Plasmonic modulator utilizing three parallel metal–dielectric–metal waveguide directional coupler and elasto-optic effects

Optics Communications 284 (2011) 1418–1423

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Optics Communications j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / o p t c o m

Plasmonic modulator utilizing three parallel metal–dielectric–metal waveguide directional coupler and elasto-optic effects Ram Prakash Dwivedi, Hyun-Shik Lee, Jun-Hwa Song, Shinmo An, El-Hang Lee ⁎ Optics and Photonics Elite Research Academy (OPERA), Graduate School of Information Technology, Inha University, Incheon-402751, South Korea

a r t i c l e

i n f o

Article history: Received 6 July 2010 Received in revised form 5 October 2010 Accepted 11 October 2010 Keywords: MDM waveguide Elasto-optic effect Modulator and directional coupler

a b s t r a c t We report, for the first time, on the design of a plasmonic modulator working on the principle of the elastooptic effects in a directional coupling structure, utilizing three parallel metal–dielectric–metal waveguides. We propose to achieve the active switching of the power propagation using the elasto-optic effect and optimize the extinction ratio of the optical modulation. The device is characterized and numerically analyzed using the finite-element-method at the wavelengths of 1.55 μm. For the modulator length of 2.33 μm, the extinction ratio of the modulation is nearly 14 dB, and the calculated attenuation loss is 4.5 dB. The calculated driving voltage is 4.8 V for the given modulator. The effect of the applied voltage on the modulation is also analyzed. © 2010 Elsevier B.V. All rights reserved.

1. Introduction The possibility of guiding light on a subwavelength scale is of great interest in optoelectronics [1]. The integration of micro/nanophotonic devices is an area of increasing importance in information technology [2,3] and has recently motivated significant research activities in exploring surface plasmonic waveguide (WG) structures. Among various plasmonic waveguide configurations, those utilizing surface plasmon polariton modes supported by a dielectric gap between two metal surfaces [4] show the possibility of achieving a better trade-off between the lateral confinement and propagation loss [5]. Dynamic control over the plasmonic propagation properties has been realized on the micro/nanometer scale using a range of approaches. Most of the related devices rely on the manipulation of the refractive index of the dielectric layer adjacent to the metal surface. As plasmonic propagation is critically dependent on the material parameter, modulation can be easily attained by controlling the propagation behavior [6]. Thermo-optic, acousto-optic, and electro-optic materials have been explored for use in the intensity and phase modulations. The effective refractive index of a metal–dielectric–metal (MDM) plasmonic waveguide is highly sensitive to the thickness of the dielectric film, making it attractive for applications such as modulators and switches. An elastomer layer sandwiched between two metal electrode layers can form an MDM optical waveguide, whose mode properties can be tuned by electrically controlled mechanical thickness changes, suggesting its potential applications for elasto-

⁎ Corresponding author. Tel.: + 82 32 860 8804; fax: + 82 32 865 8845. E-mail address: [email protected] (E.-H. Lee). 0030-4018/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.optcom.2010.10.038

optical modulators [7]. Activated strains up to 117% have been demonstrated with silicone elastomers, and up to 215% with acrylic elastomers, which are higher than any other strains of high-strain electroactive polymers [8]. Here, we propose an effective method to switch the power propagation of a plasmonic modulator working on the principle of the elasto-optic effects in a directional coupling structure, utilizing three parallel metal–dielectric–metal waveguides. Using this method we could design and optimize an optical modulator of a high extinction ratio. The enhanced performance has been obtained owing to the advantage of the MDM plasmonic waveguiding property and the unique design structure of the modulator. In order to verify the model theory, full wave simulations have been carried out using the Comsol Multiphysics software package (formerly known as FEMLAB). 2. Modulator design and theory A schematic diagram of the proposed structure is shown in Fig. 1. The planar structure and the on–off states of the modulator using three parallel MDM waveguides are shown in Fig. 1(a).The side view of the layered MDM structure and the change in the effective refractive index of the modulator using three parallel MDM waveguides are shown in Fig. 1(b). The modulator structure is simply composed of three MDM waveguides to function as directional couplers, where the center waveguide is an MDM waveguide using an active elasto-optic material, and the other two waveguides on the side use passive dielectric materials. The metals are laid over the active elasto-optic or dielectric layer of thickness (d). The length of the directional coupler, the width of each MDM waveguide, and the central distance between the two coupled MDM waveguide are denoted by L,W and s, respectively. The input and the output power of

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the elastomer film with respect to the applied voltage could be explained using the elasto-optic effect, and the change in the effective refractive index with respect to the thickness could be explained using the dispersion relation in the MDM waveguide. 2.2. Elasto-optic effect When a voltage is applied across the MDM electrodes having elasto-optic material as a dielectric film, the two opposite charges on the two electrodes attract, and the elastomer film is compressed by the resulting electrostatic forces. The force per unit area that acts to squeeze the film is 2

2

ffilm = εd ε0 E = εd ε0 ðV =dÞ

where ffilm is the force per unit area, εd is the relative dielectric constant of the elastomer film, ε0 is the dielectric constant of free space, V is the applied voltage, E is the electric field and d is the film thickness. If the elastomer film is unconstrained and unloaded, then the strain in the film resulting from the squeezing pressure is e=−

ffilm ε ε V2 = − d 20 Y d Y

where Y is the modulus of elasticity of the elastomer film. For strains greater than about 20%, the above equation becomes unsatisfactory because Y generally depends on the strain itself. For a low strain, the elastic strain energy density is typically expressed as Ues = (1/2)Y × e2. For a high strain, a more useful measure of performance will be the electromechanical energy density Uem, which we define as the amount of electrical energy converted to mechanical energy per unit volume of material for one cycle. The electromechanical energy density can then be written as [8] Fig. 1. Three parallel MDM waveguide coupler type modulator in switch-off and switchon states (a) planar structure and (b) side view structure.

the modulator are calculated at locations I and O, respectively. The purpose of using the three parallel MDM waveguides is to reduce the modulator length and to reduce the propagation loss of the system. The purpose of using the elasto-optic effect is to achieve a maximum output power in the switch-on state of the modulator.

2

Uem = ffilm × lnð1 + eÞ where Uem = Y × e

Hence, for elastomers showing a higher strain, the voltage–strain relation can be written as

V=

sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Yd2 e2 ε0 ε d lnð1 + eÞ

ð1Þ

2.1. Modulator concept In the switch-off state, all the three MDM waveguides are identical and ensure the same phase velocities for the guided modes in each waveguide. When the power is launched in waveguide 1, it leads to energy coupling from waveguide 1 to waveguides 2 and 3. The distance, within which all the energy from waveguide 1 is coupled to waveguides 2 and 3, is called the coupling length x = L0. Due to this coupling, the power reaches its minimum value at the output port of the modulator. In switch-on mode, an applied voltage V creates an electric field E ≈ V/d where d is an effective distance. Applying voltage in waveguide 1 reduces the thickness of the elastomer film and hence the effective refractive index of the propagating wave increases. Reducing thickness and increasing the effective refractive index of waveguide 1 cause mode and phase mismatching for its coupling with waveguides 2 and 3. Because of the phase and mode mismatching, the coupling between the waveguides is abruptly reduced, and most of the incident power remains in waveguide 1, resulting in a maximum power in the output of the modulator. The change in the thickness of

Fig. 2(a) shows the strain characteristics of the dielectric elastomer film with applied voltage for an MDM waveguide within the limit of the dielectric breakdown. To investigate the dynamics of the modulation, we calculate the strain response of the elastomer film for a different periodic drive voltage by using Eq. (1). It can be seen that the strain increases with the voltage applied across the metal electrodes. The strain reaches its maximum value of 100% for a drive voltage of 7.2 V. There are several elastomers having modulus of elasticity of the order of 106 Pa. For example, we may consider a synthetic dielectric elastomer having dielectric constant (εd = 4.84) and tensile strength (Y = 1.5 MPa) [9]. If V = 4.8 V and d = 50 nm, then from Eq. (1), the calculated strain would be e ≈ 50%. 2.3. Dispersion It is well known that when a dielectric film is sandwiched between two identical metals, two degenerate surface plasmonic modes on the upper and lower sides of the dielectric film could interact and split into two non-degenerate surface plasmonic modes having symmetric

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and neff, therefore, asymptotically approaches the effective index of the surface plasmon mode of a single metal–dielectric interface. If we apply an electric field across the MDM electrode structure with dielectric layer as an elastomer film, the effective refractive index of the MDM waveguide would increase due to the decrease in the effective distance, d, between the metal electrodes. 3. Optimization of optical modulator parameters We optimized the optical modulator parameters for active switching of power. We first analyzed the changes in the coupling power ratio for varied applied voltages, which cause phase mismatching and changes in the fractional power transferred for varied thickness of the dielectric film inducing mode mismatching. Finally, after optimizing these parameters, we improved the extinction ratio of the optical modulator. 3.1. The effect of phase mismatching on coupling It is known that the optical powers carried by two parallel MDM waveguides, P1(x) and P2(x), are periodically exchanged along the direction of propagation, x. Two parameters govern the strength of this process: the coupling coefficient (C) and the mismatch of propagation constant Δβ = β1 − β2 = Δn × k0, where Δn is the difference between the effective refractive indices of the two MDM waveguides. From Fig. 1, it is clear that Δn = neff − n. If the waveguides are identical, with Δβ = 0 and P2(0) = 0, then at a distance x = L0 = π/2C, called the transfer distance or coupling length, the power is coupled from waveguide 1 to waveguide 2, i.e., P1(L0) = 0 and P2(L0) = P1(0). For the two waveguides of length L0 and Δβ ≠ 0, the coupling power ratio Rcp = P2(L0)/P1(0) is a function of the phase mismatch and is defined as

Rcp Fig. 2. (a) Illustrates the effect of applied voltage on the produced strain in dielectric elastomer film. (b) Variation of the real part of the effective index for the fundamental modes versus thickness of the dielectric film for an MDM waveguide.

and anti-symmetric field distributions with respect to the waveguide medium [10]. The dispersion equation of the symmetric transverse magnetic (TM) mode in a 2D–MDM waveguide is:   1 ε α tanh α d d = − d m 2 εm α d

ð2Þ

where εd and εm are the dielectric constants of the insulator and metal, respectively, d is the thickness of the dielectric film, and the transverse wave vectors αd, m (in the dielectric and metal, respectively) are related by   2 2 1=2 α d;m = β −εd;m k0 where k0(k0 = 2π/λ) is the wave number in free space and β = neff k0 is the propagation constant. Fig. 2(b) is plotted by using the dispersion relation given in Eq. (2) and shows the change in the effective refractive index neff for the fundamental mode of an MDM structure as a function of the width of the central dielectric region (d). As d decreases, the fraction of the modal power in the metal increases, and neff, therefore, increases. In the opposite limit, as d → ∞, the coupling between the surface plasmonic modes of the two metal–dielectric interfaces vanishes,

(    1 = 2 ) π2 ΔβL0 2 2 1 1+ = sinc 2 2 π

where Δβ = 2π λ ðΔnÞ and Δn have been obtained in terms of voltage using the elasto-optic effect in the Section 2.2. In terms of the applied voltage, the above expression can be written as

Rcp

(   2 1 = 2 ) π 2 V 2 1 1+3 = sinc 2 2 V0

ð5Þ

where V0 is switching voltage. At V = V0, Rcp = 0. Fig. 3(a) illustrates the dependence of the power coupling ratio (Rcp) from waveguide 1 to waveguides 2 and 3 induced by the phase mismatching when an electric field is applied across the MDM electrode structure, has its maximum value of unity at ΔβL0 = 0 (i.e. V = 0) and decreases with pffiffiffi increasing ΔβL0 (i.e. V ≠ 0). The ratio Rcp vanishes when ΔβL0 = 3π and at this point the optical power is not transferred from waveguide 1 to waveguides 2 and 3. If the mismatch pffiffiffi is switched from 0 to 3π, then the light remains in waveguide 1. The electrical control of Δβ can be pffiffiffiachieved by using the elasto-optic effects. Numerically, for Δβ≈ 3π; Δn≈0:6; e = 90% and V = 7.2 V. Ordinary dielectric elastomers may not have this much strain within the limit of the dielectric breakdown. Therefore, we have considered a strain of e = 50% throughout the calculation. 3.2. The effect of mode mismatching on coupling When the two MDM waveguides have differences in their dielectric film thickness, the fundamental mode propagation constants differ. Without loss of generality, we assume that waveguide 1 has dielectric film thickness d − δd. When Δβ is due to variation in

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propagation and coupling effect, FEM simulations using three dimensional RF modules Electromagnetic Wave in Harmonic Propagation Analysis are conducted for both the switch-off and switch-on states, and the results are presented in Fig. 4. We show the active switching of power propagation in the MDM waveguide 1 by applying a voltage across its metal electrodes. In the simulation, the permittivity of gold is taken from the well accepted experimental data, εm = − 118 + j11.58 at the wavelength λ = 1.55 μm[11]. W and s are 100 nm and 50 nm, respectively. In the absence of any applied voltage, the thickness of the metal film (t) and the dielectric (d) film in each MDM waveguide are 30 nm and 50 nm, respectively. We choose a relatively higher dielectric constant (ε = 4.84) of the dielectric films in each MDM waveguide because a higher refractive index of the dielectric films in the MDM waveguide produces a smaller coupling length, a larger coupling coefficient, a smaller distance between waveguides, and a greater net transfer power [12]. With the aforementioned design parameters, the observed coupling length (L0) is approximately 2.33 μm, therefore, the device length is taken equal to 2.4 μm in all subsequent results. 4.1. Active switching of power and modulation We show that the transmitted power through waveguide 1 is quite low in the switch-off state and quite high in the switch-on state, thereby leading to a high extinction ratio of the modulation. We also discuss the improvement of the device performance by optimizing the

Fig. 3. Dependence of the fraction of total power transferred between coupled MDM waveguides by the application of a voltage (a) due to the phase mismatching and (b) due to the mode mismatching.

dielectric thickness, the fraction of the total power transferred from waveguide 1 to waveguide 2 is 1

2

F = 1+

wv4 2π

where, v =

K04 ðwÞ ss 0

 δd2 exp 2w ss 0 d

2π pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi λ d εd −εm ,

w=

d 2

ð6Þ

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi n2eff k20 −εd k20 . The parameters Km(w)

and s are the modified Bessel function of the second kind of order m and the distance between the two coupled waveguides, respectively. Fig. 3(b) illustrates the dependence of the fraction of total power transferred (F) from waveguide 1 to waveguides 2 and 3 induced by the mode mismatching when an electric field is applied across the MDM electrode structure. The fraction F has its maximum value of unity when there is no difference in the thickness of the coupled waveguide (i.e. δd = 0), and it decreases exponentially with increasing δd. The change δd is caused by the elasto-optic effects. In Fig. 3(b), other parameters have been taken as constants. One can see that there is a major loss in the coupling due to the change in the thickness of the dielectric film. Numerically, F is approximately 0.46 for a strain of e = 50% in the elastomeric film. This is another reason that the maximum power remains in waveguide 1 in the switch-on mode. 4. Modulation characteristics In order to verify the modal theory presented above, a full wave simulation study has been carried out using the Comsol Multiphysics software package (formerly known as FEMLAB). To visualize the wave

Fig. 4. Three dimensional FEM simulation results (a) magnetic field distribution of ycomponent demonstrating the switching of magnetic field using three parallel MDM waveguide coupler type modulator and (b) change in the extinction ratio of modulation by changing the strain of the elastomer film.

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design structure. The power is calculated at points I and O along the cross-sectional area of the MDM waveguide 1 using the Postprocessing Boundary Integration in three dimensional FEM simulations. The fundamental transverse magnetic (TM) mode of the plasmonic waveguide is excited by a source at location S. Fig. 4(a) illustrates the coupling of the magnetic field Hy component in the switch-off and switch-on states. In the switch-off state, the symmetric eigenmode of the coupled waveguides is formed by coupling of the two fundamental plasmonic modes of the two neighboring MDM waveguides. In this case, the phase shift between the two modes is zero. Therefore, in the symmetric eigenmode of the coupled MDM waveguides, the field in the middle between the two MDM waveguides is non-zero. The anti-symmetric eigenmode is formed by coupling of the two fundamental modes of the two neighboring waveguides. In this case, the phase shift between the two modes is π. Therefore, in the anti-symmetric eigenmode of the coupled MDM waveguides, the field in the middle between the two MDM waveguides is zero. The interference between the symmetric and anti-symmetric modes of the coupled MDM waveguides results in an interference pattern with a spatial beat period of 2L0. As a result, we can have the periodic energy transferred from one waveguide to another. The coupling length L0 is determined by determining the temporal period of the energy transfer and the phase velocity of the guided plasmonic modes in the MDM waveguides. We have optimized a modulator length (2.4 μm) that is approximately equal to the coupling length (2.33 μm) in order to achieve the highest extinction ratio of the modulation and for the smallest modulator length. Hence, in the off state, the power is coupled from waveguide 1 to waveguides 2 and 3 within the coupling distance L0. Because of this coupling, there exists a region around x = L0, where all the power in waveguide 1 is transferred to the waveguides 2 and 3 and a minimum power appears in the output of the modulator. In the switch-on state, when a voltage is applied across the metal electrodes of waveguide 1, there occurs a phase and mode mismatching between the coupled MDM waveguides, which leads to a decreased power transfer. This means that the coupling strength will be weakened due to the elasto-optic effect, and that most of the power remains in waveguide 1, letting the maximum power appear in the output of the modulator. In the simulation study, the strain in the elastomer film is taken as 50%, which can be obtained by applying a voltage approximately 4.8 V according to Fig. 2 (a). The dependence of the coupled power on phase and mode mismatching is the key to making the electrically activated MDM waveguide a plasmonic modulator. Both phenomena take place using the elasto-optic effects in our design structure. The extinction ratio of modulation (R) is defined as R = 10 log

P2 dB P1

Where P1 and P2 are the resultant output power at the point O in the switch-off and the switch-on states, respectively. Using the above formula, we obtain a modulation ratio of approximately 14 dB. The attenuation loss (A) in the modulator is defined as A = 10 log

Pin dB Pout

Where Pin and Pout are the power at the input (I) and output (O) port, respectively, in the maximum power propagation (i.e., switchon) state. The calculated power loss is around 4.5 dB. Further improvement in the extinction ratio is possible by reducing the output power of the modulator in the switch-off state. Fig. 4 (a) shows a small amount of coupling from waveguides 2 and 3 to waveguide 1. By taking the most optimized structure, zero power

flow in the output of the modulator could be achieved, where the extinction ratio becomes nearly infinite by its definition. 4.2. The Effect of Applied Voltage on Modulation We calculated the extinction ratio using the three dimensional FEM simulation method for different applied voltages and we showed the optimum performance of the modulator. The power transmission is sensitive to the applied voltage. As was already shown in Fig. 2 (a), as the applied voltage increases, the strain of elastomer film also increases. Now in Fig. 4 (b), we observe that the extinction ratio increases by increasing the produced strain, as predicted by theory. This is because an increasing strain decreases the thickness of the elastomer film, which causes a phase and mode mismatching between the waveguides of the directional couplers. The coupling coefficient decreases and the propagating power in waveguide 1 increases, which finally raises the extinction ratio. There is no further increment in the extinction ratio after a certain strain where the modulation becomes as large as 14.7 dB. This could be explained as follows. Increasing the voltage certainly decreases the thickness of the elastomer film in waveguide 1, which, according to the dispersion relation, increases the propagation vector constant and hence the power intensity. But, at the same time, the average power decreases due to the decrement in the cross-sectional area of the waveguide 1. After certain reduction in the cross-sectional area, the resultant output power (P2) starts decreasing in the output of the modulator, which finally leads to a slight decrease in the extinction ratio. 5. Discussion The simple structure that we designed reduces the fabrication difficulties compared with other proposed modulators. This MDM waveguide device offers the possibility of high density integration because its size is on the subwavelength-scale. Further improvements in the performance of the modulator can be achieved through the use of materials having high elasto-optic coefficients and optimization in the design structure. The results of our study using the elasto-optic effect suggest a great potential of forming a modulator of high extinction ratio and practical plasmonic components of superior characteristics. 6. Conclusion In this paper, we reported for the first time on the design of a plasmonic modulator working on the principle of the elasto-optic effects in a directional coupling structure, utilizing three parallel metal– dielectric–metal waveguides. We propose to carry out the active switching of the power propagation using the elasto-optic effect and we propose to optimize the extinction ratio of the optical modulation. We find that MDM waveguides using the elasto-optic effect have a great advantage for modulation due to phase and mode mismatching. The thickness of the dielectric film in the MDM waveguide is an important parameter to design the proposed modulator. The analytical solution is consistent with the numerical solution and verifies the feasibility of the concept of the new modulator. Acknowledgement This work has been supported by the Korea Research Foundation through the grant for the Integrated Photonics Technology Research Center (2010-0001473) at the Optics and Photonics Elite Research Academy (OPERA), Inha University, Incheon, South Korea. References [1] W.L. Barnes, A. Dereux, T.W. Ebbesen, Nature 424 (2003) 824. [2] El-Hang Lee, et al., Microelectron. Eng. 83 (2006) 1767.

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