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Abstract
We propose, for the first time to our knowledge, tunable true time delay line operation for radiofrequency signals on a few-mode fiber link. In particular, the custom design of a 7-LP-mode ring-core few-mode fiber together with a set of 5 broadband long period gratings inscribed at the proper positions along the fiber allows 4-sample true time delay line tunability over a 20-nm optical wavelength range. We study the performance of the designed true time delay line in the context of reconfigurable microwave photonics signal processing by theoretically evaluating microwave signal filtering and optical beamforming networks for phased array antennas.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Although space-division multiplexing (SDM) technologies emerged as a solution to the upcoming transmission capacity bottleneck in optical fiber networks [1], they are gathering an increasing interest in other applications beyond high-capacity digital communications, such as multi-parameter optical fiber sensing [2] and radiofrequency (RF) signal processing [3].
Recently, we have demonstrated the potential of different SDM optical fibers to implement what we coined as “fiber-distributed signal processing”, where the data signal is processed while it is distributed through the optical fiber, [3]. The idea is to exploit the inherent parallelism of a single SDM optical fiber to implement a compact and efficient approach for sampled true time delay line (TTDL) operation, which is actually the basis of discrete-time incoherent signal processing, [4]. The goal of a TTDL is to provide a set of time-delayed samples of the RF signal with tunable group delays within a given RF frequency range. Different approaches have been reported for the implementation of true time delay lines over the past 30 years, where the required diversity is realized by exploiting either the time or the wavelength multiplexing domains. Tunable configurations built upon single-core singlemode fibers include switched fibers [5], dispersive fibers [6], Fiber Bragg Grating (FBG) inscription [7] and exploitation of nonlinearities such as Stimulated Brillouin Scattering [8].
Time delay line operation is of special interest in the context of next-generation fiber-wireless communications systems, such as 5G radio access networks and the Internet of Things, which demand a variety of microwave photonics (MWP) signal processing functionalities, including signal filtering, optical beamforming for phased-array antennas and arbitrary waveform generation [9]. In this sense, we foresee that MWP signal processing and radio-over-fiber distribution can benefit greatly from the use of different SDM fiber technologies in terms of compactness and weight, while assuring broadband versatility and reconfigurability. This brings a relevant challenge that involves the development of novel multicore fiber (MCF) [10,11] or few-mode fiber (FMF) [12,13] solutions where the different spatial paths (cores or modes) provide the required time-delayed signal samples.
Figure 1 shows the general rationale behind the implementation of a tunable TTDL for RF signals with an FMF. The goal is to obtain at the output of the fiber link, a set of time-delayed replicas of the modulated signal assuring a constant differential delay between adjacent replicas (named as basic differential delay, Δτ) at a given optical wavelength [9]. We must ensure, in addition, a low level of coupling between non-degenerate modes, what calls in general for refractive step-index (SI) profiles and the use of short distances combined with direct detection. We can say that the scheme illustrated in Fig. 1 corresponds to 1-dimensional (1D) operation since all the replicas result from exploiting the fiber spatial diversity (modes or groups of modes) inherent to the FMF. If we feed the TTDL by a multi-carrier optical source (instead of a single-carrier source), the same fiber link will offer 2-dimensional (2D) operation since we can exploit, in addition to the spatial diversity, the optical wavelength diversity, [2].
We have previously reported different solutions for FMF-based TTDLs that work only in the 1D diversity regime by exploiting the spatial diversity at a single optical wavelength, [12,13]. In [12], we experimentally demonstrated 3-sampled TTDL operation on a 60-m SI 4-LP-mode fiber where 3 LP modes were injected at the fiber input and a long period grating (LPG) was inscribed to generate and adjust the time delay of the sample associated to the LP02 mode. Two different configurations (with different basic differential delays) were implemented on the same FMF-based device by selecting a different set of 3 modes at the fiber output for a particular optical wavelength of 1558.3 nm. That idea was improved in a latter work [13], where we experimentally demonstrated 4-sampled TTDL operation on a 44.4-m link of the same SI 4-LP-mode fiber. There, the inscription of a set of LPGs at specific locations along the fiber allowed the excitation of the 3 higher-order modes while adjusting the individual sample group delays and amplitudes. Since one requires only to inject the fundamental mode, this second approach is independent of any preceding additional fiber link that may be required to distribute the signal. However, as it happened in [12], that TTDL only works properly for a single optical wavelength around 1558 nm and does not allow continuous tunability with an external parameter such as the optical wavelength.
In the general context of MWP signal processing, it is desirable to have the capability to tune the basic differential delay so we can reconfigure our target application (changing, for instance, the free spectral range of a signal filter or the beam-pointing angle of a phased array antenna). This means that the basic differential delay must vary linearly with the optical wavelength. In other words, we need different values of the chromatic dispersion (spectral group delay slopes) associated to each sample.
With this aim in mind, we propose here an FMF-based 4-sample TTDL approach that offers, for the first time to our knowledge in the context of FMFs, time delay tunability over a given optical wavelength range. This solution combines the custom design of a 7-LP-mode ring-core fiber and the inscription of 5 LPGs at the appropriate locations along the FMF to achieve both constant differential time delay and differential chromatic dispersion values between the TTDL signal samples. Section 2 proposes the concept for tunable TTDL in an FMF link with inscribed LPGs, while section 3 describes the specific design of both the FMF and the LPGs to be inscribed. In section 4, we theoretically evaluate the proposed TTDL in the context of reconfigurable microwave signal filtering and radio beam-steering in phased array antennas. Finally, section 5 closes the paper with the relevant conclusions and future directions of research.
2. Few-mode fiber tunable true time delay line concept
The use of sampled TTDLs for time-discrete signal processing implies that the differential delay between adjacent samples, i.e. the basic differential delay Δτ, must be constant for all the samples at a given optical wavelength. Time-delay tunability with the wavelength implies in addition, a linear increment of this basic differential delay with the optical wavelength. In the particular case of an FMF-based TTDL, if we exploit the space-diversity domain, the samples correspond to different modes (or groups of modes) that propagate along the fiber for a given wavelength. If we use wavelength diversity instead, the samples are given by the different optical wavelengths carried by a given mode (or group of modes).
We can expand the group delay per unit length of a given LPlm mode, τlm, in 1st-order Taylor series around a central or reference wavelength λ0 as
where τlm(λ0) is the group delay per unit length at λ0 and Dlm is the chromatic dispersion at λ0 for the LPlm mode. TTDL tunability with the wavelength requires the set of parameters Dlm to follow as well an incremental law with a constant increment between adjacent samples ΔD, [3]. This way, the basic differential delay when we operate in the spatial diversity domain can be expressed as:To overcome these limitations, we propose to obtain a subset of TTDL samples as a combination of different modes that propagate through the fiber instead of using a single mode per sample. With the help of in-line mode converters based on LPGs inscribed at specific positions along the FMF link [14], we can adjust the final group delay and chromatic dispersion values associated to each signal sample. This idea can be explained as follows. Suppose that the ith TTDL sample is created in first place by a particular mode LPlm that is injected at the fiber input and propagates over that mode for a certain distance Llm(i) = llm(i)L (with a specific group delay and chromatic dispersion), where llm(i) is the normalized length along which the ith sample is propagated by a given LPlm mode and L is the total length of the FMF link. Then, a given LPG transforms that incoming LPlm mode into a different outgoing LPlm mode (with a different group delay and chromatic dispersion). We can repeat this mode conversion mechanism as many times as necessary by concatenating different LPGs inscribed at the positions ∑lm∈I llm(i)L, where I is the set of indices lm of the LPlm modes in which the ith sample has been propagated before passing through the current LPG. This way, at the output of the fiber, the group delay of the ith TTDL sample τi at a given wavelength λ0 can be expressed as a combination of the LPlm modes involved to create that sample as
Fig. 2. (a) Evolution of the differential group delay of the samples, τi – τ1, as a function of the normalized length; (b) Evolution of the differential chromatic dispersion, Di – D1, as a function of the normalized length; and (c) Time-delay dependence of the samples with the optical wavelength for a generic FMF link with inscribed LPGs.
Fig. 3. (a) Refractive index profile of the designed ring-core fiber. (b) Computed effective index neff for every propagated mode as a function of the fiber scale factor.
3. Design of true time delay line on a 7-mode fiber
We have described in the previous section the conditions that the FMF-based device must fulfil to operate as a sampled TTDL. But we need to ensure as well a low level of intermodal crosstalk between signal samples along the fiber link to avoid degradation on the target MWP signal processing functionality, what calls for modal phase propagation constants (or effective indices) as different as possible. In addition, modes with a set of chromatic dispersions as diverse as possible are desirable to allow the accomplishment of Eq. (3) with higher ΔD (larger delay tunability). In this regard, we have designed a particular FMF whose refractive index profile follows a ring-core step-index architecture. The use of a step-index profile reduces the mode coupling by increasing the effective index difference between modes, while the ring-core architecture provides more design versatility and allows to manage the propagation characteristics of the symmetric modes with certain independence from the asymmetric modes. Figure 3(a) depicts the refractive index profile of the designed ring-core fiber. It consists of a SiO2 inner layer doped with a low GeO2 concentration (radius a1 = 3 µm and inner-core-to-cladding relative index difference Δ1 = 0.21%) surrounded by a SiO2 ring-core layer doped with a higher GeO2 concentration (radius a2 = 10 µm and core-to-cladding relative index difference Δ2 = 0.72%) inside a pure silica cladding. Figure 3(b) shows the computed effective index as a function of the scale factor (i.e., the parameter that expands/compacts the whole refractive index profile in the radial axis r). When the scale factor equals 1, the refractive index profile corresponds to the designed profile. At this point, the fiber supports 7 LP modes. Table 1 summarizes the main characteristics of the fiber modes at a 1550-nm wavelength.
Table 1. Propagation characteristics of the modes for the designed FMF at λ0 = 1550 nm.
In order to reduce the crosstalk among non-degenerate modes, we have designed the fiber to increase as much as possible the effective index difference between the modes Δneff [15,16]. In this case, the effective index difference between neighboring modes is bigger than 0.5·10−3 for all the modes, which is similar to the values of typical low-crosstalk commercial step-index FMFs. This is the case, for instance, of the FMF we reported in our previous articles for propagation of only 4 modes (Δneff > 0.8·10−3, ensuring low mode coupling below -30 dB/km) [12,13], where no significant distortions of TTDL performance were observed.
The evaluation of the modal propagation characteristics gathered in Table 1 suggests that a total of 5 LPGs acting as mode converters are required to perform 4-sample TTDL operation, that is, mode conversions: LP02 to LP12, LP12 to LP01, LP01 to LP41, LP12 to LP11 and LP11 to LP31. Figure 4 illustrates the designed ring-core fiber with the inscription of the LPGs along the fiber. We see there how the modes are combined through the different LPGs to generate the output samples. Starting from the 4th sample (the one with the largest group delay), we can see that it travels into the LP21 mode along the whole fiber length L. The remaining samples are created through LPG mode conversion, starting from the excitation of the LP02 mode at the fiber input. After a given length L02 = l02·L, LPG1 couples all the power coming from this mode into the LP12 mode. After propagating through a length L12(1) = l12(1)·L, the LP12 mode creates at the output of the fiber the 1st sample (the one with the smallest group delay). The group delay of the 2nd and 3rd samples is adjusted by performing two additional mode transformations in each case. For the 2nd sample, LPG3 couples part of the LP12 mode into the LP01 mode that propagates a distance L01(2) = l01(2)·L before being transformed into the LP41 mode in LPG5. In the case of the 3rd sample, LPG2 couples part of the LP12 mode into the LP11 mode that propagates a distance L11(3) = l11(3)·L before being transformed into the LP31 mode in LPG4.
Fig. 4. Scheme of the designed TTDL based on a ring-core FMF link of length L with a set of 5 LPGs inscribed at specific longitudinal positions. On the right, one can see the 4 output TTDL samples in the time domain characterized by a constant basic differential delay Δτ.
With the help of Eq. (3) and following the procedure illustrated in Fig. 4, we obtain the following expressions for the group delays per unit length of the samples at the end of the FMF link:
Table 2. Normalized lengths llm(i) along which the i-th sample travels on mode LPlm.
The TTDL tunability is limited by the spectral bandwidth of the LPGs. From the effective indices of the fiber modes involved, we can calculate the period of each LPG Λ as, [17],
where neff, i and neff, j represent the effective indices of the involved modes. For the conversion between symmetrical and asymmetrical modes, we must inscribe the LPGs with a certain tilt angle to improve the mode conversion efficiency. We have recently demonstrated efficient symmetric-to-asymmetric and asymmetric-to-asymmetric mode conversions with tilted LPGs in a 4-LP-mode fiber, as well as symmetric-to-symmetric mode conversions without any tilt angle, [12,13]. Finally, we must note that the inscription of the LPGs with a certain chirp can provide up to a 20-nm wavelength operability range [18]. Table 3 summarizes the main characteristics of the designed LPGs.Table 3. Calculated LPG periods and chirps for mode conversions and 20-nm tunability.
Figure 5 shows the computed differential group delay per unit length between the ith and the first sample, τi – τ1, (i = 2, 3, 4), as a function of the optical wavelength λ. As shown, the basic differential group delay can be tuned from 49 ps/km at λ = 1540 nm up to 151 ps/km at λ = 1560 nm. We can observe as well a constant incremental value of the group delay slopes, that is, a constant incremental chromatic dispersion ΔD of 5.1 ps/km/nm. We must note that, up to a certain degree, this approach is robust against possible fiber fabrication deviations. Once the fiber is fabricated and its propagation characteristics are known (i.e., modal differential group delays and chromatic dispersions), we can modify the LPG positions to balance out possible group delays and chromatic dispersions mismatches between experimental and theoretical values.
Fig. 5. Differential sample group delays per unit length with respect to the first sample as a function of the optical wavelength. TTDL tunability is ensured from 1540 up to 1560 nm.
4. Validation on microwave signal processing scenarios
We have evaluated theoretically the performance of the proposed tunable TTDL when it is applied to two typical MWP functionalities: tunable microwave signal filtering and optical beamforming for phased array antennas. A microwave photonic signal filter can be implemented when we couple (interfere) together the four optical time-delayed signal samples at the ring-core fiber output before detecting them with a single photodetector, [19]. Following the same idea, we can implement a beamforming network for phased array antennas if each of the time-delayed signals at the output of the ring-core fiber is photodetected individually (instead of collectively) to feed a particular radiating element, [20].
Figure 6(a) shows the computed RF transfer function of the resulting microwave signal filter for different operation wavelengths and an RF frequency up to 50 GHz. We consider here a 1-km FMF link. Blue-dashed, orange-dashed and purple-solid lines correspond, respectively, to operation wavelengths of λ = 1540.2, 1550 and 1559.8 nm. We see that we can tune the Free Spectral Range (FSR) of the filter from 20 GHz down to 10 GHz and 6.67 GHz by changing the operation wavelength of the optical source from 1540.2 up to 1550 and 1559.8 nm, respectively. This corresponds to increasing the basic differential delay from 50 up to 100 and 150 ps, respectively. On the other hand, Fig. 6(b) depicts the simulated far-field radiation pattern (or array factor) of the resulting 4-element phased array antenna as a function of the beam angle (in degrees) for different basic differential delays for the same 1-km link. The distance between radiating elements is 1.5 cm and the RF frequency is set to 10 GHz. We see that we can tune the antenna beam-pointing angle by changing the operation wavelength with a tuning ratio of 5 degrees per nanometer. In particular, the beam-pointing angle varies from 36 down to 11 degrees by tuning the optical wavelength from 1543.7 up to 1547.7 nm.
Fig. 6. (a) RF transfer function of the microwave photonic filter for three different operation wavelengths. (b) Array factor of the phased array antenna for five different operation wavelengths (RF frequency of 10 GHz and 1.5 cm antenna element separation).
5. Conclusions
Beyond high-capacity optical communications, SDM optical fibers can be exploited as a compact medium to implement “fiber-distributed signal processing” if they are engineered to operate as sampled TTDLs. One of the most desired features in this context relates to the capability to tune the basic differential delay of the TTDL with the optical wavelength linearly.
In summary, we have presented, for the first time to our knowledge, TTDL operation for RF signals over an FMF link exhibiting time delay tunability with the optical wavelength. We propose to achieve the required control over both the group delay and the chromatic dispersion of the signal samples by the custom design of a ring-core SI FMF where the inscription of a series of LPGs allows to excite higher-order modes at specific longitudinal locations along the fiber. In particular, we have designed a 4-sample TTDL approach that combines the design of a 7-LP-mode ring-core fiber and the inscription of 5 LPGs at the appropriate longitudinal locations. This scheme requires to inject only the LP02 and LP21 modes into the fiber input while the 4 TTDL samples are given by the signals recovered from the LP21, LP12, LP31 and LP41 modes at the fiber output. A particular potential field of application can be found in fiber-wireless radio access networks where different functionalities can be implemented while transmitting the signal, for instance, between a central office and a given remote antenna. We have evaluated the performance of the designed tunable TTDL when it is applied to reconfigurable microwave signal filtering and radio beam-steering in phased array antennas.
The future experimental implementation of this concept requires, first, the actual fabrication of the ring-core fiber and the pertinent multiplexing/demultiplexing devices, what we consider feasible given the current state of SDM fabrication techniques. Second, we must bear in mind that the TTDL tunability range is subject to the optical bandwidth of the inscribed LPGs. Therefore, one has to ensure the LPGs are inscribed with the required grating periods and chirps to perform the proposed mode transformations along a 20-nm wavelength operability range.
Funding
European Research Council (Consolidator Grant 724663); Ministerio de Economía, Industria y Competitividad, Gobierno de España (BES-2015-073359 for S. García, RYC-2014-16247 for I. Gasulla, TEC2016-80150-R).
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