April 15, 2015 / Vol. 40, No. 8 / OPTICS LETTERS
1679
Optical vector network analyzer with improved accuracy based on polarization modulation and polarization pulling Wei Li, Jian Guo Liu, and Ning Hua Zhu* State Key Laboratory on Integrated Optoelectronics, Institute of Semiconductors, Chinese Academy of Sciences, Beijing 100083, China *Corresponding author: [email protected] Received February 9, 2015; revised March 3, 2015; accepted March 9, 2015; posted March 11, 2015 (Doc. ID 234303); published April 7, 2015 We report a novel optical vector network analyzer (OVNA) with improved accuracy based on polarization modulation and stimulated Brillouin scattering (SBS) assisted polarization pulling. The beating between adjacent higherorder optical sidebands which are generated because of the nonlinearity of an electro-optic modulator (EOM) introduces considerable error to the OVNA. In our scheme, the measurement error is significantly reduced by removing the even-order optical sidebands using polarization discrimination. The proposed approach is theoretically analyzed and experimentally verified. The experimental results show that the accuracy of the OVNA is greatly improved compared to a conventional OVNA. © 2015 Optical Society of America OCIS codes: (060.5625) Radio frequency photonics; (300.6320) Spectroscopy, high-resolution; (120.0120) Instrumentation, measurement, and metrology; (290.5900) Scattering, stimulated Brillouin. http://dx.doi.org/10.1364/OL.40.001679
In optical device fabrication and optical link design, it is highly desirable to characterize the transmission response of an optical component or an optical link. Thus, optical vector network analyzer (OVNA) is proposed to measure the magnitude and phase response of a device under test (DUT). OVNAs can be constructed using modulation phase shift or interferometric scheme [1,2]. However, the limited resolution of a wavelength swept laser source prevents the OVNA from characterizing the transmission response of a DUT with highquality factor or high precision. In this context, OVNAs based on single-sideband (SSB) modulation have been proposed to characterize the DUT with very high resolution [3–6]. Although the SSB-based OVNAs can reach a resolution as high as kHz level, they suffer from considerable measurement errors because of the nonlinearity of the electro-optic modulators (EOMs) [7–10]. A series of higher-order optical sidebands are produced at the output of the EOM. The beating between the higher-order sidebands in a photodetector (PD) contributes significantly to the measurement errors. To reduce the higherorder sidebands, the modulation index of the EOM should be very small, which results in a large carrier-tosideband ratio. The weak sideband in turn generates measurement error due to the limited sensitivity of the PD. In addition, it also limits the dynamic range of the OVNA. Thus, there is a trade-off between the dynamic range and the accuracy of the conventional OVNA. Many efforts have been made to reduce the measurement errors of the OVNAs without affecting the dynamic range [7–10]. In [7], a 120° hybrid coupler was used to realize SSB modulation. However, a broadband 120° hybrid coupler is still a challenge up to now. In [8,9], the measurement errors were reduced using a two-step measurement and post signal processing. To simplify the procedure, a method using balanced photodetection [10] has been proposed based on the same concept as [8,9]. However, new measurement errors might be introduced 0146-9592/15/081679-04$15.00/0
to the OVNA because of the unbalanced influence of the vibrations on two fibers as discussed in [10]. In this Letter, we report a new OVNA with improved accuracy based on polarization modulation and SBSassisted polarization pulling. Compared with the previous schemes, only a single-step measurement is required using the proposed OVNA. In addition, the modulated optical signal propagates in a single optical fiber, avoiding the unbalanced influence of the vibrations on two fibers [10]. The measurement errors induced by higher-order sidebands are significantly reduced by removing the even-order sidebands using polarization discrimination. The proposed technique is theoretically analyzed and experimentally verified. The schematic configuration of the proposed OVNA is shown in Fig. 1(a). An optical carrier from a tunable laser source (TLS) is split into two parts. The upper part is sent to a polarization modulator (PolM) which is driven by a sinusoidal microwave signal. The PolM is a special phase modulator that supports phase modulation on two orthogonal polarization states with opposite modulation indices. The state of polarization (SOP) of the optical carrier is aligned at 45° to one principal axis of the PolM (e.g., E x ). The optical field at the output of the PolM is given by exp jω0 t β cosωm t E ; E PolM t p0 2 exp jω0 t − β cosωm t φ
⇀
(1)
where ω0 and E 0 is the angular frequency and amplitude of the optical carrier sent to the PolM. β is the phase modulation index of the PolM which is given by β πV m ∕V π · V π is the half-wave voltage of the PolM. V m and ωm are the amplitude and angular frequency of the microwave signal, respectively. φ is the static phase difference between E x and E y polarization states, which is controlled by the bias of the PolM. We assume φ 0. Applying Jacobi–Anger expansion to Eq. (1), we have [11] © 2015 Optical Society of America
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OPTICS LETTERS / Vol. 40, No. 8 / April 15, 2015 Phase & Magnitude Processing Unit DSF
TLS
OC
OF PC2 Pol
PolM
PD
DUT
fB
PC1 EDFA Pump CS-SSB wave
(a) x’
1st
x’
3rd
1st
… y’ Carrier 2nd
(b)
4th
Carrier x’ 1st
3rd
3rd
…
… y’ Carrier 2nd
(c)
4th
y’
(d)
orthogonal SOPs of the amplified signal wave, corresponding to maximum (Gmax ) and minimum (Gmin ) SBS gain. The two orthogonal SOPs are determined by the pump SOP. Since, within the SBS bandwidth Gmax ≫ Gmin , the SOP of the input signal is pulled toward that of the conjugate of the pump wave [13–15]. Detailed analysis of the SBS-assisted polarization pulling can be found in [13–15]. In our analysis, it is assumed that the SOP of the optical carrier is pulled toward the x0 -axis by θ in the SBS process, as shown in Fig. 1(c), and the gain of the optical carrier is denoted as G. Since the SBS bandwidth is very narrow (∼20–30 MHz), the optical sidebands are not affected by the SBS if the frequency of the microwave signal is larger than half of the SBS bandwidth. Thus, the optical field at the output of the OF is rewritten as
⇀
Fig. 1. (a) Schematic configuration of the proposed OVNA. (b)–(d) Schematic principal of the proposed OVNA (TLS, tunable laser source; PolM, polarization modulator; DSF, dispersion-shifted fiber; OC, optical circulator; CS-SSB, carrier suppressed single sideband; EDFA, erbium-doped fiber amplifier; PC, polarization controller; OF, optical filter; Pol, polarizer; DUT, device under test; PD, photodetector).
X 1 E 1 0 n∞ E PolM t p0 J 2n cosω0 2nωm t × 1 2 0 1 n−∞ n∞ X 1 ; J 2n1 cosω0 2n 1ωm t × −1 n−∞
E OF t 2 6 6 ×6 4
E x0
E y0
G sin θJ 0 −
E p0 2 n−1 X n−∞
G cos θJ 0
−1n J 2n1 expω0 2n1ωm t
n−1 X n−∞
−1n J 2n cosω0 2nωm t
where J n J n β is the Bessel function of the first kind of order n. As can be seen from Eq. (2), the SOP of the even-order sidebands is aligned at 45° to E x polarization state, while the SOP of the odd-order sidebands is aligned at −45° to E x polarization state. The polarization modulated optical signal goes through a spool of dispersion shifted fiber (DSF) and an optical circulator (OC). An optical filter (OF) is used to realize SSB modulation by removing the higher frequency sidebands (or lower wavelength sidebands), as shown in Fig. 1(b) where the x0 -axis is aligned at a −45° to E x polarization state of the PolM. The microwave signal at fundamental frequency cannot be recovered in a PD because the SOP of the even-order sidebands is orthogonal to that of the odd-orders ones. To recover the fundamental microwave tone, SBS-assisted polarization pulling is used to pull the SOP of the optical carrier toward that of the odd-order sidebands. The lower part of the optical carrier shown in Fig. 1(a) goes to a carrier suppressed (CS)-SSB modulator [12]. The optical carrier is upshifted by a Brillouin frequency shift (f B ). This signal acts as the pump wave to excite the SBS in the DSF. The power and the SOP of the pump wave is adjusted by an erbium-doped fiber amplifier (EDFA) and a polarization controller (PC1). Since the signal and pump wave come from the same laser source, the stability of the SBS process can be assured. SBS amplification over optical fibers is highly polarization dependent [13–15]. This amplification is related to two
7 7 7: 5
(3)
⇀
(2)
3
A polarizer (Pol) at an angle of ψ with respective to the x0 -axis is attached after the OF. The optical field at the output of the Pol can be expressed as E E out t p0 fGJ 0 sinθ ψ 2 n−1 X −1n J 2n1 expω0 2n 1ωm t − cos ψ n−∞
sin ψ
n−1 X n−∞
−1n J 2n expω0 2nωm tg:
(4)
The SSB modulated optical signal is sent to a DUT, and the optical field at the output of the DUT is given by E D ω E out ω · Hω p 2πE 0 GJ 0 sinθ ψHω0 δω − ω0 sin ψ
n−1 X n−∞
−1n J 2n Hω0 2nωm
· δω − ω0 2nωm − cos ψ
n−1 X n−∞
−1n J 2n−1 βHω0 2n − 1ωm
· δω − ω0 2n 1ωm ;
(5)
where Hω and E out ω are the transmission response of the DUT and the Fourier transform of Eout t, respectively. After detection in a PD, the photocurrent at the angular frequency of ωm can be expressed as
April 15, 2015 / Vol. 40, No. 8 / OPTICS LETTERS
iωm ∝ GJ 0 sinθ ψJ 1 H ω0 Hω0 ωm J n1 J n
· Hω0 n 1ωm H ω0 nωm ∕2:
(6)
For most of the OVNAs, it is assumed that the SSB modulated optical signal consists of only the optical carrier and the first-order sideband. In this condition, the measured transmission response of the system, including the OVNA and the DUT, is given by H S ω0 ωm
iS ωm : GJ 0 sinθ ψJ 1 H S ω0
(7)
A calibration process has to be done in advance to remove the response of the OVNA, H V ω0 ωm . Thus, the transmission response of the DUT can be rewritten as H D ω0 ωm
H S ω0 ωm : H V ω0 ωm
(8)
However, the higher-order optical sidebands have to be considered in a real-world OVNA. The beating between adjacent sidebands also contributes to the fundamental tone at ωm . If the contribution of higher-order sidebands is considered, Eq. (8) is rewritten as H D ω0 ωm
H S ω0 ωm εS ω0 ωm ; H V ω0 ωm εV ω0 ωm
(9)
where εS ω0 ωm and εV ω0 ωm are the contributions of the higher-order sidebands to the magnitude and phase of the fundamental microwave signal for the whole system and the OVNA, respectively. They can be expressed as εS ω0 ωm P sin2ψ ∞ n1 J n1 J n H S ω0 n 1ωm H S ω0 nωm ; 2GJ 0 sinθ ψJ 1 H S ω0 (10) εV ω0 ωm P sin2ψ ∞ n1 J n1 J n H V ω0 n1ωm H V ω0 nωm : 2GJ 0 sinθ ψJ 1 H V ω0 (11) As can be seen from Eqs. (10)–(11), significant measurement errors are added to the measured result because of the beating between adjacent higher-order sidebands. To improve the accuracy of the OVNA, these errors have to be eliminated. To do so, we adjust the angle of the Pol to let ψ 0. The Pol is thus aligned with the x0 -axis. The schematic optical spectrum is shown in Fig. 1(d). In this case, we have εS ω0 ωm εV ω0 ωm 0. It means that the measurement errors are completely removed. The transmission response of the DUT is given by
iS ωm H V ω0 : iV ωm H S ω0
(12)
Equation (12) shows that the accuracy of the proposed OVNA is significantly improved by eliminating the measurement errors induced by higher-order sidebands. Moreover, the measured result is independent of the modulation index of the PolM, β. It also means that the measurement errors can be reduced without affecting the dynamic range because the dynamic range is related to the modulation index. This is very promising for a real-world OVNA because the OVNA is no longer restricted by the small modulation condition, i.e., β ≪ 1. We carried out an experiment to verify the proposed OVNA based on the setup shown in Fig. 1(a). An optical carrier from a TLS is divided into two parts. The upper part was coupled to a PolM which has an integrated Pol at 45° with respect to one principal axis of the PolM. The deviation of the SOP of the optical carrier from 45° results in optical power attenuation. However, the influence of power attenuation can be removed by the calibration process. For the lower part, the CS-SSB modulator was driven by a sinusoidal microwave signal at 9.2 GHz, corresponding to the Brillouin frequency shift in our case. The frequency shifted optical signal was amplified by an EDFA to 15 dBm and acted as the pump wave to excite the SBS. The SOP of the pump wave was controlled by a PC1. An OC was used to counterpropagate the pump wave and the polarizationmodulated signal in a 1 km DSF. An OF was used to realize SSB modulation. Figure 2(a) shows the measured optical spectra of a double sideband (DSB) and SSB modulated signal, as well as the transmission response of the OF. In this measurement, the pump wave was disconnected. The microwave signal driven to the PolM is 15 GHz. The modulation index β is 1.2 rad. A series of optical sidebands was generated because of the nonlinearity of the PolM. For SSB modulation, the undesired first-order sideband is 42 dB lower than the desired one. As discussed in the previous part, the sidebands higher than the first order introduce measurement error to the result. A Pol was thus attached after the OF to realize polarization discrimination. Figure 2(b) shows the measured optical spectra at the output of the Pol with and without the SBS effect. A PC2 was used to adjust the SOP of the SSB modulated signal with respect to the Pol to satisfy ψ 0, as discussed in the theoretical part. 0 -20
(a)
DSB SSB Filter
-40 -60 1549.5 1549.8 1550.1 1550.4
Wavelength (nm)
(b) Power (dBm)
n1
Power (dBm)
sin2ψ
∞ X
H D ω0 ωm
1681
-20 -40
Carrier
W/O SBS With SBS
1st 3rd 2nd 4th
-60 1549.5 1549.8 1550.1 1550.4
Wavelength (nm)
Fig. 2. (a) Measured optical spectra of the DSB and SSB modulated signals, (b) measured optical spectra at the output of the Pol with and without the SBS (DSB, double-sideband; SSB, single-sideband; SBS, stimulated Brillouin scattering).
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OPTICS LETTERS / Vol. 40, No. 8 / April 15, 2015 200
Magnitude (dB)
0
-10
150
Phase (Deg.)
The proposed OVNA ASE The conventional OVNA
(a)
(b)
100 50 0 -50
-20
The proposed OVNA The conventional OVNA
-100 5
10
15
20
25
Frequency (GHz)
30
35
10
20
30
Frequency (GHz)
Fig. 3. Measured (a) magnitude and (b) phase responses of the DUT (OVNA: optical vector network analyzer).
The angle deviation of the Pol from ψ 0 and the limited suppression ratio of the Pol will result in residual evenorder sidebands. The beating between adjacent sidebands will generate considerable measurement errors to the OVNA. The optical carrier and the even-order sidebands were well suppressed by the Pol when the SBS was turned off. The optical carrier and the even-order sideband is 33 dB lower than the first-order sideband. The residual optical carrier and even-order sidebands can be attributed to the limited suppression ratio of the Pol and the polarization mode dispersion (PMD) of the DSF. Because of the polarization dependent SBS effect, the SOP of the optical carrier was pulled toward that of the odd-order sidebands by adjusting the SOP of the pump wave. After the SBS effect, the optical carrier can also be observed at the output of the Pol as shown in Fig. 2(b). The optical carrier is 29 dB higher than that in the case without SBS. Since only the beating between the optical carrier and the first-order sideband has contributed to the fundamental tone and the beating between adjacent sidebands is very small, the accuracy of the OVNA can be improved significantly. The proposed OVNA was used to measure the transmission response of a notch filter which is actually a programmable optical processer (WaveShaper Finisar 4000S). First of all, the magnitude response of the DUT was characterized using an amplified spontaneous emission (ASE) source and an optical spectrum analyzer (OSA) with a resolution of 0.01 nm. The measured response is shown in Fig. 3(a) in a red dashed line. For comparison, the DUT was measured using a conventional OVNA scheme. To construct the conventional OVNA, the Pol was aligned at 45° with respective to the x0 -axis. The pump wave was disconnected. In this case, the combined use of the PolM and Pol is equivalent to an intensity modulator biased at the quadrature point [16]. The measured magnitude response is shown in Fig. 3(a) in a blue solid line. Significant errors were generated because of higher-order sidebands. The maximum deviation from the result measured by ASE and OSA is 5.5 dB. The result measured using our proposed OVNA is shown in Fig. 3(a) in a black solid line. The measurement errors are significantly reduced compared with the conventional OVNA. The deviation from the result measured by ASE and OSA is within 0.8 dB. A general match between the proposed and the conventional OVNAs can
only be found outside the frequency interval 20 10 GHz. There are 1601 effective measurement points over a frequency range of 30 GHz. Thus, the resolution of the OVNA is 18.7 MHz. The resolution can be further improved by reducing the steps of the microwave source. The measured result using the proposed OVNA agrees well with that using the ASE source and OSA in the frequency range greater than 10 GHz. This is because of the limited roll-off property of the OF. The phase response of the DUT measured by the conventional OVNA and the proposed OVNA is shown in Fig. 3(b). Significant phase errors are also introduced in the phase response of the DUT using the conventional OVNA. It is noted that the phase response cannot be obtained using the ASE and OSA schemes. Thus, we cannot provide more phase measurement data. However, the excellent accuracy of the proposed OVNA has already been verified as shown in Fig. 3(a). In principle, the measurement error can be completely suppressed. However, some errors might still be introduced to the measured results because of the limited suppression ratio of the Pol and the PMD of the DSF. In summary, we have demonstrated an accurate OVNA based on polarization modulation and SBS-assisted polarization pulling. The proposed method has been theoretically analyzed and experimentally verified. The proof-of-concept experiment confirmed that the measurement errors induced by higher-order sidebands have been significantly reduced. This work was supported in part by the National Natural Science Foundation of China under 61377069, and 61335005 and, in part, by the Beijing Nova program. References 1. T. Niemi, M. Uusimaa, and H. Ludvigsen, IEEE Photon. Technol. Lett. 13, 1334 (2001). 2. G. D. van Wiggeren, A. R. Motamedi, and D. M. Baney, IEEE Photon. Technol. Lett. 15, 263 (2003). 3. R. Hernandez, A. Loayssa, and D. Benito, Opt. Eng. 43, 2418 (2004). 4. W. Li, W. T. Wang, L. X. Wang, and N. H. Zhu, IEEE Photon. J. 6, 7901108 (2014). 5. W. Li, W. H. Sun, W. T. Wang, L. X. Wang, J. G. Liu, and N. H. Zhu, IEEE Photon. Technol. Lett. 26, 866 (2014). 6. M. Sagues and A. Loayssa, Opt. Express 18, 17555 (2010). 7. M. Xue, S. L. Pan, and Y. J. Zhao, J. Lightwave Technol. 32, 3317 (2014). 8. M. Xue, S. L. Pan, and Y. J. Zhao, Opt. Lett. 39, 3595 (2014). 9. W. T. Wang, W. Li, J. G. Liu, W. H. Sun, W. Y. Wang, and N. H. Zhu, IEEE Photon. J. 6, 5501310 (2014). 10. M. Xue, S. Pan, and Y. Zhao, Opt. Lett. 40, 569 (2015). 11. A. L. Campillo, Opt. Lett. 32, 3152 (2007). 12. M. Sagues and A. Loayssa, Opt. Express 18, 22906 (2010). 13. M. O. van Deventer and A. J. Boot, J. Lightwave Technol. 12, 585 (1994). 14. A. Zadok, E. Zilka, A. Eyal, L. Thevenaz, and M. Tur, Opt. Express 16, 21692 (2008). 15. S. Preussler, A. Zadok, A. Wiatrek, M. Tur, and T. Schneider, Opt. Express 20, 14734 (2012). 16. Y. Chen, A. Wen, and J. P. Yao, IEEE Photon. Technol. Lett. 25, 2319 (2013).
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Optical vector network analyzer with improved accuracy based on polarization modulation and polarization pulling Wei Li, Jian Guo Liu, and Ning Hua Zhu* State Key Laboratory on Integrated Optoelectronics, Institute of Semiconductors, Chinese Academy of Sciences, Beijing 100083, China *Corresponding author: [email protected] Received February 9, 2015; revised March 3, 2015; accepted March 9, 2015; posted March 11, 2015 (Doc. ID 234303); published April 7, 2015 We report a novel optical vector network analyzer (OVNA) with improved accuracy based on polarization modulation and stimulated Brillouin scattering (SBS) assisted polarization pulling. The beating between adjacent higherorder optical sidebands which are generated because of the nonlinearity of an electro-optic modulator (EOM) introduces considerable error to the OVNA. In our scheme, the measurement error is significantly reduced by removing the even-order optical sidebands using polarization discrimination. The proposed approach is theoretically analyzed and experimentally verified. The experimental results show that the accuracy of the OVNA is greatly improved compared to a conventional OVNA. © 2015 Optical Society of America OCIS codes: (060.5625) Radio frequency photonics; (300.6320) Spectroscopy, high-resolution; (120.0120) Instrumentation, measurement, and metrology; (290.5900) Scattering, stimulated Brillouin. http://dx.doi.org/10.1364/OL.40.001679
In optical device fabrication and optical link design, it is highly desirable to characterize the transmission response of an optical component or an optical link. Thus, optical vector network analyzer (OVNA) is proposed to measure the magnitude and phase response of a device under test (DUT). OVNAs can be constructed using modulation phase shift or interferometric scheme [1,2]. However, the limited resolution of a wavelength swept laser source prevents the OVNA from characterizing the transmission response of a DUT with highquality factor or high precision. In this context, OVNAs based on single-sideband (SSB) modulation have been proposed to characterize the DUT with very high resolution [3–6]. Although the SSB-based OVNAs can reach a resolution as high as kHz level, they suffer from considerable measurement errors because of the nonlinearity of the electro-optic modulators (EOMs) [7–10]. A series of higher-order optical sidebands are produced at the output of the EOM. The beating between the higher-order sidebands in a photodetector (PD) contributes significantly to the measurement errors. To reduce the higherorder sidebands, the modulation index of the EOM should be very small, which results in a large carrier-tosideband ratio. The weak sideband in turn generates measurement error due to the limited sensitivity of the PD. In addition, it also limits the dynamic range of the OVNA. Thus, there is a trade-off between the dynamic range and the accuracy of the conventional OVNA. Many efforts have been made to reduce the measurement errors of the OVNAs without affecting the dynamic range [7–10]. In [7], a 120° hybrid coupler was used to realize SSB modulation. However, a broadband 120° hybrid coupler is still a challenge up to now. In [8,9], the measurement errors were reduced using a two-step measurement and post signal processing. To simplify the procedure, a method using balanced photodetection [10] has been proposed based on the same concept as [8,9]. However, new measurement errors might be introduced 0146-9592/15/081679-04$15.00/0
to the OVNA because of the unbalanced influence of the vibrations on two fibers as discussed in [10]. In this Letter, we report a new OVNA with improved accuracy based on polarization modulation and SBSassisted polarization pulling. Compared with the previous schemes, only a single-step measurement is required using the proposed OVNA. In addition, the modulated optical signal propagates in a single optical fiber, avoiding the unbalanced influence of the vibrations on two fibers [10]. The measurement errors induced by higher-order sidebands are significantly reduced by removing the even-order sidebands using polarization discrimination. The proposed technique is theoretically analyzed and experimentally verified. The schematic configuration of the proposed OVNA is shown in Fig. 1(a). An optical carrier from a tunable laser source (TLS) is split into two parts. The upper part is sent to a polarization modulator (PolM) which is driven by a sinusoidal microwave signal. The PolM is a special phase modulator that supports phase modulation on two orthogonal polarization states with opposite modulation indices. The state of polarization (SOP) of the optical carrier is aligned at 45° to one principal axis of the PolM (e.g., E x ). The optical field at the output of the PolM is given by exp jω0 t β cosωm t E ; E PolM t p0 2 exp jω0 t − β cosωm t φ
⇀
(1)
where ω0 and E 0 is the angular frequency and amplitude of the optical carrier sent to the PolM. β is the phase modulation index of the PolM which is given by β πV m ∕V π · V π is the half-wave voltage of the PolM. V m and ωm are the amplitude and angular frequency of the microwave signal, respectively. φ is the static phase difference between E x and E y polarization states, which is controlled by the bias of the PolM. We assume φ 0. Applying Jacobi–Anger expansion to Eq. (1), we have [11] © 2015 Optical Society of America
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OPTICS LETTERS / Vol. 40, No. 8 / April 15, 2015 Phase & Magnitude Processing Unit DSF
TLS
OC
OF PC2 Pol
PolM
PD
DUT
fB
PC1 EDFA Pump CS-SSB wave
(a) x’
1st
x’
3rd
1st
… y’ Carrier 2nd
(b)
4th
Carrier x’ 1st
3rd
3rd
…
… y’ Carrier 2nd
(c)
4th
y’
(d)
orthogonal SOPs of the amplified signal wave, corresponding to maximum (Gmax ) and minimum (Gmin ) SBS gain. The two orthogonal SOPs are determined by the pump SOP. Since, within the SBS bandwidth Gmax ≫ Gmin , the SOP of the input signal is pulled toward that of the conjugate of the pump wave [13–15]. Detailed analysis of the SBS-assisted polarization pulling can be found in [13–15]. In our analysis, it is assumed that the SOP of the optical carrier is pulled toward the x0 -axis by θ in the SBS process, as shown in Fig. 1(c), and the gain of the optical carrier is denoted as G. Since the SBS bandwidth is very narrow (∼20–30 MHz), the optical sidebands are not affected by the SBS if the frequency of the microwave signal is larger than half of the SBS bandwidth. Thus, the optical field at the output of the OF is rewritten as
⇀
Fig. 1. (a) Schematic configuration of the proposed OVNA. (b)–(d) Schematic principal of the proposed OVNA (TLS, tunable laser source; PolM, polarization modulator; DSF, dispersion-shifted fiber; OC, optical circulator; CS-SSB, carrier suppressed single sideband; EDFA, erbium-doped fiber amplifier; PC, polarization controller; OF, optical filter; Pol, polarizer; DUT, device under test; PD, photodetector).
X 1 E 1 0 n∞ E PolM t p0 J 2n cosω0 2nωm t × 1 2 0 1 n−∞ n∞ X 1 ; J 2n1 cosω0 2n 1ωm t × −1 n−∞
E OF t 2 6 6 ×6 4
E x0
E y0
G sin θJ 0 −
E p0 2 n−1 X n−∞
G cos θJ 0
−1n J 2n1 expω0 2n1ωm t
n−1 X n−∞
−1n J 2n cosω0 2nωm t
where J n J n β is the Bessel function of the first kind of order n. As can be seen from Eq. (2), the SOP of the even-order sidebands is aligned at 45° to E x polarization state, while the SOP of the odd-order sidebands is aligned at −45° to E x polarization state. The polarization modulated optical signal goes through a spool of dispersion shifted fiber (DSF) and an optical circulator (OC). An optical filter (OF) is used to realize SSB modulation by removing the higher frequency sidebands (or lower wavelength sidebands), as shown in Fig. 1(b) where the x0 -axis is aligned at a −45° to E x polarization state of the PolM. The microwave signal at fundamental frequency cannot be recovered in a PD because the SOP of the even-order sidebands is orthogonal to that of the odd-orders ones. To recover the fundamental microwave tone, SBS-assisted polarization pulling is used to pull the SOP of the optical carrier toward that of the odd-order sidebands. The lower part of the optical carrier shown in Fig. 1(a) goes to a carrier suppressed (CS)-SSB modulator [12]. The optical carrier is upshifted by a Brillouin frequency shift (f B ). This signal acts as the pump wave to excite the SBS in the DSF. The power and the SOP of the pump wave is adjusted by an erbium-doped fiber amplifier (EDFA) and a polarization controller (PC1). Since the signal and pump wave come from the same laser source, the stability of the SBS process can be assured. SBS amplification over optical fibers is highly polarization dependent [13–15]. This amplification is related to two
7 7 7: 5
(3)
⇀
(2)
3
A polarizer (Pol) at an angle of ψ with respective to the x0 -axis is attached after the OF. The optical field at the output of the Pol can be expressed as E E out t p0 fGJ 0 sinθ ψ 2 n−1 X −1n J 2n1 expω0 2n 1ωm t − cos ψ n−∞
sin ψ
n−1 X n−∞
−1n J 2n expω0 2nωm tg:
(4)
The SSB modulated optical signal is sent to a DUT, and the optical field at the output of the DUT is given by E D ω E out ω · Hω p 2πE 0 GJ 0 sinθ ψHω0 δω − ω0 sin ψ
n−1 X n−∞
−1n J 2n Hω0 2nωm
· δω − ω0 2nωm − cos ψ
n−1 X n−∞
−1n J 2n−1 βHω0 2n − 1ωm
· δω − ω0 2n 1ωm ;
(5)
where Hω and E out ω are the transmission response of the DUT and the Fourier transform of Eout t, respectively. After detection in a PD, the photocurrent at the angular frequency of ωm can be expressed as
April 15, 2015 / Vol. 40, No. 8 / OPTICS LETTERS
iωm ∝ GJ 0 sinθ ψJ 1 H ω0 Hω0 ωm J n1 J n
· Hω0 n 1ωm H ω0 nωm ∕2:
(6)
For most of the OVNAs, it is assumed that the SSB modulated optical signal consists of only the optical carrier and the first-order sideband. In this condition, the measured transmission response of the system, including the OVNA and the DUT, is given by H S ω0 ωm
iS ωm : GJ 0 sinθ ψJ 1 H S ω0
(7)
A calibration process has to be done in advance to remove the response of the OVNA, H V ω0 ωm . Thus, the transmission response of the DUT can be rewritten as H D ω0 ωm
H S ω0 ωm : H V ω0 ωm
(8)
However, the higher-order optical sidebands have to be considered in a real-world OVNA. The beating between adjacent sidebands also contributes to the fundamental tone at ωm . If the contribution of higher-order sidebands is considered, Eq. (8) is rewritten as H D ω0 ωm
H S ω0 ωm εS ω0 ωm ; H V ω0 ωm εV ω0 ωm
(9)
where εS ω0 ωm and εV ω0 ωm are the contributions of the higher-order sidebands to the magnitude and phase of the fundamental microwave signal for the whole system and the OVNA, respectively. They can be expressed as εS ω0 ωm P sin2ψ ∞ n1 J n1 J n H S ω0 n 1ωm H S ω0 nωm ; 2GJ 0 sinθ ψJ 1 H S ω0 (10) εV ω0 ωm P sin2ψ ∞ n1 J n1 J n H V ω0 n1ωm H V ω0 nωm : 2GJ 0 sinθ ψJ 1 H V ω0 (11) As can be seen from Eqs. (10)–(11), significant measurement errors are added to the measured result because of the beating between adjacent higher-order sidebands. To improve the accuracy of the OVNA, these errors have to be eliminated. To do so, we adjust the angle of the Pol to let ψ 0. The Pol is thus aligned with the x0 -axis. The schematic optical spectrum is shown in Fig. 1(d). In this case, we have εS ω0 ωm εV ω0 ωm 0. It means that the measurement errors are completely removed. The transmission response of the DUT is given by
iS ωm H V ω0 : iV ωm H S ω0
(12)
Equation (12) shows that the accuracy of the proposed OVNA is significantly improved by eliminating the measurement errors induced by higher-order sidebands. Moreover, the measured result is independent of the modulation index of the PolM, β. It also means that the measurement errors can be reduced without affecting the dynamic range because the dynamic range is related to the modulation index. This is very promising for a real-world OVNA because the OVNA is no longer restricted by the small modulation condition, i.e., β ≪ 1. We carried out an experiment to verify the proposed OVNA based on the setup shown in Fig. 1(a). An optical carrier from a TLS is divided into two parts. The upper part was coupled to a PolM which has an integrated Pol at 45° with respect to one principal axis of the PolM. The deviation of the SOP of the optical carrier from 45° results in optical power attenuation. However, the influence of power attenuation can be removed by the calibration process. For the lower part, the CS-SSB modulator was driven by a sinusoidal microwave signal at 9.2 GHz, corresponding to the Brillouin frequency shift in our case. The frequency shifted optical signal was amplified by an EDFA to 15 dBm and acted as the pump wave to excite the SBS. The SOP of the pump wave was controlled by a PC1. An OC was used to counterpropagate the pump wave and the polarizationmodulated signal in a 1 km DSF. An OF was used to realize SSB modulation. Figure 2(a) shows the measured optical spectra of a double sideband (DSB) and SSB modulated signal, as well as the transmission response of the OF. In this measurement, the pump wave was disconnected. The microwave signal driven to the PolM is 15 GHz. The modulation index β is 1.2 rad. A series of optical sidebands was generated because of the nonlinearity of the PolM. For SSB modulation, the undesired first-order sideband is 42 dB lower than the desired one. As discussed in the previous part, the sidebands higher than the first order introduce measurement error to the result. A Pol was thus attached after the OF to realize polarization discrimination. Figure 2(b) shows the measured optical spectra at the output of the Pol with and without the SBS effect. A PC2 was used to adjust the SOP of the SSB modulated signal with respect to the Pol to satisfy ψ 0, as discussed in the theoretical part. 0 -20
(a)
DSB SSB Filter
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(b) Power (dBm)
n1
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sin2ψ
∞ X
H D ω0 ωm
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W/O SBS With SBS
1st 3rd 2nd 4th
-60 1549.5 1549.8 1550.1 1550.4
Wavelength (nm)
Fig. 2. (a) Measured optical spectra of the DSB and SSB modulated signals, (b) measured optical spectra at the output of the Pol with and without the SBS (DSB, double-sideband; SSB, single-sideband; SBS, stimulated Brillouin scattering).
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OPTICS LETTERS / Vol. 40, No. 8 / April 15, 2015 200
Magnitude (dB)
0
-10
150
Phase (Deg.)
The proposed OVNA ASE The conventional OVNA
(a)
(b)
100 50 0 -50
-20
The proposed OVNA The conventional OVNA
-100 5
10
15
20
25
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30
35
10
20
30
Frequency (GHz)
Fig. 3. Measured (a) magnitude and (b) phase responses of the DUT (OVNA: optical vector network analyzer).
The angle deviation of the Pol from ψ 0 and the limited suppression ratio of the Pol will result in residual evenorder sidebands. The beating between adjacent sidebands will generate considerable measurement errors to the OVNA. The optical carrier and the even-order sidebands were well suppressed by the Pol when the SBS was turned off. The optical carrier and the even-order sideband is 33 dB lower than the first-order sideband. The residual optical carrier and even-order sidebands can be attributed to the limited suppression ratio of the Pol and the polarization mode dispersion (PMD) of the DSF. Because of the polarization dependent SBS effect, the SOP of the optical carrier was pulled toward that of the odd-order sidebands by adjusting the SOP of the pump wave. After the SBS effect, the optical carrier can also be observed at the output of the Pol as shown in Fig. 2(b). The optical carrier is 29 dB higher than that in the case without SBS. Since only the beating between the optical carrier and the first-order sideband has contributed to the fundamental tone and the beating between adjacent sidebands is very small, the accuracy of the OVNA can be improved significantly. The proposed OVNA was used to measure the transmission response of a notch filter which is actually a programmable optical processer (WaveShaper Finisar 4000S). First of all, the magnitude response of the DUT was characterized using an amplified spontaneous emission (ASE) source and an optical spectrum analyzer (OSA) with a resolution of 0.01 nm. The measured response is shown in Fig. 3(a) in a red dashed line. For comparison, the DUT was measured using a conventional OVNA scheme. To construct the conventional OVNA, the Pol was aligned at 45° with respective to the x0 -axis. The pump wave was disconnected. In this case, the combined use of the PolM and Pol is equivalent to an intensity modulator biased at the quadrature point [16]. The measured magnitude response is shown in Fig. 3(a) in a blue solid line. Significant errors were generated because of higher-order sidebands. The maximum deviation from the result measured by ASE and OSA is 5.5 dB. The result measured using our proposed OVNA is shown in Fig. 3(a) in a black solid line. The measurement errors are significantly reduced compared with the conventional OVNA. The deviation from the result measured by ASE and OSA is within 0.8 dB. A general match between the proposed and the conventional OVNAs can
only be found outside the frequency interval 20 10 GHz. There are 1601 effective measurement points over a frequency range of 30 GHz. Thus, the resolution of the OVNA is 18.7 MHz. The resolution can be further improved by reducing the steps of the microwave source. The measured result using the proposed OVNA agrees well with that using the ASE source and OSA in the frequency range greater than 10 GHz. This is because of the limited roll-off property of the OF. The phase response of the DUT measured by the conventional OVNA and the proposed OVNA is shown in Fig. 3(b). Significant phase errors are also introduced in the phase response of the DUT using the conventional OVNA. It is noted that the phase response cannot be obtained using the ASE and OSA schemes. Thus, we cannot provide more phase measurement data. However, the excellent accuracy of the proposed OVNA has already been verified as shown in Fig. 3(a). In principle, the measurement error can be completely suppressed. However, some errors might still be introduced to the measured results because of the limited suppression ratio of the Pol and the PMD of the DSF. In summary, we have demonstrated an accurate OVNA based on polarization modulation and SBS-assisted polarization pulling. The proposed method has been theoretically analyzed and experimentally verified. The proof-of-concept experiment confirmed that the measurement errors induced by higher-order sidebands have been significantly reduced. This work was supported in part by the National Natural Science Foundation of China under 61377069, and 61335005 and, in part, by the Beijing Nova program. References 1. T. Niemi, M. Uusimaa, and H. Ludvigsen, IEEE Photon. Technol. Lett. 13, 1334 (2001). 2. G. D. van Wiggeren, A. R. Motamedi, and D. M. Baney, IEEE Photon. Technol. Lett. 15, 263 (2003). 3. R. Hernandez, A. Loayssa, and D. Benito, Opt. Eng. 43, 2418 (2004). 4. W. Li, W. T. Wang, L. X. Wang, and N. H. Zhu, IEEE Photon. J. 6, 7901108 (2014). 5. W. Li, W. H. Sun, W. T. Wang, L. X. Wang, J. G. Liu, and N. H. Zhu, IEEE Photon. Technol. Lett. 26, 866 (2014). 6. M. Sagues and A. Loayssa, Opt. Express 18, 17555 (2010). 7. M. Xue, S. L. Pan, and Y. J. Zhao, J. Lightwave Technol. 32, 3317 (2014). 8. M. Xue, S. L. Pan, and Y. J. Zhao, Opt. Lett. 39, 3595 (2014). 9. W. T. Wang, W. Li, J. G. Liu, W. H. Sun, W. Y. Wang, and N. H. Zhu, IEEE Photon. J. 6, 5501310 (2014). 10. M. Xue, S. Pan, and Y. Zhao, Opt. Lett. 40, 569 (2015). 11. A. L. Campillo, Opt. Lett. 32, 3152 (2007). 12. M. Sagues and A. Loayssa, Opt. Express 18, 22906 (2010). 13. M. O. van Deventer and A. J. Boot, J. Lightwave Technol. 12, 585 (1994). 14. A. Zadok, E. Zilka, A. Eyal, L. Thevenaz, and M. Tur, Opt. Express 16, 21692 (2008). 15. S. Preussler, A. Zadok, A. Wiatrek, M. Tur, and T. Schneider, Opt. Express 20, 14734 (2012). 16. Y. Chen, A. Wen, and J. P. Yao, IEEE Photon. Technol. Lett. 25, 2319 (2013).
