**3.2.5 Noise calculation**

The optical output from an optical amplifier is composed of an amplified optical signal and an amplified spontaneous emission (ASE) with broad spectral width. Moreover interference is created between ASE components and light signal [Shiraz]. So several types of noises (the shot noise belonging to signal and spontaneous emissions, beat noise between signal and spontaneous emissions, beat noise between spontaneous emission components, thermal noise of the receiver and excess noise belonging to incoherence of the input signal) can be observed, when the output photons are detected by a photodetector. In the unsaturated region the beat noise between the ASE components dominates. The installation of an optical bandpass filter into the microwave photonics link decreases the noise bandwidth and the equivalent noise power. In SCM system only a single optical carrier is applied, hence small optical bandwidth (1-2nm) should be specified in the link for decreasing the noise build-up.

The noise generated by a SOA acting as a detector is different from the noise generated by a SOA acting as an amplifier or modulator. There are several similar contributions to the total noise power at electrical connection of SOA-detector. However interference between ASE components and light signal is created inside the SOA device. So the noise components originating from the light amplification depend on input parameters as wavelength, input power or driving current with different aspect, than in case of other applications. Shot noise caused by random generation and flow of mobile charge carriers and thermal noise of the load resistor are well known and can be expressed like in a traditional PIN detector [Agraval]. The thermal noise due to electrical amplification has been included as well [Gustavsson].

$$\dot{i}\_{\text{shot}}^2 = \mathbf{2} \cdot \mathbf{e} \cdot \mathbf{I} \cdot \mathbf{B}\_0 \prime \qquad \dot{i}\_{\text{therm}}^2 = \left[ \frac{\mathbf{1}}{R\_L} + \frac{\mathbf{1} - F}{R\_N} \right] \cdot \mathbf{4} \cdot \mathbf{k} \cdot \mathbf{T} \cdot \mathbf{B}\_0 \tag{4}$$

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

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.

Where IdetSOA is the current detected by SOA, IDC is the average detected current, ∆IdetSOA is

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

The optical output from an optical amplifier is composed of an amplified optical signal and an amplified spontaneous emission (ASE) with broad spectral width. Moreover interference is created between ASE components and light signal [Shiraz]. So several types of noises (the shot noise belonging to signal and spontaneous emissions, beat noise between signal and spontaneous emissions, beat noise between spontaneous emission components, thermal noise of the receiver and excess noise belonging to incoherence of the input signal) can be observed, when the output photons are detected by a photodetector. In the unsaturated region the beat noise between the ASE components dominates. The installation of an optical bandpass filter into the microwave photonics link decreases the noise bandwidth and the equivalent noise power. In SCM system only a single optical carrier is applied, hence small optical bandwidth (1-2nm) should be

The noise generated by a SOA acting as a detector is different from the noise generated by a SOA acting as an amplifier or modulator. There are several similar contributions to the total noise power at electrical connection of SOA-detector. However interference between ASE components and light signal is created inside the SOA device. So the noise components originating from the light amplification depend on input parameters as wavelength, input power or driving current with different aspect, than in case of other applications. Shot noise caused by random generation and flow of mobile charge carriers and thermal noise of the load resistor are well known and can be expressed like in a traditional PIN detector [Agraval]. The thermal noise due to electrical amplification has been included as well

0 0

*R R*

*L N*

(4)

*<sup>P</sup> a P I Rm <sup>R</sup>*

*in mod LD DC SOA\_ in P (t) a a P ( m cos t) P P* (1)

*DC* 2 *in detSOA*

*in DC*

*a mP Z* (3)

*I I I cos t detSOA DC detSOA* (2)

2 2 2

1 *opt*

Hence the detected electrical current has cosine type component

amplitude of the detected cosinusoidal signal.

*detSOA*

where Z is the microwave impedance of SOA.

specified in the link for decreasing the noise build-up.

2 2

1 1 2 4 *shot therm*

*<sup>F</sup> i eI B, i kTB*

input optical signal

(PdetSOA)

**3.2.5 Noise calculation** 

[Gustavsson].

where RN is a standard 50Ω resistance, F is the electrical amplifier noise figure, k is the Boltzmann constant, T is the temperature, B0 is the detection bandwidth.

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].

$$\dot{\mathbf{u}}\_{\text{ph}}^2 = e^2 \cdot \left(\Gamma \cdot \mathbf{g}\_m \cdot \mathbf{L}\right)^2 \cdot \overline{\sigma}^2 \cdot \mathcal{B}\_0 \tag{5}$$

where L is the device length, <sup>2</sup> is the photon variance averaged over the amplifier length. 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 variance of the detected current can be calculated [Gustavsson].

$$\mathbf{h}\_{ph}^{2} = e^{2} \cdot \left(\Gamma \cdot \mathbf{g}\_{m} \cdot \mathbf{L}\right)^{2} \cdot \frac{\left(\mathbf{G} - \mathbf{1}\right)^{2}}{\ln \mathbf{G}} \cdot \mathbf{B}\_{0} \cdot \begin{vmatrix} 2 \cdot n\_{sp} \cdot \frac{\lambda}{h \cdot c} \cdot P\_{in} + \frac{2}{\mathbf{G} - \mathbf{1}} \cdot \frac{\lambda}{h \cdot c} \cdot P\_{in} + \\\\ + n\_{sp}^{2} \cdot \Delta f \cdot \left(1 - 2 \cdot \frac{\mathbf{G} - \ln \mathbf{G} - 1}{\left(\mathbf{G} - 1\right)^{2}}\right) + \\\\ + 2 \cdot n\_{sp} \cdot \Delta f \cdot \frac{\mathbf{G} - \ln \mathbf{G} - 1}{\left(\mathbf{G} - 1\right)^{2}} \end{vmatrix} \tag{6}$$

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 spontaneous shot noise over the entire amplifier spectrum.

The signal-to-noise ratio is given by the following equation:

$$SNR = \frac{\dot{i}\_{\text{sig}}^2}{\dot{i}\_{\text{ph}}^2 + \dot{i}\_{\text{therm}}^2} \tag{7}$$

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 decrease as the optical gain decreases.

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

Multi-Functional SOAs in Microwave Photonic Systems 97

The modulation operation can be derived based on the slope of the measured optical gain

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

> 000 <sup>2</sup> *Gm I m P d mod d mod <sup>m</sup> G G GZ*

> > 2 2 2 2 *in det d mod <sup>P</sup> P mP a*

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

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

2 22 2

Based on this calculation the experimentally realized optical modulation depth is 5-10

Practically, the average optical gain and the slope of the optical gain - bias current curve determine the optimum working state of the SOA as a modulator. The curve can be divided into three parts (Fig.14.). In the first one the amplification just starts and it is not effective, the second one is the almost linear region and after it the slope of the optical gain starts to decrease. The middle of linear region of this curve should be chosen for operation point,

Fig.14. shows the measured optical gain and modulation behavior of the SOA-modulator versus bias current. The three regions are well seen in this figure, too. The injection current

because of the low static non-linear distortion effect and the high slope [Udvary2].

2 2 *det opt in det det det a P det P*

*PG Z P Z* 

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

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

relation) increase (Eq.17). Same conclusions can be observed from the experiments.

2

*m*

percent with sufficiently low (-30dBm) modulation power.

0

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

0 0 *mod I t I I cos t G t G G cos t* (8)

*P G P m cos t out in* <sup>0</sup> 1 (9)

(10)

(11)

(12)

curve (md) and the average optical gain (G0). The current and the gain of the device are:

output of the SOA-modulator takes the form

where the modulation index (m) is

the detected electrical modulation power

input average optical power of the detector:

Where *opt*

**3.3.2 Intensity modulation** 

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 desirable for the system.

Fig. 12. Calculated noise and signal powers versus input optical power (a) and optical gain (b), calculation based on measured data
