Optical 8PSK Modulation Format Generator Basedon Three Microring Modulators

We have proposed an 8PSK modulator based on three microring modulators (MRM). The design consists of three MRMs, each with a radius of 11.1 µm . Of these three, two MRMs are connected in parallel and they together generate a QPSK (Quadrature phase shift keying) signal. While at the output port of the QPSK, a third MRM is connected in series works as an angle modulator, which is basically a 45 o phase shift modulator; i.e., the output of the MRM varies by 45 o depending on the bit pattern fed to it, ’0’or ’1’ respectively. In the result section, we have simulated and shown the performance of the proposed 2.5 GBaud 8PSK modulator after transmitting the modulated signal through various lengths of optical ﬁber. The bit error rate (BER) vs. optical signal to noise ratio (OSNR) curve shows that, 10 − 3 BER has been achieved at 13.5dB OSNR.

using photo-detectors [1,2]. However, as we move towards higher bit rate communications, there can be seen some limitations of OOK modulation format, and hence the use of phase shift keying (PSK) [3,4] came into the optical fiber communication system. Compare to amplitude modulation, which is used in OOK, the PSK modulation formats are much more resilient to optical fiber induced impairments. Binary PSK (BPSK) [5] compared to OOK, can transmit data over a higher distance. But BPSK still carries the same spectral efficiency as OOK. To overcome the limitation, higher-order modulation formats like QPSK [3], 8PSK [6], Quadrature amplitude modulation (QAM) [7] are used in optical fiber communication systems. For instance, in QPSK, 2 bits are encoded per symbol, 8PSK provides 3bits of information per symbol, 4QAM allows 2bits of information per symbol, and so on. However, increasing data rates reduces robustness to noise and is required a higher signal-to-noise ratio (SNR) at the receiver for achieving a certain BER [8].
Compared to other silicon-based modulators, the carrier-injection-based p-i-n modulator provides more significant variations in refraction index and high modulation depths in micro and nano-scale devices. Nevertheless, carrier injection modulators are comparatively slow because of the slow carrier recombination process. On the other hand, carrier depletion based modulators have a relatively faster operational speed [25,36].
Further analyzing the electro-optic (EO) effect in MRR, optical 16QAM modulator transmitting at 112 Gbit/s. The device has an extinction ratio (ER) of > 26 dB, but its insertion loss is relatively high-30 dB. 8PSK, on the other hand, is another choice that can withstand nonlinear effects and has a mild implementation complexity [37,38], allowing for more demodulation versatility [20,39]. In the past, 8PSK was generated by using quad-parallel MZM to combine four BPSK signals [37]. Using the series arrangement of IQ modulator with dual-drive MZM was recently demonstrated, which allowed achieving higher-order modulation formats [40][41][42].
In our previous work, we have designed an optical 8PSK modulator employing four silicon micro ring modulators by cascading serially balanced and unbalanced QPSK in I-Q configuration, 8PSK is demonstrated [43]. The input field is passed through two serially cascaded IQ modulators, each having an upper arm and lower arm are splitted using 50/50 power splitters to adjust the amplitude levels of different 8PSK symbols. By adding an 8dB loss in Q-arm of one of the IQ modulator, the un-balanced 8PSK modulator was developed. The constellation at the output demonstrates that design was capable of producing 8PSK modulation efficiently. The flaw in the design was using 4 MRMs and one of the ports was also not utilized. In this paper, we have used minimal number of MRMs to generate 8PSK modulation thereby decreasing the device footprint also eradicate the unused MRM in our previous work.
2 Working principle

Microring modulator
An MRR usually is made of a straight waveguide coupled to a ring waveguide. A section of the incident light couples into the ring, travels through the entire length of the ring and interferes with the incident light. Resonance occurs if the optical length of the ring matches precisely with the integer multiple of the guided wavelength. Figure 1 shows a typical microring resonator structure.

Fig. 1 Typical single microring resonator
The interaction of light in a ring resonator can be explained by matrix relation [44]: Where, E i1 and E t1 are the fields at input and through port respectively, whereas E i2 are E t2 are the incoming and outgoing fields inside the ring. κ and t are the coupler parameters, and κ * and t * denotes the complex conjugate of κ and t, respectively.
Transmission power in the output waveguide is given by [44], The phase change of the coupled light after a roundtrip inside the ring waveguide is given by [44]: Where α = ring loss co-efficient, ϕ t is the phase introduced while coupling, ω = angular frequency, L = circumference of ring waveguide, c = c o /n ef f = phase velocity of the ring mode, c o = speed of light in vacuum, n ef f = effective refractive index of the waveguide, R = radius of the ring, λ being the operating wavelength.
From equation 3, we can observe that MRR can be modulated by changing the ring's optical length or effective length, which varies with the refractive index. Silicon microring modulators work on the plasma dispersion effect, in which change in the real and imaginary part of the refractive index is achieved by changing the concentration of free charge carriers. Other effects such as Franz-Keldysh, Kerr effect, and Pockels effect are negligible in silicon modulators and therefore are not used. Soref and Benett evaluated the expressions for change in refractive index [32]: Where, ∆n and ∆α are the change in refractive index and change in absorption coefficient, respectively. ∆N e and ∆N h are the numbers of free electrons and holes, respectively. In practice, modulators using absorption co-efficient are not commonly used.
Change in bias voltage across the MRM varies the charge density and refractive index, which changes the effective length of the ring. Tuning the laser properly, π phase shift can be achieved with a fixed amplitude producing a BPSK signal. The phase shift introduced by changing the effective length can be used to map '0' and '1'. For an MRM phase modulator, a phase difference of π is ensured between the two bits keeping the amplitude constant. [45]. Similar structures have already been fabricated [24,20].  The second section, which is at point D and consists of MRM3, basically acts as an angle modulator and it shifts the incoming optical signal by an angle +22.5 o when the input bit to the MRM3 is '1' and when the input bit is '0' it shifts the signal by -22.5 o . So there is a total of 45 o phase difference between bit '0' and '1' in the angle modulator MRM3. Figure 4 shows the constellation points for bit '0' and bit '1' after passing through MRM3. Thus we get an 8PSK modulated signal at point E shown in figure 5  3 Performance analysis of the proposed 8PSK modulator

8PSK modulator design
In the transmitter side, the NRZ data (I 1 , Q 1 , I 1 , Q 1 ) are fed at 2.5Gbaud with 2 10 − 1 pseudo-random bit sequence (PRBS) signal. Observing figure  6, the transfer functions of MRM1 and MRM2 shows the wavelength shift required to obtain a π phase difference, and for MRM3, (π/4) phase shift is obtained. Simulations are carried out under back to back condition (B2B) and also for 20km and 50km. An erbium-doped fiber amplifier (EDFA) amplifies the signal; in other words, it increases OSNR and adds ASE noise into the system. An optical bandpass filter (OBPF) having a bandwidth of 6.25 GHz is placed at the receiver end. To demodulate the signal, an optical hybrid and a local oscillator (LO) are used at the receiver. Subsequently, the constellation diagrams, eye diagrams, and spectral bandwidth shown in subfigures I,II and III of figure 7 are obtained for B2B condition, 20km and 50km length of the fiber. BER as a function of OSNR is depicted in figure 8 and 10 −3 BER is obtained at around 13.5dB OSNR.

Conclusion
An 8PSK modulator using three MRMs has been proposed and simulations were carried out for B2B condition and at fiber spans of 20km and 50km, subsequently eye diagrams are also obtained. The required OSNR at 10 −3 8 Satyabrata Singha a et al.