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Abstract
Ghost imaging in the time domain has opened up new possibilities to retrieve ultrafast waveforms. A pre-requisite to ghost imaging in the time domain is a light source with random temporal intensity fluctuations that are fully uncorrelated over the duration of the temporal waveform being imaged. Here, we show that random fiber lasers are excellent candidates for ghost imaging in the time domain. We study the temporal correlations of the intensity fluctuations of a random fiber laser in different operating regimes and compare its performance in temporal ghost imaging configurations with that of a conventional multi-mode cavity-based fiber laser. Our results demonstrate that random fiber lasers can achieve superior performance for ghost imaging as compared to cavity-based fiber lasers where strong correlations at the cavity round-trip time can yield artefacts for waveforms of long duration.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Ghost imaging (GI) enables to generate an image of an object by correlating the intensity of two light beams: a reference beam that do not interact with the object whose spatial intensity distribution is resolved with a high-resolution detector, and a test beam illuminating the object whose intensity is integrated by a single-pixel detector. Neither of the two beams carries sufficient information to generate an image of the object but it is their correlation over multiple and distinct illuminating spatial intensity profiles that allows to obtain an image [1]. An important benefit of GI is that, unlike direct imaging techniques, it is insensitive to (linear) perturbations that may occur between the object and single-pixel detector in the test arm, and indeed GI has been shown to be a powerful approach to obtain high resolution images of object in the presence of turbulence or large attenuation [2–4]. Ghost imaging is not restricted to spatial objects, and it has been extended to the measurement of absorption spectrum of molecules [5], the recovery of hidden states of polarizations [6], and reconstruction of temporal objects [7–10].
When applied in the time domain, temporal ghost imaging (TGI) uses fast temporal intensity fluctuations of a multimode laser to probe a temporal object in the form of an ultrafast waveform [8,11,12]. The TGI has potential applications to the dynamic characterization of free electron lasers [13], secure and quantum communications [14–16], and quantum device characterization [17]. A critical pre-requisite to ghost imaging in the time domain is that the temporal intensity fluctuations of the light source must be uncorrelated within the duration of the temporal object to be reconstructed [8,12,17]. Previous demonstrations have typically utilized cavity-based multimode quasi-continuous wave (CW) fiber lasers [8,12]. However, this type of laser generally exhibits time delay signatures at the cavity round-trip time in the autocorrelation function that can limit the duration of measured object [18]. Fiber amplified spontaneous emission (ASE) sources can be an alternative, but the power of filtered ASE source is typically low and needs to be further boosted by another fiber amplifier [17], increasing the complexity and the cost of the system.
Recently, random fiber lasers based on Rayleigh scattering feedback inside the fiber have been experimentally demonstrated and attracted great interest for their simple designs and unique properties in terms of output power, efficiency, multi-wavelength generation, and broad tunability [19,20]. Quasi-CW random fiber lasers have been shown to be associated with stochastic temporal intensity variations with no stationary cavity modes due to the cavity-free nature of the design [21,22]. This makes quasi-CW random fiber lasers promising candidates as fiber-based chaotic light sources and in particular for GI in the time domain. Here, we explore the feasibility to use a Rayleigh feedback assisted ytterbium-doped random fiber laser (YRFL) which has relatively broad bandwidth as the light source to perform GI in the time domain. We experimentally demonstrate that, while relatively strong correlations are manifested when the random fiber laser operates near threshold, it exhibits random temporal intensity fluctuations when the pump power is well above the threshold. This enables near-perfect retrieval of ultrafast temporal objects, in contrast with conventional cavity-feedback based fiber lasers that give rise to artefacts in the retrieved temporal object when the object duration exceeds the cavity round-trip time.
2. Principle of TGI
We begin by briefly introducing the principle of GI in the time domain. A schematic illustration of a typical setup is shown in Fig. 1. We use a quasi-CW YRFL or a cavity-based ytterbium-doped fiber laser (YFL) as the light source in TGI. The quasi-CW laser is then divided into a reference and test arms. In the reference arm, a fast detector is used to record the random temporal intensity fluctuations Iref (t) from the laser. In the test arm, an intensity modulator imposing a temporal intensity modulation T(t) acts as the temporal object. Light transmitted through the temporal object Itest is detected by a slow (integrating) detector with no temporal resolution. The temporal object can then be retrieved from the correlation function defined as [8,12]
3. Experimental characterization of YRFL
The layout of the random fiber laser used in this work is shown in Fig. 2(a). A 3.5 m-long ytterbium-doped double-cladding fiber (Nufern LMA-YDF-10/130) with 10/130 µm core and cladding dimensions, respectively, is cladding-pumped by a 976 nm laser diode (LD). Random Rayleigh scattering from an 8 km-long standard single-mode fiber (SMF) provides the random distributed feedback for lasing. The cavity is half-open with a fiber Bragg grating (FBG) attached to the signal port of the pump combiner. The FBG reflectivity is centered at 1080 nm with a 3-dB bandwidth of 0.1 nm, and maximum reflectivity of 63%. An optical isolator with 1.5 dB insertion loss is used at the end of the SMF together with an angle-cleaved fiber termination to prevent unwanted back-reflection that may influence the random lasing process. The output power of the random fiber laser at 1080 nm is shown as a function of pump power in Fig. 2(b). Above threshold (corresponding to a pump power of 0.6 W), the output power of the random fiber laser increases quasi-linearly with a 10% slope efficiency and maximum output power close to 300 mW. It is worth noting that, in principle, the slope efficiency could be increased by using a longer doped fiber allowing to reach an output power exceeding the watt-level [23].
Fig. 2. Experimental setup and output power of ytterbium-doped random fiber laser (YRFL). (a) Experimental setup of YRFL; and (b) lasing output power versus laser diode (LD) pump power
We first characterize the properties of the random fiber laser at different pump powers as shown in Fig. 3 and Fig. 4. The figures show the optical spectra (a) recorded by an optical spectrum analyzer with 0.02 nm spectral resolution, typical examples of real-time temporal intensity fluctuations (b) measured over 100 ns temporal window with a high speed DC-blocked photodetector (Conquer, 10 GHz bandwidth) and real-time oscilloscope (RS, 4 GHz bandwidth, 20 Gsa/S sampling rate), and the time-to-time intensity fluctuation (Pearson) correlation map (c) calculated over 10,000 consecutive temporal windows. One can see in Figs. 3(a) and 3(b) that for a pump power of 0.8 W, just beyond threshold, the optical spectrum is highly structured, and in the time-domain the intensity consists of an irregular and noisy train of pulses. These observations are consistent with the generation of narrow-band spectral components and the cascaded stimulated Brillouin scattering (SBS) [19,20,25]. In this case, the generation of discrete random lasing modes [24,25] and the cascaded SBS process would lead to partial intensity correlations in the time domain among consecutive pulses. As shown in Fig. 3(c), multiple lines are indeed manifested in the time-to-time correlation map, confirming that the temporal intensity fluctuations are partially correlated, which would be highly detrimental for GI in the time-domain.
Fig. 3. Characterization of ytterbium-doped random fiber laser (YRFL) with 0.8 W of pump power. (a) The measured spectrum of YRFL; (b) the recorded temporal intensity fluctuations over a 100 ns time window; and (c) time-to-time intensity fluctuations correlation map calculated over 10000 temporal windows.
Fig. 4. Characterization of YRFL with 3 W of pump power. (a) Spectrum of ytterbium-doped random fiber lasing; (b) Recorded temporal intensity fluctuations over a 100 ns time window; (c) Time-to-time intensity fluctuations correlation map calculated over 10000 temporal windows
The temporal correlation of the YRFL is further investigated in a regime well-above threshold. For a pump power of 3 W, we can see the lasing characteristics differ significantly from that seen near-threshold. The optical spectrum shown in Fig. 4(a) is smoother and broader compared to that in Fig. 3(a). This is caused by four-wave mixing and self-phase modulation [19,20]. Correspondingly, in the time domain, the intensity profile shown in Fig. 4(b) is quasi-continuous with fast fluctuations that are of the order of the inverse spectral bandwidth (note that with the DC-blocked photodetector the recorded temporal intensity shows fluctuations around zero). The time-to-time intensity fluctuations correlation map plotted in Fig. 4(c) only exhibits non-zero values on the diagonal line, indicating that the intensity fluctuations within the measurement window are now fully uncorrelated such that the YRFL is suitable to perform TGI of bit sequences in excess of 100 ns duration for a pump power well beyond threshold.
For comparison, a conventional multimode cavity-based ytterbium-doped fiber laser (YFL) with a pair of FBGs is also constructed as shown in Fig. 5(a). The passive SMF in the YRFL is replaced by a FBG with 2 nm of 3-dB bandwidth and 95% of reflectivity. The cavity length between the FBGs pair is about 8 m (including the length of ytterbium-doped fiber and the passive fiber), corresponding to a cavity round-trip time of 80 ns. The YFL shows the slope efficiency of about 15%, and the output power of cavity based YFL is 0.4 W for a pump power of 3 W. The temporal intensity variations recorded over a 100 ns temporal window for a pump power of 3 W are shown in Fig. 5(b). The time-to-time intensity fluctuation correlation map calculated over 10,000 consecutive measurement windows is shown in Fig. 5(c). One can clearly see the strong correlation at a time interval corresponding to the cavity round-trip time. This type of cavity-induced correlations in the temporal intensity fluctuations will limit the length of the temporal window for TGI applications, and hence the duration of the ultrafast waveform that can be retrieved.
Fig. 5. Characterization of cavity-based ytterbium-doped fiber laser. (a) Experimental setup; (b) Recorded temporal intensity fluctuations over a 100 ns time window; (c) time-to-time intensity fluctuations correlation map calculated over 10000 temporal windows at 3 W pump power.
4. Simulated TGI results
We next compare the performances of the random fiber laser and cavity-based fiber laser for TGI using numerical implementation. We use the experimentally recorded temporal intensity fluctuations as Iref (t). In the test arm, we define a numerical temporal object in the form of a bit sequence as shown in Fig. 6 and calculate the (time) integrated intensity Itest of the light transmitted through the temporal object. The ghost image of the temporal object is then retrieved from the normalized intensity correlation function C(t) defined by Eq. (1).
Fig. 6. Stimulated temporal GI images with different laser sources. Upper panel: temporal object; Middle panel: temporal GI image with YRFL; Lower panel: temporal GI image with cavity-based YFL.
The simulated TGI images with the random and cavity-based fiber lasers computed over 10,000 recorded temporal windows of 100 ns duration are shown in Fig. 6. We can see that in the case of the random fiber laser, the temporal ghost image is nearly perfectly retrieved, while for the cavity-based fiber laser one can see the emergence of artefacts signals in the ghost image arising from the cavity-induced correlations visible in Fig. 5(c). For the cavity-based fiber laser, the strong correlation at the cavity round-trip time of 80 ns generates artefacts at around 7 and 95 ns in the reconstructed bit sequence. More specifically, the artefacts are located 80 ns apart from the real object in the bit sequence. This means that the artefact at 7 ns arises from the bit in the sequence at 87 ns while that at 95 ns arises from the bit in the sequence at 15 ns. Note that no artefact corresponding to the bit at 47 ns is observed in the ghost image as the artefacts in this case falls outside the measurement window. These results confirm the ability of random fiber lasers to perform GI in the time domain while cavity-based fiber laser sources may lead to the generation of artefacts in the retrieved image due to cavity-induced intensity correlations. Of course, in principle one can still use cavity-based multimode lasers, however in this case one should ensure that the length of measurement window is shorter than the cavity round-trip time in order to avoid artefacts signals. However, since the duration of the temporal object may vary dramatically depending on the particular application, this may necessitate the use of different laser configurations. Random fiber laser on the other hand can flexibly adapt to different TGI applications independently of the temporal object duration.
In addition to the absence of artefacts in the TGI image, we discuss below other potential benefits of random fiber lasers. The “cavity-free” nature of random fiber laser reduce the need for point reflectors as compared to the cavity-based fiber lasers where a pair of wavelength-matched reflectors is required, such that random fiber laser sources can offer simpler and more cost-effective solutions to perform GI in different spectral regions. Random fiber laser sources based on rare-earth-doped fibers can operate over a broad range of wavelengths, depending on the gain medium, e.g. at 1 µm, 1.4 µm, 1.5 µm and 2 µm with ytterbium-doped fiber, bismuth-doped fiber [26], erbium-doped fiber [27] and thulium-doped fiber [28], respectively. One can also construct compact Raman gain-based random fiber lasers operating in the 1-2 µm wavelength region [29,30]. The bandwidth of random fiber lasers can be further tuned by the gain mechanism and/or the spectral filtering inside the cavity. The bandwidth can typically vary from 0.01 nm to 1 nm [31–33], enabling in principle ghost imaging of ultrafast waveform with 1 Gb s-1 to 100 Gb s-1 speed. For slower temporal objects, random fiber lasers based on Brillouin gain or semiconductor gain with much narrower bandwidth ranging from kHz to MHz could be employed [34,35]. Another advantage of random fiber lasers as compared e.g. to ASE sources is the higher output power [36–38], which makes them also suitable for TGI with wavelength-conversion [12] where relatively high power is typically required for the nonlinear process.
5. Conclusions
In summary, we have explored the possibility to use a random fiber laser as a light source for time-domain GI applications. Using a time-to-time correlation analysis, we have shown that the temporal intensity fluctuations of random fiber lasers are uncorrelated when the pump power is well above the threshold, while relatively strong correlations exist near threshold. This behavior is in contrast with a conventional cavity-based fiber laser where temporal intensity fluctuations are correlated from roundtrip to roundtrip. Simulations of a TGI process shows that the random fiber laser has superior performances, resulting in accurate reconstructed temporal objects unlike a cavity-based fiber laser where the roundtrip-to-roundtrip correlations leads to the generation of artefacts in the ghost image. Our results not only increase our understanding of temporal correlation properties of random fiber laser with relatively broad bandwidth, but also indicate that random fiber laser could be an excellent candidate for GI applications and other correlation-based systems [39].
Funding
National Natural Science Foundation of China (NSAF U1730141); Fundamental Research Funds for the Central Universities (YJ201979, YJ201982); Academy of Finland (298463, 318082, Flagship PREIN 320165).
Acknowledgment
H.Wu acknowledges the fruitful discussions with Dr. Piotr Ryczkowski in Tampere University.
Disclosures
The authors declare no conflicts of interest.
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