## Theoretical and experimental study on generation of stable and high-quality multi-carrier source based on re-circulating frequency shifter used for Tb/s optical transmission |

Optics Express, Vol. 19, Issue 2, pp. 848-860 (2011)

http://dx.doi.org/10.1364/OE.19.000848

Acrobat PDF (1272 KB)

### Abstract

The generation of stable and high-quality single-sideband (SSB) multi-carrier source based on recirculating frequency shifter (RFS) is analyzed theoretically and realized experimentally. The impact factors originated from the modulator intrinsic imperfections, deviation from the right operation bias voltage, as well as the unbalanced amplitude and phase of the radio frequency (RF) drive signals, have different influences on the output spectrum of the transfer function, which is the decisive factor in generating the high-quality multi-carrier output. Based on the theoretical analysis, the stable and high-quality 50-tone output was successfully realized. The experiments under some implementation imperfections have also been carried out. The imperfect and low-quality output results are in good agreement with the theoretical analysis.

© 2011 OSA

## 1. Introduction

3. G. Gavioli, E. Torrengo, G. Bosco, A. Carena, S. Savory, F. Forghieri, and P. Poggiolini, “Ultra-Narrow-Spacing 10-Channel 1.12 Tb/s D-WDM Long-Haul Transmission Over Uncompensated SMF and NZDSF,” IEEE Photon. Technol. **22**(19), 1419–1421 (2010). [CrossRef]

6. S. Chandrasekhar and X. Liu, “Experimental investigation on the performance of closely spaced multi-carrier PDM-QPSK with digital coherent detection,” Opt. Express **17**(24), 21350–21361 (2009). [CrossRef] [PubMed]

7. X. Liu, D. Gill, S. Chandrasekhar, L. Buhl, M. Earnshaw, M. Cappuzzo, L. Gomez, Y. Chen, F. Klemens, E. Burrows, Y. Chen, and R. Tkach, “Multi-Carrier Coherent Receiver Based on a Shared Optical Hybrid and a Cyclic AWG Array for Terabit/s Optical Transmission,” IEEE Photon. J. **2**(3), 330–337 (2010). [CrossRef]

18. T. Healy, F. Gunning, A. Ellis, and J. Bull, “Multi-wavelength source using low drive-voltage amplitude modulators for optical communications,” Opt. Express **15**(6), 2981–2986 (2007). [CrossRef] [PubMed]

2. G. Gavioli, E. Torrengo, G. Bosco, A. Carena, V. Curri, V. Miot, P. Poggiolini, M. Belmonte, F. Forghieri, C. Muzio, S. Piciaccia, A. Brinciotti, A. Porta, C. Lezzi, S. Savory, S. Abrate, “Investigation of the Impact of Ultra-Narrow Carrier Spacing on the Transmission of a 10-Carrier 1Tb/s Superchannel,” OFC. **OThD3**, (2010).

3. G. Gavioli, E. Torrengo, G. Bosco, A. Carena, S. Savory, F. Forghieri, and P. Poggiolini, “Ultra-Narrow-Spacing 10-Channel 1.12 Tb/s D-WDM Long-Haul Transmission Over Uncompensated SMF and NZDSF,” IEEE Photon. Technol. **22**(19), 1419–1421 (2010). [CrossRef]

13. Y. Ma, Q. Yang, Y. Tang, S. Chen, and W. Shieh, “1-Tb/s single-channel coherent optical OFDM transmission over 600-km SSMF fiber with subwavelength bandwidth access,” Opt. Express **17**(11), 9421–9427 (2009). [CrossRef] [PubMed]

20. Y. Ma, Q. Yang, Y. Tang, S. Chen, and W. Shieh, “1-Tb/s single-channel coherent optical OFDM transmission with orthogonal-band multiplexing and subwavelength bandwidth access,” J. Lightwave Technol. **28**(4), 308–315 (2010). [CrossRef]

21. J. Li, X. Li, X. Zhang, F. Tian, and L. Xi, “Analysis of the stability and optimizing operation of the single-side-band modulator based on re-circulating frequency shifter used for the T-bit/s optical communication transmission,” Opt. Express **18**(17), 17597–17609 (2010). [CrossRef] [PubMed]

22. W. Peng, B. Zhang, X. Wu, K. Feng, A. Willner, and S. Chi, “Compensation for I/Q Imbalances and Bias Deviation of the Mach–Zehnder Modulators in Direct-Detected Optical OFDM Systems,” IEEE Photon. Technol. **21**(2), 103–105 (2009). [CrossRef]

## 2. Theoretical analysis of the impact factors

*S*

_{I}(t),

*S*

_{Q}(t) and

*S*

_{PM}(t) respectively. The phase shifts

*ϕ*

_{I1},

*ϕ*

_{I2},

*ϕ*

_{Q1},

*ϕ*

_{Q2}and

*ϕ*

_{PM}correspond to the upper and lower arms of sub-MZMs and PM, which are induced by corresponding voltages respectively.

21. J. Li, X. Li, X. Zhang, F. Tian, and L. Xi, “Analysis of the stability and optimizing operation of the single-side-band modulator based on re-circulating frequency shifter used for the T-bit/s optical communication transmission,” Opt. Express **18**(17), 17597–17609 (2010). [CrossRef] [PubMed]

*δ*and the voltage amplitude deviations Δ

*V*

_{I}and Δ

*V*

_{Q}which come from the upper and lower arms of each sub-MZM), (ii) the deviation of bias operation voltage, and (iii) the imbalance of RF clock drive signal. We represent the input signal as

*E*

_{in}(t) =

*A*exp(

*j*2π

*f*

_{0}t), operation drive signals as

*S*

_{I}(t) =

*V*

_{bI}+

*V*

_{ppI}cos(2π

*f*

_{m}t),

*S*

_{Q}(t) =

*V*

_{bQ}

*+ V*

_{ppQ}sin(2π

*f*

_{m}t + Δ

*θ*), and

*S*

_{PM}(t) =

*V*

_{bPM}. Assuming a positive frequency shifting process with

*N*+ 1 desired carriers, the generated carriers of the multi-carrier generator can be denoted as

*f*

_{0},

*f*

_{1}, …,

*f*

_{N}. Namely, the desired signal after the first round trip (RT) is

*f*

_{1}whose frequency equals to

*f*

_{0}+

*f*

_{m}, and

*f*

_{N}with its frequency equals to

*f*

_{0}+

*Nf*

_{m}. By considering these impact factors, the normalized transfer function which is defined as the output of multi-carrier source after the first RT can be given bywhere

*ϕ*

_{RT}is the phase delay per RT. The phase differences induced by the phase modulators (PMs) for different arms are shown as follows

*V*

_{πI},

*V*

_{πQ},

*V*

_{πPM}represent the half-wave voltage of Sub-MZM1, Sub-MZM2 and PM respectively. Δ

*V*

_{bI}, Δ

*V*

_{bQ}, Δ

*V*

_{bPM}represent the deviation of DC bias voltage from the right bias operation point, and Δ

*V*

_{m}is the amplitude imbalance between I and Q ports RF drive signals (so

*V*

_{ppQ}=

*V*

_{ppI}+ Δ

*V*

_{m}). In Eq. (2), we can see that there are so many impact factors to affect the output of IQM. Therefore, to achieve a good quality of multi-carrier output, we should apply the parameters properly in practice.

### 2.1 The analysis of the impact of the intrinsic imperfections due to manufacture

*δ*, Δ

*V*

_{I}, Δ

*V*

_{Q}are analyzed and the other parameters such as Δ

*V*

_{bI}, Δ

*V*

_{bQ}, Δ

*V*

_{bPM}, Δ

*V*

_{m}and Δ

*θ*are all equal to zero. Neglecting all the harmonics beyond 3rd-order, then Eq. (1) can be expressed by the Jacobi-Anger expansion with substituting the phase shifts in Eq. (2) where the coefficients of the 0th - to 3rd - order harmonics are as follows

*δ*

_{mI}= (

*πV*

_{ppI})/(2

*V*

_{πI}) =

*δ*

_{mQ}= (

*πV*

_{ppQ})/(2

*V*

_{πQ}) denote the phase modulation depth; Δ

*δ*

_{mI}= (

*π*Δ

*V*

_{I})/(4

*V*), Δ

_{πI}*δ*

_{mQ}= (

*π*Δ

*V*

_{Q})/(4

*V*

_{πQ}) denote the deviation of phase modulation due to intrinsic imperfections of IQM, and

*J*(.) (

_{k}*k*= 0, 1, 2, 3) are the first kind Bessel functions respectively. From Eq. (3) and (4), we can see that the output spectrum after the 1st RT will generate the 0th to 3rd order harmonics which contain all the unwanted crosstalk components

*f*

_{0},

*f*

_{-1},

*f*

_{± 2}, and

*f*

_{± 3}. These crosstalk components will affect the final output of SSB modulator. Therefore, we must lower the power of all the undesired tones to make the power difference between the desired signal and undesired tones as lager as possible. However, there will be still a dominant crosstalk component whose frequency (denoted by

*f*

_{c}briefly, and will be used in the following sections) will be higher or lower than the desired signal

*f*

_{1}, and then affect the final output quality. We can analyze the property of these harmonics in frequency- domain by using Eq. (4). Taking into account the symmetric property of the harmonics in frequency-domain, we can just need to analyze the property of crosstalk component with its frequency higher or lower than

*f*

_{1}after the first RT. Here, we choose the crosstalk components with their frequencies lower than

*f*

_{1}, namely, the crosstalk components will contain

*f*=

_{c}*f*

_{0},

*f*

_{-1},

*f*

_{-2}and

*f*

_{-3}. This choice will also be used and convinced to be appropriate in following sections.

*V*

_{πI}=

*V*

_{πQ}, and the amplitude of RF drive signal

*V*

_{m}is 0.36

*V*

_{πI}, which is equal to the optimum value obtained in [21

21. J. Li, X. Li, X. Zhang, F. Tian, and L. Xi, “Analysis of the stability and optimizing operation of the single-side-band modulator based on re-circulating frequency shifter used for the T-bit/s optical communication transmission,” Opt. Express **18**(17), 17597–17609 (2010). [CrossRef] [PubMed]

*P*

_{i}(i = 0, 1, 2, 3) =

*P*

_{f}_{c}–

*P*

_{f}_{1}represents the normalized power difference between the crosstalk component and desired signal. For instance, Δ

*P*

_{0}=

*P*

_{f}_{0}–

*P*

_{f}_{1}. In Fig. 2(a), we find that only the odd-order harmonics crosstalk appears when Δ

*V*

_{I}= Δ

*V*

_{Q}= 0 which corresponds to the situation of the two arms of each sub-MZM which are balanced. In addition, the symmetric increasing trend as the function of intrinsic loss

*δ*is shown for the crosstalk component

*f*

_{-1}. Compared with Fig. 2(b) and (c), this symmetric increasing trend vs. absolute of

*δ*is maintained while the output spectrum will not contain

*f*

_{-1}as long as (Δ

*V*

_{I}/

*V*

_{πI}) = (Δ

*V*

_{Q}/

*V*

_{πQ}). However, the even-order crosstalk components, especially for

*f*

_{0}, begin to be the dominant factor to affect the output spectrum under the case of less insertion loss, which is the actual operational condition. When (Δ

*V*

_{I}/

*V*

_{πI}) ≠ (Δ

*V*

_{Q}/

*V*

_{πQ}), the component of

*f*

_{-1}will appear (Fig. 2(c)). With the variation of

*δ*from −1 to 1, the crosstalk components

*f*

_{-2}and

*f*

_{-3}keep increasing trends but can be neglected within a little range of

*δ*. To validate the theoretical analysis, the simulation results are shown in the bottom line of Fig. 2 corresponding to the cases which are shown in the top line of Fig. 2. In these figures, the horizontal axis is labeled with

*λ*

_{n}=

*λ*

_{0}+

*n*∆

*λ*, corresponding to

*f*

_{-n}=

*f*

_{0}–

*n*∆

*f*, where

*λ*

_{0}=

*c*/

*f*

_{0}, ∆

*λ*=

*c*∆

*f*/(

*f*

_{0})

^{2}(

*c*is the speed of light). This label will also be used in following sections. The conditions corresponding to the case 1 ~case 3 are Δ

*V*

_{I}/

*V*

_{πI}= Δ

*V*

_{Q}/

*V*

_{πQ}= 0, Δ

*V*

_{I}/

*V*

_{πI}= Δ

*V*

_{Q}/

*V*

_{πQ}= −0.1, and Δ

*V*

_{I}/

*V*

_{πI}= −0.1, Δ

*V*

_{Q}/

*V*

_{πQ}= −0.3 under the same

*δ*= 0 respectively. According to these figures, we can see that the trends of the crosstalk components change are in good agreement with the above theoretical analysis.

### 2.2 The analysis of the impact of bias operation voltage

*V*

_{bI}, Δ

*V*

_{bQ}, Δ

*V*

_{bPM}, with all the other parameters being equal to zero. Under this condition, we obtain the transfer function followed the same way in section 2.1 as follows

*δ*

_{bI}= (

*π*Δ

*V*

_{bI})/(2

*V*

_{πI}), Δ

*δ*

_{bQ}= (

*π*Δ

*V*

_{bQ})/(2

*V*

_{πQ}), and Δ

*δ*

_{PM}= (

*π*Δ

*V*

_{bPM})/(2

*V*

_{πPM}) represent the bias voltage deviations from the right operation voltage respectively. The parameters

*δ*

_{mI}and

*δ*

_{mQ}are the same as defined in section 2.1. From Eq. (5) and (6), we can see clearly that the even-order harmonics appear as long as the bias voltage deviation is not equal to zero. Obviously, to reduce the harmonics crosstalk, we should apply the bias voltage at the right operation voltage as accurate as possible in practice.

*V*

_{bPM}from right bias operation voltage of PM on the output transfer function is shown in the top and bottom lines in Fig. 3 . With the increase of Δ

*V*

_{bPM}from −

*V*

_{πPM}to

*V*

_{πPM}, we can see that, (i) the crosstalk component

*f*

_{0}keeps in decreasing trend and is the dominant component if Δ

*V*

_{bI}and Δ

*V*

_{bQ}are not equal to zero; (ii)

*f*

_{-1}firstly decreases to the minimum value at Δ

*V*

_{bPM}= 0 and then increases with a symmetric property; (iii)

*f*

_{-2}keeps increasing, but

*f*

_{-3}keeps a relative fix value in all cases. In addition, there will be the 1st-order harmonics crosstalk when (Δ

*V*

_{bI}/

*V*

_{πI}) ≠ (Δ

*V*

_{bQ}/

*V*

_{πQ}) even if Δ

*V*

_{bPM}= 0. The simulation results are shown in the bottom line of Fig. 3 corresponding to the cases which are shown in the top line of Fig. 3. The parameters in these figures are: (i) case 1, Δ

*V*

_{bI}/

*V*

_{πI}= Δ

*V*

_{bQ}/

*V*

_{πQ}= −0.1, Δ

*V*

_{bPM}/

*V*

_{πPM}= 0; (ii) case 2, Δ

*V*

_{bI}/

*V*

_{πI}= −0.1; Δ

*V*

_{bQ}/

*V*

_{πQ}= −0.3, Δ

*V*

_{bPM}/

*V*

_{πPM}= 0; (iii) case 3, Δ

*V*

_{bI}/

*V*

_{πI}= Δ

*V*

_{bQ}/

*V*

_{πQ}= −0.1, Δ

*V*

_{bPM}/

*V*

_{πPM}= −0.2; and (iv) case 4, Δ

*V*

_{bI}/

*V*

_{πI}= −0.1; Δ

*V*

_{bQ}/

*V*

_{πQ}= −0.3, Δ

*V*

_{bPM}/

*V*

_{πPM}= −0.2 respectively. Obviously, the trends of the crosstalk components are also in good agreement the above theoretical analysis.

*V*

_{bPM}is at a certain value, the impact curves are shown in Fig. 4(a)–(d) . From (a) and (b), we can see that all crosstalk components give the symmetric properties with the variation of Δ

*V*

_{bI}. Further, to obtain the acceptable deviation value from Fig. 4(a) and (b), the theoretical curves within a small range of [−0.1 0.1]

*V*

_{πI}are shown in Fig. 4(e) and (f) corresponding to these detailed range denoted by the case A and B respectively. In case A,

*f*

_{0}will be the dominant crosstalk component as long as |Δ

*V*

_{bI}| > 0.005

*V*

_{πI}. When |Δ

*V*

_{bI}| < 0.005

*V*

_{πI},

*f*

_{-3}will be the dominant crosstalk component. In addition, to keep the power difference of the dominant crosstalk lower than desired signal around 30dB, the acceptable range of Δ

*V*

_{bI}is only from −0.012

*V*

_{πI}to 0.012

*V*

_{πI}. With the consideration of the symmetric property, Δ

*V*

_{bQ}will be also within in the range of [−0.012 0.012]

*V*

_{πQ}when Δ

*V*

_{bI}= 0. However, when Δ

*V*

_{bQ}is not equal to zero at arbitrary value of Δ

*V*

_{bPM}, the

*f*

_{0}will be the dominant crosstalk component as shown in (c) and (d). In the view of actual implementation, this case will be unacceptable.

### 2.3 Analyzing the impact of the imbalance of RF drive signals

*θ*and ∆

*V*

_{m}are considered. Then the transfer function is expressed as follows

*δ*

_{m}=

*δ*

_{mI}=

*δ*

_{mQ}, Δ

*δ*

_{m}= (

*π∆V*

_{m})/(2

*V*),

_{π}*C*

_{1}= (

*δ*

_{m}+ Δ

*δ*

_{m}) cos(Δ

*θ*),

*C*

_{2}= (

*δ*

_{m}+ Δ

*δ*

_{m}) sin(Δ

*θ*).

*θ*and ∆

*V*

_{m}of RF drive signals on the output transfer function is shown in Fig. 5 . In (a), we can see that there are only the odd-order harmonics in the output spectrum and the power of

*f*

_{-1}and

*f*

_{-3}shows the symmetric variation property vs. the variation of phase deviation ∆

*θ*when ∆

*V*

_{m}= 0. This symmetric property can be deduced from Eq. (8) easily. However, the output property of the crosstalk component with the variation of amplitude deviation ∆

*V*

_{m}is asymmetric as shown in Fig. 5(b) when ∆

*θ*= 0. We can see that the power of

*f*

_{-1}changes much faster when ∆

*V*

_{m}<0 than that when ∆

*V*

_{m}>0. Compared to the above two imbalance situations in Section 2.1 and 2.2, the significant difference here is that the even-order harmonics crosstalk will not appear under the imbalance of two RF signals which can be convinced by Eq. (7). As shown in Fig. 5(c) and (d), to keep the power differences of dominant crosstalk components lower than desired signal

*f*

_{1}round 30dB, ∆

*θ*and ∆

*V*

_{m}should be within the range of [−0.02 0.02]π and [−0.024 0.026]

*V*

_{ppI}respectively.

*V*

_{m}= 0, Δ

*θ*= −0.1π; (ii) case 2, Δ

*V*

_{m}= 0, Δ

*θ*= −0.33π; (iii) case 3, Δ

*V*

_{m}= 0, Δ

*θ*= −0.5π; and (iv) case 4, Δ

*θ*= 0, Δ

*V*

_{m}= −0.2

*V*

_{PPI}; (v) case 5, Δ

*θ*= 0, Δ

*V*

_{m}= −0.72

*V*

_{PPI}; and (vi) case 6, Δ

*θ*= 0, Δ

*V*

_{m}= −0.8

*V*

_{PPI}, respectively. Take case 2 for example, in which ∆

*θ*= −0.33π, the component of

*f*

_{-1}is just a slight lower than of

*f*

_{1}, while

*f*

_{-3}has the lowest value. This simulation result is in good agreement with the above theoretical analysis (Fig. 5(a)). Concurrently, the other simulation results are also coincident with the theoretical analysis under the other different cases.

### 2.4 Analysis of the output stability due to the impact factors

*f*

_{1}in most cases (see the bottom line of Fig. 2 and 3, Fig. 6). Therefore we will only consider the crosstalk components of

*f*

_{c}<

*f*

_{1}. To analyze the impact of the crosstalk components on the final output spectrum, the normalized transfer function shown as in Eq. (1) can be rewritten simply as followswhere

*b*and

*n*

_{0}( = −3, −2, −1, 0) are the normalized coefficient and the order of crosstalk component respectively.

*f*

_{0}and higher than

*f*

_{N}, so the final output of SSB multi-carrier is obtained as follows when

*f*

_{c}<

*f*

_{1}where the normalized crosstalk coefficient

*C*

_{n}can be expressed as follows

*N*-

*n*

_{0}+ 1)-th RT when

*f*

_{c}<

*f*

_{1}. This conclusion has a good agreement with [21

**18**(17), 17597–17609 (2010). [CrossRef] [PubMed]

*n*. The worst-case crosstalk values

*C*

_{max}are |

*Nb*|, |(

*N*−1)

*b*| and |(

*N*−2)

*b*| respectively corresponding to the dominant crosstalk component of the

*f*

_{0},

*f*

_{-}_{1}and

*f*

_{-2}harmonics.

**18**(17), 17597–17609 (2010). [CrossRef] [PubMed]

*P*

_{out}is the saturation power of the OA,

*NF*is the noise figure, and

*L*

_{total}is the total loss containing the losses of coupler, filter, IQM insertion and others. So the effective OSNR of the multi-carrier source can be obtained by combining the above two equations as follows

*P*

_{out},

*NF*,

*L*

_{total},

*N*and |

*b*| are the same, we can see from Eq. (12)–(14) that the effective OSNR for the different cases will be little different even if the dominant crosstalk component originated from different harmonics (

*N*is large and fixed,

*n*

_{0}is small and different).

*f*

_{0}and

*f*

_{-1}will be the dominant crosstalk components to affect the entire multi-carrier output quality under the implementation imperfections. To study their influence on the entire output, the simulation results are shown in Fig. 7 and Fig. 8 respectively. In Fig. 7(a),

*f*

_{0}(

*λ*

_{0}in wavelength) is the dominant crosstalk component whose power is about 25dB lower than

*f*

_{1}. With the assumption of the total desired carriers number is 50, we can see from Fig. 7(b) that the last tone will undergo the maximum crosstalk in the final output spectrum of multi-carrier source. However, when the

*f*

_{-1}(

*λ*

_{1}) turns out to be the dominant harmonic as shown in Fig. 8(a), the last two tones will undergo the maximum crosstalk from Fig. 8(b). Again, these simulation results are in good agreement with the Eq. (10) and (11).

## 3. Experimental setup and results

*λ*

_{0}= 1549.9nm (

*f*

_{0}= 193.425THz), the bandwidth of optical band-pass filter is set to 5nm, and the frequency of clock drive signal is 12.5GHz. In addition, the saturation output power of Raman amplifier is 27dBm, and the insertion loss of our IQM, filter and coupler are about 13dB, 3dB, and 4dB respectively. In order to achieve the good performance, we use two microwave power amplifiers to amplify the amplitude of I- and Q- ports RF drive signals independently, and use two power attenuators to make them be balanced.

*f*

_{1}(

*λ*

_{-1}) and

*f*

_{0}(

*λ*

_{0}) is around 25dB. Under the appropriate adjusting, the flat and stable 50-tone multi-carrier output with the spacing of 12.5GHz, which the total bandwidth is 5nm, is successfully achieved as shown in Fig. 9(b). We can see that the last tone (as marked with

*f*

_{49}in the red circle) indeed undergoes the maximum crosstalk as analyzed in Section 2.4 and shown in Fig. 7(b), and the effective OSNR of the last tone is around 20dB.

*V*

_{bI}= 0.1V; (b) ∆

*V*

_{bI}= 0.3V; (c) ∆

*V*

_{bI}= 0.5V; (d) ∆

*V*

_{bI}= −0.2V; and (e) ∆

*V*

_{bI}= −0.4V; (f) ∆

*V*

_{bI}= −0.6V. Insert (g) shows the experimental data of the maximum output power difference among the carriers with the variation of ∆

*V*

_{bI}. Obviously, this experimental result shows the approximately symmetric property which is again in a good agreement with the above analysis in Fig. 4(a).

*P*

_{m}= 0.5dB; (b) ∆

*P*

_{m}= 1dB; (c) ∆

*P*

_{m}= 1.5dB; and (d) ∆

*P*

_{m}= −0.5dB; (e) ∆

*P*

_{m}= −1dB; (f) ∆

*P*

_{m}= −1.5dB respectively. With the comparison of the figures in the top and bottom lines in Fig. 12 , we can see that the entire output deteriorates much faster with the increasing of ∆

*P*

_{m}in the range of negative (∆

*V*

_{m}< 0) than that in positive values (∆

*V*

_{m}> 0). This experimental result is still in good agreement with the theoretical analysis in Fig. 5(b).

*θ*on the entire output of the multi-carrier source. The parameters used in the figure are as follows, (a) ∆

*θ*= −π/4; (b) ∆

*θ*= −π/2; (c) ∆

*θ*= π/4; (d) ∆

*θ*= π/2. We can see that the output performance goes worse with the increasing of ∆

*θ*. However, the variation of ∆

*θ*will be within the period of π with considering the periodicity of trigonometric function. Furthermore, the output of multi-carrier generated indeed shows the symmetric property just as shown in Fig. 5(a).

## 5. Conclusions

*f*

_{0}will be the dominant crosstalk component under the intrinsic imperfections of IQM (which we cannot control) and DC bias imbalances. On the other hand,

*f*

_{-1}will be just the dominant crosstalk component when the two RF drive signals have some imbalance. The entire output stability of the multi-carrier generator has been analyzed with different dominant crosstalk component. The experimental results are in good agreement with the theoretical results. The theoretical and experimental results may provide a useful guide for achieving the high-quality of the SSB-based RFS multi-carrier source for Tb/s multi-carrier transmission in practice.

## Acknowledgements

## References and links

1. | A. Ellis, F. Gunning, B. Cuenot, T. Healy, E. Pincemin, “Towards 1TbE using coherent WDM,” OECC. |

2. | G. Gavioli, E. Torrengo, G. Bosco, A. Carena, V. Curri, V. Miot, P. Poggiolini, M. Belmonte, F. Forghieri, C. Muzio, S. Piciaccia, A. Brinciotti, A. Porta, C. Lezzi, S. Savory, S. Abrate, “Investigation of the Impact of Ultra-Narrow Carrier Spacing on the Transmission of a 10-Carrier 1Tb/s Superchannel,” OFC. |

3. | G. Gavioli, E. Torrengo, G. Bosco, A. Carena, S. Savory, F. Forghieri, and P. Poggiolini, “Ultra-Narrow-Spacing 10-Channel 1.12 Tb/s D-WDM Long-Haul Transmission Over Uncompensated SMF and NZDSF,” IEEE Photon. Technol. |

4. | X. Zhou, J. Yu, M. Huang, Y. Shao, T. Wang, P. Magill, M. Cvijetic, L. Nelson, M. Birk, G. Zhang, S. Ten, H. Matthew, and S. Mishra, “32Tb/s (320 × 114Gb/s) PDM-RZ-8QAM transmission over 580km of SMF-28 ultra-low-loss fiber”. OFC. |

5. | J. Yu, X. Zhou, and M. Huang, “High-Speed PDM-RZ-8QAM DWDM Transmission (160 × 114 Gb/s) Over 640 km of Standard Single-Mode Fiber,” IEEE Photon. Technol. |

6. | S. Chandrasekhar and X. Liu, “Experimental investigation on the performance of closely spaced multi-carrier PDM-QPSK with digital coherent detection,” Opt. Express |

7. | X. Liu, D. Gill, S. Chandrasekhar, L. Buhl, M. Earnshaw, M. Cappuzzo, L. Gomez, Y. Chen, F. Klemens, E. Burrows, Y. Chen, and R. Tkach, “Multi-Carrier Coherent Receiver Based on a Shared Optical Hybrid and a Cyclic AWG Array for Terabit/s Optical Transmission,” IEEE Photon. J. |

8. | R. Dischler, F. Buchali, “Transmission of 1.2 Tb/s Continuous Waveband PDM-OFDM-FDM signal with Spectral Efficiency of 3.3 bit/s/Hz over 400 km of SSMF,” OFC. |

9. | H. Masuda, E. Yamazaki, A. Sano, T. Yoshimatsu, T. Kobayashi, E. Yoshida, Y. Miyamoto, S. Matsuoka, Y. Takatori, M. Mizoguchi, K. Okada, K. Hagimoto, T. Yamada, S. Kamei, “13.5-Tb/s (135 × 111-Gb/s/ch) No-Guard-Interval Coherent OFDM Transmission over 6,248 km using SNR Maximized Second-order DRA in the Extended L-band,” OFC. |

10. | Y. Tang and W. Shieh, “Coherent Optical OFDM Transmission Up to 1 Tb/s per Channel,” J. Lightwave Technol. |

11. | S. Chandrasekhar, X. Liu, “Terabit superchannels for high spectral efficiency transmission,” ECOC. |

12. | Y. Ma, Q. Yang, Y. Tang, S. Chen, W. Shieh, “1-Tb/s per Channel Coherent Optical OFDM Transmission with Subwavelength Bandwidth Access,” OFC. |

13. | Y. Ma, Q. Yang, Y. Tang, S. Chen, and W. Shieh, “1-Tb/s single-channel coherent optical OFDM transmission over 600-km SSMF fiber with subwavelength bandwidth access,” Opt. Express |

14. | S. Chandrasekhar, X. Liu, B. Zhu, D. Peckham, “Transmission of a 1.2-Tb/s 24-Carrier No-Guard-Interval Coherent OFDM Superchannel over 7200-km of Ultra-Large-Area Fiber,” ECOC. |

15. | B. Zhu, X. Liu, S. Chandrasekhar, D. Peckham, and R. Lingle, “Ultra-Long-Haul Transmission of 1.2-Tb/s Multicarrier No-Guard-Interval CO-OFDM Superchannel Using Ultra-Large-Area Fiber,” IEEE Photon. Technol. |

16. | X. Liu, S. Chandrasekhar, B. Zhu, D. Peckham, “Efficient Digital Coherent Detection of A 1.2-Tb/s 24-Carrier No-Guard-Interval CO-OFDM Signal by Simultaneously Detecting Multiple Carriers Per Sampling,” OFC. |

17. | S. Chen, Y. Ma, W. Shieh, “110-Gb/s Multi-band Real-time Coherent Optical OFDM Reception after 600-km Transmission over SSMF Fiber”. OFC. |

18. | T. Healy, F. Gunning, A. Ellis, and J. Bull, “Multi-wavelength source using low drive-voltage amplitude modulators for optical communications,” Opt. Express |

19. | R. Maher, P. Anandarajah, S. Ibrahim, L. Barry, A. Ellis, P. Perry, R. Phelan, B. Kelly, and J. Gorman, “Low Cost Comb Source in a Coherent Wavelength Division Multiplexed System” ECOC. |

20. | Y. Ma, Q. Yang, Y. Tang, S. Chen, and W. Shieh, “1-Tb/s single-channel coherent optical OFDM transmission with orthogonal-band multiplexing and subwavelength bandwidth access,” J. Lightwave Technol. |

21. | J. Li, X. Li, X. Zhang, F. Tian, and L. Xi, “Analysis of the stability and optimizing operation of the single-side-band modulator based on re-circulating frequency shifter used for the T-bit/s optical communication transmission,” Opt. Express |

22. | W. Peng, B. Zhang, X. Wu, K. Feng, A. Willner, and S. Chi, “Compensation for I/Q Imbalances and Bias Deviation of the Mach–Zehnder Modulators in Direct-Detected Optical OFDM Systems,” IEEE Photon. Technol. |

**OCIS Codes**

(060.2330) Fiber optics and optical communications : Fiber optics communications

(060.2630) Fiber optics and optical communications : Frequency modulation

(230.2090) Optical devices : Electro-optical devices

**ToC Category:**

Fiber Optics and Optical Communications

**History**

Original Manuscript: October 25, 2010

Revised Manuscript: December 7, 2010

Manuscript Accepted: December 7, 2010

Published: January 6, 2011

**Citation**

Jianping Li, Xiaoguang Zhang, Feng Tian, and Lixia Xi, "Theoretical and experimental study on generation of stable and high-quality multi-carrier source based on re-circulating frequency shifter used for Tb/s optical transmission," Opt. Express **19**, 848-860 (2011)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-2-848

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### References

- A. Ellis, F. Gunning, B. Cuenot, T. Healy, and E. Pincemin, “Towards 1TbE using coherent WDM,” OECC. WeA-1, (2008).
- G. Gavioli, E. Torrengo, G. Bosco, A. Carena, V. Curri, V. Miot, P. Poggiolini, M. Belmonte, F. Forghieri, C. Muzio, S. Piciaccia, A. Brinciotti, A. Porta, C. Lezzi, S. Savory, and S. Abrate, “Investigation of the Impact of Ultra-Narrow Carrier Spacing on the Transmission of a 10-Carrier 1Tb/s Superchannel,” OFC. OThD3, (2010).
- G. Gavioli, E. Torrengo, G. Bosco, A. Carena, S. Savory, F. Forghieri, and P. Poggiolini, “Ultra-Narrow-Spacing 10-Channel 1.12 Tb/s D-WDM Long-Haul Transmission Over Uncompensated SMF and NZDSF,” IEEE Photon. Technol. 22(19), 1419–1421 (2010). [CrossRef]
- X. Zhou, J. Yu, M. Huang, Y. Shao, T. Wang, P. Magill, M. Cvijetic, L. Nelson, M. Birk, G. Zhang, S. Ten, H. Matthew, and S. Mishra, “32Tb/s (320 × 114Gb/s) PDM-RZ-8QAM transmission over 580km of SMF-28 ultra-low-loss fiber”. OFC. PDPB4, (2009).
- J. Yu, X. Zhou and M. Huang, “High-Speed PDM-RZ-8QAM DWDM Transmission (160 × 114 Gb/s) Over 640 km of Standard Single-Mode Fiber,” IEEE Photon. Technol. 21(18), 1299–1301 (2009). [CrossRef]
- S. Chandrasekhar and X. Liu, “Experimental investigation on the performance of closely spaced multi-carrier PDM-QPSK with digital coherent detection,” Opt. Express 17(24), 21350–21361 (2009). [CrossRef] [PubMed]
- X. Liu, D. Gill, S. Chandrasekhar, L. Buhl, M. Earnshaw, M. Cappuzzo, L. Gomez, Y. Chen, F. Klemens, E. Burrows, Y. Chen, and R. Tkach, “Multi-Carrier Coherent Receiver Based on a Shared Optical Hybrid and a Cyclic AWG Array for Terabit/s Optical Transmission,” IEEE Photon. J. 2(3), 330–337 (2010). [CrossRef]
- R. Dischler and F. Buchali, “Transmission of 1.2 Tb/s Continuous Waveband PDM-OFDM-FDM signal with Spectral Efficiency of 3.3 bit/s/Hz over 400 km of SSMF,” OFC. PDPC2, (2009).
- H. Masuda, E. Yamazaki, A. Sano, T. Yoshimatsu, T. Kobayashi, E. Yoshida, Y. Miyamoto, S. Matsuoka, Y. Takatori, M. Mizoguchi, K. Okada, K. Hagimoto, T. Yamada, and S. Kamei, “13.5-Tb/s (135 × 111-Gb/s/ch) No-Guard-Interval Coherent OFDM Transmission over 6,248 km using SNR Maximized Second-order DRA in the Extended L-band,” OFC. PDPB5, (2009).
- Y. Tang and W. Shieh, “Coherent Optical OFDM Transmission Up to 1 Tb/s per Channel,” J. Lightwave Technol. 27(16), 3511–3517 (2009). [CrossRef]
- S. Chandrasekhar and X. Liu, “Terabit superchannels for high spectral efficiency transmission,” ECOC. Tu.3.C.5, (2010).
- Y. Ma, Q. Yang, Y. Tang, S. Chen, and W. Shieh, “1-Tb/s per Channel Coherent Optical OFDM Transmission with Subwavelength Bandwidth Access,” OFC. PDPC1, (2009).
- Y. Ma, Q. Yang, Y. Tang, S. Chen, and W. Shieh, “1-Tb/s single-channel coherent optical OFDM transmission over 600-km SSMF fiber with subwavelength bandwidth access,” Opt. Express 17(11), 9421–9427 (2009). [CrossRef] [PubMed]
- S. Chandrasekhar, X. Liu, B. Zhu, and D. Peckham, “Transmission of a 1.2-Tb/s 24-Carrier No-Guard-Interval Coherent OFDM Superchannel over 7200-km of Ultra-Large-Area Fiber,” ECOC. PD2.6, (2009).
- B. Zhu, X. Liu, S. Chandrasekhar, D. Peckham, and R. Lingle, “Ultra-Long-Haul Transmission of 1.2-Tb/s Multicarrier No-Guard-Interval CO-OFDM Superchannel Using Ultra-Large-Area Fiber,” IEEE Photon. Technol. 22(11), 826–828 (2010). [CrossRef]
- X. Liu, S. Chandrasekhar, B. Zhu, and D. Peckham, “Efficient Digital Coherent Detection of A 1.2-Tb/s 24-Carrier No-Guard-Interval CO-OFDM Signal by Simultaneously Detecting Multiple Carriers Per Sampling,” OFC. OWO2, (2010).
- S. Chen, Y. Ma, and W. Shieh, “110-Gb/s Multi-band Real-time Coherent Optical OFDM Reception after 600-km Transmission over SSMF Fiber”. OFC. OMS2, (2010).
- T. Healy, F. Gunning, A. Ellis, and J. Bull, “Multi-wavelength source using low drive-voltage amplitude modulators for optical communications,” Opt. Express 15(6), 2981–2986 (2007). [CrossRef] [PubMed]
- R. Maher, P. Anandarajah, S. Ibrahim, L. Barry, A. Ellis, P. Perry, R. Phelan, B. Kelly, and J. Gorman, “Low Cost Comb Source in a Coherent Wavelength Division Multiplexed System” ECOC. P3.07, (2010).
- Y. Ma, Q. Yang, Y. Tang, S. Chen, and W. Shieh, “1-Tb/s single-channel coherent optical OFDM transmission with orthogonal-band multiplexing and subwavelength bandwidth access,” J. Lightwave Technol. 28(4), 308–315 (2010). [CrossRef]
- J. Li, X. Li, X. Zhang, F. Tian, and L. Xi, “Analysis of the stability and optimizing operation of the single-side-band modulator based on re-circulating frequency shifter used for the T-bit/s optical communication transmission,” Opt. Express 18(17), 17597–17609 (2010). [CrossRef] [PubMed]
- W. Peng, B. Zhang, X. Wu, K. Feng, A. Willner, and S. Chi, “Compensation for I/Q Imbalances and Bias Deviation of the Mach–Zehnder Modulators in Direct-Detected Optical OFDM Systems,” IEEE Photon. Technol. 21(2), 103–105 (2009). [CrossRef]

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