Generation of logic gates based on a photonic crystal fiber Michelson interferometer

Optics Communications 322 (2014) 143–149

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Generation of logic gates based on a photonic crystal fiber Michelson interferometer J.R.R. Sousa a,b,n, A.F.G.F. Filho a, A.C. Ferreira a, G.S. Batista a,b, C.S. Sobrinho a,d, A.M. Bastos a,b, M.L. Lyra c, A.S.B. Sombra a a Laboratório de Telecomunicações e Ciência e Engenharia de Materiais LOCEM, Departamento de Física, Universidade Federal do Ceará, Caixa Postal 6030, Fortaleza 60455-760, Ceará, Brazil b Departamento de Engenharia de Teleinformática (DETI), Centro de Tecnologia, Universidade Federal do Ceará, Fortaleza 60455-760, Ceará, Brazil c Instituto de Física, Universidade Federal de Alagoas, 57072-970 Maceió, Alagoas, Brazil d Departamento de Engenharia de Energias, Instituto de Engenharias e Desenvolvimento Sustentável, Universidade da Integração Internacional da Lusofonia Afro-Brasileira (UNILAB), Redenção, Ceará, Brazil

art ic l e i nf o

a b s t r a c t

Article history: Received 30 November 2013 Received in revised form 4 February 2014 Accepted 5 February 2014 Available online 17 February 2014

We present a numerical investigation of all-optical logical gates based in a Michelson interferometer (MI) of micro structured fibers, also known as photonic crystal fibers (PCF). We considered an ultra-short pulse propagating along the system in three distinct regimes of pump power. We determine several relevant quantities to characterize the system performance such as transmission, extinction ratio and crosstalk as a function of the dephasing added to one of the Bragg gratings of the Michelson interferometer (MI). High-order effects, such as third-order dispersion, intrapulse Raman scattering and self-steepening were included in the nonlinear generalized Schrödinger equation governing the pulse propagation. Our results show that the proposed device can be used to obtain all-optical XOR, OR and NOT logic gates. & 2014 Elsevier B.V. All rights reserved.

Keywords: Michelson interferometer Photonic crystal fiber Coupler Nonlinear Logic gates

1. Introduction In the last few decades, the scenario of photonics has experienced substantial progresses, both in basic research and in the development of new devices. The future of photonic networks will require ultrafast all-optical switches and logic gates not only to perform high speed signal processing but also to overcome the speed limitations of electronics [1–5]. These studies aim to tackle many problems that limit the optical bandwidth communications. Many of these efforts are focused in the search for new all-optical devices with potential to improve the general field of photonics and optical technologies [6–40]. Nowadays, photonic crystal fibers (PCF) are emerging as an alternative fiber technology. PCF's, which were first developed in 1995, are optical fibers with a periodic arrangement of a low index material on a higher refractive index medium. Non doped silica is usually considered as a typical high refractive index material, n Corresponding authors at: Universidade Federal do Ceará, Laboratório de Telecomunicações e Ciência e Engenharia de Materiais LOCEM, Departamento de Física, Caixa Postal 6030, 60455-760 Fortaleza, Brazil. Tel.: þ55 85 8864 4574; fax: þ55 853 366 9334. E-mail addresses: [email protected], [email protected] (J.R.R. Sousa). URL: http://www.locem.ufc.br (J.R.R. Sousa).

http://dx.doi.org/10.1016/j.optcom.2014.02.023 0030-4018 & 2014 Elsevier B.V. All rights reserved.

while periodically distributed air holes play the role of the low refractive index medium [40]. The structure of a two-core PCF is shown in Fig. 1, where d is the air-hole diameter, Λ is the hole-tohole distance, and C is the core separation [41]. In this work, we will present a numerical investigation of an all-optical logical gate device based in a Michelson interferometer (MI) of photonic crystal fibers (PCF). We will consider an arrangement of two identical photo-imprinted Bragg gratings symmetrically located in each arm of a Michelson interferometer acting as an add-drop filter. The use of photonic crystal fiber in the configuration of a Michelson interferometer with reduced dimensions is attractive because it is a low-loss structure, avoids asymmetrical, since symmetric devices are simple to manufacture. Also this configuration allows us to select wavelengths from the gratings. We will evaluate the potential of such device to perform all-optical logical operations using ultra-short optical pulses (100 fs) for the three different regimes pump powers.

2. Michelson interferometers as optical add-drop multiplexers Michelson interferometers (Fig. 2) [42] can be configured by using two pieces of fiber separated in the output ports of a coupler, with mirrors or Bragg gratings reflecting 100% of the input signal

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acting as a nonlinear mirror [43]. Michelson interferometers have been used intensively in research and development in recent times [28–39]. Due to its flexibility and versatility, it is expected that this device will play a major role in optical photonic research and technology. Optical fiber interferometers have been widely used in metrology due to their prominent advantages such as non-contacting measurement mode, compactness, light weight, immunity to electromagnetic interference, wide bandwidth, multiplexing capability, high resolution, and low cost. As the components that configure an optical fiber interferometer are connected together, there is no need for adjusting and keeping the components in their correct positions, a critical feature in standard optical interferometers. Hence, there is a great amount of interest in exploiting optical Michelson fiber interferometers for the measurement of a large variety of parameters such as displacement, vibration, acceleration, velocity, strain, refractive index (RI), and temperature [28–35,38]. For example, an optical fiber Michelson interferometer has been recently used to determine the refractive index of a liquid to high precision, with an accuracy limited only by the normal random variables encountered in interferometric measurements and, ultimately, by the accuracy to which the wavelength of the laser light is known [29]. The Michelson and Mach–Zehnder interferometers with identical gratings in the output arms form important all-optical components such as multiplexers “add/drop” [44,45]. The Bragg gratings act as reflection filters and play the role of selecting the wavelengths while the coupler differentiates the channels. The transfer characteristics have recently been reported and it was shown that the integrity of the Bragg wavelengths of the two gratings is of primary importance for a reflection backward

Fig. 1. Cross-section of a dual-core PCF, where the shaded areas are air holes.

[46,47]. The filter Bragg grating coupler, demonstrated recently by Orlov [48], is an attractive device due to its simplicity, requiring a single grid at the waist of a directional coupler.

3. Theoretical framework The equations expressing the evolution of an electromagnetic field in a nonlinear coupler with the effects of higher order dispersion are given in the following equations known as nonlinear coupled mode equations, that do not differentiate the two orthogonal polarization modes of the fiber [49,50]:

2

2 ∂A1 β 2 ∂2 A1 β 3 ∂3 A1 i  þ γ ð
A1
þ η
A2
Þa1 i ∂z 2 ∂t 2 6 ∂3 t

2

2 γ ∂ð
A1
A1 Þ i ∂
A1
∂A2  γ A1 T R þ k0 A2 þ ik1 ¼0 þi ∂t ω ω0 ∂t ∂t

2

2 ∂A2 β 2 ∂2 A2 β 3 ∂3 A2 i  þ γ ð
A2
þ η
A1
ÞA2 i ∂z 2 ∂t 2 6 ∂3 t

2

2 γ ∂ð
A2
A2 Þ i ∂
A2
∂A2  γ A2 T R þ k0 A2 þ ik1 ¼0 þi ∂t ω ω0 ∂t ∂t

ð1Þ

ð2Þ

In the above equations, A1 and A2 are respectively the modal amplitudes of the field cores 1 and 2, z is the distance along the fiber; t is the time coordinate with reference to the transit time of the pulses; A1 and A2 are the amplitude envelopes of the pulses carried by the two cores, respectively; β2, β3, are the groupvelocity dispersion (GVD), third-order dispersion; γ is nonlinear parameter that accounts for self-phase modulation (SPM); η is a small parameter that measures the relative importance of crossphase modulation (XPM) with regard to SPM, the time-varying term next to the SPM and XPM terms represents self-steepening (where ω is the angular optical frequency); TR is the Raman scattering coefficient; κ0 is the coupling coefficient (κ0 ¼ 87.266 m  1 for our simulations); and κ1 is the coupling coefficient dispersion (κ1 ¼ 4.1  10  13 m  1 for our simulations) given by κ1 ¼∂κ0/∂ω (evaluated at the pulse carrier frequency) [41]. The spectral profile from a Bragg grating structure may be simulated resolving the equations of coupled-mode, which it also is based on the (NLSE). For this analysis, two counter-propagating plane waves are considered confined to the core of an optical fibre in which an intra-core uniform Bragg grating of length z ¼e (e¼1 mm for our simulations) centered in 1.55 μm and uniform period Λ. The electric fields of the backward and forward waves can be expressed as EA ðz; tÞ ¼ A  exp½iðωt  β zÞ and þ þ EA ðz; tÞ ¼ A exp½iðωt þ β zÞ respectively, where β is the wave propagation constant [51]. In the same way as the directional coupler, we can write the coupled mode equations that describe the dynamic evolution of the Bragg gratings as: dA  ¼ ikA þ expð  i2Δβ zÞ dz

Fig. 2. Michelson interferometer of photonic crystal fiber.

ð3Þ

J.R.R. Sousa et al. / Optics Communications 322 (2014) 143–149

dA þ ¼  ikA  expði2ΔβzÞ dz

ð4Þ

where k (5  103 m  1 for our simulations) is the coupling coefficient between modes propagating backward A  and forward A þ , Δβ is the phase mismatch and is given by:

Δβ ¼

2π nef f

λB



ð1Þπ

Λ

ð5Þ

where nef f is the effective index of the fiber core and Λ is the modulation period of the Bragg gratings and λB is the Bragg wavelength. This is the simplest configuration of the Michelson interferometer, assuming that they grating are linear and ensuring the reflection of pulses. Being clear considerations of our work here, no harm in opening remarks of the subject. As such, the reflected pulse field amplitude can be obtained by multiplying the appropriate grating frequency response, which can be obtained by numerically solving (4) along with the boundary conditions A þ ðLB Þ ¼ 1andA  ðLB Þ ¼ 0 where LB is the length of the grating (LB ¼1  10  3 m for our simulations), with the input pulse spectrum. The corresponding time waveforms can then be recovered by taking an inverse Fourier transform [52]. We analyze the two-core PCF considered in [41], which has an air-hole diameter d ¼2.0 mm, a hole-to-hole distance Λ ¼d/0.9, a core separation C ¼2Λ, and a coupling length LC ¼ 1.8 cm. The corresponding parameters for (1 and 2) are β2 ¼  47 ps2/km, β3 ¼ 0.1 ps3/km, η ¼0, γ ¼3.2  10  3 (W m)  ) [41] and γ/ω ¼1.44  10  2 s/(W m). The carrier wavelength is λ ¼1.55 mm. 4. Numerical procedure We excited the device using an ultra-short pulsed signal (  100 fs) [41], with a hyperbolic secant profile to excite our device. We emphasize that this study does not simulate the fiber, because its length after the coupler is very small and so we despise the effects in it. Initially, to characterize the main properties of the output signal, we assume that the pulse is launched into the core of PCF such that A1 ð0; TÞ ¼ A0 sechðT=T 0 Þ

ð6Þ

A2 ð0; TÞ ¼ 0

ð7Þ

We solved the propagation equations numerically using a standard Runge–Kutta fourth order method [53,54]. The Bragg gratings will reflect the signals aiming at to drop in the channel 2, being necessary that an extra phase of the type expðiϕπ Þ (see Fig. 2) be added to one of the amplitude reflections of the Bragg gratings. In the Return to the coupler, we performed a variation in the phase added to the amplitude reflection of the Bragg grating of the arm 3, with the intent to obtain the best phase, so that a large concentration of energy is transferred to the output. This behavior is similar to the all-optical delay line used in the literature [1,8,10,14,16,17,55] on other devices and that achieve the same purpose, with the same goal, and that also favors the contrast needed to obtain logic gates. The transmission Ti can be defined in the function of the input signal as: R þ1 jAi ðLC Þj2 dt T i ¼ Rþ11 ; ð8Þ 2  1 jA1 ð0Þj dt where i¼1, 2 and LC is the length of the Michelson interferometer, where LC ¼ L þLB (L¼ coupler length and LB ¼Bragg grating length). The extinction ratio of a switching on–off device is the ratio between the output power in the on-state, channel 2, and the output power in the off-state, channel 1, or vice-versa. This relationship should be as high as possible to allow for a clear

145

differentiation between ON and OFF states. For the device in this study, it is expressed as R þ1 jA2 ðLC Þj2 dt Extinction  ratio ¼ XR ¼ R þ1 ; ð9Þ 1 2  1 jA1 ðLC Þj dt which is usually measured in decibels as XRatio½dB ¼ 10Log 10 XR

ð10Þ

The crosstalk (XT) is the presence of an unwanted signal due to some coupling mechanism between the disturbed and disturbing channels. This must be maintained at a minimum for a proper device operation. Expressed in dB units, the crosstalk is given by Cross  talk½dB ¼ Xtalki ¼ 10  log 10 ðT i Þ

ð11Þ

The compression factor (CF) is also an important quantity, which is defined as being the ratio between the temporal width of the input pulse (guide 1) and output pulse (guide 2): CF ¼

Tð0Þ τinput ¼ ; TðLÞ τoutput

ð12Þ

where τoutput represents the time duration of the output pulse and τinput represents the temporal width of the input pulse. Physically, the compression factor determines how much the pulse broadened or compressed along the Michelson interferometer. This parameter, together with crosstalk and transmission are essential to verify the operating characteristics of the device. In the following, we have studied the performance of the proposed device considering three different regimes of pumping power having as reference the critical pumping power for switching Pc ¼ 177 kW. Initially we used an excitation power P ¼150 kW below the critical value for switching. In a second case, we used an excitation power equal to the critical value P ¼177 kW. Finally, a case of input power higher than critical (P ¼196 kW) was considered. The critical power is the power that the component splits the energy by 50% for the output guides and can be obtained from the equation [2]: P0 ¼

1 LNL γ

ð13Þ

where P0 is the input power, LNL is the non-linearity length and γ is non-linearity coefficient. To visualize the nonlinear effects in a device of 1.8 cm, LNL should use much less than 1.8 cm. Changing the length of non-linearity, switching power also changes inversely proportional, such that LNL ¼ 2:08  10  3 m, LNL ¼ 1:76  10  3 m, LNL ¼ 1:59  10  3 e γ ¼ 3:2  10  3 (m W)  1, we find P0 oPc ¼ 150 kW, P0 ¼ Pc ¼177 kW/e P0 4Pc ¼ 196 kW, respectively, according to our simulations. Thus we can analyze the dynamics of the component in various powers.

5. Results and discussions 5.1. Michelson interferometer operation Initially we analyzed the transmission, Xratio, crosstalk and compression factor as a function of the dephasing for three different cases of pump powers by analyzing the output pulse at channel 2. Fig. 3(a), provides a minimum transmission of 34% and a maximum transmission of 69% in the phases φ ¼0.81π and φ ¼1.79π, respectively. These extremal values are achieved when using a pump power below the critical power P ¼150 kW. Fig. 3 (b) provides a minimum crosstalk  5.2 dB and a maximum of  1.86 dB at phases φ ¼1.8π and φ ¼ 0.78π, respectively, thus showing that the phase that allocates less interference is φ ¼1.8π. We note that the values of crosstalk (dB) suffer strong fluctuations. Fig. 3(c) shows that we obtain a minimum Xratio of  2.65 dB and a maximum Xratio of 3.65 dB at phases φ ¼0.81π

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Transmission

0.7

12 10

0.6

8 0.5

6 P o=150 KW

4

P c=177 KW

0.4

P o=196 KW Channel 2

2

Crosstalk (dB)

-1.5 -2.0

P 0 =150 KW

-2.5

P c =177 KW

-3.0

Channel 1

0 0.0

P 0 =196 KW

0.5

1.0

1.5

Fig. 4. Compression factor (CF) as a function of dephasing. Pump powers are (a) P0 ¼ 150 kW, (b) Pc ¼177 kW, and (c) P0 ¼ 196 kW.

-3.5 -4.0

1.0

Phase=0.55π P0=150 kW

-4.5 0.8

-5.0

Intensity u.a

4 3

XRatio (dB)

2.0

2

0.6

0.4

1 0.2

0 P o=150 KW

-1 -2

P c=177 KW

0.0

P o=196 KW

1.0

Phase = 0.56 π P0=177 kW

Channel 2 1.0π

1.5π

0.8

2.0π

Phase (φ) Fig. 3. (a) Transmission looking into the output pulse at channel 2, (b) crosstalk looking into the channel 1, and (c) XRatio looking into the output pulse at channel 2, for the three pump powers considered in the present study (see text).

and φ ¼1.79π, respectively, both also using a pump power below the critical one. We verify that the values of XR (dB) changes sign as the dephasing varies. This behavior is due to the fact that, under this condition, practically all energy is transferred periodically between the two channels. We emphasize that the reference for our results is the output gate, see Fig. 2. Fig. 4 shows the compression factor. We can observe a similar behavior for the three cases of pumping powers. We observed that throughout the entire phase range the pulse compresses, with a maximum of CF ¼10.26 in phase φ ¼1.62π. Further, we observed that the transmission, Xratio, crosstalk and compression factor curves shown a nonlinear behavior as a function of the dephasing. Fig. 5(a)–(c) shows the profile of the pulse for a dephasing at which we get logic gates (see discussion below), except in the case of the critical pump power. Analyzing Fig. 5(a), which corresponds to a pump power below the critical power (150 kW) and phase φ ¼ 0.55π, we observe that the pulse temporal extension is 380 fs. Fig. 5(b) corresponds to the case of a critical pump power (177 kW) and phase φ ¼0.56π. The output pulse temporal extension pulse is 350 fs. Finally, Fig. 5(c) shows the case of a pump power above the critical one (196 kW) and phase φ ¼0.59π, for

Intensity u.a

0.5π

0.6

0.4

0.2

0.0

Phase = 0.59 π P 0 = 196 kW

1.0

0.8

Intensity u.a

-3 0.0

0.6

0.4

0.2

0.0 0

1

2

3

4

Time (ps) Fig. 5. Temporal pulse profiles for: (a) φ¼ 0.55π and P0 ¼ 150 kW; (b) φ¼0.56π and Pc ¼ 177 kW; (c) φ¼ 0.59π and P0 ¼196 kW.

J.R.R. Sousa et al. / Optics Communications 322 (2014) 143–149

All-optical data processing devices are key components for future integrated photonic circuits. One category of such devices is logic gates. All-optical gates capable of performing basic logical operations are still in the early stages of development and many of the reported works are based on nonlinear optics [56–60]. In this section, we will evaluate the performance of the present device to perform logical operations. Considering the signal at the input I1 and I2 are introduced according to the following sequence of combinations (0; 0), (0; 1), (1; 0), (1; 1). The configuration (0, 0) corresponds to the absence of light in both guides. (1, 0) states for the absence of light at the input guide 2 while (0, 1) the absence of light at the input guide 1. Finally in (1, 1) light is inserted in both guides. Considering the signal at the output gate, we calculate the extinction ratio, represented as XR2. We took the reference line y¼  2.31 at which we could observe several logic operations. However, the main picture we are going to describe below remains for other choices of such reference line. The region for bit 1 (0) is located above (below) this reference or decision line. In Fig. 6 (a) and (b) we report the case on which the pump power to excite

[I1;I2]=[0;1] [I1;I2]=[1;0] P0=177KW

0.6 1.42π

0.4

0.2 4

2

0

[I1;I2]=[1;0] [I1;I2]=[1;1]

-2

P0=177kW OR

-4 0.0

0.5 π

1.5 π

1.0π

2.0π

Phase (φ)

[I1;I2]=[0;1] [I1;I2]=[1;0] XOR

1.0

[I1;I2]=[1;1] P0=150KW

[I1;I2]=[1;1]

0.8

0.6

1.45π

0.4

[I1;I2]=[0;1] [I1;I2]=[1;0]

OR

Transmission

Transmission

[I1;I2]=[0;1]

Fig. 7. (a) Transmission and (b) extinction ratio as a function of the dephasing when using a pumping power of 177 kW. One obtains the OR logic gate within the dephasing range φ¼[0.87, 1.98]π.

1.0

0.8

OR

[I1;I2]=[1;1]

0.8

Transmission

5.2. Logical gates operation

1.0

XRatio (dB)

which one has an output pulse with temporal extension pulse of 290 fs. A decrease in the peak intensity of the pulse due to the time broadening was also verified. Furthermore, the pulse is considerably deformed, however principle of generation of logic gates is based on the energy level, which in turn is related to the reference line, as we shall see in the next section.

147

P0=196kW NOT

OR

0.6

1.51π

0.4

0.2 0.2

4

4

2 XOR

XRatio (dB)

XRatio (dB)

2

0 [I1;I2]=[0;1] [I1;I2]=[1;0] [I1;I2]=[1;1]

-2

Not

0

[I1;I2]=[0;1] [I1;I2]=[1;0] [I1;I2]=[1;1]

P0=196kW

-2

P0=150kW

OR

-4 0.0

OR

0.5π

1.0π Phase (φ)

1.5π

2.0π

Fig. 6. (a) Transmission and (b) extinction ratio as a function of the dephasing when using a pumping power of 150 kW. One obtains the XOR and OR logic gates in the dephasing ranges φ¼[0.5, 0.6] and φ¼[0.95, 1.9]π, respectively.

-4 0.0

0.5π

1.0π Phase (φ)

1.5π

2.0π

Fig. 8. (a) Transmission and (b) extinction ratio as a function of the dephasing when using a pumping power of 196 kW. One obtains the NOT and OR logic gates in the diphasing ranges φ¼[0.54, 0.62] and φ¼[0.76, 2.0]π, respectively.

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Table 1 Truth table for the operation of the OR, XOR and NOT (output pulse in fiber 2) logic gates, in the three settings of pumping power (P0 ¼ 150 kW, Pc ¼ 177 kW and P0 ¼196 kW). The reported values of XR2 are those corresponding to the optimal dephasing to achieve each logic operation, namely:

φ ¼ 0.55π (XOR at P¼ 150 kW); φ ¼ 1.44π (OR at

P¼ 150 kW); φ ¼1.42π (OR at P ¼177 kW); φ ¼ 1.39π (OR at P¼ 196 kW); and φ ¼ 0.59π (NOT at P ¼196 kW). Where I1 and I2 are the input ports 1 and 2 and O2 output gate, see Fig. 2, for the analysis of logic functions. P0 ¼150 kW I1 0 0 1 1

I2 0 1 0 1

O2 - XR2 (dB) 0 1–1.86 dB 1–1.86 dB 0–3.32 dB XOR φ ¼[0.52,0.62]π

O2 - XR2 (dB) 0 1–1.84 dB 1–1.84 dB 1–3.33 dB OR φ ¼ [0.95, 1.90]π

the device is smaller than the critical power. We analyzed the three possible cases of excitation. First we excited channel 1 (1, 0), then the second channel (0, 1), and finally, both channels (1, 1) with pulsed signals of 100 fs. We measured the transmission and XRatio and as a function of the nonlinear dephasing. With an output power below the critical power (150 kW), it was possible to mount the XOR and OR gates when observing the output at channel 2. In Fig. 6(a) and (b) we highlight the phase intervals φ ¼ [0.55π, 0.62π] and φ ¼ [0.95π, 1.90π], where the XOR and OR gates are achieved, respectively. Fig. 7(a) and (b) shows similar data for the case of pumping power equals to the critical one. In this case only the OR gate is operational. We also highlight the phase interval φ ¼[0.88π, 1.98ππ], where such OR gate can be mounted, with a maximum transmission rate of 0.68. Finally, the transmission and XRatio diagrams for the case of pump power above the critical value is reported in Fig. 8(a) and (b). In this case it is possible to mount logic gates NOT and OR. The OR gate is achieved in the phase interval φ ¼ [0.76π, 2.0π] while the NOT gate operates in the phase interval φ ¼ [0.54π, 0.63π]. The truth Table 1 shows the optimized situations in which we can build logic gates, for the three representative cases of input pump powers considered in the present work.

6. Conclusion In this work, we presented a numerical investigation of the propagation and switching of pulsed signals using a Michelson interferometer (MI) of micro structured fibers. We explored the potential of such device to act as all-optical logic gates when excited with an ultra-short pulse of approximately 100 fs. We studied the characteristics of transmission, extinction ratio, crosstalk and compression factor as a function of the nonlinear dephasing added to one of the Bragg gratings of the Michelson interferometer. The pulse propagation was considered to be influenced by high-order dispersion effects, such as: third-order dispersion, intrapulse Raman scattering and self-steepening [1]. Analyzing three different configurations, namely exciting the device with pump powers below, equal and above the critical switching power, we were able to identify several dephasing ranges at which optical logic gates such as OR, XOR and NOT can be realized. Therefore, a MI device based in photonic fibers seems to be a potential candidate for the development of all-optical ultrafast logical gates. It would be valuable to explore alternative configurations able to perform a more extensive set of logic operations. Future developments along this line would contribute to build a more complete scenario of the potential applications of structured MI as all-optical devices.

Pc ¼177 kW

P0 ¼ 196 kW

O2 - XR2 (dB) 0 1–2.16 dB 1–2.16 dB 1–3.33 dB OR φ ¼ [0.88, 1.98]π

O2 - XR2 (dB) 0 1–2.31 dB 1–2.31 dB 1–3.27 dB OR φ ¼[0.76, 2]π

O2 - XR2 (dB) 0 0–2.34 dB 0–2.34 dB 0–3.26 dB NOT φ ¼[0.54,0.62]π

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