**3.2.4 Responsivity extraction from the measurements**

The responsivity of the SOA-detector can be calculated from the measurement. If the input signal is intensity modulated, the fluctuation in the optical intensity due to modulation will

Multi-Functional SOAs in Microwave Photonic Systems 95

where RN is a standard 50Ω resistance, F is the electrical amplifier noise figure, k is the

The mean value and the variance of the number of output photons per second due to light amplification process can be calculated. The variance of the detected current due to the photon noise can be obtained from the variance of photons in the amplifier medium. The

generated current is proportional to the photon density in the cavity [Gustavsson].

2

*SNR*

*<sup>G</sup> G lnG i e gL B n f lnG <sup>G</sup>*

<sup>2</sup> <sup>2</sup> 2 2

In the case of a true traveling wave amplifier (the face reflections are zero) the equivalent noise bandwidth for the beat noise between spontaneous emission components and the equivalent noise bandwidth for spontaneous emission shot noise are equal (∆f) and the

*ph <sup>m</sup>* <sup>0</sup> *i e gL B* (5)

1

(6)

1

2

(7)

*sp in in*

*nP P hc G hc*

1

0 2

<sup>1</sup> <sup>2</sup>

*G lnG n f <sup>G</sup>*

<sup>1</sup> <sup>1</sup> 1 2

*sp*

where nsp is the population inversion parameter, *nin* is the mean value of the number of input photons per second. The first term of equation represents the beat noise between the signal and the spontaneous mode, the second term represents signal shot noise, the third term represents spontaneous- spontaneous beat noise, and the last term represents

> 2 2 2 *sig ph therm*

*i*

*i i*

It is of interest to determine the magnitude of each contribution to the total noise in order to see which component dominates at different system parameters. The different noise components depend on the optical signal level with different aspect. The thermal noise, the spontaneous shot noise and the spontaneous beat noise are independent in the unsaturated regime, the signal shot noise and signal- spontaneous beat noise have linear relation with the input optical power. In case of small input optical power one of the constant noises dominates. Then signal shot noise or signal- spontaneous beat noise overcomes this limit. These relationships are illustrated in Fig.12 in which the different noise components and the total noise are calculated as a function of the link loss or input optical power of the SOAdetector. The calculation uses the measured SOA parameters and takes into account the gain saturation effect. Hence the spontaneous shot noise and the spontaneous beat noise start to

Similar results can be observed in case of constant input optical power as a function of the SOA gain (Fig.12). For low gain values thermal noise and shot noise dominate and for larger

<sup>2</sup> <sup>2</sup>

is the photon variance averaged over the amplifier length.

Boltzmann constant, T is the temperature, B0 is the detection bandwidth.

variance of the detected current can be calculated [Gustavsson].

spontaneous shot noise over the entire amplifier spectrum. The signal-to-noise ratio is given by the following equation:

decrease as the optical gain decreases.

2 2 2 2

*ph m sp*

where L is the device length, <sup>2</sup>

induce fluctuation in the injection current. We shall consider sinusoidal intensity modulated input optical signal

$$P\_{in}(\mathbf{t}) = \mathbf{a} \cdot \mathbf{a}\_{mod} \cdot P\_{LD} \cdot (\mathbf{1} + m \cdot \cos \alpha t) = P\_{DC} + \Delta P\_{SOA\_{\omega}}^{opt} \tag{1}$$

where Pin is the input optical power of SOA-detector, PLD is the average optical power of the laser, amod is the optical loss of the modulator, a is the optical loss between the modulator and SOA-detector, m is the modulation depth and ω is the angular modulation frequency. Hence the detected electrical current has cosine type component

$$I\_{\text{detSOA}} = I\_{\text{DC}} + \Delta I\_{\text{detSOA}} \cdot \cos(\text{out}) \tag{2}$$

Where IdetSOA is the current detected by SOA, IDC is the average detected current, ∆IdetSOA is amplitude of the detected cosinusoidal signal.

The SOA-detector responsivity (R) can be computed from the detected electrical power (PdetSOA)

$$
\Delta I\_{\text{detSOA}} = R \cdot m \cdot \frac{P\_{\text{DC}}}{a\_{\text{in}}} \qquad \Rightarrow \qquad R = \sqrt{\frac{2 \cdot a\_{\text{in}}^2 \cdot P\_{\text{detSOA}}}{m^2 \cdot P\_{\text{DC}}^2 \cdot Z}} \tag{3}
$$

where Z is the microwave impedance of SOA.
