Microwave photonics has been studied for improving the performance of microwave systems by incorporating the advantage of optics into the microwave technologies [1]. The main research areas in microwave photonics include photonic generation of high-frequency microwave signals [2-5], arbitrary microwave waveforms [6], antenna remoting [7], photonic beamforming for phased arrays [8], and RF phase shifter [9].

Among them, the photonic microwave filter (PMF) has been one of the hot research topics [10-13] in the field of fiber optics for microwave engineering. Despite competing microwave technology over longer years, it still attracts considerable research interest due to its ability to offer low loss, high bandwidth, immunity to electromagnetic interference (EMI), and tunability.

In recent years, a number of studies on PMFs have been published including all-optical RF filter using amplitude inversion [14], microwave photonic delay-line filter with negative coefficients [15-17], or complex coefficients [18, 19]. However, these filters usually have a complicated structure, which may limit their potential for practical applications. To achieve arbitrary bandpass response, a photonic microwave delay-line filter was proposed to use a microwave delay-line filter with nonuniformly spaced positive taps [20]. They use five tunable lasers of different wavelengths to tune the wavelengths and the power of each laser for nonuniformly-spaced time delay differences and the desired tap coefficients, respectively.

In this paper, we propose a tunable photonic bandpass microwave filter with a Fabry-Perot laser diode (FP-LD) injection-locked with a reflective semiconductor optical amplifier (RSOA). The FP-LD generates multiple wavelengths (modes) with the same wavelength spacing without using a number of lasers. The RSOA is employed as a gain medium to those wavelengths, and their amplitudes can be varied by the gain spectrum and the offset between the peak wavelengths of the RSOA and the FP-LD, which can be carefully controlled to change the filter characteristic. The multiple wavelength components are phase modulated together. The combined effect of phase modulation to intensity modulation (PM-IM) conversion and wavelength-dependent time delay due to the dispersive fiber removes baseband resonance, showing a notch characteristic at DC. To implement tunable function, the FP-LD is temperature controlled by the thermal electric cooler (TEC) inside the laser. The technical merit of the proposed scheme is that the tunability is easily obtained by changing the temperature of the FP-LD and the tapped-delay-line is implemented through a single-mode fiber without multiple tapped-delay line fibers.

The paper is organized as follows: Section 2 describes the principle of operation. Section 3 contains the experimental setup and measurement results showing the spectral response of the PMF. Section 4 describes the technical discussions on the experiment and the improvement of the proposed scheme. We finally summarize the paper in Section 5.

Figure 1 shows the schematic diagram of a PMF. The scheme is composed of multi-wavelength optical component generation, phase modulation, and fiber propagation. Multiple wavelength optical components are considered to implement a single tapped-delay-line filter. The time delays between the different wavelength components are determined by the wavelength-dependent dispersion between those signals with the dispersive fiber, i.e., time delay dependent on chromatic dispersion. The phase modulator is used to remove baseband resonance, i.e., to obtain a null at DC. Finally, the output is detected by a high-speed photodiode.

Figure 2 shows the proposed simple scheme to generate multiple wavelengths. We use a pair of an FP-LD and an RSOA, cheaper than multiple optical sources. The FP-LD produces multiple wavelengths around the center wavelength.

The RSOA is operated in the gain-saturation regime and the offset between the center wavelengths of the FP-LD and the RSOA is controlled by the temperature of the RSOA in order to mitigate the difference in the amplitudes of the wavelength components and obtain an optical gain as shown in Fig. 3. The injection-locked multiple wavelengths are detected. The PM-IM conversion provides wavelength-dependent bandpass filtering [12]. The frequency response of the PM-IM conversion is the function of fiber dispersion and frequency of phase modulation, which is given by

where c is the velocity of light in free space, x is the total dispersion of the standard single-mode fiber, λ is the central wavelength of the carrier.

Multiple wavelength components propagate through a length of single-mode fiber, experiencing different time delays due to fiber chromatic dispersion, and the time delay for the kth wavelength is calculated [20] by

where τ₀ is the time delay at the 0th wavelength, λ₀ and λ_k are the 0th and kth wavelengths. D(λ) is the chromatic dispersion parameter of the standard single-mode fiber (D = 17 ps/nm/km at 1550 nm) and L is the length of the standard single-mode fiber. And, the frequency response is changed with the phase differences between all the wavelength components and is expressed in [12, 20] as

where N is the number of the wavelength components, ϕ_k is the phase of the kth recovered RF signal, α_k is the amplitude of kth wavelength component, ω is the modulating angular frequency, T(=2π/Ω) is the time difference between two adjacent wavelength components, Ω is the free spectral range of the tapped delay line filter, and Δτ_k is the time delay shift of the kth wavelength component. Therefore, for a given fiber length and dispersion value, the filter response is dependent on the wavelength spacing. However, the dispersion value varies with the operating wavelength. By changing the lasing wavelength using the TEC inside the FP-LD (about 50 GHz/°C), we can change the filter frequency response.

The experimental setup of the proposed PMF is shown in Fig. 4. Multiple wavelength components are generated in the combination of an FP-LD and an RSOA by injection locking. The injection-locked multi-wavelength optical signal is extracted using a 3-dB optical coupler. The erbium-doped fiber amplifier (EDFA1 of Fig. 4) and the following optical bandpass filter (OBPF1 of Fig. 4) are used for amplitude limiting for each wavelength component and rejection of amplified spontaneous emission (ASE) noise outside the wavelength range of interest. The optical power of the FP-LD and RSOA are 0.32 dBm and 0.31 dBm at I_bias of 14.43 mA and 18 mA, respectively.

The photomixing of the whole wavelength components at the photodiode recovers the filtered RF signal after experiencing PM-IM conversion and tapped-delay line filter. In our experiment, the fiber length was 10.66 km. The photodiode has the bandwidth of 55 GHz (Discovery Semiconductor DSC10ER). The recovered electrical signal is amplified with a 26.5 GHz wideband amplifier. The bandpass filtering characteristics of the proposed PMF is measured using a 40 GHz network analyzer (Agilent N5230A).

The center wavelength of the generated optical signal by injection locking is mainly dependent on the lasing characteristics of the FP-LD and shifted by temperature control. Usually, it is not capable of having wavelength components of equal optical power levels since the FP-LD inherently has a gain profile as shown in Fig. 5(a) and the RSOA has the gain spectrum shown in Fig. 5(b), as depicted in Fig. 3. Therefore, the combination of lasing characteristics (Fig. 5(a)) of the FP-LD and gain spectrum (Fig. 5(b)) of the RSOA cannot generate wavelength components of equal optical power level. It is noted that the center wavelength of the FP-LD lasing and the peak wavelength of the RSOA gain spectrum are dislocated since it is desired to have even optical power levels of each wavelength component for phase modulation.

Considering the inherent spectral characteristics of FP-LD and RSOA, we try to generate wavelength components of even power levels, resulting in six wavelength components. However, we could not avoid the severely uneven optical power levels at edge wavelengths in spite of center wavelength adjustments and optical spectral filtering using OBPF1 before phase modulation since the power difference of lasing components from injection locking is larger than the range of power control by OBPF1. Therefore, depending on the center wavelength of FP-LD lasing, the lowest power components can appear on the leftmost or rightmost sides. The inevitable uneven optical power distribution of wavelength components is confirmed in Figs. 6(a), 6(c), 6(e), and 6(g). The set of figures shows wavelength tuning due to temperature change of the FP-LD. Figures. 6(b), 6(d), 6(f), and 6(h) are their corresponding frequency responses of the recovered RF signals, measured at the output of the photodiode after electrical amplification in the RF amp. The other filter responses (dashed lines) show the calculated results based on Eq. (3) for comparison under the same condition of parameters and scale. By varying the temperature of the FP-LD from 15°C to 30°C, the wavelength of the rightmost component moved from 1540 nm to 1550 nm, which was severely suppressed since it moved to low gain region of the overlapped RSOA spectrum. Also, the whole frequency response moved from right to left.

When we draw a figure for peak frequency values of a selected RF passband for Figs. 6(b), 6(d), 6(f), and 6(g) vs. temperature variation, we notice that each RF passband moves from right to left for temperature increase. As an example, the peak frequency of passband-1 is changed by an amount of 394.9 MHz for 15°C temperature change, as shown in Fig. 7. Therefore, it is confirmed that the proposed PMF provides the passband tunability based on temperature control of the FP-LD. In this experiment, the tuning range is mainly limited to the FP-LD specification.

To design a specific shape of frequency response including the frequencies of passband peaks and notches in this scheme, rigorous mathematical calculations considering the wavelengths and different power values for all the wavelength components are required and will be a future work.

From the principle of the proposed PMF, it is required in design viewpoint to generate the multi-wavelength components with equal amplitudes before phase modulation. Inherently, the FP-LD injection locking and the limitation of optical power adjustment of each wavelength component based on OBPF urges the outer components to have weaker power compared with those near the center wavelength.

We have simulated the frequency response of the PMF incorporating unequal wavelength components and we have confirmed that the proposed filter provides a filter characteristic whose frequency response is tunable, similar to the proposed filter. The set of unequal wavelength components is obtained by multiplying the shape of optical filter gain in Fig. 8 to an output of a multi-wavelength laser. We have calculated the filter response considering optical filter response of Fig. 8, accompanying accumulation of fiber dispersion (181.22 ps/nm), which is shown as a solid line (denoted as filter response) in Fig. 9. If we considered the response of PM-IM conversion only, it is shown as a dashed line (denoted as PM-IM conversion) in Fig. 9. Including the effect of phase modulation for the whole wavelength components, the final filter response is modified due to PM-IM conversion, shown in a diamond marked solid line (denoted as filter response after PM-IM conversion) in Fig. 9. It is understood that the filter response is the cascade of the optical filter response caused by an optical filter and PM-IM conversion due to fiber dispersion.

In FP-LDs, Δλ/℃ is positive, i.e., the lasing wavelength is shifted towards longer wavelength for increased temperature. Correspondingly, the peaks of the passbands move toward lower frequencies, as shown in Fig. 7. The accumulated dispersion x is obtained by x = D · L = 17 ps/nm/km⋅10.66 km = 181.22 ps/nm . The time interval T of any two wavelength components of Δλ is calculated by T = x · λ. Around 15°C, Δλ is 1.4 nm, which gives T = 253.708 ps (corresponding to the FSR of 3.94 GHz). The FSR corresponding to the time interval is equal to the notch frequency response of H_tapped-delay (ω) contributed by the two wavelength components. Although the mode spacing of 3.81 GHz and the peak frequency of 19.43 GHz are different from those of our experiment (the mode spacing of 4.106 GHz and the peak frequency of 17.096 GHz for 20°C), the filter response of our photonic microwave filter is verified by this simulation.

In this paper, we have proposed and experimentally demonstrated a tunable photonic microwave filter (PMF) based on a pair of a Fabry-Perot laser diode (FP-LD) and a reflective semiconductor optical amplifier (RSOA). Since we implemented an optical source using the FP-LD laser diode injection-locked to the RSOA, the scheme has a technical merit that it is simple compared with those of using multiple laser sources and achieves the tunable spectral response by only temperature controlling of the FP-LD. Although the present experiment has been limited to a degree of tunable range due to the devices used, i.e., tuning frequency of about 390 MHz due to temperature change of 15°C, the proposed scheme has successfully confirmed the possibility of a tunable filter. In our experimental results, we have shown that the frequency response could be controlled by FP-LD temperature. It is expected that the proposed scheme will provide a simple tunable PMF.