4. All-optical memory loop based on SOA MZI

shift becomes π [9]. Then, if both data have the same value, they will cancel, and at the T-port 0 will appear, if data have different value, then it will not cancel and 1 will appear at the T-port [9]. In MZI counter-propagating gates, the clock and data pulse propagate in opposite directions through MZI [9]. If any of the data is 1, then XPM between the clock and data pulse inside SOA creates the differential phase shift between the two clock components, MZI becomes unbalanced, and the clock pulse exits at T-port [9]. If both the data are the same, the total

Consider now a typical all-optical logic element based on transforming of XPM into an intensity modulation and implemented as the MZI copropagating push-pull gate with SOA in the two arms shown in Figure 3 [9]. The optical fibers are used as interconnects. The SOA-based MZI with couplers at the input and output is shown in Figure 4. At the SOA-based MZI block output, there is a coupler shown in Figure 4. The outputs at the right side of this coupler are

Note that the co-propagating data streams configuration permits to avoid the SOA length restriction, and the MZI with push-pull configuration allows increasing the memory bit-rate beyond the limitation of the SOA carrier recovery time [8]. The copropagating data streams A and B of the same wavelengths are inserted into upper and lower arm of MZI shown in

The data A in the upper arm is ahead of one bit period to data B traveling in the lower arm of MZI, and the lower arm data B is one bit period ahead to upper arm data A [9]. As a result, a

phase shift will become π, and the clock pulse is cancelled at T-port [9].

connected to the T-port and R-port shown in Figure 3.

284 Optical Fiber and Wireless Communications

Figure 4.

Figure 3. MZI with push-pull configuration.

Figure 4. SOA–based MZI.

Consider now an all-optical memory loop consisting of an AND gate and a regenerator based on the two push-pull co-propagating MZI with a SOA in each arm and couplers at the input and the output shown in Figure 4 and discussed in the previous section [8]. The scheme of the all-optical memory loop is shown in Figure 5 [8]. The input data burst at the wavelength λ<sup>2</sup> is inserted into the memory through the AND gate is converted into the output data burst at the wavelength λ<sup>1</sup> [8]. A regenerator is used into the loop in order to improve the quality of the data burst at the wavelength λ<sup>1</sup> eliminating the signal degradation caused by dispersion, nonlinearity, and other physical impacts [8]. The output of the regenerator is fed back to the AND gate as a pump at the wavelength λ<sup>3</sup> [8]. The data can be stored in the loop for a long term [8]. The length of the data burst nT must be less than or equal to the length of the memory loop NT where T is the bit period [8].

The data format of the all-optical memory shown in Figure 5 is OOK, while for the PSK modulation format the memory should be modified [8].

Recently, we proposed a novel architecture of an all-optical memory loop combining the ultrafast all-optical signal processor based on QD-SOA MZI [12] and the DSP block for the mitigation of the dispersion and nonlinearity impairments [6]. The proposed all-optical memory loop is shown in Figure 6. The advantages of the novel all-optical memory loop are following [6].


Figure 5. Schematic setup of the all-optical memory based on SOA MZI.

Figure 6. The architecture of the all-optical memory loop based on QD-SOA–based MZI.


In our case, the phase difference at the output of the QD-SOA–based MZI is caused by the signal power difference in the upper and lower MZI arms, unlike the MZI copropagating push-pull gate mentioned above [9]. Typically, 80 and 20% of the input signal power were fed through the coupler into the upper and lower arm of the MZI, respectively [6]. As a result, dynamic processes in QD-SOA placed into the upper and lower arms of MZI are characterized by different carrier relaxation time and gain recovery time, and the flatness of the switching window is significantly improving [6].

The QD-SOA MZI output light intensity Pout and phase difference ∅1ðtÞ � ∅2ðtÞ are given by Refs. [12–14]:

$$P\_{out} = \frac{P\_{in}}{4} \left\{ G\_1(t) + G\_2(t) - 2\sqrt{G\_1(t)G\_2(t)} \cos\left[\phi\_1(t) - \phi\_2(t)\right] \right\} \tag{3}$$

$$
\phi\_1(t) - \phi\_2(t) = -\frac{\alpha}{2} \ln \left( \frac{G\_1(t)}{G\_2(t)} \right) \tag{4}
$$

where the Pin is continuous wave (CW) clock stream optical signal divided and introduced into the two QD-SOA, G1, <sup>2</sup> ¼ expðg1,2LÞ and ∅1,2ðtÞ are the gain and phase shift, respectively, in the two arms of QD-SOA MZI, α is the line width enhancement factor (LEF), g1,2 is the SOA gain, and L is the active medium length. In order to evaluate the QD-SOA gain, we must use the theoretical model of the QD-SOA, which will be briefly discussed in Section 5.

#### 5. The theoretical model of the QD-SOA

3. DSP block can improve the signal quality as compared to an MZI-based regenerator.

Figure 6. The architecture of the all-optical memory loop based on QD-SOA–based MZI.

and to increase the loop length.

Figure 5. Schematic setup of the all-optical memory based on SOA MZI.

286 Optical Fiber and Wireless Communications

window is significantly improving [6].

4. An additional SOA is inserted into the loop in order to compensate the optical fiber losses

In our case, the phase difference at the output of the QD-SOA–based MZI is caused by the signal power difference in the upper and lower MZI arms, unlike the MZI copropagating push-pull gate mentioned above [9]. Typically, 80 and 20% of the input signal power were fed through the coupler into the upper and lower arm of the MZI, respectively [6]. As a result, dynamic processes in QD-SOA placed into the upper and lower arms of MZI are characterized by different carrier relaxation time and gain recovery time, and the flatness of the switching QD-SOA had been thoroughly investigated both theoretically and experimentally (see, for example, [15, 16] and references therein). The promising features of QD-SOA such as high saturation power, broad gain bandwidth, pattern-free amplification of single- and multichannel signals, efficient WC can provide high-performance amplifiers and all-optical switches for optical networks [16].

QD is a nanostructure where the electron and hole movement is confined in the three dimensions, and these dimensions are of a few nanometers [15]. In QD, the charge carriers occupy only a restricted number of discrete energy levels like the electrons in an atom [15]. The density of states in QD is quantized, and the number of carriers necessary to fill these states decreases as compared to the structures with higher dimensionality. Consequently, the threshold current density in QD lasers substantially reduces, while the transparency and the population inversion necessary for the optical gain can be achieved more easily [15]. The QD grown by using the Stranski-Krastanov technology typically has a pyramidal shape with a base of about 15–20 nm and a height of about 5 nm [15]. The QD has a significant size dispersion, which results in the inhomogeneous broadening of the QD laser and SOA spectrum [15]. QD structures exhibit ultrafast gain recovery time which results in the ultrafast carrier dynamics [15]. The active layer of a QD-SOA contains one or several quantum wells (QW) referred to as a wetting layer (WL) with a continuous carrier energy band [15]. The electrons in the Stranski-Krastanov grown QD are typically characterized by two energy levels: the ground state (GS) situated about 100 meV below the band gap of WL and the excited state (ES), or the first excited level [15]. The energy level structure of a QD laser or QD-SOA is presented in Figure 7.

The carrier dynamics in QD is described by the system of the rate equations taking into account the following electron transitions: the fast electron transitions from WL to ES with the relaxation time τwE � 3 ps; the fast electron transitions between ES and GS with the corresponding relaxation timesτEG ≈ 0:16 ps; τGE � 1:2 ps; the slow electron transitions from ES to WL with the escape time τEw � 1 ns. The QD-SOA rate equations have the form [12, 17]:

Figure 7. The energy level structure and the electron transitions in a QD.

$$\frac{\partial N\_w}{\partial t} = \frac{f}{eL\_w} - \frac{N\_w(1-h)}{\tau\_{w\to}} + \frac{N\_w}{\tau\_{Ew}} - \frac{N\_w}{\tau\_{w\to}} \tag{5}$$

$$\frac{\partial h}{\partial t} = \frac{N\_w L\_w (1 - h)}{N\_Q \tau\_{w\to}} - \frac{N\_w L\_w h}{N\_Q \tau\_{Ew}} - \frac{(1 - f)h}{\tau\_{EG}} + \frac{f(1 - h)}{\tau\_{GE}} \tag{6}$$

$$\begin{split} \frac{\partial f}{\partial t} &= \frac{(1-f)h}{\tau\_{EG}} - \frac{f(1-h)}{\tau\_{GE}} - \frac{f^2}{\tau\_R} - \frac{g\_p L}{N\_Q} (2f-1) S\_p \frac{c}{\sqrt{\varepsilon\_r}} \\ &- \frac{g\_s L}{N\_Q} (2f-1) S\_s \frac{c}{\sqrt{\varepsilon\_r}} \end{split} \tag{7}$$

where J is injection current density, Nw is the WL carrier density per unit volume, f is the electron occupation probability of GS, h is the electron occupation probability of ES, Sp,s are the pump (data A or data B) and signal (clock stream) wave photon densities averaged over the length of SOA L, gp,s are the pump and signal wave modal gains, respectively, e is the electron charge, NQ � ð1010 � 1012<sup>Þ</sup> cm�<sup>2</sup> is the QD density per unit area, Lw is the effective thickness of the active layer, ε<sup>r</sup> is the SOA material permittivity, and c is the free space light velocity. The average photon densities Sp,s are given by Ben Ezra [12]:

$$S\_{p,s}(\tau) = \frac{[S\_{p,s}(\tau)]\_{in}}{L} \int\_0^L dz \exp\left(\int\_{p,s}^z (g\_{p,s} - a\_{\text{int}}) dz'\right) \tag{8}$$

where <sup>τ</sup> <sup>¼</sup> <sup>t</sup> � <sup>z</sup> vg � �, t, z, vgare time, coordinate, and the optical wave group velocity, respectively. The pump and signal wave phase ∅p,s and modal gain gp,s are given by, respectively [12]:

Ultra-Fast All-Optical Memory based on Quantum Dot Semiconductor Optical Amplifiers (QD-SOA) http://dx.doi.org/10.5772/intechopen.68527 289

$$\theta\_{p,s}(\tau) = -\frac{\alpha}{2} \Big| \limits\_{0}^{L} g\_{p,s} dz \tag{9}$$

$$\mathcal{g}\_{p,s}(\omega) = \frac{2\Gamma N\_Q}{a} \int d\omega F(\omega)\sigma(\omega\_0)(2f - 1) \tag{10}$$

where Γ is the confinement factor, l is the number of QD layers, a is the mean size of QD, σ(ω0) is the cross section of interaction of photons of frequency ω<sup>0</sup> with carriers in QD at the transition frequency ω including the homogeneous broadening factor, F(ω) is the Gaussian distribution of the transition frequency in the QD ensemble related to the inhomogeneous broadening. The inhomogeneous broadening is caused by the QD shape and size variations as it was mentioned above. It is given by Ben Ezra [12]:

$$F(\omega) = \frac{1}{\Delta\omega\sqrt{\pi}} \exp\left[-\frac{\left(\omega - \overline{\omega}\right)^2}{\left(\Delta\omega\right)^2}\right] \tag{11}$$

where Δω is related to the inhomogeneous bandwidth, <sup>γ</sup>inhom <sup>¼</sup> <sup>2</sup>Δ<sup>ω</sup> ffiffiffiffiffiffiffiffi ln<sup>2</sup> <sup>p</sup> , and <sup>ω</sup> is the average transition frequency.

#### 6. The simulation results

∂Nw <sup>∂</sup><sup>t</sup> <sup>¼</sup> <sup>J</sup> eLw

Figure 7. The energy level structure and the electron transitions in a QD.

<sup>∂</sup><sup>t</sup> <sup>¼</sup> NwLwð<sup>1</sup> � <sup>h</sup><sup>Þ</sup> NQτwE

> <sup>¼</sup> <sup>ð</sup><sup>1</sup> � <sup>f</sup>Þ<sup>h</sup> τEG

> > � gsL NQ

∂h

288 Optical Fiber and Wireless Communications

∂f ∂t

photon densities Sp,s are given by Ben Ezra [12]:

where <sup>τ</sup> <sup>¼</sup> <sup>t</sup> � <sup>z</sup>

vg � � � Nwð<sup>1</sup> � <sup>h</sup><sup>Þ</sup> τwE

� NwLwh NQτEw

> c ffiffiffiffi εr p

� f 2 τR

where J is injection current density, Nw is the WL carrier density per unit volume, f is the electron occupation probability of GS, h is the electron occupation probability of ES, Sp,s are the pump (data A or data B) and signal (clock stream) wave photon densities averaged over the length of SOA L, gp,s are the pump and signal wave modal gains, respectively, e is the electron charge, NQ � ð1010 � 1012<sup>Þ</sup> cm�<sup>2</sup> is the QD density per unit area, Lw is the effective thickness of the active layer, ε<sup>r</sup> is the SOA material permittivity, and c is the free space light velocity. The average

� <sup>f</sup>ð<sup>1</sup> � <sup>h</sup><sup>Þ</sup> τGE

ð2f � 1ÞSs

Sp,sðτÞ ¼ <sup>½</sup>Sp,sðτÞ�in

L

ð L

dz exp

tively. The pump and signal wave phase ∅p,s and modal gain gp,s are given by, respectively [12]:

�ðz

0

, t, z, vgare time, coordinate, and the optical wave group velocity, respec-

ðgp,s � αintÞdz<sup>0</sup>

�

0

þ Nw τEw

� <sup>ð</sup><sup>1</sup> � <sup>f</sup>Þ<sup>h</sup> τEG

� gpL NQ

� Nw τwR

ð2f � 1ÞSp

<sup>þ</sup> <sup>f</sup>ð<sup>1</sup> � <sup>h</sup><sup>Þ</sup> τGE

> c ffiffiffiffi εr p

ð5Þ

ð6Þ

ð7Þ

ð8Þ

We solved numerically Eqs. (3)–(11) for the typical values of parameters [12] for the QD-SOA– based all-optical loop shown in Figure 6 [6]. The numerical simulations have been carried out for the OOK and pulse amplitude modulation 4 (4-PAM) formats [6]. We used the MATLAB environment. Simulation results for the eye diagrams in the case of the OOK modulation format are shown in Figures 8 and 9.

We used the QD-SOA–based all-optical memory model with the loop length of L = 2 km and the input OOK modulated signal with the bit rate of 50 Gb/s and the quality factor at the input Q = 15.8932. The comparison of the eye diagrams presented in Figures 8 and 9 shows that after 4 rounds in the loop, the quality factor of the signal decreases by approximately 18%.

Figure 8. The eye diagram for the OOK modulation format, a bit rate of 50 Gb/s after one round in the QD-SOA–based all-optical memory loop. The memory loop length L = 2 km, T = 10 μs, the quality factor Q = 13.3156.

Figure 9. The eye diagram for the OOK modulation format, a bit rate of 50 Gb/s after four rounds in the QD-SOA–based all-optical memory loop. The memory loop length L = 2 km, T = 40 μs, the quality factor Q = 13.0327.

The simulations results for the 4-PAM modulation format, QD SOA–based all-optical memory loop with the length of L = 1 km and bit rates of 50 and 100 Gb/s are shown in Figures 10–13, respectively.

Eye diagrams in Figures 10 and 11 clearly show that for the bit rate of 50 Gb/s, the patterning effect is negligible after two rounds in the memory loop. In the case of the bit rate of 100 Gb/s, the patterning effect is slightly pronounced after the two rounds in the memory loop as it is

Figure 10. The eye diagram for 4-PAM modulation format and a bit rate of 50 Gb/s, the memory loop length L = 1 km. The signal is at the input of the all-optical memory loop.

Figure 11. The eye diagram for 4-PAM modulation format and a bit rate of 50 Gb/s, the memory loop length L = 1 km. The signal is after two rounds in the all-optical memory loop.

Ultra-Fast All-Optical Memory based on Quantum Dot Semiconductor Optical Amplifiers (QD-SOA) http://dx.doi.org/10.5772/intechopen.68527 291

Figure 12. The eye diagram for 4-PAM modulation format and a bit rate of 100 Gb/s, the memory loop length L = 1 km. The signal is at the input of the all-optical memory loop.

Figure 13. The eye diagram for 4-PAM modulation format and a bit rate of 100 Gb/s, the memory loop length L = 1 km. The signal is after two rounds in the all-optical memory loop.

seen from Figures 12 and 13. The QD-SOA–based all-optical memory performance does not deteriorate up to the bit rate of 100 Gb/s.

The numerical estimations show that for loop length L = 1 km, the light velocity in the optical fiber <sup>v</sup> <sup>≈</sup> <sup>2</sup> <sup>10</sup><sup>8</sup> m/s and the bit rates of 50 and 100 Gb/s the all-optical memory storage values are of 0.25 and 0.5 Mb, the storage times are 5 and 10 μs, respectively [6].

### 7. Conclusions

The simulations results for the 4-PAM modulation format, QD SOA–based all-optical memory loop with the length of L = 1 km and bit rates of 50 and 100 Gb/s are shown in Figures 10–13,

Figure 9. The eye diagram for the OOK modulation format, a bit rate of 50 Gb/s after four rounds in the QD-SOA–based

all-optical memory loop. The memory loop length L = 2 km, T = 40 μs, the quality factor Q = 13.0327.

Eye diagrams in Figures 10 and 11 clearly show that for the bit rate of 50 Gb/s, the patterning effect is negligible after two rounds in the memory loop. In the case of the bit rate of 100 Gb/s, the patterning effect is slightly pronounced after the two rounds in the memory loop as it is

Figure 10. The eye diagram for 4-PAM modulation format and a bit rate of 50 Gb/s, the memory loop length L = 1 km. The

Figure 11. The eye diagram for 4-PAM modulation format and a bit rate of 50 Gb/s, the memory loop length L = 1 km. The

respectively.

290 Optical Fiber and Wireless Communications

signal is at the input of the all-optical memory loop.

signal is after two rounds in the all-optical memory loop.

Optical signal processing substantially increases the device processing speed, provides an alternative to electronic techniques, and, at the same time, can enhance the processing capabilities of electronics when the optical and electronic signal processing techniques are combined. Optical packet-switched networks are promising candidates for the advanced optical telecommunication systems. All-optical signal processing is essential for ultrafast OPS in such networks. Flip-flop memory is a basic component of an all-optical packet switch. We discussed the all-optical memory based on SOA-MZI. It is characterized by the high performance due to the SOA high nonlinearity, low switching power, wide gain bandwidth, compact size, and integration capability with other photonic devices. Unfortunately, the SOA operation rate is limited by its comparatively slow gain recovery time.

We proposed a novel architecture of the ultrafast all-optical memory based on MZI with two QD-SOA. QD-SOA is characterized by high operation rate and low threshold current caused by the 3D carrier confinement and fast electron transitions in QD. For this reason, the operation rate of the proposed all-optical memory loop increases up to 100 Gb/s. The time delay in the typical push-pull scheme of the memory loop is replaced with the output signal phase difference caused by the signal power difference in the MZI arms due to the highly efficient XPM in QD-SOA. The DSP block is inserted for the dispersion and nonlinearity impairment mitigation. The proposed all-optical memory loop includes only one MZI with two QD-SOA and reduces the complexity of electronic synchronization scheme. We carried out numerical simulations of the proposed all-optical memory loop based on the QD-SOA rate equations and the expression for the MZI output power for the OOK and 4-PAMmodulation formats. The simulation results show that the proposed all-optical memory exhibits a high performance up to the bit rate of 100 Gb/s and the corresponding memory storage and storage time values of 0.5 Mb and 10 μs, respectively.
