Open access peer-reviewed chapter

# Wired/Wireless Photonic Communication Systems Using Optical Heterodyning

By Alejandro García Juárez, Ignacio Enrique Zaldívar Huerta, Antonio Baylón Fuentes, María del Rocío Gómez Colín, Luis Arturo García Delgado, Ana Lilia Leal Cruz and Alicia Vera Marquina

Submitted: April 30th 2014Reviewed: September 1st 2014Published: November 19th 2014

DOI: 10.5772/59081

## 2. Optical heterodyne technique

The basic principle for generating microwave carriers is based on optical heterodyne technique, it represents a physical process called optical beating or frequency beating, where two phase-locked optical sources with angular frequencies ω1and ω2are superimposed and injected into a high frequency photodetector that permits to obtain a photocurrent at a frequency ω2ω1. To explain this in more detail, let us consider the relation between the generated electrical output signal and the two superimposed optical input waves from a more physical point of view. For simplicity, we assume that the two optical input waves are linearly polarized monochromatic plane waves in the infrared which propagate in the +z direction. Let

E1=E^1exp[i(ω1tk1z+φ1)]e1,E1

and

E2=E^2exp[i(ω2tk2z+φ2)]e2,E2

be the complex electrical field vectors of the two optical waves, with field amplitudes E^1and E^2, angular frequencies ω1and ω2and wave numbers k1and k1. The phase of each optical input wave is considered by φ1and φ1and e1and e2are the unit vectors determining the orientation of the electrical field vector of the linearly polarized optical input waves. The intensities of the constituent waves are given by the magnitude of their Poynting vectors and are therefore given by 

I1=12(εrεoμo)1/2|E1|2.E3
I2=12(εrεoμo)1/2|E2|2.E4

If the two incident optical waves are perfect plane waves and have precisely the same polarization (e1=e2), the resulting electrical field Eoof the optical interference signal is the sum of the two constituent input fields and hence we can write Eo=E1+E2. Taking the squared absolute value of the optical interference signal we obtain

|Eo|2=|E1+E2|2=|E1|2+|E2|2+E1E2*+E1*E2=|E1|2+|E2|2+2|E1||E2|cos((ω2ω1)t(φ2φ1)).E5

From equation (5) and by using equations (3) and (4), it follows that the intensity of the interference signal Iois given by 

Io=I1+I2+2(I1I2)1/2cos((ω2ω1)t(φ2φ1)).E6

By launching this optical interference signal into a photodetector, a photocurrent iis generated which can be expressed as 

i=ηoqhf1P1+ηoqhf2P2+2ηfcqh(P1P2f1f2)1/2cos((ω2ω1)t(φ2φ1)),E7

where qis the electron charge and P1and P2denote the optical power levels of the two constituent optical input waves. The photodetector’s DC and high-frequency quantum efficiencies are represented by ηoand ηfc. It is of course important to consider that the detector’s quantum efficiency is not independent of the frequency. Several intrinsic and extrinsic effects such as transit time limitations or microwave losses will eventually limit the high-frequency performance of the detector and thus the detector’s DC responsivity ηois typically much larger than its high-frequency responsivity ηfc. In our case, we can further simplify the photocurrent equation (Eq. (7)) by considering the fact that the two optical input waves are close in frequency (f1f2) whereas the difference frequency fcis by far smaller (fc=|f2f1|<<f1,f2). If we further assume for simplicity that the power levels of the two optical input waves are equal (PoptP1P2), Eq. (7) becomes 

i=2soPopt+2sfcPoptcos(2πfct+Δφ).E8

Where Δφ=φ2φ1. Here so=ηoqhfand sfc=ηfcqhfare the photodetector’s DC and high frequency responsivities given in A/W. Eq. (8) is the fundamental equation describing optical heterodyning in a photodetector. The first term is the DC photocurrent generated by the constituent optical input waves and the second term is the desired high-frequency signal oscillating at the difference frequency fc(down-converter) or intermediate frequency (IF) . In our case it represents the microwave signal that we will use as both information carriers, and as a local oscillator for transmitting and receiving TV signals in a wireless communication system.

## 3. Experimental scheme for generating microwave signals

The heterodyne technique for generating microwave signals has been done using the experimental setup shown in Figure 1. In this experiment, two laser diodes emitting at different wavelengths are used. One of them is a tunable laser (New Focus, model TLB-3902) which can be tuned over the C band with a channel spacing of 25 GHz, and the other one is a fiber coupled distributed feedback (DFB) laser source (Thorlabs, model S3FC1550) with a central wavelength at 1550 nm. For the generation of the microwave signals, the outputs of both lasers are coupled to optical isolators to avoid a feedback into the lasers and consequently instabilities to the system. A pair of polarization controllers is used to minimize the angle between the polarization directions of both optical sources. Thus, the polarization of the light issued from each optical source is matched and therefore, there is not degradation of the power levels in the microwave signals generated from the photodetector. The output of each controller is launched to a 3 dB coupler to combine both optical spectrums. After that, an optical output signal is received by a fast photodetector (MITEQ model SCMR-50K6G-10-20-10) with a typical gain of 25 dB, and –3 dB bandwidth of 6 GHz, The resulting photocurrent from the photodetector corresponds to the microwave beat signal which is analyzed with an Electrical Spectrum Analyzer (ESA), (Agilent model E4407B). The other optical output resulting from optical coupler is applied to an Optical Spectrum Analyzer (OSA) (Anritsu model MS9710C), for monitoring the wavelength of the two beams. Figure 1.Experimental setup for generating microwave signals by using optical heterodyne technique.

DFB laser can be used to control not only the output power of the fiber coupled laser diode, but also the precise control of the temperature at which the laser is operating. Both controls can be used to tune the fiber coupled laser diode to an optimum operating point, providing a stable output. In this way, it is possible to observe that the wavelength of the DFB laser is shifting, by varying its temperature with a scale of 1 °C. Consequently, the beat signal frequency is continuously over the band of photodetector. On the other hand, the frequency difference from both lasers can be expressed by 

Δf=cλ1cλ2=c(λ2λ1)λ1λ2cλ2|Δλ|,E9

where λ1and λ2are the wavelengths of the two beams, respectively, and Δλis the difference between the two wavelengths. To obtain a microwave signal, in a first step, the tunable laser is biased and its optical spectrum is displayed on the OSA screen. In a second step, the DFB laser is also biased, fixing an optical power of 2.2 mW and its central wavelength is settled as near as possible to the central wavelength of the tunable laser. As can be seen from Figure 2, the value of Δλ = 0.023739 nm is the wavelength difference between both lasers and it corresponds to the beat signal frequency of 2.8 GHz. Figure 2.Optical spectrum corresponding to the mixed optical sources. The peaks located at λ1=1550.3197 nm and λ2=1550.3435 nm corresponds to the tunable and DFB lasers, respectively.

A precise control of the difference, between the two central wavelengths and by consequence over the frequency difference, is obtained by tuning the DFB. The wavelength variation of the laser source is obtained by changing the junction temperature between 22.8 °C, 23.2 °C and 23.7 °C corresponding to the frequency range of 0 to 5.0 GHz. Figure 3 illustrates the electrical spectrums of four generated microwave signals by using optical heterodyne. These signals are located at f1=1.0, f2=2.0, f3=2.8and f4=4.0GHz respectively. It can be seen, that the microwave signals are in good agreement with theoretical value given by Eq. (9). Therefore, when one laser source is operating at a fixed wavelength and the other is being continuously tuned, the beat frequency will shift correspondingly. In particular, the frequency of the microwave drive signal is set at 2.8 GHz. Figure 3.Spectrum for the microwave signal generated by using optical heterodyne.

## 4. Modulation and demodulation

Some form of modulation is always needed in an RF system to translate a baseband signal (e.g., audio, video, data) from its original frequency bandwidth to a specified RF frequency spectrum. There are many modulation techniques, for example, amplitude modulation (AM), frequency modulation (FM), amplitude shift keying (ASK), frequency shift keying (FSK), phase shift keying (PSK), biphase shift keying (BPSK), quadriphase shift keying (QPSK), 8-phase shift keying (8-PSK), 16-phase shift keying (16-PSK), minimum shift keying (MSK), and quadrature amplitude modulation (QAM). AM and FM are classified as analog modulation techniques, and the others are digital modulation techniques . In this section we describe the AM modulation and demodulation due to it was used in our proposed wireless communication system.

### 4.1. Amplitude modulation

Analog modulation uses the baseband signal (modulating signal) to vary one of three variables: amplitude Ac, electrical frequency (ω1ω2)=ωc=2πfc; or phase (ϕ1ϕ2)=Δϕ. According to Eq. (8), the obtained carrier signal by using optical heterodyne technique can be written by

p(t)=Accos((ω1ω2)t+ϕ1ϕ2)=Accos(2πfct+Δϕ).E10

Where Ac=2sfcPopt. In amplitude modulation, if we assume that s(t)is the information signal, and considering Ac=1, Δϕ=0, then a modulated signal can be written by

g(t)=s(t)cos2πfct.E11

Applying the modulation property of the Fourier transform to Eq. (11), we can find the density spectral of g(t)is

G(f)=12S(ffc)+12S(f+fc).E12

Amplitude modulation therefore translates the frequency spectrum of a signal by ±fchertz, but leaves the spectral shape unaltered. This type of amplitude modulation is called suppressed-carrier because the spectral density of g(t)has no identifiable carrier in it, although the spectrum is centered at the frequency fc.

### 4.2. Amplitude demodulation

Recovery the signal information s(t)from the signal p(t)requires another translation in frequency to shift the spectrum to its original position. This process is called demodulation or detection. Because the modulation property of the Fourier transform proved useful in translating spectra for modulation, we try it again for demodulation. Assuming that g(t)=s(t)cos2πfctis the transmitted signal, we have

g(t)cos2πfct=s(t)cos22πfct=12s(t)+12cos4πfct.E13

Taking the Fourier transform of both sides of Eq. (13) and using the modulation property, we get

[g(t)cos2πfct]=12S(f)+14S(f+2fc)+14S(f2fc).E14

The mathematical process described in this section can be obtained by convolving the spectrum of the received signal g(t)with that of cos2πfct(i.e., with impulses at ±fc). A low-pass filter is required to separate out the double frequency terms from the original spectral components. Obviously we need a filter with a cut frequency fcut>2fmfor proper signal recovery. In this case fmrepresents the information frequency.

### 4.3. Effects in frequency and phase variations

When the local oscillator at the receiver, has a small frequency error Δfand a phase error Δθ, then this signal can be written as

pL(t)=cos[2π(fc+Δf)t+Δθ].E15

Assuming again that g(t)=s(t)cos2πfctis the transmitted signal; then we have that at the receiver, the recovered signal can be written by

g(t)cos[2π(fc+Δf)t+Δθ]=s(t)cos(2πfct)cos[2π(fc+Δf)t+Δθ]=s(t)(cos(2πΔft+Δθ)2+cos[2π(2fc+Δf)t+Δθ]2).E16

The second term on the right hand side of Eq. (16) is centered at ±2fc+Δfand can be filtered out by using a low pass filter. The output of this filter sF(t)will then be given by the remaining term in Eq. (16).

sF(t)=[s(t)2(cos2π(Δf)tcos(Δθ)sen2π(Δf)tsen(Δθ))].E17

As can been from equation (17), the output signal is not s(t)2, unless both Δfand Δθare zero. The effects of both frequency errors and random phase errors render this demodulation of the signal unsatisfactory. It is necessary, therefore, to have synchronization in both frequency and phase between the transmitter and the receiver when amplitude modulation is used. The synchronization of the carrier signals presents no major problem when the transmitter and the receiver are in close proximity. Recovering the original signal s(t)from the modulated signal g(t)using a synchronized oscillator is called coherent demodulation. In our case we take advantage of proposed optical heterodyne technique permits to obtain microwave carrier and local oscillator simultaneously in the transmitter and receiver respectively.

## 5. Design of a patch antenna at 2.8 GHz

The microstrip patch antenna is a popular printed resonant antenna for narrow-band microwave wireless links that require semihemispherical coverage. Due to its planar configuration and ease of integration with microstrip technology, the microstrip patch antenna has been studied heavily and is often used as an element for an array. Common microstrip antenna shapes are square, rectangular, circular, ring, equilateral triangular, and elliptical, but any continuous shape is possible . Furthermore, a patch antenna is an excellent device due to its small size, low cost, and good performance [14-16]. In this chapter, a rectangular printed patch antenna is proposed. Simulation results have been obtained by using Advanced Design System (ADS) that is a computer-aided-engineering software tool. The radiating structure consists of a patch and a microstrip inset-feed line, allowing that the characteristic impedance (Zo) to be improved. Figure 4 shows the geometry and configuration of the top layer. The proposed antenna in this work was designed to operate in the band S of telecommunications (2.8 GHz). FR4 is used as a dielectric substrate exhibiting a thickness h=1.524mm, and relative dielectric constant εr=4.2. In a first step, the width (W) of the patch is computed by using :

W=co2fc2εr+1,E18

where cois the light velocity in the free space, and fois the operation frequency. Next, the value of the effective dielectric constant εeffis evaluated considering W/h>1.

εeff=εr+12+εr12(1+12hW)1/2E19

Border effects  must to be considered in the design of the antenna. For this reason, ΔLfrom Figure 4 can be evaluated as:

ΔLh=0.412(εeff+0.3)(Wh+0.264)(εeff0.258)(Wh+0.8)E20

This allows that the length (L) of the patch to be evaluated as:

L=co2foεr2ΔLE21

Considering the values previously obtained, the effective dimensions (Leffand Weff) can be calculated, respectively as:

Leff=L+2ΔLE22
Weff=W+tπ(1+ln(2ht))E23

From Eq. (23), t is the conductor thickness and W/h>1/2πmust to be considered. The ground plane dimensions are computed as:

L1=6h+LeffW1=6h+WeffE24

The best dimensions which assure a good matching between the impedances (Rin=Zo=50Ω) of the antenna and generator can be calculated by the use of LineCalc tool from ADS and by the next expression:

Rin(y=yo)=12(G1±G12)cos2(πLyo)E25

where G1and G12are the conductance values obtained by the cavity method. Finally, Table 1 shows a summary of the dimensions for the patch and the ground plane.

 Operation Frequency(Antenna) Dimensions (cm) Wo Lo W L W1 L1 yo 2.8 GHz 0.13 3.08 3.32 2.56 10 10 0.93

### Table 1.

Dimensions of the fabricated antenna.

Figure 5(a) shows a picture of the fabricated patch antenna where a SubMiniature version A (SMA) connector is added. Figure 5(b) illustrates simulation and experimental results corresponding to the S11parameter. Electrical measurements are obtained by using a Vector Network Analyzer (VNA) (Agilent Technologies model: E8361A). It is clearly observable that experimental result is in good agreement with the simulation. Figure 5.Fabricated antenna (a), Experimental and simulation return loss curve for the antenna (b).

## 6. Transmission of TV signals by using heterodyne technique

In order to show a potential application of optical heterodyne technique in the field of the wireless communications, we have proposed a coherent wired/wireless photonic communication system as shown in Figure 6. This system is not a truly wireless communication system, since an optical fiber is required to deliver both microwave carrier and local oscillator for transmitting and receiving information of TV signals as an approximation to point to point indoor wireless communications systems. From the photodetector 1 in the transmitter, a microwave signal located at 2.8 GHz is obtained and mixed with an analog TV signal located at 62.25 MHz. Then the resulting signal is amplified before being applied to our fabricated microstrip antenna. After that, the obtained modulated signal as shown in Figure 7, is transmitted through a point to point wireless link by using the microstrip antenna. Finally in the receiver, another microstrip antenna is used to receive the transmitted information, which it is processed using optical heterodyne technique again to recover in this case the TV signal (66-72 MHz). From the photodetector 2 in the receiver, a local oscillator that is synchronized, in frequency as well as in phase with to that obtained from the photodetector 1, is mixed with the received signal. Then the resulting signal is filtered and the power spectral density obtained is displayed on an electrical spectrum analyzer, where it is analyzed to measure the power level of recovered information. Figure 6.Wired/wireless photonic communication system for transmitting and receiving TV signals.

Figure 8 shows the frequency spectrum of an analog National Television System Committee (NTSC) TV signal at the input of the transmitter located at 67.25 MHz (before being applied to frequency mixer). In the same figure we can see the obtained analog NTSC TV signal at the output of the receiver. In order to measure the quality of the received signal, it is necessary to quantify the parameter of signal-to-noise ratio (SNR), in this case it is approximately 45 dB. The analog information is successfully transmitted from the transmitter to the receiver, and the received signal is satisfactorily reproduced on TV monitor. The differential gain and differential phase were not measured Nevertheless we demonstrated that the generated microwave signal by using optical heterodyning can be used as carrier information in a traditional communication system and we have used a TV signal of test to verify it.

## 7. Analytical model of the microwave photonic filter

The scheme of the MPF is illustrated in Figure 9. Consider that the optical signal of a polychromatic source with spectrum P(ω), centered at an optical frequency ωn, is launched into the input of the Mach-Zehnder intensity modulator (MZ-IM). A single spectral component of such an optical signal can be modeled by a stochastic process e(t)=Eo(t)exp(jωnt), where Eo(t)is the complex amplitude and ωnis the optical angular frequency. If the intensity of such optical signal is externally modulated by an electrical signal Vm=1+2mcos(ωmt), where mis the modulation index and ωmis the angular frequency of external modulation, then the optical field at the input of the optical fiber can be expressed by Eq. (26). The modulation index mis related to the electrical input signal amplitude, Vm, as: 2m=π(Vm/Vπ), where Vπis the half wave voltage of the MZ-IM .

ei(t)=e(t)s(t)E26

The optical fiber can be considered as a linear time invariant (LTI) system. If, for simplicity, the attenuation is ignored, then the transfer function of the optical link, for a given length L, is H(jω)=exp(jβL), where βis the propagation constant. Thus, the optical field at the end of the link is given by

eL(t)=ei(t)exp(jβL)E27

Substituting e(t)and s(t)in Eq. (26), and then replacing this in Eq. (27), it becomes:

eL(t)=Eo(t)exp(j(ωmtβL))+Eo(t)mexp(j[(ωmωn)tβL])+Eo(t)mexp(j[(ωm+ωn)tβL])E28

In the frequency domain Eq. (28) can be expressed as:

EL(ω)=Eo(ωωn)exp(jβL)+Eo(ω(ωnωm))exp(jβL)+Eo(ω(ωn+ωm))exp(jβL)E29

There are three spectral components. In the presence of chromatic dispersion, there is a propagation constant associated to each one of them, i.e. β(ωωn), β(ω(ωn+ωm))and β(ω(ωnωm)). By denoting W=ωωn, Eq. (29) then becomes:

EL(ω)=Eo(W)exp(jβ(W)L)+Eo(W+ωm)exp(jβ(W+ωm)L)+Eo(Wωm)exp(jβ(Wωm)L)E30

Assuming that within the frequency range ωnωmto ωn+ωm, centered at ωnthe propagation constant varies only slightly and gradually with ω, it can be approximated by the first three terms of a Taylor series expansion, and it can be shown that

β(W±ωm)=β(W)±β1ωm+β2[12ωm2±ωm(ωωn)]E31

where βi=[diβ(ω)/dωi](ω=ωn).

The optical intensity, I, is obtained by integrating the power spectral density over all the frequency range, i.e.

I=|EL(ω)|2dωE32

Considering that the MZ-IM is operating on its linear region, it is valid to note that m20. On the other hand, if ωn>>ωmthen Eo(W)Eo(W+ωm)Eo(Wωm). Furthermore, in the frequency domain, the spectrum of the source is defined as P(ω)=Eo(ω)Eo*(ω). Thus, developing the product |EL(ω)|2in Eq. (32) and replacing Eq. (31), it is possible to demonstrate that the intensity at the end of the optical fiber is given by:

I=P(W)dW+4mcos(β2ωm22L)cos(β1ωmL){P(W)exp(j2πZW)dW}E33

where Z=β2ωmL/2π, W=ωωnand its derivative, dW=dω. The total average intensity is Io=P(W)dW, and the integral {P(W)exp(j2πZW)dW}corresponds to the real part of the Fourier transform of the spectrum of the optical source. This means that the optical intensity which reaches the surface of the photodetector is proportional to:

F(W)={FT{P(W)}}E34

A spectrum with Gaussian shape can be modeled by an analytical expression as:

P(ω)=2PoΔωπexp(4(ωωm)2Δω2)E35

where ωis the angular frequency, ωis the central angular frequency, ωis the maximum power emission and Δωis the full width at half maximum (FWHM) of the optical source. If the emission spectrum of the optical source has a Gaussian shape, as defined in Eq. (35), then the Eq. (34) becomes:

F(ω)=exp((β2ωmLΔω4)2)E36

In such case the FWHM of the frequency response can be determined equating F(ω)=0.5, which implies:

(β2ωmLΔω4)2=ln(2)E37

For finding the value of the frequency fmthat yields that condition, it is necessary to express ωmin terms of fm, i.e. ωm=2πfm. But this, in turn, yields an expression that can be reduced by expressing Δωin terms of Δλand β2in terms of dispersion D. For Δωthis is done as follows: given dω/dλ=(2πc/λ2), where cis the speed of light in the free space and λis the wavelength of the optical signal, it is possible to establish the following correspondence:

dω=2πcλ2dλΔω=2πcλ2ΔλE38

Now, for the factor β2, given that the group velocity, vg=L/τgwhere τgis the group delay, is related to β(ωn)as τg/L=dβ(ωn)/dω, and its derivative is (dτg/dω)/L=d2β(ωn)/dω2=β2, then (1/L)(dτg)=dωβ2. Thus, the derivative of this expression by dλis (1/L)(dτg/dλ)=(dω/dλ)β2. Furthermore, the dispersion, as a function of the wavelength is defined as D=(1/L)(dτg/dλ). This means that β2=D(λ2/2πc). Finally, by substituting ωm=2πfm, Δω, in Eq. (38), and the expression for β2in Eq. (37), the frequency fm, which corresponds to the low-pass bandwidth Δflp, can be expressed as:

Δflp=2ln(2)πDLΔλE39

where the dispersion Dhas units of ps nm-1 km-1, length Lis given in km, and the FWHM of the optical source, Δλ, in nm. This means that in the presence of an optical source, like a super luminescent light-emitting diode (LED), the frequency response of the system is low-pass, and its bandwidth is given by Eq. (39). In the context of this chapter, the optical source is an multimode laser diode (MLD). The emission spectrum of this type of optical sources can be modeled by means of an analytical expression as expressed in Eq. (40):

P(ω)=2PoΔωπexp(4(ωωn)2Δω2)[2Poσωπexp(4(ωωn)2σω2)*n=δ(ωnδω)]E40

where ωis the angular frequency, ωnis the central angular frequency, Pois the maximum power emission, Δωis the FWHM of the optical source, σωis the FWHM of each emission mode and δωis the free spectral range (FSR) between the emission modes. By using variables Zand W, as defined earlier, and substituting Eq. (40) in Eq. (34), it can be expressed as:

F(ω)=exp((β2ωmLΔω4)2)*[exp((β2ωmLσω4)2)1δωn=δ(β2ωmL2πnδω)]E41

The term between crochets indicates the presence of a periodic pattern. The frequency of the first maximum can be determined by equating:

β2ω1L2π=1δωE42

For finding the value of the frequency f1that yields that condition, it is necessary to express δωin terms of f1. In a similar way as in Eq. (38), it is possible to establish the following correspondence:

dω=2πcλ2dλδω=2πcλ2δλE43

thus, substituting δωin Eq. (42), expressing ω1in terms of f1and using β2=D(λ2/2πc)then the frequency f1can be expressed as:

f1=1DLδλE44

and, in general, the central frequency of the n-th band-pass lobe is given by

fn=nDLδλE45

where nis a positive integer, dispersion Dis given in ps nm-1 km-1, length Lin km, and the FSR δλin nm. The bandwidth of each of these band-pass lobes is equal to:

Δfbp=4ln(2)πDLΔλE46

which is twice Eq. (39). The periodic pattern in the frequency response of the system will appear only when an MLD is used in the system. This behavior will allow that microwave signals to be filtered and transmitted over a wide range of frequencies.

## 8. Experimental setup of optical and wireless transmission

In a ﬁrst step, the MLD used in this experiment (OKI OL5200N-5) is optically characterized by means of an optical spectrum analyzer (Agilent, model 86143B). Figure 10 corresponds to the measured optical spectrum obtaining λo=1553.53nm, Δλ=5.65nm, and δλ=1.00nmfor a driver current of 25 mA. The use of a laser diode temperature-controller (Thorlabs, model LTC100-C) allows us to guarantee the stability of the optical parameters to thermal ﬂuctuations.

In a second step, considering a length L=20.70 km of single-mode-standard-fiber (SM-SF) exhibiting a chromatic fiber-dispersion parameter of D=16.67 ps/nm km. Eq. (45) allows us to determine the value of the central frequency corresponding to the first filtered microwave or first band-pass as

f1=1DLδλ=1(16.67x1012seg/nmkm)(20.70km)(1.0nm)=2.8GHz

Eq. (39) permits us to determine the value of the low-pass band as

Δflp=2ln(2)πDLΔλ=2ln2(π)(16.67x1012seg/nmkm)(20.70km)(5.65nm)=271.85MHz

Finally, according to Eq. (46), the corresponding bandwidth of the band-pass window is Δfbp=543.70MHz.

At this point, it is well worth highlighting the advantageous use of the chromatic dispersion parameter to obtain the filtered microwave signal. Once the main parameters are known, the topology illustrated in Figure 11 is assembled in order to evaluate the frequency response of the MPF.

At the output of the MLD, an optical isolator (OI) is placed in order to avoid reflections to the optical source. Since the MZ-IM (Photline MX-LN-10) is polarization-sensitive, a polarization controller (PC) is used to maximize the modulator output power. The optical signal is launched into the MZ-IM. The microwave electrical signal (RF) for modulating the optical intensity is supplied by using optical heterodyne as described in Figure 1. The registered frequency response is located from 0.01 to 4 GHz at 0 dBm. The intensity-modulated optical signal is then coupled into a 20.70 km of SM-SF coil. The length of the optical fiber is corroborated by using an optical time domain reflectometer, OTDR (EXFO, model FTB-7300E). At the end of the link, the optical signal is applied to a fast Photo-Detector (PD, Miteq DR-125G-A), and its output connected to an electrical spectrum analyzer (Anritsu, model MS2830A-044), in order to measure the frequency response of the MPF. Figure 12 corresponds to the measured experimental frequency response where a low-pass band centered at zero frequency and the presence of a band-pass band centered at 2.8 GHz are clearly appreciable.

The bandwidth of 543.70 MHz associated to the band-pass window centered at 2.8 GHz allows us to guarantee enough bandwidth in case of ﬂuctuations (in the order of nanometers) between mode spacing. On the other hand, a considerable increase on the length of the optical ﬁber due to thermal expansion is practically impossible. These considerations permit us to guarantee a good stability for the microwave photonic ﬁlter. Once the frequency response of the MPF is determined, the setup illustrated in Figure 13 is assembled for carrying out the ﬁber-radio transmission.

Now, the electrical signal generator provides a signal of 2.8 GHz at 0 dBm that is used as the electrical carrier and demodulated signal. This signal is separated by using a power divider. Part of this signal is transmitted via radio frequency by the fabricated microstip antenna shown in Figure 5, and the rest is mixed with an analog NTSC TV signal of 67.25 MHz. The resulting mixed electrical signal is then applied to the electrodes of the MZ-IM for modulating the light emitted by the MLD. The modulated light is coupled into the 20.70 km SM-SF coil. At the end of the optical link, the signal is injected to a fast photo-detector (PD), and its electrical output is then ampliﬁed and launched to an electrical mixer. Another microstrip patch antenna placed at a distance of 10 meters is connected to a port of the mixer in order to recuperate the microwave signal that plays the role of the demodulated signal. Finally, by using another power divider, recovered analog TV signal can be launched to a digital oscilloscope or to the electrical spectrum analyzer in order to evaluate the quality of the recovered signal and at the same time display the TV signal on a TV monitor. Figure 14 (a) shows the measured electrical spectrum (Agilent, E4407B) corresponding to the transmitted TV signal where the SNR is 52.67 dB, whereas Figure (b) corresponds to the recovered TV signal with a SNR of 46.5 dB.

Finally, Figure 15 corresponds to a photograph of the screen of the oscilloscope where upper and lower traces are the waveforms of the transmitted and recuperated signal, respectively.

## 9. Conclusions

Wireless communication systems require compact sources for the generation of mm-wave signals, that must have high spectral purity (linewidth < 100 kHz, phase noise < 100 dBc @100 kHz offset), tuneability, low power consumption and low cost, and although optical heterodyne of two DFB lasers has phase noise of –75 dBc/Hz even at an offset frequency of 100 MHz and it does not very compact, we have demonstrated in this chapter that by using optical heterodyne technique, a TV signal was transmitted and received satisfactory as a result of our proposed communication system generates a microwave carrier and a local oscillator simultaneously ensuring synchronization in frequency as well as in phase between microwave carrier and a local oscillator and avoiding in this case the use of an analog phase locked loop in the receiver to recover the TV information. The authors consider that the first proposed scheme in this chapter is not a truly wireless communication system, since an optical fiber is required to deliver the local oscillator in the receiver, however in order to obtain a wireless communication systems by using optical heterodyne technique, it is necessary to have collimated beams from optical fiber to photodetectors. On the other hand, due to the fact that the distribution of TV over microwave signals in the electrical domain presents loss associated with electrical distribution lines, the authors consider that the optical fiber is an ideal solution to fulfill this task because of its extremely broad bandwidth and low loss. In that case the distribution of TV over microwave can be directly by using optical fiber. In this way the second proposed experiment in this chapter represents a novel fiber-radio scheme to transmit an analog NTSC TV signal coded on a microwave band-pass located at 2.8 GHz. Filtering of microwave signal was achieved through the appropriate use of the chromatic fiber dispersion parameter, the physical length of the optical fiber, and the free spectral value of the multimode laser. Transmission of a TV signal was achieved over an optical link of 20.70 km, whereas a demodulated signal was transmitted via radiofrequency using the fabricated microstrip patch antennas. Although the distance between antennas was short, this distance can be lengthened if an array of antennas is used. Besides, a mathematical analysis corresponding to the microwave photonic filter was described demonstrating that the frequency response of the microwave photonic filter is proportional to the Fourier transform of the spectrum of the optical source used. The proposed microwave photonic filter represents an interesting technological alternative for transmitting information by using optoelectronic techniques. The results obtained in this work ensure that as an interesting alternative, several modulation schemes can be used for transmitting not only analog information but also digital information. Besides as optical heterodyne technique described here can generate microwaves continually tuned, we can use this feature to transmit several TV signals using frequency division multiplexing schemes FDM  and wavelength division multiplexing WDM techniques, not only point to point but also with bidirectional schemes by using simultaneous wired and wireless systems.

## Acknowledgments

This work was supported by CONACyT (grants No 102046 and 154691).

## How to cite and reference

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Alejandro García Juárez, Ignacio Enrique Zaldívar Huerta, Antonio Baylón Fuentes, María del Rocío Gómez Colín, Luis Arturo García Delgado, Ana Lilia Leal Cruz and Alicia Vera Marquina (November 19th 2014). Wired/Wireless Photonic Communication Systems Using Optical Heterodyning, Advances in Optical Communication, Narottam Das, IntechOpen, DOI: 10.5772/59081. Available from:

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