# Mach–Zehnder Modulator Output in Time and Frequency Domain—Calculation and Experimental Confirmation

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## Abstract

**:**

## 1. Introduction

## 2. Experimental Setup

## 3. Mach–Zehnder Intensity Modulator Fundamentals

## 4. Calculation of MZM Output Signal

## 5. Comparison of Experimental and Analytical Results

`curve_fit()`function was used to fit the data, which is a non-linear least squares optimization. Scipy is a Python library for scientific computing. Normalization is archived by dividing the measured transmission by the maximum transmission of the fitted function ${\tau}_{\mathrm{a}}^{\prime}={I}_{\mathrm{a}}/max\left({I}_{\mathrm{fit}}\right)$. At maximum destructive interference, 10% of the normalized transmission is retained, resulting in a resulting modulation depth of 90%.

`curve_fit()`function.

## 6. Discussion and Conclusions

## Supplementary Materials

`mzm.py`to generate Figure 2 and Figure 3; Source code S2: Python script

`mzm_halfwavevoltage.py`to generate Figure 5; Source code S3: Python script

`mzm_validation.py`to generate Figure 6; Data S4: Matlab formatted data

`2022-09-20 SV mzm_voltagesweep.mat`used in

`mzm_halfwavevoltage.py`; Data S5: Matlab formatted data

`2022-09-22 SV mzm_fundamental.mat`used in

`mzm_validation.py`; Data S6: Matlab formatted data

`2022-09-22 SV mzm_firstharmonic.mat`used in

`mzm_validation.py`.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Abbreviations

MZM | Mach–Zehnder intensity Modulator |

AC | Alternating Current |

DC | Direct Current |

PAS | Photoacoustic Spectroscopy |

PS | Phase Shifter |

OPO | Optical Parametric Oscillator |

nMAE | normalized Mean Absolute Error |

LT | Lithium Tantalate |

## Appendix A

## References

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**Figure 1.**Mach–Zehnder intensity Modulator (MZM) including Phase Shifter (PS) for phase modulation, input ${I}_{\mathrm{e}}$, and outputs ${I}_{\mathrm{a}}$ and ${I}_{\mathrm{b}}$.

**Figure 2.**Phase $\varphi $ modulation of the PS. Solid line: within one period ${T}_{\mathrm{m}}$, dashed line: outside the period.

**Figure 3.**Transmission ${\tau}_{\mathrm{a}}$ of the MZM with ${\varphi}_{0}=0.8\pi $ and ${\varphi}_{\mathrm{m}}=1.2\pi $. Solid line: within one period ${T}_{\mathrm{m}}$, dashed line: outside the period.

**Figure 4.**Amplitude spectrum of MZM output signal with ${\varphi}_{0}=0.8\pi $ and ${\varphi}_{\mathrm{m}}=1.2\pi $ and the summands of $\underline{S}\left(f\right)$: DC part A, left shifted sinc function B, and right shifted sinc function C.

**Figure 5.**Normalized transmission ${\tau}_{\mathrm{a}}^{\prime}$ of MZM dependent on applied Voltage V.

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**MDPI and ACS Style**

Vervoort, S.; Saalberg, Y.; Wolff, M.
Mach–Zehnder Modulator Output in Time and Frequency Domain—Calculation and Experimental Confirmation. *Photonics* **2023**, *10*, 337.
https://doi.org/10.3390/photonics10030337

**AMA Style**

Vervoort S, Saalberg Y, Wolff M.
Mach–Zehnder Modulator Output in Time and Frequency Domain—Calculation and Experimental Confirmation. *Photonics*. 2023; 10(3):337.
https://doi.org/10.3390/photonics10030337

**Chicago/Turabian Style**

Vervoort, Sander, Yannick Saalberg, and Marcus Wolff.
2023. "Mach–Zehnder Modulator Output in Time and Frequency Domain—Calculation and Experimental Confirmation" *Photonics* 10, no. 3: 337.
https://doi.org/10.3390/photonics10030337