Optical millimeter wave generated by octupling the frequency of the local oscillator

Vol. 7, No. 10 / October 2008 / JOURNAL OF OPTICAL NETWORKING 837 Optical millimeter wave generated by octupling the frequency of the local oscillator Jianxin Ma, 1, * Xiangjun Xin, 1 J. Yu, 2 Chongxiu Yu, 1 Kuiru Wang, 1 Huiying Huang, 1 and Lan Rao 1 1 Key Laboratory of Optical Communication and Lightwave Technologies, Ministry of Education, School of Electronic Engineering, Beijing University of Posts and Telecommunications, Beijing, 100876, China 2 School of Computer and Communication, Hunan University, Changsha, Hunan, 410082, China *Corresponding author: majianxinxy@163.com Received June 18, 2008; revised August 22, 2008; accepted August 22, 2008; published September 19, 2008 Doc. ID 97614 What we believe to be a new scheme to generate an optical millimeter wave with octupling of the local oscillator via a nested LiNbO 3 Mach Zehnder modulator (MZM) is proposed and implemented by numerical simulation. Since the response frequency of the modulator and the local frequency are largely reduced, the bandwidth requirement of the transmitter to the optical and electrical components is reduced greatly. Then, the parameters of the nested modulator are analyzed theoretically, and we find that both the extinction ratio of the MZM and the phase imbalance between its two arms have influence on the performance of the generated optical millimeter wave. 2008 Optical Society of America OCIS codes: 060.2330, 060.2360, 350.4010. 1. Introduction With the rapid development of ultrabroadband wireless access in the millimeter- (mm-) wave band, it is of ultimate importance to cost-effectively generate a mm-wave radio signal suited for long-distance transmission [1]. Since generation of the mm-wave signal with tens of gigahertz meets the electric bottleneck and the mm-wave signal suffers from large loss during transmission along a coaxial cable or in the air, it is difficult to generate and distribute a high-frequency mm-wave in the electrical domain. Radio-over-fiber (RoF) technology can generate the mm-wave signal based on microwave photonics, which is called an optical mm-wave, and distribute it over the fiber in the optical domain; thus it has many advantages and is an attractive potential method [2,3]. Essentially, an optical mm-wave is a laser beam consisting of two or more coherent longitudinal modes with frequency spacing equal to the wanted mm-wave. As the longitudinal modes beat with each other in the photodiode, the required electrical mm-wave is generated. Recently, many methods have been developed to generate such multimode laser beams as a dual-mode laser [4], dual lasers with different wavelengths locked by optical phase locking and/or injection phase locking [5,6], optical external modulation [7], and optical nonlinear effects of four-wave mixing or stimulated Brillouin scattering [8,9]. Since the two longitudinal modes generated by a dual-mode laser or two separate lasers have low coherency, the mm-wave generated by their beating has poor spectral purity. The longitudinal modes generated by the nonlinear effects have higher coherency, but higher pump powers are required and their conversion efficiencies are low. Moreover, since the Brillouin frequency shift is fixed in the fiber, the generated optical mm-wave is frequency limited. Optical external modulation is a promising scheme for generating an optical mm-wave because of its many merits: (1) the generated optical mm-wave has higher coherency since the longitudinal modes come from the same source by frequency shift via radio-frequency (rf) modulation, (2) the frequency of the optical mm-wave may be several times the local oscillator frequency, (3) the optical source noise has little influence on the mm-wave after it is detected by the photocurrent, (4) and external modulation has a higher conversion efficiency. Since the modulator response frequency and the local oscillator frequency increase as 1536-5379/08/100837-9/$15.00 2008 Optical Society of America

Vol. 7, No. 10 / October 2008 / JOURNAL OF OPTICAL NETWORKING 838 the frequency of the generated optical mm-wave increases, the equipment performance requirements are improved greatly, especially for the optical mm-wave band signal generated on the basis of linear modulation. The nonlinear modulation can generate higher-order harmonics, which reduces the frequency requirement of the modulator and the local oscillator greatly [10 14]. Based on the periodical response characteristic of the LiNbO 3 Mach Zehnder modulator (LN-MZM), the local frequency is reduced to half or a quarter of the generated mm-wave by properly configuring the modulator [10,11,14]. In this paper, what we believe to be a new scheme is proposed to generate the optical mm-wave with eightfold frequency of the local oscillator with a nested LN-MZM, and the frequency requirement of the modulator and the local oscillator is further reduced. 2. Principle The principle scheme of optical mm-wave generation is shown in Fig. 1. The lightwave emitted from the laser diode (LD) is injected into an integrated nested MZM, which consists of two sub-mzms (MZ-a and MZ-b) in parallel with identical optical length. V a and V b are their switching voltages, and V a and V b are their bias voltages, respectively. The input lightwave at c is equally split into two beams by the Y branch with an optical power splitting ratio of 0.5. The two sub-mzms are dc biased at the maximum optical output point V a =V b =0 and are driven by the rf local oscillator V rf cos m t with a /2 phase shift, so the output lightwave can be expressed as Et = 1 4 E 0 e j c texpj V rf cos m t V a +expj V rf cos m t + /2 V b = 1 2 E 0 e j c tcos V rf cos m t V a + exp j V rf cos m t V a + exp j V rf cos m t + /2 V b + cos V rf cos m t + /2 V b = 1 2 E 0 e j c t cosm h cos m t + cosm h sin m t = 1 2 E 0 e j c t + + = E 0 e j c t + 1 n J 2n m h e j2n m t + J 2n m h e j2n m t J 4n m h e j c +4n m t E 0 J 0 m h e j c t + J 4 m h e j c +4 m t + e j c 4 m t + J 8 m h e j c +8 m t + e j c 8 m t +. 1 Here E 0 and c are the lightwave amplitude and angular frequency, respectively, and 1 is the modulator insertion loss. We define the modulation index Fig. 1. Proposed scheme to generate the optical mm-wave with octupling of the frequency of the local oscillator via a nested MZM. PD, photodiode; EDFA, erbium-doped fiber amplifier.

Vol. 7, No. 10 / October 2008 / JOURNAL OF OPTICAL NETWORKING 839 Fig. 2. Bessel functions of the first kind. m h V pp /2V =V rf /V, where V pp =2V rf is the peak-to-peak voltage of the rf local oscillator signal. J k is the kth-order Bessel function of the first kind. Equation (1) indicates that both MZ-a and MZ-b generate only the even-order sidebands while the odd-order sidebands are suppressed. But, the 4+2th-order sidebands of the two outputs have reverse phase, so the 4+2th-order sidebands are added destructively and cancelled, as shown in Fig. 1. According to the characteristics of the Bessel functions given in Fig. 2, the eighthorder and other higher-order sidebands have much smaller amplitudes, so the optical carrier and the two fourth-order sidebands are dominant. With the increase of the modulation index m h, the optical carrier varies periodically while the two fourth-order sidebands increase until m h =5.34. According to Fig. 2, when the modulation indices are m h =2.405 or 5.52, the optical carrier becomes zero, whereas the amplitude of the fourth-order sidebands is nonzero. The generated optical mm-waves at the two modulation indices mainly consist of the two fourth-order sidebands, but the two cases also show some difference. Since J 4 2.405=0.064 is much smaller than J 4 5.52=0.397, the fourth-order sidebands have a much larger amplitude at m h =5.52 than that at m h =2.405. Although the eighth-order sidebands increase to some degree, it is still 21 db smaller than the fourth-order sidebands at m h =5.52 and has little influence on the optical mm-wave. With modulation indices at m h =2.405 and 5.52, the output can be expressed as E0,t = E 0 J 4 m h e j c 4 m t + e j c +4 m t. 2 If the input optical power is expressed as P in = 1 2 E 0 2, the output power of the optical mm-wave with octupling of the local oscillator is P out =2 1 2 E 0Jm h 2. The conversion efficiency of the optical mm-wave signal can be expressed as = P out P in =2 2 J 4 2 m h. 3 It can be seen that the power of the generated optical mm-wave and the conversion efficiency are related to the insertion loss and the modulation index of the two sub- MZMs. The insertion loss of the MZM is 5 db =0.438 typically. The conversion efficiency is proportional to the square of the fourth-order Bessel function, and it increases gradually until m h =5.34, then decreases with the increase of the modulation index m h, as shown in Fig. 2. 3. Simulation Setup and Results A simulation system is set up on the basis of the simulation software OptSystem. The cw laser from the LD has a linewidth of 100 MHz at a wavelength of 1552.52 nm. Two parallel sub-mzms with a switching voltage of 4 V and an extinction ratio of 100 db are connected by two 3 db optical couplers in parallel. Both are dc biased at the maximum optical output point and driven by a 5 GHz rf local oscillator with different rf peak-to-peak voltage V pp. The rf local oscillator applied on the two sub-mzms has a /2 phase shift introduced by a time delay of 0.05 ns. According to our calculation, when V pp =6.124 and 14.057 V, which correspond to m h =2.405 and 5.52, respectively,

Vol. 7, No. 10 / October 2008 / JOURNAL OF OPTICAL NETWORKING 840 Fig. 3. (a) Optical spectrum, (b) rf spectrum, and (c) waveform of the generated 40 GHz optical mm-wave with the rf modulation voltage at V pp =6.124 V. the optical carrier is suppressed completely. To compensate the insertion loss of the integrated MZM, an EDFA is used to enhance the output optical power before it is injected into the photodiode. Figures 3 and 4 show the optical spectra, rf spectra, and waveforms of the generated optical mm-wave with rf peak-to-peak voltages at V pp =6.124 and 14.057 V, respectively. It can be seen that both cases can generate an optical mm-wave consisting of two main tones with a frequency spacing of 40 GHz, but their optical powers show some differences. The optical spectrum in Fig. 3(a) shows that, at V pp =6.124 V, the generated optical mm-wave mainly has two tones (positive and negative fourth-order sidebands) with a frequency spacing of 40 GHz, and the optical carrier and the other sidebands are suppressed well, so the rf spectrum mainly consists of dc and the 40 GHz harmonic, and the signal-to-noise ratio is 44 db according to the rf spectrum in Fig. 3(b). The rf photocurrent has good performance as can be seen from the waveform in Fig. 3(c). However, since the fourth-order Bessel is small at m h =2.405 according to Fig. 2, the generated optical mm-wave has a much smaller output power. As the rf modulation voltage is enhanced, the optical powers of two fourth-order sidebands increase correspondingly according to the fourth-order Bessel function in Fig. 2. AtV pp =14.057 V, the optical carrier is also suppressed completely and the eighth-order sidebands increase obviously, as can be seen in Fig. 4(a). At the same time, the eighth-order sidebands increase 17 db compared with the case at V pp =6.124 V in Fig. 3(a), but they are still 20 db smaller than the fourth-order sidebands. Since the eighth-order sidebands beat with the fourth-order sidebands in the photodiode and generate the 20 and 60 GHz rf components as shown by the rf spectrum in Fig. 4(b), they have some effect on the generated optical mm-wave. The waveform of the photocurrent in Fig. 4(c) shows that the 20 and 60 GHz rf components are superposed on the 40 GHz harmonic and distort the waveform. In the real system, the 60 GHz rf component has smaller influence than the 20 GHz because of the limited response frequency of the photodiode. Fig. 4. (a) Optical spectrum, (b) rf spectrum, and (c) waveform of the generated 40 GHz optical mm-wave with the rf modulation voltage at V pp =14.057 V.

Vol. 7, No. 10 / October 2008 / JOURNAL OF OPTICAL NETWORKING 841 4. Analysis and Discussion The theoretical deduction and simulation above are based on the assumption that the Y branches of the two sub-mzms have a much higher extinction ratio =0.5. In fact, the extinction ratio is usually limited to approximately 20 db, which means that 0.45. In addition, the two arms of the main MZ construction may be imbalanced and there is a length difference of L between the two arms. The length difference will lead to the phase imbalance between the two beams output from the two parallel MZMs with =2nL/; here n is the refractive index of the waveguide of MZMs and is the wavelength of the lightwave. The limited extinction ratio and phase imbalance of the two arms will cause the degradation of the generated optical mm-wave. If the limited extinction ratio and phase imbalance of the two arms are considered, the mm-wave generated t by our scheme can be expressed as Et = E 0 e j c 1 expj V rf cos m t V a + 1 1 exp j V rf cos m te j + 1 V a 2 expj V rf cos m t + /2 V b e j + 1 2 exp j V rf cos m t + /2 V b = E 0 e j c t 1 e jm h cos m t + 1 1 e jm h cos m t e j + 1 2 e jm h sin m t + 1 2 e jm h sin m t = E 0 e j c t 1 2 + j n J n m h e jn m t + 1 1 1 n J n m h e jn m t + 1 2 t J n m h e jn m = E 0 1 e j j n + 1 1 e j j n + 1 2 1 n + 1 1 2 J n m h e j c +n m t j n J n m h e jn m te j + 1 + = E 0 A n J n m h e j c +n m t, 4 and there is A n = ej + 1, n =4m j1 2 1 e j + 1 1 2 2, n =4m +1 e j 5 + 1, n =4m +2 j1 2 1 e j + 1 1 2 2, n =4m +3. Here we assume that the Y branch of the main MZM has a splitting ratio of, and the Y branches of the two sub-mzms have splitting ratios of 1 and 2, respectively. It can be seen that Eq. (4) becomes Eq. (1) when = 1 = 2 =0.5 and =0, where the 4m +1th-, 4m+2th-, and 4m+3th-order sidebands are cancelled completely. However, the deviation of the ideal values causes the reduction of the amplitude of the 4mth-order sidebands and the appearance of the 4m+1th-, 4m+2th-, and 4m +3th-order sidebands. Their amplitudes depend on the splitting ratios as well as the phase imbalance. We will discuss them in detail below. For the 4mth -order sideband, its amplitude can be expressed as A 4m = 1+2 2 2 +21 cos, 6 which is related to the optical splitting ratio of the main MZ and the phase imbalance between its two arms, but is independent of 1 and 2, as shown in Fig. 5. When the two arms have no phase imbalance =0, the amplitude of the 4mth-order sideband is independent of ; namely, the deviation of the optical splitting ratio from 0.5 does not cause the amplitude of the 4mth-order sideband to decrease. However, with the increase of the phase imbalance until =90, the amplitude of the

Vol. 7, No. 10 / October 2008 / JOURNAL OF OPTICAL NETWORKING 842 Fig. 5. Influence of the optical splitting ratio and the phase imbalance on the amplitude of the 4mth-order sideband of the generated optical mm-wave. 4mth-order sideband decreases and becomes more dependent on the optical splitting ratio simultaneously. When =0.5, the amplitude of the 4mth-order sideband decreases the worst with the increase of the phase imbalance. From the analysis above, it can be seen that the phase imbalance has greater influence on the amplitude of the 4mth-order sideband than the optical splitting ratio does. The amplitude of the 4m+1th-order sideband can be expressed as A 4m+1 = 2 1 2 1 2 + 1 2 1 2 2 2 +21 1 2 1 1 2 2 sin. 7 According to Eq. (7), when 1 = 2 =0.5, the 4m+1th-order sideband will be suppressed completely in spite of the value of and. If 1 and 2 deviate from 0.5, the 4m+1th-order sideband will appear, and its amplitude depends on the nested MZM parameters as shown in Fig. 6. Figure 6(a) shows that the two sub-mzms with a Fig. 6. Amplitude of the 4m+1th-order sideband versus the parameters, 1, 2, and.

Vol. 7, No. 10 / October 2008 / JOURNAL OF OPTICAL NETWORKING 843 20 db extinction ratio 1,2 =0.45 cause the 4m+1th-order sideband to be unable to be suppressed, and its amplitude varies with and. Of course, the vestigial 4m+1th-order sideband gets the minimal amplitude as =0.5 and =0. From Figs. 6(b) 6(d), it can be seen that the amplitude A m+1 is sensitive to 1 and 2, but the variation is relatively small when the extinction ratio is limited to within 20 db. This can be realized easily in the real system. Therefore, if the optical splitting ratios, 1, and 2 are limited near 0.5, the vestigial 4m+1th-order sideband can be suppressed to be a much smaller amplitude even if the phase between the two arms is imbalanced. The amplitude of the vestigial 4m+2th-order sideband can be expressed as A 4m+2 = 1+2 2 2 21 cos. 8 It can be seen that A 4m+2 is sensitive to the splitting ratio and the phase imbalance, as shown in Fig. 7. When =0.5 and =0, the 4m+2th-order sideband is suppressed completely. However, a slight deviation of these values will cause the vestigial amplitude to increase obviously. Therefore, to suppress the 4m+2th-order sideband, the main MZM is required to be of more symmetrical construction. The amplitude of the 4m+3th-order sideband can be expressed as A 4m+3 = 2 1 2 1 2 + 1 2 1 2 2 2 21 1 2 1 1 2 2 sin. 9 The amplitude of the 4m+3th-order sideband A 4m+3 is related with the optical splitting ratio (, 1, and 2 ) and the phase imbalance between the two arms, as shown in Fig. 8. When the optical splitting ratios are close to 0.5, the vestigial amplitude of the 4m+3th-order sideband is smaller than 0.1. Although the phase imbalance can vary the vestigial amplitude of the 4m+3th-order sideband, it does not worsen the case obviously. The sideband can be suppressed completely when the parameters are chosen properly, as can be observed in Fig. 8. From the analysis above, we find that (1) the amplitude of the 4mth-order sideband is related to the optical splitting ratio and the phase imbalance of the main MZM. The deviation of their ideal values will reduce the amplitude of the 4mth-order sideband. (2) Although the amplitude of the 4m+2th-order sideband is not related to the optical splitting ratio 1 and 2 of the two sub-mzms, it is very sensitive to and. The deviation of =0.5 and =0 will cause an obvious vestigial amplitude. (3) Although the amplitude of the 4m+1th- and 4m+3th-order sideband is related to the optical splitting ratios, 1, 2, and, they have much smaller amplitudes when the optical splitting ratios are close to the ideal value (0.5). In this case, the phase imbalance has little effect on the vestigial amplitudes. Thus, although the ideal case is difficult to implement in practice, the slight deviation of the ideal values of the nested MZM will never cause great degradation of the generated optical mm-wave. Fig. 7. Amplitude of the 4m+2th-order sideband versus the parameters and.

Vol. 7, No. 10 / October 2008 / JOURNAL OF OPTICAL NETWORKING 844 Fig. 8. Amplitude of the 4m+3th-order sideband versus the parameters, 1, 2, and. 5. Conclusion This paper proposes what we believe to be a novel scheme to generate an optical mm-wave with octupling of the local oscillator via a nested LiNbO 3 Mach Zehnder modulator with a lower response frequency. According to the theoretical analysis on the characteristics of the modulator, an optical mm-wave with frequency octupling of the local oscillator can be generated by properly adjusting its dc bias voltages and the local oscillator voltages and phases. The simulation results show the generated optical mm-waves at two different modulation depths. When the modulation index is m h =2.405, the generated optical mm-wave has a much purer spectrum while its power is smaller. As the modulation index is increased to m h =5.52, the power of the optical mm-wave increases greatly, but its spectral purity is degraded to some degree. Since the scheme realizes the frequency eightfold as the local oscillator is modulated on the optical carrier, the scheme largely reduces the response frequency of the modulator and the local oscillator frequency. The analysis of the optical splitting ratio and the phase imbalance of the nested MZM show that the performance of the generated optical mm-wave does not degrade obviously even if the parameters of the nested MZM deviate away from the ideal values to some degree. Acknowledgments This research was supported partly by the National High Technology Research and Development Program of China (863 program, 2007AA01Z263), the Key Project of the Chinese Ministry of Education (107011), and the Teaching and Scientific Research Foundation for the Returned Overseas Chinese Scholars, Ministry of Education. References 1. B. Lannoo, D. Colle, M. Pickavet, and P. Demeester, Radio-over-fiber-based solution to provide broadband internet access to train passengers, IEEE Commun. Mag. 45(2), 56 62 (2007). 2. G.-K. Chang, Z. Jia, J. Yu, A. Chowdhury, T. Wang, and G. Ellinas, Super-broadband optical wireless access technologies, in Optical Fiber Communication Conference and Exposition and the National Fiber Optic Engineers Conference, OSA Technical Digest (CD) (Optical Society of America, 2008), paper OThD1.

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