Arbitrary-ratio power splitter based on nonlinear

Arbitrary-ratio power splitter based on nonlinear multimode interference coupler Mehdi Tajaldini and Mohd Zubir Mat Jafri Citation: AIP Conference Proceedings 1657, 140005 (2015); doi: 10.1063/1.4915239 View online: http://dx.doi.org/10.1063/1.4915239 View Table of Contents: http://scitation.aip.org/content/aip/proceeding/aipcp/1657?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Contribution of single-mode waveguides width on switching operation in ultra-compact nonlinear multimode interference coupler AIP Conf. Proc. 1621, 149 (2014); 10.1063/1.4898459 Nonlinear modal propagation analysis method in multimode interference coupler for operation development AIP Conf. Proc. 1528, 450 (2013); 10.1063/1.4803643 Electrically Tunable 2×2 Multimode Interference Coupler AIP Conf. Proc. 992, 276 (2008); 10.1063/1.2926870 Intelligent integration of optical power splitter with optically switchable cross-connect based on multimode interference principle in Si Ge ∕ Si Appl. Phys. Lett. 85, 1119 (2004); 10.1063/1.1781736 New high‐power arbitrary ratio power splitter at microwave frequencies Rev. Sci. Instrum. 58, 1123 (1987); 10.1063/1.1139569

Arbitrary-ratio Power Splitter based on Nonlinear Multimode Interference Coupler Mehdi Tajaldinia,b and Mohd Zubir Mat Jafria a

School of Physics, Universiti Sains Malaysia, 11800 Pulau Pinang, Malaysia Young Researchers and Elite Club, Baft Branch, Islamic Azad University, Baft, Iran

b

Abstract. We propose an ultra-compact multimode interference (MMI) power splitter based on nonlinear effects from simulations using nonlinear modal propagation analysis (NMPA) cooperation with finite difference Method (FDM) to access free choice of splitting ratio. Conventional multimode interference power splitter could only obtain a few discrete ratios. The power splitting ratio may be adjusted continuously while the input set power is varying by a tunable laser. In fact, using an ultra- compact MMI with a simple structure that is launched by a tunable nonlinear input fulfills the problem of arbitrary-ratio in integrated photonics circuits. Silicon on insulator (SOI) is used as the offered material due to the high contrast refractive index and Centro symmetric properties. The high-resolution images at the end of the multimode waveguide in the simulated power splitter have a high power balance, whereas access to a free choice of splitting ratio is not possible under the linear regime in the proposed length range except changes in the dimension for any ratio. The compact dimensions and ideal performance of the device are established according to optimized parameters. The proposed regime can be extended to the design of M×N arbitrary power splitters ratio for programmable logic devices in all optical digital signal processing. The results of this study indicate that nonlinear modal propagation analysis solves the miniaturization problem for all-optical devices based on MMI couplers to achieve multiple functions in a compact planar integrated circuit and also overcomes the limitations of previously proposed methods for nonlinear MMI Keywords: MMI, all-optical digital signal processing, SOI, arbitrary-ratio power splitter, NMPA, FDM. PACS: 92.40.qc

INTRODUCTION Multimode interference coupler (MMI) could uses in high-q ring resonator [1], loop mirror partial reflectors [2], and power taps [3] which as are very interested in planner photonic circuits, the application of MMI in mentioned photonic devices is strongly depended to the performance of power splitting ratio so that should demonstrate unequal intensity in cross and bar facets. Notably a MMI coupler with continuous splitting ratio is demanded to give the ability to choose. For instance, Implementing in a Makh- Zehnder interferometer (MZI) when gain and loss are distributed un-symmetrically between two arms [4]. Conventional 2×2 MMI couplers just able to demonstrate seven different cross- coupling ratios 0.85, 0.72, 0.5, 0.28, 0.15, and 0 [5]. Cross-coupling ratio as our define from power splitting ratio in this paper, is obtained from dividing the cross intensity on whole output intensity. Some proposed studies have shown that the way of continuous cross-ratio is inserted phase- differences on MMI couplers by some approaches [6]. Although, some procedures have been arranged in complicated structure, such as, partially control refractive index, using bent MMI coupler, and butterfly MMI. However, all mentioned approach suffer from some limitations, complicated structures even to add a phase shifter between two coupled MMI, big dimension, and in applying MMI in the ring resonator due to field enhancement (FE) nonlinear effects are appeared, but, no proposed research that showed nonlinear MMI for arbitrary power splitting ratio. However, it is seem that nonlinear MMI (NLMMI) could overcome the limitations. For instance, NLMMI coupler could introduce in ultra-compact dimension, single-MMI, and high bandwidth for showing a continuous cross- ratio or free power splitting ratio, generally. Definitely, the base of studying a MMI as power splitter is modal interference and propagation. Therefore, the method like beam propagation analysis (BPM) is not responsible. However, other researchers have more effort to apply BPM in studying NLMMI, but, just had access to some big dimension switches. Nonlinear modal propagation analysis (NMPA) method practically show that able to investigate the some critical application in all- optical signal processing of a NLMMI, specially, power splitter [7-9]. In this paper, we propose a continuous power splitting ratio using MMI based on NMPA method. Result is established based on studying the cross and bar output intensities as a function of input intensity. It will be show that

National Physics Conference 2014 (PERFIK 2014) AIP Conf. Proc. 1657, 140005-1–140005-6; doi: 10.1063/1.4915239 © 2015 AIP Publishing LLC 978-0-7354-1299-6/$30.00

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by changing input intensity the output intensities have more oscillations and give the continuous cross-ratio or power splitting ratio. Furthermore, capability of NMPA is determined due to show the demonstration. This paper is arranged, second section belongs to study NMPA and explain influences of nonlinearity on modal propagation. In third section, we show the result and discuss about the considered application. Finally, in forth section, conclusion and future of this work will bring.

MODAL PROPAGATION IN PRESENCE OF NONLINEAR EFFECTS The MMI coupler is introduced to the photonic devices as the simplest structure. Although this device has broad applications in the integrated photonic circuits and telecommunications, these applications increase with the appearance of nonlinear effects due to the change in the modes of electric field in terms of amplitudes or phases. This application exchanges energy among modes [9]. This advantage leads to an ability to control the wave propagation in the medium contributing to signal processing in all-optical functions [7]. The central region of MMI coupler is the multimode waveguide. The access waveguides which are usually single mode are fixed at the input and output facets of the multimode waveguide. The performance of these devices depends on the interference of guided modes, where the complete constructive interference contributes to the formation of the single or multiple self-images at precise distances in the input facet. The interference property of the MMI waveguide intensely depends on the refractive indices of the core and cladding regions of the Multimode waveguide. In other words, by varying the refractive index in the core region, modal interferences phenomena are also changed. In fact, by imposing the intense light into the multimode region, core refractive index becomes a function of intensity in the presence of Kerr nonlinear effect; as the result, the modes propagate in a different situation according to changes of optical properties. By studying this effect in the Multimode interference couplers and applying the obtained results, we can design an all-optical sensor to have small MMIs. In this section, we theoretically study the nonlinear effects in an MMI coupler by studying the Nonlinear Modal Propagation Analysis (NMPA) method in the central region.

FIGURE 1. Schematic structure of (2×2) MMI coupler.

The refractive index is shown in Fig. 2 indicates our design. In fact, MMI coupler is assumed as a conventional structure. Notably, nMMI must higher than nclad to confine the light in core region that originate from total reflection basis. In this paper core material is silicon and clad is air. Critical angle determines the mode expansion in lateral direction depends on core and cladding layer refractive index and corporation the boundary condition, guided modes are discreet, which as shown in theory of optical waveguides. In other word, critical angle indicates the guided modes number.

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FIGURE 1. Refractive index in a ridge waveguide.

The MMI region is isotropic, and the field in this region is a superposition of all the modal fields of the MMI. The details of MPA method exist anywhere. For studying the NMPA, the amplitude of the modes are considered as a function of propagation direction not only shows phase and amplitude changes in region but also the exchange of energy among modes (in the z direction) whereas in linear regime, the amplitude of the modal fields is constant in the nonlinear regime. Therefore, we follow the conventional MPA while considering the mode amplitudes as a function of propagation direction, and then solve the nonlinear coupled equations of guided modes to obtain the electric field throughout the MMI region for applying the Kerr effect on MPA and proposing NMPA. When an intense input light launches into the MMI region from the input waveguide, the refractive index of the region changes by an amount that is proportional to the intensity of the input light. In fact, varying the intensity of the input light produces a nonlinear change in the refractive index of the MMI region. The change of the refractive index leads to a change in the interference of the modes and in the fold-imaging formation. The height of MMI coupler is considered to be 1µm that lead to just excitee a mode in vertical direction (y) so that there is a propagation constant in this direction. The light distribution in 3D is expressed as n

ψ (x, z, t) = ∑ ϕν ( z )e jβν z e jγν x e

jk y y ( −ω t +φ0 )

e

(1)

ν =0

After substitute above equation in nonlinear wave equation the below equation is obtained { ∑ ν

d 2ϕν ( z ) dϕ ( z ) + 2 j βν ν − ( βν 2 + γ ν 2 + k y 2 )ϕν ( z ) dz 2 dz

n 2ω 2 jk y ϕν ( z )}e jγν x e jβν z e y e − jωt c2 {(ϕ pϕqϕ s* )e j (γ p +γ q −γ s ) x e j ( β p + βq − β s ) z e− jωt }  jk y 3χ (3)ω 2 e y = − e 2 ∑∑∑  j ( γ p + γ q + γ s ) x j ( β p + β q + β s ) z − j 3ωt c p q s  +{(ϕ ϕ ϕ ) e e e } p q s  +

(2)

-harmonic generation here. The explained procedure in our study can be used for The second term indicates third-harmonic third-harmonic generation too with considering the mentioned term in solving the nonlinear coupled equations and obtain the modes electric field in the launched and gener generated ated frequency; however, because of switching application on ω frequency (same frequency as the input) we avoid to consider the third harmonic generation and omit the related term. From the above equation we have a dispersion equation as

βν 2 + γ ν 2 + k y 2 = n 2 k0 2 βν 2 + γν 2 = n2 k0 2 − k y 2 = (n2 − (k y 2 k0 2 ))k0 2

(3) (4)

In compare the above equation with Eq. (6) the effective refractive index for core layer is obtained as nMMI = [(n2 − k y 2 k0 2 )]0.5

(5)

The core refractive index affects from surrounding layer refractive index as shown in Eq. 5.

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Notably, the penetration depth of each mode into the cladding region is very small, and has the negligible effect on the device performance, then the clad refractive index does not has contribution to this effective refractive index in this study, the negligible penetration and single mode in the vertical direction make procedure of EIM easy. In the above method EIM is not an approximation against the other. Notably the vertical profile of electric field does not change from input waveguide to the MMI then access waveguides should follow the MMI and consider in 2D because they have 100% overlap in the y direction due to the having same mode in y direction. In fact, the electric field in y direction is not affected from the nonlinear medium and no need to indicate it in the electric field that is the deal of study the medium in 2D. Therefore field distribution of the light in MMI region is expressed by: n

E(x,z,t) =

∑ Aν(z)e jγ x e jβ z e( −ωt + φ ν

ν

0

)

(6)

ν =0

where ν is the mode number, A஝ (z) is the amplitude of the ν୲୦ mode that contains real and imaginary parts, γ஝ and β஝ are lateral and longitudinal propagation constants of the ν୲୦ mode, respectively. With the appearance of the nonlinear effect in the MMI region, the refractive index of this region changes and takes a nonlinear part. The total refractive index of the MMI region is then given by:

n = nMMI + n2 I = nMMI + nNl

(7)

where n୑୑୍ is the usual weak-field refractive index of guiding structure (linear term), I denotes the intensity of the input light, and n୒୐ is the nonlinear refractive of the Kerr nonlinear effect determined by the Kerr nonlinear effect. Here, the most important purpose is applying the NMPA to study the nonlinear phenomenon which are induced in the multimode waveguide that launched with linearly polarized wave, such phenomenon could induce some desirable effects on mode propagations and interactions as in the next will be discussed. The nonlinear modes equation for MMI coupler which is fulfilled NMPA is (from Eq. 2) 2 j βν

dϕν ( z ) 3χ (3)ω 2 = − e 2 ∑∑ Cν ( p, q, s)(ϕ pϕqϕs* ) dz c p q

(8)

Where Cν ( p, q) are the overlap coefficients of the different modes. Here, it is important to highlight that the righthand side of Eq. (10) includes self-phase modulation terms ( p = q = ν = s ), cross-phase modulation terms ( p = ν ≠ q = s ), and terms that lead to power exchange among the modes. This set of coupled numerical differential equations can be solved using a high-accuracy FDM, but this is time consuming, and memory limitations restrict its application to small low- intensity nonlinear MMI. By solving the set of υ coupled equations of the field amplitudes (ν = 0,±1,±2,±3,...), the field amplitude A஝ (z) of the modes is obtained. Consequently, by using Eq. (1), the field in MMI region will be obtained; numerical solve shows the amplitudes as Interpolating Function that are complex numbers. For clarify, we bring some result of self-phase and cross-phase modulation and wave-mixing.

FIGURE 3. nonlinear mode amplitudes as a function of propagation direction.

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In self-phase modulation effect, the sinusoidal profile is converted to the Gaussian profile without change in the amplitude maximum. Fig. 3 shows self-phase modulation. However, changes in wavelength, amplitude maximum and wavelength shift between two modes originate from cross-phase modulation, wave-mixing, respectively. The field profile of the guided modes, in general, consists of a superposition of sine and cosine light waves, with zero fields at the boundaries of the guiding region. In addition, we assume that there is negligible penetration of the fields in the cladding layer as well as Goos-Hanchen shift due to the high contrast index which is increased by imposing the nonlinearity. The field amplitude in output port is obtained by evaluating the summation of overlap integral between the profile of an output waveguide and the profile of the excited modes of the MMI region. E0 r , m,ν =

∫ Aν ( L)e

jγ ν x

cos[k x ( x − ( −1) m +1 d ) + φ0 ]

1/ 2 2   jγ ν x 2 dx ∫ cos[k x ( x − ( −1) m +1 d ) + φ0 ] dx ∫ e  

(9)

By calculating the summation of above equation regards to the outputs, the electric field in slightly output is obtained.

RESULT AND DISCUSSION Our purpose is proposes a novel continuous power splitter ratio using a 2×2 MMI coupler based on NMPA method to achieve a free cross or bar- ratio. For this goal, we study the devise by tunable left input on intense light and study the output electric field as a function of input electric field. In our assumption, normalized electric field might a god candidature of intensity or power. Our considerations are limited to the MMI coupler with the following structure, nc=1, nMMI=3.74, WMMI=10µm, LMMI=80µm, d=1.25µm, b=0.5µm, χe3=2.8×10-18m2⁄w at λ0=1.55µm. These parameters show: refractive index of clad and core, effective width, length, transversal distance between of multimode waveguide center and single input waveguide centers, input waveguides width, third order susceptibility and input wavelength.

FIGURE 4. Normalized electric fields at the outputs as a function of the input electric field amplitude

Some points are observed on bar and cross-ratio 1 and 0 and between them other ratios are exist. It is mean that we have access to a continuous power splitting ratio either defined for bar or cross. Therefore, NMPA give us this opportunity that introduce first nonlinear arbitrary power splitter ratio.

CONCLUSIONS Continuous power splitting ratio is more desired due to application in photonics circuits and the way of phase shift on device increase the loss and dimension, also needed complicated structure that at least consist of two parts. In this paper, NMPA on MMI coupler show us that nonlinear effect could be the best candidature due to no

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limitation in the amount of ratio and dimension. In future, a M×N NLMMI coupler is more desirable to demonstrate the functionality of switching the light in free choice of splitting ratio amount.

ACKNOWLEDGMENTS This research project was funded by Universiti Sains Malaysia Research University Grant No. 1001/PFIZIK/811220, Malaysia Ministry of Education Fundamental Research Grant Scheme (FRGS) 203/PFIZIK/6711349, and Department of Higher Education Exploratory Research Grant (ERGS) 203/PFIZIK/6730051.

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