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Microwave photonic filter with negative coefficients based on counter-phase modulation using a single electro-optic phase modulator
Optics Communications 282 (2009) 845–848
Contents lists available at ScienceDirect
Optics Communications journal homepage: www.elsevier.com/locate/optcom
Microwave photonic filter with negative coefficients based on counter-phase modulation using a single electro-optic phase modulator Jianqiang Li *, Kun Xu, Jian Wu, Jintong Lin Key Laboratory of Optical Communication & Lightwave Technologies, Ministry of Education, Beijing University of Posts and Telecommunications, Beijing 100876, China
a r t i c l e
i n f o
Article history: Received 29 June 2008 Received in revised form 8 November 2008 Accepted 8 November 2008
Keywords: Microwave photonic filter Negative coefficient Electro-optic phase modulator
a b s t r a c t A simple photonic approach is proposed for the implementation of a reconfigurable multi-tap microwave filter with negative coefficients. In this scheme, a dual-optical-input intensity modulation module which can perform counter-phase modulation is constructed using a single electro-optic phase modulator. Two inter-complementary microwave signals are experimentally obtained for verification of the function of counter-phase modulation. A reconfigurable four-tap microwave filter with two negative coefficients is implemented by experiment. Ó 2008 Elsevier B.V. All rights reserved.
1. Introduction Microwave photonic filter, which is known as a favorable technique of processing radio-frequency (RF) signals with the help of photonic devices or subsystems, has been widely investigated for many years. The unique advantages of microwave photonic filter, including low loss, light weight, broad bandwidth, and immunity to electromagnetic interference (EMI), bring a wide range of applications [1]. Due to the strong dependence on environmental fluctuations, stable microwave photonic filters are difficult to implement under coherent operation. Therefore, most of the previous microwave photonic filters have been demonstrated by using incoherent laser sources in so-called inherent systems. It is known that only positive taps can be implemented in incoherent systems due to the positive sign of optical intensity. Microwave photonic filters with only positive coefficients have severe limitations in practical applications due to the limited range of transfer function and the presence of a resonance at baseband [2]. In order to solve this problem, many methods have been proposed to obtain complex or negative coefficients including differential detection [3], hybrid optoelectronic approach [4], and all-optical techniques [5–11]. Among the diverse all-optical techniques to achieve negative coefficients, the approaches by means of employing external electro-optic modulators feature simple structures and high flexibility for tap weighting [7–11]. The positive and negative taps are achieved based on counter-phase modulation in two Mach-Zehnder modulators (MZMs) [7] or a single newly-designed dual-opti* Corresponding author. E-mail address: [email protected] (J. Li). 0030-4018/$ - see front matter Ó 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.optcom.2008.11.014
cal-input MZM [8] by applying appropriate bias voltages to guarantee operations in the linear region of the transfer function with opposite slopes. Electro-optic phase modulators (EOPMs) can also be employed based on phase-to-intensity conversion by cascading a Sagnac loop filter [9] or polarization modulation by following a section of high birefringence (Hi-Bi) fiber [10]. In [9], the wavelength spacing of the used incoherent laser sources is constrained by the fixed comb response of a given Sagnac loop filter, and the process of phase-to-intensity conversion experiences high insertion loss. The scheme presented in [10] suffers from the unfeasibility of arbitrary tap number and reconfigurability by using Hi-Bi fibers. In this paper, we report a novel approach also based on polarization modulation in a single EOPM, which can nevertheless overcome the limitations mentioned above. The crucial difference lies on the design of a dual-optical-input intensity modulation module whose function is similar to the presented modulator in [8]. In the proposed approach, single-mode fibers (SMFs) serve as the delay lines to obtain different sample delays, rather than the Hi-Bi fibers. Experiments have been carried out to verify the function of counter-phase modulation and to implement a four-tap transversal reconfigurable filter with negative coefficients.
2. Fundamental principle and its experimental verification Fig. 1 illustrates the structure and operation principle of the designed dual-optical-input intensity modulation module which consists of a polarization beam splitter (PBS), a commercial LiNbO3 EOPM, a polarizer and several polarization controllers (PCs). As
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J. Li et al. / Optics Communications 282 (2009) 845–848
Fig. 1. Setup and operation principle of the designed dual-optical-input modulator.
shown in the inset of Fig. 1, we define a reference coordinate system in which the light propagates along with z-axis, x and y axes represent the principle axes of EOPM, and the cross section of each component is within the x–y plane. Two linearly-polarized lights labeled by k1 and k2 in Fig. 1 are orthogonally combined via the PBS after adjusting the polarization orientations by PC1 and PC2, respectively. PC3 is inserted between the PBS and EOPM in order to align the polarization orientations of the orthogonally-polarized lights both at 45° with respect to the principle axes of the EOPM. For clarity, the cross section view is also illustrated in the inset of Fig. 1. The modulation signal is applied from the RF input port of the EOPM. The output optical signal then passes through a polarization selective element which is composed of a polarizer and PC4 in our scheme. The transmission polarization direction of the polarization selective element is aligned at 45° relative to the principle axes of the EOPM by adjusting PC4. Once the desired polarization alignments of both PC3 and PC4 are accomplished, the overall setup described in Fig. 1 can be considered as a dual-optical-input intensity modulator whose output electric field can be described as follows assuming a lossless link
1 Ein ðtÞ½ejuTM ðtÞþju0 ejuTE ðtÞ 2 ( " # " #) 1 V RF ðtÞ V RF ðtÞ ¼ Ein ðtÞ exp jp TM þ ju0 exp jp TE 2 Vp Vp
( " ! #) 1 1 1 T¼ 1 cos pV RF ðtÞ TM TE þ u0 2 Vp Vp
ð2Þ
As can be seen from Eq. (2), the transfer functions for the two optical input ports possess inter-complementary raised cosine profiles. Therefore, counter-phase intensity modulation is achieved by means of the designed dual-optical-input modulation module which performs the same function as the integrated 2 1 MZM in [8]. Notice that the schematic waveform evolution is also shown in the insets of Fig. 1 when a sinusoidal signal is applied on the RF port of the EOPM. According to the setup shown in Fig. 2a, the relevant experiment was carried out to verify the feasibility of counter-phase modulation. One laser diode (LD) at 1556.55 nm was used as a continuous-wave (CW) light source. A 1 GHz sinusoidal signal generated by a microwave source was applied on the RF port of a commercial EOPM (COVEGA Mach-10 053-10PFFBNL) via a bias tee. The power of the sinusoidal signal and the direct-current (DC) bias were both optimized to obtain the best waveforms. The electrical signal detected by a 10 GHz photodiode (PD) is finally monitored by an oscilloscope. By connecting the LD with different
Eout ðtÞ ¼
ð1Þ
where Ein ðtÞ is the input electric field, the sign ± corresponds to two optical input ports, uTM ðtÞ and uTE ðtÞ are the phase retardations when the orthogonally-polarized lights from the two input ports pass the EOPM along the principle axes by transverse-magnetic (TM) and transverse-electric (TE) modes respectively, u0 is the initial phase difference between the two principle axes of the EOPM at zero applied voltage, V RF ðtÞ is the applied voltage on the RF port of TE the EOPM as a function of time, V TM p and V p are the half-wave voltages for transmitted TM and TE modes respectively. For a z-cut LiNTE bO3 EOPM, V TM p < V p since the TM mode is more efficiently modulated than the TE mode, which can lead to a phase difference between the orthogonally-polarized lights from the two input ports when they pass the EOPM in TM and TE modes, respectively [11]. Therefore, the optical-intensity transfer function of the designed dual-optical-input intensity modulation module is given by
Fig. 2. Verification of counter-phase modulation. (a) Experiment setup; (b) measured waveforms.
J. Li et al. / Optics Communications 282 (2009) 845–848
847
3. Experimental implementation of reconfigurable four-tap microwave photonic filters
Fig. 3. Proposed generic setup for microwave photonic filters with negative coefficients.
input ports, we obtained two RF signals out of phase which can be clearly seen in Fig. 2b. The experimental result enables the successful implementation of microwave photonic filters with negative coefficients employing the proposed method with the assistance of a dispersive element (e.g. a fiber coil in this paper) to perform tap differential delay. The generic setup for implementation of microwave photonic filters with negative coefficients is shown in Fig. 3. Several weighted lasers from a multi-wavelength source (e.g. a laser array or a sliced broadband source) are selectively combined and injected into the designed dual-optical-input intensity modulation module which is drove by the RF signal to be processed. The carried RF signals on these wavelengths from different input ports will act as either positive samples or negative ones. The theoretical transfer function of the target filter is denoted as [12]
HðxRF Þ ¼ cos
N bLx2RF X ðIn Þ exp½jxRF ðn 1ÞbLDx 2 n¼1
Several experiments have been carried out based on the setup in Fig. 3 for implementation of four-tap microwave photonic filters with negative coefficients. The tap number can be extended by using multiple laser sources for higher Q-factor. Four CW lights were emitted from four LDs at k1 ¼ 1553:35 nm, k2 ¼ 1554:95 nm, k3 ¼ 1556:55 nm and k4 ¼ 1558:15 nm, respectively and selectively combined via two wavelength division multiplexers (WDMs). k1 ; k3 corresponded to one input port, and k2 ; k4 corresponded to the other one. The power and the polarization state of each CW light were first adjusted to obtain the desired weighted values. A section of 11.5 km standard SMF was used as the dispersive element with a dispersion parameter 17 ps/nm/km around 1550 nm, which corresponds to a time delay between adjacent taps of about 312.8 ps. Thus the free spectral range (FSR) is expected to be 3.2 GHz. The measurement of filter transfer function was carried out by a vector network analyzer (VNA) after O/E conversion. Note that the RF signal from the VNA was amplified by an electrical amplifier (EA) and then applied on the RF port of the EOPM via a bias tee with an optimal power. Meanwhile, the direct-current (DC) bias was optimized to achieve best performance. The experimental results are summarized in Fig. 4, where the theoretical transfer functions are also plotted in dashed line for comparison. Two cases are involved for different weighted tap coefficients to verify the filter reconfigurability. The theoretical and experimental results agree well and all show bandpass profiles with a FSR of about 3.2 GHz. The transfer function for an arbitrary window [0.5, 1, 1, 0.5] possesses a higher passband-to-stopband contrast ratio compared with the case for a rectangular window [1, 1, 1, 1].
4. Further discussion
ð3Þ
where b ¼ Dk20 =2pc, ±In represents the weighted intensity of the nrd optical carrier with either positive or negative coefficient. xRF is the angular frequency of the under-processing RF signal, D is the dispersion parameter of the used fiber coil, k0 is the optical wavelength, c is the light velocity in vacuum, L is the length of the used fiber coil, N is the number of optical carriers, and Dx is frequency spacing between adjacent optical carriers.
As can be seen from Fig. 4, the agreement between theoretical and experimental results exhibits more degradation for higher RF carrier frequencies, which is attributed to the chirp arising from the designed dual-optical-input intensity modulation module. Although the designed dual-optical-input intensity modulation module has a raised cosine transfer function similar to the one of a typical MZM, it is not able to operate in a push-pull mode which can eliminate the chirp during modulation. The presence of the
Fig. 4. Experimental results for reconfigurable four-tap microwave photonic filters with negative coefficients. (a) Rectangular window [1, 1, 1, 1]; (b) arbitrary window [0.5, 1, 1, 0.5].
848
J. Li et al. / Optics Communications 282 (2009) 845–848
Fig. 5. Simulation and experiment results when taking into account the chirp or not. (a) Rectangular window [1, 1, 1, 1]; (b) arbitrary window [0.5, 1, 1, 0.5].
chirp can be explained by Eq. (1) from which one can deduce an additional phase term as follows.
" # ! 1 V RF ðtÞ 1 1 u0 þ j þ Ein ðtÞ exp jp 2 2 2 V TM V TE p p |fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl} Phase Term ( " # ! V RF ðtÞ 1 1 u0 þ j exp jp 2 2 V TM V TE p p " #) ! V RF ðtÞ 1 1 u0 exp jp j 2 2 V TE V TM p p
Eout ðtÞ ¼
coefficients has been experimentally demonstrated. The experiment results show well filtering performance at low frequencies. The impact of the existing chirp on the filter characteristics was also discussed. Acknowledgements
ð4Þ
TM For a z-cut LiNbO3 EOPM, the condition V TE p 3 V p is typically fulTM ¼ 3 V and the same paramefilled. With the assumption of V TE p p ters with the experiment, we have carried out numerical simulations based on Eq. (4) with the help of split-step Fourier method. Taking into account the chirp, an excellent agreement can be observed between simulation and experiment results from Fig. 5. Without regard to the chirp, the simulated transfer function strictly accord with the theoretical predication by Eq. (3), indicating that the degradation of transfer function at high frequencies is mainly owing to the chirp. Despite the presence of the chirp in the scheme, the implemented filters behave well characteristics at low frequencies.
5. Conclusion
This work was partially supported by the National 863 Program of China (2007AA01Z264, 2006AA01Z256), MOST International Cooperation Program (2008DFA11670), the National Natural Science Foundation of China (60702006, 60736002 and 60837004), the New Century Excellent Talent Project in Ministry of Education of China (NCET-06-0093), PCSIRT (No.IRT0609) and the 111 Project (B07005).
References [1] [2] [3] [4] [5] [6] [7] [8]
We have proposed a simple scheme by constructing a dual-optical-input intensity modulation module for implementation of reconfigurable multi-tap microwave transversal filters with arbitrary negative coefficients. The designed dual-optical-input intensity modulation module is based on the counter-phase modulation in a single EOPM. A four-tap filter with two negative
[9] [10] [11] [12]
R.A. Minasian, IEEE Trans. Microw. Theory Tech. 54 (2) (2006) 832. J. Capmany, B. Ortega, D. Pastor, J. Lightwave Technol. 24 (1) (2006) 201. B. Moslehi, J. Goodman, M. Tur, H.J. Shaw, Proc. IEEE 72 (7) (1984) 909. T. Yost, P. Herczfeld, A. Rosen, S. Singh, IEEE Microw. Guided Wave Lett. 5 (9) (1995) 287. F. Coppinger, S. Yegnanarayanan, P.D. Trinh, B. Jalali, IEEE Trans. Microw. Theory Tech. 45 (8) (1997) 1473. J. Mora, B. Ortega, M.V. Andrés, J. Capmany, J.L. Cruz, D. Pastor, S. Sales, Opt. Lett. 28 (15) (2003) 1308. J. Capmany, D. Pastor, A. Martinez, B. Ortega, S. Sales, Opt. Lett. 28 (16) (2003) 1415. D. Pastor, J. Capmany, B. Ortega, A. Martinez, L. Pierno, M. Varasi, IEEE Photon. Technol. Lett. 16 (9) (2004) 2126. J. Wang, F. Zeng, J. Yao, IEEE Photon. Technol. Lett. 17 (10) (2005) 2176. T.-Y. Kim, C.K. Oh, S.-J. Kim, C.-S. Park, IEEE Photon. Technol. Lett. 19 (12) (2007) 907. G.L. Li, P.K.L. Yu, J. Lightwave Technol. 21 (9) (2003) 2010. J. Capmany, D. Pastor, B. Ortega, IEEE Trans. Microw. Theory Tech. 47 (7) (1999) 1321.
Contents lists available at ScienceDirect
Optics Communications journal homepage: www.elsevier.com/locate/optcom
Microwave photonic filter with negative coefficients based on counter-phase modulation using a single electro-optic phase modulator Jianqiang Li *, Kun Xu, Jian Wu, Jintong Lin Key Laboratory of Optical Communication & Lightwave Technologies, Ministry of Education, Beijing University of Posts and Telecommunications, Beijing 100876, China
a r t i c l e
i n f o
Article history: Received 29 June 2008 Received in revised form 8 November 2008 Accepted 8 November 2008
Keywords: Microwave photonic filter Negative coefficient Electro-optic phase modulator
a b s t r a c t A simple photonic approach is proposed for the implementation of a reconfigurable multi-tap microwave filter with negative coefficients. In this scheme, a dual-optical-input intensity modulation module which can perform counter-phase modulation is constructed using a single electro-optic phase modulator. Two inter-complementary microwave signals are experimentally obtained for verification of the function of counter-phase modulation. A reconfigurable four-tap microwave filter with two negative coefficients is implemented by experiment. Ó 2008 Elsevier B.V. All rights reserved.
1. Introduction Microwave photonic filter, which is known as a favorable technique of processing radio-frequency (RF) signals with the help of photonic devices or subsystems, has been widely investigated for many years. The unique advantages of microwave photonic filter, including low loss, light weight, broad bandwidth, and immunity to electromagnetic interference (EMI), bring a wide range of applications [1]. Due to the strong dependence on environmental fluctuations, stable microwave photonic filters are difficult to implement under coherent operation. Therefore, most of the previous microwave photonic filters have been demonstrated by using incoherent laser sources in so-called inherent systems. It is known that only positive taps can be implemented in incoherent systems due to the positive sign of optical intensity. Microwave photonic filters with only positive coefficients have severe limitations in practical applications due to the limited range of transfer function and the presence of a resonance at baseband [2]. In order to solve this problem, many methods have been proposed to obtain complex or negative coefficients including differential detection [3], hybrid optoelectronic approach [4], and all-optical techniques [5–11]. Among the diverse all-optical techniques to achieve negative coefficients, the approaches by means of employing external electro-optic modulators feature simple structures and high flexibility for tap weighting [7–11]. The positive and negative taps are achieved based on counter-phase modulation in two Mach-Zehnder modulators (MZMs) [7] or a single newly-designed dual-opti* Corresponding author. E-mail address: [email protected] (J. Li). 0030-4018/$ - see front matter Ó 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.optcom.2008.11.014
cal-input MZM [8] by applying appropriate bias voltages to guarantee operations in the linear region of the transfer function with opposite slopes. Electro-optic phase modulators (EOPMs) can also be employed based on phase-to-intensity conversion by cascading a Sagnac loop filter [9] or polarization modulation by following a section of high birefringence (Hi-Bi) fiber [10]. In [9], the wavelength spacing of the used incoherent laser sources is constrained by the fixed comb response of a given Sagnac loop filter, and the process of phase-to-intensity conversion experiences high insertion loss. The scheme presented in [10] suffers from the unfeasibility of arbitrary tap number and reconfigurability by using Hi-Bi fibers. In this paper, we report a novel approach also based on polarization modulation in a single EOPM, which can nevertheless overcome the limitations mentioned above. The crucial difference lies on the design of a dual-optical-input intensity modulation module whose function is similar to the presented modulator in [8]. In the proposed approach, single-mode fibers (SMFs) serve as the delay lines to obtain different sample delays, rather than the Hi-Bi fibers. Experiments have been carried out to verify the function of counter-phase modulation and to implement a four-tap transversal reconfigurable filter with negative coefficients.
2. Fundamental principle and its experimental verification Fig. 1 illustrates the structure and operation principle of the designed dual-optical-input intensity modulation module which consists of a polarization beam splitter (PBS), a commercial LiNbO3 EOPM, a polarizer and several polarization controllers (PCs). As
846
J. Li et al. / Optics Communications 282 (2009) 845–848
Fig. 1. Setup and operation principle of the designed dual-optical-input modulator.
shown in the inset of Fig. 1, we define a reference coordinate system in which the light propagates along with z-axis, x and y axes represent the principle axes of EOPM, and the cross section of each component is within the x–y plane. Two linearly-polarized lights labeled by k1 and k2 in Fig. 1 are orthogonally combined via the PBS after adjusting the polarization orientations by PC1 and PC2, respectively. PC3 is inserted between the PBS and EOPM in order to align the polarization orientations of the orthogonally-polarized lights both at 45° with respect to the principle axes of the EOPM. For clarity, the cross section view is also illustrated in the inset of Fig. 1. The modulation signal is applied from the RF input port of the EOPM. The output optical signal then passes through a polarization selective element which is composed of a polarizer and PC4 in our scheme. The transmission polarization direction of the polarization selective element is aligned at 45° relative to the principle axes of the EOPM by adjusting PC4. Once the desired polarization alignments of both PC3 and PC4 are accomplished, the overall setup described in Fig. 1 can be considered as a dual-optical-input intensity modulator whose output electric field can be described as follows assuming a lossless link
1 Ein ðtÞ½ejuTM ðtÞþju0 ejuTE ðtÞ 2 ( " # " #) 1 V RF ðtÞ V RF ðtÞ ¼ Ein ðtÞ exp jp TM þ ju0 exp jp TE 2 Vp Vp
( " ! #) 1 1 1 T¼ 1 cos pV RF ðtÞ TM TE þ u0 2 Vp Vp
ð2Þ
As can be seen from Eq. (2), the transfer functions for the two optical input ports possess inter-complementary raised cosine profiles. Therefore, counter-phase intensity modulation is achieved by means of the designed dual-optical-input modulation module which performs the same function as the integrated 2 1 MZM in [8]. Notice that the schematic waveform evolution is also shown in the insets of Fig. 1 when a sinusoidal signal is applied on the RF port of the EOPM. According to the setup shown in Fig. 2a, the relevant experiment was carried out to verify the feasibility of counter-phase modulation. One laser diode (LD) at 1556.55 nm was used as a continuous-wave (CW) light source. A 1 GHz sinusoidal signal generated by a microwave source was applied on the RF port of a commercial EOPM (COVEGA Mach-10 053-10PFFBNL) via a bias tee. The power of the sinusoidal signal and the direct-current (DC) bias were both optimized to obtain the best waveforms. The electrical signal detected by a 10 GHz photodiode (PD) is finally monitored by an oscilloscope. By connecting the LD with different
Eout ðtÞ ¼
ð1Þ
where Ein ðtÞ is the input electric field, the sign ± corresponds to two optical input ports, uTM ðtÞ and uTE ðtÞ are the phase retardations when the orthogonally-polarized lights from the two input ports pass the EOPM along the principle axes by transverse-magnetic (TM) and transverse-electric (TE) modes respectively, u0 is the initial phase difference between the two principle axes of the EOPM at zero applied voltage, V RF ðtÞ is the applied voltage on the RF port of TE the EOPM as a function of time, V TM p and V p are the half-wave voltages for transmitted TM and TE modes respectively. For a z-cut LiNTE bO3 EOPM, V TM p < V p since the TM mode is more efficiently modulated than the TE mode, which can lead to a phase difference between the orthogonally-polarized lights from the two input ports when they pass the EOPM in TM and TE modes, respectively [11]. Therefore, the optical-intensity transfer function of the designed dual-optical-input intensity modulation module is given by
Fig. 2. Verification of counter-phase modulation. (a) Experiment setup; (b) measured waveforms.
J. Li et al. / Optics Communications 282 (2009) 845–848
847
3. Experimental implementation of reconfigurable four-tap microwave photonic filters
Fig. 3. Proposed generic setup for microwave photonic filters with negative coefficients.
input ports, we obtained two RF signals out of phase which can be clearly seen in Fig. 2b. The experimental result enables the successful implementation of microwave photonic filters with negative coefficients employing the proposed method with the assistance of a dispersive element (e.g. a fiber coil in this paper) to perform tap differential delay. The generic setup for implementation of microwave photonic filters with negative coefficients is shown in Fig. 3. Several weighted lasers from a multi-wavelength source (e.g. a laser array or a sliced broadband source) are selectively combined and injected into the designed dual-optical-input intensity modulation module which is drove by the RF signal to be processed. The carried RF signals on these wavelengths from different input ports will act as either positive samples or negative ones. The theoretical transfer function of the target filter is denoted as [12]
HðxRF Þ ¼ cos
N bLx2RF X ðIn Þ exp½jxRF ðn 1ÞbLDx 2 n¼1
Several experiments have been carried out based on the setup in Fig. 3 for implementation of four-tap microwave photonic filters with negative coefficients. The tap number can be extended by using multiple laser sources for higher Q-factor. Four CW lights were emitted from four LDs at k1 ¼ 1553:35 nm, k2 ¼ 1554:95 nm, k3 ¼ 1556:55 nm and k4 ¼ 1558:15 nm, respectively and selectively combined via two wavelength division multiplexers (WDMs). k1 ; k3 corresponded to one input port, and k2 ; k4 corresponded to the other one. The power and the polarization state of each CW light were first adjusted to obtain the desired weighted values. A section of 11.5 km standard SMF was used as the dispersive element with a dispersion parameter 17 ps/nm/km around 1550 nm, which corresponds to a time delay between adjacent taps of about 312.8 ps. Thus the free spectral range (FSR) is expected to be 3.2 GHz. The measurement of filter transfer function was carried out by a vector network analyzer (VNA) after O/E conversion. Note that the RF signal from the VNA was amplified by an electrical amplifier (EA) and then applied on the RF port of the EOPM via a bias tee with an optimal power. Meanwhile, the direct-current (DC) bias was optimized to achieve best performance. The experimental results are summarized in Fig. 4, where the theoretical transfer functions are also plotted in dashed line for comparison. Two cases are involved for different weighted tap coefficients to verify the filter reconfigurability. The theoretical and experimental results agree well and all show bandpass profiles with a FSR of about 3.2 GHz. The transfer function for an arbitrary window [0.5, 1, 1, 0.5] possesses a higher passband-to-stopband contrast ratio compared with the case for a rectangular window [1, 1, 1, 1].
4. Further discussion
ð3Þ
where b ¼ Dk20 =2pc, ±In represents the weighted intensity of the nrd optical carrier with either positive or negative coefficient. xRF is the angular frequency of the under-processing RF signal, D is the dispersion parameter of the used fiber coil, k0 is the optical wavelength, c is the light velocity in vacuum, L is the length of the used fiber coil, N is the number of optical carriers, and Dx is frequency spacing between adjacent optical carriers.
As can be seen from Fig. 4, the agreement between theoretical and experimental results exhibits more degradation for higher RF carrier frequencies, which is attributed to the chirp arising from the designed dual-optical-input intensity modulation module. Although the designed dual-optical-input intensity modulation module has a raised cosine transfer function similar to the one of a typical MZM, it is not able to operate in a push-pull mode which can eliminate the chirp during modulation. The presence of the
Fig. 4. Experimental results for reconfigurable four-tap microwave photonic filters with negative coefficients. (a) Rectangular window [1, 1, 1, 1]; (b) arbitrary window [0.5, 1, 1, 0.5].
848
J. Li et al. / Optics Communications 282 (2009) 845–848
Fig. 5. Simulation and experiment results when taking into account the chirp or not. (a) Rectangular window [1, 1, 1, 1]; (b) arbitrary window [0.5, 1, 1, 0.5].
chirp can be explained by Eq. (1) from which one can deduce an additional phase term as follows.
" # ! 1 V RF ðtÞ 1 1 u0 þ j þ Ein ðtÞ exp jp 2 2 2 V TM V TE p p |fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl} Phase Term ( " # ! V RF ðtÞ 1 1 u0 þ j exp jp 2 2 V TM V TE p p " #) ! V RF ðtÞ 1 1 u0 exp jp j 2 2 V TE V TM p p
Eout ðtÞ ¼
coefficients has been experimentally demonstrated. The experiment results show well filtering performance at low frequencies. The impact of the existing chirp on the filter characteristics was also discussed. Acknowledgements
ð4Þ
TM For a z-cut LiNbO3 EOPM, the condition V TE p 3 V p is typically fulTM ¼ 3 V and the same paramefilled. With the assumption of V TE p p ters with the experiment, we have carried out numerical simulations based on Eq. (4) with the help of split-step Fourier method. Taking into account the chirp, an excellent agreement can be observed between simulation and experiment results from Fig. 5. Without regard to the chirp, the simulated transfer function strictly accord with the theoretical predication by Eq. (3), indicating that the degradation of transfer function at high frequencies is mainly owing to the chirp. Despite the presence of the chirp in the scheme, the implemented filters behave well characteristics at low frequencies.
5. Conclusion
This work was partially supported by the National 863 Program of China (2007AA01Z264, 2006AA01Z256), MOST International Cooperation Program (2008DFA11670), the National Natural Science Foundation of China (60702006, 60736002 and 60837004), the New Century Excellent Talent Project in Ministry of Education of China (NCET-06-0093), PCSIRT (No.IRT0609) and the 111 Project (B07005).
References [1] [2] [3] [4] [5] [6] [7] [8]
We have proposed a simple scheme by constructing a dual-optical-input intensity modulation module for implementation of reconfigurable multi-tap microwave transversal filters with arbitrary negative coefficients. The designed dual-optical-input intensity modulation module is based on the counter-phase modulation in a single EOPM. A four-tap filter with two negative
[9] [10] [11] [12]
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