We present a technique using a dual-output Mach-Zehnder modulator (MZM) with two wavelength inputs, one operating at low-bias and the other operating at high-bias, in order to cancel unwanted even-order harmonics in analog optical links. By using a dual-output MZM, this technique allows for two suppressed optical carriers to be transmitted to the receiver. Combined with optical amplification and balanced differential detection, the RF power of the fundamental is increased by 2 dB while the even-order harmonic is reduced by 47 dB, simultaneously. The RF noise figure and third-order spurious-free dynamic range (SFDR3) are improved by 5.4 dB and 3.6 dB, respectively. Using a wavelength sensitive, low Vπ MZM allows the two wavelengths to be within 5.5 nm of each other for a frequency band from 10 MHz to 100 MHz and 10 nm for 1 GHz.
©2009 Optical Society of America
Analog fiber optic links are used in various applications including antenna remoting  and delay lines . Most of these links use a Mach-Zehnder intensity modulator (MZM) to impose an RF signal on a single optical carrier. The MZM is quadrature-biased as it adds no even-order distortion to the RF signal. The modulated optical signal is then amplified and passed down the optical fiber link. Finally the RF signal is recovered by direct detection at a photodiode. Since the various analog metrics improve with increased photocurrent, the amplifier is necessary to maximize the optical power reaching the photodiode. Unfortunately, the nonlinear Stimulated Brillouin Scattering (SBS) effect limits the amount of optical power that can enter the fiber. One method to increase the SBS threshold is to suppress the optical carrier by low-biasing the MZM . Much work has been done on analyzing low-biased MZM links as they are simple to implement [4,5]. In addition to improving the SBS threshold, the use of a high power laser with a low-biased MZM has been shown to improve the RF noise figure of an analog link . However, the previous works have not considered the benefits of post-modulator amplification for low-biased MZM links. Beyond simply increasing the optical power at the photodiode, recent work has shown that a low-biased MZM followed by optical amplification increases the RF gain of an analog link [7,8]. While the various low-biased MZM techniques have been shown to improve the RF performance of fiber-optic analog links, they have a serious disadvantage when compared to quadrature-biased MZM links. The even-order harmonics become quite large and limit the use of low-biased MZMs to single-octave applications. Some techniques have been shown to reduce the even-order harmonics due to biasing the MZM off-quadrature. One demonstration used two separate MZMs in order to cancel the unwanted harmonics . However this method requires the RF signal be split to two MZMs which results in higher loss for the RF signal. An easier method is to input two optical carriers at different wavelengths through a single MZM. The use of two optical carriers has been shown to linearize unwanted harmonics in a fiber link . Unfortunately the linearization process reduces the RF power of the fundamental while reducing the harmonic, as well as requiring over 200 nm of separation in the wavelengths of the two optical carriers. Another technique cancels the even-order harmonics by low-biasing two wavelengths on either side of the null of the bias curve with a single output MZM . However this method does not demonstrate an improvement in the RF metrics from low-biasing the wavelengths. An alternative to operating on either side of the null is to operate each wavelength on either side of the quadrature bias point. By using a dual-output MZM, each wavelength can then be low-biased at their respective output. Combining the low-bias outputs through an optical amplifier can simultaneously improve the various RF metrics as compared to a quadrature-biased MZM through the same optical amplifier. This paper describes the theory and experimental demonstration for using a dual-output MZM with two wavelength inputs that cancels the even-order harmonics. In addition, when the proper bias point is chose, the various RF metrics are measured and shown to improve when compared to a quadrature-biased MZM operating under the same conditions. Finally a theoretical analysis is used to match the measured increase in RF gain for two low-biased wavelengths as compared to a single low-biased wavelength.
2. Theory of operation
It is important to define some operating bias points of the MZM before going into detail of the operation of the technique. An ideal MZM has a sinusoidal output power transfer curve as a function of DC phase shift, as shown in Fig. 1(a) . There are a few operating points along the transfer curve that are worth noting. The first is the quadrature-bias point which is at a DC phase shift of π/2 or -π/2 and lies at the point where the output power is half the maximum output power. The maximum output power is denoted as a transmittance of 1 in Fig. 1(a). The null-bias point is the one at which the DC phase shift is 0 and the output power is 0. The max-bias point is the one at which the DC phase shift is π or - π and the output power is maximum. The high-bias point, φ dc-high-bias, is slightly lower than the max-bias point as shown in Fig. 1(a). The low-bias point, φ dc-low-bias, is slightly higher than the null-bias point as also shown in Fig. 1(a). Note that the transfer function shown in Fig. 1(a) is for one output of the MZM. The transfer function of the second output of the MZM has a complementary relation to the first output as a function of DC phase shift as shown in Fig. 1(b). For example, the low-bias point for the first output will be at the high-bias point on the second output and vice-versa. By wavelength multiplexing the low-biased output from one arm and the complementary low-biased output from the other arm, one can transmit two suppressed carrier wavelengths from the dual-output MZM. In order to exploit the dual-output symmetry, we need to use two wavelengths in order to achieve the simultaneous high-bias and low-bias from one output for a given DC phase shift.
Since most MZMs have a bias voltage dependence on wavelength , the transfer curve of the modulator as a function of DC bias voltage varies for different wavelength inputs. Specifically the transfer curve will shift as a function of wavelength as shown in Fig. 2 . By correctly choosing the two wavelengths and the DC bias, the first wavelength will operate at the high-bias point of its transfer curve while the second will operate at the low-bias point of its transfer curve at one output of the MZM as illustrated in Fig. 2. In general, the required wavelength separation is dependent on the wavelength sensitivity and Vπ of the MZM, with the lower the Vπ of the MZM, the lower the wavelength separation. In order to determine the DC phase relationship between wavelengths to cancel the even-order harmonics, we turn to the analysis of the received photocurrents.
We have previously derived and experimentally validated the photocurrent as a function of phase shift due to the DC bias from a single output MZM . Since the second output of the MZM is the complement of the first, extending the general equation for the photocurrent from a dual-output MZM yields the following,Eq. (1), we can see that each line represents a different component to the overall photocurrent. Line 1 is the expression for the DC photocurrent. Line 2 represents the components due to the odd-harmonics, which includes the fundamental. Line 3 represents the components due to the even-order harmonics. In order for the cancellation to work we tune the wavelength of λ2 with relation to λ1 such that the following DC phase shift relation is metEq. (3) into Eq. (2) and then subtract Eq. (2) from Eq. (1), we get the following
3. Experimental demonstration
The experimental apparatus for demonstration of the even-order harmonic cancellation appears in Fig. 3 . In this architecture, two lasers, each with a different operating wavelength,are combined into one input of a dual-output MZM. The MZM has a Vπ of 0.9 V at 10 MHz and 1.2 V at 1 GHz. The MZM has a reflector at one end which passes the optical wave through the waveguide twice. Such a configuration reduces the Vπ, by effectively doubling the interaction length. This configuration also makes the phase bias highly sensitive to wavelength, due to the high dispersion of the dielectric mirror used as a reflector in the MZM. Typically most MZMs are designed to have as small a wavelength sensitivity as possible so that they can work in traditional WDM networks. In this case, it is the wavelength sensitivity of this MZM that is exploited in order to make this system work with small wavelength separation. As shown in Fig. 3, one of the outputs, λ1, is low-biased while λ2 is high-biased; at the other output λ2 is low-biased while λ1 is high-biased. Note that the colors are consistent with Fig. 2, with green and brown representing the wavelength sensitive transfer curve of the MZM at each output. Each of the outputs of the MZM is then combined through a wavelength multiplexer that passes the low-biased wavelength and filters out the high-biased wavelength of each output. The two filtered low-biased wavelengths then pass through an optical amplifier. The optical amplifier is fed to a fiber optic link that is connected to a wavelength demultiplexer. The separated wavelengths are each sent to a balanced photodiode. The electronic output of the balanced photodiode yields the final RF signal.
In order to improve the RF metrics for this setup, the phase bias φdc has to be determined. By moving the bias lower than quadrature, the RF gain can be improved as it moves the EDFA out of saturation [7,8]. However moving the EDFA out of saturation raises the noise floor, which degrades the RF noise figure and linearity . Therefore a careful balancing act must be considered when moving away from quadrature. The RF gain should be increased while the noise floor from the EDFA is not increased enough to negate the RF gain improvement. For the EDFA and MZM used in our system, the difference between RF gain and EDFA noise floor is maximized for a reference wavelength of 1550.1 nm at a phase bias φdc of 0.29π, which occurs at a DC bias of 2.12 V. Beyond this point the noise floor degrades faster than the RF gain increases, so this is the ideal phase bias to improve the RF metrics. 1550.1 nm is chosen as the reference wavelength due to the filters used in the system. Now the second wavelength is tuned from 1550.1 nm until transmitted power is at the appropriate high bias point determined by Eq. (3) for the same DC bias. For an RF input of 10 MHz, the second wavelength of 1555.6 nm meets this condition. As shown in Fig. 4 , the measured power transfer curves for the two wavelengths demonstrates that the modulator high-biases the 1555.6 nm input while simultaneously low-biasing the 1550.1 nm input. This appears at one of the outputs of the MZM. At the other output the 1550.1 nm input is high-biased and the 1555.6 nm input is low-biased. By using the MUX after the MZM, the two low-biased outputs can be combined and passed to the EDFA. As a comparison, for the same MZM, using the single output method described in Ref. 11 requires a wavelength difference of 8 nm to achieve the required phase bias φdc of 0.29π. While this result at first appears to be counter-intuitive, a closer examination reveals that the dual output MZM can have an advantage over the single output MZM when the required bias point is taken into account.
3.1 Comparison of single output MZM versus dual output MZM
In order to compare the single output MZM technique to the dual output MZM technique, we begin by looking at the transmission curve curves for the two MZMs. For a single output MZM, the transfer function can be written as 0.5*(1 + cos(φdc)). Figure 5(a) shows the transfer function for a single output MZM as a function of phase bias from 0 to 2π. The dual output MZM has the same transfer function for one output and the complementary output for the other arm, which is written as 0.5*(1-cos(φdc)). Figure 5(b) shows the two transfer curves for the dual output MZM, with one output in red and other in blue. The two curves cross at φdc = π/2, with one output having a positive slope and the other having a negative slope. Now a second wavelength can be added to the MZM which will provide a shift in the transfer curve relative to the reference curve. Mathematically the function will have the form of 0.5*(1-cos(φdc-φΔλ)), where φΔλ is the phase difference between the transfer curves and is directly related to the difference in the reference wavelength and the second wavelength. In other words, as the difference in the reference wavelength and the second wavelength increases, the φΔλ increases. In order to improve all of the RF metrics, the transmission point where the two curves intersect has to be at 0.5*(1-cos(0.29π)) = 0.193. Figure 6(b) shows a φΔλ of 0.42π is required for the two transfer curves from the dual output MZM to cross at 0.193. In Fig. 6(a)the single output MZM curves cross at 0.105 for a φΔλ of 0.42π, which translates to a phase bias φdc of 0.21π. Thus the single output MZM requires a larger φΔλ in order to cross at the required phase bias φdc of 0.29π. This in turn means a larger wavelength separation is required for the single output MZM technique. As a final point of comparison, the two methods will meet when φΔλ is 0.5π. As shown in Figs. 7(a) and 7(b), both sets of curves cross at a transmission of 0.146, which is a phase bias φdc of 0.25π. The conclusion is that the dual MZM method will require a smaller wavelength separation for phase bias φdc greater than 0.25π and the single MZM method will require a smaller wavelength separation for phase bias φdc less than 0.25π. The optimal phase bias point for improving the RF metrics depends strongly on the Vπ of the MZM and the small signal gain and saturated output power of the EDFA. Thus the preferred method is application dependent as well as device dependent. For this setup, with the current devices, the dual output MZM requires a smaller wavelength separation when compared the single output MZM in order to improve the RF metrics.
3.2 Measurement of RF power of fundamental and second harmonic and improvement in RF metrics compared to quadrature-biased MZM
Now that the wavelength and DC bias point have been determined, the fundamental and second harmonic results are measured. Figure 8(a) shows the RF power for an input tone at 10 MHz. The fundamental RF power is measured at the point that the even-order cancellation is strongest. The curves in black and blue are the RF power of the fundamental when only onewavelength input is on. The RF power for the two wavelength case is ~2 dB higher than the single wavelength case as shown in red. Figure 8(b) shows the cancellation of the second- order harmonic at 20 MHz for an input RF tone of 10 MHz. Again, the curves in black and blue are the RF power of the second-order harmonics when only one wavelength input is on. When both wavelength inputs are on, the second-order harmonic is cancelled by 47 dB, as shown in red. The cancellation is limited by the second harmonic of the measurement system. To verify this, the second harmonic is measured for a single laser when the MZM is quadrature-biased. Under these conditions, the measured second harmonic for a 10 MHz signal is limited to −82 dBm, which matches with the second harmonic of the dual wavelength system.
In order to see if this system is third-order limited, a spurious-free dynamic range (SFDR) measurement is made. The results appear in Fig. 9 . In this case, the SFDR3H is 100.6 dB∙Hz2/3 while the SFDR2H is 102.6 dB∙Hz1/2, again limited by the second harmonic generated by the signal generator. Note that these are measured in terms of the second and third harmonic. In order to translate these into the more traditional two-tone intermodulation distortion, a correction factor of −3.0 dB and −3.1 dB must be applied to the second and third harmonic SFDR, respectively . This yields a SFDR3 of 97.5 dB and a SFDR2 of 99.6 dB in 1 Hz bandwidth. Thus the system is third-order limited for this cancellation. For a measured noise floor of −147 dBm/Hz, the RF noise figure for this link is 39 dB. When compared to a quadrature-biased link operating at the same photocurrent, the RF gain is 9 dB higher. The quadrature-biased link has a noise floor of −150.6 dBm/Hz, which comes from the fact that the strong carrier of a quadrature biased signal saturates the EDFA and lowers the noise floor . Since the RF gain improvement is much higher than the increase in the noise floor of the link (9 dB versus 3.6 dB), the RF noise figure and the SFDR3 will improve. In fact, in this case, the RF noise figure of this link is 5.4 dB better than the quadrature-biased link and the SFDR3 is 3.6 dB better than the quadrature-biased link.
In order to demonstrate the multi-octave operation of this link, the RF frequency is increased to 100 MHz while the wavelengths are kept the same. Since the Vπ of the MZM is flat over this frequency range, the second harmonic cancellation is expected to be the same as in the 10 MHz case. The fundamental and the second harmonic are measured and the results are shown in Figs. 10(a) and 10(b), respectively. Figure 10(a) again shows the same 2 dB improvement in the RF gain for the fundamental at 100 MHz. However, Fig. 10(b) demonstrates the power of the second harmonic at 200 MHz is down to only −79 dBm. At this operating point, the SFDR2 is 98 dB∙Hz1/2. Since the RF gain and the noise floor of the system is the same as in the 10 MHz case, the SFDR3 is still 97.5 dB∙Hz2/3. This is the highest RF frequency that the system can operate at for the same wavelength and still be third-order limited. The operating range of 10 MHz to 100 MHz covers more than three octaves and demonstrates the multi-octave operation of the link.
Finally in order to demonstrate the wide operational bandwidth of the system, the same measurement was made for an input RF tone of 1 GHz. Since the Vπ is larger for 1 GHz than at 10 MHz, the wavelengths had to be reset. In order to get the correct bias, the wavelengths are now set to 1550.1 nm and 1559.8 nm. Again the second-order harmonic and fundamentals are measured. Figure 11(a) shows an improvement in the fundamental of 1.8 dB over the individual lasers, while Fig. 11(b) demonstrated that the second harmonic at 2 GHz is reduced by ~40 dB. The second harmonic of the measurement system limits the cancellation of the second harmonic power to −85 dBm for a 1 GHz signal. Note that the fundamentals of the individual lasers are about 1 dB different. This is due to the fact that the gain of the EDFA is slightly different at the two wavelengths.
In all of these cases, it is not clear why the fundamentals are not 6 dB higher when both lasers are on as compared to the individual lasers as predicted by our above calculations. In order to answer this discrepancy we have to look at the output power of a low-biased MZM with two wavelength inputs.
4. Improvement in RF gain due to dual wavelengths
We would now like to see how the RF power of the fundamental for two wavelengths compares to the RF power of a single optical wavelength as it is low-biased. Beginning with the general expression for the RF power of a single wavelength as a function of DC bias phase shift ,Eq. (6) is we have twice the optical power coming from the MZM. Since the optical power after the EDFA is then split equally to each of the photodiodes, we can now write the difference in photocurrents asEq. (8) into Eq. (5) yields the following RF output powerTable 1 contains the experimental parameters for the theoretical curves plotted in Fig. 12 .
From Fig. 12, a couple of interesting points can be observed. First, the maximum RF gain occurs at a different DC bias phase shift for a single wavelength than for the two wavelength case. Second, the RF gain does not increase by 3 dB over the entire phase shift region. In fact it varies from 0.33 dB to 3 dB. Thus, the RF gain improvement is not simply described and depends on where the initial RF gain was optimized. In this technique, the RF gain was optimized for one wavelength and then the second wavelength was added to cancel the second harmonic. Looking at the point where RF gain is maximized for the single wavelength in Fig. 12, the increase in RF power is only ~2 dB for dual wavelengths, which matches the measurements in Figs. 8(a), 10(a) and 11(a).
We have theoretically and experimentally demonstrated a method to cancel unwanted even-order harmonics for off-quadrature biased dual output MZM by using two optical carriers. Making use of a wavelength sensitive, low Vπ Mach-Zehnder modulator, two optical wavelengths are passed through the MZM in order to high-bias one while the other is low-biased. Combined with the complementary nature of the two outputs of an MZM, two low-biased optical carriers are transmitted out of the MZM through an optical amplifier to a balanced photodiode in order to increase the RF metrics while canceling the second harmonic. The second harmonic of the dual wavelength system is reduced by 47 dB compared to a single low-biased wavelength, enough to make the system third-order limited. All of the RF metrics are improved when compared to a quadrature-biased wavelength with the same amplifier; the RF gain and SFDR3 are increased by 9 dB and 3.6 dB, respectively, while the RF noise figure is reduced by 5.4 dB. The system is shown to work over three octaves (from 10 MHz to 100 MHz) for the same wavelength shift of 5.5 nm. The system also cancels second harmonic with a wavelength separation of 10 nm for an RF signal of 1 GHz. Finally, the gain dynamics in the EDFA explain why the RF gain improves by only 2 dB for the fundamental as compared to the 6 dB predicted by the initial theory. This technique has uses for multi-octave analog fiber links in the HF and VHF frequency bands that require improved RF metrics with suppressed optical carriers.
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