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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 19, Iss. 2 — Jan. 17, 2011
  • pp: 883–895
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Linearized electrooptic microwave downconversion using phase modulation and optical filtering

Vincent R. Pagán, Bryan M. Haas, and T. E. Murphy  »View Author Affiliations


Optics Express, Vol. 19, Issue 2, pp. 883-895 (2011)
http://dx.doi.org/10.1364/OE.19.000883


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Abstract

We propose and demonstrate an electrooptic technique for relaying microwave signals over an optical fiber and downconverting the microwave signal to an intermediate frequency at the receiver. The system uses electrooptic phase modulation in the transmitter to impose the microwave signal on an optical carrier followed by re-modulation with a microwave local oscillator at the receiver. We demonstrate that by subsequently suppressing the optical carrier using a notch filter, the resulting optical signal can be directly detected to obtain a downconverted microwave signal. We further show that by simply controlling the amplitude of the microwave local oscillator, the system can be linearized to third-order, yielding an improvement in the dynamic range.

© 2011 Optical Society of America

1. Introduction

A surprising feature of the system is that by simply adjusting the amplitude of the microwave LO, it is possible to eliminate the third-order intermodulation distortion (IMD3) introduced by the modulation and demodulation processes. This linearization method does not require multiple wavelengths, additional modulators, polarization states, or precise splitting of the optical and RF powers, and can be implemented entirely in the receiver. Despite a penalty in the down-conversion gain, we show that the linearized system increases the spur-free dynamic range (SFDR) from 103.5 dB/Hz2/3 to 114.0 dB/Hz4/5.

2. Principle of operation

Fig. 1 Diagram of the downconverting RoF link presented here. The system uses two cascaded optical phase modulators, one in the transmitter and one in the receiver, followed by a fiber Bragg grating (FBG) and a square-law photoreceiver. The FBG is chosen to suppress the optical carrier at νc. The receiver phase modulator is driven by a strong microwave LO to produce IF beat products that are detected by an optical photoreceiver.

The signal emerging from the RX phase modulator was sent through a fiber Bragg grating (FBG) in transmission mode to suppress the optical carrier. The FBG was designed for add/drop filtering of dense wavelength division multiplexing systems having 25 GHz channel spacings. This filter provided approximately 23 dB attenuation to the carrier with respect to the sidebands at 1552.470 nm and approximately 2.5 dB of out-of-band insertion loss. The 3 dB notch-width of the FBG was measured to be approximately 14 GHz and the frequency offset between the optical carrier and the filter center frequency was less than 1 GHz. The optical output from the filter was connected to an InGaAs PIN photodiode having a 50 Ω internal termination resistor and a nominal 3 dB bandwidth of 12 GHz.

Figure 2 illustrates the downconversion process by showing the optical and electrical spectra measured at various points in the link. The optical spectra were captured using a high resolution Brillouin optical spectrum analyzer (Aragon Photonics) with a spectral resolution of 80 fm (10 MHz). The fiber laser spectrum is shown in Fig. 2(a) where Pc denotes the optical carrier power. At the transmitter, the optical signal is modulated by a weak 20 GHz microwave signal with modulation depth m1 0.1. This produces a series of optical sidebands with intensities proportional to Jl2(m1) at frequencies of lf1 about the optical carrier where l = 0, ±1,±2,... as shown in Fig. 2(b).

Fig. 2 (a) Optical spectrum of the laser (closed circle). (b) Optical spectrum measured after the transmitter phase modulator, showing the optical carrier (closed circle) and sidebands at ±f1 = ±20 GHz (open circles). (c) Optical spectrum measured after the receiver phase modulator driven by a LO, showing additional sidebands at ±f0 = ±19.6 GHz (open squares), ±f1 2f0 = ±19.2 GHz (open triangles), and ±f1f0 = ±400 MHz (no symbol). (d) Measured transmission of the FBG. (e) Optical spectrum measured after the FBG, showing suppression of the optical carrier and sidebands at ±f1f0 = ±400 MHz. (f) Electrical spectrum measured at the photodetector, showing the downconverted tone at f10 = 400 MHz.

In the receiver, the phase modulated optical signal is re-modulated by a strong microwave LO having a modulation depth m0 1.08 and frequency f0 = 19.6 GHz. This generates additional optical sidebands with frequency spacings of mf0, where m = 0,±1,±2,..., about each of the the lf1 frequency components. The resulting spectrum is shown in Fig. 2(c) where each spectral component is proportional to Jl2(m1)Jm2(m0).

The twice-modulated optical signal is then sent through a FBG with the measured optical transmission shown in Fig. 2(d). The FBG filters out the optical carrier for which l + m = 0 while allowing the sidebands to pass. The carrier-suppressed optical spectrum is shown in Fig. 2(e).

After the notch filter, the resulting optical signal is detected by a square-law photoreceiver. As explained later in Section 3, the photocurrent contains terms at the downconverted frequency, Ω10 = Ω1 − Ω0, that are proportional to the power of the microwave input signal. Fig. 2(f) shows the measured electrical spectrum of the photodetected signal which is clearly centered at the downconverted frequency of f10 = 400 MHz.

3. Theoretical analysis

We begin with a continuous wave optical signal with optical frequency ωc, that can be described by the complex optical field
uA(t)=Pcejωct
(1)
where we have normalized the field such that |uA|2 represents the optical power. For simplicity, in the analysis that follows, we neglect the optical insertion losses of the modulators, filter, and transmission fiber. These losses can be accounted for by proportionately reducing Pc. Alternatively, one may define Pc to be the optical power measured at the input of the receiver modulator when the signal and LO are turned off.

In the transmitter, the signal is phase modulated by a sinusoidal microwave signal with amplitude V1 and frequency Ω1 to produce an optical field
uB(t)=Pcejωctejm1sinΩ1t
(2)
where m1 is the input signal modulation depth, expressed in radians as
m1=πV1Vπ
(3)
and Vπ is the half-wave voltage of the phase modulator. At the receiver, the signal is remodulated by a strong microwave LO tone to give
uC(t)=Pcejωctejm1sinΩ1tejm0sinΩ0t
(4)
where m0 is the modulation depth produced by the LO, defined analogously to Eq. (3). Applying the Jacobi-Anger expansion to Eq. (4), we obtain
uC(t)=PcejωctlmJl(m1)Jm(m0)ej(lΩ1+mΩ0)t
(5)
where both summations run from −∞ to +∞.

The optical notch filter can be mathematically modeled by excluding those terms in Eq. (5) for which l + m = 0,
uD(t)=Pcejωctlm(l+m0)Jl(m1)Jm(m0)ej(lΩ1+mΩ0)t
(6)

Following the FBG notch filter, the optical field is detected by a square-law photoreceiver with responsivity R to produce a photocurrent given by
i(t)=R|uD(t)|2=RPclm(l+m0)np(n+p0)[Jl(m1)Jm(m0)Jn(m1)Jp(m0)ej[(ln)Ω1+(mp)Ω0]t]
(7)

4. Linearization

Intermodulation distortion is associated with nonlinearities in the EO modulation and demodulation transfer functions. Even in the single tone case, distortion is present in the down-converted photocurrent at Ω10 as evident in the term proportional to m13 in Eq. (12). This contribution to signal distortion can be eliminated by appropriately choosing the LO modulation depth m0, which leads to the following linearization condition:
3J0(m0)J1(m0)J1(m0)J2(m0)=0
(18)
As shown in Appendix A, in the two-tone analysis, this condition also eliminates the IMD3 products at 2f1f2f0 and 2f2f1f0. The smallest value of m0 that solves Eq. (18) was numerically found to be m0 = 2.17. When this value of m0 is substituted into Eq. (17), the downconversion gain evaluates to G = 0.081 GMZ, which is 13.6 dB lower than for the maximum gain case.

To experimentally confirm this result, we conducted a two-tone measurement in which the LO strength (m0) was swept while the power of the downconverted fundamental tones and third order intermodulation (IMD3) were measured. For these measurements, the single microwave tone at the TX phase modulator shown in Fig. 1 was replaced by a pair of closely spaced tones with frequencies f1 = 20.00 GHz and f2 = 20.02 GHz and equal modulation depths m1 = m2 = 0.14. In order to improve the electrical isolation between the two synthesizers, three-port ferrite circulators configured as electrical isolators were used at the synthesizer outputs. The two microwave tones were then combined using a four-port hybrid coupler. The LO frequency was set to f0 = 19.6 GHz to produce downconverted tones at 400 and 420 MHz and sub-octave IMDs at 380 and 440 MHz. The DC photocurrent, downconverted fundamental power, and downconverted IMD power were measured as a function of the LO modulation depth.

Figure 3 shows the results of this measurement along with the corresponding theoretically calculated curves. When calculating the output powers for Fig. 3, an additional factor of 1/4 was incorporated to account for the presence of an internal 50 Ω terminating resistor in the photoreceiver. The measurements and theory show excellent agreement across all values of m0. It is clear that the fundamental power is maximized at m0 = 1.08 while the IMD3 power is minimized by choosing m0 = 2.17, which reduces the fundamental power by 13.6 dB relative to it’s maximum value.

Fig. 3 Calculated (solid lines) and measured DC photocurrent (squares), downconverted signal power (open circles), and third-order intermodulation distortion (IMD3) power (filled circles) as a function of the LO modulation depth m0. The downconverted signal and IMD3 powers grow in proportion to m1 and m13, respectively, but here they are evaluated at an input modulation depth of m1 = 0.14.

Figure 4(a) shows the electrical spectrum measured for a LO modulation depth of m0 = 1.08, which produces the maximum downconversion gain. The IMD products are clearly visible at frequencies of 2f1f2f0 = 380 MHz and 2f2f1f0 = 440 MHz. To linearize the system, we increased the LO power to achieve m0 = 2.17, which produced the electrical spectrum shown in Fig. 4(b). The fundamental tones are reduced by 13.8 dB from their value in Fig. 4(a), which agrees well with the theoretically calculated gain penalty of 13.6 dB, and the IMD products fell below the noise floor of the electrical spectrum analyzer. Finally, we increased the input signal powers by +13.8 dB to compensate for the linearization gain penalty. As shown in Fig. 4(c), even in this case, the IMD products are suppressed relative to the non-linearized case shown in Fig. 4(a). This confirms that, despite the gain penalty, this linearization technique can improve the dynamic range.

Fig. 4 Measured downconverted electrical spectra, showing the suppression of intermodulation distortion products achieved by adjusting the LO strength m0. (a) Downconverted spectrum obtained when the LO power was adjusted for maximum gain (i.e., m0 = 1.08). (b) Spectrum obtained under same conditions as (a), but with the LO amplitude increased to m0 = 2.17. (c) Output spectrum obtained under same conditions as in (b), but with the input signal strength increased by +13.8 dB to compensate for the gain penalty. Notice that even when the input amplitude is increased to compensate for the gain penalty, the dynamic range is improved in comparison to the non-linearized case shown in (a).

When the IMD3 products are suppressed by choosing m0 according to Eq. (18), the residual sub-octave IMD products are expected to be dominated by fifth-order contributions. Thus, we do not expect complete suppression of the IMD products in the linearized case, but only the elimination of the third-order dependence. To verify this, we measured the downconverted and IMD powers as a function of the input power. Figure 5 shows the results of these measurements for the maximum gain and linearized cases. The solid curves were simulated while the circles indicate experimentally measured points. The dashed curves and open circles correspond to the maximum-gain case, m0 = 1.08, and the green curves and filled circles indicate the linearized case, m0 = 2.17. For the latter case, the IMD products clearly have a fifth-order dependence on the input power, indicating that the third-order dependence has in fact been suppressed. All measurements in Fig. 5 were performed using a resolution bandwidth of 100 kHz. The IMD products were measured using a low-noise IF preamplifier and tunable RF bandpass filter at the output of the photodetector to isolate the weaker IMD tones from the stronger fundamental tones and to overcome the poor noise figure of the spectrum analyzer. Despite the gain penalty, the linearized system achieves a normalized dynamic range of 114.0 dB/Hz4/5, whereas the maximum-gain case reaches only 103.5 dB/Hz2/3.

Fig. 5 Downconverted signal and intermodulation powers as a function of the input microwave power. The blue curves and open symbols were obtained with a LO amplitude of m0 = 1.08, which gives the highest downconversion gain. The green curves and filled symbols were obtained with m0 = 2.17, which suppresses the third-order intermodulation distortion.

5. System bandwidth

Theoretically, the bandwidth of the optical notch filter limits the minimum frequency that can be transmitted through the system. To experimentally investigate this effect, we measured the downconversion gain as a function of the input signal frequency, f1. The LO frequency was adjusted in parallel with the input signal frequency in order to maintain a constant downconverted IF of f1f0 = 400 MHz. Since the half-wave voltage of EO modulators vary with frequency, the LO power was adjusted to maintain a constant LO modulation depth of m0 = 1.08 for all measurements. When varying the signal frequency f1, the half-wave voltage Vπ was independently measured so that the electrical response of the TX phase modulator could also be factored out.

Fig. 6 Downconversion gain as a function of the signal carrier frequency f1, normalized relative to GMZ, the gain of a comparable non-downconverting link employing a quadrature-biased Mach-Zehnder intensity modulator with direct detection.

Chromatic dispersion in the fiber is well-known to produce phase modulation to intensity modulation conversion, and vice versa [31

31. A. R. Chraplyvy, R. W. Tkach, L. L. Buhl, and R. C. Alferness, “Phase Modulation to Amplitude Modulation Conversion of CW Laser Light in Optical Fibres,” Electron. Lett. 22, 409–411 (1986). [CrossRef]

34

34. G. H. Smith, D. Novak, and Z. Ahmed, “Overcoming Chromatic-Dispersion Effects in Fiber-Wireless Systems Incorporating External Modulators,” IEEE Trans. Microw. Theory Tech. 45, 1410 –1415 (1997). [CrossRef]

]. In systems where the modulation frequencies are known, an appropriately chosen dispersive medium inserted after a phase modulator can be used in place of the optical notch filter to achieve EO frequency mixing [20

20. F. Zeng and J. Yao, “All-Optical Microwave Mixing and Bandpass Filtering in a Radio-Over-Fiber Link,” IEEE Photon. Technol. Lett. 17, 899–901 (2005). [CrossRef]

, 21

21. Y. Le Guennec, G. Maury, J. Yao, and B. Cabon, “New Optical Microwave Up-Conversion Solution in Radio-Over-Fiber Networks for 60-GHz Wireless Applications,” J. Lightwave Technol. 24, 1277–1282 (2006). [CrossRef]

, 27

27. H. Chi, X. Zou, and J. Yao, “Analytical Models for Phase-Modulation-Based Microwave Photonic Systems With Phase Modulation to Intensity Modulation Conversion Using a Dispersive Device,” J. Lightwave Technol. 27, 511–521 (2009). [CrossRef]

].

This system, however, is designed to accommodate a wide range of possible input frequencies. In this case, chromatic dispersion limits the bandwidth, transmission length, and down-conversion gain. The derivation presented in Section 3 can be generalized to include the effect of chromatic dispersion between the transmitter and receiver. If the two phase modulators are separated by a fiber of length L, then to first-order, the amplitude of the downconverted photocurrent can be shown to be
I10=2RPcm1J0(m0)J1(m0)cos(πLDcλc2f12)
(19)
where D is the chromatic dispersion of the fiber, typically expressed in ps/nm·km, λc is the carrier wavelength, and f1 is the signal frequency. Apart from the additional sinusoidal factor, Eq. (19) is seen to be identical to the leading linear term in Eq. (12).

The downconverted signal will be completely extinguished when the dispersion and frequency satisfy the following relation:
2L|D|cλc2f12=1,3,5,...
(20)
For the case of D = 17 ps/nmkm, λc = 1552.470 nm, and f1 = 20 GHz, the first null occurs at a fiber length of L = 9.15 km, and the −3 dB point occurs at L = 4.58 km.

Conversely, for a given fiber length, chromatic dispersion limits the maximum frequency that can be transmitted. The downconversion gain is reduced by −3 dB at a frequency of
f1=12λccL|D|
(21)

Another configuration of interest is when the input signal and LO modulators are both co-located at the transmitter, which is then separated from the FBG and photodetector by a dispersive fiber. In this case, the analysis of the downconversion gain is slightly more complex [27

27. H. Chi, X. Zou, and J. Yao, “Analytical Models for Phase-Modulation-Based Microwave Photonic Systems With Phase Modulation to Intensity Modulation Conversion Using a Dispersive Device,” J. Lightwave Technol. 27, 511–521 (2009). [CrossRef]

]. Numerical simulations suggest, however, that although fading can occur under these conditions, the signal fading criterion is dictated primarily by the downconverted IF, f1f0. Using f1 = 20 GHz, f0 = 19.6 GHz and m0 = 1.08, we numerically calculate that the first null in transmission should occur at a length of L ≃ 200 km.

6. Conclusions

In this paper, we reported a downconverting radio-over-fiber system that employs two cascaded optical phase modulators followed by an optical notch filter for carrier suppression. The system offers several advantages over competing downconversion schemes. Unlike conventional electrical downconversion, the system does not require a high-speed photoreceiver or electrical mixer. In contrast to optical heterodyne downconversion methods, the system does not require two phase-locked optical sources. Because it does not use intensity modulators, active bias control is not needed. We further demonstrated that by simply adjusting the strength of the microwave LO, it is possible to eliminate the third-order intermodulation distortion in the system, which is shown to improve the dynamic range of the link.

A. Two-Tone Analysis

In Section 3, expressions for the downconversion gain for the single tone case were derived up to third-order. In this Appendix, the case where the input signal is comprised of two closely spaced tones is considered. The fundamental, IMDs, and DC terms are evaluated up to fifth-order.

At the transmitter, an optical carrier with power Pc and frequency ωc is phase modulated by two closely spaced sinusoidal tones v1(t) = V1 sinΩ1t and v2(t) = V2 sinΩ2t, to produce an optical field given by
uB(t)=Pcejωctejm1sinΩ1tejm2sinΩ2t
(22)
where, as before, the ith modulation depth (in radians) is given by miπVi/Vπ. At the receiver, the signal is modulated again by a strong LO tone with modulation depth m0 and frequency Ω0, to produce an optical field given by
uC(t)=Pcejωctejm1sinΩ1tejm2sinΩ2tejm0sinΩ0t
(23)
The exponentials in Eq. (23) are expanded in terms of Bessel functions to obtain
uC(t)=PcejωctlmnJl(m1)Jm(m2)Jn(m0)ej(lΩ1+mΩ2+nΩ0)t
(24)
An ideal optical notch filter will extinguish all of the terms in Eq. (24) for which l + m + n = 0, i.e.,
uD(t)=Pcejωctlmn(l+m+n0)Jl(m1)Jm(m2)Jn(m0)ej(lΩ1+mΩ2+nΩ0)t
(25)

The detected photocurrent is then given by
i(t)=R|uD(t)|2
(26)
=RPclmn(l+m+n0)pqr(p+q+r0)Jl(m1)Jm(m2)Jn(m0)Jp(m1)Jq(m2)Jr(m0)×ej[(lp)Ω1+(mq)Ω2+(nr)Ω0]t
(27)

Expanding Eq. (27) up to fifth-order in m1 and m2, and retaining only the downconverted in-band products and DC terms, we find
i(t)=RPc{[Φ0(m0)+Φ2(m0)(m12+m22)+Φ4(m0)(m14+4m12m22+m24)]
(28)
+[Φ1(m0)m1+Φ3(m0)(m13+2m1m22)+Φ5(m0)(m15+6m13m22+3m1m24)]cos(Ω10t)
(29)
+[Φ3(m0)m12m2+Φ5(3m12m23+2m14m2)]cos((2Ω10Ω20)t)
(30)
+Φ5(m0)m13m22cos((3Ω102Ω20)t)+similartermsatΩ20,(2Ω20Ω10)and(3Ω202Ω10)}
(31)
where Ωij ≡ (Ωi − Ωj) and the coefficients Φn(m0) are tabulated below:
Φ0(m0)1J02(m0)Φ1(m0)2J0(m0)J1(m0)Φ2(m0)12[J02(m0)J12(m0)]Φ3(m0)14[3J0(m0)J1(m0)J1(m0)J2(m0)]Φ4(m0)132[3J02(m0)4J12(m0)+J22(m0)]Φ5(m0)196[10J0(m0)J1(m0)5J1(m0)J2(m0)+J0(m0)J1(m0)]
(32)

We note that the linearization condition given by Eq. (18) is equivalent to requiring Φ3(m0) = 0, which eliminates not only the third-order IMD products in Eq. (30), but also the cubic contribution to the fundamental tones in Eq. (29).

Equation (31) indicates that there will be fifth-order intermodulation products present at the downconverted frequency 3Ω10 − 2Ω20. For clarity, these terms were not plotted in Fig. 5, because for m1 = m2 they are always smaller than the dominant IMD3 contributions at 2Ω10 − Ω20 for small input signals (m1, m2 << 1).

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A. F. Elrefaie, R. E. Wagner, D. A. Atlas, and D. G. Daut, “Chromatic Dispersion Limitations in Coherent Lightwave Transmission Systems,” J. Lightwave Technol. 6, 704–709 (1988). [CrossRef]

33.

U. Gliese, S. Nørskov, and T. N. Nielsen, “Chromatic Dispersion in Fiber-Optic Microwave and Millimeter-Wave Links,” IEEE Trans. Microw. Theory Tech. 44, 1716–1724 (1996). [CrossRef]

34.

G. H. Smith, D. Novak, and Z. Ahmed, “Overcoming Chromatic-Dispersion Effects in Fiber-Wireless Systems Incorporating External Modulators,” IEEE Trans. Microw. Theory Tech. 45, 1410 –1415 (1997). [CrossRef]

OCIS Codes
(060.0060) Fiber optics and optical communications : Fiber optics and optical communications
(060.5060) Fiber optics and optical communications : Phase modulation
(230.0250) Optical devices : Optoelectronics
(060.5625) Fiber optics and optical communications : Radio frequency photonics

ToC Category:
Fiber Optics

History
Original Manuscript: November 9, 2010
Revised Manuscript: December 22, 2010
Manuscript Accepted: December 24, 2010
Published: January 6, 2011

Citation
Vincent R. Pagán, Bryan M. Haas, and T. E. Murphy, "Linearized electrooptic microwave downconversion using phase modulation and optical filtering," Opt. Express 19, 883-895 (2011)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-2-883


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