**3.3.1 Calculation of the realizable modulation depth**

The modulation functionality is studied with the following link (Fig.13.). The optical signal from the laser diode is intensity modulated by SOA with time dependent optical gain. The intensity modulated optical signal is detected by traditional PIN photodiode.

Fig. 13. Simplified block diagram of the link for calculation of modulation behaviour

The modulation operation can be derived based on the slope of the measured optical gain curve (md) and the average optical gain (G0).

The current and the gain of the device are:

96 Selected Topics on Optical Amplifiers in Present Scenario

gain the beat noises give the dominating contribution. So the signal-to-noise ratio (SNR) increases up to a certain gain, reaches a maximum, finally it decreases. There exists an optimum amplifier bias point corresponding to maximum SNR of the SOA-detector. Although higher gains would yield higher responsivity, the SNR decreases and it is not

Fig. 12. Calculated noise and signal powers versus input optical power (a) and optical gain

The optical gain of the amplifier depends on the bias current and taking advantage of this effect could be used as an external modulator. The bias current of the SOA is modulated; therefore the material gain and the intensity of the output signal are modulated [Mork]. If small signal current modulation is considered, the electrical signal contains an invariant and a modulation parts, hence the number of charge carriers and photons are also time dependent [Conelly]. The magnitude and purity of the signal depend on the modulation signal, the bias current, the input power and the operation parameters. The SOA modulator requires low modulation power, and the detected electrical power is high because of the optical gain in contrary to the optical insertion loss of other modulators. However the SOA

The modulation functionality is studied with the following link (Fig.13.). The optical signal from the laser diode is intensity modulated by SOA with time dependent optical gain. The

intensity modulated optical signal is detected by traditional PIN photodiode.

G=G0(1+mcos(t))

Imod0+Imodcos(t)

DC Information

GPLD

Fig. 13. Simplified block diagram of the link for calculation of modulation behaviour

**LD detector** 

a

aGPLD

Idet0+Idetcos(t)

desirable for the system.

(b), calculation based on measured data

has noticeable optical noise [Udvary1].

CW

**3.3.1 Calculation of the realizable modulation depth** 

PLD **SOA modulator**

**3.3 Modulation function** 

$$I(t) = I\_0 + \Delta I\_{mod} \cdot \cos(\alpha t) \qquad G(t) = G\_0 + \Delta G \cdot \cos(\alpha t) \tag{8}$$

where I0 is the constant (dc) current, ΔI is the current modulation amplitude, G0 is the constant optical gain of SOA, ΔG is the modulation part. Hence the optical signal at the output of the SOA-modulator takes the form

$$P\_{out} = G\_0 \cdot P\_{in} \cdot \left(1 + m \cdot \cos\left(\alpha t\right)\right) \tag{9}$$

where the modulation index (m) is

$$m = \frac{\Delta G}{G\_0} = \frac{m\_d \cdot \Delta I\_{mod}}{G\_0} = \frac{m\_d}{G\_0} \cdot \sqrt{\frac{2 \cdot P\_{mod}}{Z}}\tag{10}$$

where Pmod is the modulation electrical power, Z is the microwave impedance of SOA. The output signal of the SOA-modulator is detected by an optical-electrical converter, Pdet is the detected electrical modulation power

$$P\_{det} = \eta^2 \cdot \frac{P\_{in}^2}{a^2} \cdot m\_d^2 \cdot P\_{mod} \tag{11}$$

is the detection efficiency, a is the optical loss between the SOA and the detector.

The modulation depth is proportional to the slope of the gain curve and the electrical modulation power, but it is in inverse relation to the average optical gain (Eq.16). However, the detected electrical power increases with the modulation power (direct relation), the slope of the gain curve and the input optical power of the SOA-modulator (quadratic relation) increase (Eq.17). Same conclusions can be observed from the experiments.

Naturally, the modulation depth realized by the SOA-modulator can be computed from the measured detected electrical power with the knowledge of the modulation power and the input average optical power of the detector:

$$\eta m = \frac{\mathbf{2} \cdot \mathbf{a}^2 \cdot \mathbf{P} \, \det}{\mathbf{P}\_{\text{in}}^2 \cdot \mathbf{G}\_0^2 \cdot \mathbf{\eta}\_{\text{det}}^2 \cdot \mathbf{Z}} = \frac{\mathbf{2} \cdot \mathbf{P}\_{\text{det}}}{\mathbf{P}\_{\text{det}}^{opt} \cdot \mathbf{\eta}\_{\text{det}}^2 \cdot \mathbf{Z}} \tag{12}$$

Where *opt det P* is the average optical power at the input of the detector.

Based on this calculation the experimentally realized optical modulation depth is 5-10 percent with sufficiently low (-30dBm) modulation power.
