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The Kerr effect enhancement in non-quarter-wave lossy magnetophotonic crystals
Physica B 405 (2010) 4488–4491
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Physica B journal homepage: www.elsevier.com/locate/physb
The Kerr effect enhancement in non-quarter-wave lossy magnetophotonic crystals M. Moradi, H. Alisafaee, M. Ghanaatshoar Laser and Plasma Research Institute, Shahid Beheshti University, G.C., Evin 1983963113, Tehran, Iran
a r t i c l e in f o
a b s t r a c t
Article history: Received 4 May 2010 Received in revised form 1 July 2010 Accepted 6 August 2010
Lossy one-dimensional (1-D) magnetophotonic crystals (MPCs) consisting of a highly absorptive magnetic layer and two types of dielectric layers are assumed. Magnetic medium is a TbFeCo alloy mostly used for application in magneto-optical data storage disks. Bringing to account the problematic effects of optical loss on the photonic band gap of MPC, two compensative approaches are introduced to attain proper modified PBGs regarding operational wavelength of the structure. Both approaches, gap-shift and resonance-tuning, utilize non-quarter-wave design of MPC structures, and although each one is non-conventional in the realm of MPC design, they offer well suited solutions for the problem. Having applied these approaches, we obtained enhanced magneto optic Kerr effect accompanied with desired optical response. & 2010 Elsevier B.V. All rights reserved.
Keywords: Magnetophotonic crystal Photonic band gap Magneto optic Kerr effect
1. Introduction Magnetophotonic crystals (MPCs) are capable of providing unique optical and magneto-optical characteristics by exploiting properties of band gaps and defects [1–3]. A cavity-type MPC can be constructed by incorporating a magnetic layer into photonic band gap (PBG) structures which are periodic systems of lower and higher refraction index materials [4]. Because of the existence of PBG, certain wavelengths of light are strongly reflected from ordered photonic crystals (PCs), whereas presence of the magnetic defect layer creates a transmission resonance that allows some wavelengths to penetrate the PC. Therefore, as shown by theoretical and experimental works, insertion of a magnetic layer into a PBG structure can remarkably increase the magneto optical (MO) response through partial confinement of lightwave around the magnetic media [5–7]. There is, usually, a trade-off between MO response and light reflection in such structures; i.e., the more the MO response, the less the reflection of light. However, there are some theoretical works indicating possibility of obtaining both large MO effects and high reflection using 1-D PBG structures [8–10]. These works were performed by exploiting multiple magnetic layers and substacks, assuming either non-absorptive magnetic materials to avoid light absorption or infrared region of electromagnetic spectrum where MO parameters are typically large. In contrast, there are applications such as high density data storage, requiring only a single magnetic layer and so the PBG structure can only take the cavity-type form. The required Corresponding author.
E-mail address: [email protected] (M. Ghanaatshoar). 0921-4526/$ - see front matter & 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.physb.2010.08.020
operating wavelengths of these structures are usually short visible ones for which most magnetic materials have small MO parameters and large extinction coefficients, resulting in a low MO response accompanied with a high absorption amount of incident light. In this paper, we introduce two nontraditional designs of 1-D cavity-type MPCs including the absorptive magnetic material TbFeCo. We assume operational wavelength of MPCs to be at short visible wavelength of 405 nm that is the operating wavelength of blue-ultraviolet laser diodes based on GaN. For analysis, a universal 4 4 matrix method [11] is utilized to calculate structures reflectance as well as the MO Kerr response which is the variation in the polarization state of light upon reflection. Finally, we demonstrate that our approaches exploiting non-quarter-wave optical thicknesses of individual layers will lead to proper modified PBGs for the problem in hand.
2. Approaches and results As mentioned above, the magnetic layer, as a defect in a cavitytype MPC, dictates a transmission resonance in the PBG of the structure. Hereafter, we denote the wavelength of transmission resonance as lr . In general, all the layers of PCs and MPCs are considered to have an optical thickness equal to a quarter of incident wavelength li . As a result, a defect layer provides a lr which coincides with li . But, for an absorptive defect layer, it is not reasonable to use an optical thickness of li =4. To avoid elimination of light, a thinner defect layer should be employed, which in turn leads to a shift in the location of lr within the PBG,
M. Moradi et al. / Physica B 405 (2010) 4488–4491
and it may consequently prohibit entrance of li . Therefore, we have to obtain a PBG with a proper lr such that provides enhancement of both optical and magneto-optical responses at li . In this section, we introduce two non-conventional approaches to modify the PBG of cavity-type MPCs. We also try to keep the structure very simple, thin and with a low number of stacking layers to be appropriate for practical purposes. For structures, 1D-MPCs are assumed to be composed of a TbFeCo magnetic layer and a dielectric stack. There are varieties of researches on TbFeCo for characterization of magnetic and magneto optical properties of this rare-earth transition-metal alloy, showing its suitability for data storage application by providing perpendicular anisotropy, high Curie temperature and relatively high coercivity. The dielectric stack is comprised of subsequent layers of dielectric films SiO2 and TiO2. Therefore, the MPCs take the form of cavitytype structure (SiO2/TiO2)f/TbFeCo/(TiO2/SiO2)r, where f and r are stacking numbers of the front and rear substacks, respectively. We have also considered an Al layer as reflector to increase the amount of reflection and a glass layer as substrate. Since the operation wavelength of the system is li ¼ 405 nm, at the first stage of calculations, we set optical thickness of each layer as 405/4 nm, except for the magnetic layer. Also, normal incidence with linear polarization and typical values of dielectric tensor elements at li are assumed. For TbFeCo, these elements have been extracted from literature [12], and for SiO2 and TiO2, dielectric constants are eSiO2 ¼ 2:56 and eTiO2 ¼ 7:29. Hereafter, we denote SiO2, TiO2 and TbFeCo layers as L (low index), H (high index) and M (magnetic), respectively. In order to inspect PBGs, we compute the reflection spectra of MPC structures. Fig. 1 shows reflection spectra of six typical structures. From this figure, the effect of stacking number and
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substitution of M into the structure can be understood: increase of the former would result in narrowing the resonance width, and placement of M would shift the resonance wavelength. In the MPCs of this figure, a 13 nm M layer has used for subsequent comparisons. It is also easy to show that as the thickness of M increases, lr occurs at longer wavelengths.
2.1. Gap-shift approach The desired lr can be achieved by shifting the PBG to shorter wavelengths. To accomplish this, we have assumed the optical thicknesses of dielectric layers to be a quarter of a wavelength which we call it the design wavelength (ld ). Regarding the information from Fig. 1, we had to shift the whole gap to the left. Therefore, ld must be found in a wavelength shorter than 405 nm. Then, in our calculations, we have examined two parameters for a series of stacking numbers: thickness of M layer (dM) and ld . By searching different values of dM from 10 to 25 nm and values of ld which are shorter than li , we found that when optical thicknesses of dielectric layers are equal to a quarter of ld ¼ 375 nm and dM ¼13 nm, proper structures can be achieved. Through this approach, it is possible to displace the PBG until lr coincides with li . Fig. 2 shows contour plots of the Kerr rotation and reflectivity for such MPCs with different numbers of front and rear stacks. As can be seen in this figure, there are two structures having Kerr rotations larger than 11: Glass/(L/H)4M(H/L)3/Al and Glass/ (L/H)4M(H/L)4/Al. It should be noted that the former has resulted in a larger Kerr rotation ( 33 ) at the cost of lower reflectivity ( o 10%). Hence, as a potential structure for practical purposes, the latter structure which has a Kerr rotation around 11, reflectivity of 20%, and a total length of 0:8 mm is preferable. The reflection and the Kerr rotation spectra of this structure is shown in Fig. 3. Note that at wavelength of 405 nm, the maximum Kerr rotation of a single TbFeCo layer on glass substrate is about 0.151, and the enhancement acquired by this gap-shift approach is more than 550% accompanied with an acceptable level of reflectivity. As mentioned earlier, enhancement of the Kerr rotation in MPC structures is attributed to the localization of light around the magnetic layer, which is caused by multi-reflections of light in the multilayered structure of the MPCs. To investigate this, we have computed field distribution of light in two Glass/(L/H)4M(H/L)4/Al structures with different values of ld , illustrated in Fig. 4. Clearly, the localization effect can be observed in the vicinity of magnetic layer for the structure designed in a nontraditional manner. It should be remembered that the wavelength of incident light in both cases is 405 nm. Thus, such a non-quarter-wave design can provide a proper solution for deficient short wavelength MO signals of absorptive magnetic materials. In contrast to this nonquarter-wave structure, the Kerr rotation of the MPC with ld ¼ 405 nm hardly can reach 0.021. This poor MO response is due to lack of efficient light-matter interaction, which in turn is a result of weak localization of light around the magnetic layer ( Fig. 4b).
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Fig. 1. Reflection spectra of (a) (L/H)3L(H/L)3 (solid), (L/H)3(H/L)3 (dashed), (L/H)3 M(H/L)3 (dotted), (b) (L/H)5L(H/L)5 (solid), (L/H)5(H/L)5 (dashed) and (L/H)5M(H/L)5 (dotted).
As it was shown in Fig. 1, when a thin magnetic layer is substituted in a PC with dielectric layers having optical thicknesses of li =4, lr occurs at a wavelength longer than li . In the previous section, we presented a gap-shift approach to make lr closer to li . In this section, we introduce another approach to accomplish this by use of tuning the lr itself, instead of shifting the whole PBG.
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Fig. 2. Contour plots of (a) reflectivity and (b) the Kerr rotation for Glass/(L/H)fM(H/L)r/Al. The dielectric layers thicknesses are a quarter of 375 nm and magnetic layer thickness is 13 nm.
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where the optical thickness of each individual layer, ðn dÞL,H , is a quarter of incident wavelength. Thus, the optical path ratio of dielectric layers, Z ¼ ðn dÞL =ðn dÞH , is unity in such conventional structures. We show that adjustment of lr can be achieved by varying the optical path ratio of dielectric layers, while still satisfying Eq. (1) as the optical thickness relation. Therefore, the thicknesses of L and H layers can be defined as dL ¼ Zli =2nL ðZ þ 1Þ and dH ¼ li =2nH ðZ þ1Þ. Using this technique, we can modify the crystal structure to achieve a desired MO response at li . We have examined influence of Z on the PBG of Glass/ (L/H)4M(H/L)4/Al MPC and found that increase of Z shifts lr toward 405 nm which is the target wavelength. Results of our computations are shown in Fig. 5 in which the corresponding reflection spectra of four Zs are also plotted. Again, the best value of dM found to be 13 nm. Using this resonance-tuning method, we have successfully tuned lr to li . In this order, Z has been set to be 1.75, which led to a 30 nm shift in lr , whereas PBG range remained nearly the same as before. The MO Kerr response of the MPC at this tuned state is about 0.81 with a 17% optical reflection ( Fig. 5b). These are satisfactory values for practical purposes.
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Fig. 4. Illustration of field distribution for 405 nm incident light in two Glass/(L/ H)4M(H/L)4/Al structures. The dielectric layers thicknesses are a quarter of (a) ld ¼ 375 nm and (b) ld ¼ 405 nm.
Finally, by investigation of field distribution, the localization of lightwave is verified in this approach, too. By a comparison between Fig. 6 and the field distribution of Fig. 4a (both of them have been normalized identically), it can be seen that the localization effect is stronger in the resonance-tuning approach. This phenomenon can be a result of complying with Eq. (1) that dictates higher in-phase propagation of light, and hence more constructive interferences in the interior of the structure.
2.3. The case of Faraday effect So far, we have exploited our approaches in order to enhance the MO Kerr effect. Here, to demonstrate the applicability of the
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modified in such a way that a shift in the transmission resonance of the band gap occurs. As it was expected, this shift leads to appearance of transmission resonance close to 405 nm, and consequently enhancement of Faraday rotation up to 5 times. The resultant MPC structure provides 0.5 Faraday rotation at 405 nm wavelength along with sufficient reflection of about 15%.
3. Conclusion
Fig. 5. (a) Reflection spectra of Glass/(L/H)4M(H/L)4/Al at li for different values of Z: 1.00 (solid), 1.30 (dashed), 1.45 (dash-dotted) and 1.75 (dotted). (b) Kerr rotation and reflection spectra for Z ¼ 1:75:
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We have used photonic band gap structures to enhance MO response of TbFeCo at short visible wavelength of 405 nm. For this purpose, we have designed a magneto-photonic crystal and removed some restrictions on its configuration. Two nonconventional approaches, based on non-quarter-wave design, have been introduced to compensate the effect of extinction coefficient of magnetic material. In the first approach, the whole PBG has been shifted until the resonance transmission coincided with the incident light wavelength. The second approach involves tuning of the band gap’s resonance wavelength to the incident light wavelength. In both approaches, the MO response has increased at desired wavelength which along with an acceptable level of reflectivity and reduced length of the device, can lead to improved high density data storage systems.
Structure Depth (nm) Fig. 6. Illustration of field distribution for Z ¼ 1:75 in Glass/(L/H)4M(H/L)4/Al structure.
mentioned enhancement procedures, as another important MO phenomenon, the Faraday effect of TbFeCo would be optimized by resonance-tuning approach. The amount of Faraday rotation depends on thickness of the layer, i.e the more the thickness, the higher the rotation. However, concerning highly absorptive nature of TbFeCo at wavelength of 405 nm, the thickness of this magnetic material is restricted by required transmission, which is considered to be more than 10%. For a bare layer of TbFeCo with 13 nm thickness, the Faraday rotation is less than 0.1. Incorporation of this layer into MPC structure with {r,f} ¼ {6,6} produces a PBG according to its transmission spectrum that is plotted in Fig. 7. By finding the right value of Z to be equal to 1.68, the PBG is
References [1] M. Levy, A.A. Jalali, X. Huang, J. Mater. Sci. Mater. Electron. 20 (2009) S43. [2] M. Inoue, R. Fujikawa, A. Baryshev, A. Khanikaev, P.B. Lim, H. Uchida, O. Aktsipetrov, A. Fedyanin, T. Murzina, A. Granovsky, J. Phys. D 39 (2006) R151. [3] V.I. Belotelov, A.K. Zvezdin, J. Opt. Soc. Am. B 22 (2005) 286. [4] J.D. Joannopoulos, R.D. Meade, J.N. Winn, Photonic Crystals: Molding the Flow of Light, Princeton University Press, NJ, 1995. [5] M. Inoue, K. Arai, T. Fujii, M. Abe, J. Appl. Phys. 85 (1999) 5768. [6] M. Inoue, K. Arai, T. Fujii, M. Abe, J. Appl. Phys. 83 (1998) 6768. [7] H. Kato, T. Matsushita, A. Takayama, M. Egawa, K. Nishimura, M. Inoue, J. Appl. Phys. 93 (2003) 3906. [8] H. Kato, M. Inoue, J. Appl. Phys. 91 (2002) 7017. [9] M.J. Steel, M. Levy, R.M. Osgood Jr., J. Lightwave Technol. 18 (2000) 1289. [10] M.J. Steel, M. Levy, R.M. Osgood Jr., J. Lightwave Technol. 18 (2000) 1297. [11] Z.Q. Qiu, S.D. Bader, Rev. Sci. Instrum. 71 (2000) 1244. [12] W.R. Hendren, R. Atkinson, R.J. Pollard, I.W. Salter, C.D. Wright, W.W. Clegg, D.F.L. Jenkins, J. Phys. Condens. Matter 15 (2003) 1461.
Contents lists available at ScienceDirect
Physica B journal homepage: www.elsevier.com/locate/physb
The Kerr effect enhancement in non-quarter-wave lossy magnetophotonic crystals M. Moradi, H. Alisafaee, M. Ghanaatshoar Laser and Plasma Research Institute, Shahid Beheshti University, G.C., Evin 1983963113, Tehran, Iran
a r t i c l e in f o
a b s t r a c t
Article history: Received 4 May 2010 Received in revised form 1 July 2010 Accepted 6 August 2010
Lossy one-dimensional (1-D) magnetophotonic crystals (MPCs) consisting of a highly absorptive magnetic layer and two types of dielectric layers are assumed. Magnetic medium is a TbFeCo alloy mostly used for application in magneto-optical data storage disks. Bringing to account the problematic effects of optical loss on the photonic band gap of MPC, two compensative approaches are introduced to attain proper modified PBGs regarding operational wavelength of the structure. Both approaches, gap-shift and resonance-tuning, utilize non-quarter-wave design of MPC structures, and although each one is non-conventional in the realm of MPC design, they offer well suited solutions for the problem. Having applied these approaches, we obtained enhanced magneto optic Kerr effect accompanied with desired optical response. & 2010 Elsevier B.V. All rights reserved.
Keywords: Magnetophotonic crystal Photonic band gap Magneto optic Kerr effect
1. Introduction Magnetophotonic crystals (MPCs) are capable of providing unique optical and magneto-optical characteristics by exploiting properties of band gaps and defects [1–3]. A cavity-type MPC can be constructed by incorporating a magnetic layer into photonic band gap (PBG) structures which are periodic systems of lower and higher refraction index materials [4]. Because of the existence of PBG, certain wavelengths of light are strongly reflected from ordered photonic crystals (PCs), whereas presence of the magnetic defect layer creates a transmission resonance that allows some wavelengths to penetrate the PC. Therefore, as shown by theoretical and experimental works, insertion of a magnetic layer into a PBG structure can remarkably increase the magneto optical (MO) response through partial confinement of lightwave around the magnetic media [5–7]. There is, usually, a trade-off between MO response and light reflection in such structures; i.e., the more the MO response, the less the reflection of light. However, there are some theoretical works indicating possibility of obtaining both large MO effects and high reflection using 1-D PBG structures [8–10]. These works were performed by exploiting multiple magnetic layers and substacks, assuming either non-absorptive magnetic materials to avoid light absorption or infrared region of electromagnetic spectrum where MO parameters are typically large. In contrast, there are applications such as high density data storage, requiring only a single magnetic layer and so the PBG structure can only take the cavity-type form. The required Corresponding author.
E-mail address: [email protected] (M. Ghanaatshoar). 0921-4526/$ - see front matter & 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.physb.2010.08.020
operating wavelengths of these structures are usually short visible ones for which most magnetic materials have small MO parameters and large extinction coefficients, resulting in a low MO response accompanied with a high absorption amount of incident light. In this paper, we introduce two nontraditional designs of 1-D cavity-type MPCs including the absorptive magnetic material TbFeCo. We assume operational wavelength of MPCs to be at short visible wavelength of 405 nm that is the operating wavelength of blue-ultraviolet laser diodes based on GaN. For analysis, a universal 4 4 matrix method [11] is utilized to calculate structures reflectance as well as the MO Kerr response which is the variation in the polarization state of light upon reflection. Finally, we demonstrate that our approaches exploiting non-quarter-wave optical thicknesses of individual layers will lead to proper modified PBGs for the problem in hand.
2. Approaches and results As mentioned above, the magnetic layer, as a defect in a cavitytype MPC, dictates a transmission resonance in the PBG of the structure. Hereafter, we denote the wavelength of transmission resonance as lr . In general, all the layers of PCs and MPCs are considered to have an optical thickness equal to a quarter of incident wavelength li . As a result, a defect layer provides a lr which coincides with li . But, for an absorptive defect layer, it is not reasonable to use an optical thickness of li =4. To avoid elimination of light, a thinner defect layer should be employed, which in turn leads to a shift in the location of lr within the PBG,
M. Moradi et al. / Physica B 405 (2010) 4488–4491
and it may consequently prohibit entrance of li . Therefore, we have to obtain a PBG with a proper lr such that provides enhancement of both optical and magneto-optical responses at li . In this section, we introduce two non-conventional approaches to modify the PBG of cavity-type MPCs. We also try to keep the structure very simple, thin and with a low number of stacking layers to be appropriate for practical purposes. For structures, 1D-MPCs are assumed to be composed of a TbFeCo magnetic layer and a dielectric stack. There are varieties of researches on TbFeCo for characterization of magnetic and magneto optical properties of this rare-earth transition-metal alloy, showing its suitability for data storage application by providing perpendicular anisotropy, high Curie temperature and relatively high coercivity. The dielectric stack is comprised of subsequent layers of dielectric films SiO2 and TiO2. Therefore, the MPCs take the form of cavitytype structure (SiO2/TiO2)f/TbFeCo/(TiO2/SiO2)r, where f and r are stacking numbers of the front and rear substacks, respectively. We have also considered an Al layer as reflector to increase the amount of reflection and a glass layer as substrate. Since the operation wavelength of the system is li ¼ 405 nm, at the first stage of calculations, we set optical thickness of each layer as 405/4 nm, except for the magnetic layer. Also, normal incidence with linear polarization and typical values of dielectric tensor elements at li are assumed. For TbFeCo, these elements have been extracted from literature [12], and for SiO2 and TiO2, dielectric constants are eSiO2 ¼ 2:56 and eTiO2 ¼ 7:29. Hereafter, we denote SiO2, TiO2 and TbFeCo layers as L (low index), H (high index) and M (magnetic), respectively. In order to inspect PBGs, we compute the reflection spectra of MPC structures. Fig. 1 shows reflection spectra of six typical structures. From this figure, the effect of stacking number and
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substitution of M into the structure can be understood: increase of the former would result in narrowing the resonance width, and placement of M would shift the resonance wavelength. In the MPCs of this figure, a 13 nm M layer has used for subsequent comparisons. It is also easy to show that as the thickness of M increases, lr occurs at longer wavelengths.
2.1. Gap-shift approach The desired lr can be achieved by shifting the PBG to shorter wavelengths. To accomplish this, we have assumed the optical thicknesses of dielectric layers to be a quarter of a wavelength which we call it the design wavelength (ld ). Regarding the information from Fig. 1, we had to shift the whole gap to the left. Therefore, ld must be found in a wavelength shorter than 405 nm. Then, in our calculations, we have examined two parameters for a series of stacking numbers: thickness of M layer (dM) and ld . By searching different values of dM from 10 to 25 nm and values of ld which are shorter than li , we found that when optical thicknesses of dielectric layers are equal to a quarter of ld ¼ 375 nm and dM ¼13 nm, proper structures can be achieved. Through this approach, it is possible to displace the PBG until lr coincides with li . Fig. 2 shows contour plots of the Kerr rotation and reflectivity for such MPCs with different numbers of front and rear stacks. As can be seen in this figure, there are two structures having Kerr rotations larger than 11: Glass/(L/H)4M(H/L)3/Al and Glass/ (L/H)4M(H/L)4/Al. It should be noted that the former has resulted in a larger Kerr rotation ( 33 ) at the cost of lower reflectivity ( o 10%). Hence, as a potential structure for practical purposes, the latter structure which has a Kerr rotation around 11, reflectivity of 20%, and a total length of 0:8 mm is preferable. The reflection and the Kerr rotation spectra of this structure is shown in Fig. 3. Note that at wavelength of 405 nm, the maximum Kerr rotation of a single TbFeCo layer on glass substrate is about 0.151, and the enhancement acquired by this gap-shift approach is more than 550% accompanied with an acceptable level of reflectivity. As mentioned earlier, enhancement of the Kerr rotation in MPC structures is attributed to the localization of light around the magnetic layer, which is caused by multi-reflections of light in the multilayered structure of the MPCs. To investigate this, we have computed field distribution of light in two Glass/(L/H)4M(H/L)4/Al structures with different values of ld , illustrated in Fig. 4. Clearly, the localization effect can be observed in the vicinity of magnetic layer for the structure designed in a nontraditional manner. It should be remembered that the wavelength of incident light in both cases is 405 nm. Thus, such a non-quarter-wave design can provide a proper solution for deficient short wavelength MO signals of absorptive magnetic materials. In contrast to this nonquarter-wave structure, the Kerr rotation of the MPC with ld ¼ 405 nm hardly can reach 0.021. This poor MO response is due to lack of efficient light-matter interaction, which in turn is a result of weak localization of light around the magnetic layer ( Fig. 4b).
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Fig. 1. Reflection spectra of (a) (L/H)3L(H/L)3 (solid), (L/H)3(H/L)3 (dashed), (L/H)3 M(H/L)3 (dotted), (b) (L/H)5L(H/L)5 (solid), (L/H)5(H/L)5 (dashed) and (L/H)5M(H/L)5 (dotted).
As it was shown in Fig. 1, when a thin magnetic layer is substituted in a PC with dielectric layers having optical thicknesses of li =4, lr occurs at a wavelength longer than li . In the previous section, we presented a gap-shift approach to make lr closer to li . In this section, we introduce another approach to accomplish this by use of tuning the lr itself, instead of shifting the whole PBG.
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where the optical thickness of each individual layer, ðn dÞL,H , is a quarter of incident wavelength. Thus, the optical path ratio of dielectric layers, Z ¼ ðn dÞL =ðn dÞH , is unity in such conventional structures. We show that adjustment of lr can be achieved by varying the optical path ratio of dielectric layers, while still satisfying Eq. (1) as the optical thickness relation. Therefore, the thicknesses of L and H layers can be defined as dL ¼ Zli =2nL ðZ þ 1Þ and dH ¼ li =2nH ðZ þ1Þ. Using this technique, we can modify the crystal structure to achieve a desired MO response at li . We have examined influence of Z on the PBG of Glass/ (L/H)4M(H/L)4/Al MPC and found that increase of Z shifts lr toward 405 nm which is the target wavelength. Results of our computations are shown in Fig. 5 in which the corresponding reflection spectra of four Zs are also plotted. Again, the best value of dM found to be 13 nm. Using this resonance-tuning method, we have successfully tuned lr to li . In this order, Z has been set to be 1.75, which led to a 30 nm shift in lr , whereas PBG range remained nearly the same as before. The MO Kerr response of the MPC at this tuned state is about 0.81 with a 17% optical reflection ( Fig. 5b). These are satisfactory values for practical purposes.
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Fig. 4. Illustration of field distribution for 405 nm incident light in two Glass/(L/ H)4M(H/L)4/Al structures. The dielectric layers thicknesses are a quarter of (a) ld ¼ 375 nm and (b) ld ¼ 405 nm.
Finally, by investigation of field distribution, the localization of lightwave is verified in this approach, too. By a comparison between Fig. 6 and the field distribution of Fig. 4a (both of them have been normalized identically), it can be seen that the localization effect is stronger in the resonance-tuning approach. This phenomenon can be a result of complying with Eq. (1) that dictates higher in-phase propagation of light, and hence more constructive interferences in the interior of the structure.
2.3. The case of Faraday effect So far, we have exploited our approaches in order to enhance the MO Kerr effect. Here, to demonstrate the applicability of the
M. Moradi et al. / Physica B 405 (2010) 4488–4491
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Fig. 7. The resonance-tuning approach for Faraday rotation enhancement in the Glass/(L/H)6M(H/L)6 structure. All curves are obtained for 405 nm incident light.
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modified in such a way that a shift in the transmission resonance of the band gap occurs. As it was expected, this shift leads to appearance of transmission resonance close to 405 nm, and consequently enhancement of Faraday rotation up to 5 times. The resultant MPC structure provides 0.5 Faraday rotation at 405 nm wavelength along with sufficient reflection of about 15%.
3. Conclusion
Fig. 5. (a) Reflection spectra of Glass/(L/H)4M(H/L)4/Al at li for different values of Z: 1.00 (solid), 1.30 (dashed), 1.45 (dash-dotted) and 1.75 (dotted). (b) Kerr rotation and reflection spectra for Z ¼ 1:75:
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We have used photonic band gap structures to enhance MO response of TbFeCo at short visible wavelength of 405 nm. For this purpose, we have designed a magneto-photonic crystal and removed some restrictions on its configuration. Two nonconventional approaches, based on non-quarter-wave design, have been introduced to compensate the effect of extinction coefficient of magnetic material. In the first approach, the whole PBG has been shifted until the resonance transmission coincided with the incident light wavelength. The second approach involves tuning of the band gap’s resonance wavelength to the incident light wavelength. In both approaches, the MO response has increased at desired wavelength which along with an acceptable level of reflectivity and reduced length of the device, can lead to improved high density data storage systems.
Structure Depth (nm) Fig. 6. Illustration of field distribution for Z ¼ 1:75 in Glass/(L/H)4M(H/L)4/Al structure.
mentioned enhancement procedures, as another important MO phenomenon, the Faraday effect of TbFeCo would be optimized by resonance-tuning approach. The amount of Faraday rotation depends on thickness of the layer, i.e the more the thickness, the higher the rotation. However, concerning highly absorptive nature of TbFeCo at wavelength of 405 nm, the thickness of this magnetic material is restricted by required transmission, which is considered to be more than 10%. For a bare layer of TbFeCo with 13 nm thickness, the Faraday rotation is less than 0.1. Incorporation of this layer into MPC structure with {r,f} ¼ {6,6} produces a PBG according to its transmission spectrum that is plotted in Fig. 7. By finding the right value of Z to be equal to 1.68, the PBG is
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