# Optical-Frequency-Comb Generation Based on Single-Tone Modulation and Four-Wave Mixing Effect in One Single Semiconductor Optical Amplifier

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Operation Principle

_{c}is input into an SOA, whose injection current is a sinusoidal RF signal I(t) with angular frequency ω

_{m}. The polarization direction of the input optical carrier is controlled by a polarization controller to excite the TE mode in the SOA. The injected RF current causes a change in the carrier density of the SOA, which, in turn, changes the gain of the SOA. Therefore, the input CW light is directly modulated by the injected RF current to generate several new frequency components that have the same polarization direction as the input at frequency ω

_{c}+ nω

_{m}, where n = ±1, ±2, ±3, … [18]. Meanwhile, the FWM effect will occur among these equally spaced lightwaves, resulting in additional new frequency components with the same adjacent-frequency interval ω

_{m}[15]. Therefore, the combination of single-tone modulation and FWM generates a large number of new frequency components. The optical spectrum produced by single-tone modulation has a Gaussian distribution and the FWM effect can make the power difference between frequency components smaller. Thus, an OFC with frequency interval ω

_{m}can be achieved using this scheme.

## 3. Broad-Band Dynamic Model

- A.
- The traveling-wave equations.

_{j}in the subsection $i$ can be expressed as [15,19]

_{j,i}is the normalized slowly varying envelope of the light field, Г is the mode confinement factor, g

_{j,i}(N) is the material-gain coefficient of the SOA, P

_{i}= Σ

_{j}|A

_{j,i}|

^{2}is the total optical power inside i subsection, α is the linewidth enhancement factor, α

_{int}is the loss of the SOA, Ρ

_{sat}is saturation power, and coefficients η

_{jj’}(j ≠ j′, j = 1, 2, … n) represent the non-linear interactions among the mixing waves [15].

_{j}and the others; and the third term represents the FWM effects among lightwaves satisfying the condition of ω

_{j}+ ω

_{l}= ω

_{k}+ ω

_{m}.

_{j,i}(N) can be expressed as [20]

_{0}is the vacuum permittivity, m

_{0}is the free-electron mass, m

_{c}is the effective mass of an electron in the conduction band, m

_{hh}is the effective mass of a heavy hole in the valence band, c is the speed of light in vacuum, n

_{g}is the refractive index, |M|

^{2}is the momentum matrix element, E

_{g}is the bandgap energy, and ƒ

_{c}and ƒ

_{v}are the Fermi–Dirac distributions for the conduction and valence bands, respectively. They can be expressed as

- B.
- The traveling-wave equations for the ASE spectrum.

_{x}

_{−1}and λ

_{x}can be expressed as [21]

_{x,i}(z, t) is the power spectrum density at wavelength λ

_{x}in subsection I and g

_{x,i}′ is the stimulated emission rate per unit length, and it is given by

- C.
- The carrier-density-rate equation.

_{0}exp(iω

_{m}t) is the modulation current with angular frequency ω

_{m}; I

_{0}is the magnitude of the modulation current; w, d, and L are the width, thickness, and length of the active region, respectively; c

_{1}is the non-radiative recombination coefficient; c

_{2}is the bimolecular recombination coefficient; and c

_{3}is the Auger recombination coefficient. G

_{j,i}=exp(g

_{j, i}L/q) is the gain in subsection i.

## 4. Simulation Results and Discussion

_{c}+ nω

_{m}.

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 1.**The schematic diagram of the OFC based on single-tone modulation and FWM effect in an SOA.

**Figure 2.**The optical spectrum of OFC output from the SOA (

**a**) when the FWM effect is ignored and (

**b**) when the FWM effect is considered.

**Figure 3.**The optical spectra of OFC with different amplitudes of the RF-modulated current: (

**a**) 160 mA, (

**b**) 170 mA, (

**c**) 180 mA, (

**d**) 190 mA, (

**e**) 200 mA, and (

**f**) 210 mA.

**Figure 4.**The optical spectra of OFC with a different frequency of injected RF current: (

**a**) 10 GHz, (

**b**) 15 GHz, (

**c**) 20 GHz, and (

**d**) 25 GHz.

**Figure 5.**The optical spectra of OFC for different input optical powers: (

**a**) 15 dBm, (

**b**) 20 dBm, (

**c**) 25 dBm, and (

**d**) 30 dBm.

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**MDPI and ACS Style**

Tan, Z.; Huang, L.
Optical-Frequency-Comb Generation Based on Single-Tone Modulation and Four-Wave Mixing Effect in One Single Semiconductor Optical Amplifier. *Photonics* **2022**, *9*, 746.
https://doi.org/10.3390/photonics9100746

**AMA Style**

Tan Z, Huang L.
Optical-Frequency-Comb Generation Based on Single-Tone Modulation and Four-Wave Mixing Effect in One Single Semiconductor Optical Amplifier. *Photonics*. 2022; 9(10):746.
https://doi.org/10.3390/photonics9100746

**Chicago/Turabian Style**

Tan, Zeyu, and Lirong Huang.
2022. "Optical-Frequency-Comb Generation Based on Single-Tone Modulation and Four-Wave Mixing Effect in One Single Semiconductor Optical Amplifier" *Photonics* 9, no. 10: 746.
https://doi.org/10.3390/photonics9100746