Dynamic Effects on Pulse Amplification

SOAs are mostly used in the telecommunication systems for amplification of modulated signals. The injected charged carriers produce electron and hole pairs, which provide optical gain to the input pulse. SOAs are capable of amplifying optical pulses as short as few pico- seconds without any distortion. The processes which determine the amplification of optical pulses and gain variations after propagation of an optical pulse in SOAs are classified as the inter-band processes and intraband processes.

3.10.1 Inter-band Processes

The inter-band processes are generally slow processes (few hundred picoseconds), they depends on recovery of the carriers density. In SOAs, inter-band processes are dominant when long (few picoseconds) optical pulses are used as input signals. To investigate the inter-band processes during pulses amplification in the SOAs, carrier lifetime is an important parameter. This is due to the fact that gain response time of the SOAs is associated to its carrier lifetime. Various carrier recombination mechanisms that influence the carrier lifetime in the SOAs are defect recombination, surface carriers recombination, spontaneous emission recombination and Auger recombination. The carrier recombination in the absence of stimulated emission is given by [3]:

Equation 3.18

where A is coefficient for unimolecular recombination caused by the defects or trapping sites,

B is the coefficient for radiative (bimolecular) spontaneous recombination and C is the

coefficient for Auger recombination. The spontaneous carrier lifetime may be approximated by [3]:

Chapter 3 Device Background Theory - 45 - Equation 3.19

The plot of the carrier lifetime versus the carrier density for AlGaInAs material is shown in Figure 3.16. Carriers lifetime is calculated using Equation 3.19, with _,

_{and [31].}

Figure 3.16: Calculated carrier lifetime vs. carrier density of AlGaInAs epitaxial material.

For carrier density of around _{, the calculated carrier lifetime (τ) is 460 ps. This}

carrier lifetime is much larger than pulse duration of an isolated pulse, which is generally few picoseconds. This means that the gain of the amplifier will react relatively quickly to the changes in the input signal. Generally, when the repetition rate (Tr) of input pulse is greater

than 1/ τ, the pulses are amplified with negligible distortion because the gain does not recover to its unsaturated value between the pulses. However, if the input pulse repetition rate is of order of 1/ τ, then the carrier density reach to steady value between the two consecutive pulses, which leads to pulses distortion and pattern effects. These effects on input pulses during pulse amplification are deleterious for linear amplification. In the erbium doped fiber amplifiers (EDFA), the fluorescence lifetime of Erbium is quite long (~10 ms) as compared to SOAs. The long carrier lifetime in EDFAs causes lower distortion of the input pulses for repetition rate down to kHz [32].

As given in Chapter 2 (Equation 2.1), the pulse saturation energy of a semiconductor gain medium depends on the photon energy (hυ), the modal cross-sectional area (A), the optical confinement factor (Γ) and the differential gain ( ) [33].

Chapter 3 Device Background Theory

- 46 - If the energy (E) of an input pulse is less than or comparable to , then the pulse can be

amplified without any significant distortions. However, if the energy of the input pulse is larger than the saturation energy of the gain medium, the gain significantly reduces due to the gain saturation. The gain saturation induced non-linearities lead to temporal gain difference between the leading and trailing edge of the pulse and causes pulse broadening. In saturation regime, the pulse broadening as well as pulse compression, depending on operating condition and input pulse shape, has been theoretically explained and experimentally observed [34]. During propagation in the SOA, the leading edge of an input pulse saturates the gain medium of SOA and thus reduces the gain available for the trailing edge of the pulse. This difference of the gain for the leading and trailing edges of the input pulse normally causes pulse broadening. Similarly, pulse compression is due to slight trimming of the trailing edge of the pulse due to gain saturation.

The gain saturation in the SOAs also causes changes in the refractive index, which shifts the pulse spectrum towards longer wavelengths. The carrier density in the SOAs changes as the input pulse propagates through the SOA. The time dependent changes in the carrier density cause changes in effective index, which are responsible for self-phase modulation (SPM) [21]. The induced phase shifts due to SPM on the leading and trailing edges of the input pulses are different and hence the pulses at output of the amplifier get chirped.

3.10.2 Intra-band Processes

Intra-band carrier dynamics becomes more important when very short optical pulses (sub- picosecond) are injected into the SOAs. Intra-band effects changes the distribution of electrons in CB and holes in the VB. The following non-linear effects influence the gain dynamics of short input pulses to the SOAs:

 Spectral hole burning (SHB)

 Two-photon absorption (TPA)

 Carrier heating (CH)

When a short optical pulse enters the SOA, it causes reduction (holes) in the carrier distribution at particular photon energy. This process is called spectral hole burning (SHB). In SHB process, the carrier distribution is deviated from Fermi-distribution and the time (τSHD)

needed to restore the Fermi-distribution by scattering process is around 70-200 femto-seconds [35]. SHB modulates the occupation probability of the carriers within a band, which leads to

Chapter 3 Device Background Theory

- 47 - fast gain modulation. Carrier heating (CH) process increase temperature of carrier distribution, which decreases the optical gain. The CH is mainly caused due to stimulated emission and free carriers absorption. The carrier distribution cools down to lattice temperature by emitting phonons. The CH recovery time (τCH) is in range from several hundred femtoseconds to few

picoseconds [36]. Two photons absorption (TPA) also contribute to the carriers heating. The TPA excites carriers to higher energy states inside both the CB and VB. The hot carriers in the higher energy states give their excess energy to the carrier distribution through carriers- carriers scattering and causes heating the carrier distribution. Through phonons emission, the carrier distribution cools down to the lattice temperature. The TPA process is strongly dependent on the input pulse intensity.

Analysis of the intra-band processes and their effects on input pulses is reported in [33, 37]. The detailed analysis of intra-band processes and its effects on amplification of input pulses is out of scope of this work.