Porous silicon based all-optical modulator using asymmetrical Mach–Zehnder interferometer configuration

Optics Communications 338 (2015) 246–252

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Optics Communications journal homepage: www.elsevier.com/locate/optcom

Porous silicon based all-optical modulator using asymmetrical Mach–Zehnder interferometer configuration Lei Xiao a, Jian-Wei Wu a,b,n a b

College of Physics and Electronic Engineering, Chongqing Normal University, Chongqing 401331, PR China State Laboratory of Information Photonics and Optical Communications, Beijing University of Posts and Telecommunications, Beijing 100876, PR China

art ic l e i nf o

a b s t r a c t

Article history: Received 5 August 2014 Received in revised form 5 October 2014 Accepted 25 October 2014 Available online 31 October 2014

In this paper, nonlinear porous silicon based all-optical modulator is proposed and investigated by utilizing an asymmetrical Mach–Zehnder Interferometer (MZI) configuration consisted of two couplers with equal splitting ratio, and two unbalance arms, in which a porous silicon (PS) waveguide as the nonlinear element is only placed in one arm of MZI, and another arm is short fiber delay line. Results show that both a pulsed pump and continuous probe wave are simultaneously launched into the input port with the result that an outcome signal with
14.10 dB modulation depth at probe wavelength is obtained at the end of the device under the conditions of an initial pulsed pump with 47.07 dB m peak, 10.88 extinction ratio and 100 ps duration, continuous probe wave of 0 dB m power, and 3-mm long PS waveguide. Extinction ratio and eye opening ratio of eye diagram are observed for various operation speeds. & Elsevier B.V. All rights reserved.

Keywords: Nonlinear optics Porous silicon waveguide All-optical modulation

1. Introduction It is well-known that silicon photonics has been attracted much attention and intensively researched in integrated optic technologies which should be attributed to some high nonlinear effects in silicon material [1,2]. In the previous reports, one can see that silicon waveguide with a very high refractive index is surrounded by silica with the result that the transmission light is strongly limited in the waveguide region, at which a high optical intensity can be obtained at an introduced low power level. As a consequence, optical intensity related nonlinear processes including self-phase modulation (SPM), cross-phase modulation (XPM), two-photon absorption (TPA), free-carrier absorption (FCA), freecarrier dispersion (FCD), and so on, become very significant in silicon material, which can be extensively applied to perform various optical functions such as laser [3,4], modulation [5–7], wavelength conversion [8–10], signal generation [11–13], switching [14–16], amplification [17], filter [18], slow light [19,20], and soliton compression [21], etc. Compared with the conventional silicon-on-insulator waveguide, one should be noted that freecarrier related FCA and FCD in porous silicon (PS) waveguide are significantly faster, and stronger than those in crystalline silicon [22]. Here, the referred faster free-carrier lifetime should be explained by the much higher surface recombination rate as a n Corresponding author at: College of Physics and Electronic Engineering, Chongqing Normal University, Chongqing 401331, PR China E-mail address: [email protected] (J.-W. Wu).

http://dx.doi.org/10.1016/j.optcom.2014.10.057 0030-4018/& Elsevier B.V. All rights reserved.

developed surface and much faster Auger recombination lifetime. FCA cross section for PS is approximate two orders of magnitude larger than that in crystalline silicon resulting from higher collision frequency due to the lower mobility of the heavily doped PS skeleton [23]. The FCD efficient is also remarkably enhanced in comparison with that in crystalline silicon with the result that the propagation wave will obtain strong additional time-dependent phase to cause the large blue shift of spectrum in the case of a high input intensity level. In addition, both nonlinear TPA and Kerr coefficient are slightly lower than those in crystalline silicon-on insulator (SOI) waveguide by judiciously fabricate the PS waveguide. Based on these mentioned nonlinear effects, it is obvious that porous silicon technology may offer an interesting alternative to SOI structure, which has some potential applications for alloptical signal process that should exhibit significant behaviors owing to the faster carrier lifetime and enhanced free-carrier related effects. To date, it is regretful that porous silicon based devices have not been extensively explored and presented in the telecommunications wavelength regime. In this study, to further explore potential functions of PS waveguide, an asymmetrical Mach–Zehnder interferometer (MZI) device with porous silicon waveguide as a phase shift element is timely presented for performing an all-optical modulation behavior in which both phase and amplitude in continuous probe wave are modulated by the presence of another pulsed pump beam with enough high peak intensity along the porous silicon waveguide with the result that the outcome signal with high modulation depth can be achieved at the end of the MZI device. Undoubtedly, optical modulation have thoroughly discussed and researched based on other

L. Xiao, J.-W. Wu / Optics Communications 338 (2015) 246–252

semiconductor media and designed structure in which semiconductor laser and semiconductor optical amplifiers (SOA) are often adopted in modulation technologies [24,25]. Of course, through the investigation in this work, semiconductor waveguide based modulation technologies are further flourished. The paper is organized as follows. Section 2 presents the designed diagram. A theoretical model for porous silicon waveguide is given in Section 3. Numerical result are presented and discussed in Section 4. Section 5 summarizes the main results and concludes this work.

2. Device and principle Fig. 1 depicts the schematic structure of the proposed asymmetrical MZI for performing optical modulation. One arm contains the porous silicon waveguide for phase shift of probe wave, and another arm is fiber delay line. In numerical simulation, pumpprobe configuration is adopted, and both a pulsed pump and continuous probe wave are simultaneously launched into the MZI device through a coupler with equal splitting ratio. And then, the signal component with a half power level of injected waves passes through the porous silicon waveguide, where both amplitude and phase in probe wave are effectively controlled by the pulsed pump wave with enough high peak by means of nonlinear processes including SPM, XPM, TPA, FCA, and FCD. The remained optical power directly transmits along another fiber arm that is very short so that nonlinear interaction between two waves is ignored in the delay line, in which no other additional phase shift is concerned for probe wave. As a result, there is obvious phase difference between two probe waves that experience various arms in MZI with the result that they will produce significant interference when they are recombined through output coupler with equal splitting ratio. Finally, modulation signal with high modulation depth can be achieved at the end of setup by judiciously adjusting the initial pump peak intensity. In addition, note that the characteristics of pulsed pump wave such as peak intensity, and pulse duration will also influence the modulation behavior.

3. Theoretical model in porous silicon waveguide In order to simulate modulation behavior, while two optical waves are co-propagating along the PS waveguide, their interaction process can be modeled by the nonlinear coupled equations that are given by [22,26,27]

∂A p ∂z −

=−

247

⎛ 2 2 1 1 β T ⎛⎜ 2⎞ 2⎞ α p A p + i ⎜γpp A p + 2γpc A c ⎟ A p − A p + 2 Ac ⎟ A p ⎝ ⎠ ⎠ 2 2 A eff ⎝

1 2π σ FCA NA p − i k FCD NA p 2 λp

⎛ ∂A c 1 = − α c A c + i ⎜γcc A c ⎝ ∂z 2

2

(1)

+ 2γcp A p

2⎞

⎟ Ac

⎠

−

1 β T ⎛⎜ Ac 2 A eff ⎝

2

+ 2 Ap

2⎞

⎟ Ac

⎠

1 2π − σ FCA NA c − i k FCD NA c λc 2

(2)

where the group velocity dispersion coefficients in the equations are ignored because the adopted waveguide effective length in the simulation is shorter than the estimated dispersion length. The subscript p and c represent the pulsed pump wave and continuous probe wave, respectively. A is the slowly varying envelope, z is the waveguide length, α is linear attenuation coefficient, γ is the Kerr effect related nonlinear parameter denoted by 2πn2/(λAeff) with n2 being the Kerr coefficient, λ the central wavelength of transmission wave, Aeff the effective area of TE mode. βT is the two-photon absorption coefficient, and sFCA is the free-carrier absorption cross section, kFCD is the free-carrier dispersion coefficient, and N is the free-carrier density of excess holes and electrons induced by TPA and cross-TPA in porous silicon media. Strictly, parameters values including effective area, linear and nonlinear coefficients are different from each other for various wavelengths. However, the difference is very small that can be ignored in this study in which these corresponding parameters are, respectively, equal at pump and probe central wavelength. The time-dependent free-carrier density can be described by the rate equation 2 ⎛ ⎛ 2 ⎞2 2⎞ βT ⎜ A p ⎟ βT ⎛⎜ A c 2 ⎞⎟ βT ⎜ A p ⎟ ⎛⎜ A c 2 ⎞⎟ dN = + + ⋅ ⎜ ⎟ ⎜ 2hν p ⎜ A eff ⎟ 2hνc ⎜⎝ A eff ⎟⎠ dt hν p ⎜ A eff ⎟⎟ ⎜⎝ A eff ⎟⎠ ⎝ ⎝ ⎠ ⎠

+

⎛ 2⎞ βT ⎜ A p ⎟ ⎛⎜ A c 2 ⎞⎟ N ⋅ − hνc ⎜⎜ A eff ⎟⎟ ⎜⎝ A eff ⎟⎠ τ ⎝ ⎠

(3)

where t is the time, |A|2/Aeff stands for the optical intensity, hv is the photon energy, and τ is the free-carrier lifetime. To observe optical waves' dynamic behaviors, Eqs. (1)–(3) are simultaneously solved by numerical method with the result that N (z, t) and A(z, t) can be determined for any distance and time in the waveguide. In practice, the peak power of pump wave is higher than that of probe wave so that the generated free-carrier is mainly dominated by the pump related TPA and cross-TPA in this work. The parameters for simulation are given in the following Table 1, in which the corresponding parameters for crystalline silicon waveguide are also shown to compare the simulation results.

Table 1 Parameters used in simulations.

Pump wave

Porous silicon waveguide Modulated output signal

Probe wave Fiber delay line Fig. 1. The schematic of proposed MZI device for all-optical modulation.

Parameter Value for SOI waveguide [22, 27]

Value for PS waveguide [22]

(Unit)

Aeff βT n2 sFCA kFCD τ α

19.3 0.8 2.3  10  14 100  10  17 90  10  21 0.2 9

(μm2) (cm/GW) (cm2/W) (cm2) (cm3) (ns) (dB/cm)

19.3 1.0 3.5  10  14 1.45  10  17 1.35  10  21 1.1 5

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4. Results and discussion

1

1.2

Normalized intensity

1 0.8 0.6 0.4 0.2 0 -10

-5

0 T/T0

5

10

Fig. 2. Output modulation signals from PS waveguide (black dotted line), the MZI configuration with PS waveguide (blue solid line), and MZI configuration with crystalline silicon waveguide (red dashed line). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

0.8

Phase difference Δφ/π

Nonlinear processes including TPA, cross-TPA, and free-carrier related effects play dominated role to perform the all-optical modulation in porous silicon material. TPA (cross-TPA) that is occurred for the case at which the sum of the energies of two photons bridges the band-gap energy in silicon is the direct result of causing excess free-carrier such as electrons and holes which will produce the influences of FCA and FCD on the optical waves in the waveguide. To compare the modulation behaviors between crystalline SOI waveguide and porous silicon waveguide, the various output modulation signals from PS waveguide, PS-based MZI setup, and crystalline SOI-based MZI setup are plotted with black dotted line, blue solid line, and red dashed line, respectively, in Fig. 2, in which a free-chirp pulsed pump wave that has Gaussian energy distribution, 10.88 dB extinction ratio, and 47.07 dB m peak is adopted, whose time duration (T0) of half width at 1/e intensity point is 100 ps without considering the pedestal energy. The probe wave power is fixed at 0 dB m in simulation. It is well-known that the temporal response and modulation depth (¼ 10log 10[Imax/Imin], Imax (Imin) is the maximum (minimum) intensity) of modulation signal are very important parameters to evaluate the modulation performance. As can be seen from Fig. 2, the achieved modulation signal from PS waveguide has about 3.57 dB modulation depth that is strictly limited for more potential applications. In addition, the shown impulse has an inverted response relative to the pump wave as a result of cross-TPA depletion that denotes the absorbed two photons at pump and probe beam, respectively. Another phenomenon shown in the modulated time response is that there is a slow recovery due to the carrier recombination effect. By contrast, as can be seen in Fig. 2, a surprising result is that the focused modulation depth (blue solid line) is significantly improved using the presented MZI setup, which is as high as
14.10 dB that is very high compared to some previous reports. By numerical analysis, one finds that the enhanced modulation depth should be attributed to interference effect between recombined two probe waves. In Fig. 1, one can know that the phase in probe wave is remarkably changed along the high nonlinear porous silicon waveguide by the co-propagating pump wave with high intensity that produces strong TPA and

0.6

0.4

0.2

0 -10

-5

0

5

10

T/T0 Fig. 3. Phase difference of output probe waves from two arms of MZI.

free-carrier related effects such as FCA, and FCD. However, the corresponding phase change is ignored while probe wave transmits through the short fiber delay line. As a consequence, the concerned phase difference is shown in Fig. 3, whose maximum value is close to π that can cause the sufficient destructive interference with the result that the outcome modulation depth at probe wave shown in Fig. 2 is effectively improved. On the other hand, after the PS waveguide in MZI setup is replaced by the crystalline SOI waveguide, the amplitude of outcome signal illustrated with red dashed line in Fig. 2 is slightly modulated resulting from reduced free-carrier related effects including FCA, and FCD shown in Table 1. Here, the input power levels for pump wave and probe wave are identical to case of PS waveguide. In addition, an issue should be pointed out that the coupling loss is ignored in simulation for simplicity. Finally, one can conclude that the significant phase shift on probe wave should mainly be attributed to the enhanced FCA and FCD in PS waveguide shown in Table 1. In the operation mechanism, it is obvious that the properties of pulsed pump wave including intensity and time duration have remarkable influence on the modulation depth of outcome signal at probe wave. These behaviors are discussed in detail using PS-based MZI structure in the following presentation. Modulation depths of output signals from PS waveguide and MZI setup with various input pump peak are, respectively, shown in Fig. 4(a), in which the input pump width T0 is still 100 ps. In the case of low input pump intensity (e.g. o43 dB m), both of modulation depths are very shallow, which have no obvious difference resulting from weak TPA and free-carrier related effect in PS waveguide. Nevertheless, with the increase of input pump intensity, the nonlinear processes including TPA, cross-TPA, FCA, and FCD are gradually enhanced, which lead to the further enhanced modulation depth. However, the modulation depth of output outcome signal from MZI configuration is significantly improved owing to the enhanced destructive interference effect as a result of increased phase difference shown in Fig. 4(b), which is remarkably higher than that of output signal from PS waveguide. While the input pump wave is increased to
47 dB m, the outcome modulation depth reaches maximum that is as high as
14.79 dB. At this time, it implies that there is phase difference of around π, leading to a sufficient destructive interference. It should be noted that the modulation depth begins to decay as the pump intensity overruns the value of
49 dB m. This is because the further enhanced phase difference (4 π) will cause the oscillation

15

249

a

10 5 0

2.5

b

2 1.5 1 0.5

39

41

43 45 47 Input peak power (dBm)

49

51

Phase difference Δφ/π

Modulation depth (dB)

L. Xiao, J.-W. Wu / Optics Communications 338 (2015) 246–252

0

Fig. 4. (a) Modulation depth from PS waveguide (red line with circle mark) and MZI setup (blue line with square mark), and (b) maximum phase difference (green line with triangle mark) against input pump peak power. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

51 0.9

Input peak power (dBm)

49

0.8 0.7

47

0.6

45

0.5 0.4

43

0.3 0.2

41

0.1

39 -10

-5

0

5

10

T/T0 Fig. 5. Modulation signal evolution as a function of input pump peak. (For well observing the evolution in this figure, the reader is referred to the web version of this article.)

500

T (ps)

400 300 200 100 0

40

41

42

43 44 45 46 Input peak power (dBm)

47

48

Fig. 6. Rising time (green line with square mark) and falling time (blue line with circle mark) via input pump peak. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

structure of modulation signal that can be seen in Fig. 5, where it is clearly shown that the time duration of outcome signal is extended as a result of the enhanced nonlinear absorption in the case of high pump intensity. Therefore, to obtain high quality modulation signal in this work, the pump peak intensity launched into MZI setup should be judiciously controlled to achieve
π phase difference between recombined two probe waves. In reality, it is important to observe the response time (rising time and falling time) of modulation signal to evaluate the modulation performance, which is illustrated in Fig. 6, where the falling time is remarkably faster than the rising time. The behavior is explained that slow rising time is due to free carrier recovery, and fast falling time is attributed to TPA process. With the increase of input pump peak, response time has slight change. In the case of a fixed input pump peak of
51 dB m, the influence of pump duration (T0) on the modulation depth of outcome signal at the probe wave is plotted in Fig. 7(a), in which one can see that the modulation depth is sub-linearly increased as pump duration is extended from 0.03 ns to
0.2 ns that is comparable with the carrier lifetime. Additionally, the generated free carrier is proportional to the total optical energy that is gradually enhanced with increase of pulse width so that various nonlinear processes are also remarkably enhanced leading to an improved modulation performance. It is obvious that the corresponding phase difference shown in Fig. 7(b) approaches also gradually to
π. However, as the pulse width is further broadened, all of parameters illustrated in Fig. 7 trend to stable values because the adopted time duration is longer than 0.2 ns free-carrier lifetime in material with the result that the PS waveguide has a dynamic stable state in this case. Another behavior depicted in Fig. 8 is that time duration of modulation signal is proportional to pulse width of initial pump pulse. In addition, the response time including rising time and falling time is plotted as a function of pulse width in Fig. 9, which is monotonically increased when the pump width varies from 0.03 ns to 5 ns. This is because pump pulse has long edges in the case of large duration time comparing to those of short duration pulse. Another noticeable issue shown in Fig. 9 is that falling time is significantly faster than rising time for short pump duration resulting from free-carrier recovery. But, the difference between rising and falling time is very small due to the carrier dynamic stable in the case of large pump duration that is remarkably longer than the free-carrier lifetime.

250

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a

12 8 4 0

1.2

b

1 0.8 0.6 0.4 -2

-1

10

0

10

Phase difference Δφ/π

Modulation depth (dB)

16

1

10

10

T0 (ns) Fig. 7. (a) Modulation depth from PS waveguide (red line with circle mark) and MZI setup (blue line with square mark), and (b) maximum phase difference (green line with triangle mark) against pump duration (T0) with
42.81 dB m initial pump peak intensity. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

2

1

1

10

0.8

1.5

0.7

0

10

0.6 0.5

1

0.4 0.3 0.5

T (ns)

Input pump duration (ns)

0.9

-1

10

0.2 0.1

0.1 -5

-4

-3

-2

-1

0 1 T (ns)

2

3

4

5

-2

10

Fig. 8. Modulation signal evolution as a function of input pump duration. (For well observing the evolution in this figure, the reader is referred to the web version of this article.)

The eye diagram of achieved modulation signal is depicted in Fig. 10, in which the operation speed is 1 Gb/s, 2.5 Gb/s, and 5 Gb/s, respectively, and pseudorandom bit sequence (PRBS) nonreturnto-zero (NRZ) data is used for input pump stream with square shape. In order to evaluate the quality of eye diagram, extinction ratio (X) and eye opening ratio (O) are defined by [9]

⎛ I1 ⎞ avg X ≡ 10 log 10 ⎜⎜ 0 ⎟⎟ ⎝ Iavg ⎠

O≡

(4)

1 0 Imin − Imax 1 0 Iavg − Iavg

where

1 Iavg

0 (Iavg )

(5) is average intensity level of “1” logic (“0” logic),

0 1 is minimum intensity level of “1” logic, Imax is maximum inImin tensity level of “0” logic.

-2

10

-1

0

10

10

1

10

T0 (ns) Fig. 9. Rising time (green line with square mark) and falling time (blue line with circle mark) against input pump duration. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

As can be seen in Fig. 10, the extinction ratio is
13.51 dB, and eye opening ratio is as high as
0.99 in the case of 1 Gb/s operation speed. These positive behaviors are because the one bit pump signal duration is remarkably longer than free-carrier lifetime. On the other hand, due to free-carrier effect, both extinction ratio and eye opening ratio are gradually decayed with increase of operation speed, which are, respectively, reduced to
13.20 dB and
0.95 with 2.5 Gb/s data rate. It is obvious that, while one bit signal duration of pump beam is further shortened, the quality of eye diagram is quickly decayed, e.g. extinction ratio of
10.63 and eye opening ratio of
0.76 are achieved in the case of 5 Gb/s. Here, one noticeable issue is that the effective modulation signal (clear eye opening) cannot be obtained for high operation rate because limitation of 0.2 ns free-carrier lifetime. Therefore, to further

251

Normalized intensity

L. Xiao, J.-W. Wu / Optics Communications 338 (2015) 246–252

Normalized intensity

Normalized intensity

100 ps/div

40 ps/div

20 ps/div

Fig. 10. Eye diagram for various operation speed, (a) 1 Gb/s, (b) 2.5 Gb/s, (c) 5 Gb/s.

improve the modulation speed, reduction in free-carrier lifetime is an effective technology.

5. Conclusions All-optical modulation technology with high modulation depth is performed based on a porous silicon based asymmetrical Mach– Zehnder interferometer consisted of two couplers with equal splitting ratio, a nonlinear arm with PS waveguide and fiber delay arm. The operation speed is significantly increased owing to the short carrier recovery time in PS material compared to conventional crystalline SOI waveguide. Modulation depth of more than 10 dB and clear eye opening ratio can be obtained by properly changing the pulsed pump peak intensity and duration. Undoubtedly, Compared to previous reports, the presented setup in this work has obvious competition ability in various optical modulation technologies.

Acknowledgments The authors acknowledge support from the National Natural Science Foundation of China (Grant no. 61205111), Scientific and Technological Research Program of Chongqing Municipal Education Commission (Grant no. KJ130633), and Open Fund of State Key Laboratory of Information Photonics and Optical Communications (Beijing University of Posts and Telecommunications).

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