Experimental study of time-delay signature of chaos in mutually ...

Experimental study of time-delay signature of chaos in mutually coupled vertical-cavity surface-emitting lasers subject to polarization optical injection Yanhua Hong School of Electronic Engineering, Bangor University, Bangor, Gwynedd LL57 1UT, Wales, U.K [email protected]

Abstract: Time-delay signature of chaos in mutually coupled verticalcavity surface-emitting lasers subject to polarization rotated optical injection has been investigated experimentally. Autocorrelation function and permutation entropy are used to quantitatively identify the time-delay signature of chaos. The experiment results show that the time-delay signature is sensitive to the polarization rotated angle. Minimum time-delay signature has been observed in the intermediate polarization rotated angle for the lower bias current. This is in good agreement with the theoretical prediction. At higher bias currents, the lower time-delay signature has been obtained with parallel optical injection. ©2013 Optical Society of America OCIS codes: (140.1540) Chaos; (140.7260) Vertical cavity surface emitting lasers.

References and links 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14.

C. Masoller, “Anticipation in the synchronization of chaotic semiconductor lasers with optical feedback,” Phys. Rev. Lett. 86(13), 2782–2785 (2001). Y. Takiguchi, K. Ohyagi, and J. Ohtsubo, “Bandwidth-enhanced chaos synchronization in strongly injectionlocked semiconductor lasers with optical feedback,” Opt. Lett. 28(5), 319–321 (2003). Y. H. Hong, M. W. Lee, P. S. Spencer, and K. A. Shore, “Synchronization of chaos in unidirectionally coupled vertical-cavity surface-emitting semiconductor lasers,” Opt. Lett. 29(11), 1215–1217 (2004). A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. García-Ojalvo, C. R. Mirasso, L. Pesquera, and K. A. Shore, “Chaos-based communications at high bit rates using commercial fiber-optic links,” Nature 438(7066), 343–346 (2005). M. Sciamanna, I. Gatare, A. Locquet, and K. Panajotov, “Polarization synchronization in unidirectionally coupled vertical-cavity surface-emitting lasers with orthogonal optical injection,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 75(5), 056213 (2007). A. Uchida, K. Amano, M. Inoue, K. Hirano, S. Naito, H. Someya, I. Oowada, T. Kurashige, M. Shiki, S. Yoshimori, K. Yoshimura, and P. Davis, “Fast physical random bit generation with chaotic semiconductor lasers,” Nat. Photonics 2(12), 728–732 (2008). I. Kanter, Y. Aviad, I. Reidler, E. Cohen, and M. Rosenbluh, “An optical ultrafast random bit generator,” Nat. Photonics 4(1), 58–61 (2010). K. Hirano, T. Yamazaki, S. Morikatsu, H. Okumura, H. Aida, A. Uchida, S. Yoshimori, K. Yoshimura, T. Harayama, and P. Davis, “Fast random bit generation with bandwidth-enhanced chaos in semiconductor lasers,” Opt. Express 18(6), 5512–5524 (2010), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-6-5512. F. Y. Lin and J. M. Liu, “Chaotic lidar,” IEEE J. Sel. Top. Quantum Electron. 10(5), 991–997 (2004). K. E. Chlouverakis and M. J. Adams, “Optoelectronic realisation of NOR logic gate using chaotic two-section lasers,” Electron. Lett. 41(6), 359–360 (2005). Y. C. Wang, B. J. Wang, and A. B. Wang, “Chaotic correlation optical time domain reflectometer utilizing laser diode,” IEEE Photon. Technol. Lett. 20(19), 1636–1638 (2008). D. Rontani, A. Locquet, M. Sciamanna, D. S. Citrin, and S. Ortin, “Time-delay identification in a chaotic semiconductor laser with optical feedback: a dynamical point of view,” IEEE J. Quantum Electron. 45(7), 879– 891 (2009). R. M. Nguimdo, P. Colet, L. Larger, and L. Pesquera, “Digital key for chaos communication performing time delay concealment,” Phys. Rev. Lett. 107(3), 034103 (2011). N. Q. Li, W. Pan, S. Y. Xiang, L. S. Yan, B. Luo, and X. H. Zou, “Loss of time delay signature in Broadband cascade-coupled semiconductor lasers,” IEEE Photon. Technol. Lett. 24(23), 2187–2190 (2012).

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15. S.-S. Li, Q. Liu, and S.-C. Chan, “Distributed feedbacks for time-delay signature suppression of chaos generated from a semiconductor laser,” IEEE Photonics J. 4(5), 1930–1935 (2012). 16. A. B. Wang, Y. B. Yang, B. J. Wang, B. B. Zhang, L. Li, and Y. C. Wang, “Generation of wideband chaos with suppressed time-delay signature by delayed self-interference,” Opt. Express 21(7), 8701–8710 (2013). 17. J.-G. Wu, Z.-M. Wu, G.-Q. Xia, and G.-Y. Feng, “Evolution of time delay signature of chaos generated in a mutually delay-coupled semiconductor lasers system,” Opt. Express 20(2), 1741–1753 (2012), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-2-1741. 18. Z.-Q. Zhong, Z.-M. Wu, J.-G. Wu, and G.-Q. Xia, “Time-delay signature suppression of polarization-resolved chaos outputs from two mutually coupled VCSELs,” IEEE Photonics J. 5(2), 1500409 (2013). 19. S. Y. Xiang, W. Pan, B. Luo, L. S. Yan, X. H. Zou, N. Jiang, L. Yang, and H. N. Zhu, “Conceal time-delay signature of chaotic vertical-cavity surface-emitting lasers by variable-polarization optical feedback,” Opt. Commun. 284(24), 5758–5765 (2011). 20. L. Y. Zhang, W. Pan, L. S. Yan, B. Luo, X. H. Zou, S. Y. Xiang, and N. Q. Li, “Conceal time-delay signature of mutually coupled vertical-cavity surface-emitting lasers by variable polarization optical injection,” IEEE Photon. Technol. Lett. 24(19), 1693–1695 (2012). 21. P. Xiao, Z.-M. Wu, J.-G. Wu, L. Jiang, T. Deng, X. Tang, L. Fan, and G.-Q. Xia, “Time-delay signature concealment of chaotic output in a vertical-cavity surface-emitting laser with double variable-polarization optical feedback,” Opt. Commun. 286, 339–343 (2013). 22. S. Priyadarshi, Y. Hong, I. Pierce, and K. A. Shore, “Experimental investigations of time-delay signature concealment in chaotic external cavity VCSELs subject to variable optical polarization-angle of feedback,” IEEE J. Sel. Top. Quantum Electron. 19(4), 1700707 (2013). 23. C. Bandt and B. Pompe, “Permutation entropy: a natural complexity measure for time series,” Phys. Rev. Lett. 88(17), 174102 (2002). 24. S. Bandyopadhyay, Y. H. Hong, P. S. Spencer, and K. A. Shore, “Experimental observation of anti-phase polarisation dynamics in VCSELs,” Opt. Commun. 202(1-3), 145–154 (2002).

1. Introduction Optical chaos has attracted considerable research interests because of its potential applications in secure optical communications [1–5], random number generators [6–8], chaotic lidar [9], chaotic logic gates [10] and time domain reflectometry [11]. One of the common methods used to generate optical chaos is using optical feedback or optical injection in semiconductor lasers. The typical chaos generated by optical feedback includes recurrence features termed time delay (TD) signature because of optical round trip in the external cavity. The time delay signature is a harmful feature for the applications of chaotic optical communications and random number generators. The TD signature may provide the opportunity for an eavesdropper to extract a key parameter, which may compromise the security of chaotic optical communications. The TD signature reduces the randomness of the chaotic optical signal and affects the symmetrical distribution of random bits. There are many reports on the suppression of the TD signature in semiconductor laser. Rontani et al. [12] identified two conditions - lower optical feedback ratio and similar value of the time delay and the relaxation oscillation period of the laser, to eliminate the TD signature. Nguimdo et al. [13] used the binary sequence to hide the TD signature. Li et al. concealed the TD signature by using cascade-coupled semiconductor lasers [14]. Recently distributed feedback from a fiber Bragg grating was used for reducing the TD signature [15] and delayed self-interference scheme was employed to generate wideband chaos with suppressed time-delay signature [16]. The evolution of TD signature of chaos in a mutually coupled semiconductor lasers has also been studied experimentally and theoretically elsewhere [17]. Compared with external cavity feedback systems, the mutually coupled systems have a unique advantage. Chaos generated by mutually coupled semiconductor lasers has a weaker TD signature because each laser can be considered as a nonlinear reflector for another laser and provides nonlinear optical feedback. In such cases, the recurrence feature can be reduced [18]. Most of the cases studied to date are perform with edge-emitting semiconductor lasers [12–17]. Vertical-cavity surface-emitting semiconductor lasers (VCSELs), as special type of semiconductor lasers, have many advantages compared to edge-emitting semiconductor lasers, such as low cost, compact size, low threshold current, circular output-beam profile and wafer-scale integrability. They have attracted some attentions to suppress TD signature [18–

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Received 12 Jun 2013; revised 15 Jul 2013; accepted 15 Jul 2013; published 18 Jul 2013 29 July 2013 | Vol. 21, No. 15 | DOI:10.1364/OE.21.017894 | OPTICS EXPRESS 17895

21], but all the studies are concentrated on theoretical simulations. Recently we have investigated experimentally the TD signature in a chaotic VCSEL with variable polarization optical feedback [22]. In this paper, the study is extended to mutually coupled VCSELs. The results show that the TD signature is sensitive to the polarization angle of optical injection and a lower TD signature has been obtained at an intermediate polarization rotated angle, which is in good agreement with the simulation [20]. 2. Experimental setup

Fig. 1. Experimental setup. BS-beamsplitter; HWP- half wave plate; ATTN- optical variable attenuator; ISO-isolator; PD – photodetector; OSC -oscilloscope

A schematic of the experimental setup is shown in Fig. 1. In this experiment, two commercial VCSELs named VCSEL1 and VCSEL2 were used. Both VCSELs were driven by ultra-low noise current sources and were temperature controlled to an accuracy of 0.01°C. These two VCSELs were mutually coupled and their polarization direction of optical injection was varied by a half wave plate (HWP3). An optical variable attenuator (ATTN) was used to change the injection ratio. The flight time τf between VCSEL1 and VCSEL2 was approximately 3.9 ns. For polarization-resolved measurement, optical isolators (ISOs) were employed to prevent any unwanted optical feedback from the photodetectors (PDs). Only in the measurement of the total output of VCSELs, the isolators were removed and the laser beams were slightly misaligned to prevent the optical feedback into the VCSELs. The outputs of the VCSELs were detected by 12 GHz bandwidth photodetectors and were recorded by a 6 GHz bandwidth oscilloscope (OSC). The sampling rate of the oscilloscope was set at 10 GS/s and 100000 samples were recorded for each time trace, therefore the duration of each time trace is 10 µs. In the experiment, the temperatures of VCSEL1 and VCSEL2 were fixed at 18.5°C and 27°C, respectively. In this paper, the optical injection ratio is defined as the ratio of the injection power to the output power of stand-alone VCSEL with the injection power measured just before the beam was injected into the VCSEL. 3. Time delay signature analysis methods Several methods, such as autocorrelation function (ACF) [12–22], permutation entropy (PE) [17–20, 22] and mutual information [12–14] can be used to qualitatively evaluate the TD signature. For mutually coupled laser systems, cross-correlation between the outputs of two lasers can also be used to identify the time delay if the outputs of two lasers are measured simultaneously and the difference between the travelling times from each laser to the oscilloscope is recorded. In this work, both the AFC and PE methods are adopted to identify the TD signature. The ACF is defined as follows

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Received 12 Jun 2013; revised 15 Jul 2013; accepted 15 Jul 2013; published 18 Jul 2013 29 July 2013 | Vol. 21, No. 15 | DOI:10.1364/OE.21.017894 | OPTICS EXPRESS 17896

C (Δt ) =

< [ I (t + Δt )− < I (t + Δt ) >][ I (t )− < I (t ) >] >) < [ I (t + Δt )− < I (t + Δt ) >]2 >< [ I (t )− < I (t ) >]2 >

,

(1)

where I is the output intensity of the VCSEL, denotes time average, Δt is the delay time. The PE method was first introduced by Bandt and Pompe [23]. In this method, the measured output intensities of a VCSEL have N samples It, where t = 1, …, N. For a given time series {It, t = 1,2,…,N}, let subsets Sq contain M samples (M>1) of the measured intensities and an embedding delay time τ = nTs (n is an integer number and Ts is the reciprocal of the sampling rate), the ordinal pattern of the subset is Sq = [I(t), I(t + τ), …I(t + (M-1)τ)]. For the practical purpose, Bandt and Pompe have suggested to choose M between 3 and 7 [23]. In this paper, M is set at 4. Sq can be arranged as [I(t + (r1-1)τ)≤I(t + (r21)τ)≤…≤I(t + (rM-1)τ)]. Hence, any subset can be uniquely mapped into an “ordinal pattern” π = (r1, r2,…,rM), which is one of the permutations of subset Sq with M dimensions. For all the M! possible permutations, the probability distribution p(π) is defined as [23] P (π ) =

#{t | t ≤ N − M − n + 1; S q has type π } N − M − n +1

,

(2)

where # stands for “number”. From the probability p(π) the permutation entropy is defined as: h( p ) = − p(π ) log p (π ),

(3)

4. Experimental results and discussion In this work, the bias current of VCSEL2 was fixed at 3.18mA, 3.68mA, 5mA and 5.99mA. The frequency detuning between VCSEL1 and VCSEL2 was changed by tuning VCSEL1’s bias current. The frequency detuning Δf is defined as Δf = f1-f2, where f1 and f2 are the frequencies of the free-running VCSEL1 and VCSEL2, respectively. 4.1 Polarization-resolved L-I curve of the stand-alone VCSELs Figure 2 shows the polarization-resolved light-current (L-I) curves of the stand-alone VCSELs. The threshold currents Ith for VCSEL1 and VCSEL2 are 1.9 mA and 2.3 mA, respectively. Near threshold currents, both VCSEL1 and VCSEL2 lase in one polarized direction, which is defined as the X-polarized direction. For VCSEL1, when the bias current increases to 8.3 mA, the polarization switches to the orthogonal direction, which is defined as the Y-polarized direction. In this case no hysteresis has been observed. For VCSEL2, the polarization switches to Y-polarization at the bias current of 3.3mA and then switched back to X-polarization at 3.9mA for increasing bias current. For decreasing bias current, the polarization switched to Y-polarization at 3.65mA and switched back to X-polarization at 3.3mA. So there is a hysteresis for the bias current between 3.65mA and 3.9mA.

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Received 12 Jun 2013; revised 15 Jul 2013; accepted 15 Jul 2013; published 18 Jul 2013 29 July 2013 | Vol. 21, No. 15 | DOI:10.1364/OE.21.017894 | OPTICS EXPRESS 17897

X Y

2

(a)

4

6

8

10

Output Power (mW)

Output Power (mW)

2.5 2.0 1.5 1.0 0.5 0.0

2.0

(b)

X increasing Y increasing X decreasing Y decreasing

1.5 1.0 0.5 0.0

Bias Current (mA)

2

4

6

8

10

Bias Current (mA)

Fig. 2. Polarization-resolved L-I curve of (a) VCSEL1, (b) VCSEL2

4.2 Effect of polarization rotated angle on the TD signature

0.02

a2

0.00 -0.02 -0.04 0.02 0.01

c1

b1 1.000 h(P)

-0.02

0.8 0.6 0.4 0.2 0.0 -0.2 0.8 0.6 0.4 0.2 0.0 -0.2 0.8 0.6 0.4 0.2 0.0 -0.2 -0.4

a3

0.00 -0.01 -0.02 -0.03 100 120 140 160 180 200 Time (ns)

0.995 0.990

b2

c2

1.000

C

Intensity (a. u.)

C

0.00

-0.04 0.04

Intensity (a. u.)

a1

h(P)

0.02

0.995 0.990

b3

c3

1.000 h(P)

0.04

C

Intensity (a. u.)

When the bias current of VCSEL2 was fixed at 3.18mA (~1.38 Ith), which is below the bias current of the first polarization switching, the lasing wavelength is around 1535.55nm. By tuning the bias current of VCSEL1 to 3.02 mA (~1.59Ith), the frequency detuning Δf = 0 has been achieved.

0

5

10

Delay Time (ns)

15

0.995 0.990

0

5

10

15

Embedding Delay Time (ns)

Fig. 3. The time trace (first column), autocorrelation coefficient curve (second column) and the PE curves (third column) of the X-polarization of VCSEL 2 with a fixed optical injection ratio of −9.4dB and Δf = 0. The polarization rotated angles are 0° (top row), 60° (middle row) and 90° (bottom row).

In this experiment, the results of VCSEL1 and VCSEL2 are similar. Briefly, only the results for VCSEL2 are discussed unless stated otherwise. The top, middle and bottom rows

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Received 12 Jun 2013; revised 15 Jul 2013; accepted 15 Jul 2013; published 18 Jul 2013 29 July 2013 | Vol. 21, No. 15 | DOI:10.1364/OE.21.017894 | OPTICS EXPRESS 17898

in Fig. 3 are for the polarization rotated angles of 0°, 60°, 90°, respectively. The 0° polarization rotated angle is referred to the polarization direction of the injection beam being parallel to the polarization direction of the stand-alone injected VCSEL. The 90° polarization rotated angle is referred to the polarization direction of the injection beam being orthogonal to the polarization direction of the stand-alone injected VCSEL. The optical injection ratio of VCSEL2 is −9.4dB. The first column of Fig. 3 shows the time traces of X-polarization. Three time traces show random fluctuations, so the TD cannot be identified. Their corresponding autocorrelation coefficient C as a function of the delay time are calculated and shown in the second column of Fig. 3. In Figs. 3(b1) and 3(b3), peaks occur at twice the flight time τ = 2τf of 7.8 ns, which are similar to the simulation results [18]. So the TD signature is revealed for parallel or orthogonal optical injection. However, the TD signature disappears with the injection beam polarization rotated to 60°, as shown in Fig. 3(b2). The PE has also been analysed to explore the effect of the polarization rotated angle of the optical injection on the TD signature, as shown in the third column of Fig. 3. Many troughs are seen in Figs. 3(c1) and (c3) due to the harmonics and sub-harmonics of the flight time and relaxation oscillation period. The deepest troughs in Figs. 3(c1) and 3(c3) also appear at τ = 7.8 ns. With the polarization direction of the injection beam rotated to 60°, the TD signature has been suppressed significantly. The above results indicate the sensitivity of the TD signature to the polarization rotated angle. The TD signature may not be located exactly at τ [21, 22]. In this paper, if the measured TD signature is located in the interval of [7.5ns, 8.1ns], the TD will be considered retrieved. Cp denotes the peak value of the autocorrelation within [7.5ns, 8.1ns] and is used to evaluate the TD signature. The higher Cp is, the more easily to identify the TD signature, and vice versa. Figure 4 shows the amplitude Cp of the X-polarization of VCSEL2 as a function of polarization rotated angle when the optical injection ratio is −9.4dB. In this Fig., it is obvious that the values of Cp are very sensitive to the polarization orientation. The lowest Cp is measured at an intermediate polarization angle (60°), which is in good agreement with the theoretical prediction [20].

0.20

Cp

0.16 0.12 0.08 0.04 0

20

40

60

80

Polarization Rotated Angle (degree) Fig. 4. The amplitude Cp of the X-polarization of VCSEL2 as a function of polarization rotated angle when the optical injection ratio of VCSEL2 is −9.4dB

The optical injection ratio is a key parameter to control the TD signature [12, 17]. Cp of the X-polarization as a function of polarization rotated angle for various optical injection ratios is plotted in Fig. 5. The squares, circles, up triangles and down triangles represent the injection ratio of −8.8 dB, −9.4dB, −14.7dB and −16.5dB, respectively. It should be noted

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Received 12 Jun 2013; revised 15 Jul 2013; accepted 15 Jul 2013; published 18 Jul 2013 29 July 2013 | Vol. 21, No. 15 | DOI:10.1364/OE.21.017894 | OPTICS EXPRESS 17899

Cp

that for −14.7dB and −16.5 dB injection ratios, not all the polarization rotated angles are plotted. This is because the VCSEL is not in a fully chaotic regime for higher polarization rotated angles with a lower injection ratio. In Fig. 5, Cp decreases in line with the decreasing optical injection ratio between −8.8 dB and −14.7dB for the lower polarization rotated angles. On the other hand, Cp is almost independent to the injection ratio between −8.8 dB and −9.4dB for the higher polarization rotated angles. When the injection ratio reduced to −14.7dB, Cp increases dramatically at a polarization rotated angle of 80°. The reason for this phenomenon is not totally clear. It may due to the lower dimension chaos. With a further reduction of the injection ratio, Cp starts to increase even at a lower polarization rotated angles. The Fig. also shows that the minimum Cp shifts to lower polarization angle for the lower injection ratio. -8.8 dB -9.4 dB -14.7 dB -16.5 dB

0.35 0.30 0.25 0.20 0.15 0.10 0.05 0

20

40

60

80

Polarization Rotated Angle (degree) Fig. 5. The amplitude Cp of the X-polarization of VCSEL2 as a function of polarization rotated angle with the different injection ratio. The squares, circles, up triangles and down triangles are for the injection ratio of −8.8 dB, −9.4dB, −14.7dB and −16.5dB, respectively.

18

Power Ratio

16 14 12 10 8 6

0

20

40

60

80

100

Polarization Roatated Angle (Degree) Fig. 6. The power ratio of VCSEL2 as a function of polarization rotated angle.

To better understand good TD concealment at the intermediate polarization rotated angles, time average output powers of X- and Y-polarizations are measured. The power ratio between X- and Y-polarizations is defined as #192145 - $15.00 USD (C) 2013 OSA

Received 12 Jun 2013; revised 15 Jul 2013; accepted 15 Jul 2013; published 18 Jul 2013 29 July 2013 | Vol. 21, No. 15 | DOI:10.1364/OE.21.017894 | OPTICS EXPRESS 17900

R=

Px , Py

(4)

Cp

where Px and Py are the time average output powers of X- and Y-polarizations, respectively. Figure 6 shows the power ratio as a function of polarization rotated angle. The injection ratio is set to −8.8 dB. Because the power ratio is smaller in the intermediate polarization rotated angles, the interaction between the X-polarization and Y-polarization becomes stronger, which leads to a lower TD signature. A special feature of VCSELs is that their output often includes two orthogonal linearly polarizations. The instabilities in two orthogonal polarizations induced by optical injection often are in anti-phase [24]. Here the TD signatures for both the polarization-resolved and total output power are compared. Figure 7 plots the TD signature of X-polarization, Ypolarization and the total output power as a function of polarization rotated angle. The injection ratio is set at −8.8 dB. The squares, circles and triangles represent X-polarization, Ypolarization and the total power, respectively. All three curves show similar trend – lower TD signatures are achieved at the intermediate polarization rotated angles. For lower polarization rotated angles, the TD signature of the total power is lower than that of the polarization– resolved output power. In this case, partial anti-phase relationship between X- and Ypolarizations will probably removes some TD signature. X-Pol. Y-Pol. Total power

0.35 0.30 0.25 0.20 0.15 0.10 0.05 0

20

40

60

80

Polarization Rotated Angles (degree) Fig. 7. The amplitude Cp of VCSEL2 as a function of polarization rotated angle. The squares, circles and triangles are for X-polarization, Y-polarization and the total power, respectively.

4.3 Effect of bias current on TD signature The influence of the VCSEL bias current on the TD signature is discussed here. The injection ratio and the frequency detuning are fixed at −8.8 dB and Δf = 0, respectively. Figure 8 shows the amplitude Cp of the total power as a function of polarization rotated angle with the different bias currents. For a bias current of 3.68mA, the lowest TD signature is achieved at the intermediate polarization rotated angle (60 o), which is similar to the result for the bias current of 3.18mA. However, Cp for 3.68mA is lower than that of 3.18 mA when the polarization rotated angles are smaller than 80°. This is because the VCSEL operates at the polarization bistability regime at a bias current of 3.68 mA, the competition between the Xpolarization and Y-polarization becomes stronger, which leads to a lower TD signature. For the bias currents of 5mA and 5.99mA, Cp increases with the increasing polarization rotated angle, the minimum TD signature is obtained at a parallel optical injection. It is of interest to note that the TD signature at non-bistability regime is almost independent on the bias current

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Received 12 Jun 2013; revised 15 Jul 2013; accepted 15 Jul 2013; published 18 Jul 2013 29 July 2013 | Vol. 21, No. 15 | DOI:10.1364/OE.21.017894 | OPTICS EXPRESS 17901

for the low polarization rotation angles, however, for high polarization rotated angles, the TD signature is suppressed better at a lower bias current. The exactly reason for this is unclear; further investigation will be carried out in the future.

3.18mA 3.68mA 5mA 5.99mA

0.6 0.5 Cp

0.4 0.3 0.2 0.1 0.0

0

20

40

60

80

Polarization Rotated Angle (degree) Fig. 8. The amplitude Cp of the total power of VCSEL2 as a function of polarization rotated angle with the different bias currents.

4.4 Effect of the frequency detuning on the TD signature

0.4

Cp

0.3 0.2 0.1 -15 -10 -5

0

5

10 15

Frequency Detuning (GHz) Fig. 9. The amplitude Cp of the total power of VCSEL2 as a function of the frequency detuning

The frequency detuning is another important parameter in optical injection systems. In Fig. 9, the maximum autocorrelation of the total power in τ region (Cp) is displayed as a function of detuned frequency. The injection ratio is set at −8.8 dB and the polarization rotated angle is set at 0°. In this result, the minimum value of Cp occurs at around zero frequency detuning, which is similar to that for mutually coupled DFB lasers with low or intermediate injection ratio [17]. It is also in agreement with the numerical simulation results for polarizationresolved chaotic output in mutually coupled VCSELs with low injection ratio [18].

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Received 12 Jun 2013; revised 15 Jul 2013; accepted 15 Jul 2013; published 18 Jul 2013 29 July 2013 | Vol. 21, No. 15 | DOI:10.1364/OE.21.017894 | OPTICS EXPRESS 17902

5. Conclusion The effect of polarization rotated angle of optical injection on the time-delay signature in mutually coupled VCSELs has been studied experimentally. The results indicate that the minimum TD signature is obtained at the intermediate polarization angle for low bias current, which is in good agreement with the theoretical prediction. The strong interaction between the X-polarization and Y-polarization at the intermediate polarization rotated angle is believed to be the reason for the low TD signature. The TD signature for the total power is lower than that of the polarization-resolved output power because of a partially anti-phase relationship between the X-and Y-polarization. The optical injection ratio mainly affects the TD signature at lower polarization rotated angles. There is an optimum injection ratio to achieve the best TD concealment at low polarization rotated angles. The frequency detuning is another parameter to influence the TD signature; the minimum TD signature is achieved around zero frequency detuning. The TD signature is independent of the bias current for the lower polarization rotated angle except in a bistable regime. However, the TD signature increases with increasing bias current for the intermediate to higher polarization rotated angles. Therefore the TD signature concealment of chaos can be achieved in mutually coupled VCSELs by properly selecting polarization rotated angle, bias current, injection ratio and frequency detuning.

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Received 12 Jun 2013; revised 15 Jul 2013; accepted 15 Jul 2013; published 18 Jul 2013 29 July 2013 | Vol. 21, No. 15 | DOI:10.1364/OE.21.017894 | OPTICS EXPRESS 17903