Hybrid Spectrum Inversion and Dispersion Compensation for Mitigating Fiber Losses in Optical Systems ^†

Abstract

Optical fiber systems are integral to various applications ranging from telecommunications to medical technologies. These systems, however, face significant challenges due to power losses and nonlinear phase changes that occur as signals propagate through the fiber core. To address these issues, this study introduces a hybrid optical method combining spectrum inversion and fiber dispersion compensation. The primary objective is to enhance system performance by mitigating both linear and nonlinear fiber losses. A comparative evaluation reveals that employing optical phase conjugation in the system leads to a substantial improvement in performance metrics. Specifically, the Q-Factor, a measure of signal quality, increases to 20 at an input laser power of 5 mw when using the proposed method, compared to a Q-Factor of 5 achieved with traditional methods. The findings highlight the effectiveness of the proposed technique in compensating for fiber losses and suggest its potential utility in improving the performance of optical fiber systems across various applications.

1. Introduction

Optical fiber technology has revolutionized the fields of telecommunications and medical applications by enabling high-speed, long-distance data transmission [1]. Despite its advantages, one significant challenge remains: signal losses during transmission through the optical fiber core. These losses are often attributed to both linear and nonlinear effects, such as dispersion, self-phase changes, and cross-phase changes, which limit the overall system performance [1]. The present study aims to address these challenges by introducing and evaluating two fiber loss mitigation techniques. The first technique is based on classical dispersion compensation methods, while the second employs optical phase conjugation to invert the signal spectrum [2]. The overarching objective is to improve system performance by mitigating nonlinear phase changes in the transmitted signal. To achieve these aims, the study utilizes mathematical modeling and simulations [3,4]. Various parameters, including the Q-Factor, are assessed to evaluate the effectiveness of the proposed methods [4]. The paper is organized as follows: Section 2 describes the methods employed, Section 3 presents the results, and Section 4 discusses the implications of these findings. The paper concludes with an overall summary and recommendations for future work.

2. Methods

2.1. Power Effect on Refractive Index

The relationship between the material’s refractive index and the optical power in the transmitted signal is a crucial aspect of optical systems. This relationship is expressed as given by Equation (1) [3]:

$$n_{\mathrm{ref}}=n_0+\frac{n_2·P}{A_{\mathrm{eff}}}$$

(1)

In the Equation (1), $n_{\mathrm{ref}}$ represents the effective refractive index, $n_0$ is the base refractive index, $n_2$ is the nonlinear refractive index, P is the optical power of the propagated signal, and $A_{\mathrm{eff}}$ is the effective area of the optical fiber. With the advent of optical amplifiers and extended transmission distances, the influence of the refractive index has become increasingly subtle, albeit still significant. The nonlinear effects in fiber optics, such as four-wave mixing and changes in the phase of individual transmitted signals, are functions of this power-dependent refractive index [4,5,6,7,8].

2.2. Methods of Compensation

Mitigating fiber transmission losses remains a critical challenge in optical fiber systems. The losses often manifest as both linear and nonlinear effects, including dispersion and phase changes, which collectively degrade system performance. This study introduces two primary strategies for fiber loss mitigation: classical dispersion compensation techniques and optical phase conjugation methods [2].

2.2.1. Classical Dispersion Compensation

The first strategy employs dispersion compensation fiber (DCF) to counteract linear fiber losses. DCF is effective in mitigating the pulse broadening caused by group velocity dispersion, material dispersion, and polarization dispersion, ultimately enhancing the system’s data bitrate by minimizing inter-symbol interferences (ISI).

2.2.2. Optical Phase Conjugation

The second strategy leverages optical phase conjugation to perform spectrum inversion on the transmitted signal. This approach aims to mitigate nonlinear phase changes, such as cross-phase modulation and self-phase modulation. By inverting the signal spectrum, the method compensates for both linear and nonlinear effects, thus improving the overall system performance. Both strategies are subject to evaluation based on various parameters, including the Q-Factor, to determine their effectiveness in improving system performance [9,10].

2.3. Mathematical Models

Various mathematical equations are employed in this study to quantify and analyze the performance metrics and phenomena in optical fiber systems. These equations enable a thorough evaluation of factors such as the Q-Factor and phase changes under different compensation methods.

• Nonlinear phase shift: The nonlinear phase shift experienced when passing through a glass fiber is represented by the following equation [11]:

  $${\varphi }_{\mathrm{NL}}=\gamma ·P·L$$

  (2)
• Nonlinear factor: The nonlinear factor $\gamma$ is described by the equation [12]:

  $$\gamma =\frac{2\pi n_2}{A_{\mathrm{eff}}\lambda }$$

  (3)
• Nonlinear phase shift in self-phase modulation: The nonlinear phase shift caused by self-phase modulation (SPM) is given by [13,14]:

  $${\varphi }_{\mathrm{NL}}^{\mathrm{SPM}}\left(L\right)=\frac{2\pi }{\lambda }{n}_2{\left|E\right|}^2{L}_{\mathrm{eff}}=\gamma P{L}_{\mathrm{eff}}$$

  (4)
• Multi-signal phase change: Cross-phase shifting occurs when the power of one laser influences the phase change of another laser signal. Specifically, in a nonlinear medium like a Kerr medium, the change in a light beam’s optical phase is caused by its interaction with another light beam. This phenomenon is known as cross-phase modification.
  The extent of these changes is influenced by the manipulation of other channels in a wavelength division multiplexing system and can be attributed to variations in the material’s refraction coefficient [15].

  $$\Delta n\left({\lambda }_2\right)=2n_{2}P\left({\lambda }_1\right)$$

  (5)
  In this context, variations in optical power in one channel of a wavelength division multiplexing system result in phase changes in other co-propagating channels. The equation for Cross XPM is given as [16,17]:

  $$\frac{\partial E_1}{\partial z}=j\gamma \left[P_1(z,t)+2\sum _{i=2}^M{P}_i(z,t)\right]E_1$$

  (6)

These equations constitute the analytical framework of the study, facilitating the precise modeling and evaluation of the optical fiber system under different conditions.

3. Results and Discussion

3.1. Compensation Using DCF

The application of dispersion compensation fiber (DCF) as a linear fiber loss compensator was the first method of compensation explored. Figure 1 illustrates the DCF’s configuration at a data rate of 30 Gb/s. Using DCF effectively mitigates the pulse broadening caused by various forms of dispersion, such as group velocity dispersion (GVD), material dispersion, and polarization dispersion. These dispersive effects can severely limit the bitrate of data transmission due to inter-symbol interferences (ISI). The application of DCF serves to counteract these limitations.

3.2. Compensation Using MID-OSI

The second approach for fiber loss mitigation involved the use of optical phase conjugation, specifically a technique called MID-OSI. The optical fiber telecommunication system under study consisted of three main components: the transmitter, receiver, and fiber channel. Simulations were carried out using OptiSystem 15 software and MATLAB Release 2019a at a high bit rate of 30 Gb/s. Figure 2 demonstrates the effect of positioning the OPC compensator at mid-distance within the optical fiber channel. Orthogonally pumped four-wave mixing was employed to achieve polarization-independent conjugation of the signal band. Two pump laser sources with wavelengths at 1541.45 nm and 1535.04 nm were utilized to reduce amplified out-of-band spontaneous emission. The results indicate that the performance of systems employing MID-OSI was markedly superior compared to systems using only DCF for compensation. Specifically, for an input laser power of 5 mw, the Q-Factor for systems using MID-OSI reached 20, while it was only 4.8 for systems using DCF, as illustrated in Figure 3.

3.3. Performance Evaluation

A critical aspect of this study involved evaluating the performance of the optical fiber system under different compensation techniques. The primary metric for this evaluation was the Q-Factor, which serves as an indicator of the system’s signal quality. In systems employing dispersion compensation fiber (DCF), the Q-Factor was observed to reach a value of 4.8 at an input laser power of 5 mw. On the other hand, systems using the MID-OSI technique for optical phase conjugation demonstrated a significantly higher Q-Factor of 20 under the same input power conditions. The disparity in Q-Factor values between the two methods underscores the superior efficacy of the MID-OSI technique in mitigating both linear and nonlinear fiber losses. This result is particularly notable given that both methods were evaluated under identical conditions, thereby highlighting the advantages of incorporating optical phase conjugation in optical fiber systems.

4. Conclusions

This study introduced two techniques for mitigating fiber losses in optical fiber systems: classical dispersion compensation and optical phase conjugation. The primary objective was to compensate for linear losses, such as dispersion, as well as nonlinear losses like cross-phase and self-phase modulation, with the ultimate goal of enhancing overall system performance. The evaluation was based on the configuration in which the optical phase conjugator (OPC) was positioned at the mid-span of the fiber system. The results demonstrated a marked improvement in system performance when employing optical phase conjugation, as evidenced by a Q-Factor of 20 at an input laser power of 5 mw.

In contrast, the system using classical dispersion compensation fiber (DCF) reached a Q-Factor of only 4.8 under the same conditions. These findings highlight the superior effectiveness of optical phase conjugation techniques in compensating for both linear and nonlinear fiber losses. Future research may focus on optimizing the placement of the OPC and exploring other advanced compensation techniques to further improve system performance.