ spheres and forming a sequence of two-dimensional hexagonal layers [32] – the (111) ones in terms of the fcc lattice. The fabricated films were about ten (111) layers in thickness; the (111) layers were parallel to the substrate. The Bi:YIG layer was fabricated on top of the first opal film by ion-beam sputtering using a Bi₁Y_2.5Fe₅O₁₂ sputtering target. The thickness of the defect Bi:YIG layer was d_def = 0.56⋅D ≈154 nm, which was chosen in accordance with Ref [36]. Finally, the second opal film was deposited onto the Bi:YIG layer. The as-grown opal/Bi:YIG/opal heterostructure was subjected to annealing for 10 min at 750 °C in order to crystallize Bi:YIG and to harden the opal films.

For each fabrication step, structural, optical and MO properties were evaluated using a Jeol JSM-6700 field emission scanning electron microscope (SEM), a Shimadzu UV-3100PC spectrophotometer and a Neo Ark BH-M600VIR-FKR-TU setup, respectively. Responses of samples were measured at illumination with the linearly polarized light; the cross-sectional size of the light beam was about 2 mm². Angle-resolved spectra were measured when scanning the Brillouin zone of the fcc lattice in LΓK plane [34], and the angle of incidence, ϕ, was measured from the normal to the (111) planes. For MO measurements, an external magnetic field of 2.5 kOe was directed along incident directions.

3. Results and discussion

Figure 1 shows a SEM image of an opal thin film and an opal/Bi:YIG/opal heterostructure. Basal surface of opal films, the (111) plane, was flat over hundreds of microns demonstrating an extended 2D hexagonal arrangement of SiO₂ spheres; the $(\overline{1}11)$ planes were also seen. SEM observation showed that 2D periodicity of the (111) planes was transposed in the Bi:YIG layer when sputtering it on top of the first opal film. Namely, this patterned Bi:YIG layer was a replica of the surface of the opal film.

 

Fig. 1 SEM image of an opal/Bi:YIG/opal heterostructure. The patterned Bi:YIG defect layer is sandwiched in between two opal films. Inset shows a cross-section of the opal/Bi:YIG/opal structure.

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Evolution of optical properties at each fabrication step is illustrated in Fig. 2 . Transmission spectra were measured at normal incidence; attenuation of light propagation was due to the Bragg diffraction from the (111) planes. It should be noted that the spectral position of the (111) stop band in annealed opal films shifted to shorter wavelengths in comparison with that of as-deposited films [see spectra 1 and 2; these spectra are for the first opal film deposited onto a quartz substrate]. The detected spectral shift of ≈5% was in agreement with SEM observations showed that the diameter of SiO₂ spheres was smaller in the annealed films. This transformation can be explained as the result of evaporation of ethylene glycol from surfaces of SiO₂ spheres during annealing (comment from [42]). That resulted in a reduction of the spheres’ diameter and of the interplanar distances. It might be, by the mentioned reason, that the effective refractive index of opal films could be also decreased at annealing. Spectrum 3 shows transmissivity of a double opal film obtained after deposition (and annealing) of the second opal film on the top of the first one. Transmissivity of the double film decreased, and the interference fringes, which can be seen in spectra 1 and 2, became shallow. One can say with certainty that the second film had disordered structure, and its thickness varied on the surface area illuminated by the incident light beam.

 

Fig. 2 Transmission spectra of constituents of the opal/Bi:YIG/opal heterostructure at each fabrication step. (1) as-grown thin opal film. (2) thin opal film after annealing at 750°C. (3) annealed opal film composed of two subsequently deposited opal films. (4) annealed Bi:YIG film, (5) opal/Bi:YIG structure where the Bi:YIG layer as-sputtered on top on the opal film. (6) annealed opal/Bi:YIG/opal heterostructure. Inset: envelope-subtracted transmission spectra 2 and 6 for the annealed opal film and the opal/Bi:YIG/opal heterostructure.

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Spectrum 4 is for the transmissivity of a 154-nm-thick Bi:YIG film. The spectrum shows that light absorption in Bi:YIG rose in the short wavelength range. This is why the transmissivity of the opal/Bi:YIG structure (spectrum 5) was suppressed. Spectrum 6 of the target opal/Bi:YIG/opal heterostructure (the sample hereafter) shows a resonant peak within the (111) stop band of the opal films. The spectral position of this peak was 567 nm that was close to that of the (111) stop band for the annealed film (570 nm). Note that interference fringes were observed in spectrum 6. Surely, deposition of the second opal film on top the patterned Bi:YIG layer gave better result compared with opal-onto-opal deposition. It should be noted that the sample exhibited fast fading of the intensity of the resonant peak with rise of ϕ.

Figure 3 plots angle-resolved transmission spectra of the sample [plot (a)] and of the opal/Bi:YIG structure [plot (b)]. The spectra were measured along the L_g–K–L path on the Brillouin zone surface of the fcc lattice [34]. When changing the angle of incidence ϕ, spectral shifts of the (111) and $(\overline{1}11)$ stop bands were observed in the spectra. The (111) stop band shifted from 570 nm (ϕ = 0) to short wavelengths, and the $(\overline{1}11)$ stop band, which became detectable at the larger angles of incidence, shifted to long wavelengths. These shifts are shown by gray solid lines. An unexpectedly intensive additional band was observed in the spectra; its shift is shown by the gray dashed line. With increase of the angle of incidence, the additional band moved to the wavelength of 725 nm. The same band was observed in spectra of the opal/Bi:YIG structure. Angle-dependent spectral shift of this band cannot be matched by the Bragg diffraction condition for the fcc lattice of the constituent opal films. Definitely, there is no any possible diffraction process from the fcc lattice of opals which is the “longer-wavelength” one than the (111) diffraction. Only 2D periodicity of the {111} hexagonal layers may provide such diffraction processes [43] resulting in the observed band.

 

Fig. 3 Angle-resolved transmission spectra of the opal/Bi:YIG/opal (a) and the Bi:YIG/opal (b) heterostructures. The vertical shift was made for each spectrum except 70° (and 80° for Bi:YIG/opal sample). Solid gray lines present evolution of the {111} stop bands. Dashed grey lines are for the evolution of the band corresponding to the patterned Bi:YIG layer. External angles of incidence ϕ and vertical shifts (in brackets) of transmission spectra are given for each spectrum.

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Angle-dependent spectral shifts of the observed bands in spectra of the sample are plotted in Fig. 4 . Here, for clarity’s sake, only the angle-resolved spectra of the annealed opal film (the film discussed in Fig. 2, spectrum 2) and the patterned 2D Bi:YIG layer were analysed. Spectral shifts of the {111} stop bands are fitted well by Bragg’s law (shown by solid lines) taking into account refraction at the film surface: ${\lambda }_{(111)}=2d{n}_{eff}\cos \left\{\text{arcsin}\left(1/n_{eff}\sin \phi \right)\right\}$ and ${\lambda }_{(\overline{1}11)}=2d{n}_{eff}\cos \left\{\alpha -\text{arcsin}\left(1/n_{eff}\sin \phi \right)\right\}$, where d is the (111) interplanar distance, n_eff is the effective refractive index of the opal film, ϕ is the angle of incidence, and α is the angle between the (111) and $(\overline{1}11)$ planes. The effective refractive index of the opal films was found to be n_eff ≈1.305 and ≈1.32 for the as-deposed and annealed films, respectively. Extracted from optical spectra values of d and α [d = 0.8165 D ≈231 nm (as-deposed film) and 225 nm (annealed film), α = 68 deg.] were in a good agreement with data of Ref [34]. and that evaluated by SEM. Spectral position of the band corresponding to the patterned Bi:YIG layer is shown by squares (the dashed line guided to the eye). As for analytical treatment of this 2D grating-related diffraction, it will be done elsewhere.

 

Fig. 4 Processing of spectra shown in Fig. 3(a): spectral positions of the {111} stop bands of the annealed opal film (open circles and triangles) and of the patterned Bi:YIG layer (open squares). Solid lines are the calculated Bragg wavelengths. Dashed line is an approximation of spectral position of 2D Bi:YIG pattern lattice.

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MO (line 1) and transmission (line 2) spectra of the sample are plotted in Fig. 5 ; line 3 is for an MO spectrum of a 154-nm-thick Bi:YIG single film. All the spectra were measured at normal incidence.

 

Fig. 5 Faraday rotation (1) and transmission (2) spectra of an opal/Bi:YIG/opal heterostructure. Spectra were measured at normal incidence. For reference, a Faraday rotation spectrum (3) of an 154-nm-thick Bi:YIG single film is presented.

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One can see an enhancement of Faraday rotation up to –0.30° for the transmission peak of ~24% at λ = 567 nm corresponding to light localization. Unfortunately, low dielectric contrast in and quality of the opal films (especially quality of the top film) lead to weakening and broadening of the optical resonance. That resulted in decrease of the MO response of the sample.

It should be noted that there observed a dramatic variation of Faraday rotation of the sample in the range of 480–520 nm. It is most likely that this variation was due to light coupling to the 2D hexagonal lattice of the patterned Bi:YIG layer. In accord with the approximation shown in Fig. 4, transmittance of the sample at normal incidence has to have the Bi:YIG layer-related band with the centre at λ = 505 nm. Thought this band is not resolved in the transmission spectrum, we can see that the spectrum exhibits a dip at λ = 520 nm and a peak at λ = 495 nm, and a significant variation of the magnitude of Faraday rotation follows the decrease and increase of the intensity of transmitted light in the range 480–520 nm.

The MO response of the Bi:YIG/opal heterostructure was also measured in the Kerr geometry; the angle of light incidence and the detection angle were 7°. Polarization rotation spectrum (line 1) together with the reflectance (line 2) from the Bi:YIG/opal heterostructure is demonstrated in Fig. 6 . Reflection peak at λ = 595 nm was due to diffraction from the (111) planes of the opal film. MO response from the heterostructure in the vicinity of the reflection peak deviated from that of the reference Bi:YIG film. This result shows that the diffracted from non-magnetic opal light suppresses the MO response from the heterostructure. The Bi:YIG/opal heterostructure exhibited a specific regime where the angle of polarization rotation (θ _K) reversed sign and changed from + 1.6° to –1.6° in a narrow spectral range of 15 nm (485–500 nm). Note that the polarization rotation in the single Bi:YIG film was less than + 0.47° for λ = 500 nm. It should be noted that the observed change of Δθ _K in the range of λ = 485–500 nm for the heterostructure was more then twenty times as high as Δθ _K for the single Bi:YIG film. We observed that maximal magnitudes of θ _K were accompanied with a band (with the minimum at λ = 494 nm) in the specular reflection spectrum. That is this band, λ = 480–520 nm, corresponds to diffraction from the 2D patterned Bi:YIG layer. It is also seen in the transmission spectra; see the shift of this band in Figs. 3 and 4 (dashed lines). Thus, one can conclude that resonant light coupling to the patterned Bi:YIG layer results in (i) longer optical paths for rays emerging from the layer – this stands for enhancement, and (ii) a nontrivial interference between them providing both the change of the sign of polarization rotation and also contributes to the enhancement.

 

Fig. 6 Angle of rotation of polarization plane (1) and reflection spectra (2) of a Bi:YIG/opal heterostructure. Spectra were measured in the specular reflection (Kerr) geometry; the angle of incidence was 7°. For reference, a Kerr rotation spectrum (3) of an 154-nm-thick Bi:YIG single film is presented.

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It is known that the ray reflected from the air/Bi:YIG interface has the phase shift of π with respect to that of the incident and transmitted rays. Provided that the spectra of the single Bi:YIG film measured in the Faraday and Kerr geometries (spectrum 3 in Figs. 5 and 6) have the opposite sign (spectrum 3 in Figs. 5 and 6), one can state the following. For the Kerr geometry (Fig. 6), the ray reflected from the air/Bi:YIG film interface inverses the sign of the polarization rotation when interfering with the rays emerging from the “bulk” of the single Bi:YIG film (or patterned layer). Elementary diagrams for the electric field vectors of such rays are in favor of that. Issue (ii) is likely governed by magnitudes of the electric field vectors of rays reflected from the air/Bi:YIG interface and rays accumulating rotation. Rays running from the interfaces and the “bulk” of the patterned Bi:YIG layer interfere such that the polarization plane of the resultant light beam experiences sharp modulation in the regime of diffraction, λ = 480–520 nm.

Similar effects are discussed in Refs. [44] and [45] where a diffractional enhancement of Kerr rotation from planar gratings made of magnetic metal stripes is studied. Note that interplay of anisotropy and MO activity is discussed in the context of birefringence in anisotropic 1D MPCs structures with longitudinal magnetization geometry [24].

4. Conclusion

For fabricated magnetophotonic opal/Bi:YIG/opal heterostructures, transformations of the MO response of Bi:YIG were demonstrated. Being sputtered on top of the opal film, the Bi:YIG layer happened to transpose the shape and the 2D symmetry of the opal surface. These patterned Bi:YIG layers were shown to diffract light; the corresponding bands were seen in transmission and reflection spectra. For light from a narrow spectral range associated with this diffraction, the large enhancement of Kerr rotation was observed together with change of the sign of rotation. It is worthy of note that large absolute modulations of the MO response in extremely narrow spectral ranges can be attractive for sensing applications.

Since opal photonic crystals and Bi:YIG layer worked as Bragg mirrors and a defect layer, respectively, transmission and Faraday rotation spectra of such samples exhibited characteristic features – the Fabri-Perot resonant peak within the (111) stop bands of the opal films and enhancement of Faraday rotation for wavelengths corresponding to the peak. This shows that fast and relatively cheap vertical deposition of spherical particles is applicable for fabrication of high quality factor microcavities.