Optical Waveguide Crosstalk SPICE Modeling

For Package System Signal Integrity Simulation

Zhaoqing Chen

IBM Corporation

2455 South Rd B002, Poughkeepsie NY 12601

zhaoqing@us.ibm.com, (845)435-5595

Abstract

A SPICE modeling method for optical waveguide

crosstalk in intensity modulated optical link is proposed based

on the data from hardware sample measurements or

electromagnetic simulations at optical wave frequencies. The

proposed equivalent baseband SPICE model is for the

applications of signal integrity transient simulation by using

general-purpose SPICE or SPICE-like circuit simulators with

marching time steps in the electrical signal envelop regime. In

addition to crosstalk modeling, the proposed method can also

be applied to transmission modeling directly.

The amplitude of the optical transmission/crosstalk in

optical wave frequency-domain is applied directly to the

equivalent baseband SPICE model. The group delay of the

optical wave transmission/crosstalk is taken as the phase delay

of the transmission/crosstalk in the equivalent baseband

SPICE model. The phase of the optical wave carrier is

handled by DC nodes and nets in the SPICE model for

superposition of crosstalk and victim signal.

To estimate the worst case scenario of the crosstalk effect

on the electrical signal eye diagram caused by the optical

carrier phase difference between crosstalk aggressor and

victim, two or more transient simulations are applied to

combine different optical wave phase offsets between

crosstalk aggressor and victim.

Signal integrity test cases on optical waveguide SPICE

models combined with the VCSEL optical transmitter or

Mach-Zehnder intensity modulator and optical receiver SPICE

models are shown to test the proposed modeling and transient

simulation method. Test examples include polymer multimode

optical waveguide on card/board level and some single mode

optical waveguide structures at in-package and on-chip levels

such as Silicon, SiO2, and plasmonic optical waveguides.

1 Introduction

In high-speed package system, the conductive and

dielectric loss by copper interconnects become very

significant at high bit-rate applications even at a distance of

about half a meter on printed circuit board. The optical

waveguides have attracted a lot of research and development

attentions as an alternative or replacement to traditional

copper interconnects in card/board, package module, and on-

chip levels.

After many years of research and development, optical

waveguides becomes a realistic low-cost interconnect

approach implemented in printed circuit board and package

module. Since the length of the optical waveguide in these

optical waveguide applications is usually below one meter, the

dispersion effect is very small and can be ignored in regular

signal integrity simulations. In addition, the crosstalk between

optical waveguides is usually much smaller than the one in the

copper wire/via design approach. However, in some high

density applications with tight waveguide-to-waveguide

spacing, the crosstalk between two adjacent optical

waveguides may still be around or even worse than -30dB.

The crosstalk may significantly degrade the signal integrity

quality of the packaging system. In these cases, accurate

signal integrity modeling and simulation methods are

necessary to take into account the crosstalk effects on signal

integrity properties such as the eye diagram opening in the

packaging system design.

The crosstalk between optical waveguides can be modeled

by many analytic and numerical methods. Some of the

numerical methods are implemented in commercially available

software tools already. However, the crosstalk models by most

methods represent the optical crosstalk which are derived at

the light-wave frequencies. They cannot be used directly in

transient simulations on electrical signal integrity using the

marching time steps in electrical signal, or envelop, regime.

SPICE or SPICE-like transient simulations have been

applied in the optic fiber and silicon photonics [7] [13] by

special modeling and simulation techniques. To use the

traditional signal integrity electrical simulation method, the

proposed method in this paper will focus on a regular

electrical or envelope regime SPICE circuit model of the

electrical crosstalk between parallel optical waveguides based

on measured optical crosstalk data for both single-mode and

multi-mode optical waveguides. Electromagnetic simulation

can also be used as an alternative to derive the optical

crosstalk in the case of single-mode optical waveguide.

Fig.1 Schematic of an application of optical waveguide in

electronic packaging system

978-1-4799-8609-5/15/$31.00 ©2015 IEEE 2003 2015 Electronic Components & Technology Conference

In this paper only the intensity modulation is assumed in

the system optical link. The signal crosstalk in an intensity

modulation system is caused by the crosstalk of the carrier

optical wave and affected by the optical wave phase difference

between the crosstalk aggressor and victim. To estimate the

worst case scenario of the crosstalk effect on the electrical

signal eye diagram, two or more transient simulations are

applied to combine different optical wave phase offsets

between crosstalk aggressor and victim. The transient

simulation runs on the time steps for electrical signal which is

actually the envelope of the modulated optical signal.

2 Modeling and Simulation Method

The modeling method can be illustrated by a simple case

of single-mode optical waveguide. In this case, an

electromagnetic simulation tool can be used to derive the

optical regime (near the laser optical wave frequency with a

required bandwidth) S-parameter model on a short section of

an optical waveguide as shown in Fig.2. The waveguide ports

are defined in the electromagnetic (EM) simulation for the S-

parameters. The port reference impedance of the S-parameter

models in this paper is the simulated port waveguide

characteristic impedance by a 2D electromagnetic simulation

on the port cross section. The 2D EM simulator is usually

implemented in the 3D EM simulation tool. No

renormalization to a user assigned impedance such as 50Ω is

used in the exported S-parameter models from the EM tools.

Theoretically, this reference impedance is frequency-

dependent and should be simulated at each frequency point of

the S-parameter model. However, in some electromagnetic

simulation tools, the port impedance is calculated at a single

frequency point only. For simplicity, in this paper we will not

analyze the error caused by this wideband port impedance

mismatch and just ignore the effect.

Fig.2 Optical waveguide structure with waveguide ports

The optical regime (or carrier regime) S-parameter model

So derived from the commercially available EM simulation

tools can be used directly in the optical frequency band only.

In other words, it supports the transient circuit simulation with

very small marching time step for details of optical carrier

waveforms. It does not support the system signal integrity

transient simulation with the marching time step

corresponding to a fraction of the modulated signal or

envelope waveforms. For applications in ordinary signal

integrity simulation, a transformation from the optical wave

regime S-parameters So to the electrical signal regime (or

envelope regime) S-parameters Se is proposed here as shown

in Equations (1)-(4) which illustrates the transformation of S21

only and can be extended to crosstalk elements like S41, etc.

Equation (1) describes the decomposition of amplitude and

phase for So21 which comes from the EM simulation.

Equations (3)-(4) transform amplitude and phase from So21 to

Se21. Equation (2) composites Se21 from the amplitude and

phase by Equations (3)-(4). The reflection elements in the S-

parameters are not discussed in this paper. It is assumed that

S11=S22=S33=S44=0 even if the calculated corresponding So

elements are non-zero. This is equivalent to an assumption

that all reflected optical waves will go outside and never come

back to the system.

The physical meaning of Equation (4) is to take the group

delay of So as the phase delay of Se which is actually an

equivalent baseband (in frequency-domain) model or envelope

model (in time-domain).

A SPICE circuit model can be derived from the electrical

regime S-parameter model Se by a SPICE model generator

like IdEM Plus [14] as shown in the flowchart in Fig.3

(illustrated for unilateral transmission S21 only, can be

extended to the crosstalk element like S41 directly). In opto-

electronic circuit simulation, the carrier phase is necessary to

be included in an optical element model [13]. In the proposed

approach, the Se SPICE model is accompanied by a carrier

phase DC circuit SPICE model which is derived by the phase

of So21 at the carrier central frequency fo0 through a phase

truncation by a function ATAN2(y,x)=tan-1(y/x) to limit the

phase range to (-π, π]. The optical envelope SPICE model is

for signal integrity transient simulation where vin and vout are

the envelope equivalent voltages, and φin and φout are optical

carrier phase information which is useful in optical signal-

crosstalk superposition. For the applications not involving

optical signal-crosstalk superposition, there is no need to

count the carrier phase in the signal integrity transient

simulation and the carrier phase DC circuit SPICE model

(Nodes φin and φout in Fig.3) can be eliminated from the

envelope SPICE model.

Fig.3 Flowchart on deriving Se SPICE model for unilateral

transmission and carrier optical wave phase

2004

The SPICE model can be used in a signal integrity

transient circuit simulation by any SPICE or SPICE-like

simulator with the time marching at larger time steps in the

envelope regime instead of smaller time steps in the currier

regime.

To illustrate and verify this modeling and simulation

method by a single SPICE-like transient simulator, a simple

example is provided here by using a higher electrical

frequency carrier to emulate the optical wave carrier. The

example is a 2cm long standard loss printed circuit board wire

with W=2.8mil. The carrier frequency is fo0=10GHz, the

intensity modulated signal is with trise=tfall=1ns, tbit=5ns,

plow/pmax=0.1, phigh/pmax=0.9 (Extinction Ratio ER = 9.0 =

9.54dB). The carrier regime S-parameter element So21 is

derived by a per-unit-length RLGC transmission line model

from CZ2D, a 2D EM simulation tool. The currier regime S-

parameter element So21 is shown in Fig.4 and the derived

envelope regime S-parameter element Se21 by Equations (1)-

(4) is shown in Fig.5.

Fig.4 Carrier regime transmission So21

Fig.5 Envelope regime transmission Se21

Two transient simulations are performed, one is on the

complete modulated signal including the details of the carrier

waveforms by using the original carrier regime S-parameter

model, the other is on the envelope only by using the envelop

regime S-parameter model. In the transient simulation shown

in Fig.6, the curves represent the real voltage, not the

intensity. In Fig.7 shows node intensity calculated from the

node voltage. In Fig.7, the intensity of the envelope by the

envelope time marching using the original carrier regime S-

parameter model is also shown for comparison. We can see

clearly the validation of the proposed method while the

original carrier regime S-parameter model cannot be used

directly in the envelope marching transient simulation.

Fig.6 Far-end voltages by the carrier regime and envelope

regime transient simulations.

Fig.7 Far-end intensity by the carrier regime and envelope

regime transient simulations

The above illustration of the modeling and simulation

method is based on So from the EM simulation. Another

approach to derive the transmission and crosstalk data is by

the lab measurement on test samples especially in the case of

multi-mode optical waveguides. Usually only amplitude can

be measured. In this case, there is no phase information

available for applying Equations (1)-(4). To make use of the

amplitude only, a SPICE model as shown in Fig.8 is applied

instead.

Fig.8 SPICE model for optical waveguide transmission or

crosstalk using amplitude data only

2005

The SPICE model in Fig.8 uses SPICE node voltage to

represent the equivalent optical voltage (v-domain) in the

optical part. This is different from the approach in [8] which

uses SPICE node voltage to represent optical power (p-

domain) in the optical part. We can replace |So21|(dB)/20 with

|So21|(dB)/10 in Fig.8 to get a SPICE model compatible with

the approach in [8]. It should be mentioned that the p-domain

SPICE model cannot be used directly for crosstalk

superposition purpose.

In the proposed method, we need to perform superposition

of crosstalk with the victim channel signal. The superposition

can only be performed in the v-domain, not the p-domain. For

convenient application, unilateral SPICE transformer models

between the two domains are proposed here in Fig.9 for

transition in a SPICE simulation deck.

(a) Unilateral transformer from the p-domain to the v-domain

(b) Unilateral transformer from the v-domain to the p-domain

Fig.9 Unilateral transformer models for transition between

the p- and v-domains.

Fig.10 SPICE model of a two-aggressor crosstalk case

using complex data including both envelope waveform and

carrier phase of transmission and crosstalk

In the v-domain, the superposition of the crosstalk to the

victim signal can be realized by a SPICE model using a

Unilateral Directional Junction SPICE model as shown in

Fig.10. The SPICE model covers two crosstalk aggressors

(OWG1 and OWG3) and one crosstalk victim (OWG2). The

building block SPICE models of the transmission and

crosstalk in Fig.10 are derived by the method as described in

Fig.3. Details of a general N-to-1 Unilateral Directional

Junction SPICE model (N=3 for the case of Fig.10) are shown

in Fig.11.

Fig.11 SPICE model of an N-to-1 Unilateral Directional

Junction

3 Modeling and Simulation Examples

The proposed optical waveguide crosstalk SPICE

modeling and simulation method is applied to a few examples

for test and verification purpose on several different

applications including multi-mode polymer waveguide, single-

mode SiO2 waveguide, plasmonic nanostrip waveguide, and

SOI waveguide.

The first example is a polynorbornene-based graded-

index(GI) core polymer optical waveguide array on the

card/board level as reported in [2] with 40µm X 40µm core,

62.5µm core center-to-center pitch, sandwiched between two

25µm think polyimide (PI) films (nPI=1.70) and waveguide

length L=70mm. This is a multi-mode optical waveguide

structure. It is not feasible to use a full-wave electromagnetic

simulation tool to derive the optical regime S-parameters of

the multi-mode optical waveguide because of the large size of

the structure compared with the optical wavelength and the

complex in both modeling and model application related to a

large number of the propagation modes. It should be possible

to use some particular computational method like the Ray-

Tracing Method [16] and the Beam Propagation Method [17]

to derive the crosstalk values for modeling.

In this example, the data from a crosstalk lab measurement

available in [2] is used for the proposed optical waveguide

2006

crosstalk SPICE modeling (Fig.12). The signal integrity

transient simulation results for estimating the crosstalk effects

on system eye diagram as shown in Fig.13.

The system bit time is tbit=100ps and the input signal

rise/fall time is trise=tfall=20ps. The SPICE models for VCSEL,

pin photo detector and trans-impedance amplifier can be

found in [8].

Since the coherence of the multi-mode optical waveforms

in aggressor and victim waveguides is usually very bad

especially in the case of the optical signal source using direct

modulation like individual VCSEL, we need to cover a wide

range of dA=φina-φinv (where φina and φinv are the input phase of

aggressor and victim, respectively, in Fig.11) to capture the

worst-case optical phase scenario. For simplicity, we assume

all aggressors have the same input phase although the model

covers a more general case. The simulated eye diagrams

observed at the output node of the trans-impedance amplifier

which is after pin photo detector are shown in Fig.13 by

different dA values. Further statistical analysis should be

performed to combine the effect of dA for a realistic statistical

eye diagram.

Fig.12 Measured crosstalk amplitudes from [2]

(a) dA=(-90+22.55) and (-90-22.5) Degrees

(b) dA=(-90+45) and (-90-45) Degrees

(c) dA=(-90+90) and (-90-90) Degrees, and the reference case

with no crosstalk.

Fig.13 Eye diagrams at the trans-impedance amplifier

output using different dA values

The second example is a two-coupled SiO2 optical

waveguides as described in [9] with 2.8µm X 2.8µm square

core, waveguide-to-waveguide separations of 7, 10, and

13µm, length of 1000µm, and three different combinations of

the core/cladding compositions for testing and verifying the

accuracy of the full-wave electromagnetic simulation on

single-mode waveguides by CST Microwave Studio (MWS)

[15]. The three combinations of the core/cladding

compositions are PS2.8 (n1=1.4589, n0=1.4440), GS2.8

(n1=1.4655, n0=1.4440), and GF2.8 (n1=1.4655, n0=1.4394),

where n1 and n0 are refractive indexes of core and cladding of

the optical waveguide, respectively.

A short section of optical waveguide with L=20µm is

simulated by CST MWS as shown in Fig.2 and Fig.14. The S-

parameter model is directly exported without any

renormalization. The S-parameter model for L=1000µm is

derived by matrix operation for cascading S-parameter models

with L=20µm and longer sections from intermediate cascading

(L=40 µm, 80 µm, 160 µm, etc.). The crosstalk between two

adjacent SiO2 optical waveguides by CST MWS using

waveguide port after cascading is compared with those by [9]

based on supermode formulation with corner corrections as

shown in Fig.15. The difference between the two methods is in

a reasonable range.

Fig.14 SiO2 optical waveguide structure for verifying

crosstalk EM simulation

2007

Fig.15 Model crosstalk comparison between those by CST

MWS and by reference for three different combinations of the

core/cladding compositions

The third example is on a silver-based-MIM nanostrip

structure applied as an optical waveguide as described in [12].

The structure consists of two silver (Ag) nanostrips with strip

length L=10µm, strip width W=100nm, strip thickness

T=30nm, and strip edge-to-edge spacing S=898nm above a

SiO2 core with thickness Tcore=80nm and ncore=1.444 (or

εrcore=2.085). Below the SiO2 core there is a 30nm thick Ag

layer which is on a 200nm thick SiO2 substrate. In

electromagnetic simulation, plasmonic material model should

be assigned to the metal structures to replace regular lossy

metal model which is no longer valid at the optical wave

frequencies and nanometer structure dimension [18]-[20].

For comparison purpose, the structures are simulated by

CST MWS respectively with two different Ag material models

for the nanostrips, the first one using the regular lossy metal

model with σ=6.3012 X 107 S/m and the second one using the

plasmonic material model “Silver(Johnson) (optical)” which is

available in the CST MWS material library as a special

dielectric model with negative dielectric constant as shown in

Fig.17(d). We can see the difference in simulated carrier

regime transmission, crosstalk, and electric field distribution

by using two different Ag material models in the

electromagnetic simulations. The model from CST MWS

simulation by plasmonic Ag material model has smaller

attenuation, crosstalk and phase velocity than that by regular

Ag lossy metal model. The model property difference caused

by different Ag material models is very large. It is very

important to use correct material model in the electromagnetic

simulation on nano-structure at the optical wave frequencies.

(a)

(b)

(c)

Fig.16 Simulated electrical field of the transmission and

crosstalk of two-coupled silver-based-MIM nanostrips by

regular lossy metal material model for Ag.

(a)

(b)

2008

(c)

(d)

Fig.17 Simulated electrical field of the transmission and

crosstalk of two-coupled silver-based-MIM nanostrips by

plasmonic material model for Ag

The fourth example is a micro-ring using Silicon-on-

Insulator (SOI) optical waveguide structure similar to that

reported in [10] with core width of W=500nm and core

thickness of H=250nm on a SiO2 layer of Hsio2=1µm above a

Si substrate of Hsub=1µm. The race-trace micro-ring radius is

Rring=4.5µm with an initial straight section length Lso=3µm.

The gap between the straight section in the race-trace micro-

ring and the outside straight optical waveguide (with L=18µm)

is S=200nm (Fig.18).

This micro-ring can be used as a wavelength-division

multiplexing (WDM) filter to drop optical signal with

particular wavelength by adjusting straight section length in

the race-trace micro-ring. The micro-ring is a resonance

structure so that the energy stays for a relatively long time

after a group of short pulses are excited in CST MWS time-

domain simulation. In this case, the time domain

electromagnetic simulation is performed for a time of 80ps

with a -80dB energy convergence criteria. As mentioned by

the tool vendor, the time domain engine may not be the best

choice for simulating the resonance structure due to a longer

convergence time.

Fig.19 shows the magnitude the input port to drop port

transmissions of five different circumferences of the race-track

micro-ring with respect to the one with initial straight section

length Lso=3µm. We can see sharp peaks in the frequency-

domain transmission property curve which looks different

from the flat ones in Figs 16(a) and 17(a) of the non-resonance

structures. Fig.20 is the phase of the input port to drop port

transmission with ∆L=-40nm. The envelope regime S-

parameters Se41 is derived by the proposed method as shown in

Fig.21 which can be used in the signal integrity transient

simulation directly. The simulated eye diagrams observed at

the micro-ring drop port and after the photo detector including

parasitic effects are shown in Figs 22 and 23, respectively. A

simplified single-drive Mach-Zehnder Intensity Modulator

SPICE model as shown in Fig.24 is used as the external

modulated optical signal source for signal integrity simulation.

In this example, the signal bit time tbit=100ps, the signal rise

and fall time are trise=tfall=20ps, vinhigh=7.6V, vinlow=5.3V,

Vπ=4.3V, Pcwin=1mW. The photo detector and trans-

impedance SPICE model are the same as described in [8].

Fig.18 Full-wave electromagnetic simulation of an SOI

optical waveguide micro-ring as a WDM filter

Fig.19 Input port to drop port transmissions of five

different race-track micro-ring circumferences with respect to

the one with initial straight section length Lso=3µm.

2009

Fig. 20 Phase of optical regime S41 with ∆L= -40nm

Fig.21 Envelope regime S41

Fig. 22 Simulated eye diagram at the drop port of the

micro-ring.

Fig.23 Simulated eye diagram at the trans-impedance

amplifier output

Fig.24 Simplified single-drive Mach-Zehnder Intensity

Modulator SPICE model

Conclusions

A SPICE modeling method for optical waveguide

crosstalk in intensity modulated optical link has been

proposed based on the data from hardware sample

measurements or electromagnetic simulations. The SPICE

model can be used directly in signal integrity transient

simulation by using general-purpose SPICE or SPICE-like

circuit simulators with marching time steps in the electrical

signal envelope regime.

Signal integrity test cases on optical waveguide SPICE

models combined with the VCSEL optical transmitter or

Mach-Zehnder intensity modulator and optical receiver SPICE

models are shown to test the proposed modeling and transient

simulation method. Test examples show a wide coverage of

the method to traditional SPICE signal integrity simulation

including Polymer multimode optical waveguide on printed

circuit board and some in-package and on-chip single mode

optical waveguide structures such as Silicon, SiO2, and

plasmonic optical waveguides.

2010

Acknowledgments

The author would like to thank Dale Becker and Alan

Benner of IBM Poughkeepsie, NY for helpful discussions.

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