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An intensity-modulation direct-detection radio-over-fiber link with a tunable transfer function
Optics Communications 284 (2011) 2126–2130
Contents lists available at ScienceDirect
Optics Communications j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / o p t c o m
An intensity-modulation direct-detection radio-over-fiber link with a tunable transfer function Haiyan Ou a,⁎, Kun Zhu b, Chenhui Ye b, Ying Hu b a b
Institute of Applied Physics, University of Electronic Science and Technology of China, 610054, Chengdu, PR China Centre for Optical and Electromagnetic Research, Zhejiang University, Hangzhou 310058, PR China
a r t i c l e
i n f o
Article history: Received 26 March 2010 Received in revised form 26 September 2010 Accepted 24 December 2010 Available online 7 January 2011
a b s t r a c t An intensity-modulation direct-detection (IMDD) radio-over-fiber link with a tunable transfer function is presented. It utilizes a bias drift free intensity modulator based on a Sagnac fiber loop interferometer containing an optical phase modulator. By adjusting the polarization controller in the interferometer, the transfer function of the whole system can be tuned. The present method is simple and easy to implement. © 2010 Elsevier B.V. All rights reserved.
Keywords: Radio-over-fiber Sagnac fiber loop Optical signal processing Fiber optical communication
1. Introduction Radio-over-fiber (RoF) technology is one of the most attractive solutions for future high speed broadband wireless communication [1]. In a millimeter-wave (mm-wave) band RoF system, a central station (CS) should distribute different signals to many base stations (BSs) through optical fibers to provide different kinds of services to customers. It also takes the advantages of a standard single-mode fiber (SMF) such as the low loss, high bandwidth, lightweight, compactness, and immunity to electromagnetic interference, etc. There are many different approaches to transmit mm-wave signals from CS to BSs through optical fibers, among which the intensitymodulation and direct-detection (IMDD) technique is a relatively simple and practical method [2]. In an IMDD link, the mm-signals are intensity modulated on the optical carrier and then transmitted through an optical fiber. At a BS, the mm-wave signals are recovered by direct detection in a photodiode (PD). However, in a general IMDD system, the fiber chromatic dispersion intrinsically occurring in a standard 1550-nm single-mode fiber is one of the main drawbacks that limits the transmission distance and operation bandwidth [3]. The dispersion results in a carrier to noise (C/N) penalty on the mm-wave signal due to the phase shift of the modulation side bands with respect to the optical carrier. The phase shift depends on the length of the fiber, dispersion parameter, and the modulated RF frequency. In this paper, we present an IMDD RoF link with a tunable transfer function, which in turn changes the C/N penalty of the mm-wave ⁎ Corresponding author. Tel.: +86 28 83202541. E-mail address: [email protected] (H. Ou). 0030-4018/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.optcom.2010.12.078
signal. The tunability of the system is introduced by a bias-free intensity modulator, which is based on an electro-optic phase modulator in a fiber Sagnac interferometer. Experimental results are presented to verify the new concept. 2. Principle The structure of the Sagnac-loop-based intensity modulator is illustrated in Fig. 1. An optical coupler with 50:50 coupling ratio is used to form the Sagnac fiber loop interferometer. The input light is split equally with half traveling in the clockwise (CW) direction and the other half traveling in the counterclockwise (CCW) direction. In the center of the fiber loop, there is an electro-optical phase modulator, which is a commercially available product made from LiNbO3 crystal. The driving radio frequency (RF) signal is applied to the crystal through the traveling-wave electrodes. Two polarization controllers (PC) are employed: one of them is placed outside the loop at the input to the optical coupler (PC1), and the other is placed inside the loop at the right-hand side of the optical phase modulator (PC2). PC1 is used to adjust the polarization state of the optical wave that travels in the CW direction inside the Sagnac loop to let it align with the phase modulator; PC2 is used to control the phase difference between the counterpropagating waves. These two PCs work as a nonreciprocal bias unit, which introduces a phase difference between the CW and CCW phase-modulated optical signals. The output power of the structure is related to the phase difference between the CW light and CCW light as follows [4] Pout =
1 P L ð1þsinΔφÞ 2 in p
ð1Þ
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Fig. 2. A diagram showing the relation between the optical power and the total phase difference (given by Eq. (2)) between the CW and CCW signals.
Fig. 1. Structure of the Sagnac-loop-based intensity modulator. OC: optical coupler; PC: polarization controller; and PM: phase modulator. Arrow on the phase modulator indicates the microwave propagation direction.
where Pin and Pout are the input and output optical powers, Lp is the polarization-introduced optical loss when CW and CCW optical signals recombine and interfere at the coupler output, and Δφ is the total phase difference between the CW light and CCW light. Assuming a microwave signal with frequency ωRF and amplitude VRF is applied to the phase modulator, the total phase difference Δφ is then given by Δφ = ð1−r ÞβcosωRF t + Φ
ð2Þ
where β = πVRF/Vπ is the modulation index of the phase modulator for the CW signal, Φ is the polarization-related phase difference between the CW light and CCW light, and r is the ratio of backward to forward phase modulation index, which is included because the forward and backward phase modulator frequency responses can be different at high frequency due to velocity mismatch in travelling wave modulator [5]. The modulation index ratio r can be expressed as sinðωRF τx Þ r= ωRF τx
ð3Þ
where τx is the transit time in the phase modulator. One can conclude from Eq. (3) that for a given electro-optical phase modulator, the modulation index of the CW and CCW signals are almost the same when ωRF is small; however, as ωRF grows to high radio frequency, r drops dramatically. It also needs to mention that modification of the polarization not only changes the phase modulation depth β which depends on the input polarization to the waveguides, but also modifies the state of polarization (SOP) of the CW and CCW waves at recombination in the coupler output. So the output optical power of the Sagnac-loop-based intensity modulator will vary when modifying the PC, which is in accordance to Eqs. (1) and (2). And there is no response if the SOP of the CW and CCW signals is orthogonal. The principle of this intensity modulator is shown in Fig. 2. From Fig. 2 one can see that, for a given value of Φ and Lp, the output power varies periodically with the frequency of phase modulation, which indicates that an intensity modulator is formed. This structure has the advantages of eliminating the dc bias voltage that is required for
traditional electro-optic intensity modulators and exhibiting a high stability without using a feedback bias controller [6]. Fig. 3 shows the topology of the IMDD RoF link with the Sagnac-loopbased intensity modulator implemented. The input RF signal is directly applied on the intensity modulator. After transmission through a 50 km single-mode fiber (SMF), the signal is directly recovered by the PD. After the recombination of the CW light and CCW light, the optical field at the output port of the intensity modulator can be expressed as et ðt Þ = =
1 jðω0 t e 2
+ βcosωRF t + ΦÞ
1 jðω t − e 0 2
+ rβcosωRF t Þ
1 ½ J ðβÞ−J0 ðrβÞcos ω0 t + Φ0′ 2 0 h i 1 π + Φ1′ + ½ J1 ðβÞ−J1 ðrβÞcos ðω0 + ωRF Þt + 2 2 h i 1 π ′ + ½ J1 ðβÞ−J1 ðrβÞcos ðω0 −ωRF Þt− + Φ−1 2 2
ð4Þ
where ω0 is the angular frequency of the optical carrier, Jn(β) is the nth-order Bessel function of the first kind, Φ0′, Φ1′, and Φ−1′ are polarization-induced phase delays of the optical carrier ω0, and first order sidebands ω0 + ωRF, and ω0 − ωRF, respectively. After transmission through the SMF, the optical field can be expressed as [7] eðt Þ = Acosðω0 t + Φ0′ + Φ0 Þ h i 1 π + Φ1′ + Φ1 + ½ J1 ðβÞ−J1 ðrβÞcos ðω0 + ωRF Þt + 2 2 h i 1 π ′ + Φ−1 + ½ J1 ðβÞ−J1 ðrβÞcos ðω0 −ωRF Þt− + Φ−1 2 2
ð5Þ
where Φ0, Φ1, and Φ−1 are the phase delays of the spectral components ω0, ω0 + ωRF, and ω0 − ωRF induced by the chromatic dispersion of the SMF. The transfer function (defined as the ratio of the output and input mm-wave powers) of the system can then be approximately expressed as ′ Φ1 + Φ−1 + Φ′1 + Φ−1 H ð f Þ∝cos − Φ0 + Φ′0 2 !! ′ Φ′1 + Φ−1 Φ1 + Φ−1 ′ = cos −Φ0 + −Φ0 2 2
ð6Þ
It is well known that the phase delay induced by the fiber chromatic dispersion can be given by an expansion in a Taylor
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Fig. 3. Structure of the IMDD RoF link. ISO: optical isolator; EDFA: erbium-doped fiber amplifier; SMF: single-mode fiber; and PD: photodiode.
series of the frequency-dependent propagation constant βfiber [3], i.e. Φ0 = βfiber ðω0 ÞL ″ 2 ′ ðω0 Þðω1 −ω0 ÞL + βfiber ðω0 Þðω1 −ω0 Þ L + ::: Φ1 = βfiber ðω0 ÞL + βfiber ″ 2 ′ ðω0 Þðω−1 −ω0 ÞL + βfiber Φ−1 =βfiber ðω0 ÞL + βfiber ðω0 Þðω−1 −ω0 Þ L+ :::
ð7Þ where L is the fiber length, and ω1 = ω0 + ωRF ω−1 = ω0 −ωRF
ð8Þ
From Eqs. (6)–(8), it can be deduced that the transfer function of the proposed filter can be expressed as ! 2 2 πDλ0 fRF þζ H ð f Þ∝cos c
ð9Þ
′ where D (D= β″fiberL) is the dispersion parameter, ζ ζ = Φ1′ +2 Φ−1 −Φ0′ is the relative phase difference between the optical carrier and the first order sidebands at the output port of the intensity modulator. For example, when the first order sidebands are π out of phase compared to optical carrier, i.e. ζ = π/2, the transfer function at zero frequency can be very small (corresponding to power extinction); however, when the first order sidebands are in phase compared to optical carrier, i.e. ζ = π or ζ = 0, the transfer function at zero frequency would be 0 dB. The cosine function in Eq. (9) also indicates that for a fixed fiber length, the mm-wave power vanishes at frequency
vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi u u Nπ uc −ζ 1 t 2 f = N = 1; 3; 5… πD λ0
RoF link is measured by the 40 GHz network analyzer (37369D, Anritsu). The frequency range of the RF signal (generated by the network analyzer) applied to the phase modulator was set at 0.04 GHz – 20 GHz. The simulated and measured transfer function when ζ = π/15 is shown in Fig. 4, inset shows the detail in the frequency range of 0.04 GHz – 1 GHz. The disagreement between the simulated and measured results at high frequencies is due to the limited bandwidth of the phase modulator (3 dB–BW = 12.5 GHz) and the microwave transmission lines. The measured transfer function is a little noisy, which is due to the asymmetrically placed phase modulator in the loop (about 2.5 m in the actual experimental setup). The asymmetric imparts a phase shift on the CCW lightwave which is different to the phase shift imparted on the clockwise wave. The constructive and destructive interference of the two phase-modulated optical signals results in passbands and notches in the response, as is shown in inset of Fig. 4. But this phenomenon vanishes as the driving frequency grows, which is due to the poor modulation index of the CCW light at high frequency. One can also see from Fig. 4 that a periodical degradation of the output mm-wave power can be observed for a fixed fiber length, which owns to the chromatic dispersion. For several frequencies, measured to
ð10Þ
One can conclude from Eqs. (9) and (10) that the transfer function of the IMDD RoF link can be tuned by simply adjusting PC2 in the fiber loop (i.e., changing the polarization-related phase difference), which in turn changes the frequencies at which power cancellation occurs. 3. Experimental results and analysis An experiment was carried out to verify the principle of the proposed method. The experimental setup is the same as Fig. 3. The laser source (LD) is centered at 1554.7 nm and its output power is 0 dBm. An optical isolator is used after the LD to stop the backward light. An electro-optic phase modulator with 12.5 GHz bandwidth is employed in the Sagnac-loop-based intensity modulator. After being amplified by the erbium-doped fiber amplifier (EDFA), the modulated signal is then launched into a 50 km-SMF to send the RF signal to a BS. At the BS, the signal is recovered by a high speed PD with 65 GHz bandwidth (MN4765A, Anritsu). The transfer function of the IMDD
Fig. 4. Measured and simulated transfer functions of the IMDD RoF link when ζ = π/15 (inset shows the detail in the frequency range of 0.04 GHz – 1 GHz).
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the system stability to some extent. To enhance the stability of the whole system, polarization-maintaining fiber and temperature-maintaining scheme would further be used. 4. Conclusion
Fig. 5. Measured and simulated transfer functions of the IMDD RoF link when ζ = π/4.
be 7.9 GHz, 14.4 GHz, and 18.9 GHz, the mm-wave power vanishes after the 50 km SMF. By simply adjusting PC2 in the fiber loop, the transfer function of the IMDD link can be changed according to Eq. (6). In this case, the frequencies where mm-wave power vanishes can change to 6.2 GHz, 13.7 GHz, and 18.3 GHz, as is shown in Fig. 5 when ζ = π/4. The tunability of the transfer function of the IMDD link is demonstrated experimentally. The results are shown in Fig. 6(a)–(d). From Fig. 6 one sees that the transfer function at zero frequency can be 1 (i.e., 0 dB) or very small (corresponding to power extinction). This also means that the transfer function can be modified over a full 180° range (i.e. ζ in Eq. (9) can be tuned from 0 to π) by changing the polarization controller in the Sagnac fiber loop. It's needed to mention that the scheme is based on a loop configuration, which is polarization and temperature sensitive. The small fluctuation in polarization would affect the state of polarization of the CW and CCW waves at recombination in the coupler output, which would lead to intensity fluctuation of the RF signal. This limits
In conclusion, we have proposed and demonstrated an IMDD RoF link with a tunable transfer function, which is implemented with a Sagnac-loop-based intensity modulator. For a RoF system with a fixed fiber length, the transfer function of the whole system can be tuned by simply adjusting the polarization controller in the fiber loop, which indicates that the limitation caused by fiber chromatic dispersion has been overcome. Experimental results show that the transfer function can be tuned over a full 180° range. In case of multi-channel transmissions, when fiber length is fixed for most situations in access network, the proposed approach can provide more flexibility compared to the traditional IMDD RoF system. By simply adjusting the polarization state in the fiber Sagnac loop, the frequencies at which power cancellation occurs would shift to other frequencies, which gives more flexibility when allocating the multi RF channels. The proposed method can also find applications in frequency conversion [8], microwave photonic signal processing [9], etc., in a RoF system. It is worth noting that the tunable transfer function of the IMDD link can also be modeled as a microwave photonic filter with complex coefficient. Unlike the microwave photonic filtering (with complex coefficients) methods (using Stimulated Brillouin Scattering-based optical phase shifter [9] or electrical phase shifter [10]), which are complicated and bulky, the present method is simple and easy to implement. Acknowledgment This work was supported by the National 863 Project (grant no.2008AA01Z221). The author also wants to thank the China Scholarship Council (CSC) for the support.
Fig. 6. Transfer function of the IMDD RoF link with different phase differences.
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References [1] D. Wake, M. Webster, G. Wimpenny, K. Beacham, L. Crawford, Radio over fiber for mobile communications, Proc. IEEE Int. Topica lMeeting Microwave Photonics, Ogunquit, ME, Oct. 2004, p. 157. [2] A.F. Elrefaie, R.E. Wagner, IEEE Photonics Technol. Lett. 3 (1) (1991) 71. [3] A.F. Elrefaie, R.E. Wagner, D.A. Atlas, D.G. Daut, J. Lightwave Technol. 6 (5) (May 1988). [4] Ralph A. Bergh, H.C. Lefevre, Herbert J. Shaw, J. Lightwave Technol. LT-2 (2) (April 1984).
[5] [6] [7] [8]
G.K. Gopalakrishnan, et al., J. Lightwave Technol. 12 (10) (1994) 1807. M.L. Dennis, I.N. Duling, W.K. Burns, Electron. Lett. 32 (6) (1996) 547. Zeng Fei, Yao Jianping, J. Lightwave Technol. 23 (4) (April 2005) 1721. Yao Jianping, Maury Ghislaine, Guennec Yannis Le, Cabon Beatrice, IEEE Photonics Technol. Lett. 17 (11) (Nov 2005). [9] Losyssa Alayn, J. Campany, Sagues Mikel, J. Mora, IEEE Photonics Technol. Lett. 18 (16) (Aug 2006) 1744. [10] Yan Yu, Yao Jianping, IEEE Photonics Technol. Lett. 19 (19) (Oct 2007) 1472.
Contents lists available at ScienceDirect
Optics Communications j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / o p t c o m
An intensity-modulation direct-detection radio-over-fiber link with a tunable transfer function Haiyan Ou a,⁎, Kun Zhu b, Chenhui Ye b, Ying Hu b a b
Institute of Applied Physics, University of Electronic Science and Technology of China, 610054, Chengdu, PR China Centre for Optical and Electromagnetic Research, Zhejiang University, Hangzhou 310058, PR China
a r t i c l e
i n f o
Article history: Received 26 March 2010 Received in revised form 26 September 2010 Accepted 24 December 2010 Available online 7 January 2011
a b s t r a c t An intensity-modulation direct-detection (IMDD) radio-over-fiber link with a tunable transfer function is presented. It utilizes a bias drift free intensity modulator based on a Sagnac fiber loop interferometer containing an optical phase modulator. By adjusting the polarization controller in the interferometer, the transfer function of the whole system can be tuned. The present method is simple and easy to implement. © 2010 Elsevier B.V. All rights reserved.
Keywords: Radio-over-fiber Sagnac fiber loop Optical signal processing Fiber optical communication
1. Introduction Radio-over-fiber (RoF) technology is one of the most attractive solutions for future high speed broadband wireless communication [1]. In a millimeter-wave (mm-wave) band RoF system, a central station (CS) should distribute different signals to many base stations (BSs) through optical fibers to provide different kinds of services to customers. It also takes the advantages of a standard single-mode fiber (SMF) such as the low loss, high bandwidth, lightweight, compactness, and immunity to electromagnetic interference, etc. There are many different approaches to transmit mm-wave signals from CS to BSs through optical fibers, among which the intensitymodulation and direct-detection (IMDD) technique is a relatively simple and practical method [2]. In an IMDD link, the mm-signals are intensity modulated on the optical carrier and then transmitted through an optical fiber. At a BS, the mm-wave signals are recovered by direct detection in a photodiode (PD). However, in a general IMDD system, the fiber chromatic dispersion intrinsically occurring in a standard 1550-nm single-mode fiber is one of the main drawbacks that limits the transmission distance and operation bandwidth [3]. The dispersion results in a carrier to noise (C/N) penalty on the mm-wave signal due to the phase shift of the modulation side bands with respect to the optical carrier. The phase shift depends on the length of the fiber, dispersion parameter, and the modulated RF frequency. In this paper, we present an IMDD RoF link with a tunable transfer function, which in turn changes the C/N penalty of the mm-wave ⁎ Corresponding author. Tel.: +86 28 83202541. E-mail address: [email protected] (H. Ou). 0030-4018/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.optcom.2010.12.078
signal. The tunability of the system is introduced by a bias-free intensity modulator, which is based on an electro-optic phase modulator in a fiber Sagnac interferometer. Experimental results are presented to verify the new concept. 2. Principle The structure of the Sagnac-loop-based intensity modulator is illustrated in Fig. 1. An optical coupler with 50:50 coupling ratio is used to form the Sagnac fiber loop interferometer. The input light is split equally with half traveling in the clockwise (CW) direction and the other half traveling in the counterclockwise (CCW) direction. In the center of the fiber loop, there is an electro-optical phase modulator, which is a commercially available product made from LiNbO3 crystal. The driving radio frequency (RF) signal is applied to the crystal through the traveling-wave electrodes. Two polarization controllers (PC) are employed: one of them is placed outside the loop at the input to the optical coupler (PC1), and the other is placed inside the loop at the right-hand side of the optical phase modulator (PC2). PC1 is used to adjust the polarization state of the optical wave that travels in the CW direction inside the Sagnac loop to let it align with the phase modulator; PC2 is used to control the phase difference between the counterpropagating waves. These two PCs work as a nonreciprocal bias unit, which introduces a phase difference between the CW and CCW phase-modulated optical signals. The output power of the structure is related to the phase difference between the CW light and CCW light as follows [4] Pout =
1 P L ð1þsinΔφÞ 2 in p
ð1Þ
H. Ou et al. / Optics Communications 284 (2011) 2126–2130
2127
Fig. 2. A diagram showing the relation between the optical power and the total phase difference (given by Eq. (2)) between the CW and CCW signals.
Fig. 1. Structure of the Sagnac-loop-based intensity modulator. OC: optical coupler; PC: polarization controller; and PM: phase modulator. Arrow on the phase modulator indicates the microwave propagation direction.
where Pin and Pout are the input and output optical powers, Lp is the polarization-introduced optical loss when CW and CCW optical signals recombine and interfere at the coupler output, and Δφ is the total phase difference between the CW light and CCW light. Assuming a microwave signal with frequency ωRF and amplitude VRF is applied to the phase modulator, the total phase difference Δφ is then given by Δφ = ð1−r ÞβcosωRF t + Φ
ð2Þ
where β = πVRF/Vπ is the modulation index of the phase modulator for the CW signal, Φ is the polarization-related phase difference between the CW light and CCW light, and r is the ratio of backward to forward phase modulation index, which is included because the forward and backward phase modulator frequency responses can be different at high frequency due to velocity mismatch in travelling wave modulator [5]. The modulation index ratio r can be expressed as sinðωRF τx Þ r= ωRF τx
ð3Þ
where τx is the transit time in the phase modulator. One can conclude from Eq. (3) that for a given electro-optical phase modulator, the modulation index of the CW and CCW signals are almost the same when ωRF is small; however, as ωRF grows to high radio frequency, r drops dramatically. It also needs to mention that modification of the polarization not only changes the phase modulation depth β which depends on the input polarization to the waveguides, but also modifies the state of polarization (SOP) of the CW and CCW waves at recombination in the coupler output. So the output optical power of the Sagnac-loop-based intensity modulator will vary when modifying the PC, which is in accordance to Eqs. (1) and (2). And there is no response if the SOP of the CW and CCW signals is orthogonal. The principle of this intensity modulator is shown in Fig. 2. From Fig. 2 one can see that, for a given value of Φ and Lp, the output power varies periodically with the frequency of phase modulation, which indicates that an intensity modulator is formed. This structure has the advantages of eliminating the dc bias voltage that is required for
traditional electro-optic intensity modulators and exhibiting a high stability without using a feedback bias controller [6]. Fig. 3 shows the topology of the IMDD RoF link with the Sagnac-loopbased intensity modulator implemented. The input RF signal is directly applied on the intensity modulator. After transmission through a 50 km single-mode fiber (SMF), the signal is directly recovered by the PD. After the recombination of the CW light and CCW light, the optical field at the output port of the intensity modulator can be expressed as et ðt Þ = =
1 jðω0 t e 2
+ βcosωRF t + ΦÞ
1 jðω t − e 0 2
+ rβcosωRF t Þ
1 ½ J ðβÞ−J0 ðrβÞcos ω0 t + Φ0′ 2 0 h i 1 π + Φ1′ + ½ J1 ðβÞ−J1 ðrβÞcos ðω0 + ωRF Þt + 2 2 h i 1 π ′ + ½ J1 ðβÞ−J1 ðrβÞcos ðω0 −ωRF Þt− + Φ−1 2 2
ð4Þ
where ω0 is the angular frequency of the optical carrier, Jn(β) is the nth-order Bessel function of the first kind, Φ0′, Φ1′, and Φ−1′ are polarization-induced phase delays of the optical carrier ω0, and first order sidebands ω0 + ωRF, and ω0 − ωRF, respectively. After transmission through the SMF, the optical field can be expressed as [7] eðt Þ = Acosðω0 t + Φ0′ + Φ0 Þ h i 1 π + Φ1′ + Φ1 + ½ J1 ðβÞ−J1 ðrβÞcos ðω0 + ωRF Þt + 2 2 h i 1 π ′ + Φ−1 + ½ J1 ðβÞ−J1 ðrβÞcos ðω0 −ωRF Þt− + Φ−1 2 2
ð5Þ
where Φ0, Φ1, and Φ−1 are the phase delays of the spectral components ω0, ω0 + ωRF, and ω0 − ωRF induced by the chromatic dispersion of the SMF. The transfer function (defined as the ratio of the output and input mm-wave powers) of the system can then be approximately expressed as ′ Φ1 + Φ−1 + Φ′1 + Φ−1 H ð f Þ∝cos − Φ0 + Φ′0 2 !! ′ Φ′1 + Φ−1 Φ1 + Φ−1 ′ = cos −Φ0 + −Φ0 2 2
ð6Þ
It is well known that the phase delay induced by the fiber chromatic dispersion can be given by an expansion in a Taylor
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Fig. 3. Structure of the IMDD RoF link. ISO: optical isolator; EDFA: erbium-doped fiber amplifier; SMF: single-mode fiber; and PD: photodiode.
series of the frequency-dependent propagation constant βfiber [3], i.e. Φ0 = βfiber ðω0 ÞL ″ 2 ′ ðω0 Þðω1 −ω0 ÞL + βfiber ðω0 Þðω1 −ω0 Þ L + ::: Φ1 = βfiber ðω0 ÞL + βfiber ″ 2 ′ ðω0 Þðω−1 −ω0 ÞL + βfiber Φ−1 =βfiber ðω0 ÞL + βfiber ðω0 Þðω−1 −ω0 Þ L+ :::
ð7Þ where L is the fiber length, and ω1 = ω0 + ωRF ω−1 = ω0 −ωRF
ð8Þ
From Eqs. (6)–(8), it can be deduced that the transfer function of the proposed filter can be expressed as ! 2 2 πDλ0 fRF þζ H ð f Þ∝cos c
ð9Þ
′ where D (D= β″fiberL) is the dispersion parameter, ζ ζ = Φ1′ +2 Φ−1 −Φ0′ is the relative phase difference between the optical carrier and the first order sidebands at the output port of the intensity modulator. For example, when the first order sidebands are π out of phase compared to optical carrier, i.e. ζ = π/2, the transfer function at zero frequency can be very small (corresponding to power extinction); however, when the first order sidebands are in phase compared to optical carrier, i.e. ζ = π or ζ = 0, the transfer function at zero frequency would be 0 dB. The cosine function in Eq. (9) also indicates that for a fixed fiber length, the mm-wave power vanishes at frequency
vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi u u Nπ uc −ζ 1 t 2 f = N = 1; 3; 5… πD λ0
RoF link is measured by the 40 GHz network analyzer (37369D, Anritsu). The frequency range of the RF signal (generated by the network analyzer) applied to the phase modulator was set at 0.04 GHz – 20 GHz. The simulated and measured transfer function when ζ = π/15 is shown in Fig. 4, inset shows the detail in the frequency range of 0.04 GHz – 1 GHz. The disagreement between the simulated and measured results at high frequencies is due to the limited bandwidth of the phase modulator (3 dB–BW = 12.5 GHz) and the microwave transmission lines. The measured transfer function is a little noisy, which is due to the asymmetrically placed phase modulator in the loop (about 2.5 m in the actual experimental setup). The asymmetric imparts a phase shift on the CCW lightwave which is different to the phase shift imparted on the clockwise wave. The constructive and destructive interference of the two phase-modulated optical signals results in passbands and notches in the response, as is shown in inset of Fig. 4. But this phenomenon vanishes as the driving frequency grows, which is due to the poor modulation index of the CCW light at high frequency. One can also see from Fig. 4 that a periodical degradation of the output mm-wave power can be observed for a fixed fiber length, which owns to the chromatic dispersion. For several frequencies, measured to
ð10Þ
One can conclude from Eqs. (9) and (10) that the transfer function of the IMDD RoF link can be tuned by simply adjusting PC2 in the fiber loop (i.e., changing the polarization-related phase difference), which in turn changes the frequencies at which power cancellation occurs. 3. Experimental results and analysis An experiment was carried out to verify the principle of the proposed method. The experimental setup is the same as Fig. 3. The laser source (LD) is centered at 1554.7 nm and its output power is 0 dBm. An optical isolator is used after the LD to stop the backward light. An electro-optic phase modulator with 12.5 GHz bandwidth is employed in the Sagnac-loop-based intensity modulator. After being amplified by the erbium-doped fiber amplifier (EDFA), the modulated signal is then launched into a 50 km-SMF to send the RF signal to a BS. At the BS, the signal is recovered by a high speed PD with 65 GHz bandwidth (MN4765A, Anritsu). The transfer function of the IMDD
Fig. 4. Measured and simulated transfer functions of the IMDD RoF link when ζ = π/15 (inset shows the detail in the frequency range of 0.04 GHz – 1 GHz).
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the system stability to some extent. To enhance the stability of the whole system, polarization-maintaining fiber and temperature-maintaining scheme would further be used. 4. Conclusion
Fig. 5. Measured and simulated transfer functions of the IMDD RoF link when ζ = π/4.
be 7.9 GHz, 14.4 GHz, and 18.9 GHz, the mm-wave power vanishes after the 50 km SMF. By simply adjusting PC2 in the fiber loop, the transfer function of the IMDD link can be changed according to Eq. (6). In this case, the frequencies where mm-wave power vanishes can change to 6.2 GHz, 13.7 GHz, and 18.3 GHz, as is shown in Fig. 5 when ζ = π/4. The tunability of the transfer function of the IMDD link is demonstrated experimentally. The results are shown in Fig. 6(a)–(d). From Fig. 6 one sees that the transfer function at zero frequency can be 1 (i.e., 0 dB) or very small (corresponding to power extinction). This also means that the transfer function can be modified over a full 180° range (i.e. ζ in Eq. (9) can be tuned from 0 to π) by changing the polarization controller in the Sagnac fiber loop. It's needed to mention that the scheme is based on a loop configuration, which is polarization and temperature sensitive. The small fluctuation in polarization would affect the state of polarization of the CW and CCW waves at recombination in the coupler output, which would lead to intensity fluctuation of the RF signal. This limits
In conclusion, we have proposed and demonstrated an IMDD RoF link with a tunable transfer function, which is implemented with a Sagnac-loop-based intensity modulator. For a RoF system with a fixed fiber length, the transfer function of the whole system can be tuned by simply adjusting the polarization controller in the fiber loop, which indicates that the limitation caused by fiber chromatic dispersion has been overcome. Experimental results show that the transfer function can be tuned over a full 180° range. In case of multi-channel transmissions, when fiber length is fixed for most situations in access network, the proposed approach can provide more flexibility compared to the traditional IMDD RoF system. By simply adjusting the polarization state in the fiber Sagnac loop, the frequencies at which power cancellation occurs would shift to other frequencies, which gives more flexibility when allocating the multi RF channels. The proposed method can also find applications in frequency conversion [8], microwave photonic signal processing [9], etc., in a RoF system. It is worth noting that the tunable transfer function of the IMDD link can also be modeled as a microwave photonic filter with complex coefficient. Unlike the microwave photonic filtering (with complex coefficients) methods (using Stimulated Brillouin Scattering-based optical phase shifter [9] or electrical phase shifter [10]), which are complicated and bulky, the present method is simple and easy to implement. Acknowledgment This work was supported by the National 863 Project (grant no.2008AA01Z221). The author also wants to thank the China Scholarship Council (CSC) for the support.
Fig. 6. Transfer function of the IMDD RoF link with different phase differences.
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