Abstract

Microwave photonic filters (MPFs) with only one ultra-narrow passband are able to provide high frequency selectivity and wide spectral range, and they are of great importance in radio-frequency (RF) signal processing. However, currently all MPFs are limited by trade-offs between key parameters such as spectral resolution and range, tunability, and stability. Here, we report the first demonstration of a single passband MPF with unprecedented performance including ultrahigh spectral resolution of 650 kHz, 0–40 GHz spectral range, and high stability of center frequency drifting within ±50 kHz. This record performance is accomplished by breaking the amplitude equality of a phase-modulated signal via a Brillouin dynamic grating (BDG) which has an ultra-narrow reflection spectrum of sub-MHz. The results point to new ways of creating high performance microwave photonic systems, such as satellite and mobile communications, radars, and remote-sensing systems.

© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. Introduction

Radio-frequency (RF) filters are a basic and crucial frequency-selective building block in microwave systems, providing RF signal filtering functionality to separate signals of interest from the noise background or remove undesirable-frequency portions of input signals [1,2]. Driven by the applications such as wireless communications, radars, sensors, and radio astronomy [36], there are increasingly stringent requirements on the spectral resolution, broadband operation, tuning range and stability of an RF filter. These features, however, are not straightforward to implement using traditional electronic circuitry, for example, microstrip or coplanar waveguide lines, substrate-integrated waveguides, superconducting circuits and ferroelectric materials [712].

Microwave photonic filters (MPFs), unlike the conventional electronic RF filters accomplished in the electrical domain, are a photonic subsystem that utilizes optoelectronic devices and photonic technologies to implement RF signals filtering directly in the optical domain [1316]. The MPFs have great potential to provide promising solutions to meet the above requirements. To date, although a variety of solutions [1737], such as discrete-time signal processing [1719], multi-filters cascading [2021], optical slicing [29], RF fading [30], frequency comb [31], optical injection of a laser [28] and optical-to-RF mapping based on optical filters such as fiber Bragg grating (FBG) [23,26], microring resonator [24] and stimulated Brillouin scattering [25,27] have been presented to achieve above objectives, these filters currently still suffer from low spectral resolution (tens of MHz to GHz), limited frequency tuning range (typically 20 GHz) and instability (center frequency drifting and selectivity varying), which limits their practical applications. An RF filter that can be tuned over tens of GHz whilst keeping kHz-scale spectral resolution and high stability is highly desirable.

Brillouin dynamic grating (BDG) is a moving Bragg grating that is created in an optical fiber by the Stimulated Brillouin Scattering (SBS) process induced acoustic wave [38,39]. BDG is demonstrated to be advantageous with ultra-narrow reflection spectrum of sub-MHz, compact structure and extremely flexibility [4042], and it is already considered as a highly efficient technique to achieve numerous photonic functionalities like high spatial resolution sensing [43,44], all-optical calculus [45], slow and stored light [46,47], optical spectroscopy [48], optical delay lines [49,50], microwave photonic systems [51,52] and so on [53,54].

In order to break the limitation between the spectral resolution, frequency tuning range and stability, a single ultra-narrow passband MPF scheme based on a BDG is proposed. A phase-modulated signal is fed into a BDG, and the magnitude of one of first-order sidebands is modified if it falls in the notch of the BDG, and correspondingly an RF electrical signal is generated in a photodetector (PD). For other sidebands that lie outside of the notch, their magnitude are maintained equally, and therefore corresponding RF electrical signals are canceled out. Consequently, a MPF with only one passband is realized. In addition, owing to the ultra-narrow notch of the BDG, the MPF achieves ultrahigh spectral resolution. The proposed MPF is theoretically analyzed and experimentally verified. Single passband RF filtering with spectral resolution of 650 kHz, 0–40 GHz spectral range, and center frequency drifting of ±50kHz over 30 minutes is achieved. To the best of our knowledge, this is the highest spectral resolution single passband MPF reported to date, with wide spectral range, large tunable capability, high stability and a simple structure.

2. Principle

Stimulated Brillouin scattering (SBS) is widely used to implement MPFs, in which one sideband of a microwave-modulated optical signal is attenuated or amplified by the SBS loss or gain resonance generated by one pump waves in an optical fiber. However, this approach suffers from low spectral resolution due to inherent limitations in the SBS gain or loss resonance, whose bandwidth $\Delta {f_B}$ is about tens of megahertz. By contrast, a BDG is used to manipulate the sideband of the microwave-modulated optical signal in the proposed MPF, as shown in Figs. 1(a) and 1(b). The BDG is actually an optical fiber that is pumped by two optical waves (pump 1 and pump 2) with same polarization ($x - \textrm{pol}.$) and opposite propagation direction. The frequencies of pump 1 and pump 2 are respectively ${f_1}$ and ${f_2}$, and the frequency offset between pump 1 and pump 2 is equal to the Brillouin frequency shift (BFS) ${f_B}$ of the optical fiber. SBS process between the two optical waves create a longitudinal acoustic wave that travels along the optical fiber at the sound velocity. The acoustic wave periodically modulates the fiber refractive index through electrostriction effect, therefore a moving fiber Bragg grating (FBG) called BDG is created. The BDG moves in the same direction as the higher frequency optical wave, pump 1.

 figure: Fig. 1.

Fig. 1. Schematic diagram and operation principle of an ultrahigh resolution single passband MPF. (a) Schematic of the MPF. EOPM, electro-optical phase modulator; ISO, isolator; BDG, Brillouin dynamic grating; PC, polarization controller; PBS, polarization beam splitter (PBS); PD, photodetector; VNA, vector network analyzer. (b) Illustration of the principle of the MPF. (c) Illustrated response of the MPF.

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In the proposed MPF, the optical carrier with frequency of ${f_c}$, which is from the laser, is sent to the electro-optical phase modulator (EOPM). The RF electrical signals ${f_{RF}}$ generated by a vector network analyzer (VNA) are modulated on the optical carrier ${f_c}$ at the EOPM, and then the phase-modulated signal in the orthogonal polarization ($y - \textrm{pol}$.) is fed into the BDG in the direction of pump 1. The BDG shows maximum reflectance $R_{BDG}^{max}$ to the phase-modulated signal at the frequency of ${f_1} + {f_{BDG}}$. The frequency offset ${f_{BDG}}$ can be simply expressed as follows [38]:

$${f_{BDG}} = \frac{{\Delta n}}{{{n_g}}}{f_1}, $$
where $\Delta n = {n_x} - {n_y}$ is the birefringence (difference between the refractive indexes in the $x$ and y polarizations), and ${n_g}$ is the group refractive index of $y$-polarized wave at ${f_1}$.

The maximum reflectance $R_{BDG}^{max}$ can be given by [55,56]

$$R_{BDG}^{max} = tan{h^2}({\kappa L} ), $$
where $\kappa = {g_0}\sqrt {{P_1}{P_2}} /2{A_{eff}}$, ${g_0}$ is the peak Brillouin gain factor, ${A_{eff}}$ is the effective core area of the optical fiber, ${P_1}$ and ${P_2}$ are respectively the optical power of pump 1 and pump 2, L is the length of the BDG. In our case, due to the pump waves are continuous wave, the BDG length L is equal to the length of the optical fiber. Equation (2) shows that the reflectance $R_{BDG}^{max}$ is in proportion to ${P_1}$, ${P_2}$ and L.

The reflection spectrum of the BDG is a symmetric Gaussian-like curve, and the BDG bandwidth (FWHM) $\Delta {f_{BDG}}$ can be approximated as [4042]

$$\Delta {f_{BDG}} = 0.443\frac{c}{{nL}},$$
where $n$ is the fiber refractive index. Therefore, the magnitude response ${H_{BDG}}(f )$ and the phase response ${\theta _{BDG}}(f )$ of the BDG transmission can be written as
$${H_{BDG}}(f )= 1 - R_{BDG}^{max}\textrm{exp}\left[ { - \frac{{{{({f - {f_1} - {f_{BDG}}} )}^2}}}{{ln2{{({\Delta {f_{BDG}}} )}^2}}}} \right],$$
$${\theta _{BDG}}(f )= \alpha f, $$
where $\alpha $ is the phase coefficient. The magnitude response is flat except a notch at ${f_1} + {f_{BDG}}$, and phase response is linear.

The phase-modulated signal can be expressed as [26]

$$\begin{array}{l} \begin{array}{l} {{E_{PM}}(t)}={{E_0}{J_0}(\beta )\exp ({j2\pi {f_c}t} )+ {E_0}{J_1}(\beta )\exp [{j2\pi ({{f_c} + {f_{RF}}} )t} ]}\\\,\,\,\,\,\,\,\,\,\,{ - {E_0}{J_1}(\beta )\exp [{j2\pi ({{f_c} - {f_{RF}}} )t} ],} \end{array}\\ \end{array}$$
where ${E_0}$ is the electrical amplitude of the optical carrier, $\beta \; $ is the phase modulation index and ${J_n}({\cdot} )\; $ is the $n$th-order Bessel function of the first kind. In Eq. (5) only the optical carrier and the two first-order sidebands are considered due to the small signal modulation.

After transmitting through the BDG, the phase-modulated signal is modified by the BDG and can be expressed as

$$\begin{array}{l} {\quad {E_{out}}(t )= \sqrt {{H_{BDG}}({{f_c}} )} {E_0}{J_0}(\beta )\textrm{exp}[{j2\pi {f_c}t + j{\theta_{BDG}}({2\pi {f_c}} )} ]}\\ { + \sqrt {{H_{BDG}}({{f_c} + {f_{RF}}} )} \; {E_0}{J_1}(\beta )\textrm{exp}\{{j2\pi ({{f_c} + {f_{RF}}} )t + j{\theta_{BDG}}[{2\pi ({{f_c} + {f_{RF}}} )} ]} \}}\\ { - \sqrt {{H_{BDG}}({{f_c} - {f_{RF}}} )} \; {E_0}{J_1}(\beta )\textrm{exp}\{{j2\pi ({{f_c} - {f_{RF}}} )t + j{\theta_{BDG}}[{2\pi ({{f_c} - {f_{RF}}} )} ]} \},} \end{array}$$
The modified phase-modulated signal is then applied to PD and converted into RF electrical signals, whose power are given by
$$\begin{array}{l} {P_{out}}({{f_{RF}}} )\approx {A^2}[{H_{BDG}}({{f_c} + {f_{RF}}} )+ {H_{BDG}}({{f_c} - {f_{RF}}} )- \\ \quad \; 2\sqrt {{H_{BDG}}({{f_c} + {f_{RF}}} ){H_{BDG}}({{f_c} - {f_{RF}}} )} cos({{\theta_1} - {\theta_2}} )] \end{array}, $$
where
$$A = 2{\cal R}{E_0}^2{J_0}(\beta ){J_1}(\beta )\sqrt {{H_{BDG}}({{f_c}} )} , $$
$${\theta _1} = \; {\theta _{BDG}}({2\pi ({{f_c} + {f_{RF}}} )} )- {\theta _{BDG}}({2\pi {f_c}} ), $$
$${\theta _2} = \; {\theta _{BDG}}({2\pi {f_c}} )- {\theta _{BDG}}({2\pi ({{f_c} - {f_{RF}}} )} ), $$
where $\cal R$ is the responsivity of the PD.

Due to the phase response is linear to frequency, therefore ${\theta _1} - {\theta _2} = 0$. If no sidebands fall in the notch, the transmission response satisfies ${H_{BDG}}({{f_c} + {f_{RF}}} )= {H_{BDG}}({{f_c} - {f_{RF}}} )$, and ${P_{out}}({{f_{RF}}} )= 0$, so there is no RF electrical signals generated at the PD. However, if one sideband falls in the notch of BDG transmission, and ${P_{out}}({{f_{RF}}} )> 0$, therefore a RF electrical signal is generated at the PD. Consequently, a MPF with single passband is realized, as shown in Fig. 1(c).

The center frequency ${f_{pass}}$ of the MPF is determined by the difference between optical carrier ${f_c}$ and the notch position at ${f_1} + {f_{BDG}}$, and ${f_{pass}}$ can be written as

$${f_{pass}} = {f_c} - {f_1} - {f_{BDG}}. $$
The bandwidth $\Delta {f_{pass}}$ of the MPF is determined by the bandwidth of BDG reflection, namely,
$$\Delta {f_{pass}} \approx \Delta {f_{BDG}}. $$
As can be seen from Eq. (9), the center frequency ${f_{pass}}$ can be tuned by altering the optical carrier frequency ${f_c}$ or pump 1 frequency ${f_1}$. In addition, the BDG bandwidth $\Delta {f_{BDG}}$ is inversely proportional to the optical fiber length L, thus much narrower bandwidth $\Delta {f_{BDG}}$ can be obtained by using longer length L. However, the fluctuation of the birefringence $\Delta n$, which increases with the length L, broadens the bandwidth $\Delta {f_{BDG}}$. A single-mode fiber (SMF) shows better birefringence uniformity than that of polarization maintaining fibers (PMF). Consequently, a SMF instead of a PMF is used to create a BDG. A SMF BDG experimentally shows ultra-narrow reflection of 500 kHz [48]. Hence, a SMF-BDG can be easily utilized to obtain an ultra-narrow bandwidth single passband MPF.

3. Experiments

To investigate the performance of the proposed MPF, a variety of experiments are performed, and Fig. 2 shows the experimental implementation. The optical carrier, which is from a tunable laser (NKT E15, linewidth 100 Hz) centered at 1550.0 nm, is split into two branches by a 50:50 polarization maintaining optical coupler (OC). In the lower branch, the optical carrier is modulated in a EOPM (EOspace, 40 GHz 3 dB bandwidth) by swept RF signals ${f_{RF}}$ from a VNA (Rohde & Schwarz, ZVA 40). The frequency drifts between optical carrier and pump waves can cause instability of center frequency of the MPF. In order to avoid this instability, pump waves are generated by shifting the frequency of optical carrier in the upper branch via a frequency shift module (FSM). The inset of Fig. 2 shows the schematic diagram of the FSM, which consists of a RF signal generator, an electro-optic modulator (EOM) cascaded with a tunable optical filter. An electrical signal from the RF signal generator is modulated on the optical light in the EOM, and the optical filter is finely tuned to remove the optical carrier and upper sideband, leaving only the lower sideband. Therefore, a single-sideband suppressed-carrier (SSB-SC) modulation is realized, and the optical light frequency downshift ${f_{RF1}}$ and ${f_{RF2}}$ in the FSM1 and FSM2 respectively. The frequency ${f_{RF2}}$ is equal to the BFS ${f_B}$ of the SMF, and it is around 10.82 GHz in the experiments. Two erbium-doped fiber amplifiers (EDFAs) are used to adjust the optical power of pump waves. Three isolators (ISOs) are utilized to eliminate the counter-propagating optical light. The polarizations of pump 1 and pump 2 are controlled by using PC1 and PC2 respectively. Pump 1 and the phase-modulated signal are combined by a PBS1 to keep the orthogonal states of the polarization (SOPs) along the SMF, and pump 2 is injected into the SMF in the same polarization ($x - \textrm{pol}.$) of pump 1 via a circulator (Cir). The total length of the SMF is 155 meter, and it is loosely wound with a radius of about 65 cm in order to reduce the birefringence nonuniformity. In addition, the environmental noise and temperature fluctuation are suppressed by putting the SMF in a sealed stainless steel box packed with vibration isolation foam in order to reduce the random birefringence variations. Strong SBS between pump 1 and pump 2 is excited, and a BDG is created in the SMF. After transmitting through the SMF BDG, the phase-modulated signal is separated from the pump 1 by PBS2 with proper control of their SOPs via PC3. The output of the PBS2 is detected by PD1, and the transfer function of the MPF is measured by a VNA.

 figure: Fig. 2.

Fig. 2. Experimental implementation of the ultrahigh resolution single passband MPF. Pump 1 and pump 2 are generated by shifting frequency of the optical carrier to avoid the frequency drifts between different Lasers. The inset shows schematic diagram of the frequency-shift module (FSM). EOPM, electro-optic phase modulator; ISO, isolator; PC, polarization controller; PBS, polarization beam splitter (PBS); PD, photodetector; VNA, vector network analyzer. EDFA, erbium-doped fiber amplifier; EOM, electro-optic modulator.

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4. Results

4.1. BDG with an ultra-narrow reflection spectrum of sub-MHz

As the bandwidth $\Delta {f_{pass}}$ of the MPF is determined by the bandwidth $\Delta {f_{BDG}}$ of BDG reflection, we perform measurement of the bandwidth and reflectance of the BDG. The dash box within Fig. 2 illustrate the setup of reflection spectrum measurement. An optical filter is inserted into the propagating link of the phase-modulated signal to remove its optical carrier and the upper sideband, leaving only the lower sideband. The frequency offset $\Delta f$ between the lower sideband and pump 1 is swept within a span of 100 MHz with a step of 10 kHz via changing the RF signals ${f_{RF}}$ from VNA. The reflection spectrum of the BDG is measured by PD2 connected to a digital oscilloscope. The measured reflection spectrum is plotted as function of $\Delta f$ in Fig. 3, obtained for ${P_1} = 16.4\; \textrm{dBm}$ and ${P_2} = 8.4\; \textrm{dBm}$. It is observed the reflection spectrum decently fits with a Gaussian curve (red), and the bandwidth $\Delta {f_{BDG}}$ is about 600 kHz, shows good agreement with result predicted through Eq. (3). In addition, it is seen that the peak reflectance is about 15%, corresponding to the BDG frequency offset ${f_{BDG}}$ of 0.4 MHz. In our experiment, the SMF bended with a radius of 65 cm induces a birefringence $\Delta n$ of ∼3×10−9 [57], which corresponds to a deviation of ∼0.4 MHz in the center frequency of the BDG as predicted in Eq. (1), producing good agreement with the observed one.

 figure: Fig. 3.

Fig. 3. (a) Measured reflection spectrum. (b) Measured transmission and phase spectrum of a SMF BDG as a function of frequency offset $\Delta f$ between the pump 1 and lower sideband of SSB-SC modulated signal.

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The BDG transmission is also investigated through the following experiment. The phase-modulated signal converts into a single-sideband (SSB) modulated signal by removing its upper sideband through the optical filter. The frequency offset $\Delta f$ between the lower sideband and pump 1 is also swept within a span of 100 MHz. Parts of the lower sidebands are reflected by the BDG. Transmitting through the BDG, the SSB modulated signal is separated from the pump 1 via accurate controlling of PC3 and PBS2, and then it is detected by PD1. The magnitude and phase of corresponding RF electrical signals are measured by the VNA. Figure. 3(b) presents the BDG transmission, and the notch of the transmission matches the reflection spectrum as shown in Fig. 3(a). The phase response is linear as predicted in Eq. (4b).

4.2. Ultrahigh spectral resolution single passband MPF

The response of the MPF is measured. Figure 4(a) depicts the optical spectra of input light of the BDG and the output of the PBS2. In this measurement, the VNA is operated at a CW mode with 10 GHz RF signal ${f_{RF}}$, and the RF signal ${f_{RF1}}$ used to driven the FSM1 is 10 GHz + 0.0004 GHz, where the 0.0004 GHz is the BDG frequency offset ${f_{BDG}}$. In this way, the lower sideband of the phase-modulated signal fall in the notch of the BDG. It’s observed that from Fig. 4(a), after transmitting through the BDG, the phase-modulated signal is modified, and there is 2.1 dB magnitude difference between its lower sideband and upper sideband. Moreover, in order to minimize the crosstalk from pump 1 to the modified phase-modulated signal, the pump 1 should be well suppressed. However, since the typical polarization extinction ratio (PER) for a conventional PBS is limited to ∼20 dB, which is not sufficient to suppress the pump 1 due to its high optical power. In our experiment, a polarization maintaining fiber optical circulator is utilized to replace the PBS2, the circulator is fast axis blocked, and the polarization of the modified phase-modulated signal is adjusted to align its slow axis. Figure 4(a) presents that the pump 1 is well supressed with an excellent PER of 40 dB through finely adjustment of the PC3. The amplitude of the first order sideband is 20 dB larger than the second order sideband. So the modification of second order sideband has no influence on the passband response of the MPF.

 figure: Fig. 4.

Fig. 4. (a) Measeured optical spectra of input light of the BDG and the output of the PBS2. (b) Measured frequency response of the MPF with a center frequency of 7.5 GHz. (c) Zoomed-in view of the passband, inset: a zoomed-in view of the passband center with a span of 8 MHz.

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By sweeping the RF signal ${f_{RF}}$ from the VNA, the response of the MPF can be measured. Figure 4(b) shows an example of the measured normalized frequency response of the MPF operating at a center frequency of 7.5 GHz. As can be seen, there is only one passband center at 7.5 GHz within the spectral range 0-20 GHz, so the single passband is realized. The spectral range in the experiment is limited by the 20 GHz bandwidth of PD1. It should be noted that the spectral range could be increased by utilization of broadband electro-optic phase modulator and photodetector. Moreover, Fig. 4(c) shows the zoomed-in view of the passband with a frequency span of 200 MHz. The inset of Fig. 4(c) shows the bandwidth $\Delta {f_{pass}}\; $ of the passband is around 650 kHz, which is in agreement with the calculated results based on Eq. (3) and Eq. (10). To the best of our knowledge, this is the narrowest single passband MPF.

It’s observed from Fig. 4(c) that the passband of the MPF can be divided into two parts, the upper part with suppression of around 15 dB is caused by BDG, while the lower part is induced by SBS loss from pump2. Theoretically, the SBS efficiency between the phase-modulated signal and the pump2 is zero because their polarization states are orthogonal. In fact, the birefringence nonuniformity of the fiber breaks their orthogonality. Therefore, one sideband of the phase-modulated signal is attenuated by the SBS loss, generating a passband with bandwidth of tens of MHz (SBS inherent bandwidth $\Delta {f_B}$). The suppression of the lower passband is small due to the low SBS efficiency and pump 2 optical power. The lower passband could be avoided by using a fiber with low birefringence fluctuation. In this way, the suppression of the whole passband can be enlarged. Moreover, Eq. (2) shows that the reflectance $R_{BDG}^{max}$ is in proportion to ${P_1}$, ${P_2}$ and L. Increasing those parameter values is an effective method to get large suppression.

4.3. Tunability

The tunability of the MPF is investigated by altering the pump 1 frequency ${f_1}$ via varying the frequency ${f_{RF1}}$. It should be noted the pump 2 frequency ${f_2}$ changes with the pump 1 frequency ${f_1}$, while their frequency difference maintains constant ${f_B}$. Figure 5(a) shows the measured normalized frequency responses of the MPF with center frequency from 2.5 GHz to 15 GHz with an increment of 2.5 GHz. It’s observed that the peak amplitudes of the MPF response decrease with the growth of center frequency owing to the uneven responses of optoelectronic devices, especially the modulators and PD. As can be predicted from Eq. (9), the center frequency can be tuned over the whole spectral range. In addition, ultrahigh center frequency tuning resolution can be achieved due to the small frequency tuning step of the pump 1 frequency ${f_1}$. The bandwidths $\Delta {f_{pass}}$ of the passbands at different center frequency are shown in Fig. 5(b). The results show that the bandwidths $\Delta {f_{pass}}$ are almost stable and around 650 kHz when the center frequency tuned within the range of 2.5-15 GHz.

 figure: Fig. 5.

Fig. 5. (a) Measured frequency response of the single passband MPF with center frequency tuned from 2.5 GHz to 15 GHz with an increment of 2.5 GHz. (b) Zoomed-in view of the passbands at different center frequencies with a span of 10 MHz.

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4.4. Stability

The stability of the proposed MPF with center frequency of 10 GHz is tested by running the system for 30 mintues at room temperature. As shown in Fig. 6, the measured results show the center frequency drifting within ±50 kHz and the peak response variating within ±0.25 dB. The high stability is achieved by utilization of same optical source for pump waves and phase-modulated signal. The SMF refractive index and length variations caused by temperature fluctuation and vibration are the main reason for the the center frequency drift and magnitude variation.

 figure: Fig. 6.

Fig. 6. Measured stability of the single passband MPF with center frequency of 10 GHz within 30 mintues, left vertical axis: center frequency drift, right vertical axis: peak response variation.

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4.5. Spurious-free dynamic range

Another important measure of performance in MPF system is linearity. To further signify the filter performance, an experimental demonstration of the filter linearity was carried out by using two-tone modulation with center frequency of 10 GHz and a tone spacing of 10 kHz. The generated third-order intermodulation (IMD3) products is measured. The measured IMD3 powers as a function of the input RF power is shown Fig. 7. Taking into account the measured noise floor of −125 dBm/Hz, the spurious-free dynamic range (SFDR) of the proposed MPF is measured to be 84.8 dB·Hz2/3 at 10 GHz. The main source of the nonlinearity is from the electro-optic modulator. A more advanced electro-optic modulator could be used to suppress the high-order optical sidebands [58]. The noise figure (NF), which is defined as the ratio of the signal-to-noise at the input to that at the output, is high for this MPF. However, it’s convenient to achieve a low noise figure by increasing the optical power in MPF link and minimizing the noise (relative-intensity noise from laser and amplification noise from RF or optical amplifiers).

 figure: Fig. 7.

Fig. 7. Measured spurious-free dynamic range (SFDR) at 10 GHz. The noise floor is −125 dBm/Hz.

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5. Discussion

5.1 Spectral range extension

Although only 20 GHz spectral range is experimentally demonstrated, the spectral range can be extended. As shown in Fig. 8 (a), if the spectral range of the MPF is extended beyond 21.6 GHz ($2{f_B}$), except for the first passband located at frequency of ${f_c} - {f_1} - {f_{BDG}}$, the SBS gain induced by the pump 2 cause another passband with center frequency of ${f_c} - {f_1} - {f_{BDG}} - 2{f_B}$ and bandwidth of $\Delta {f_B}$. By utilization of a broadband photodetector (Finisar, 50 GHz 3 dB bandwidth), spectral range of 40 GHz and tunability with a frequency step of 5 GHz can be measured, as shown in Fig. 8 (b). The bandwidths $\Delta {f_{pass}}$ for different center frequency in Fig. 8 (b) are around 650 kHz as same as that in Fig. 5 (b).

 figure: Fig. 8.

Fig. 8. (a) Illustration of the principle of the MPF with spectral range of 40 GHz. For better illustration, the distance between ${f_1}$ and ${f_1} + {f_{BDG}}$ is enlarged in this figure. (b) Measured frequency response and tunability of the MPF with a frequency step of 5 GHz over spectral range of 40 GHz.

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The second passbands can be observed over the spectral range. However, the peak amplitudes of the second passbands are much lower than that of the corresponding first ones due to low SBS efficiency between the phase-modulated signal and the pump 2. The reason for low SBS efficiency is the orthogonal polarization states between the phase-modulated signal and the pump 2 and the low optical power of pump 2. Therefore, these second passbands can be ignored. The frequency differences between the second passbands and the corresponding first ones are 21.6 GHz ($2{f_B}$). The peak amplitudes of the MPF response decrease with the growth of center frequency are caused by the uneven responses of optoelectronic devices, especially the modulators and PD. In addition, considering that the pump 1 and the phased-modulated signal have same propagation direction, the influence of the phased-modulated signal induced by the pump 1 can be eliminated.

5.2. Performance comparison and spectral resolution improvement

The SMF BDG is subtly designed and constructed to operate RF signal filtering, and bandpass filter is experimentally demonstrated. It should be noted that, if the PM is replaced by a dual-parallel Mach-Zehnder modulator (DPMZM) and an electrical 90° hybrid, an asymmetric dual-sideband modulated signal is generated [37]. The proposed experimental implementation could be easily reconfigured to realize bandstop filter. In that case, the notch linewidth of the bandstop filter is same as the bandwidth of SMF BDG reflection.

The proposed filter is compared to other competing bandpass MPF implementations, and a summary of critical parameters can be found in Table 1. Figure 9 (a) shows the spectral resolution of passband MPFs based on different-material-based photonic devices. To the best of our knowledge, the 650 kHz bandwidth of the proposed MPF is the narrowest among the reported MPFs. In contrast, the bandwidths of typical microwave photonic tunable filters, whether they're based on a conventional fiber platform, or leading integrated platforms such as indium phosphide, silicon, chalcogenide, and silicon nitride, are much larger than tens of MHz except for the reported 900 kHz in [21]. Whereas, the MPF in [21] is extremely unstable due to the optical coherent interference of the fiber ring resonator. It should be noted that the BDG bandwidth $\Delta {f_{BDG}}$ is inversely proportional to its length, as shown in Fig. 9 (b). Therefore, the bandwidth of the proposed filter could be easily reduced if longer single mode fiber is used to generate the BDG. Moreover, the proposed MPF enables a very large operating spectral range, mainly limited by the photodetector. In addition, the out-of-band rejection of the proposed MPF is about 20 dB, which could be enhanced by increasing the pump wave’s powers or the BDG length. Appealingly, the proposed MPF shows superior stability on the center frequency and passband shape over other reported MPFs due to the pump waves and carrier sharing some laser source and the utilization of long optical fiber. Optical fiber length change caused by environmental factors variations can be neglected compared to its origin long length, which determines the MPF bandwidth. Consequently, the proposed MPF shows invariable passband shape.

 figure: Fig. 9.

Fig. 9. (a) Evolution of spectral resolution of passband MPFs based on different-material-based photonic devices. (b) Calculated BDG bandwidth $\Delta {f_{BDG}}$ with respect to the fiber length.

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Tables Icon

Table 1. Performance comparison of state-of-the-art bandpass MPF technologies

5.3. Polarization analysis

Considering that the pump 1 and phase-modulated signal propagate along the BDG with same direction. Their SOPs should be maintained orthogonally in order to separate them through the PBS. However, the birefringence nonuniformity of the fiber, produced by its intrinsic core asymmetry and the environmental factors such as bend, twist, and anisotropic stress, breaks the orthogonality of their SOPs. Therefore, a fiber with low birefringence nonuniformity is essential to realize the proposed MPF. In addition, their SOPs are also influenced by their optical power through the cross-phase modulation (XPM). Their SOPs change while they are propagating along the fiber, and therefore their output SOP from the PC3 also keeps fluctuating with time. Suppose only the relative SOPs changing between the pump 1 and phase-modulated signal are considered, namely the SOP of the phase-modulated signal preserves linearly in the $y - \textrm{pol}.$ while only the SOP of the pump 1 changes. As sketched in Fig. 10, the output SOP of pump 1 from PC3 is rotated by a degree of $\theta $ from its original SOP due to the birefringence nonuniformity and the XPM contribution. The self-phase modulation (SPM) contribution is neglected. The XPM contribution from the pump 2 is also neglected owing to its relative low optical power. Randomly drastic birefringence variation can be eliminated because the SMF is kept in a stable box. Therefore, the maximum ${\theta _{max}}$ can be written as [59],

$${\theta _{max}} = \frac{{2\pi L}}{{{\lambda _1}}}({\mathrm{\Delta }\tilde{n} + 2{n_2}b{{|{{E_{signal}}} |}^2}} ), $$
where ${\lambda _1}$ is the wavelength of the pump 1, $\mathrm{\Delta }\tilde{n}$ is the average birefringence nonuniformity of the SMF, ${n_2}$ is the nonlinear-index coefficient related to the third-order susceptibility ${\chi ^{(3 )}}$, $b = 1/3$, and $|{E_{signal}}{|^2}$=${P_{signal}}/{A_{eff}}$ is the phase-modulated signal light intensity, where ${A_{eff}}$ is the effective mode area.

 figure: Fig. 10.

Fig. 10. Evolution of the polarization states of the pump 1 and phase-modulated signal after propagating through the BDG.

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As seen from Eq. (11), the ${\theta _{max}}$ increases with the growth of average birefringence nonuniformity $\mathrm{\Delta }\tilde{n}$, fiber length L and the optical power ${P_{signal}}$. The minimum $\textrm{PE}{\textrm{R}_{out}}$ between the pump 1 and phase-modulated signal at the output of PBS is given by

$$\textrm{PE}{\textrm{R}_{out}} = 10lo{g_{10}}\frac{{{P_{signal}}}}{{si{n^2}(\theta ){P_1}}} = \textrm{PE}{\textrm{R}_{in}} + 10lo{g_{10}}\left[ {\frac{1}{{si{n^2}({{\theta_{max}}} )}}} \right]({\textrm{dB}} ), $$
where $\textrm{PE}{\textrm{R}_{in}} = 10lo{g_{10}}({{P_{signal}}/{P_1}} )$. The reported average intrinsic birefringence of fibers is of the order of ∼10−9 [60]. Using ${n_2} \approx 3 \times {10^{ - 16}}\textrm{c}{\textrm{m}^2}/\textrm{W}$, ${A_{eff}} \approx 100\mu {m^2}$, and ${P_1} = 100\; mW$, the $\textrm{PE}{\textrm{R}_{out}}$ is ploted versus average birefringence nonuniformity $\mathrm{\Delta }\tilde{n}$, fiber length L and the optical power ${P_{signal}}$, as shown in Fig. 11. It can been seen that, the $\textrm{PE}{\textrm{R}_{out}}$ is inversely proportional to the average birefringence nonuniformity $\mathrm{\Delta }\tilde{n}$ and fiber length L, and proportional to the optical power ${P_{signal}}$ It should be noted that, the $\textrm{PE}{\textrm{R}_{out}}$ shown in the Fig. 11 is theoretical minimum due to both average birefringence nonuniformity and XPM have positive contribution to the SOP evolution of pump 1. The $\textrm{PE}{\textrm{R}_{out}}$ may be larger in the experiments while average birefringence nonuniformity and SPM preserve opposite contribution to the SOP evolution. This conclusion is evidenced by the fact that a 40 dB PER is measured as shown in Fig. 4(a). Precise optical power control, coupled with careful choose of the fiber provides a convenient method to obtain larger $\textrm{PE}{\textrm{R}_{out}}$ to separate the phase-modulated signal from the pump 1. By optimizing the above parameters, a MPF with passband bandwidth of 200∼300 kHz could be realized. The proposed MPF scheme has great potential for microwave photonics signal generation and processing.

 figure: Fig. 11.

Fig. 11. Calculated polarization extinction ratio $\textrm{PE}{\textrm{R}_{out}}$ between the pump 1 and phase-modulated signal at the output of PBS as a function of average birefringence nonuniformity, fiber length, and optical power for ${P_1} = 100mW$.

Download Full Size | PPT Slide | PDF

6. Conclusion

In conclusion, an ultrahigh spectral resolution single passband MPF is presented, theoretically analyzed and experimentally demonstrated. The RF filtering is accomplished by breaking the amplitude equality of a phase-modulated signal via a Brillouin dynamic grating (BDG) which has an ultra-narrow reflection spectrum of sub-MHz. Experimental results demonstrated the MPF is able to provide RF signal filtering with spectral resolution of 650 kHz within 20 GHz spectral band. This represents nearly dozens of times improvement in the spectral resolution over most of previous results. The tunability of the MPF from 2.5 GHz to 15 GHz with 2.5 GHz step, and the stability of center frequency drifting within ±50 kHz over 30 minutes, are also demonstrated. In addition, the MPF allows the passband width to be further reduced to 200∼300 kHz by increasing the BDG length. The spectral range of the MPF is widened to 40 GHz by utilization of a broadband photodetector. Limitations between the filter spectral resolution, frequency tuning range and stability are broken by this proposed MPF. The performance of satellite and mobile communications, radar, electronic warfare, metrology, and remote-sensing systems is able to improve benefiting from the utilization of this highly practical MPF.

Funding

National Key Research and Development Program of China (2019YFB2203104, 2020YFB2205801); National Natural Science Foundation of China (61805231, 61835010, 61620106013).

Acknowledgment

The authors thank Difei Shi and Tenfei Hao for help on the experimental setup.

Disclosures

The authors declare no conflicts of interest.

Data availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

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References

  • View by:

  1. V. J. Urick, J. D. Mckinney, and K. J. Williams, Fundamentals of Microwave Photonics (Wiley, 2015).
  2. R. J. Cameron, C. M. Kudsia, and R. R. Mansour, Microwave Filters for Communication Systems (Wiley, 2018).
  3. L. Maleki, “Sources: The optoelectronic oscillator,” Nat. Photonics 5(12), 728–730 (2011).
    [Crossref]
  4. J. Hervás, A.L. Ricchiuti, W. Li, N.H. Zhu, C.R. Fernández-Pousa, S. Sales, M. Li, and J. Capmany, “Microwave Photonics for Optical Sensors,” IEEE J. Sel. Top. Quantum Electron. 23(2), 327–339 (2017).
    [Crossref]
  5. P. Ghelfi, F. Laghezza, F. Scotti, G. Serafino, A. Capria, S. Pinna, D. Onori, C. Porzi, M. Scaffardi, A. Malacarne, V. Vercesi, E. Lazzeri, F. Berizzi, and A. Bogoni, “A fully photonics-based coherent radar system,” Nature 507(7492), 341–345 (2014).
    [Crossref]
  6. H. Tang, Y. Yu, Z. Wang, L. Xu, and X. Zhang, “Wideband tunable optoelectronic oscillator based on a microwave photonic filter with an ultra-narrow passband,” Opt. Lett. 43(10), 2328–2331 (2018).
    [Crossref]
  7. J. Long, C. Li, W. Cui, J. Huangfu, and L. Ran, “A tunable microstrip bandpass filter with two independently adjustable transmission zeros,” IEEE Microw. Wireless Compon. Lett. 21(2), 74–76 (2011).
    [Crossref]
  8. A. Velez, F. Aznar, M. Duran-Sindreu, J. Bonache, and F. Martin, “Tunable coplanar waveguide band-stop and band-pass filters based on open split ring resonators and open complementary split ring resonators,” IET Microw. Antennas Propag. 5(3), 277–281 (2011).
    [Crossref]
  9. V. Sekar, M. Armendariz, and K. Entesari, “1.2-1.6-GHz substrate-integrated-waveguide RF MEMS tunable filter,” IEEE Trans. Microwave Theory Tech. 59(4), 866–876 (2011).
    [Crossref]
  10. M. R. Rafique, T. Ohki, B. Banik, H. Engseth, P. Linner, and A. Herr, “Miniaturized superconducting microwave filters,” Supercond. Sci. Technol. 21(7), 075004 (2008).
    [Crossref]
  11. G. Velu, K. Blary, L. Burgnies, A. Marteau, G. Houzet, D. Lippens, and J. Carru, “A 360° BST phase shifter with moderate bias voltage at 30 GHz,” IEEE Trans. Microwave Theory Tech. 55(2), 438–444 (2007).
    [Crossref]
  12. K. Koh and G. M. Rebeiz, “A 6–18 GHz 5-bit active phase shifter,” in Proceedings of IEEE MTT-S International Microwave Symposium (IEEE, 2010), pp. 792–795.
  13. J. Capmany and D. Novak, “Microwave photonics combines two worlds,” Nat. Photonics 1(6), 319–330 (2007).
    [Crossref]
  14. J. Yao, “Microwave photonics,” J. Lightwave Technol. 27(3), 314–335 (2009).
    [Crossref]
  15. J. Capmany, B. Ortega, and D. Pastor, “A Tutorial on Microwave Photonic Filters,” J. Lightwave Technol. 24(1), 201–229 (2006).
    [Crossref]
  16. R.A. Minasian, “Photonic signal processing of microwave signals,” IEEE Trans. Microwave Theor. Tech. 54(2), 832–846 (2006).
    [Crossref]
  17. J. Capmany, J. Mora, I. Gasulla, J. Sancho, J. Lloret, and S. Sales, “Microwave Photonic Signal Processing,” J. Lightwave Technol. 31(4), 571–586 (2013).
    [Crossref]
  18. R.A. Minasian, E.H.W. Chan, and X. Yi, “Microwave photonic signal processing,” Opt. Express 21(19), 22918–22936 (2013).
    [Crossref]
  19. J. Capmany, “On the Cascade of Incoherent Discrete-Time Microwave Photonic Filters,” J. Lightwave Technol. 24(7), 2564–2578 (2006).
    [Crossref]
  20. J. Liu, N. Guo, Z. Li, C. Yu, and C. Lu, “Ultrahigh-Q microwave photonic filter with tunable Q value utilizing cascaded optical-electrical feedback loops,” Opt. Lett. 38(21), 4304–4307 (2013).
    [Crossref]
  21. H.S. Wen, M. Li, W. Li, and N.H. Zhu, “Ultrahigh-Q and tunable single-passband microwave photonic filter based on stimulated Brillouin scattering and a fiber ring resonator,” Opt. Lett. 43(19), 4659–4662 (2018).
    [Crossref]
  22. T. Chen, X. Yi, L. Li, and R. Minasian, “Single passband microwave photonic filter with wideband tunability and adjustable bandwidth,” Opt. Lett. 37(22), 4699–4701 (2012).
    [Crossref]
  23. C. Wang and J. Yao, “Fiber Bragg gratings for microwave photonics subsystems,” Opt. Express 21(19), 22868–22884 (2013).
    [Crossref]
  24. J. Palaci, G.E. Villanueva, J.V. Galan, J. Marti, and B. Vidal, “Single Bandpass Photonic Microwave Filter Based on a Notch Ring Resonator,” IEEE Photonics Technol. Lett. 22(17), 1276–1278 (2010).
    [Crossref]
  25. W. W. Zhang and R. A. Minasian, “Widely tunable single-passband microwave photonic filter based on Stimulated Brillouin scattering,” IEEE Photonics Technol. Lett. 23(23), 1775–1777 (2011).
    [Crossref]
  26. W. Li, M. Li, and J. Yao, “A Narrow-Passband and Frequency-Tunable Microwave Photonic Filter Based on Phase-Modulation to Intensity-Modulation Conversion Using a Phase-Shifted Fiber Bragg Grating,” IEEE Trans. Microwave Theor. Tech. 60(5), 1287–1296 (2012).
    [Crossref]
  27. S. Preußler, A. Wiatrek, K. Jamshidi, and T. Schneider, “Brillouin scattering gain bandwidth reduction down to 3.4 MHz,” Opt. Express 19(9), 8565–8570 (2011).
    [Crossref]
  28. T. Zhang, J. Xiong, J. Zheng, X. Chen, and T. Pu, “Wideband tunable single bandpass microwave photonic filter based on FWM dynamics of optical-injected DFB laser,” Electron. Lett. 52(1), 57–59 (2016).
    [Crossref]
  29. X. Xue, X. Zheng, H. Zhang, and B. Zhou, “Widely tunable single-bandpass microwave photonic filter employing a non-sliced broadband optical source,” Opt. Express 19(19), 18423–18429 (2011).
    [Crossref]
  30. L. Li, X. Yi, T. Huang, and R. Minasian, “Shifted dispersion-induced radio-frequency fading in microwave photonic filters using a dual-input Mach-Zehnder electro-optic modulator,” Opt. Lett. 38(7), 1164–1166 (2013).
    [Crossref]
  31. V.R. Supradeepa, C.M. Long, R. Wu, F. Ferdous, E. Hamidi, D.E. Leaird, and A.M. Weiner, “Comb-based radiofrequency photonic filters with rapid tunability and high selectivity,” Nat. Photonics 6(3), 186–194 (2012).
    [Crossref]
  32. Y. Yu, J. Dong, E. Xu, X. Li, L. Zhou, F. Wang, and X. Zhang, “Single Passband Microwave Photonic Filter With Continuous Wideband Tunability Based on Electro-Optic Phase Modulator and Fabry-Perot Semiconductor Optical Amplifier,” J. Lightwave Technol. 29(3), 3542–3550 (2011).
  33. H. Qiu, F. Zhou, J. Qie, Y. Yao, X. Hu, Y. Zhang, X. Xiao, Y. Yu, J. Dong, and X. Zhang, “A Continuously Tunable Sub-Gigahertz Microwave Photonic Bandpass Filter Based on an Ultra-High-Q Silicon Microring Resonator,” J. Lightwave Technol. 36(19), 4312–4318 (2018).
    [Crossref]
  34. X. Xu, M. Tan, J. Wu, T.G. Nguyen, S.T. Chu, B.E. Little, R. Morandotti, A. Mitchell, and D.J. Moss, “High performance RF filters via bandwidth scaling with Kerr micro-combs,” APL Photo. 4(2), 02610 (2019).
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2020 (1)

2019 (3)

2018 (4)

2017 (2)

J. Hervás, A.L. Ricchiuti, W. Li, N.H. Zhu, C.R. Fernández-Pousa, S. Sales, M. Li, and J. Capmany, “Microwave Photonics for Optical Sensors,” IEEE J. Sel. Top. Quantum Electron. 23(2), 327–339 (2017).
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M.A. Soto, A. Denisov, X. Angulo-Vinuesa, S. Martin-Lopez, L. Thévenaz, and M. Gonzalez-Herraez, “All-optical flip-flops based on dynamic Brillouin gratings in fibers,” Opt. Lett. 42(13), 2539–2542 (2017).
[Crossref]

2016 (1)

T. Zhang, J. Xiong, J. Zheng, X. Chen, and T. Pu, “Wideband tunable single bandpass microwave photonic filter based on FWM dynamics of optical-injected DFB laser,” Electron. Lett. 52(1), 57–59 (2016).
[Crossref]

2015 (1)

2014 (3)

2013 (8)

2012 (7)

S. Chin, N. Primerov, and L. Thevenaz, “Sub-Centimeter Spatial Resolution in Distributed Fiber Sensing Based on Dynamic Brillouin Grating in Optical Fibers,” IEEE Sens. J. 12(1), 189–194 (2012).
[Crossref]

J. Sancho, N. Primerov, S. Chin, Y. Antman, A. Zadok, S. Sales, and L. Thévenaz, “Tunable and reconfigurable multi-tap microwave photonic filter based on dynamic Brillouin gratings in fibers,” Opt. Express 20(6), 6157–6162 (2012).
[Crossref]

S. Chin and L. Thévenaz, “Tunable photonic delay lines in optical fibers,” Laser Photon. Rev. 6(6), 724–738 (2012).
[Crossref]

V.R. Supradeepa, C.M. Long, R. Wu, F. Ferdous, E. Hamidi, D.E. Leaird, and A.M. Weiner, “Comb-based radiofrequency photonic filters with rapid tunability and high selectivity,” Nat. Photonics 6(3), 186–194 (2012).
[Crossref]

W. Li, M. Li, and J. Yao, “A Narrow-Passband and Frequency-Tunable Microwave Photonic Filter Based on Phase-Modulation to Intensity-Modulation Conversion Using a Phase-Shifted Fiber Bragg Grating,” IEEE Trans. Microwave Theor. Tech. 60(5), 1287–1296 (2012).
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A. Byrnes, R. Pant, E. Li, D.-Y. Choi, C.G. Poulton, S. Fan, S. Madden, B. Luther-Davies, and B.J. Eggleton, “Photonic chip based tunable and reconfigurable narrowband microwave photonic filter using stimulated Brillouin scattering,” Opt. Express 20(17), 18836–18845 (2012).
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T. Chen, X. Yi, L. Li, and R. Minasian, “Single passband microwave photonic filter with wideband tunability and adjustable bandwidth,” Opt. Lett. 37(22), 4699–4701 (2012).
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2011 (9)

L. Maleki, “Sources: The optoelectronic oscillator,” Nat. Photonics 5(12), 728–730 (2011).
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J. Long, C. Li, W. Cui, J. Huangfu, and L. Ran, “A tunable microstrip bandpass filter with two independently adjustable transmission zeros,” IEEE Microw. Wireless Compon. Lett. 21(2), 74–76 (2011).
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A. Velez, F. Aznar, M. Duran-Sindreu, J. Bonache, and F. Martin, “Tunable coplanar waveguide band-stop and band-pass filters based on open split ring resonators and open complementary split ring resonators,” IET Microw. Antennas Propag. 5(3), 277–281 (2011).
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V. Sekar, M. Armendariz, and K. Entesari, “1.2-1.6-GHz substrate-integrated-waveguide RF MEMS tunable filter,” IEEE Trans. Microwave Theory Tech. 59(4), 866–876 (2011).
[Crossref]

K.Y. Song, “Operation of Brillouin dynamic grating in single-mode optical fibers,” Opt. Lett. 36(23), 4686–4688 (2011).
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S. Preußler, A. Wiatrek, K. Jamshidi, and T. Schneider, “Brillouin scattering gain bandwidth reduction down to 3.4 MHz,” Opt. Express 19(9), 8565–8570 (2011).
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X. Xue, X. Zheng, H. Zhang, and B. Zhou, “Widely tunable single-bandpass microwave photonic filter employing a non-sliced broadband optical source,” Opt. Express 19(19), 18423–18429 (2011).
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Y. Yu, J. Dong, E. Xu, X. Li, L. Zhou, F. Wang, and X. Zhang, “Single Passband Microwave Photonic Filter With Continuous Wideband Tunability Based on Electro-Optic Phase Modulator and Fabry-Perot Semiconductor Optical Amplifier,” J. Lightwave Technol. 29(3), 3542–3550 (2011).

W. W. Zhang and R. A. Minasian, “Widely tunable single-passband microwave photonic filter based on Stimulated Brillouin scattering,” IEEE Photonics Technol. Lett. 23(23), 1775–1777 (2011).
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2010 (4)

2009 (1)

2008 (2)

M. R. Rafique, T. Ohki, B. Banik, H. Engseth, P. Linner, and A. Herr, “Miniaturized superconducting microwave filters,” Supercond. Sci. Technol. 21(7), 075004 (2008).
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K. Y. Song, W. Zou, Z. He, and K Hotate, “All-optical dynamic grating generation based on Brillouin scattering in polarization maintaining fiber,” Opt. Lett. 33(9), 926–928 (2008).
[Crossref]

2007 (3)

G. Velu, K. Blary, L. Burgnies, A. Marteau, G. Houzet, D. Lippens, and J. Carru, “A 360° BST phase shifter with moderate bias voltage at 30 GHz,” IEEE Trans. Microwave Theory Tech. 55(2), 438–444 (2007).
[Crossref]

J. Capmany and D. Novak, “Microwave photonics combines two worlds,” Nat. Photonics 1(6), 319–330 (2007).
[Crossref]

Z. Zhu, D.J. Gauthier, and R.W. Boyd, “Stored light in an optical fiber via stimulated Brillouin scattering,” Science 318(5857), 1748–1750 (2007).
[Crossref]

2006 (3)

1997 (1)

T. Erdogan, “Fiber grating spectra,” J. Lightwave Technol. 15(8), 1277–1294 (1997).
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1980 (1)

Agrawa, G.

G. Agrawa, Nonlinear Fiber Optics, 4th ed. (Academic, 2006)

Angulo-Vinuesa, X.

Antman, Y.

Armendariz, M.

V. Sekar, M. Armendariz, and K. Entesari, “1.2-1.6-GHz substrate-integrated-waveguide RF MEMS tunable filter,” IEEE Trans. Microwave Theory Tech. 59(4), 866–876 (2011).
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Aznar, F.

A. Velez, F. Aznar, M. Duran-Sindreu, J. Bonache, and F. Martin, “Tunable coplanar waveguide band-stop and band-pass filters based on open split ring resonators and open complementary split ring resonators,” IET Microw. Antennas Propag. 5(3), 277–281 (2011).
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Banik, B.

M. R. Rafique, T. Ohki, B. Banik, H. Engseth, P. Linner, and A. Herr, “Miniaturized superconducting microwave filters,” Supercond. Sci. Technol. 21(7), 075004 (2008).
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Bao, X.

Bergman, A.

A. Bergman and M. Tur, “Brillouin Dynamic Gratings-A Practical Form of Brillouin Enhanced Four Wave Mixing in Waveguides: The First Decade and Beyond,” Sensors 18(9), 2863 (2018).
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Berizzi, F.

P. Ghelfi, F. Laghezza, F. Scotti, G. Serafino, A. Capria, S. Pinna, D. Onori, C. Porzi, M. Scaffardi, A. Malacarne, V. Vercesi, E. Lazzeri, F. Berizzi, and A. Bogoni, “A fully photonics-based coherent radar system,” Nature 507(7492), 341–345 (2014).
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Blary, K.

G. Velu, K. Blary, L. Burgnies, A. Marteau, G. Houzet, D. Lippens, and J. Carru, “A 360° BST phase shifter with moderate bias voltage at 30 GHz,” IEEE Trans. Microwave Theory Tech. 55(2), 438–444 (2007).
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Bogoni, A.

P. Ghelfi, F. Laghezza, F. Scotti, G. Serafino, A. Capria, S. Pinna, D. Onori, C. Porzi, M. Scaffardi, A. Malacarne, V. Vercesi, E. Lazzeri, F. Berizzi, and A. Bogoni, “A fully photonics-based coherent radar system,” Nature 507(7492), 341–345 (2014).
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Bonache, J.

A. Velez, F. Aznar, M. Duran-Sindreu, J. Bonache, and F. Martin, “Tunable coplanar waveguide band-stop and band-pass filters based on open split ring resonators and open complementary split ring resonators,” IET Microw. Antennas Propag. 5(3), 277–281 (2011).
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Bowers, J.E.

Boyd, R.W.

Z. Zhu, D.J. Gauthier, and R.W. Boyd, “Stored light in an optical fiber via stimulated Brillouin scattering,” Science 318(5857), 1748–1750 (2007).
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Buckwalter, J.F.

Burgnies, L.

G. Velu, K. Blary, L. Burgnies, A. Marteau, G. Houzet, D. Lippens, and J. Carru, “A 360° BST phase shifter with moderate bias voltage at 30 GHz,” IEEE Trans. Microwave Theory Tech. 55(2), 438–444 (2007).
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Byrnes, A.

Cameron, R. J.

R. J. Cameron, C. M. Kudsia, and R. R. Mansour, Microwave Filters for Communication Systems (Wiley, 2018).

Capmany, J.

J. Hervás, A.L. Ricchiuti, W. Li, N.H. Zhu, C.R. Fernández-Pousa, S. Sales, M. Li, and J. Capmany, “Microwave Photonics for Optical Sensors,” IEEE J. Sel. Top. Quantum Electron. 23(2), 327–339 (2017).
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J. Capmany, J. Mora, I. Gasulla, J. Sancho, J. Lloret, and S. Sales, “Microwave Photonic Signal Processing,” J. Lightwave Technol. 31(4), 571–586 (2013).
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J. Capmany and D. Novak, “Microwave photonics combines two worlds,” Nat. Photonics 1(6), 319–330 (2007).
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J. Capmany, B. Ortega, and D. Pastor, “A Tutorial on Microwave Photonic Filters,” J. Lightwave Technol. 24(1), 201–229 (2006).
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J. Capmany, “On the Cascade of Incoherent Discrete-Time Microwave Photonic Filters,” J. Lightwave Technol. 24(7), 2564–2578 (2006).
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Capria, A.

P. Ghelfi, F. Laghezza, F. Scotti, G. Serafino, A. Capria, S. Pinna, D. Onori, C. Porzi, M. Scaffardi, A. Malacarne, V. Vercesi, E. Lazzeri, F. Berizzi, and A. Bogoni, “A fully photonics-based coherent radar system,” Nature 507(7492), 341–345 (2014).
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Carru, J.

G. Velu, K. Blary, L. Burgnies, A. Marteau, G. Houzet, D. Lippens, and J. Carru, “A 360° BST phase shifter with moderate bias voltage at 30 GHz,” IEEE Trans. Microwave Theory Tech. 55(2), 438–444 (2007).
[Crossref]

Chan, E.H.W.

Chen, L.

Chen, T.

Chen, X.

T. Zhang, J. Xiong, J. Zheng, X. Chen, and T. Pu, “Wideband tunable single bandpass microwave photonic filter based on FWM dynamics of optical-injected DFB laser,” Electron. Lett. 52(1), 57–59 (2016).
[Crossref]

Chin, S.

M. Santagiustina, S. Chin, N. Primerov, L. Ursini, and L. Thévenaz, “All-optical signal processing using dynamic Brillouin gratings,” Sci. Rep. 3(1), 1594 (2013).
[Crossref]

S. Chin, N. Primerov, and L. Thevenaz, “Sub-Centimeter Spatial Resolution in Distributed Fiber Sensing Based on Dynamic Brillouin Grating in Optical Fibers,” IEEE Sens. J. 12(1), 189–194 (2012).
[Crossref]

S. Chin and L. Thévenaz, “Tunable photonic delay lines in optical fibers,” Laser Photon. Rev. 6(6), 724–738 (2012).
[Crossref]

J. Sancho, N. Primerov, S. Chin, Y. Antman, A. Zadok, S. Sales, and L. Thévenaz, “Tunable and reconfigurable multi-tap microwave photonic filter based on dynamic Brillouin gratings in fibers,” Opt. Express 20(6), 6157–6162 (2012).
[Crossref]

K.Y. Song, S. Chin, N. Primerov, and L. Thévenaz, “Time-Domain Distributed Fiber Sensor With 1 cm Spatial Resolution Based on Brillouin Dynamic Grating,” J. Lightwave Technol. 28(14), 2062–2067 (2010).
[Crossref]

Choi, D.-Y.

Choudhary, A.

Chu, S.T.

X. Xu, M. Tan, J. Wu, T.G. Nguyen, S.T. Chu, B.E. Little, R. Morandotti, A. Mitchell, and D.J. Moss, “High performance RF filters via bandwidth scaling with Kerr micro-combs,” APL Photo. 4(2), 02610 (2019).
[Crossref]

Cui, W.

J. Long, C. Li, W. Cui, J. Huangfu, and L. Ran, “A tunable microstrip bandpass filter with two independently adjustable transmission zeros,” IEEE Microw. Wireless Compon. Lett. 21(2), 74–76 (2011).
[Crossref]

Daulay, O.

Deng, Y.

Denisov, A.

Dong, J.

Dong, Y.

Duran-Sindreu, M.

A. Velez, F. Aznar, M. Duran-Sindreu, J. Bonache, and F. Martin, “Tunable coplanar waveguide band-stop and band-pass filters based on open split ring resonators and open complementary split ring resonators,” IET Microw. Antennas Propag. 5(3), 277–281 (2011).
[Crossref]

Eggleton, B.

Eggleton, B.J.

Eickhoff, W.

Engseth, H.

M. R. Rafique, T. Ohki, B. Banik, H. Engseth, P. Linner, and A. Herr, “Miniaturized superconducting microwave filters,” Supercond. Sci. Technol. 21(7), 075004 (2008).
[Crossref]

Entesari, K.

V. Sekar, M. Armendariz, and K. Entesari, “1.2-1.6-GHz substrate-integrated-waveguide RF MEMS tunable filter,” IEEE Trans. Microwave Theory Tech. 59(4), 866–876 (2011).
[Crossref]

Erdogan, T.

T. Erdogan, “Fiber grating spectra,” J. Lightwave Technol. 15(8), 1277–1294 (1997).
[Crossref]

Fan, S.

Ferdous, F.

V.R. Supradeepa, C.M. Long, R. Wu, F. Ferdous, E. Hamidi, D.E. Leaird, and A.M. Weiner, “Comb-based radiofrequency photonic filters with rapid tunability and high selectivity,” Nat. Photonics 6(3), 186–194 (2012).
[Crossref]

Fernández-Pousa, C.R.

J. Hervás, A.L. Ricchiuti, W. Li, N.H. Zhu, C.R. Fernández-Pousa, S. Sales, M. Li, and J. Capmany, “Microwave Photonics for Optical Sensors,” IEEE J. Sel. Top. Quantum Electron. 23(2), 327–339 (2017).
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Galan, J.V.

J. Palaci, G.E. Villanueva, J.V. Galan, J. Marti, and B. Vidal, “Single Bandpass Photonic Microwave Filter Based on a Notch Ring Resonator,” IEEE Photonics Technol. Lett. 22(17), 1276–1278 (2010).
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Gasulla, I.

Gauthier, D.J.

Z. Zhu, D.J. Gauthier, and R.W. Boyd, “Stored light in an optical fiber via stimulated Brillouin scattering,” Science 318(5857), 1748–1750 (2007).
[Crossref]

Ghelfi, P.

P. Ghelfi, F. Laghezza, F. Scotti, G. Serafino, A. Capria, S. Pinna, D. Onori, C. Porzi, M. Scaffardi, A. Malacarne, V. Vercesi, E. Lazzeri, F. Berizzi, and A. Bogoni, “A fully photonics-based coherent radar system,” Nature 507(7492), 341–345 (2014).
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Gonzalez-Herraez, M.

Guo, J. J.

Guo, N.

Hamidi, E.

V.R. Supradeepa, C.M. Long, R. Wu, F. Ferdous, E. Hamidi, D.E. Leaird, and A.M. Weiner, “Comb-based radiofrequency photonic filters with rapid tunability and high selectivity,” Nat. Photonics 6(3), 186–194 (2012).
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He, Z.

Helkey, R.

Herr, A.

M. R. Rafique, T. Ohki, B. Banik, H. Engseth, P. Linner, and A. Herr, “Miniaturized superconducting microwave filters,” Supercond. Sci. Technol. 21(7), 075004 (2008).
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Hervás, J.

J. Hervás, A.L. Ricchiuti, W. Li, N.H. Zhu, C.R. Fernández-Pousa, S. Sales, M. Li, and J. Capmany, “Microwave Photonics for Optical Sensors,” IEEE J. Sel. Top. Quantum Electron. 23(2), 327–339 (2017).
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Horiguchi, Tsuneo

Shinya Takigawa and Tsuneo Horiguchi, “Reflection properties of Brillouin dynamic gratings in coiled single-mode fibers,” Proc. SPIE8421, 84219U–84219U-4 (2012).
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Hosseinzadeh, N.

Hotate, K

Houzet, G.

G. Velu, K. Blary, L. Burgnies, A. Marteau, G. Houzet, D. Lippens, and J. Carru, “A 360° BST phase shifter with moderate bias voltage at 30 GHz,” IEEE Trans. Microwave Theory Tech. 55(2), 438–444 (2007).
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Hu, X.

Huang, N.

Huang, T.

Huangfu, J.

J. Long, C. Li, W. Cui, J. Huangfu, and L. Ran, “A tunable microstrip bandpass filter with two independently adjustable transmission zeros,” IEEE Microw. Wireless Compon. Lett. 21(2), 74–76 (2011).
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Jain, A.

Jamshidi, K.

Jiang, T.

Koh, K.

K. Koh and G. M. Rebeiz, “A 6–18 GHz 5-bit active phase shifter,” in Proceedings of IEEE MTT-S International Microwave Symposium (IEEE, 2010), pp. 792–795.

Kudsia, C. M.

R. J. Cameron, C. M. Kudsia, and R. R. Mansour, Microwave Filters for Communication Systems (Wiley, 2018).

Laghezza, F.

P. Ghelfi, F. Laghezza, F. Scotti, G. Serafino, A. Capria, S. Pinna, D. Onori, C. Porzi, M. Scaffardi, A. Malacarne, V. Vercesi, E. Lazzeri, F. Berizzi, and A. Bogoni, “A fully photonics-based coherent radar system,” Nature 507(7492), 341–345 (2014).
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Langer, T.

Lazzeri, E.

P. Ghelfi, F. Laghezza, F. Scotti, G. Serafino, A. Capria, S. Pinna, D. Onori, C. Porzi, M. Scaffardi, A. Malacarne, V. Vercesi, E. Lazzeri, F. Berizzi, and A. Bogoni, “A fully photonics-based coherent radar system,” Nature 507(7492), 341–345 (2014).
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Leaird, D.E.

V.R. Supradeepa, C.M. Long, R. Wu, F. Ferdous, E. Hamidi, D.E. Leaird, and A.M. Weiner, “Comb-based radiofrequency photonic filters with rapid tunability and high selectivity,” Nat. Photonics 6(3), 186–194 (2012).
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Levanon, N.

Li, C.

J. Long, C. Li, W. Cui, J. Huangfu, and L. Ran, “A tunable microstrip bandpass filter with two independently adjustable transmission zeros,” IEEE Microw. Wireless Compon. Lett. 21(2), 74–76 (2011).
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Li, E.

Li, L.

Li, M.

H.S. Wen, M. Li, W. Li, and N.H. Zhu, “Ultrahigh-Q and tunable single-passband microwave photonic filter based on stimulated Brillouin scattering and a fiber ring resonator,” Opt. Lett. 43(19), 4659–4662 (2018).
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J. Hervás, A.L. Ricchiuti, W. Li, N.H. Zhu, C.R. Fernández-Pousa, S. Sales, M. Li, and J. Capmany, “Microwave Photonics for Optical Sensors,” IEEE J. Sel. Top. Quantum Electron. 23(2), 327–339 (2017).
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Data availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

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Figures (11)

Fig. 1.
Fig. 1. Schematic diagram and operation principle of an ultrahigh resolution single passband MPF. (a) Schematic of the MPF. EOPM, electro-optical phase modulator; ISO, isolator; BDG, Brillouin dynamic grating; PC, polarization controller; PBS, polarization beam splitter (PBS); PD, photodetector; VNA, vector network analyzer. (b) Illustration of the principle of the MPF. (c) Illustrated response of the MPF.
Fig. 2.
Fig. 2. Experimental implementation of the ultrahigh resolution single passband MPF. Pump 1 and pump 2 are generated by shifting frequency of the optical carrier to avoid the frequency drifts between different Lasers. The inset shows schematic diagram of the frequency-shift module (FSM). EOPM, electro-optic phase modulator; ISO, isolator; PC, polarization controller; PBS, polarization beam splitter (PBS); PD, photodetector; VNA, vector network analyzer. EDFA, erbium-doped fiber amplifier; EOM, electro-optic modulator.
Fig. 3.
Fig. 3. (a) Measured reflection spectrum. (b) Measured transmission and phase spectrum of a SMF BDG as a function of frequency offset $\Delta f$ between the pump 1 and lower sideband of SSB-SC modulated signal.
Fig. 4.
Fig. 4. (a) Measeured optical spectra of input light of the BDG and the output of the PBS2. (b) Measured frequency response of the MPF with a center frequency of 7.5 GHz. (c) Zoomed-in view of the passband, inset: a zoomed-in view of the passband center with a span of 8 MHz.
Fig. 5.
Fig. 5. (a) Measured frequency response of the single passband MPF with center frequency tuned from 2.5 GHz to 15 GHz with an increment of 2.5 GHz. (b) Zoomed-in view of the passbands at different center frequencies with a span of 10 MHz.
Fig. 6.
Fig. 6. Measured stability of the single passband MPF with center frequency of 10 GHz within 30 mintues, left vertical axis: center frequency drift, right vertical axis: peak response variation.
Fig. 7.
Fig. 7. Measured spurious-free dynamic range (SFDR) at 10 GHz. The noise floor is −125 dBm/Hz.
Fig. 8.
Fig. 8. (a) Illustration of the principle of the MPF with spectral range of 40 GHz. For better illustration, the distance between ${f_1}$ and ${f_1} + {f_{BDG}}$ is enlarged in this figure. (b) Measured frequency response and tunability of the MPF with a frequency step of 5 GHz over spectral range of 40 GHz.
Fig. 9.
Fig. 9. (a) Evolution of spectral resolution of passband MPFs based on different-material-based photonic devices. (b) Calculated BDG bandwidth $\Delta {f_{BDG}}$ with respect to the fiber length.
Fig. 10.
Fig. 10. Evolution of the polarization states of the pump 1 and phase-modulated signal after propagating through the BDG.
Fig. 11.
Fig. 11. Calculated polarization extinction ratio $\textrm{PE}{\textrm{R}_{out}}$ between the pump 1 and phase-modulated signal at the output of PBS as a function of average birefringence nonuniformity, fiber length, and optical power for ${P_1} = 100mW$.

Tables (1)

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Table 1. Performance comparison of state-of-the-art bandpass MPF technologies

Equations (15)

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f B D G = Δ n n g f 1 ,
R B D G m a x = t a n h 2 ( κ L ) ,
Δ f B D G = 0.443 c n L ,
H B D G ( f ) = 1 R B D G m a x exp [ ( f f 1 f B D G ) 2 l n 2 ( Δ f B D G ) 2 ] ,
θ B D G ( f ) = α f ,
E P M ( t ) = E 0 J 0 ( β ) exp ( j 2 π f c t ) + E 0 J 1 ( β ) exp [ j 2 π ( f c + f R F ) t ] E 0 J 1 ( β ) exp [ j 2 π ( f c f R F ) t ] ,
E o u t ( t ) = H B D G ( f c ) E 0 J 0 ( β ) exp [ j 2 π f c t + j θ B D G ( 2 π f c ) ] + H B D G ( f c + f R F ) E 0 J 1 ( β ) exp { j 2 π ( f c + f R F ) t + j θ B D G [ 2 π ( f c + f R F ) ] } H B D G ( f c f R F ) E 0 J 1 ( β ) exp { j 2 π ( f c f R F ) t + j θ B D G [ 2 π ( f c f R F ) ] } ,
P o u t ( f R F ) A 2 [ H B D G ( f c + f R F ) + H B D G ( f c f R F ) 2 H B D G ( f c + f R F ) H B D G ( f c f R F ) c o s ( θ 1 θ 2 ) ] ,
A = 2 R E 0 2 J 0 ( β ) J 1 ( β ) H B D G ( f c ) ,
θ 1 = θ B D G ( 2 π ( f c + f R F ) ) θ B D G ( 2 π f c ) ,
θ 2 = θ B D G ( 2 π f c ) θ B D G ( 2 π ( f c f R F ) ) ,
f p a s s = f c f 1 f B D G .
Δ f p a s s Δ f B D G .
θ m a x = 2 π L λ 1 ( Δ n ~ + 2 n 2 b | E s i g n a l | 2 ) ,
PE R o u t = 10 l o g 10 P s i g n a l s i n 2 ( θ ) P 1 = PE R i n + 10 l o g 10 [ 1 s i n 2 ( θ m a x ) ] ( dB ) ,

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