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Analog links in a 5-km few mode fiber (FMF) are experimentally investigated by exploiting fundamental and high-order linearly polarized (LP) and OAM modes (LP01, LP11a, LP11b, OAM+1, OAM-1). We use spurious free dynamic range (SFDR) of the second-order harmonic distortion (SHD) to evaluate the analog transmission performance. The dependence of analog link performance on the mode relative loss (MRL) between the fundamental and high-order LP and OAM modes is studied. The obtained results indicate that the analog signal transmission performance through a 5-km FMF is affected by MRL of different modes. High-order LP and OAM modes with relatively large MRL suffer degradation of analog link performance. In addition, we further assess the impacts of different modes themselves on the analog link performance. The obtained results imply that all the modes (LP01, LP11a, LP11b, OAM+1 and OAM-1) show similar analog link performance after transmitting through a 5-km FMF.
© 2017 Optical Society of America
1. Introduction
Microwave photonics has been proved great success in improving the performance of photonic communication networks and systems by incorporating various techniques used in microwave engineering [1–5]. As one important part of microwave photonic systems, analog signal transmission in optical links has been studied for decades of years and applied in numerous areas, such as broadband wireless access networks, sensor networks, cable television networks, radar systems, cellular communications, remote or phased array antennas, radio-over-optical transmission systems, and integrated silicon devices [6–14].
For analog signal transmission links, it is considerably important to maintain high-gain, high signal-to-noise ratio (SNR) and the linearity of transmitted analog signals, especially for analog fiber links which are useful in covering rural and sparsely populated areas [15–19]. Several previous interesting works were reported to improve the linearity of analog signal transmission in various systems: (1) using a tunable bandpass filter to rise the linearity of phase modulated analog links by changing the bandwidth and center wavelength of the filter [20]; (2) realizing the linear multicasting of an analog signal by a self-seeded parametric mixer [21]. For fiber analog links, different kinds of fibers might be employed. Recently, few-mode fiber (FMF) has attracted increasing interest in optical fiber transmission systems. Remarkably, beyond fundamental mode, FMF can also support several high-order linearly polarized (LP) modes which are able to increase the fiber transmission capacity through the mode multiplexing of multiple LP modes [22–24]. Note that LP modes exploit the spatial domain of light waves. In addition to LP modes, another spatial mode known as orbital angular momentum (OAM) mode having helical phase front has also seen potential applications of OAM multiplexing both in free-space and fiber optical transmission systems [25–27]. Note that we also call OAM mode as twisted light because of its twisting phase structure. Additionally, free-space analog signal transmission in an OAM multiplexing system has been demonstrated showing favorable analog link performance [28]. However, fiber-based OAM analog links have not yet been studied. Actually, FMF can also guide OAM modes which can be considered to be the linear combination of even and odd eigenmodes of FMF with a relative π/2 phase shift. Utilizing high-order LP modes and OAM modes in an FMF to carry analog signals might find interesting applications in radio-over-fiber systems such as cellular networks, hybrid-fiber-radio-based indoor distributed antenna systems and wireless local area networks (WLANs) [1]. For instance, using multiple modes in an FMF can reduce the number of required fibers in a distribute antenna system where a central unit connects numerous remote antenna units [18]. In this scenario, a laudable goal would be to study the analog signal transmission performance in an FMF using high-order LP modes and OAM modes.
In this paper, we experimentally evaluate the analog signal transmission performance in a 5-km FMF by exploiting LP01, LP11a (b) and OAM ± 1 modes. The spurious free dynamic range (SFDR) of the second-order harmonic distortion (SHD) is used to assess the analog link performance. The impacts of mode relative loss (MRL) of different modes and different modes themselves on SHD SFDR are also comprehensively studied in the experiment.
2. Concept
The concept of analog link system using an FMF can be seen in Fig. 1. At the transmitter side, different RF signals (signal 1, signal 2, … signal n) are respectively modulated on different modes such as LP modes and OAM modes that can be supported in an FMF. Then the modulated modes are multiplexed and coupled into an FMF using a multiplexer. At the receiver side, the multiplexed modes can be divided by utilizing a demultiplexer. Then the RF signal carried by each mode can be recovered by the photo-detector. By exploiting spatial dimension of an FMF, the message capacity in radio-over-fiber systems using an FMF can be improved than that using a single-mode fiber (SMF). For the radio-over-fiber systems using an FMF, the influence of different modes supported in an FMF on the performance of analog links is important.
3. Experimental setup and results
The experimental setup is displayed in Fig. 2(a). At the transmitter side, the output of an external cavity laser (ECL) is injected to a Mach-Zehnder modulator (MZM). The light source is modulated by a 4-GHz radio frequency (RF) in the MZM, amplified by an erbium doped fiber amplifier (EDFA), adjusted by a variable optical attenuator (VOA), and then followed by a polarization controller (PC). Using a collimator, the light is sent from single-mode fiber (SMF) to the first spatial light modulator (SLM), modulated by the phase pattern on the first SLM and then coupled to FMF by an objective lens (OL) with a numerical aperture (NA) of 0.26. At the receiver side, the signal is coupled from FMF to free space with the same OL and then demodulated by the second SLM. After demodulation, the light is coupled into SMF using a collimator and amplified by an EDFA. At last the signal is sent to a photo-detector (PD) and then measured by an electric spectrum analyzer (ESA). Here we set the operation mode of the second EDFA to be ‘auto-power-control’ to maintain the optical power in PD relatively constant, which eliminates the impacts caused by optical power changes on PD. A beam splitter (BS) is placed on the light path between the second SLM and the collimator and followed by a camera to observe the intensity profiles of modes in FMF. Figure 2(b) depicts the cross-section view of the employed FMF. The radii of the FMF core and cladding are rcore = 6.35 μm and rcladding = 62.5 μm, respectively. The refractive index of the cladding and core are approximately 1.444 and 1.449 at the wavelength of 1550 nm, respectively. The FMF supports six eigenmodes in total that are , , , , , and, whose mode properties including effective modal index (neff), chromatic dispersion coefficient (Dλ), and differential mode delay (DMD) are displayed in Fig. 2(c). One can get LP modes and OAM modes through proper linear combinations of those eigenmodes. The measured mode transmission losses are about 0.24 dB/km.
Fig. 2 (a) Experimental setup for analog signal transmission in FMF (OAMF). ECL: external cavity laser, PC: polarization controller, MZM: Mach-Zehnder modulator, PD: photo-detector, ESA: electric spectrum analyzer, EDFA: erbium-doped fiber amplifier, VOA: variable optical attenuator. Col.: collimator; NDF: neutral density filter; Pol.: polarizer; HWP: half-wave plate; SLM: spatial light modulator; L: lens; BS: beam splitter; OL: objective lens. Insert is the image of FMF compared with SMF. (b) Cross-section view of the FMF. (c) Supported six eigenmodes in two mode groups of the FMF. neff: effective modal index; Dλ: chromatic dispersion coefficient; DMD: differential mode delay between HE11 and other higher-order modes, respectively.
Figure 3(a) shows the simulated intensity and phase of LP and OAM modes supported in the employed FMF. The picture indicates that this FMF can support three LP modes (LP01, LP11a and LP11b) and two OAM modes (topological charge number ± 1). Fundamental mode (LP01) can be directly inspired using OL to couple a Gaussian beam into FMF without the modulation of SLM. To excite high-order LP modes and OAM modes, the corresponding phase patterns as shown in Fig. 3(a) are required to be displayed on the SLM to modulate the wavefront of incoming Gaussian beam. For example, in order to excite OAM+1 mode in the FMF, a spiral phase pattern shown in Fig. 3(a) is loaded onto the first SLM. When a Gaussian beam is reflected by this SLM, the reflected light has a helical phase front with a topological charge number of + 1 corresponding to OAM+1 beam. The generated OAM+1 beam in free space is then coupled into FMF through an OL and the OAM+1 mode is excited in FMF. Figure 3(b) plots the measured intensity profiles of corresponding LP and OAM modes at the receiver side before the demodulation by SLM2. One can clearly see from Fig. 3(b) that the excited LP and OAM modes in the experiment are almost the same as the simulated ones even after 5-km FMF transmission. Additionally, in order to demodulate the high-order LP modes and OAM modes for easy coupling into SMF at the receiver side, inverted phase patterns are loaded onto the second SLM to recover the high-order LP modes and OAM modes into Gaussian-like beams with bright spot at the beam center. Figure 3(b) also plots the measured intensity profiles of high-order LP modes and OAM modes after demodulation by the second SLM. One can clearly see that all the demodulated beams have a bright spot at the beam center which is further coupled into SMF for detection.
Fig. 3 (a) Simulated LP and OAM modes supported in FMF at the wavelength of 1550 nm. (b) Experimentally measured intensity profiles of LP and OAM modes before and after modulation by SLM.
In the experiment, we employ these 5 modes (LP01, LP11a, LP11b, OAM+1 and OAM-1) depicted in Fig. 3 to transmit analog signals in the 5-km FMF link system. Figures 4(a)-(d) respectively show the measured RF spectra by ESA for the back to back (B-to-B) case and the 5 modes after transmitting through the 5-km FMF at the receiver side. The optical power before coupling into the FMF is about 1.5 dBm. One can see from Fig. 4 that the power of RF and SHD of all modes decreases compared to the B-to-B case. Moreover, the decreases of LP11a(b) modes and OAM ± 1 modes are relatively larger than that of the LP01 mode. To further assess the analog signal transmission performance, we measure the acquired output power of the RF carrier and distortion as a function of the RF input power at input signal wavelength of 1550 nm. Figures 5(a)-(c) show the measured results of relationship between the output RF and distortion power and the input RF power. SFDR is a pivotal common judgment criterion to measure the linearity level of an analog link. It is defined by the RF input power range at the left and right boundaries of which the fundamental RF power and the SHD power are equal to the noise floor. A higher SFDR system means a better linear analog signal transmission. SFDR can be obtained by measuring the intercepting points of output power curves (RF carrier, SHD) and the noise floor [29–31]. Figure 5(d) plots the relationship between SHD SFDR and different modes. It indicates that the fundamental mode has the largest SHD SFDR while the LP11a(b) modes and OAM ± 1 modes have degraded SHD SFDR. As shown in Fig. 5(d), the SHD SFDR of LP01, LP11a, LP11b, OAM+1 and OAM-1 modes are measured to be about 59.65 dB, 52.57 dB, 52.72 dB, 56.37 dB and 54.99 dB, respectively. The SHD SFDR of LP01 mode is almost 7 dB and 4 dB higher than LP11a(b) and OAM ± 1 modes, respectively. The degraded SHD SFDR of high-order LP and OAM modes compared to the fundamental mode can be ascribed to the mode relative loss (MRL) which is defined by the relative loss difference between the fundamental mode and higher-order modes. The relationship between the measured MRL and different high-order LP and OAM modes is also shown in Fig. 5(d), which matches well with the trend of the SHD SFDR curve. High-order LP and OAM modes show relatively large loss compared to the fundamental mode, resulting in the degradation of the analog link performance.
Fig. 4 (a)-(d) Measured RF spectra by ESA for back-to-back (B-to-B), LP01, LP11a(b) and OAM ± 1, respectively. The RF input power is 7 dBm. The optical power before coupling into FMF is about 1.5 dBm.
Fig. 5 Measured output power of RF carrier and distortion versus RF input power for (a) LP01, (b) LP11a(b) and (c) OAM ± 1,modes, respectively. (d) Measured SHD SFDR and mode relative loss (MRL) versus different modes (LP01, LP11a, LP11b, OAM+1 and OAM-1).
Furthermore, we study the impacts of modes themselves on the analog link performance. In order to eliminate the influence of different MRLs of different modes, we adjust the relative attenuation of different modes to make the MRL of all modes be the same. The relationship between output RF and distortion power and input RF power is then measured. Figures 6(a)-(c) plot the measured results of output RF and distortion power as a function of input RF power. As shown in Figs. 6(a)-(c), the decreasing amounts of output power of RF carrier and distortions for LP01, LP11a(b) and OAM ± 1 modes after transmitting through the FMF compared to the B-to-B case are almost the same. Figure 6(d) depicts the relationship between the SHD SFDR and different modes with the same MRL. As plotted in Fig. 6(d), the SHD SFDR of LP01, LP11a, LP11b, OAM+1 and OAM-1 modes are around 52.4 dB, 52.5 dB, 52.4 dB, 52.6 dB and 52.5 dB, respectively. One can clearly see that SHD SFDRs of all the modes are close to 52.5 dB, showing similar analog link performance for the fundamental mode and high-order LP and OAM modes after transmitting through a 5-km FMF.
Fig. 6 Measured output power of RF carrier and distortion versus RF input power under the same MRL for (a) LP01, (b) LP11a(b) and (c) OAM ± 1,modes, respectively. (d) Measured SHD SFDR versus different modes (LP01, LP11a, LP11b, OAM+1 and OAM-1) under the same MRL.
4. Discussion and Conclusion
The experiment results indicate that the MRL of different modes can influence the analog link performance in FMF. Apart from MRL, other factors such as mode crosstalks might also have negative effects on the analog signal transmission in FMF when multiple modes are employed in the system. The measured mode crosstalks in the experiment between LP01 and OAM ± 1, LP01 and LP11a(b), OAM+1 and OAM-1, LP11a and LP11b, and OAM ± 1 and LP11a(b) modes are about −27 dB, −22dB, −15dB, −15dB, and −4 dB, respectively. It is shown that the crosstalk between OAM ± 1 and LP11a(b) modes is relatively large because OAM ± 1 and LP11a(b) modes are in the same mode group and they are not orthogonal with each other. To reduce the effects of crosstalk in FMF, one can avoid using LP and OAM modes of the same mode group simultaneously. Besides, mode crosstalk would be improved by employing other specially designed fiber such as high-index ring fiber to increase the effective refractive index difference [32]. Furthermore, mode-dependent dispersion could also cause distortions to analog signals when OAM or higher-order LP modes are employed in FMF to perform analog links. It is because OAM or higher-order LP modes are combinations of eigenmodes whose average differential mode delay (ADMD) cannot be ignored in long-distance transmission. The calculated ADMD of mode group 2 in FMF used in the experiment is about 12.32 ps/km. To reduce the influence of mode-dependent dispersion on analog link performance, possible solutions could be various specially designed FMF with low DMD or ADMD [22,33]. Additionally, other specially designed fiber or waveguide could be also considered for potential optical interconnects link using spatial modes [34].
In summary, we have experimentally studied the link performance of analog signal transmission in a 5-km FMF. SHD SFDR is measured to evaluate the analog link performance. The influences of MRL and different modes themselves on the analog signal transmission are investigated in detail in the experiment. For the same input optical power, the analog signal transmission performance through a 5-km FMF is mainly affected by the MRL. High-order LP and OAM modes suffer degraded SHD SFDR. For the same MRL, it is interesting to note that all the modes supported in the 5-km FMF (LP01, LP11a, LP11b, OAM+1 and OAM-1) show similar analog link performance. The demonstrated analog signal transmission exploiting high-order LP and OAM modes in FMF might find interesting applications in versatile analog fiber links.
Funding
Program 973 (2014CB340004); National Natural Science Foundation of China (NSFC) (11574001, 11274131, 61222502); National Program for Support of Top-Notch Young Professionals; Program for New Century Excellent Talents in University (NCET-11-0182); Wuhan Science and Technology Plan Project under (2014070404010201); Open Program from State Key Laboratory of Advanced Optical Communication Systems and Networks (2016GZKF0JT007); Open Projects Foundation through Yangtze Optical Fiber and Cable Joint Stock Limited Company (SKLD1504).
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