Speed enhancement of all-optical pseudo random binary sequence (PRBS) generator using microring resonator

Abstract

In the present communication, we have designed and simulated an all-optical Pseudo Random Binary Sequence (PRBS) generator using a suitable multiplexing technique that exploits the PRBS decimation and shift-and-add properties for doubling the PRBS speed at a rate of 500 Gb/s without increasing the synchronization frequency of the generator. The PRBS generator comprises of serially connected D flip-flops realized with double waveguide-coupled optical microring resonator (OMRR)-based switches in a pump-probe configuration, OMRR-based 2-input XOR gates for feedback and for creating the necessary PRBS phase-shifted replicas, and OMRR-based 2:1 multiplexer. The expected PRBS doubled speed operation is theoretically validated for 4-bit and 5-bit degree PRBS generator and can be extended in a straightforward manner for any rate multiplication factor or PRBS order with extra OMRR-based D flip-flops and OMRR-based XOR gates as per the desired characteristic polynomial order. The OMRR critical parameters, including radius and coupling coefficient, are optimized against performance metrics through numerical simulation. The selection of these parameters according to the derived specifications could render feasible the practical implementation of the scheme and its exploitation for all-optical signal processing purposes at ultrafast data rates.

Appendix A: Detailed calculation of MRR Through port and Drop port output electric fields

From Fig. 6 of Sect. 4, the electric fields E_ra, E_rb, E_rc, E_rd at the point a, b, c and d can be written as

$$E_{ra} = \left( {1 - \gamma } \right)^{1/2} \left[ {j\sqrt {k_{1} } \times E_{i1} + \sqrt {\left( {1 - k_{1} } \right)} \times E_{rd } } \right]$$

(4)

$$E_{rb} = E_{ra} \times \exp \left( { - \propto \times \frac{L}{4}} \right) \times \exp \left( {jk_{n} \times \frac{L}{2}} \right)$$

(5)

$$E_{rc} = \left( {1 - \gamma } \right)^{1/2} \left[ {j\sqrt {k_{2} } \times E_{i2} + \sqrt {\left( {1 - k_{2} } \right)} \times E_{rb} } \right]$$

(6)

$$E_{rd} = E_{rc} \times \exp \left( { - \propto \times \frac{L}{4}} \right) \times \exp \left( {jk_{n} \times \frac{L}{2}} \right)$$

(7)

From Fig. 6, the electric fields at the Through port and Drop port can be written as

$$E_{t} = \left( {1 - \gamma } \right)^{1/2} \left[ {\sqrt {\left( {1 - k_{1} } \right)} \times E_{i1} + j\sqrt {\left( {k_{1} } \right)} \times E_{rd} } \right]$$

(8)

$$E_{d} = \left( {1 - \gamma } \right)^{1/2} \left[ {\sqrt {\left( {1 - k_{2} } \right)} \times E_{i2} + j\sqrt {\left( {k_{2} } \right)} \times E_{rb} } \right]$$

(9)

Replacing E_rd from Eq. (7) in Eq. (4) we get

$$E_{ra} = jD\sqrt {k_{1} } .E_{i1} + \sqrt {\left( {1 - k_{1} } \right).} x.{\text{exp}}\left( {j\varphi } \right).E_{rc}$$

(10)

where,$D = (1 - \gamma )^{1/2}$, $x = D \times \exp \left( { - \alpha \frac{L}{4}} \right)$, $\phi = \frac{{k_{n} .L}}{2}$.

Similarly replacing E_rb from Eq. (5) in Eq. (6) we get

$$E_{rc} = jD\sqrt {k_{2} } \times E_{i2} + \sqrt {\left( {1 - k_{2} } \right)} \times x \times \exp \left( {j\varphi } \right) \times E_{ra}$$

(11)

Replacing E_rc from Eq. (11) in Eq. (10) we get

$$E_{ra} = jD\sqrt {k_{1} } \times E_{i1} + \sqrt {\left( {1 - k_{1} } \right)} \times x \times \exp \left( {j\varphi } \right) \times \left( {jD\sqrt {k_{2} } \times E_{i2} + \sqrt {\left( {1 - k_{2} } \right)} \times x \times \exp \left( {j\varphi } \right) \times E_{ra} } \right)$$

(12)

or in compact form,

$$E_{ra} = \frac{{jD\sqrt {k_{1} } E_{i1} + jD\sqrt {k_{2} } \sqrt {1 - k_{1} } x\exp (j\varphi )E_{i2} }}{{1 - \sqrt {1 - k_{1} } \sqrt {1 - k_{2} } x^{2} \exp^{2} (j\varphi )}}$$

(13)

Similarly, replacing E_ra from Eq. (10) in Eq. (11) we getor in compact form,

$$E_{rc} = jD\sqrt {k_{2} } \times E_{i2} + \sqrt {\left( {1 - k_{2} } \right)} \times x \times \exp \left( {j\varphi } \right) \times \left( {jD \times E_{i1} + \sqrt {\left( {1 - k_{1} } \right)} \times x \times {\text{exp}}\left( {j\varphi } \right) \times E_{rc} } \right)$$

$$E_{rc} = \frac{{jD\sqrt {k_{2} } E_{i2} + jD\sqrt {k_{1} } \sqrt {1 - k_{2} } x\exp (j\varphi )E_{i1} }}{{1 - \sqrt {1 - k_{1} } \sqrt {1 - k_{2} } x^{2} \exp^{2} (j\varphi )}}$$

(14)

Using Eq. (7), Eq. (8) can be written as

$$E_{t} = D\sqrt {\left( {1 - k_{1} } \right)} \times E_{i1} + j\sqrt {k_{1} } \times x \times \exp \left( {j\varphi } \right) \times E_{rc}$$

(15)

Replacing E_rc from Eq. (15) in Eq. (17) we have

$$E_{t} = D\sqrt {\left( {1 - k_{1} } \right)} \times E_{i1} + j\sqrt {k_{1} } \times x \times \exp \left( {j\varphi } \right) \times \left( {\frac{{jD\sqrt {k_{2} } E_{i2} + jD\sqrt {k_{1} } \sqrt {1 - k_{2} x\exp (j\phi )E_{i1} } }}{{1 - \sqrt {1 - k_{1} } \sqrt {1 - k_{2} } x^{2} \exp^{2} (j\phi )}}} \right)$$

or,or,

$$E_{t} = D\sqrt {1 - k_{1} } .E{}_{i1} + \frac{{ - Dk_{1} \sqrt {1 - k_{1} } x^{2} \exp^{2} (j\phi )}}{{1 - \sqrt {1 - k_{1} } \sqrt {1 - k_{2} x^{2} \exp^{2} (j\phi )} }}E_{i1} + \frac{{ - D\sqrt {k_{1} } \sqrt {k_{2} } x.\exp (j\phi )}}{{1 - \sqrt {1 - k_{1} } \sqrt {1 - k_{2} x^{2} \exp^{2} (j\phi )} }}E_{i2}$$

$$E_{t} = \frac{{D\sqrt {1 - k_{1} } - D\sqrt {1 - k_{2} } x^{2} \exp^{2} (j\varphi )}}{{1 - \sqrt {1 - k_{1} } \sqrt {1 - k_{2} } x^{2} \exp^{2} (j\varphi )}}E_{i1} + \frac{{ - D\sqrt {k_{1} } \sqrt {k_{2} } x\exp (j\varphi )}}{{1 - \sqrt {1 - k_{1} } \sqrt {1 - k_{2} } x^{2} \exp^{2} (j\phi )}}E_{i2}$$

(16)

Using Eq. (5), Eq. (9) can be written as

$$E_{d} = D\sqrt {1 - k_{2} } \times E_{i2} + j\sqrt {k_{2} } \times x \times \exp \left( {j\varphi } \right) \times E_{ra}$$

(17)

Replacing E_ra from Eq. (13) in Eq. (17) we have

$$E_{d} = D\sqrt {1 - k_{2} } \times E_{i2} + j\sqrt {k_{2} } \times x \times \exp \left( {j\varphi } \right) \times \left( {\frac{{jD\sqrt {k_{1} } E_{i1} + jD\sqrt {k_{2} } \sqrt {1 - k_{1} x\exp (j\phi )E_{i2} } }}{{1 - \sqrt {1 - k_{1} } \sqrt {1 - k_{2} } x^{2} \exp^{2} (j\phi )}}} \right)$$

oror

$$E_{d} = D\sqrt {1 - k_{2} } .E{}_{i2} + \frac{{ - Dk_{2} \sqrt {1 - k_{1} } x^{2} \exp^{2} (j\phi )}}{{1 - \sqrt {1 - k_{1} } \sqrt {1 - k_{2} } x^{2} \exp^{2} (j\phi )}}E_{i2} + \frac{{ - D\sqrt {k_{1} } \sqrt {k_{2} } x.\exp (j\phi )}}{{1 - \sqrt {1 - k_{1} } \sqrt {1 - k_{2} } x^{2} \exp^{2} (j\phi )}}E_{i1}$$

$$E_{d} = \frac{{ - D\sqrt {k_{1} } \sqrt {k_{2} } x.\exp (j\phi )}}{{1 - \sqrt {1 - k_{1} } \sqrt {1 - k_{2} } x^{2} \exp^{2} (j\phi )}}E_{i1} + \frac{{D\sqrt {1 - k_{2} } - D\sqrt {1 - k_{1} } x^{2} \exp^{2} (j\phi )}}{{1 - \sqrt {1 - k_{1} } \sqrt {1 - k_{2} } x^{2} \exp^{2} (j\phi )}}E_{i2}$$

(18)

Therefore, Eq. (16) and Eq. (18) represent the expressions for the MRR Through port and Drop port output electric fields.