Mach-Zehnder Modulator

What is a Mach-Zehnder modulator? 

The Mach-Zehnder modulator (MZM) is an interferometric structure made from a material with strong electro-optic effect (such as LiNbO3, GaAs, InP). Applying electric fields to the arms changes optical path lengths resulting in phase modulation. Combining two arms with different phase modulation converts phase modulation into intensity modulation.

The Mach-Zehnder modulator structure is shown in Figure 1.

Mach-Zehnder modulator structure | Synopsys

Figure 1: Mach-Zehnder modulator structure

The optical input Ein is split into the upper and lower modulator arms that are phase modulated with two phase shifters driven by the electrical signals V1 and V2 and then recombined into the optical output Eout. Before we analyze the above implementation in more details, let’s look at a couple of MZM structures that have attracted a lot of attention lately due to advancements in data center interconnect (DCI) technologies and photonic integration.

Travelling-Wave MZM (TW-MZM)

The structure of Figure 1 is often referred to as “concentrated” or “lumped” modulator structure. In the “distributed” or “traveling-wave” structure of an MZM, the radio frequency (RF) electrical structure acts as transmission line rather than a concentrated capacitor, thereby increasing electrical and optical interaction length, and improving the tradeoff between the efficiency and bandwidth of the modulator. For more information, refer to [1].

TW-MZM schematic in OptSim Circuit | Synopsys

TW-MZM schematic in OptSim Circuit

Segmented Electrode MZM (SE-MZM)

In SE-MZM, each arm of the MZM uses multiple phase shifter segments, as shown below.

Schematic of a PAM-4 transmitter using SE-MZM | Synopsys

Schematic of a PAM-4 transmitter using SE-MZM

The longer interaction length in conventional traveling-wave MZMs (TW-MZMs) helps reduce drive voltage. However, longer electrodes result in higher RF losses and mismatch in group velocities between RF and optical signals, which in turn impact modulation bandwidth. The segmented approach offers the advantage of longer interaction lengths without increased loss by shifting the velocity matching to electronic timing circuits to control timing of applied electrical signals to match the optical delay between segments. Such structures can also accomplish multi-level modulation without using electrical digital-to-analog converters (DAC) by using inherent DAC capabilities of segmented phase-shifters. For more information, please refer to [2].

Mach-Zehnder Modulator with symmetric coupler and opposite driving voltages

Coming back to the MZM structure of Fig. 1, and assuming that the input optical field is equally split between the upper and lower arms, and that the voltages driving the phase shifters are opposite V2=−V1, we can obtain the following simplified model equation:
Output electric field for a symmetric coupler design | Synopsys

Mach-Zehnder Modulator with asymmetric coupler and opposite driving voltages

Assuming that the input optical field is not equally split between the upper and lower arms and keeping the assumption that the voltages driving the phase shifters are opposite V2=−V1 we can obtain the following model equation:
Output electric field for push-pull design | Synopsys

The splitting imbalance represented by the k factor results in the appearance of the extinction ratio. The Mach-Zehnder modulator is never completely off and we can in fact define the extinction ratio coefficient directly from the k factor as:

Extinction ratio | Synopsys

Moreover, the imaginary j factor in front of the sine component represents a spurious phase shift that appears when the extinction ratio is not ideally infinite.

Mach-Zehnder Modulator with asymmetric coupler and arbitrary driving voltages

We can now extend the last case considering arbitrary voltages V1 and V2:
Output electric field for an asymmetric MZM with arbitrary drives | Synopsys
We can define VD and VS corresponding to the difference and average of V1 and V2:
Voltage drive and average source signal | Synopsys
We can then express V1 and V2 in terms of VD and VS:
Input1 and Input2 | Synopsys

And rewrite the equation above:

MZM output field | Synopsys

There are now phase shift terms that depend on the average of the two electrical inputs, while the intensity modulation is controlled by the difference of the two electrical inputs.

Chirp factor

In the reference article [1], the chirp factor is defined as the ratio between the modulator output frequency modulation and amplitude modulation:

Chirp | Synopsys

In an ideal Mach-Zehnder modulator with perfect power split between arms and driven with opposite voltages, the chirp factor can be assumed equal to zero [3].

There might be other sources of chirp-like asymmetry of construction between the upper and lower arms [4].

The chirp factor as defined above is used in the industry to characterize spurious frequency modulation at the output of the modulator and can be measured directly, see for instance [5].

Why is accurate modeling of MZM critical?

A modulator is one of the most expensive components in a high-speed transmitter. The bandwidth, footprint (i.e., packaging density) and energy consumption of a modulator – all of which are very critical in today’s mega datacenter deployments - depend on a number of design trade-offs. If the modulator design is sub-optimal, the rest of the system cost and complexity can dramatically increase, with only marginal gains in performance.

Where and when does one choose MZM behavior modeling vs. MZM device design?

If you’re a datacenter or its transceiver supply chain, you want MZM behavior modeled in a system for the purpose of technology selection and for showing your clients that your products meet or exceed customer’s system performance specifications. OptSim and OptSim Circuit fit the bill.

If you are a supply chain to the transceiver designers, you want an optimal device-level design of the MZM to meet with the packaging, bandwidth and energy consumption specifications from your customers.

To design an MZM device, use Synopsys’ Sentaurus TCAD and BeamPROP BPM from RSoft Photonic Device Tools. This example demonstrates the simulation of a 3D Mach-Zehnder Modulator implemented on silicon-on-insulator.

How do you simulate behavior of an MZM?

To simulate behavior of an MZM, you need advanced tools to enhance and accelerate user-modeling capabilities and provide real field design scenarios using extensive industry specifications. Simulation tools from the Synopsys Photonic Solutions portfolio and the Sentaurus TCAD product can be used for accurate modeling.

  • Use OptSim Circuit, a schematic-driven simulation tool, to select the required components from the components’ library and place them into the schematic design area:
    • To simulate a TW-MZM, incoming light from the light-source is split into the interferometric structure’s two arms and moves through the travelling-wave phase-shifters in each of the arms. The optical output from both phase-shifters is then coherently mixed by the combiner model.
    • To test the performance of the TW-MZM as created above, the travelling-wave electrodes are driven by high-speed electrical signals in push-pull manner. A photodetector at the modulator output converts the modulated optical signal into an electrical signal. The post-detection electrical low-pass filter (LPF) model limits the detection noise.  
    • To observe outputs (such as modulated signal and eye diagram), optical and electrical scopes are connected at desired locations as shown in the figure below. 
  • OptSim Circuit is a schematic-driven simulation tool where a user places required components from the components’ library into a schematic design area. The TW-MZM is an interferometric structure that has incoming light from the light-source split into two arms and travelling-wave phase-shifters in each of the arms. The optical output from both phase-shifters is then coherently mixed by the combiner model.
  • In order to test the performance of the TW-MZM created as above, the travelling-wave electrodes are driven by high-speed electrical signals in push-pull manner. A photodetector at the modulator output converts the modulated optical signal into an electrical signal. The post-detection electrical low-pass filter (LPF) model limits the detection noise.  
  • Optical and electrical scopes are connected to observe outputs (such as, modulated signal and eye diagram) at desired locations as shown in the figure below.
MZM Layout in OptSim Circuit | Synopsys

MZM Layout in OptSim Circuit

  • Use BeamPROP BPM and Sentaurus TCAD to simulate a 3D MZM implemented on silicon-on-insulator
  • Use the OptSim software tool for the design and simulation of optical communication systems at the signal propagation level

Application Notes for Further Study

 

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The splitting imbalance represented by the k factor results in the appearance of the extinction ratio. The Mach-Zehnder modulator is never completely off and we can in fact define the extinction ratio coefficient directly from the k factor as:

References

[1] https://www.synopsys.com/photonic-solutions/product-applications/foundry-process-tw-mzm.html

[2] https://www.synopsys.com/photonic-solutions/whatsnew.html#pic

[3] F.Koyama and K. Iga, Frequency chirping in external modulators, J. Lightwave Technol., vol.6, no.1, pp.87-33, Feb.1988.

[4] Tetsuya Kawanishi et al., Direct measurement of chirp parameters of high-speed Mach-Zehnder-type optical modulators, Optics Communications, vol.195, Issues 5-6, 15 August 2001, Pages 399-404.

[5] F. Devaux, Y. Sorei, J.F. Kerdiles, Simple measurement of fiber dispersion and of chirp parameter of intensity modulated light emitter, J. Lightwave Technol. 11 (1993) 1937-1940.