Optical scramblers that scramble optical temporal waveform signals have significant applications in cryptography^[1–4]. For example, applying a pair of optical scramblers on a public random signal can generate two identical private random signals for physical key distribution^[5]. Furthermore, if the scrambling effect is irreversible, then optical scramblers can also be used for physical one-way functions^[6]. Note that for above cryptography applications, dissimilarity between the input and the output of the optical scrambler is very important for security.

Scrambling can be realized by the nonlinear response in an optical or opto-electronic system, typically including semiconductor lasers^[5,7–15] and optical dispersive devices^[16–18]. For semiconductor lasers, the scrambling effect originates from the nonlinear laser dynamics induced by injecting input light and by delayed self-feedback^[7]. Several types of semiconductor lasers, such as distributed feedback Bragg lasers^[7–9], Fabry–Perot lasers^[10,11], and vertical-cavity surface-emitting lasers^[12,13], have been proved to have a scrambling effect. Unfortunately, for typical complex signals, such as chaotic light^[8,12] and noise light^[9,10], the input-output correlation values are still high and thus the scrambling effect needs to be improved. For example, amplitude-constant phase-random light^[5,14] was proposed for reducing the input-output correlation of semiconductor lasers. Optical dispersive devices like chirped fiber Bragg gratings provide a scrambling scheme with low input-output correlation^[18]. The main issue is that its simple hardware structure could be duplicated by an eavesdropper.

We notice that whispering-gallery-mode (WGM) microcavities have nonlinear feature responses due to nonuniform transmission spectra^[19] and long photon lifetimes^[20]. The nonuniform transmission causes the nonuniform filter effect, and the long lifetime of photons in the cavity makes more modes interfere. Thus, the scrambling effect of a WGM microcavity in a wide-spectrum input can be expected. Most recently, Jiang et al. used a WGM microsphere cavity and self-phase modulated feedback to generate broadband chaos^[21]. Their work focused on chaos bandwidth and time-delay signature, but the input-output correlation was not studied, which is the basic feature for a scrambler.

In this Letter, we experimentally demonstrate an optical scrambler using a WGM micro-bottle cavity (MBC). Compared with the microsphere cavity, the MBC has a longer axis^[22], which provides a more complex mode-field distribution and a broader coupling area. These features could generate high efficiency coupling and increase the number of modes, which are beneficial to the scrambling effect. To experimentally verify the scrambling effect of the MBC, a chaotic light is used as the input light. The scrambling effects, as well as the signal complexity at different coupling states, have been explored. Experimental results show that high-quality scrambling with a low input-output correlation near 0.03 can be achieved under the over-coupling state, accompanied by complexity enhancement.

The schematic diagram is shown in Fig. 1(a). An optical input signal is coupled into an MBC through a tapered fiber (TF) and then its temporal waveform is scrambled. The output signal thus has a waveform uncorrelated to the input. A verification experiment was carried out by using a chaotic light as the input signal. The experimental setup is shown in Fig. 1(b). The chaotic input light is generated by a distributed feedback Bragg (DFB) laser with optical feedback from an external mirror. In the feedback path, a polarization controller and an attenuator are used to adjust the polarization state and feedback strength, respectively. A proportion of the chaotic light, after being amplified by an erbium-doped fiber amplifier, is injected into the MBC through the TF. Note that the output waveform is sensitive to the polarization state of input light, and thus a polarization controller is inserted before the MBC. A 3 dB coupler taps into a portion of the input light, which, together with the output light, is detected using a real-time oscilloscope (Tektronix DPO73000, 30 GHz bandwidth) with photodetectors (Finisar XPDV2120RA, 40 GHz bandwidth).

The inset of Fig. 1(b) shows the photomicrograph of the MBC and the TF (the horizontal thin line). The MBC was made by pulling and discharging two sections of a single-mode fiber with a fiber fusion splicer. The maximum diameter and total length of the MBC are 120 µm and 700 µm, respectively. The intrinsic Q of the cavity is up to 107. The TF was made by pulling and heating a commercial single-mode fiber, and the thinnest diameter is about 1.6 µm. The bottle was set with an angle of about 34° to the TF. Both the TF and the MBC can be precisely positioned by 3-D positioning stages, and the coupling state can be adjusted.

The scrambling effect is characterized by the cross-correlation coefficient (CC) between the input and the output waveforms. The CC is defined as 〈(Ix−〈Ix〉)(Iy−〈Iy〉)〉/σxσy, where Ix and Iy are the time series of two signals, σx and σy are their standard deviations, and 〈·〉 denotes the mean operator^[23].

In our experiments, the DFB laser was biased at 80 mA (threshold current 23 mA), and its free-running wavelength was stabilized at 1548.822 nm using a temperature controller. The length of the feedback fiber path was about 16 m, and the corresponding feedback delay τ is about 80 ns. The optical feedback strength was adjusted to 0.2, calculated by the power ratio of the feedback light to the laser output. The chaotic light output from the DFB laser was used as the input signal, and its optical spectrum is shown in the gray line (red online) in Fig. 2(a). We further measured the MBC transmission spectrum as the wavelength-dependent transmissivity by scanning the wavelength of a tunable narrow-linewidth laser (Yenista-T100s, 400 kHz linewidth). The black line in Fig. 2(a) shows a transmission spectrum of the MBC, which was obtained with a coupling position close to the waist of the TF and an angle of about 34° between the MBC axis and the TF axis. There are many transmission lines with different heights, which are a kind of Fano-like line shape, that are introduced because of the large coupling loss^[24,25]. Figure 2(b) plots the probability distribution of the transmission line heights. The transmittivity concentrates within the range from 0 to 0.2. The average transmission intensity (ATI) is calculated as 0.114, which is used to characterize the coupling strength between the TF and the MBC. As indicated in the transmission spectrum, each frequency component of the input light undergoes a different change. As a result, the scrambling effect will appear on the output signal.

Figure 3 shows the time-frequency characteristics of the input and output of the MBC under the coupling condition corresponding to Fig. 2. As shown in Fig. 3(a), the radio frequency (RF) spectrum of the input (blue online) is concentrated near the laser relaxation oscillation frequency. Clearly, the RF spectrum of the output light (red) becomes different. The low-frequency components are raised, and the peak at the relaxation frequency disappears. Moreover, the temporal waveforms of the input and the output are vastly different, as shown in Fig. 3(b). The CC between them is only calculated as 0.028, as shown in Fig. 3(c). The low correlation is also displayed in the scatter plot in the inset. The above results prove that the MBC scrambles the chaotic signal. There are no other peaks in the correlation except the time-delay signature of the feedback DFB laser, which indicates that in the output there is no intrinsic feature of the cavity.

Further, we calculate the permutation entropy (PE) to analyze whether there is complexity enhancement. The permutation entropy of the time series is calculated as hp=−(Σ(p(πi)×lnp(πi))/ln(m!), where m is the embedding dimension, p(πi) is the ordinal pattern probability, and i=1,…,m!^[26]. We chose m=4 as Ref. [27] did. Note that the embedding delay te is required for phase-space reconstruction and will affect the PE because it changes elements of the reconstructed vectors. Figure 3(d) plots the PE as a function of the embedding delay of the input and output signals. Both curves have several minima locating at τ/3, τ/2, and τ, where τ is the feedback delay of the chaotic laser. The PE value is calculated by the average of all the minima. As a result, a small PE enhancement can be found from 0.9761 to 0.9855.

By fine adjusting the coupling point position along the axis of the TF, one can obtain different scrambling effects. Figures 4(a1)–4(a3) plot three typical transmission spectra of the MBC. The time series, RF spectra, correlation curves, and PE curves of the corresponding output and input signals are plotted in columns 2–5 in Fig. 4.

Figure 4(a1) represents a state of under coupling in which about half the light power of the resonance wavelength could couple into the cavity. The ATI is 0.963. In this case, the input-output correlation is 0.855, and the PE is slightly decreased by 0.0003. The waveform and RF spectrum of the output are similar to those of the input. The coupling point moves toward the waist of the TF, where it has the thinnest diameter, the coupling strength increases accordingly, and the bottoms of some coupling notches reach 0. Here, we call the state that the bottoms of many modes reach 0 the critical coupling state, as shown in Fig. 4(a2). The ATI is 0.752. Both the coupling strength and the mode density are larger than those of the under coupling state. The CC reduces to 0.698. The low-frequency component of the RF spectrum is flat, and the PE enhancement is 0.0003, as shown in Figs. 4(d2) and 4(e2), respectively.

The cavity moves continuously and the coupling strength will keep on increasing and achieve an over coupling state. Nearly all the pump light could couple into the cavity^[28], but only some of those whose wavelength resonances with the WGMs could persist in the cavity and be coupled back to the TF, which behave as the peaks and are shown in Fig. 4(a3). In this state, most of the light on the transmission spectrum has traveled to the cavity, the ATI is low, and the filter effect on the output is evident. The RF spectrum of the output is completely different from the input one, and its CC decreases to 0.077. The energy in the RF spectrum concentrates on the low frequency in Fig. 4(d3), and the PE is clearly enhanced with the value of 0.0023.

Figure 5 shows the effects of the coupling position on the scrambling effects. The coupling position d is defined as the distance from the coupling point to the thinnest point of the TF. Figure 5(a) shows that the ATI of the MBC transmission spectrum will decrease from a plateau down to another one as d reduces. As d>6mm, the ATIs are close to 0.995, denoting states of under coupling. As d<4mm, the ATIs are below 0.390, meaning over coupling states. The middle region can be treated as critical coupling states. As shown in Figs. 5(b) and 5(c), the input-output CC changes with a highly similar trend to that of the ATI, but the PE enhancement is opposite. These trends show that effective scrambling and complexity enhancement can be achieved with over coupling states. In Ref. [21], the coupling state is similar to the critical coupling in which the coupling strength is not strong enough, and the power coupled back to the TF from the cavity is low. Thus, what they achieved is time-delay signature suppression, not time-sequence scrambling.

This scrambling effect with the over coupling state could be explained by the following mechanisms. At the over coupling state, there are a lot of modes with strong coupling strength, shown as the low intensity in the transmission spectrum. Thus, the interference among the numerous modes will be strong, and the time sequence will be distorted conspicuously, which makes the cross correlation between the input and output very low and enhances the signal’s complexity, i.e. the permutation entropy. However, at the under coupling state, the coupling strength is weak, and the number of modes in the transmission spectrum is small. The energy coupled back to the TF is small, and the inference among the modes is thin, which makes the scrambling effect insignificant. By increasing the coupling strength, the coupling modes will increase, and the interference, as well as scrambling effect, becomes stronger. The trends of parameters in Fig. 5 coincide with this theory. By the above analysis, the CC and the PE enhancement depend on the density of the modes, which is related to the size of the cavity, and this needs further study.

After demonstrating the waveform scrambling effects of the MBC, we should discuss some issues that remain for future work, to promote practical applications such as key distribution. According to Ref. [5], scramblers used for key distribution usually should be controllable by adjusting the parameters to produce uncorrelated outputs for identical input. The current MBC used in our experiment is a passive device and lacks tunable parameters. However, we experimentally found that the MBC output is sensitive to the polarization and the wavelength of the input. Thus, by inserting an additional polarization controller into the cavity before injection, the control of the output can be realized. The other possible way is to integrate an active device on the cavity to adjust the transmission spectrum by opto-thermal modulation^[29–31]. Moreover, the over coupling state leads to a large insertion loss. Fortunately, for key distribution, the output signals are used in local to extract random bits and thus are not to be transmitted. Thus, the insertion loss can be acceptable.

In summary, we have proposed an optical scrambler based on a WGM micro-bottle cavity. Due to the interference among numerous WGMs in the cavity, efficient scrambling of the chaotic signal is realized. In the experiment, the scrambling effect under different coupling states has been analyzed and illustrated. The CC between the input and the output is only 0.028, and the PE is improved clearly. It has the advantages of low cost, simple structure, and high scrambling efficiency, and has great potential for applications such as encryption, key distribution, authentication, and optical neural calculation.