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In this paper, we seek to compare the two design theories for fiber optical parametric amplifier through simulation. The two-sideband method (standard method) has been the most widely used method in fiber optical parametric amplifier design, but it does not predict the gain shrinkage around the pumps. This technique does not consider the gain shrinking dynamics around the pump(s). The four-sideband analytical technique is an alternative technique for fiber optical parametric amplifier design, and it allows for a simplified investigation of the gain shrinking dynamics around the pump(s) due to the interaction of the various arising high-order idlers within the vicinity of the pump waves. The undertaking in this paper is to present a dual-pump fiber amplifier based on the highly nonlinear fiber and another one based on the photonic crystal fiber and ascertain if gain shrinking affects both FOPAs.

The adoption of the fiber optical parametric amplifier (FOPA) in telecommunications will go a long way in enabling broadband and quality internet. The research in this area has undergone phenomenal progression in the last few years as researchers seek an alternative amplifier to compete with the traditional optical amplifiers which are limited in their bandwidth and have unstable gain dynamics due to their material composition [

In recent times, FOPAs based on FWM and six-wave mixing with bandwidth up to 600 nm and 150 nm, respectively, have been shown [

In this paper, we set out to develop an analytical model that emphasizes on linear wave-vector mismatches to explain how the sideband and its closest pump interact. Dispersion parameters have a greater role in how the interaction between idlers and pump occurs, and thus modelling around them leads to a more accurate analytical technique. Subsequently, two dual-pump FOPAs based on highly nonlinear fibers (HNLFs) and photonic crystal fibers (PCFs) are designed using the two-sideband theory and the four-sideband theory. The photonic crystal fiber and data used for FOPA design in this paper are similar to the data used by Taghizadeh et al. in [

The gain of a two-pump FOPA is obtained by solving the nonlinear Schrodinger equation with two high pump powers at frequencies,

Dual-pump fiber FOPA process based on the six-wave model.

When two pump wavelengths are placed symmetrically about the zero dispersion wavelength

If the signal is placed close to any of the pumps, secondary waves are generated. Some of these secondary waves may become phase matched and may attain levels similar to levels of the signal and idler. In such situations, to get a complete description of the dynamics, these new higher-order waves are considered as they have a bearing on the gain characteristics of the FOPA. This situation happens when a two-pump FOPA’s signal frequency is placed close to one of the pumps. This gives rise to two other new waves, which are placed at

Firstly, when a signal frequency is located between these symmetrically placed pumps, this results in a phase-matched PC process and an idler of frequency

Dual-pump fiber FOPA process based on the four-wave model.

The gain of the PC (two-sideband) as shown in (

Solving equations (

Considering (

Equation (

The conditions under which these frequencies interact in FWM is depicted as

Secondly, the waves interact differently for a six-wave arrangement (four-sideband) as shown in Figure

Pump 1, pump 2, idler, and signal are represented by

The arrangement of the system under simulation is such that the signal frequency is close to one of the pumps. The BS and MI also become phase matched, and the conversion efficiencies of the idlers

In this research, we set out to investigate the merits, demerits, and impact of two theories by designing FOPA based on each theory. The main aim was to investigate the behavior of the gain around each pump when a signal wave is placed within 10 nm of the pump(s) wave. The two-sideband theory has been extensively researched and has led to many breakthroughs in the area of FOPA. To achieve the aim, two prominent materials used in the design of FOPA were selected for simulation and design of FOPA, i.e., the traditional HNLF with a relatively low nonlinear coefficient and the new material PCF with a very high nonlinear coefficient. For the HNLF, two amplifiers were simulated, one based on the two-sideband theory and the other on the four-sideband theory, and the resulting gain spectrums were analyzed; similarly, the same simulation setup was done for the PCF. In all designs, the signal frequency was placed near one of the pumps, i.e., within 10 nm, and this allows for the investigation of the effects of BS and MI on pump performance. The pump separation was below 100 nm for all the simulations.

Equations (

The first design was based on the standard two-sideband theory. To achieve the design, the following parameters were used: _{2} = 1.3 W,

Equation (

Simulation of a dual-pump HNLF-based FOPA gain using the two-sideband theory.

The same parameters as above were used in simulating a four-sideband design: length = 243 m, _{2} = 1.3 W, and

Simulation of a dual-pump HNLF-based FOPA gain using the four-sideband theory.

Extending the four- and two-sideband theory models to FOPA designs based on PCFs, Figures

Simulation of a dual-pump PCF-based FOPA gain using the two-sideband theory.

Simulation of a dual-pump PCF-based FOPA gain using the four-sideband theory.

In [

A gain of 50.59 dB and 55 nm gain bandwidth were realized in the two-sideband model in Figure

While using the four-sideband theory, a gain and gain bandwidth of 50.59 dB and 55 nm were realized, respectively, for a dual-pump FOPA based on the PCF.

We also considered the effect of the third-order dispersion parameter on the flat gain area of the bandwidth. Considering the amplifier of Figure

Simulation graph of a HNLF-based FOPA with higher third-order dispersion coefficient.

Simulation graph of a HNLF-based FOPA with lower third-order dispersion coefficient.

The value of the third-order dispersion parameter for a fiber plays a crucial role in determining the flatness of the gain profile. Hence, it should be considered when designing FOPAs.

A validation of the two-sideband theory and the four-sideband models has been done through the design of a dual-pump HNLF-based FOPA and a dual-pump PCF-based FOPA. A gain of 36 dB and gain bandwidth of 32 nm were obtained for the HNLF-based two-pump FOPA, while a gain of 50.59 dB and gain bandwidth of 55 nm were achieved for the PCF-based two-pump FOPA. It is observed that the four-sideband theory helps in predicting the gain shrinkage around the pumps for the amplifier allowing for a complete design picture, while the two-sideband theory does not predict the gain shrinkage. The gain shrinkage predicted in four-sideband theory is attributed to two extra FWM sidebands which are due to Bragg scattering and modulation instability and occurs just outside the flat gain area on the edges of the pumps. The analytical model put emphasis on the linear wave-vector mismatches to explain how the sideband and its closest pump interact. Dispersion parameters have a greater role in how the interaction between idlers and pump occurs, and thus modelling around them leads to a more accurate analytical technique. The model clearly gives a detailed insight into the interactions of the pump and idler closest to it through the linear wave mismatches allowing a designer to manipulate the dispersion parameters for a better design. In this model, we were able to predict the gain dips around the pumps when a signal is placed close to either of the pumps (i.e., 10 nm). In [

Theoretical models of the two-sideband and four-sideband models have been developed and validated by designing a dual-pump HNLF-based FOPA and a dual-pump PCF-based FOPA. A gain of 36 dB and gain bandwidth of 32 nm were obtained for the HNLF-based two-pump FOPA, while a gain of 50.59 dB and gain bandwidth of 55 nm were achieved for the PCF-based two-pump FOPA. It is observed that the four-sideband theory helps in predicting the gain shrinkage around the pumps for the amplifier allowing for a complete design picture, while the two-sideband theory does not predict the gain shrinkage. A study of the third-order dispersion has shown that it has an adverse effect on the gain flatness.

The data used to support the findings of this study are available from the corresponding author upon request.

The authors declare that they have no conflicts of interest.

This research was funded by Pan African University.