OOK generation based on MZI incorporating a pumped nonlinear ring resonators system

P. P. Yupapin; Chat Teeka

doi:10.1364/OE.18.009891

1. Introduction

Today, most of the optical communication links use the well known modulation format called OOK (On Off Keying) [1–9], which is due to the increasing in bit rates, power and number of DWDM (Dense Wavelength Division Multiplexing) channels, where the OOK format can reach the communication requirement. However, the various modulation schemes have already been used in the electrical domain during last decade, but they have not been applied in optical schemes. Recently the use of new modulation formats in optical communications has been considered and compared for increasing the tolerance of the optical link to impairments such as chromatic dispersion, PMD (Polarization mode dispersion) or nonlinearity (Kerr Effect) [10]. Among the various modulation formats, we present here the differential phase shift keying (DPSK) and the phase shaped binary transmission (PSBT) schemes, whereas DPSK presents a better robustness to optical nonlinearities than the classical OOK, particularly for the cross phase modulation (XPM) in DWDM systems [3,9,11]. Moreover, it has also been shown that DPSK format has better performances due to PMD degradations than the classical OOK [9,11]. The disadvantage of the DPSK is that a direct detection (DD) at the end of the optical link is not possible, since DPSK is a phase modulation. Thus, an interferometric demodulation stage must be inserted in front of the photo-detector. This stage is an “Add and Delay” structure, which is composed by a MZI [9,11–15].

In this paper, we first describe the principles of light propagation in the proposed system, where the nonlinear behavior of light within the nonlinear ring resonators (NRRs) can be used to analyze for PSBT modulation. After that, the MZI structure is detailed. However, the nonlinear ring resonator has been used [16–19] for phase shifted generate by couple to one arm of a MZI [16,17]. In this structure, one arm presents an optical delay line equal to the bit duration. This MZI converts an optical DPSK to an intensity-modulated (IM) signal, which is followed by a DD. The PSBT format is encoded from a DPSK: first a DPSK signal is generated and after that a MZI structure converts the DPSK to be an intensity-modulated signal: the PSBT. MZI characteristics for the two applications are slightly different, as we will see in the next sections. The novelty of this work is that the nonlinear light pulses generated by using the triple nonlinear ring resonators in one arm of a Mach-Zehnder interferometer can be used to enhance(amplify) the light pulse output signals, where the nonlinear outputs are generated by using the nonlinear coefficient refractive index n ₂ = 2.2 × 10⁻¹³ m²/W .

2. Principles of modulation

Figure 1 shows the proposal for on-off keying model using nonlinear index of refraction in three nonlinear ring resonator coupled to one arm of Mach-Zehnder interferometer. In this figure there are similar NRRs with the field-dependent absorption and index of refraction coefficients.

Fig. 1 Schematic diagram of OOK system, system size is 10 × 40µm².

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When the input field, E_in, passes through 3dB coupler with coupling coefficient ratio, κ₁, 50:50, then light is split into two ways, which can be expressed as

E_{11} = \sqrt{1 - γ_{1}} \sqrt{1 - κ_{1}} E_{i n},

E_{21} = j \sqrt{1 - γ_{1}} \sqrt{κ_{1}} E_{i n} .

According to the linear coupling theory, the following relations can connect input-output fields for each nonlinear ring resonators (NRRs) as shown in Fig. 2 , which can be expressed by [17]

E_{R i} = \sqrt{1 - γ_{i}} \sqrt{1 - κ_{i}} E_{L i} + j \sqrt{1 - γ_{i}} \sqrt{κ_{i}} E_{i n_{i}},

E_{t_{i}} = \sqrt{1 - γ_{i}} \sqrt{1 - κ_{i}} E_{i n_{i}} + j \sqrt{1 - γ_{i}} \sqrt{κ_{i}} E_{L i},

where

γ_{i}

and

κ_{i}

are the coupler loss and coupling coefficient in each NRR, respectively. Since the NRR length and the nonlinear index of refraction are small, therefore, the nonlinear Schrodinger equation (NLS) can be used to solve light propagation through the NRRs, the solution is given by [17]

E_{L i} = E_{R i} \exp (- \frac{α}{2} L_{i} - γ_{N L_{i}} {| E_{R i} |}^{2} L_{i}),

where α,

L_{i} = 2 π R_{i}

and

γ_{N L_{i}}

are the NRR loss, NRR length (R_i is ring radius) and the nonlinear coefficient including the nonlinear index of refraction and two-photon absorption phenomenon, respectively. By using the basic concepts in nonlinear optics, the following relation can be used for the above mentioned, the nonlinear coefficient is given by

γ_{N L_{i}} = \frac{β}{2} - j \frac{ω_{0}}{c} n_{2},

where β,

ω_{0}

, C and

n_{2}

are the two-photon absorption coefficient, incident light frequency, speed of light in free space and the nonlinear index of refraction coefficient, respectively. The following relation describes the nonlinear phenomenon in the NRRs as

\begin{array}{l} \tilde{α} = α + β {| E |}^{2}, \\ \tilde{n} = n + n_{2} {| E |}^{2}, \end{array}

where both of the absorption coefficient and index of refraction includes linear and nonlinear parts and the following relations can be used for obtaining these variables in terms of the optical third order susceptibility as

Fig. 2 Schematic diagram of single NRR (i = 2, 3, 4).

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n_{2} = \frac{3}{8 n} Re [χ^{(3)}],

β = \frac{3 ω_{0}}{4 n C} Im [χ^{(3)}] .

Using Eqs. (3)-(5) and some mathematical manipulations, the following transmission functions can be obtained for each NRRs as

T = \frac{E_{t_{i}}}{E_{i n_{i}}} = \sqrt{1 - γ_{i}} \sqrt{1 - κ_{i}} - \frac{κ_{i} (1 - γ_{i}) \exp (- \frac{α}{2} L_{i} - ϕ_{N L_{i}})}{1 - \sqrt{1 - γ_{i}} \sqrt{1 - κ_{i}} \exp (- \frac{α}{2} L_{i} - ϕ_{N L_{i}})},

where

ϕ_{N L_{i}} = γ_{N L_{i}} L_{i} {| E_{R i} |}^{2}

is defined as a nonlinear phase shift.

For the obtained result in Eq. (9), the phase difference (effective phase from single NRR) can be found as follows:

ϕ_{e f f} = ϕ_{i} = \tan^{- 1} [\frac{- κ_{i} (1 - γ_{i}) e^{- 1 / 2 (α + β {| E_{R i} |}^{2}) L_{i}} \times \sin ((ω_{0} / C) n_{2} L_{i} {| E_{R i} |}^{2})}{A + B + D}],

where

A = (2 - κ_{i}) (1 - γ_{i}) e^{- 1 / 2 (α + β {| E_{R i} |}^{2}) L_{i}} \cos ((ω_{0} / C) n_{2} L_{i} {| E_{R i} |}^{2}),

B = \sqrt{(1 - κ_{i}) (1 - γ_{i})}

and

D = (1 - γ_{i}) \sqrt{(1 - κ_{i}) (1 - γ_{i})} e^{- (α + β {| E_{R i} |}^{2}) L_{i}} .

The obtained result can be simplified to the following formula, which is assumed by $γ_{i} = α = β = 0$ .

ϕ_{e f f} = ϕ_{i} = \tan^{- 1} [\frac{- κ_{i} \sin (\frac{ω_{0}}{C} n_{2} L_{i} {| E_{R i} |}^{2})}{2 \sqrt{1 - κ_{i}} - (2 - κ_{i}) \cos (\frac{ω_{0}}{C} n_{2} L_{i} {| E_{R i} |}^{2})}] .

In real system

γ_{i}, α,

and β are not be zero as shown in section 3, α = 0.5dBmm⁻¹, γ = 0.1 and β = 2 × 10⁻¹¹, respectively.

And, the output power at light propagation through the first NRR is given by

\frac{P_{t 1}}{P_{i n}} = {| \frac{E_{t 1}}{E_{i n}} |}^{2} .

The electric field of light propagation through the second NRR is given by

\frac{E_{t 2}}{E_{i n}} = \frac{\sqrt{1 - γ_{1}} \sqrt{1 - γ_{2}} \sqrt{1 - γ_{3}} \sqrt{1 - κ_{1}} (\begin{array}{l} \sqrt{1 - κ_{2}} \sqrt{1 - κ_{3}} \\ - \sqrt{1 - γ_{2}} \sqrt{1 - κ_{3}} e^{- \frac{α}{2} L_{1} - ϕ_{N L, 1}} \\ - \sqrt{1 - γ_{3}} \sqrt{1 - κ_{2}} e^{- \frac{α}{2} L_{2} - ϕ_{N L, 2}} \\ + \sqrt{1 - γ_{2}} \sqrt{1 - γ_{3}} e^{- \frac{α}{2} (L_{1} + L_{2}) - (ϕ_{N L, 1} + ϕ_{N L, 2})} \end{array})}{(\begin{array}{l} 1 + \sqrt{1 - γ_{2}} \sqrt{1 - κ_{2}} e^{- \frac{α}{2} L_{1} - ϕ_{N L, 1}} - \sqrt{1 - γ_{3}} \sqrt{1 - κ_{3}} e^{- \frac{α}{2} L_{2} - ϕ_{N L, 2}} \\ + \sqrt{1 - γ_{2}} \sqrt{1 - γ_{3}} \sqrt{1 - κ_{2}} \sqrt{1 - κ_{3}} e^{- \frac{α}{2} (L_{1} + L_{2}) - (ϕ_{N L, 1} + ϕ_{N L, 2})} \end{array})},

where

\sqrt{1 - γ_{1}}

,

\sqrt{1 - γ_{2}}

,

\sqrt{1 - γ_{3}}

,

\sqrt{1 - γ_{4}}

and

\sqrt{1 - γ_{5}}

are coupler losses in each coupler and

\sqrt{1 - κ_{1}}

,

\sqrt{1 - κ_{2}}

,

\sqrt{1 - κ_{3}}

,

\sqrt{1 - κ_{4}}

and

\sqrt{1 - κ_{5}}

are coupler separates in each coupler, respectively.

The output power of light propagation through the second NRR is given by

\frac{P_{t 2}}{P_{i n}} = {| \frac{E_{t 2}}{E_{i n}} |}^{2} .

The electric field of light propagation through third NRR the relation input-output field is

\frac{E_{t 3}}{E_{i n}} = \frac{\sqrt{1 - γ_{1}} \sqrt{1 - γ_{2}} \sqrt{1 - γ_{3}} \sqrt{1 - γ_{4}} \sqrt{1 - κ_{1}} (\begin{array}{l} \sqrt{1 - κ_{2}} \sqrt{1 - κ_{3}} \sqrt{1 - κ_{4}} \\ - \sqrt{1 - κ_{3}} \sqrt{1 - κ_{4}} e^{- \frac{α}{2} L_{1} - ϕ_{N L, 1}} \\ - \sqrt{1 - κ_{2}} \sqrt{1 - κ_{4}} e^{- \frac{α}{2} L_{2} - ϕ_{N L, 2}} \\ + \sqrt{1 - κ_{4}} e^{- \frac{α}{2} (L_{1} + L_{2}) - (ϕ_{N L, 1} + ϕ_{N L, 2})} \\ - \sqrt{1 - κ_{2}} \sqrt{1 - κ_{3}} e^{- \frac{α}{2} L_{3} - ϕ_{N L, 3}} \\ + \sqrt{1 - κ_{3}} e^{- \frac{α}{2} (L_{1} + L_{3}) - (ϕ_{N L, 1} + ϕ_{N L, 3})} \\ + \sqrt{1 - κ_{2}} e^{- \frac{α}{2} (L_{2} + L_{3}) - (ϕ_{N L, 2} + ϕ_{N L, 3})} \\ + \sqrt{1 - κ_{3}} \sqrt{1 - κ_{4}} e^{- \frac{α}{2} (L_{1} + L_{2} + L_{3}) - (ϕ_{N L, 1} + ϕ_{N L, 2} + ϕ_{N L, 3})} \end{array})}{(\begin{array}{l} 1 + \sqrt{1 - γ_{2}} \sqrt{1 - κ_{2}} e^{- \frac{α}{2} L_{1} - ϕ_{N L, 1}} \\ - \sqrt{1 - γ_{3}} \sqrt{1 - κ_{3}} e^{- \frac{α}{2} L_{2} - ϕ_{N L, 2}} - \sqrt{1 - γ_{4}} \sqrt{1 - κ_{4}} e^{- \frac{α}{2} L_{3} - ϕ_{N L, 3}} \\ + \sqrt{1 - γ_{2}} \sqrt{1 - γ_{3}} \sqrt{1 - κ_{2}} \sqrt{1 - κ_{3}} e^{- \frac{α}{2} (L_{1} + L_{2}) - (ϕ_{N L, 1} + ϕ_{N L, 2})} \\ + \sqrt{1 - γ_{3}} \sqrt{1 - γ_{4}} \sqrt{1 - κ_{3}} \sqrt{1 - κ_{4}} e^{- \frac{α}{2} (L_{2} + L_{3}) - (ϕ_{N L, 2} + ϕ_{N L, 3})} \\ - \sqrt{1 - γ_{2}} \sqrt{1 - γ_{3}} \sqrt{1 - γ_{4}} \sqrt{1 - κ_{2}} {\sqrt{1 - κ}}_{3} \sqrt{1 - κ_{4}} e^{- \frac{α}{2} (L_{1} + L_{2} + L_{3}) - (ϕ_{N L, 1} + ϕ_{N L, 2} + ϕ_{N L, 3})} \end{array})} .

The output power of light propagation through the third NRR is

\frac{P_{t 3}}{P_{i n}} = {| \frac{E_{t 3}}{E_{i n}} |}^{2} .

When light propagation through the second 3dB, upper and lower MZI arms that on-off keying (OOK) or DPSK are controlled the optical pump in each NRR that yield

(\begin{array}{l} E_{o u t_1} (On) \\ E_{o u t_2} (Off) \end{array}) = \sqrt{1 - γ_{5}} (\begin{array}{c} \sqrt{1 - κ_{5}} & j \sqrt{κ_{5}} \\ j \sqrt{κ_{5}} & \sqrt{1 - κ_{5}} \end{array}) (\begin{array}{c} E_{T 3} \\ E_{22} \end{array}) .

For phase shaped binary transmission (PSBT), we generated input light pulse through NRRs that the difference phase shift is equal to π, as shown in Fig. 3 .

Fig. 3 Simulation results of effective phase, where (a) single NRR vs. nonlinear phase (b) triple NRR vs. nonlinear phase. (α = 0.5dBmm⁻¹, γ = 0.1, n₂ = 2.2 × 10⁻¹³ m²/W, n₀ = 3.34, λ = 1.55µm, β = 0)

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In Fig. 3, shows variation of the effective phase due to nonlinear phase ( $ϕ_{N L} = (ω_{0} / C) n_{2} (2 π R_{i}) {| E_{R i} |}^{2}$ ), we assumed that $β = 0$ , realize β is not equal to zero as shown in next section. In this curve the coupling coefficient is changed as parameter and with decrease of the coupling coefficient the slope of variation, we found that the effective phase of all-optical PSBT generation is fasted when the coupling coefficient of NRRs fixed at 0.2. So, with the small coupling coefficients very fast switching on-off power can be obtained and in our case only PSBT is necessary for on-off keying (OOK) in each NRR.

3. OOK Generation

In operation, all-optical OOK generated maximum power of 3mW Gaussian modulated CW is input into the OOK system, as shown in Fig. 1. The suitable NRRs parameters are used, such as NRR radii where R ₁ = 1.5µm, R ₂ = 1.0µm and R ₃ = 0.775µm. In order to make the system associate with the practical device [20,21], the selected parameters of the system are fixed to λ₀ = 1.55µm and 1.31µm, n₀ = 3.34 (GaInAsP/InP waveguide). The effective core areas are A _eff = 0.10 µm² for NRRs. The waveguide and coupling loses are α = 0.5dBmm⁻¹ and γ = 0.1, respectively, and the coupling coefficients κ_i of the NRRs fixed 0.5 and β = 2 × 10⁻¹¹ [17]. As for the numerical simulation of all-optical OOK, PSBT and DPSK, all our numerical work has been carried out by using commercially available simulation software-the OptiFDTD simulation package [22] which is based explicitly on the model described above [23]. However, more parameters are used as shown in Fig. 1. The nonlinear refractive index is n ₂ = 2.2 × 10⁻¹³ m²/W. In this case, the waveguide loss used is 0.5 dBmm⁻¹ and the size of the waveguide desired system is 10 × 40 µm².

In Fig. 4 , we are numerical simulation OOK modulation at the wavelength center λ₀ = 1.31µm with input power 3mW Gaussian CW modulated. All-optical OOK generation that is on-off state occurred within upper (out_1) and lower (out_2) MZI arm, with differences phase shift is equal to π.

Fig. 4 OOK result as generated at wavelength center λ₀ = 1.31µm and input power 3mW.

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In Fig. 5 , we are numerical simulation OOK modulation at the wavelength center λ₀ = 1.55µm with input power 3mW Gaussian CW modulated. All-optical OOK generation that is on-off state occurred within upper (out_1) and lower (out_2) MZI arm, with differences phase shift is equal to π. Output power of out_1 and out_2 numerical simulation OOK generated is faster where compare with generation at λ₀ = 1.31µm and the delay time of on off state is 1.2fs, where the operation of the proposed circuit is transient in time as shown in Fig. 6 .

Fig. 5 OOK result as generated at wavelength center λ₀ = 1.55µm and input power 3mW.

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Fig. 6 Delay time of OOK.

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In Fig. 7 shown OOK generated at wavelength center, λ₀ = 1.55µm and λ₀ = 1.31µm, respectively and we found that the OOK at wavelength 1.55µm is switching faster than 1.31µm, there for, the switching OOK generated at wavelength center 1.55µm that high capacity packet on-off state appearance. The upper limit of the circuit in frequency domain (response) is 3.5THz, which is obtained and shown in Fig. 8 .

Fig. 7 Compare OOK generate at wavelength center, λ₀ = 1.55µm and λ₀ = 1.31µm, respectively.

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Fig. 8 OOK result as generated in frequency domain and input power 3mW.

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4. Discussion and Conclusion

We have demonstrated that the OOK modulation format by using NRRs coupled into one arm of a MZI system could be performed. The solution of the nonlinear Schrödinger equation is $E_{L i} = E_{R i} \exp (- \frac{α}{2} L_{i} - γ_{N L_{i}} {| E_{R i} |}^{2} L_{i})$ , which describes the nonlinear properties in each nonlinear ring resonator by using the term |E_Ri|² that circulates in each NRR. It is used to enhance and amplify the output signals. When the input light pulse is input through a 3dB coupler of a MZI, the coupling power is partially circulated through R₁, where it is circulated and combined with the pump light within R₁. Finally, the output of rings R₂ and R₃ are obtained in the similar manner.

The feasibility of the device by comparison to already fabricated devices with the same radius NRR radii, where R ₁ = 1.5μm, R ₂ = 1.0μm and R ₃ = 0.775μm. this parameter details are given by reference [20]. Our proposed system is the extended system of a Mach–Zehnder interferometer combined with ring resonators. It was fabricated by Rabus [21], where the system size was 700 × 2500 μm². It is larger than the system in this paper where the system size is 10 × 40μm². Moreover, our system is combined with the triple nonlinear ring resonators. Two different results at the center wavelength 1.31µm and 1.55µm are compared, where they are dominated by the nonlinear refractive indices and two-photon absorption coefficients within the NRRs. We found that the OOK generated at 1.55µm is shown the fastest switching, where the delay time of OOK is 1.2fs. We have also presented the principles of MZI operation in PSBT-based systems, where the characterization of useful parameters required for the DPSK demodulation or PSBT encoding. DPSK and PSBT have been highlighted as the suitable modulation formats for optical transmissions. The DPSK modulation format presents the better performance for transmission than the conventional OOK, justifying its utilization. However, the DPSK requires the passive MZIs for interferometric demodulation. In application, the use of DWDM (Dense Wavelength Division Multiplexing) can be employed to obtain the multi-wavelength OOK, which may be available for high capacity packet switching.

Acknowledgement

C. Teeka acknowledges Suan Dusit Rajabhat University, Bangkok, Thailand for granting the Thailand Ph.D. Program at Faculty of Science, King Mongkut’s Institute of Technology Ladkrabang, Bangkok, Thailand.

References and links

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OOK generation based on MZI incorporating a pumped nonlinear ring resonators system

Abstract

1. Introduction

2. Principles of modulation

3. OOK Generation

4. Discussion and Conclusion

Acknowledgement

References and links

Cited By

Figures (8)

Equations (18)

Optics Express