**3.3.3 Linearity**

Degradation of the transmission system will occur due to the crosstalk between the subcarriers (nonlinearity) and noise expansion (ASE). In linear regime the SOA modulator shows low nonlinearity because the noise generated by the SOA will dominate in the system. The intermodulation products overcome the noise floor in case of extraordinary high modulation indices and in the saturated operating region.

The nonlinearity causes intermodulation by different order mixing products. In practice, it is assumed that the transfer function of the device has only linear and cubic terms, because the even order terms do not produce mixing products falling into the transmission band and from order 5 the level of mixing products supposed to be very small.

In the two-tone intermodulation experiments the SOA was biased and modulated by the sum of two microwave signals. The output noise (Pnoise) and signal levels were measured for the fundamental (P1), the second (Psec) and the third (Pth) order mixing products.

For characterizing the nonlinearity the third order intercept point (IP3) or the spurious suppression in dBc is used. However, for high quality signal transmission a high linearity is not sufficient because the noise has to be low as well. Therefore, the spurious free dynamic range (SFDR) is a better characteristic. It is dependent both on the linearity and noise, it is higher when the linearity is high and the noise is small. In personal communication systems

is not enough for the expected work and the detected power is low in the first part. The power is near constant in the second linear part and after it the detected product starts to decrease because the slope of the gain curve falls. The lower curve at modulation behavior figure represents the result without input optical power, i.e. just the amplified spontaneous emission power (ASE) produces the modulated signal and the broadband O/E (optical-toelectronic) converter can detect this poor fluctuation. This effect can be dramatically

> -20 -15 -10 -5 0 5 10 15

Fig. 14. Measured Optical Gain (a) and Modulation behaviour (b) of SOA-modulator versus

The modulation bandwidth is limited by the speed at witch the carrier density can be changed, this is usually limited by the spontaneous lifetime of the carriers in the SOA (in the nanosecond range). The lifetime in the presence of a strong, saturating input signal is reduced due to stimulated recombination. The real speed depends on the structure of the

Degradation of the transmission system will occur due to the crosstalk between the subcarriers (nonlinearity) and noise expansion (ASE). In linear regime the SOA modulator shows low nonlinearity because the noise generated by the SOA will dominate in the system. The intermodulation products overcome the noise floor in case of extraordinary

The nonlinearity causes intermodulation by different order mixing products. In practice, it is assumed that the transfer function of the device has only linear and cubic terms, because the even order terms do not produce mixing products falling into the transmission band and

In the two-tone intermodulation experiments the SOA was biased and modulated by the sum of two microwave signals. The output noise (Pnoise) and signal levels were measured for

For characterizing the nonlinearity the third order intercept point (IP3) or the spurious suppression in dBc is used. However, for high quality signal transmission a high linearity is not sufficient because the noise has to be low as well. Therefore, the spurious free dynamic range (SFDR) is a better characteristic. It is dependent both on the linearity and noise, it is higher when the linearity is high and the noise is small. In personal communication systems

the fundamental (P1), the second (Psec) and the third (Pth) order mixing products.


> 0 100 200 300 400 500 600 Bias Current of SOA [mA]

Pin=850uW Pin=0

**Optical Gain [dB]**

Detected Electrical Power [dBm]

decreased by a narrow band optical bandpass filter.

50 100 150 200 250 300 350 400 **Bias Current [mA]**

device, but in general it is larger than 10GHz speed.

high modulation indices and in the saturated operating region.

from order 5 the level of mixing products supposed to be very small.

bias current of the device. Wavelength=1550nm, Temperature=20C, Modulation power=-30dBm, Modulation frequency=400MHz

**3.3.3 Linearity** 

**Optical Gain**

2/3 72 83 dB Hz SFDR is required [Olshansky]. The determination of SFDR, IP2 and IP3 are presented in Fig.15.

Fig. 15. Determination of SFDR, IP2, IP3.

Modulation frequencies=199, 200MHz, Modulation Power=4dBm, Input Optical Power=1mW, without Isolators, Temperature=20°C

$$\begin{aligned} \{IP2\{dBm\}} &= 2 \cdot P\_1 \{dBm\} - P\_{\text{sec}} \{dBm\} \\ \{IP3\{dBm\}} &= \frac{1}{2} \cdot \left( \Im \cdot P\_1 \{dBm\} - P\_{\text{flt}} \{dBm\} \right) \\ \{SFDR &= \frac{P\_{\text{int}} \{P\_{\text{fl}} = P\_{\text{noise}}\}}{P\_{\text{in}} \{P\_1 = P\_{\text{noise}}\}} = \frac{P\_1 \{P\_{\text{fl}} = P\_{\text{noise}}\}}{P\_{\text{noise}}} \\ \{SFDR \{dB\} &= \frac{2}{3} \cdot \left( \lbrack P\\$ \{dBm\} - P\_{\text{noise}} \{dBm\} \right) \end{aligned}$$

The experimental work was done on different types of SOAs. The presented results characterize a commercial SOA having 13 dB of small signal gain, 15dBm of saturation power, 100nm of optical bandwidth, 300mA of bias current. All the measuring instruments were checked to have higher dynamic range and better linearity than the value expected from the SOA-modulator. 7% modulation depth was applied, because the modulation indices are usually less than 10 % in typical SCM systems. However, it was also checked for a wide range of modulation depth (3-30%).

The nonlinear behavior depends on several parameters [Marozsak]. Fig.16. shows the noise level, IP3 and SFDR versus bias current. The graph can be divided into three parts. First, the SOA is near the transparency, the nonlinearity is high; hence the IP3 and the SFDR improve as it approached the near linear range. In the second part the modulation and nonlinear products don't change significantly but the noise level rises, hence the SFDR decreases. Finally, the intermodulation products start rising and the degradation of the SFDR is faster. The shapes of the curves are similar for the results estimated from the one tone simulations. The reason of some difference (some dB) in the exact values is that for the measurements the SOA device's internal parameters were not available. So we could only use estimated parameters for the simulations.

Multi-Functional SOAs in Microwave Photonic Systems 101

Fig. 18. Levels of noise and intermodulation products depends on the optical reflection.

Compensating dispersion penalty is a key problem when next generation Radio-over-Fiber networks are built. Several techniques have been proposed to overcome dispersion effect. An alternative method is presented to overcome the RF carrier suppression effect in optical links based on the joint effect of SOA chirp, chromatic dispersion and nonlinearities of the optical fiber. The results show that the frequency notches caused by the dispersion-induced carrier suppression effect may be sharply alleviated and the performance of the transmitted

The SOA dispersion compensator has the advantage that it is a loss-less, wide band solution with robust operation. It is more efficient than midway optical phase conjugation or self phase modulation effect introduced by the fiber. It offers optical amplification compared with high insertion loss of dispersion compensation fiber. It has high bandwidth (30-35nm), hence it is transparent for optical or electrical carrier variation and more insensitive for environmental and system parameters than Fiber Bragg Grating. It is semiconductor based device, which can be easily integrated with semiconductor optical source. So it doesn't demand expensive and complex optical device (like SSB Mach-Zehnder modulator), just an additional integrated section is necessary in the optical source. Additionally the operation of

When the incoming optical power of the laser amplifier is intensity modulated, the optical gain is affected in both magnitude and phase via the modulation of the complex refractive index caused by the electron density. Consequently, in SOA the optical signal becomes amplitude modulated (AM) and phase modulated (PM). It can be modelled using the Linewidth Enhancement Factor (LEF=Henry factor=α factor) approximation. Measurements of LEF can are found in the literature and have shown that LEF is not a mere constant factor, but it is for instance a function of bias current, wavelength and input optical power. In the unsaturated region the LEF value ranges from 2 to 7 for GaAs and GaInAsP conventional lasers and from 1.5 to 2 for quantum well lasers [Occhi]. However, the chirping parameter which is positive for light sources and unsaturated optical amplifiers is negative for saturated amplifiers [Watanabe]. It cancels the positive chirp-parameter of modulator, causing asymmetrical optical power between the sidebands [Lee] and the optical amplification causes RF signal gain

the device can easily be optimized by bias point and input optical power control.

[Marti]. However the SOA adds noticeable noise to the system.

Wavelength=1550nm, Frequencies=199, 200MHz, Input Optical Power=1mW,

Temperature=20°C

digital signal can be improved.

**3.4.1 Basic operation** 

**3.4 Dispersion compensation in RoF systems** 

Fig. 16. Nonlinear behavior of SOA modulator versus bias point. Modulation frequencies=199, 200MHz, Modulation Power=4dBm, Input Optical Power=1mW, without Isolators, Temperature=20°C

By injecting more optical power, the noise floor reduces due to the amplified spontaneous emission (ASE) reduction in saturated regime. Same time the optical gain – bias current curve is more linear. The combination of these two factors allows us to obtain a better SFDR at high input optical power.

The linearity is temperature sensitive, because the operation of semiconductor devices depends on the temperature. The degradations of SFDR and IP3 are about 2/3 2dB Hz and 3dB for 10ºC temperature change (Fig.17.).

Fig. 17. Nonlinearity dependence on the temperature and optical reflection Wavelength=1550nm, Input Optical Power=1mW, Bias Current=50mA, Modulation frequencies=199, 200MHz

In short distance RoF link, the level of optical reflection is usually determined by the optical detector. The system will be more instable in case of strong optical reflection (without optical isolators), and larger SFDR degradation can be observed as seen in the Fig.17. The change of the SFDR is caused by two different effects (Fig.18.). The noise level of the device increases as a function of the bias point, the degradation is more significant without optical isolator. On the other hand the level of the nonlinear product will fluctuate in case of strong reflection.

Fig. 16. Nonlinear behavior of SOA modulator versus bias point. Modulation

Fig. 17. Nonlinearity dependence on the temperature and optical reflection

Wavelength=1550nm, Input Optical Power=1mW, Bias Current=50mA, Modulation

In short distance RoF link, the level of optical reflection is usually determined by the optical detector. The system will be more instable in case of strong optical reflection (without optical isolators), and larger SFDR degradation can be observed as seen in the Fig.17. The change of the SFDR is caused by two different effects (Fig.18.). The noise level of the device increases as a function of the bias point, the degradation is more significant without optical isolator. On the other hand the level of the nonlinear product will fluctuate in case of strong

Isolators, Temperature=20°C

at high input optical power.

frequencies=199, 200MHz

reflection.

3dB for 10ºC temperature change (Fig.17.).

frequencies=199, 200MHz, Modulation Power=4dBm, Input Optical Power=1mW, without

By injecting more optical power, the noise floor reduces due to the amplified spontaneous emission (ASE) reduction in saturated regime. Same time the optical gain – bias current curve is more linear. The combination of these two factors allows us to obtain a better SFDR

The linearity is temperature sensitive, because the operation of semiconductor devices depends on the temperature. The degradations of SFDR and IP3 are about 2/3 2dB Hz and

Fig. 18. Levels of noise and intermodulation products depends on the optical reflection. Wavelength=1550nm, Frequencies=199, 200MHz, Input Optical Power=1mW, Temperature=20°C
