Introduction
Magneto optical material is an anisotropic material, its non-diagonal elements in dielectric constant is affected by external magnetic field [1,2]. The one-dimensional magnetophotonic crystals can be obtained by periodically arranging the magneto optical materials and dielectric materials [3,4], the enhanced magneto optic effect is obtained [5] and can be applied to the new magneto optical isolator [6,7]. Reflection-type one-dimensional magnetophotonic crystals are composed of periodic one-dimensional magnetophotonic crystals and reflective layer materials [8,9], due to magneto-optic effect, high reflectivity and large Kerr rotation angle are produced; by adjusting the structure and setting several defect layers in reflection-type one-dimensional magnetophotonic crystals [10,11], a flat reflection spectrum can be obtained. In addition, by introducing an asymmetric dielectric layer on both sides of the magneto-optic dielectric layer, higher reflectivity and larger Kerr rotation angle also can be achieved.
In this paper, the physical models of reflection-type one-dimensional magnetophotonic crystals are designed. The reflectivity and Kerr rotation angle of linearly polarized light are calculated by use of the 4×4 transfer matrix method [12,13]. By changing the angle j between the applied magnetic field and the optical axis, the effects of the angle j on the reflectivity and Kerr rotation angle are discussed.
Methodology and theoretical model
When magneto optical material is affected by the external magnetic field, this is shown in Fig. 1.
The external magnetic field affects the optical properties of magneto optical materials, and the dielectric tensor of magneto optical materials under applied magnetic field is as follows [14]:
In which exy=e2cosj and exz=e2sinj, the e2 is affected by the external magnetic field strength, and j is the angle between the applied magnetic field and the optical axis. The non-diagonal elements in dielectric constant eM of magneto optical materials can be adjusted by changing the angle j or the intensity of applied magnetic field.
In the thesis, the physical models of reflection-type one-dimensional magnetophotonic crystals are designed respectively, their structures are S1=(L/H)4/M/(L/H)2/M/(H/L)2/M/(L/H)4 and S2=(L/H)3/MM/(H/L)5/MM/(L/H)5/MM/(H/L)3/Al, where H layer the high refractive index dielectric material Si, L layer the low refractive index dielectric material SiO2, M layer the magneto optical material Ce:YIG, and the reflective layer material is Al. When the center wavelength of the polarized light is l0=1550 nm, the dielectric layers Si and SiO2 layers have refraction indices nSi=3.48 and =1.495 [15], and the thickness of the dielectric layers is set to l0/(4n); the magnetic Ce:YIG layer has dielectric tensor elements e1=e3=4.884, e2=0.009 [16], the refraction indices of Ce:YIG is nM2=e1, and the thickness of the magnetic layers is set to l0/(4nM). The incident medium is air, and the complex refractive index of the reflecting layer Al is 1.44+16i [17].
When the external magnetic field is applied, the magneto optical material exhibits anisotropy. The non-diagonal elements in dielectric constant of the material are controlled by the angle of the applied magnetic field; the optical properties can be calculated by using the 4×4 transmission matrix method.
Numerical calculation
Reflective magneto-optic isolators require high reflectivity and 45° Kerr rotation angle. When the angle j between the external magnetic field and the optical axis varies, the non-diagonal elements in dielectric constant of magneto-optical materials will change, and the reflectivity and Kerr rotation angle will also change. Firstly, when the structure is S1 and e2=0.009, linearly polarized light propagates in reflection-type one-dimensional magnetophotonic crystals. The variation of reflectivity with the wavelength l and the angle j of the normal incident light is numerically simulated and the results are shown in Fig. 2. With the increase of the angle j, the reflectivity is reduced, but the change is very small. In Fig. 3, it is numerically simulated when the normal incident wavelength is 1550 nm; the reflectivity changes with the angle j. According to Fig. 3, when the angle j increases from 0° to 90°, the reflectivity is reduced from 0.99929 to 0.99905 and the reflectivity is basically unchanged.
Then, when linearly polarized light propagates in reflection-type one-dimensional magnetophotonic crystals, the variation of Kerr rotation angle with the wavelength l and the angle j of the normal incident light is numerically simulated. The results are shown in Fig. 4. With the increase of the angle j, the Kerr rotation angle reduces. In Fig. 5, it is numerically simulated when the normal incident wavelength is 1550 nm. The Kerr rotation angle changes with the angle j. According to Fig. 5, when the angle j increases from 0° to 90°, the Kerr rotation angle reduces from 60.6° to 0. The Kerr rotation angle is adjusted to 45° when the angle j is 44.86°, which meets the requirements of reflective magneto-optical isolator.
The ε2 is affected by the external magnetic field strength, changing the intensity of the applied magnetic field, the ε2 in the magneto optical material changes from 0 to 0.009. When the structure is S1 and ϕ=0°, linearly polarized light propagates in reflection-type one-dimensional magnetophotonic crystals. The variation of reflectivity with the wavelength l and the ε2 of the normal incident light is numerically simulated, and the results are shown in Fig. 6. With the increase of the ε2, the reflectivity increases with small change. In Fig. 7, it is numerically simulated when the normal incident wavelength is 1550 nm, the reflectivity changes with the ε2. According to Fig. 7, when the ε2 increases from 0 to 0.009, the reflectivity increases from 0.99905 to 0.99929 and the reflectivity is basically unchanged.
Then, when linearly polarized light propagates in reflection-type one-dimensional magnetophotonic crystals, the variation of Kerr rotation angle with the wavelength l and the e2 of the normal incident light is numerically simulated, and the results are shown in Fig. 8. With the increase of the e2, the Kerr rotation angle is increased. In Fig. 9, it is numerically simulated when the normal incident wavelength is 1550 nm, the Kerr rotation angle changes with the angle j. According to Fig. 9, when the e2 increases from 0 to 0.009, the Kerr rotation angle increases from 0 to 60.6°. The Kerr rotation angle is adjusted to 45° when the e2 is 0.006379, which meets the requirements of reflective magneto-optical isolator.
In addition to reflection-type one-dimensional magnetophotonic crystals with the structure of S1, reflection-type one-dimensional magnetophotonic crystals can be obtained by adding reflective layer materials at the transmission end. The structure is S2. When the structure is S2 and e2=0.009, linearly polarized light propagates in reflection-type one-dimensional magnetophotonic crystals. The variation of reflectivity with the wavelength l and the angle j of the normal incident light is numerically simulated, and the results are shown in Fig. 10. With the increase of the angle j, the reflectivity is reduced, but the change is very small. In Fig. 11, it is numerically simulated when the normal incident wavelength is 1550 nm, the reflectivity changes with the angle j. According to Fig. 11, when the angle j increases from 0° to 90°, the reflectivity reduces from 0.97979 to 0.97801, the reflectivity is basically unchanged and the reflection spectrum is flat.
Then, when linearly polarized light propagates in reflection-type one-dimensional magnetophotonic crystals, the variation of Kerr rotation angle with the wavelength l and the angle j of the normal incident light is numerically simulated. The results are shown in Fig. 12. With the increase of the angle j, the Kerr rotation angle reduces. In Fig. 13, it is numerically simulated when the normal incident wavelength is 1550 nm, the Kerr rotation angle changes with the angle j. According to Fig. 13, when the angle j increases from 0° to 90°, the Kerr rotation angle reduces from 46.0° to 0. The Kerr rotation angle is adjusted to 45° when the angle j is 12.41°, which meets the requirements of reflective magneto-optical isolator.
When the structure is S2 and ϕ=0°, linearly polarized light propagates in reflection-type one-dimensional magnetophotonic crystals. The variation of reflectivity with the wavelength l and the ε2 of the normal incident light is numerically simulated, and the results are shown in Fig. 14. With the increase of the ε2, the reflectivity increases, and the change is very small. In Fig. 15, it is numerically simulated when the normal incident wavelength is 1550 nm, the reflectivity changes with the ε2. According to Fig. 15, when the ε2 increases from 0 to 0.009, the reflectivity increases from 0.97801 to 0.97979, the reflectivity is basically unchanged and the reflection spectrum is flat.
Then, when linearly polarized light propagates in reflection-type one-dimensional magnetophotonic crystals, the variation of Kerr rotation angle with the wavelength l and the e2 of the normal incident light is numerically simulated, and the results are shown in Fig. 16. With the increase of the e2, the Kerr rotation angle is increased. In Fig. 17, it is numerically simulated when the normal incident wavelength is 1550 nm, the Kerr rotation angle changes with the angle j. According to Fig. 17, when the e2 increases from 0 to 0.009, the Kerr rotation angle increases from 0 to 46.0°. The Kerr rotation angle is adjusted to 45° when the e2 is 0.00879, which meets the requirements of reflective magneto-optical isolator.
Conclusion
In conclusion, two different designs of reflective one-dimensional magnetophotonic crystals are proposed. The physical models of reflective one-dimensional magnetophotonic crystals are formed by the asymmetric structure or adding Al as the reflection layer at its transmission end. By changing the angle j or the intensity of applied magnetic field, the non-diagonal elements in dielectric constant of magneto optical materials can be changed; the reflectivity and Kerr rotation angle can be adjusted to obtain a larger reflectivity and a suitable Kerr rotation angle. The model can be applied to fabricate reflective magneto-optical isolator.