1-

Introduction

Fiber optic technology has been advancing at a surprising pace during the last three decades. It was about fifteen years ago that researchers showed the great potential of optical fiber doped with the rare-earth elements such as erbium and praseodymium, for application in long haul communications. Optical amplifiers have been successfully incorporated in the field of fiber communication, accelerating the rate at which optical links are being deployed over the continents and the transoceanics. Today, this technology is fast becoming a major part of optical communications infrastructure in many countries around the world [1, 2]. Therefore, in order to learn this technology at university level, we need to understand the procedure of optical amplification in fiber amplifiers from basic to advance. From this point of view, the education and training programs will make easy to understand the procedure of optical amplification in fiber amplifiers.

2-

Schematic Representations of Amplification

This work will enable us to understand the basic physical concepts underlying three and four level fiber amplifiers and obtaining the signal gain of amplifiers by using rate equation models. Figure 1 shows the schematic representations of the energy levels and amplifications mechanism for Er3+ (left hand side of picture) and Pr3+ (right hand side of picture) ions doped in glass hosts.

Figure 1:

Energy levels and amplification mechanism for Er3+ (left hand side of picture) and Pr3+ (right hand side of picture)-ions in glass hosts.

The energies and populations of three and four level amplifiers can be described by ^{E₀, E₁, E₂ (= E₂₁ + E₂₂), E₃} and ^{N₀, N₁, N₂ ( = N₂₁ + N₂₂), N₃}, respectively, for the thermal equilibrium. By definition, levels 0 and 1 are the lowest or ground state, level 2 is the metastable state, and level 3 is the pump level. The stimulated transition probability ^R_p is the probability of exciting the ion from level 1 to level 3 for erbium, and from level 0 to level 3 for praseodymium by pumping, and ^R_s will be referred to the stimulated transition probability between ^E₂ and ^E₁.

Let us now consider the steady-state situation, where the populations are time invariant, i.e.,

doped fiber,

doped fiber.

Here, β quantity is involved in the issue because of the E₂ and E₃ levels of Er³⁺ and the E₂₂ and E₂₁ levels of Pr³⁺-doped fibers are very closely spaced according to the Boltzmann’s population relation ^{(ΔE_m = E_m – E_m–1, k_B = 1,38x10−23J/K)}. We consider an absorbing medium for the description of the signal gain. The signal gain is given by G = exp[Γ_s (σ₂₁N₂ – σ₂₁N₁)L] for Er3+-doped fiber [3] and by G = exp[Γ_sσ_2sN₂₂L] for Pr3+-doped fiber amplifiers [1]. Here, L denotes the fiber amplifier length and the other parameters represent the standard fiber parameters.

3-

Conclusions

We have introduced simple schematic representations for energy levels and amplification mechanisms, and used the basic rate equation models, including the temperature effect to obtain the signal gain of the erbium and praseodymium-doped fiber amplifiers at university level. In addition, we have shown the possibility of deriving an analytical solution of the rate equations in some practical temperature ranges to understand the gain performance of both fiber amplifiers.