StudyMoose App
24/7 writing help on your phone
Save to my list
Remove from my list
In this work, we propose an optical isolator formed of a magneto-optical (MO) waveguide in a two dimensional photonic crystals. A two dimensional magneto-photonic crystal waveguide device is constituted by a triangular lattice of air holes embedded in Bismuth iron garnet (BIG) film. The nonreciprocal TE-TM mode conversion phenomenon is caused by the Faraday rotation (FR) if the magnetization is aligned along the direction of propagation. The nonreciprocal elements are indispensable devices in optical telecommunications systems; they are used to eliminate multipath reflection between diverse components.
The proposed optical isolator showcases enhanced performance through precise control over the nonreciprocal mode conversion, vital for optical telecommunications. By simulating conversion output and modal birefringence under various conditions, we underline the significant roles of film thickness and incident light angle, aiming to contribute to the development of ultra-compact magneto-photonic devices.
Magneto photonic crystals (MPhCs) represent an important branch of research in the field of photonic crystals; they combine the features of MO effects and photonic crystals, and offer a solution to fabricate integrated magneto-optic components.
5 (339)
“ KarrieWrites did such a phenomenal job on this assignment! He completed it prior to its deadline and was thorough and informative. ”
Nonreciprocal (NR) photonic devices such as optical isolators and circulators are the basic elements which perform guiding, isolating, modeling, and circulating of optical signal. These components are indispensable in optical communicationsystems. Isolators are based on the NR character of the Faraday rotation in the MO waveguide; they allow the transmission of light only in one direction and block it in the opposite direction. Because of this performance, optical isolator is required for protecting other optical active devices such as laser source from reflected light.
However, much research has been focused on the development of isolator utilizing NR mode conversion .
Nowadays, the material widely used to fabricate bulk optical isolators is the ferromagnetic garnet oxide crystal Yttrium Iron Garnet (YIG, Y3Fe5O12). However, in the near infrared region (780-2500nm), where optical fiber transmission is developed, rare earth elements as cerium (Ce:YIG) and terbium (Tb:YIG) iron garnet or non-magnetic ion such as bismuth iron garnets (BIG, Bi3Fe5O12) have been found to enhance the FR without significantly increasing the absorption. So, Bismuth iron garnet (BIG) is considered as a promising MO material for optical isolators due to its good transmission properties and strong faraday effect for blue to near-IR light. The pure bismuth iron garnets (BIG), which only exists in thin film form, has been found to have the highest FR angles among bismuth substituted iron garnets.
In this paper, we propose a 2D-MPhCs waveguide device, which consists of a photonic crystal slab made from MO material, with a periodic triangular lattice of air holes in a BIG wafer. The effects of the thickness film (h) and light incident angle (in) on the mode conversion and modal birefringence in 2D-MPhCs waveguide has been studied using beam propagation method.
The structure without defects proposed in this work is based on a periodic triangular lattice of air holes in Bismuth Iron Garnet (BIG) film. It is a linear and a symmetric waveguide ((W1)_A^K), which obtained by removing one row of air holes in the ΓK direction.
For the magnetization directed along the direction of light propagation (z-axis), the permittivity tensor of the magneto-optic material is given by:
[ϵ]=[(ϵ_xx&ε_xy&0@ε_yx&ε_yy&0@0&0&ϵ_zz )] (1)
Where, the off-diagonal elementsε_xy=-ε_yx=g, corresponds to the magnetic gyration and has a linear dependence on the magnetization. In addition, each element of the tensor can have real and imaginary parts, so that the imaginary part is related to absorption coefficient. In this paper, we will ignore the absorption and assume ε_xx,ε_yy,ε_zz and ε_xy to be real. So, that
ε_xx=ε_yy=ε_zz=ε_BIG=6.25and g=0.3.
The off-diagonal term (ε_xy) of permittivity tensor leads to a coupling between the TE and TM modes, it is strongly depending on the Faraday rotation F, vacuum wavelength λ and the refractive index of the MO material (n=√(ε_xx )):
ε_xy=Im(ε_MO )=(θ_F.λ.√(ε_xx ))/π(2)
If the incident mode is the transverse magnetic (TM), the conversion output R(z) is defined like the intensity ratio of the mode TE at distance Z on the intensity of the mode TM at Z=0:
R(z)=I_(TE(z))/I_(TM(0)) (3)
It can then be written as:
R(z)=([θ)_F^2/((θ)_F^2+((∆β⁄2))^2)]*sin^2[(((θ)_F^2+((∆β⁄(2)))^2 ))^(1/2) z] (4)
From Eq. (4), it is clear that TE-TM mode conversion is strongly affected by the specific Faraday rotation θ_F(°/cm) of the material forming the waveguide and by the phase mismatch between TE and TM modes ∆β (°/cm) given by:
∆β=β_TE-β_TM=((N)_TE-N_TM)*(2π/λ) (5)
The maximum rate of mode conversion which induced by FR effect can be expressed as:
( R)_M=(θ_F^2)⁄(((θ)_F^2+((Δβ⁄2))^2))(6)
The results of simulations are based on the well-known finite difference beam propagation method (BPM) of RSoft CAD [11].
Firstly, we investigate the band diagram of a 2D-MPC without defects. The structure consists of a triangular lattice of circular air holes embedded in a BIG matrix (BIG=6.25 at 1.55µm). The air holes have a radius of 0.4*a, where a isthe lattice constant (a=600 nm). However, the triangular lattice allows the opening of 2D-photonic band gaps and is expected to serve a good platform for photonic integrated circuits. Figure 2(a) reports the TE/TM gap map of the structure; it shows that the TM gap map; the red map appears when radius of air holes varied from 0.13μm to 0.38μm. Figure 2(b) shows the TE/TM band diagrams along the ΓMKΓ direction versus normalized frequency of 2D photonic crystal.
The results which are performed with the plane-wave expansion method (PWE) show clearly the existence of a TM band gap. This later extends from normalized frequency a/=0.31 to a/=0.42 whose corresponding wavelength ranges from 1.42 µm to 1.93 µm.
In this section, we look to study the mode conversion in 2D magneto photonic waveguide component. To explore the effect of slab thickness on the conversion output RM (%) and modal birefringence, we are modeling the beam propagation of light through our magneto-photonic waveguide for different values of slab thickness. Figure 3(a) shows the Electrical field distribution inside the guide for h=1.4µm and h=1.0µm and the variations of the conversion output as a function of slab thickness. From results, it is clear that the conversion output increases with slab thickness.
However, in figure 3(b), we have calculated the influence of the film thickness (h) on the modal birefringence (Δ, m=0) for the mode TM0. The obtained results show clearly that, if the slab thickness h increases, the modal birefringence decreases. Thus, for a bismuth iron garnet matrix of thickness h=0.26 µm the modal birefringence between the fundamental TE0 and TM0 modes was equal to Δ=0.40 (°/cm), and it reaches to 0.025(°/cm) for a slab thickness h=1.4 µm.
In order to studying and analyzing the effect of light incident angle on the conversion output and the modal birefringence, a series of simulations by the well-known finite difference beam propagation method were performed. Figures 4(a) report respectively, the Electrical field distribution inside the guide and the power flow through our waveguide for in=45° and in=0°, and the influence of the light incident angle on the conversion output RM. It is clear that, once the conversion output RM (%) is strongly affected by the light incident angle.
Figures 4(b) report, the influence of in on the Modal birefringence for a slab of thickness h=1.4µm. From results, we observe that, the output for in=0° is 96% and decreases to 50% for in=90°. While, the modal birefringence increases with light incident angle.
Table 1: Summary of simulation results for the optical isolator.
| Parameter | Value |
|---|---|
| TM Band Gap (λ) | 1.42µm to 1.93µm |
| Conversion Output RM (%) | Up to 96% |
| Modal Birefringence Δβ (°/cm) | 0.025 to 0.40 |
This paper offers an analysis of a 2D-MPhC waveguides formed by a triangular lattice of circular air holes embedded into BIG film. Firstly, using 2D plane wave expansion method we have studied the band diagram and the gap mapof this crystal in order to determine the photonic band gap. Afterwards, we study the effect of the film thicknesses and the light incident angle on the mode conversion output using beam propagation method (BPM). The obtained results show that,in such structure the conversion output RM reaches 96% for incidence normal and for a thickness h=1.4µm.
Finally, the calculation of the modal birefringence between the TE0 and TM0 modes show clearly that, the modal birefringence have a minimum value (λ = 0.025 °/cm) for a normal incidenceand thickness h=1.4µm. By consequently, the conversion output and the modal birefringence are strongly affected by the film thickness and light incident angle. In the future work, such a structure with a magnetic photonic crystal can find a large application in telecommunication systems, and it may be interesting to realize non-reciprocal devices.
Design of Two-Dimensional Magneto Photonic Crystal Isolator. (2024, Feb 22). Retrieved from https://studymoose.com/document/design-of-two-dimensional-magneto-photonic-crystal-isolator
👋 Hi! I’m your smart assistant Amy!
Don’t know where to start? Type your requirements and I’ll connect you to an academic expert within 3 minutes.
get help with your assignment
