Mach-Zehnder Modulators (MZMs)

The de facto standard for most optical modulation applications because of its flexibility, simplicity and unique performance.

Interferometer history

Interferometric structures have a long history of unmatched performance as they can be built and calibrated to impressive levels of precision. Therefore, it’s not a surprise that electro-optic modulators based on an interferometer, provide desirable characteristics in a seemingly simple to understand and customize architecture.

While the interferometer was first applied to measure optical spectra, the modulator serves to bring and transmit information by the means of light. The modulator was devised starting from the interferometer that was perfectioned by two physicists at the end of the 18th century, the Austrian Ludwig Mach and the Swiss Ludwig Zehnder [1].

The Mach-Zehnder modulator (MZM) uses interference between two coherent light paths, whose relative phase is controlled electrically, to modulate optical intensity. This enables high extinction ratios, allowing efficient encoding of digital signals by switching between constructive (“ON”) and destructive (“OFF”) interference.

Abstract representation of an MZM (Mach-Zehnder Modulator) with the splitter (MMI), two arms and two phase shifters and a combiner (MMI) for constructive and destructive interference of light.

Mach-Zehnder Physics

The block diagram in Figure 1 is used to explain the working principle. The incoming continuous wave (CW) light is split by a 3-dB multimode interference coupler (MMI) into two arms. With the two control signals $V_1(t)$ and $V_2(t)$ the arms are independently phase shifted by $\varphi_1(t)$ and $\varphi_2(t)$ , respectively. An additional phase shift $V_{\text{DC}}$ in one arm adjusts the operation point. This shift (or delay) can be introduced before or after the main phase shifters, but for high-frequency operation it’s preferred to do that before. The signals of both arms are then combined by means of the reverted MMI coupler to form the output $E$ _out(t).

The transfer function can then be derived as

$\begin{equation*} T_{\text{MZM}} = \frac{E_{\text{out}}(t)} {E_{\text{in}}(t)} = \begin{bmatrix} \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} \end{bmatrix} \begin{bmatrix} e^{i \math{\varphi}_1(t)} \cdot e^{i \varphi_{\text{DC}}(t) & 0 \\ 0 & e^{i \math{\varphi}_2(t) \end{bmatrix} \begin{bmatrix} 1/{\sqrt{2}} \\ 1/{\sqrt{2}} \end{bmatrix} \end{equation*}$

$\begin{equation*} = \frac{e^{i \math{\varphi}_1(t)} \cdot e^{i \varphi_{\text{DC}}(t)} + e^{\math{\varphi}_2(t)}}{2} \end{equation*}$

$\begin{equation*} = e^{j \frac{\math{\varphi}_1(t) + \math{\varphi}_2(t) + \varphi_{\text{DC}}(t)}{2}} \cos( \frac{\math{\varphi}_1(t) + \math{\varphi}_2(t) + \varphi_{\text{DC}}(t)}{2}) .\end{equation*}$

The interference between the two arms is then constructive or destructive depending on the control signals. This equation shows that there can be phase modulation with the exponential term and amplitude modulation with the cosine term. For the case of $\varphi_{1}(t) = \varphi_{2}(t)$ only phase modulation takes place, which is the so-called push-push operation mode. In case of $\varphi_{1}(t) = -\varphi_{2}(t)$ , one receives a pure amplitude modulation, called the push-pull mode. For this latter mode, ignoring the bias voltage $V_{\text{DC}}$ , the transfer function is determined as

$\begin{equation*} T_{\text{MZM, push-pull}} = \cos( \frac{2\math{\varphi}_1(t) }{2}) = \cos( \frac{\Delta\math{\varphi}(t) }{2}) .\end{equation*}$

The relative phase shift between the two arms of the MZM is described by $\Delta\varphi(t)$ and is related to the drive voltage

$\begin{equation*} \Delta\varphi(t) = \frac{V(t)}{V_{\pi \text{, MZM}}} \pi .\end{equation*}$

The parameter $V_{\pi \text{, MZM}}$ represents the voltage required to induce a phase shift of $\pi$ in the modulator, and is included to normalize the drive voltage relative to the modulator’s physical response. The corresponding intensity transfer function is then

$\begin{equation*} \left| T_{\text{MZM, push-pull}} \right| = \frac{1}{2} \bigl( 1 + \cos ( \Delta\varphi(t)) \bigr) = \frac{1}{2} \bigl( 1 + \cos ( \frac{V(t)}{V_{\pi \text{, MZM}}} \pi ) \bigr) .\end{equation*}$

It can now be seen that by changing the drive voltage $V(t)$ from 0 to $V_{\pi \text{, MZM}}$ the intensity transfer function changes from 1 to 0, which can be seen as going from an ON state to an OFF state.

The DC voltage, which was ignored for the calculation of the intensity transfer function, is used to adjust the operation point. For most amplitude applications it is of importance to find the optimal linear operation point to avoid non-linear distortion in the constellation shape. This is the so-called Null point. Intensity modulation happens at the Quadrature point. For intensity modulation (IM), as opposed to phase modulation, direct detection (DD) at the receiver side is possible, while the versatility of an interferometric device is still available.

Figure 1: MZM block diagram

Figure 2: MZM transmission diagram

MZM Applications

— Optical communication: MZMs are used to encode information in optical signals. This is used in telecommunications systems, such as fiber optic networks.

— Lasers: MZMs are used to control the frequency and output power of lasers. This is used in a variety of applications, such as spectroscopy and optical machining.

— Optical imaging: MZMs are used to create optical illusions and to control the focus of light beams. This is used in holography and other optical imaging techniques.

— Optical sensing: MZMs can be used to measure the intensity, polarization, or wavelength of light. This is used in a variety of sensors, such as optical gyroscopes and spectrometers.

References

[1] Wikipedia

[2] Destraz, M. (2021). Ensuring Efficiency and Stability of EO Plasmonic-Organic Modulators [Master’s Thesis, ETH Zurich]