1. Introduction

Within the last decade there is an increasing demand for bandwidth in optical communication networks as well as an adequate infrastructure, leading to enhanced laser sources with narrower linewidths and low noise. Increasing the dense of the communication grid requires narrower optical filters. Another important field is the utilization of frequency combs [1] for different applications like THz-Wave generation [2], Nyquist pulse generation [3, 4], for ideal rectangular-shaped microwave photonics filters with tunable passband profiles [5, 6, 7], the all optical storage of data signals [8, 9] and time measurements with unsurpassed precision [10]. All these optical components and sources need to be characterized properly in their spectral response. Additionally, most transmission effects can be directly seen in the spectral domain of the transmitted signal. Therefore, different methods are available for the analysis of the spectrum. Commonly, grating based optical spectrum analyzers (OSA) are used [11]. In principle, they use a monochromator as tunable filter. Within the monochromator a diffraction grating, basically a mirror with extremely narrow spaced grooves on its surface, separates the different wavelengths of light. Subsequently the diffracted light passes through an aperture to the photodetector. During the measurement of a broad wavelength range the grating is rotated. Thus, only specific wavelengths, depending on the position of the diffraction grating, can pass through the aperture. The width of the aperture itself is variable and determines the resolution of the device. State of the art OSA achieve resolutions of 1.25 GHz, which equals 10 pm at a wavelength of 1550 nm. All spectral components beneath can not be displayed. Different types are based on interferometers [11], e.g. Fabry-Perot and Michelson interferometers. The resolution of the Fabry-Perot based OSA depends on the reflection coefficient and the distance of the mirrors, which leads to achievable resolutions between 100 MHz (800 fm) and 10 GHz (80 pm). However the measurement range is limited by the free spectral range. The Michelson interferometer is based on creating an interference pattern between the signal and a delayed version of itself. In between commercially available devices based on an interferometer structure reach resolutions of 5 MHz, corresponding to 40 fm [12]. In parallel, another approach for the high resolution measurement of optical spectra based on the nonlinear effect of stimulated Brillouin scattering (SBS) was developed [13, 14]. Thereby, a pump wave generates a narrow bandwidth gain in a standard single mode fiber (SSMF) that amplifies a counter propagating signal [15]. The spectrum is measured by shifting the pump wave and recording the amplified signal with a power sensor. The resolution of the spectrometer depends on the SBS bandwidth which is usually in the range of 10 to 30 MHz (80 to 240 fm). Several approaches have shown the bandwidth reduction of SBS down to 3 MHz (24 fm) [16, 17, 18]. The optical rejection ratio and respectively the dynamic range can be enhanced by utilizing the polarization pulling effect of SBS [19]. Thereby, all unwanted spectral components are suppressed entirely [20]. Based on the polarization effects, Brillouin dynamic gratings can be generated. First spectral measurements with this technique have shown a resolution of 0.5 MHz (4 fm) [21]. A completely different method for the measurement of optical spectra is the heterodyne technique. Thereby, the optical signal is down converted with the help of a local oscillator (LO). The optical signal is converted to the electrical domain with a photodiode and analyzed with an electrical spectrum analyzer (ESA). The achievable measurement range depends on the bandwidth of the photodiode as well as the bandwidth of the ESA. The measured spectrum represents a convolution of the local oscillator with the signal. Therefore, the line width of the LO directly defines the resolution. However, one of the main problems with heterodyne systems is that due to the down conversion false mixing products can occur. Unwanted mixing products in the base band that arise from direct detection through the photodiode need to be filtered electrically and limit the measurement range. In general the resolution or bandwidth of common approaches is not sufficient for the above mentioned applications.

Here we present an optical spectrum analyzer with ultra-high resolution over a spectral range which, in principle, is just restricted by the transparency range of the used Brillouin medium. Therefore, a small part of the unknown spectrum is preselected with polarization pulling assisted stimulated Brillouin scattering and all unwanted out of band components are suppressed. A detailed view of the preselected part of the spectrum is enabled with a subsequent heterodyne detection. Unwanted mixing products in the base band do not occur since the measurement at the electrical spectrum analyzer takes place at an upshifted frequency. For the measurement of the complete spectrum, the pump wave, and the gain and LO respectively, are shifted through the unknown spectrum. The method operates with off the shelf telecommunication equipment and enables the high resolution measurement of optical signals without any bandwidth limitation through unwanted mixing products.

2. Method

The proposed method for the ultra-high resolution analysis of optical signals is based on narrow band optical filtering in the first instance and a subsequent heterodyne detection with a narrow linewidth local oscillator. In principle, this technique combines the wide tuning range of Brillouin optical spectrum analysis (BOSA) and the suppression of the unwanted components through the polarization pulling effect with the high achievable resolution of heterodyne systems. The basic principle of the method is illustrated in Fig. 1. During the SBS process a pump wave generates a narrow gain for counter propagating signals. The gain region is frequency down shifted by f_SBS, which is around 11 GHz, and has a natural width of 30 MHz [15]. For higher resolutions the bandwidth can be reduced down to 11 MHz with higher pump powers or special fibers [22]. Significantly lower bandwidth down to 3 MHz can be achieved with the overlapping of the gain with two losses [16], with an aperture that covers part of the signals [17] or in a multi stage system [18]. All signal components inside the gain region are amplified. Thereby the state of polarization of the amplified signal is drawn towards the state of polarization (SOP) of the pump wave [19]. The amplified components can be separated from the unamplified ones with a simple polarization filter like a polarization beam splitter or polarizer. This leads to just a small part of the spectrum under test (SUT) which can now be analyzed in detail with heterodyne detection. The LO is directly generated from the pump wave in order to simplify the setup and avoid drifting. In this regard, the pump wave is split and externally modulated with f_LO < f_SBS, which is a little smaller than the Brillouin frequency shift in the fiber. The down conversion to the electrical domain is done by a narrow bandwidth photodiode.

 

Fig. 1 Operation principle.

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Thereby, unwanted mixing products from the signal components inside the gain region are down converted to the base band and therefore outside the measurement range of interest at the ESA, represented by the gray lines part in Fig. 2. The wanted mixing products with the local oscillator arise around the frequency f_meas, depicted as red trace in Fig. 2. This frequency needs to be at least twice the Brillouin gain bandwidth in the fiber and below the cut-off frequency of the photodiode. The electrical signal is finally analyzed with an ESA within a narrow span, shown as blue range in Fig. 2, at f_meas = f_SBS − f_LO. Therefore, just the heterodyned components in the center of the SBS gain are displayed and measured at the ESA. In order to measure the complete spectrum the pump wave, and respectively the gain and LO, is shifted through the unknown spectrum.

 

Fig. 2 Illustration of the mixing products at the photodiode (gray and red) after the preselection with PPA-SBS and subsequent heterodyning, and the final measurement range of the ESA (blue).

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Exemplary, a measurement of the partial amplification of the SUT and suppression of the unwanted signal components with PPA-SBS can be seen in Fig. 3. The black curve represents the SBS gain. The red curve shows a small amplified spectral part of the SUT. Therefore, a 2⁹−1 PRBS with a data rate of 1 Gbps was used. This results in a sinc shaped discrete spectrum with a frequency distance of Δf = 1.95 MHz between the lines. With a proper polarization alignment the unwanted out of band components can be suppressed, as illustrated in Fig. 3. The gray curve demonstrates a misalignment of the polarization and therefore the result which would be achieved without polarization pulling. Due to the mixing in the photodiode this leads to significant distortions.

 

Fig. 3 The red curve shows the detailed measurement of a spectral part of the SUT from a 2⁹−1 PRBS at a data rate of 1 Gbit/s within the SBS bandwidth (black curve). An incorrect setting of the polarization, which leads to unwanted mixing products, is illustrated by the gray line.

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3. Experiment

The experimental setup for the first proof of concept experiments can be seen in Fig. 4. The main source for the system is a narrow linewidth fiber laser (FL). It acts as pump wave for SBS and local oscillator for the heterodyne detection. The PPA-SBS part of the setup is shown by the green box in Fig. 4. In order to shift the pump wave, as well as the LO, through the SUT, the laser is modulated externally with a Mach-Zehnder modulator (MZM1), which is driven in the carrier suppressed regime, with f_SBS. In order to avoid unwanted interferences, the lower sideband is filtered out with a wave shaper (WS, Finisar 1000s). Subsequently, the remaining sideband is amplified with an EDFA in order to provide sufficient power for the SBS. The polarization of the pump wave is aligned with a polarization controller (PC2) in a way that it will pass through the polarization beam splitter (PBS). The pump wave is split and one part is coupled into the fiber via a circulator (C). In the lower path the SUT is injected into the system. During the experiments two different SUTs were used. The first one was a femtosecond fiber laser, where the output spectrum is characterized. The second is directly generated out of the FL. Therefore, the signal of the FL is split at the beginning and phase modulated (PM) with different PRBS data patterns. The electrical power of the modulation signal is 11 dBm. The polarization of the SUT is aligned with PC1 in a way that it is blocked at the PBS. An isolator protects the laser source of the SUT from the pump wave. The SUT is coupled into the 20 km long standard single mode fiber (SSMF) that acts as nonlinear medium for the SBS. From the other side the pump wave is coupled into the fiber. The partially amplified SUT is coupled out through the circulator to the PBS. Here the unwanted spectral components of the SUT are blocked entirely. The other part of the split pump wave is modulated with MZM2, driven by a sine wave (LO), which is shifted by 100 MHz with respect to f_SBS (orange box). This defines the final frequency f_meas where the signal is measured in the electrical domain. The LO is then combined with the preselected and amplified part of the SUT. The down conversion to the electrical domain is carried out with a photodiode (PD) with a bandwidth of 1000 MHz. Therefore, the mixing products at higher frequencies are cut off automatically. Finally, the electrical signal is analyzed with an electrical spectrum analyzer (ESA). The measurement takes place at f_meas =100 MHz with a span of 1 MHz. In this case just the center of the SBS gain distribution is measured. The unwanted mixing products in the base band are automatically rejected. In principle, the fixed span needs to be below the SBS bandwidth. For a zero span a simple power detector can be utilized. Alternatively, a narrow bandwidth electrical quartz filter could be used. It needs to have bandpass characteristics and a bandwidth in the range of the linewidth of the laser. For the measurement of the whole spectrum, the frequency of the sideband and consequently the LO is changed by the scan frequency f_scan. The scan process as well as the data recording is done by a separate controller (CTRL). The whole data acquisition is illustrated in the blue box in Fig. 4.

 

Fig. 4 Experimental setup. FL: fiber laser, MZM: Mach-Zehnder modulator, WS: wave shaper, EDFA: erbium doped fiber amplifier, PC: polarization controller, PM: phase modulator, C: circulator, PBS: polarization beam spliter, PD: photodiode, ESA: electrical spectrum analyzer.

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4. Results

For the first proof of concept experiments a 2⁹−1 PRBS with a data rate of 500 Mbps was used. This results in a frequency distance of Δf = 957 kHz between the adjacent lines in the spectrum. For the measurement the SBS gain as well as the LO are shifted through the SUT by changing f_scan accordingly. In principle, the frequency is shifted by 10 MHz for every step and the data from the ESA is recorded. The span of the ESA needs to fit the step size of the frequency scan. Since the SBS bandwidth is larger than the actual span on the ESA, no distortions occur. The comparison of different measurement techniques can be seen in Fig. 5. The OSA can just detect the envelope of the SUT, depending on its resolution. The BOSA measurement was done in combination with a vector network analyzer [23] and reveals the sinc shaped envelope, but the distinct spectral lines, the spectrum consists of, can not be displayed. With additional help of the LO the true characteristics of the SUT can be revealed, as can be seen in the gray curve of Fig. 5.

 

Fig. 5 Measurement results for different systems. The blue curve shows the measurement with a conventional OSA and the red curve the measurement with a Brillouin OSA. All details of the spectrum under test are revealed in the gray curve.

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The complete spectrum for the proposed method is carried out by shifting the pump wave and respectively the local oscillator through the unknown spectrum. Therefore, the modulation frequency for the first modulator is adapted with an offset to f_SBS which covers the full range of the spectrum. Up to now, commercial modulators are capable to handle frequencies up to 100 GHz. For much broader spectral data the center wavelength of the pump laser diode needs to be shifted and stabilized. For this purpose, external cavity lasers with a broad tuning range and narrow linewidth could be utilized [24]. However, the overall tuning range can be significantly enhanced by employing laser arrays or using a single frequency line extracted from a frequency comb generated by a femtosecond fiber laser [25]. Frequency combs broadened in a nonlinear fiber can span over a bandwidth of hundreds of THz [26]. Therefore, a seamless tuning would be possible by switching between the different laser sources or frequency comb lines and a subsequent modulation of the lines as described above. These techniques could enable a tuning over the whole C-, L- and S-band. The minimal resolution is defined by the linewidth of the local oscillator. In the first proof of concept experiment the resolution was limited to 30 kHz (240 am). A detailed measurement of the spectrum under test is shown in Fig. 6. The different lines of the PRBS spectrum can be clearly distinguished.

 

Fig. 6 Detailed part of a PRBS 2⁹− 1 data signal at a data rate of 500 Mbps.

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The second measurement was carried out by measuring the frequency comb generated by a femtosecond fiber laser. The output spectrum measured with a conventional OSA can be seen in Fig. 7(a) and a detailed measurement was carried out with a BOSA again, as shown by the red curve in Figs. 7(b) and 7(c). The fs-laser has a repetition rate of 100 MHz. For the measurement with the BOSA the minimum resolution is restricted to the SBS bandwidth and was 10 MHz (80 fm). Therefore, the displayed linewidth with this measurement device is incorrect. The measurement was repeated with the proposed method, as is shown by the black curves in Figs. 7(b) and 7(c). Through the relative slow measurement time with the high resolution, the laser drift can be clearly seen. A detailed measurement of a single comb line is shown in Fig. 7(b). In principle, this figure shows the resolution limitations for the BOSA and the achieved resolution of the proposed method.

 

Fig. 7 Measurement of the power spectral density of a frequency comb generated by a fs-laser with a conventional OSA (a). Detailed measurements of several lines of the comb are provided by a BOSA (red line in (b) and (c)) and the proposed method (black line) with a detailed measurement of 1 line in (c) that illustrates the resolution limits of both methods.

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5. Conclusion

In conclusion we have shown optical spectrum analysis with a resolution in the attometer range. The method is based on the combination of polarization pulling assisted stimulated Brillouin scattering with heterodyne detection. Contrary to a heterodyne detection alone, the method has a much higher measurement range which, in principle, is just restricted by the transparency range of the Brillouin medium. Furthermore, unwanted mixing products do not fall into the measurement range and thus do not affect the measurement. Additionally, the method just requires commercial off-the-shelf measurement equipment. Even the small bandwidth ESA can be exchanged by an electrical bandpass filter and a power detector. First proof of concept experiments show detailed measurements of a PRBS 2⁹− 1 data signal at a data rate of 500 Mbps as well as the detailed measurement of several lines of a frequency comb generated by a fs-laser. A broad tuning range can be achieved by shifting the pump wave and accordingly the local oscillator through the spectrum under test. The minimum achievable resolution directly depends on the laser linewidth. Within the first proof of concept experiments a resolution of 30 kHz (240 am) was achieved. With commercially available laser sources linewidths in the Hz range, or the lower attometer range respectively, would be possible [24]. Therefore, the resolution could be increased even further.