design optimization of high-speed optical modulators

Design optimization of high-speed optical modulators

B M Azizur Rahman, Shyqyri Haxha*, Vesel Haxha, and Kenneth T V Grattan

School of Engineering and Mathematical Sciences City University London

Northampton Square London EC1V 0HB, UK

Tel: +44 207 040 8123, Fax: +44 207 040 8568 Email: [email protected] * University of Kent, Canterbury, England

ABSTRACT

The effects of design parameters on the modulating voltage and optical bandwidth are reported for lithium niobate, GaAs and polymer electro-optic modulators by using rigorous numerical modelling techniques. It is shown that by etching lithium niobate, the switching voltage can be reduced and the bandwidth improved. For a GaAs-based modulator using higher aluminium content in the buffer layer, the device length can be shortened for a given optical loss. It is also observed that the dielectric loss and impedance matching play a key role in velocity-matched high-speed modulators with low conductor loss. It is also indicated in the work that by using tantalium pentoxide coating, velocity matching can be achieved for GaAs modulators. The effects of a non-vertical side wall on the polarisation conversion and single mode operation and the bending loss of polymer rib waveguide for electro-optical modulators are also reported. Key Words: Electrooptic modulator, Finite element method, Velocity matching, Impedance matching, Conductor loss, Dielectric loss, Optical bandwidth.

1. INTRODUCTION High-speed integrated electro-optic modulators and switches are the basic building blocks of modern wideband optical communications systems and represent the future trend in ultra-fast signal processing technology. As a result, a great deal of research effort has been devoted to developing low-loss, efficient and broadband modulators in which the RF signal is used to modulate the optical carrier frequency [1]. Most of the work done in the area of designing electro-optic modulators has been strongly focused on using LiNbO3 [2-5]. Interest in research in this field has arisen as lithium niobate (LN) devices have a number of advantages over others [6], including large electro-optic coefficients, low drive voltage, low bias drift, zero or adjustable frequency chirp, and the facility for broadband modulation with moderate optical and insertion losses and good linearity [7]. However, on the other hand, LiNbO3 devices cannot be integrated with devices fabricated using other material systems such as semiconductors and as a result they are best suited to external modulation applications. However, with the recent developments in semiconductor technology, modulators based on semiconductor materials have been receiving increasing attention [8,9]. In particular, AlGaAs/GaAs material offers the advantage of technological maturity and potential monolithic integration with other optical and electronic devices in creating better optoelectronic integrated circuits (OEIC). Recently, electrooptic polymer modulators have also emerged as alternatives for optical modulators, particularly for low-cost applications for the next–generation metro and optical access systems. Today 2.5 Gb/s and 10 Gb/s modulators are standard commercial products and 40Gb/s modulators are also being developed for the market after successful prototype demonstrations: however, the continuous demand to increase the data rate further will push their operating frequency well into the millimeter wave range. The design of electrooptic modulators usually relies on the use of either directional coupler (DC) [10] or Mach-Zehnder (MZ) [11] arrangements. In DC-based electro-optic modulators, the externally applied electric field affects the refractive index distribution in the two coupled waveguides that are used in such a way that this change is antisymmetric and this also affects the light propagation in the two guides, the coupling length, the phase matching and hence the power coupling transfer between them. However, by contrast, in the MZ based electro-optic modulator, the two guides are relatively far apart, with either one or both of the two guides being affected by the applied field. So, at

Active and Passive Optical Components for Communications VIedited by Achyut K. Dutta, Yasutake Ohishi, Niloy K. Dutta, Jesper Moerk

Proc. of SPIE Vol. 6389, 63890X, (2006) · 0277-786X/06/$15 · doi: 10.1117/12.686040

Proc. of SPIE Vol. 6389 63890X-1

the end of the device, the two waves emerging from the two guides are either in-phase or in anti-phase and this gives rise to output switching properties related to the applied electric field. In this paper, accurate numerical studies of the optical properties of an etched LN, a deeply etched AlGaAs/GaAs and an etched polymer electro-optic modulator are presented, using the versatile finite element method. In particular, the effects of various waveguide parameters such as the waveguide width, the electrode width, the etch depth, the core height, the buffer thickness and the aluminum concentration of the buffer layers on the optical parameters such as the half-wave voltage length product, VπL, the optical losses due to the imperfect conductivity of the electrodes, the conductor losses, the dielectric losses and the velocity matching and their effect on the overall optical bandwidth are thoroughly investigated. The effect of the slanted side-wall on polarization conversion in GaAs modulators is also investigated. Besides the modulator parameters VπL, Nm and Zc, typical of a polymer modulator, the bending losses for constituent polymer rib waveguides are also presented.

2. COMPUTATIONAL METHODS

The above microwave propagation parameters and the induced electrooptic effects can be calculated by using quasi-optic techniques for their optimization. Amongst various quasi-static approaches, Kitazawa et al. [12] have used the spectral domain approach and Wu et al. [13] have employed the method-of-lines to study semiconductor electro-optical modulators. A simple and fast quasi-TEM FEM is used in this work to analyse numerically the modulator structure. The finite element method (FEM) is one of the most versatile numerical methods in the simulation of many engineering problems, widely used in the design of structural, fluid and thermodynamics systems. Since the early 1970s, this method has been adopted to analyse various low and high-frequency electromagnetic field problems, widely used in the analysis of microwave structures [14] and also optical guided-wave devices [15]. Simple quasi-TEM analysis [6, 14, 16-19] using a scalar field has been shown to yield valuable results. The FEM is capable of handling transmission lines with arbitrary configurations, such as thick metal electrodes, the slanted wall of ridge type structures and over-hanging electrodes, besides the anisotropic permittivity of the LN and lossy metal and dielectric materials, as encountered in practical devices. In the quasi-static approximation, the scalar potential function φ(x,y) is governed by Laplace’s equation, as given below:

0),(),(2

2

2

2

=∂

∂+

∂∂

yyx

xyx

yxφεφε (1)

where εx and εy are the permittivity of the dielectric regions in the x and y directions respectively and for an isotropic material εx=εy. By discretizing the modulator cross-section with many triangular elements and solving the highly sparse resultant algebraic equation generated, the nodal values of the potential, φ(x,y), may be obtained. Once the potential function φ(x,y), is determined, both the electric field components in the x-direction and y-direction Ex(x,y) and Ey(x,y), respectively, can be calculated from the equation below: E (x, y) = -∇ φ (x, y) (2) The microwave loss due to the lossy dielectrics can be determined by using perturbation theory employing the transverse electric field (Ex and Ey). The refractive index changes due to the electro-optic effect can also be calculated from this modulating electric field from:

),(21),( 3 yxErnyxn ij±=∆ (3)

where n is the refractive index of the electrooptic materials. For LN the value of the main electro-optic coefficient r33 is taken to be 30.8 pm/V [20 ] and for GaAs, 41r is the only non-zero bulk electrooptic coefficient with a value of 1.4 pm/V [21]. On the other hand for a polymer modulator the value of the electrooptic coefficient r33 used is 35pm/V [22] in the design optimisation process. The product of the half-wave voltage length product VπL of the Mach-Zehnder (MZ) electro-optic modulator is determined from the difference of the propagation constants under conditions of an applied electrical field and no field, respectively.


From the potential values φ(x,y), the capacitance of the electrodes, C, can also be calculated by using the divergence theorem [19] as given below:

dlnV

C n ∂∂

= ∫φε

0

1 (4)

where C is the capacitance of the line, V0 is the magnitude of applied voltage, S is the integration contour, and n the normal to the contour S. By replacing the dielectric materials by free space, the free space line capacitance, C0, can be calculated and from these parameters, the microwave index, Nm, and the characteristic impedance, Zc, can be obtained [17, 20] as:

0CCNm = (5)

0

1CCc

ZC = (6)

where c is the speed of light. The loss due to imperfect conductors can be calculated by using the incremental inductance formula [17,20]:

nZ

ZZR C

C

SC ∂

∂⋅= 0

02α (7)

where 0CZ is the free-space characteristic impedance of the electrode and n

ZC

∂∂ 0 denotes the derivative of Zco with

respect to the incremental recession of the electrode surfaces. Rs is the surface resistance of the conductor, and Z0 is the impedance of the free space. For a travelling-wave modulator, when wave velocities are not matched, the 3 dB optical bandwidth, ∆f, is approximately determined by [23]:

LNNcf

m−=∆

0

2π

(8)

where L is the length of the electrodes and Nm and No are the effective indices of the microwave and the optical wave respectively. However, if the perfect velocity matching condition can be achieved, that is Nm= No, then the bandwidth is limited by the electrode loss. When only the conductor loss is considered, the 3 dB optical bandwidth, ∆f, is given by [23]:

284.6

⎟⎟⎠

⎞⎜⎜⎝

⎛=∆

Lf

Cα (9)

where αc is conductor loss in dB per unit length normalized at 1 GHz. However, when the effect of both phase matching and microwave loss are considered, then the optical response )( fm is given by a more general equation [24]:

21

22

2

)2()(2cos21)( ⎥

⎦

⎤⎢⎣

⎡+

+−=

−−

uLeuefm

LL

α

αα

(10)

where c

NNfLu m )( 0−=π and fCαα =


The conductor loss, Cα is normalized at 1 GHz, in this case where f is given in GHz, and cα is the conductor loss in

cmGHzdB

⋅

The frequency-dependent drive voltage can be obtained from the optical response (in dB optical) using the relationship [25]:

)10/)((10)()( fmdcVfV −= ππ (11) where, m(f) and Vπ can be obtained from the equations shown below.

)]2exp()2/[exp()1)(()( 2112 −+−+ −+++= φρρφρψρψ jjfm (12)

010 , ββββ

ππ −=∆

∆=

VLV (13)

where β0 and β1 are the propagation constant of the active waveguide, with and without the applied voltage, Vo.

Both the unperturbed original guide and the perturbed optical waveguide under the influence of the modulating field can be analysed by employing any modal solution method. During the last two decades, many analytical, semi-analytical and numerical tools have been introduced in the literature to perform the modal analysis of optical waveguides. However, the vector finite element method, based on the H-field full vectorial FEM (VFEM) [15] has been considered to be one of the most accurate and yet numerically efficient and versatile modal solution techniques. The formulation is based on the minimization of the following functional [15], in terms of the nodal values of the full H-field vector:

( ) ( ) ( ) ( )

∫

∫Ω⋅

Ω⎥⎦⎤

⎢⎣⎡ ⋅∇⋅∇+×∇⋅×∇

=∗

∗−

∗

dHH

dHHpHH

µ

εω

1

2 (14)

where * denotes complex conjugate and transpose, and are the permittivity and permeability tensors, respectively, and p is the penalty parameter used to reduce the appearance of spurious modes. Once the potential distribution and the refractive index tensor is determined using equation (3), the vector H-field finite element modal solution is used to find the different optical modes of propagation, their propagation constants and their corresponding full vectorial field components.

3. NUMERICALLY SIMULATED RESULTS

Most high-speed modulators are based on the Mach-Zehnder approach, fabricated on Z-cut LN substrates and

operate with a vertical electric field to utilize the largest electro-optic coefficient, r33, of LN. The cross sectional configuration of the LN electro-optic modulator with coplanar waveguides (CPW) and which uses a Mach-Zehnder optical waveguide is illustrated in Fig. 1. The relative dielectric constants of the Z-cut LN substrate were 28 and 43 in the perpendicular and parallel directions to the substrate surface, respectively. To reduce the optical loss due to the lossy metal electrode, often a SiO2 buffer layer is used, which also can assist in the phase matching. The relative dielectric constant of the SiO2 buffer layer is taken as 3.9. The coplanar waveguide (CPW) electrode is commonly used as a travelling-wave electrode for a Ti:LN optical modulator because it provides a good connection to an external coaxial line.

It has been reported relatively recently [17,18,23] that for a ridge type modulator with an etched LN substrate, the overlap between the optical and modulating field can be significantly increased and as a consequence for a given operating voltage, the interaction length can be shortened, which will also increase the modulator bandwidth. Fig.2 shows the variation of the product of the half-wave voltage (Vπ) and the electrode interaction length, L, as a function of


ridge depth, H. It can be observed that the VπL product decreases as the ridge depth (H) is increased from zero (unetched) for both the buffer thicknesses, B = 0.75 µm and 1.2 µm, and reach their minimum values when H lies between 3 µm to 5 µm. The decrease of the Vπ·L product is due to the optical field being more confined in the lateral direction and an increased overlap with the modulating electric field. Also, it can be observed that the product Vπ·L decreases as the buffer layer is reduced from B = 1.2 µm and 0.75 µm.

It can be anticipated that the refractive index change is heavily concentrated under the hot electrode and largely depends upon the electrode position and the ridge depth. For a push-pull arrangement the modulating field is applied in both the left and right-side waveguides and the maximum refractive index change profiles calculated from equation (3) for an etched structure are ∆nLeft = 0.0001437 and ∆nRightt = -0.0000167 respectively, whereas for an unetched structure the maximum refractive index changes are ∆nLeft = 0.0000959 and ∆nRight = -0.0000074. It can be observed that the overall refractive index profile change is much higher on the waveguide region for an etched structure than for an unetched structure, leading to a better optical field confinement and low driving power.

The Hx optical field profile for the quasi–TM fundamental mode, xH11, for the etched LN modulator structure is illustrated in Fig.3. Due to the fact that the waveguide index profile, ne,o(x, y), is diffused, and the optical mode for unetched guide is not so well confined in the lateral dimension, it supports only the fundamental mode for each polarization. On the other hand etching strengthens the lateral confinement because of the larger index contrast, due to the presence of low index air surrounding the rib region.

The variations of Nm and Zc with the buffer layer thickness, B, are shown in Fig.4. In this case the electrode thickness, T, and width, W, were kept constant at 5 µm and 8 µm, respectively. Results for ridge heights 0 µm and 3 µm are shown by dashed and solid lines respectively for both G = 20 µm and 25 µm. It can be observed that Nm reduces and Zc increases as B or H is increased but on the other hand, Nm reduces and Zc increases as G is reduced. For the range considered here, it can be noticed that for none of the cases is Nm matched and considering a higher value of B it would be possible to match Nm, but as a consequence VπL would also increase. However, it can be observed that by etching the LN substrate, since Nm is reduced, it would be easier to match the Nm with a reasonable value of B.

In the design of a high-speed modulator, first of all it is necessary to match the microwave impedance to the optical impedance. Amongst the other parameters considered, this can be easily achieved by increasing the electrode metal thickness, T. The velocity of the optical carrier wave or its equivalent parameter, the effective index, No, of a modulator structure depends on various fabrication parameters, such as the titanium thickness, the diffusion time and the temperature. For a given structure, the velocity parameter can be accurately calculated by using an optical modal solution approach, such as the FEM [11]: however, in this study for LN devices, it is assumed that a typical value would be 2.15 for the purpose of subsequent phase matching.

The modulator bandwidth primarily depends on the phase mismatching between the optical and microwave velocities. However, when they are matched, the maximum optical bandwidth is achieved, and this value depends on the microwave loss. Variations of the 3 dB optical bandwidth with the buffer layer thickness for different metal thicknesses are shown in Fig. 5. In this case the effects of phase mismatching and electrode losses are considered, but the effect of impedance mismatch is neglected and the length of the electrodes is taken as L = 2.7 cm. When only the conductor loss is considered and the dielectric loss is neglected, the bandwidths calculated by using equation (10) are shown by solid lines. It can be noted that for T = 20 µm, a maximum bandwidth of 38 GHz is reached when B is equal to 0.52 µm, and Nm = No. It can be also noted that for T = 15 µm, the maximum bandwidth is reached when B = 0.83 µm. However, this 35 GHz maximum value is lower than that for T = 20 µm, as the microwave loss is larger in this case. The variations of the optical bandwidths with the buffer layer thickness, B, (when the dielectric losses are included) are shown by dashed lines. It can be noted that by neglecting the dielectric loss, the optical bandwidth could be overestimated by as much as 30%. This error will be even higher when the operating frequency also is higher as the dielectric loss increases faster than the conductor loss, with the operating frequency. It is obvious that at a higher operating frequency when the dielectric loss is ignored, the total microwave loss can be significantly over underestimated. The frequency dependences of the optical response calculated by using equation (11) are illustrated in Fig. 6 at the electrode length, L = 2.7 cm for both etched and unetched structures, with and without reaching the velocity matching condition. At higher operating frequencies, the velocity matching between the optical and microwave signals plays a significant role, as shown here. It can be observed that at an operating frequency of 100 GHz the optical response has been significantly improved under the velocity matching condition for both etched and unetched structures. In this case, under the velocity matching condition, the optical response is almost similar for such etched and unetched structures. This is due to the fact that under the velocity matching condition, the conductor losses of the etched structure (0.28


(dB/GHz1/2x cm)) are higher than those of the unetched structure (0.266 (dB/GHz1/2x cm)). On the other hand, the characteristic impedance for the etched structure, is 45.26 Ω which matches better to Zc, which has been taken as 50 Ω, compared to that of the unetched structure with Zc = 38.35 Ω. The effect of the dielectric losses has been also included in these simulations.

Next, a deep-etched semiconductor electro-optic modulator is considered as part of the design optimisation process. The waveguide layers for the design of the deep-etched waveguide structure considered here are shown in Fig.7. Etching through the upper cladding layer, the waveguide core and part of the lower cladding gives a very strong horizontal confinement of the light [27], and as a result the bending loss reduces, thus so it is expected to provide a much more compact system design. As shown in this figure, a 0.4 µm 10%AlGaAs layer, a thick GaAs core with a height, H(µm), and a buffer AlGaAs layer with an Al concentration of x1% and a height, B(µm), are all deposited on a 2 µm thick 5% AlGaAs layer. The whole structure is deposited on a very thick GaAs substrate, as shown in Fig.7. A highly doped ground electrode, with V=0, is introduced between the 10%AlGaAs layer and the substrate, while the hot metal electrode is deposited on top of the buffer AlGaAs layer. The width of the waveguide is W(µm), while the electrode width is Wel(µm) and the operating wavelength is 1.55 µm. Often the vertical side wall may be slightly slanted, shown here at an angle θ, which has a profound effect on the polarization conversion in an optical modulator, as will be demonstrated later.

It can be noted that the value of VπL did not change significantly with the aluminium concentration in the buffer layer. However, an increased aluminum concentration in the buffer layer would enhance its vertical confinement and as a result would push down the optical field, resulting in a reduced overlap integral between the optical and the modulating fields. Next, the effects of the buffer layer thickness, B, and the Al concentration, x1, on the optical losses are thoroughly investigated. For this purpose, the top electrode has been assumed to consist of two metal layers, gold (Au) and titanium (Ti), each with a thickness, t, of 0.1 µm. The perturbation technique combined with the VFEM modal solution [15] has been utilised to estimate the optical losses due to this imperfectly conducting electrode. The variations of the optical losses with the buffer thickness, B, for different values of the Al concentration, x1, of the buffer layer are shown in Fig. 8. As may be noted from this figure, the optical losses are drastically reduced as either the buffer thickness or the Al concentration of the buffer is increased, as in either case the optical field will be more confined to the core and a smaller portion of the field will be found near the lossy electrode region. In particular, for a buffer thickness of 0.5 µm and an Al concentration of 30%, the optical loss has been estimated to be 12 dB/cm, while if the buffer thickness is increased to 1.0 µm, the optical loss is greatly reduced to nearly 1 dB/cm. On the other hand, for a buffer thickness of 0.5 µm and as the Al concentration increased from 30% to 100%, the optical loss decreases significantly from 12 dB/cm to 0.8 dB/cm, a difference which would have a profound effect on the modulator bandwidth [28].

Previously, it was shown that for a LN modulator, a thicker electrode can be used to reduce the value of Nm to match that of No, this being typically around 2.15. However, for a GaAs modulator, Nm typically is lower than No, and hence the major design objective would be to increase it for possible velocity matching. Earlier Nees et al. [29] reported on a velocity-matched waveguide modulator by introducing a GaAs superstrate on the top, but this resulted in a very high switching voltage. Subsequently, Khan et al. [30] have reported a study on the use of a thin coating of tantalum pentoxide, Ta2O5, for a velocity-matched travelling-wave directional-coupler-based intensity modulator in the AlGaAs/GaAs structure. The waveguide layers for the design of our deep-etched waveguide structure considered here are shown in Fig.9. The waveguide width, W, and its core thickness, H, are taken as 5 µm and 1.5 µm respectively. The upper cladding (buffer) thickness, D, is varied, but the lower cladding thickness is taken as 0.5 µm. The gold hot electrode width We is 4.9 µm with a conductivity of σ = 4.1x107 s/m. The refractive indices of the core, the upper layer, and the lower cladding are taken as 3.37, 3.322 and 3.329, respectively at the operating wavelength λ = 1.55 µm. Two types of tantalum pentoxide, Ta2O5, overlayer arrangement structures have been investigated, designated A and B, as shown in Fig.9. In the structure A, as shown in Fig.12a, tantalum pentoxide is deposited all around the mesa. In the structure B, as shown in Fig.12b, the Ta2O5 thickness is deposited on the two sides of the mesa. In these cases a 0.1 µm thick highly doped (1x1018 /cm3) GaAs layer below the lower cladding is considered as the ground electrode.

Fig. 10 shows the variation of microwave effective index, Nm, with the Ta2O5 coating thickness, for the structures A and B. The buffer layer thickness, D, the core thickness, H, and the electrode thickness, E, are set to values of 0.5 µm, 1.5 µm and 0.1 µm, respectively. It can be observed that when the coating thickness of the Ta2O5 is increased, the microwave effective index is significantly increased, for both the cases studied here. The required coating thicknesses, for velocity matching for structures, A and B, are 0.75 µm and 2.25 µm, respectively. However, the numerical simulations in this work indicate (but are not shown here) that it is not possible to reduce the velocity


mismatch significantly, even when a 5.0 µm thick layer of Ta2O5 is deposited only on the top of the hot electrode. For a given structure the optical effective index, N0 can be calculated accurately by using an optical modal solution approach, such as the FEM [15]: however, for this study it is assumed that a typical value would be around 3.35 for the purpose of subsequent velocity matching. It is very important to note that for the structure A, the required Ta2O5 coating thickness to achieve velocity matching is smaller compared to the structure, B. The overlayer with a high dielectric constant of the Ta2O5 material increases the concentration of the electric field in the epitaxy layers, more specifically in the core region and the upper cladding. By contrast, in the structure B, this phenomenon is more visible when the coating thickness on the side starts to submerge into the core region. So far, in the analysis of semiconductor EO modulators, in order to determine several important device parameters, it is usually assumed that the polarization state of the modulated light wave remains the same as that of the input beam. However, this assumption can lead to totally misleading results if the waveguide structure under study has even small fabrication imperfections. For example, if the waveguide sidewalls are slightly off-vertical, as has been observed for devices fabricated away from the wafer centre, or if the hot electrode is shifted off-centre, then the non-symmetric modulating electric field, especially its horizontal component, generates an off-diagonal permittivity tensor, allowing mode coupling between the polarization states. Avoidance, or at least minimization of such polarization crosstalk, is a critical issue in the design of high-speed semiconductor EO modulators. Hence, it is particularly important to account quantitatively for such unwanted polarization conversion phenomena to identify appropriate design process for EO semiconductor modulators to minimize these effects, and this is reported here when the slant angle θ = 10o. Fig. 11 shows the evolution of the TM power along the propagation distance, z, for different values of the modulating voltage when the incident wave is the fundamental TE mode at the input side. At z = 0, the vector sum of the two highly hybrid TE and TM modes is similar to the incident mode, which was the pure TE mode in this case. However, along the axial direction, the vector sum of the two modes shows a gradual conversion to the TM mode due to the z-dependent phase difference between the modes. For a voltage equal to the crossover value of –24.2 V, because of the proper phase matching and the high level of hybridism of the TE and TM modes, the TM power reaches nearly 100% at a length equal to 93 mm, as shown by a solid line. However, as may be seen from the same figure, as the modulating voltage is slightly reduced from the crossover value, the maximum TM power converted becomes smaller. For example, for a voltage of –23 V, the maximum TM power is nearly 48% of the input power, while if that voltage were decreased to –22 V, this maximum TM power becomes only 18% of the input power. Hence, this figure reveals that the degree of polarization conversion depends on the modulating voltage. It should also be noted that when the modal degeneration is smaller (away from crossover voltage), the beat length is also shorter. Polymer materials have become increasingly important for integrated optics because of their simpler and potentially low-cost fabrication procedures that are used. Electro-optic (EO) polymer waveguide devices are very attractive for optical communications systems due to their low dispersion, high electro-optic coefficients and their fast electronic response. Decades of research on nonlinear electro-optic polymer materials have made it possible to make high frequency photonic switching and modulating devices. The cross-section of the polymer modulator considered here is shown in Fig.12. The refractive indices of the core, ng, and the cladding, ns, are taken as 1.67 and 1.43, respectively at the operating wavelength of 1.55 µm. The dielectric constants for these two core and cladding layers are given by 3.4 and 3.15, respectively at the low modulating frequency. Initially the waveguide width, Wg= 6.5 µm, the rib height, h = 0.3 µm, the core height, H = 3.5 µm, the lower cladding, A = 1.4 µm, and the upper cladding, B = 2.3 µm are considered in the numerical simulations. The electrode width We could be wider than the waveguide width and later this parameter is also adjusted to optimise the modulator design. For a MZ-based design it is necessary that the two branch waveguides should support only a single guided mode and the separation between the branches should be larger so that no appreciable evanescent coupling be present. The single mode operation, mode shape, and evanescent coupling can be controlled by adjusting the rib height. The dominant Hy field profiles of the fundamental quasi-TE (Hy

11) mode with a waveguide width Wg= 6.5 µm are shown in Figs.13 a and b, when the rib height h = 0.3 µm and 0.7 µm, respectively. Its spot-size in the vertical direction, σy, is only 3.3 µm, which is due to the strong vertical confinement between the upper and lower claddings. This spot-size is defined as the region where the field intensity is greater than 1/eth of the maximum field intensity. Its spot-size in the horizontal direction, σx, is calculated to be 14.5 µm. The weak horizontal confinement is due to a low contrast between the equivalent indices of the vertical layers. This value is much larger than its width, Wg, which arises due to a very weak confinement for a smaller value of the rib height and the field extends considerably outside the rib region. In this case, although the average transverse spot-size, σav = yxσσ = 7 µm, due to the high asymmetry (defined here as ∈ =


σx/σy = 4.5), the butt coupling factor of this modal field with a typical SMF, with its Gaussian spot-size diameter σd = 9.0 µm, has been calculated to be 0.70.

On the other hand, the modal field is shown in Fig. 13b when the rib height is increased to h = 0.7 µm, keeping the waveguide width, Wg = 6.5µm. It can be clearly observed that the symmetry of the field profile has improved significantly. In this case the increased horizontal confinement is due to the stronger index contrast in the horizontal direction and σx is reduced to 9.0 µm. Here, although σav is reduced to 5.4 µm, the coupling to a fibre with σd = 9 µm is increased to 0.77 essentially due to the increased symmetry of the modal field. By adjusting all the waveguide parameters, a suitable modal field can be obtained for optimum coupling to the input and output waveguides. However, one of the main objectives in the design of optical waveguides for an electro-optic modulator is to have an enhanced overlap between the optical mode and the modulating fields, which is critical for the optimisation of VπL.

The variations of VπL with the electrode width for different waveguide widths and rib height combinations are shown in Fig.14. It can be clearly observed that for a given electrode width the VπL value is significantly smaller for a higher rib height. In the case, when h = 0.3 µm, t = 3.5 µm, and We = Wg = 6.5 µm the maximum value of ∆n due to the electro-optic effect is 5.6 x 10-5 at the top of the waveguide core and the value of this index reduces to 70% of this maximum value at the bottom of the core. In the lateral direction it reduces to its 1/eth value at 6.6 µm from the centre and correspondingly yields the critical VπL parameter value of 9.8 V.cm. However, when h = 0.7 µm, t = 3.1 µm, Wg = 6.5 µm, and We = 10.0 µm, the maximum value of ∆ne is similar. This value reduces to only 93% at the lower interface, which means that the index profile remains almost constant in the y-direction. In the lateral direction it also reduces to its 1/eth value at a distance of 10.0 µm from the centre, so this profile also reduces slowly in the horizontal direction. Thus inside the waveguide core, the average value of the index is much higher, which yields a VπL value of 7.5 V.cm, which is a significant improvement, compared to the case when h = 0.3 µm. It can be clearly observed that for a given waveguide width, when the electrode width is increased, the VπL value is reduced and reaches a minimum value where any further increase of We does not enhance the VπL value. It can also be observed that the minimum VπL value can be obtained by using a wider guide with higher rib height and electrode wider than the waveguide width.

In the design of an optical MZ-based modulator, it is necessary to design curved sections to couple different guidedwave sections. The variation of the bending loss with the bending radius is showing in the Fig. 15. for different rib heights. It can be clearly observed that as the bending radius is reduced, (which is necessary to increase the functionality of an optical chip) the bending loss increases rapidly. However, by using a higher rib height in a rib waveguide, the bending loss can be significantly reduced since a higher rib height provides a stronger confinement in the lateral direction.

4. CONCLUSIONS In this paper, a rigorous and accurate numerical simulation study to address the optimization of the optical properties of an etched LN and a deeply-etched GaAs/AlGaAs semiconductor and a polymer rib waveguide electro-optic modulator have been presented, using the power and versatility of the finite element method. Specifically, the effect of the waveguide width, the core height, the etch depth, the buffer thickness and the Al concentration on VπL and the optical losses due to the imperfectly conducting electrodes have been investigated in some detail. Also, work showing the effect of the variations of the waveguide parameters on both the velocity and the impedance matching conditions has been presented. It is further revealed that the electrode thickness plays an essential part in determining the bandwidth of a high-speed modulator. The effect of the impedance mismatch on the bandwidth is also presented along with the clear demonstration that the dielectric loss would play a dominant role in the determination of the optical bandwidth of high-speed modulators. It has been shown that the highly dispersive coating thickness may play an important role in increasing the optical bandwidth. The numerical simulations presented here indicate that for GaAs modulators, velocity matching is possible by using a Ta2O5 coating instead of slow-wave structures with segmented electrodes, to increase the optical bandwidth.

For a polymer electro-optic modulator designs, by using rigorous numerical simulations it has been demonstrated that the increased rib height reduces the key modulator parameter, VπL. The increased rib height also increases the Nm value and matches the Zc value better to Z0, which will also improve the optical bandwidth of the modulator. It has also been shown that besides demonstrating the possibility of a much compact system design with smaller bending radius, the mode shape is also improved so that insertion loss would also reduce. The work in this paper has revealed that a wider electrode also improves the key modulator parameters, such as VπL, Nm and Zc.


REFERENCES

[1] S. K. Koroty, G. Eisenstein, R. S. Tucker, J. J. Veselka and G. Raybon, “Optical intensity modulation to 40 GHz using a wideguide eletrooptic switch,” Appl. Phys. Lett., vol. 50, no. 23, pp. 1631-1633, 1987. [2] C. M. Gee, G. D. Thurmond and H. W. Yen, “17-GHz bandwidth electrooptic modulator,” Appl. Phys. Lett., vol. 43, no. 11, pp. 998-1000, 1983. [3] K. Kubota, J. Noda and O. Mikami, “Travelling wave optical modulator using a directional coupler LiNbO3 waveguide,” IEEE J. Quantum Electron., vol. 16, no. 7, pp. 754-760, 1980. [4] R. C. Alferness, N. P. Economou and L. L. Buhl, “Fast compact optical waveguide switch modulator,” Appl. Phys. Lett., vol. 38, no. 11, pp. 214-217, 1981. [5] L. Thylen, “Integrated optics in LiNbO3: Recent developments in devices for telecommunications,” J. Lightwave Technol., vol. 4, no. 6, pp. 847-861, 1988. [6] K. Noguchi, O. Mitomi and H. Miyazawa, “Millimeter-wave Ti:LiNbO3 optical modulators,” J. Lightwave Technol., vol. 16, no. 4, pp. 615-619, 1998. [7] W. K. Burns, M. M. Howerton, R. P. Moeller, R. Krahenbuhl, R. W. McElhanon and A. S. Greenblatt, “Low drive voltage, broad-band LiNbO3 modulators with and without etched ridges,” J. Lightwave Technol., vol. 17, no. 12, pp. 2551-2555, 1999. [8] S. Y. Wang and S. H. Lin, “High speed III-V electrooptic waveguide modulators at λ=1.3 µm,” J. Lightwave Technol., vol. 6, no. 6, pp. 758-771, 1988. [9] R. G. Walker, “High-speed III-V semiconductor intensity modulators,” IEEE J. Quantum Electron., vol. 27, no. 3, pp. 654-667, 1991. [10] N. Anwar, C. Themistos, B. M. A. Rahman, and K. T. V. Grattan, Design consideration for an electrooptic directional coupler modulator, J. Lightwave Technol, 17, pp.598-605, April 1999. [11] N. Anwar, S. S. A. Obayya, S. Haxha, C. Themistos, B. M. A. Rahman, and K. T. V. Grattan, ‘The effect of fabrication parameters on a ridge mach-zender interferometric (MZI) modulator’, J. Lightwave Technology, 20, pp.826-833, 2002. [12] T. Kitazawa, D. Polifko, and H. Ogawa, ‘Analysis of CPW for LiNbO3 optical modulator by extended spectral-domain approach’, IEEE Microwave and Guided Wave Lett., 2, pp.313-315, 1992. [13] K. Wu, C. E. Tong, and R. Vahldieck. ‘Microwave characteristics of high-speed travelling-wave electrooptic modulators on III-V semiconductors’, J. Lightwave Technology, 9, pp. 1295-1304, 1991. [14] Z. Pantic and R. Mittra, ‘Quasi-TEM analysis of microwave transmission lines by the finite-element method’, IEEE Microwave Theory Tech., 34, pp.1096-1103, 1986. [15] B. M. A. Rahman and J. B. Davies, ‘Finite-element solution of integrated optical waveguides’, J. Lightwave Technology, 2, pp. 682-688, May 1984. [16] X. Zhang and T. Miyoshi, Optimum design of coplanar waveguide for LiNbO3 optical modulator, IEEE Microwave Theory Tech., 43, pp.523-528, 1995. [17] O. Mitomi, K. Noguchi, H. Miyazawa, ‘Design of ultra-broad-band LiNbO3 optical modulator with ridge structure’, IEEE Microwave Theory Tech., 43, pp.2203-2207, 1995. [18] K. Noguchi, O. Mitomi, H. Miyazawa, and S. Seki. ‘A Broadband Ti-LiNbO3 Optical Modulator with a ridged Structure’. J.Lightwave Technology, 13, NO. 6, pp. 1164-1169, June 1995. [19] J. C. Yi, S. H. Kim, and S. S. Choi, Finite-element method for the impedance analysis of travelling-wave modulators, J. Lightwave Technol., 8, pp.817-822, 1990. [20] M. Koshiba, Y. Tsuji, and M. Nishio, Finite-element modeling of broad-band traveling-wave optical modulators, IEEE Microwave Theory Tech., 47, pp.1627-1633, 1999. [21] A. Yariv and P. Yeh, ‘Optical Waves in Crystals’, New York: Wiley Interscience, 1984. [22] S. Park, J. J. Ju, J. Y. Do, S. K. Park, and M-H. Lee, ‘ Thermal Stability Enhancement of Electrooptic Polymer Modulator’ IEEE Photonics Technol. Lett., vol.16,no.1, pp.93-95, January 2004. [23] M. Minakata, ‘Recent progress of 40 GHz high-speed LiNbO3 optical modulator’, Proc. SPIE, vol. 4532, pp.16-27, Denver, August, 2001. [24] M. Rangaraj, T. Hosoi, and M. Kondo, ‘A Wide-Band Ti-LiNbO3 Optical Modulator with Conventional Coplanar Waveguide Type Electrode’, IEEE Photonics Technol. Lett.,, 4, NO.9, pp. 1020-1-22 September 1992. [25] Howerton, M.M., R. P. Moeller, A. S. Greenblatt, and R. Krähenbühl.,’ Fully packaged, broad-band LiNbO3 modulator with low drive voltage’, IEEE Photon, Photonics Technol. Lett, 12, 792, 2000.


I W=9/tmS=8im

0 1 2 3

Ridge Hight (am)

4 5

:ive

Inde

x, N

, ) 0

N I

\A /

\/

\/ \)

K '\

/ \/

\/ / /

\/ \ \\

\ \\

i !\ \\

0 (11

0)

01

0 c

Impe

danc

e,

::TiII5i:H 45 I

— .

I 1 303(330)

40 30

[26] Hui K.W., Kin Seng Chiang, Boyu Wu, and Z.H. Zhang, ’Electrode Optimization for High-Speed Traveling-Wave Integrated Optic Modulators' J. Lightwave Technol.,16, 232, 1998. [27] J. M. Heaton, M. M. Bourke, S. B. Jones, B. H. Smith, K. P. Hilton, G. W. Smith, J. C. H. Birbesk, G. Berry, S. V. Dewar, and D. R. Wight. ‘Optimization of deep-etched, single-mode GaAs/AlGaAs optical waveguides using controlled leakage into the substrate’, J. Lightwave Technology, 17, pp.267-281, 1999. [28] S S A Obayya, S. Haxha, B. M. A. Rahman, C. Themistos, and K. T. V. Grattan, Optimization of the optical properties of a deeply-etched semiconductor electroptic modulator, J. Lightwave Technol., 21, pp.1813-1819, August, 2003. [29] J. Nees, S. Williamson and G. Mourou, ‘100 GHz travelling-wave electro-optic phase modulator’, Appl. Phys. Lett., 54, pp1962-1964, 1989. [30] M. N. Khan, A. Gopinath, J.P. G. Bristow, and J. P. Donnelly, ‘Technique for velocity-matched travelling-wave electrooptic modulator in AlGaAs/GaAs’, IEEE Microwave Theory Tech., 41, pp.244-249, 1993. [31] A. G. Rickman, G. T. Reed, and F. Namavar, ‘Silicon-on-insulator optical rib waveguide loss and mode characteristics,’ J. Lightwave Technol., 12, pp.1771-1776, 1994. [32] R. A. Soref, J. Schmidtchen and K. Petermann, ‘Large single-mode rib waveguides in GeSi-Si and Si-on-SiO2,’ IEEE J. Quantum Electron., 27, pp.1971-1994, 1991.

Fig. 2 Variation of the product VπL with ridge depth, H, for two different buffer layer thicknesses, B.

Fig. 4 Variation of Nm, and Zc as a function of the buffer layer, B.

S G 5 Volt

LiNbO

Si

y

x

FEM

Y Z

X

Crystal

G

W W

H

B

T

Fig. 1 Schematic diagram of an etched LN modulator.

Fig. 3 Modal field profile of an etched LN modulator, when H= 3.0 µm.


oss,

a(d

B

1o /0 io X1=100%

4.84.64.4 D=O.5am4.2 H=1 .5.cm

E=O.litm

Structure [A]\4o3.8

3.6 N=3.353.4______3.2

— — — — —— — —

— Structure [B]

0.0 0.5 1.0 1.5 2.0 2.5 3.0

Tantalum Pentoxide thickness, T(JLm)

Fig. 5 Variation of the 3dB optical bandwidth, with B, for different electrode thickness values, T.

Fig. 9 Deep-etched GaAs/AlGaAs semiconductor modulators for two types of the Ta2O5, overlayers.

Fig. 10 Variation of Nm for two Ta2O5 structures, A and B.

Frequency (GHz)

Opticalresponse(dB)

0 20 40 60 80 100-16

-14

-12

-10

-8

-6

-4

-2

0

2

H = 3 µm H = 0 µm

Nm ≠ No

Nm= No

L = 2.7 cm

Fig.6 Variations of the optical response for etched and unetched and velocity matched and unmatched LN modulators with the modulating frequency.

Wel

10 % AlGaAs cladding, 0.2 µm

X1 % AlGaAs Buffer Layer, B (µm)

GaAs core, H (µm)

θ

GaAs Substrate

W (µm) 5% AlGaAs

Fig.7 Schematic diagram of a deeply-etched GaAs electrooptic modulator.

Fig. 8 Variation of optical loss, with buffer layer thickness, B for three values of Al (%).


0.66

0.4/ -22.00(V)

12 h.0.3,ut.3J,s,W..6J,sm 12 h.0.7,sit.llpii,W,.Opn

10

cia I a0 5 10 IS 20 25 30

a—

Fig. 17(a)

0 5 10 IS 20 25 30"'-Fig. 1b

Fig. 11. Polarisation Conversions θ = 10o.

Fig. 14 Variation of the VπL with the electrode width, We.

t

Lower cladding (ZPU430)

Upper cladding (ZPU430)

We

Wg

h

A

B

H

V ≠ 0

V = 0 Si Wafer

Core (PEI-DAIDC)

Fig. 12 Schematic of a polymer modulator.

Electrode width, We(µm)

2 4 6 8 10 12 14 166

7

8

9

10

11

12

13

VπL

h = 0.3 µm, t = 3.5 µm, Wg = 6.5 µmh = 0.3 µm, t = 3.5 µm, Wg = 10.0 µmh = 0.7 µm, t = 3.1µm, Wg= 6.5 µm

Radius, r(cm)

0 1 2 3 4 5 6 7

dB/m

m

0

1

2

3

4

5

6h = 0.3 µm, t = 3.5 µm, Wg= 6.5 µm h = 0.5 µm, t = 3.3 µm, Wg = 6.5 µm h = 0.7 µm, t = 3.1 µm, Wg = 6.5 µm

Fig. 13 Dominant Hy modal field profiles for (a) h = 0.3 µm and (b) 0.7 µm.

Fig. 15 Variation of the bending loss with the bending radius.


design optimization of high-speed optical modulators

Documents