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  • Abstract

SECTION 1

Introduction

Modern electronic warfare and radar systems require a low latency tool for detecting and roughly classifying intercepted microwave signals. An instantaneous frequency measurement (IFM) system based on photonic techniques is a promising candidate [1], [2], [3], [4], [5], [6]. Compared with conventional electronic techniques, the primary advantages of the photonic-assisted IFM are high bandwidth, low loss, light weight, and immunity to electromagnetic interference [7], [8], [9]. A number of techniques have been proposed for IFM systems [1], [2], [3], [4], [5], [6], [7], [8], [9], [10], [11], [12], [13], [14]. In these schemes, generally, the frequency information of the unknown signals can be deduced by the frequency-to-space mapping [1], [2], [3], frequency-to-time mapping [4], and frequency-to-power mapping methods [5], [6], [7], [8], [9], [10], [11], [12], [13].

For the frequency-to-power mapping technique, a unique relationship between the microwave frequency and the measured optical power [5], [6] or electrical power [7], [8], [9], [10], [11], [12], [13], [14] should be established. In [7], an amplitude comparison technique was proposed by comparing the two different dispersion-induced power-fading functions. However, the measurement errors are very large in the low- frequency range due to the flat amplitude comparison function (ACF). Therefore, the measurement range is basically restricted to the vicinity of the notch frequency. In this context, the amplitude comparison technique was improved to a wide measurement range by comparing two complementary power-fading functions using, for instance, a phase modulator plus an intensity modulator [8], a polarization modulator (PolM) [9], a polarization maintaining fiber (PMF) with a dispersion compensation fiber (DCF) [10], and a dual-electrode dual-output Mach–Zehnder modulator (MZM) [11].

The other limitation of the approach presented in [7] is the fixed measurement range and resolution. However, for many applications, it is highly desirable that the IFM system can be reconfigurable with adjustable measurement range and resolution. In [11], [12], [13], the reconfiguration of the IFM system was demonstrated by tuning the laser wavelength. The measurement range can only be adjusted in a narrowband due to the relative small dispersion variation resulting from the wavelength tuning. Recently, we have demonstrated a reconfigurable IFM system based on stimulated Brillouin scattering (SBS) [14]. However, the temperature control with high accuracy was required to guarantee the reported measurement resolution because the SBS is very sensitive to the environment. Moreover, the use of an additional frequency tunable electrical source (as well as the temperature control device) makes the system huge and expensive.

In this paper, we theoretically and experimentally demonstrate a novel reconfigurable IFM system based on dual-parallel MZM (DPMZM). Different from the previous wavelength tuning methods [11], [12], [13] and SBS-assisted approach [14], the IFM system is reconfigurable with tunable measurement range and resolution by simply adjusting the dc bias voltage of the DPMZM. In principle, the measurement range can be tuned to any frequencies, which is only limited by the bandwidth of the optical transmitter and receiver employed. Alternatively, the IFM system can also work with a fixed wide measurement range and moderate resolution by generating two complementary power-fading functions.

SECTION 2

Principle

The schematic configuration of the proposed IFM system is shown in Fig. 1. The unknown microwave signal is modulated onto two independent optical carriers (OCs) with different wavelengths (Formula$\lambda_{1}$ and Formula$\lambda_{2}$) from two laser diodes (LD1 and LD2) using DPMZM and MZM, respectively. In our scheme, the wavelengths of the two LDs are fixed. In the lower channel, the MZM is biased at quadrature to generate a double sideband (DSB) modulated signal. The bias control of the DPMZM in the upper channel will be discussed later. These signals are then passed through a dispersive medium to induce two different power-fading functions. The dispersed signals are separated by two optical tunable filters (TF1 and TF2), detected by two photodetectors (PD1 and PD2, respectively). In this way, the ACF of the two power-fading functions can be constructed to realize frequency-to-power mapping. The power-fading function in the lower channel is fixed for a given IFM system. In order to tune the measurement range and resolution of the system, the power-fading function in the upper channel should be tunable.

Figure 1
Fig. 1. Schematic configuration of the proposed IFM system (LD: laser diode; DPMZM: dual-parallel Mach–Zehnder modulator; TF: tunable optical filter; PD: photodetector).

The key component in our scheme is a commercially Formula$x$-cut integrated DPMZM, also called differential quadrature phase-shift-keying (DQPSK) modulator. Fig. 2 illustrates the layout of the DPMZM, along with the schematic optical spectra at different locations. It is structured as two MZMs (MZM1 and MZM2) set in parallel and forming a third MZM (MZM3). In the DPMZM, MZM1 is fed by the unknown microwave signal and is biased at minimum transmission to implement carrier suppressed (CS)-DSB modulation. MZM2 has no driven signal and is biased at a maximum transmission point to allow the OC to pass through. They are combined together in MZM3 to generate a CS-DSB + OC signal. A frequency independent phase difference Formula$\varphi$ between the CS-DSB and OC signals is then generated by controlling the dc bias of MZM3, i.e., Formula$V_{3}$. After passing through the dispersive medium, a frequency dependent phase shift is introduced to the CS-DSB signal with respect to the OC. This frequency-dependent phase shift results in the power-fading after photodetection. Note that the power-fading function, as well as the ACF, is tunable by adjusting the frequency-independent phase shift Formula$\varphi$ via tuning Formula$V_{3}$. As a result, the IFM system is reconfigurable by simply adjusting the dc bias Formula$V_{3}$. Next, the principle of the IFM system is investigated theoretically.

Figure 2
Fig. 2. Layout of the DPMZM, along with the schematic optical spectra at different locations.

The optical field from the MZM1 is given by Formula TeX Source $$E_{1} = E_{\rm in} \,\sin(\beta\,\cos 2\pi f_{m}t)\, \exp(j2\pi f_{0}t)/\sqrt{2}\eqno{\hbox{(1)}}$$ where Formula$V_{\rm m}$ and Formula$f_{\rm m}$ are the peak amplitude and frequency of the unknown microwave signal. Formula$E_{\rm in}\exp(j2\pi f_{0}t)$ is the input optical field, Formula$f_{0}$ is the frequency of the OC, Formula$J_{1}(\beta)$ is the first-order Bessel function of the first kind, Formula$\beta = \pi V_{m}/(2V_{\pi 1})$, and Formula$V_{\pi 1}$ is the half-wave voltage of MZM1. Under small-signal conditions, only the first-order sidebands are considered and (1) can be simplified as Formula TeX Source $$E_{1} = {E_{\rm in} \over 2\sqrt{2}}J_{1}(\beta) \,\exp\left[j2\pi (f_{0} - f_{m})t\right] + {E_{\rm in} \over 2 \sqrt{2}}J_{1}(\beta)\, \exp\left[j2\pi(f_{0} + f_{m})t\right].\eqno{\hbox{(2)}}$$ The optical field from MZM2 can be written by Formula TeX Source $$E_{2} = E_{\rm in}\, \exp(j2\pi f_{0}t)/ \sqrt{2}.\eqno{\hbox{(3)}}$$ After combination, the optical field from DPMZM can be expressed as Formula TeX Source $$E_{{\rm out}1} = \left[E_{1} + E_{2}\,\exp(j\varphi)\right]/ \sqrt{2}\eqno{\hbox{(4)}}$$ where Formula$\varphi = \pi(V_{3} - V_{\rm offset})/V_{\pi 3}$ is the phase difference between CS-DSB and OC signals, Formula$V_{\pi 3}$ is the half-wave voltage of MZM3, and Formula$V_{\rm offset}$ is the offset voltage when Formula$\varphi = 0$. After passing through a dispersive medium, the optical field is given by Formula TeX Source $$\displaylines{E_{{\rm out}2} = {E_{\rm in} \over 4}J_{1}(\beta)\, \exp\left[j2\pi(f_{0} - f_{m})t\right]\, \exp\left({j\pi D_{1}\lambda_{1}^{2}f_{m}^{2} \over c}\right) + \,{E_{\rm in} \over 2}\, \exp\left[j (2\pi f_{0}t + \varphi)\right]\hfill\cr\hfill + \ {E_{\rm in} \over 4}J_{1}(\beta)\, \exp\left[j2\pi(f_{0} + f_{m})t\right]\, \exp\left({j\pi D_{1}\lambda_{1}^{2}f_{m}^{2} \over c} \right)\quad\hbox{(5)}}$$ where Formula$D_{1}$ is the total dispersion of the dispersive medium for Formula$\lambda_{1}$. The microwave power after the PD is proportional to Formula TeX Source $$P_{m} \propto J_{1}^{\,2}(\beta)\,\cos^{2}\left({\pi D_{1}\lambda_{1}^{2}f_{m}^{\,2} \over c} - \varphi\right) = J_{1}^{\,2}(\beta)\,\cos^{2} \left[{\pi D_{1}\lambda_{1}^{2}f_{m}^{\,2} \over c} - {\pi(V_{3} - V_{\rm offset}) \over V_{\pi 3}} \right].\eqno{\hbox{(6)}}$$ The difference between the two power-fading functions of the two channels (see Fig. 1), referred to as the ACF, is given by Formula TeX Source $$\gamma = \eta{J_{1}^{\,2}(\beta)\,\cos^{2}\left[{\pi D_{1} \lambda_{1}^{2}f_{m}^{\,2} \over c} - {\pi(V_{3} - V_{\rm offset}) \over V_{\pi 3}}\right] \over J_{0}^{\,2}(\beta^{\prime})J_{1}^{\,2}(\beta^{\prime})\,\cos^{2}\left({\pi D_{2}\lambda_{2}^{2}f_{m}^{\,2} \over c}\right)}\eqno{\hbox{(7)}}$$ where Formula$D_{2}$ is the total dispersion for Formula$\lambda_{2}$, Formula$\eta$ is the power ratio coefficient, Formula$\beta^{\prime} = \pi V_{\rm m}/(2V_{\pi}^{\prime})$, and Formula$V_{\pi}^{\prime}$ is the half-wave voltage of the MZM in the lower channel. Under small-signal conditions, i.e., Formula$0 \ <\ \beta$, Formula$\beta^{\prime} \ll 1$, we have Formula$J_{0}(\beta^{\prime}) \sim 1$, Formula$J_{1}(\beta) \sim \beta/2 = \pi V_{\rm m}/(4V_{\pi 1})$, and Formula$J_{1}(\beta^{\prime}) \sim \beta^{\prime}/2 = \pi V_{\rm m}/(4V_{\pi}^{\prime})$. Then, (7) can be simplified as Formula TeX Source $$\gamma = \eta^{\prime}{\cos^{2}\left[{\pi D_{1} \lambda_{1}^{2}f_{m}^{\,2} \over c} - {\pi(V_{3} - V_{\rm offset}) \over V_{\pi 3}}\right] \over \cos^{2}\left({\pi D_{2}\lambda_{2}^{2}f_{m}^{\,2} \over c}\right)}\eqno{\hbox{(8)}}$$ where Formula$\eta^{\prime}$ includes such as the losses in the dispersive medium, the modulator, the TF, and the PD. However, the loss difference between the two channels can be compensated by adjusting the optical power of the LDs. Therefore, we have Formula$\eta^{\prime} = 1$. Then, (8) can be expressed as Formula TeX Source $$\gamma = {\cos^{2}\left[{\pi D_{1}\lambda_{1}^{2}f_{m}^{\,2} \over c} - {\pi(V_{3} - V_{\rm offset}) \over V_{\pi 3}}\right] \over \cos^{2}\left({\pi D_{2}\lambda_{2}^{2}f_{m}^{\,2} \over c}\right)}.\eqno{\hbox{(9)}}$$ As can be seen from (9), a unique relationship between the input microwave frequency and power ratio is established. In this way, the input microwave frequency can be extracted from the measured ACF. Note that the ACF consists of two parts. One is the frequency dependent phase shift of the CS-DSB signal with respect to the OC, which leads to the powerfading. The other is the frequency independent phase shift Formula$\varphi$, which is controlled by the dc bias Formula$V_{3}$. In our scheme, all the parameters including the wavelengths of the two LDs and the total dispersion of the medium are fixed, except for Formula$V_{3}$. The reconfiguration of the ACF can be simply accomplished by adjusting Formula$V_{3}$. This is the key difference between the previous methods [11], [12], [13] and ours. In order to show the advantages of our method, the limitations of the conventional methods based on wavelength tuning are analyzed first.

When Formula$V_{3} = V_{\rm offset}\ (\varphi = 0)$, (9) is simplified as Formula TeX Source $$\gamma = {\cos^{2}\left(\pi D_{1}\lambda_{1}^{2}f_{m}^{\,2}/c\right) \over \cos^{2}\left(\pi D_{2}\lambda_{2}^{2}f_{m}^{\,2}/c\right)}.\eqno{\hbox{(10)}}$$ It is the same as the conventional ACF [7], [12]. Fig. 3 shows the simulated results of the power-fading functions and the corresponding ACF in this case. As shown in Fig. 3(b), the variation of ACF is very small in the frequency range of 0 to Formula$\sim$50 GHz. Fig. 3(c) shows the calculated first-order derivative of the ACF. From 0 to Formula$\sim$50 GHz, the small variations of the ACF would result in large measurement error and frequency ambiguity. This, in turn, sets the lower measurement bound of the IFM system. It is expected that the measurement resolution near the notch frequency can be improved due to the distinct changes of the ACF in the vicinity of the notch, as shown in Fig. 3(c). In order to avoid frequency ambiguities, the upper measurement range of the IFM system is limited to the position of the first notch of the ACF, which is given by Formula TeX Source $$M_{\max} = \sqrt{c/2D_{1} \lambda_{1}^{2}}.\eqno{\hbox{(11)}}$$ In the conventional method, the measurement range is adjustable by tuning the wavelength of LD1 [12], as indicated by (11). Fig. 4 shows the simulated power-fading functions as the wavelength of LD1 is tuned. It can be seen that the first notch of the power-fading can only be adjusted in a frequency range as narrow as 11.4 GHz when the optical wavelength is tuned in the whole Formula$C$-band. Therefore, the measurement range of the IFM system could only be tuned in a narrowband [12].

Figure 3
Fig. 3. Simulated results of (a) the power-fading functions, (b) the corresponding ACF, and (c) the calculated first-order derivative of the ACF for Formula$V_{3} = V_{\rm offset}\ (\varphi = 0)$ case. The parameters used in the simulation are Formula$\lambda_{1} = 1550\ \hbox{nm}$, Formula$\lambda_{2} = 1520\ \hbox{nm}$, Formula$D_{1} = 17\ \hbox{ps/nm}$, and Formula$D_{2} = 14.9\ \hbox{ps/nm}$.
Figure 4
Fig. 4. Simulated power-fading functions when the wavelength is adjusted in the whole Formula$C$-band. The parameters used in the simulation are Formula$\lambda_{1} = 1520\ \hbox{nm}\ (D_{1} = 14.9\ \hbox{ps/nm})$, 1550 nm Formula$(D_{1} = 17\ \hbox{ps/nm})$, 1580 nm Formula$(D_{1} = 18.4\ \hbox{ps/nm})$, and 1600 nm Formula$(D_{1} = 19.7\ \hbox{ps/nm})$.

In our method, the reconfiguration of the system is accomplished by tuning the dc bias of the DPMZM Formula$V_{3}$, while keeping the wavelengths of the two LDs unchanged. Fig. 5 shows the simulated power-fading functions when Formula$V_{3}$ is tuned from 2.8 to 9.8 V. Note that the first notch of the power-fading is continuously tuned from around 0 to Formula$\sim$60 GHz. Fig. 6 shows the corresponding ACFs and the slopes of the ACFs. It is evident that the proposed system can be tuned in a much wider frequency range compared with the previous wavelength tuning methods [11], [12], [13]. Although the IFM system covers a wide frequency range, it is accomplished by tuning the dc bias Formula$V_{3}$. In other words, for a fixed Formula$V_{3}$, the measurement range is restricted around the frequency range over which the ACF varies sensibly.

Figure 5
Fig. 5. Simulated power-fading functions when Formula$V_{3}$ is tuned from 2.8 to 9.8 V.
Figure 6
Fig. 6. (a) Calculated ACFs corresponding to Fig. 5 and (b) the first-order derivative of the ACFs. The parameters used in the simulation are Formula$\lambda_{1} = 1550\ \hbox{nm}$, Formula$\lambda_{2} = 1520\ \hbox{nm}$, Formula$D_{1} = 17\ \hbox{ps/nm}$, and Formula$D_{2}$ Formula$= 14.9\ \hbox{ps/nm}$, Formula$V_{\pi 3} = 14\ \hbox{V}$, and Formula$V_{\rm offset} = 9.8\ \hbox{V}$. Formula$V_{\rm offset}$ was measured by observing the maximum peak of the beating signal between OC and sidebands on the electrical spectrum analyzer (ESA) through the PD.

For Formula$V_{3} = 2.8\ \hbox{V}\ (\varphi = \pi/2)$, (9) is simplified as Formula TeX Source $$\gamma = {\sin^{2}\left(\pi D_{1}\lambda_{1}^{2}f_{m}^{2}/c\right) \over \cos^{2}\left(\pi D_{2}\lambda_{2}^{2}f_{m}^{2}/c \right)}.\eqno{\hbox{(12)}}$$ In this case, for the optical signal at Formula$\lambda_{1}$, the intensity modulation at Formula$V_{3} = 9.8\ \hbox{V}$ (as shown in Fig. 5) is now converted to the phase modulation. As can be seen from Fig. 5, it generates power-fading functions that are bandpass (@ Formula$\lambda_{1} = 1550\ \hbox{nm}$, Formula$V_{3} = 2.8\ \hbox{V}$) and low-pass (@ Formula$\lambda_{2} = 1520\ \hbox{nm}$), respectively. The complementary nature of the two power-fading functions leads to a fast change rate versus the input frequency over a wide range as shown in Fig. 6(b). It enables us to estimate the microwave frequency with a relative high resolution over a wide frequency range.

Note that Formula$9.8 \ <\ V_{3} \ <\ 11.1\ \hbox{V}$ should be avoided. In these cases, the notch @ Formula$\lambda_{1} = 1550$ will fall into the shadow area, as shown in Fig. 7. The power-fading @ Formula$\lambda_{1}$ with Formula$V_{3} = 9.8\ \hbox{V}\ (\varphi = 0)$ and that @ Formula$\lambda_{2} = 1520\ \hbox{nm}$ are also shown for reference. For Formula$V_{3} = 11.1\ \hbox{V}$, the notch @ Formula$\lambda_{1}$ locates at the same frequency as that of Formula$\lambda_{2}$. A simulated example is shown in Fig. 7 with Formula$V_{3} = 10.74\ \hbox{V}$. The zoom-in view shows that the two power-fading functions intersect at Formula$\sim$55.5 GHz. This intersection point dictates the lower bound of the IMF system, thus resulting in a very narrow measurement range.

Figure 7
Fig. 7. Undesirable cases for the IFM system Formula$(9.8 \ <\ V_{3} \ <\ 11.1\ \hbox{V})$.

For Formula$V_{3} = 2.8\ \hbox{V}$, the upper measurement range is determined by the notch position @ Formula$\lambda_{2}\ (\lambda_{1} \ >\ \lambda_{2})$ [see Fig. 6(a)]. Therefore, the measurement range of the system is fixed in this case. For Formula$2.8 \ <\ V_{3} \leq 9.8\ \hbox{V}$, the upper measurement range of the IFM system is determined by the notch @ Formula$\lambda_{1}\ (\lambda_{1} \ >\ \lambda_{2})$. The measurement range and resolution can be adjusted in this case. If the dispersive medium with smaller total dispersion is used, a higher upper measurement bound could be available. However, no matter how high the upper measurement bound is, a bias voltage tuning of 7 V (Formula$V_{3}$, from 2.8 to 9.8 V) is enough to tune the notch of ACF [see Fig. 6(a)] through the whole frequency range. Therefore, in principle, the measurement range of the proposed IFM system can be tuned to any frequencies, which is only limited by the bandwidth of the optical transmitter and receiver employed.

SECTION 3

Experiments

The most bandwidth-limiting components in our experiment are the PDs with 18 GHz bandwidth. Therefore, a 25-km S-SMF was used as the dispersive medium. The total dispersions for Formula$\lambda_{1} = 1550\ \hbox{nm}$ and Formula$\lambda_{2} = 1520\ \hbox{nm}$ were measured to be Formula$D_{1} = 425\ \hbox{ps/nm}$ and Formula$D_{2} = 372.5\ \hbox{ps/nm}$, respectively, Fig. 8(a) shows the measured (solid lines) and simulated (dash lines) power-fading functions for the two channels (see Fig. 1). For the upper channel, the power-fading functions with Formula$V_{3} = 4.9$ and 9.8 V are shown. The power-fading functions were captured by a vector network analyzer (VNA). The output power of the continuous-wave electrical signal from the VNA was set to −5 dBm. Fig. 8(b) shows the corresponding ACFs. Experimental results match well with the theoretical prediction. As shown in Fig. 8(a), the power-fading function at Formula$\lambda_{1} = 1550\ \hbox{nm}$ can be adjusted by tuning Formula$V_{3}$. The variation of the first notch of the power-fading function influences the ACF and, finally, changes the upper measurement bound, as shown in Fig. 8(b).

Figure 8
Fig. 8. Measured (solid lines) and simulated (dash lines) results of (a) power-fading functions and (b) ACFs for Formula$V_{3} = 4.9$ and 9.8 V, respectively.

Fig. 9 shows the measured frequency versus input frequency and the measurement error as a function of input frequency for Formula$V_{3} = 4.9$ and 9.8 V cases. It can be seen that the estimation of the input frequency is best closer to the notch of the ACF. At low frequencies, variations in the ACF are very small, leading to a large measurement error and frequency ambiguity. For a given measurement error, e.g., ±0.1 GHz, the measurement range is tunable, as shown in Fig. 9(b). For Formula$V_{3} = 4.9$ and 9.8 V, the measurement range are 3.6–6.5 GHz and 8.8–12 GHz, respectively. Table 1 shows the measurement ranges and resolutions at different bias voltages. A total measurement range of 1–12 GHz with the resolution of ±0.1 GHz was accomplished by tuning Formula$V_{3}$. It should be noted that the total measurement range of 11 GHz is achieved by setting Formula$V_{3}$ to four different bias voltages. For each working voltage, the measurement range is around 3 GHz.

Figure 9
Fig. 9. (a) Measured frequency versus input frequency and (b) the measurement error as a function of input frequency for Formula${\rm V}3 = 4.9$ and 9.8 V cases.
Table 1
TABLE 1 Measurement range and resolution

Fig. 10 shows the measured (solid lines) and simulated (dash lines) power fading and the corresponding ACF for Formula$V_{3} = 2.8\ \hbox{V}\ (\varphi = \pi/2)$ case. The complementary nature of the two power-fading functions leads to a relative fast change of the ACF versus the input frequency over a wide frequency range, as shown in Fig. 10(b). Fig. 11 shows the measured frequency as a function of the input frequency and the measurement error versus the input frequency. A measurement range as large as 11 GHz (2–13 GHz) was achieved for a moderate measurement resolution of ±0.25 GHz.

Figure 10
Fig. 10. Measured (solid lines) and simulated (dash lines) (a) power-fading functions and (b) the corresponding ACFs for Formula$V_{3} = 2.8\ \hbox{V}\ (\varphi = \pi/2)$ case.
Figure 11
Fig. 11. (a) Measured frequency as a function of the input frequency and (b) the measurement error versus the input frequency for Formula$V_{3} = 2.8\ \hbox{V}\ (\varphi = \pi/2)$ case.
SECTION 4

Conclusion

We have demonstrated a reconfigurable IFM system based on DPMZM. The key component in our system is the DPMZM. In DPMZM, two sub-MZMs were biased at minimum and maximum transmission points, respectively, to generate a CS-DSB+OC modulated signal. In this way, a phase-shift between the CS-DSB and OC signals was generated by controlling the dc bias of MZM3. This tunable phase-shift leads to an adjustable power-fading function, resulting in a tunable ACF. As a result, the IFM system is reconfigurable with tunable measurement range and resolution. In principle, the measurement range can be tuned to any frequencies, which is only limited by the bandwidth of the optical transmitter and receiver employed.

Compared with the previous methods based on wavelength tuning [11], [12], [13], the proposed method has two advantages: 1) The measurement range can be tuned in a much wider frequency range; 2) the system can also work with a fixed wide measurement range and moderate resolution. A proof-of-concept demonstration of the proposed technique has been presented. A total measurement range of 1–12 GHz with the resolution of ±0.1 GHz has been achieved by tuning Formula$V_{3}$ from 3.54 to 9.8 V. For Formula$V_{3} = 2.8\ \hbox{V}\ (\varphi = \pi/2)$, a fixed measurement range as large as 11 GHz (2–13 GHz) has been accomplished with the resolution of ±0.25 GHz. The maximum measurement bound in our experiment has been restricted by the limited bandwidth of PDs.

As indicated by (9), the ACF is determined by both the frequency dependent phase shift introduced by the dispersive medium and the frequency independent phase shift which is controlled by dc bias Formula$V_{3}$. Therefore, the measurement errors can be attributed to such as the fluctuation of the optical source, the stability of the chromatic dispersion of the fiber, the stability of the bias control of the DPMZM, and the system noise. The frequency independent phase-shift Formula$\varphi$ changes with the bias voltage Formula$V_{3}$, which results in the variation of ACF, leading to the measurement error. It can be seen from Fig. 6(a) that the variation of Formula$V_{3}$ from 2.8 to 9.8 V is enough to tune the notch of the power-fading to any frequencies from around 0 to the maximum upper measurement bound. The maximum upper measurement bound is inversely proportional to the total dispersion of the dispersive medium. For a larger tunable measurement range, the measurement error, however, is more sensitive to the fluctuation of Formula$V_{3}$. Therefore, there is a tradeoff between the measurement range and resolution. The system shows an excellent short-term stability. However, due to the bias drifting of the modulator, the long-term stability of the system requires a more sophisticated voltage control.

Footnotes

This work was supported by the National Natural Science Foundation of China under 61108002, 61127018, 61021003, 61177060, 61090390, 61177080, and 60820106004. Corresponding author: W. Li (e-mail: liwei05@semi.ac.cn).

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Wei Li

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Ning Hua Zhu

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Li Xian Wang

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