## Abstract

A novel all-optical microwave filter with a frequency response equivalent to a bandpass filter is presented. An electro-optic phase modulator combined with a dispersive device is employed to eliminate the baseband resonance of a typical lowpass filter. A two-tap bandpass transversal microwave filter with a null-to-null bandwidth of 8.8 GHz and a 35-dB notch rejection level is demonstrated.

©2004 Optical Society of America

## 1. Introduction

All-optical microwave filters for the processing of microwave and millimeter-wave signals directly in the optical domain have attracted great interest because of the advantages such as large time-bandwidth products, insensitivity to electromagnetic interference, low loss and light weight. However, most reported approaches are based on the incoherent operation, in which only the intensity of the optical signal can be manipulated and hence negative taps are difficult to obtain. This results in a severe limitation of the all-optical filter functions. For example, bandpass or highpass filters cannot be implemented if only positive taps are available.

To overcome this limitation, several techniques have been proposed to realize negative coefficients and consequently achieve bandpass filtering functions. One approach proposed by Sales *et al*. [1] is to use differential detection, which requires converting the optical signal to electrical signal at the cost of increased system complexity. Other approaches with negative coefficients include wavelength conversion based on cross-gain saturation modulation in a semiconductor optical amplifier (SOA) [2], and carrier depletion effect in a Fabry-Perot (FP) laser diode [3] or in a distributed-feedback (DFB) laser diode [4]. More recently, Capmany et al. [5] proposed a bandpass filter that employed two electro-optic modulators (EOMs). Negative coefficients were obtained by biasing the two EOMs at different operation points. Mora *et al*. [6] presented a simple approach to realizing transversal filters with negative coefficients. The negative taps were obtained by use of the transmission of a broadband source through uniform Bragg gratings. Chan *et al*. [7] presented a two-tap notch filter with one negative tap, in which a dual-output EOM was used. The EOM was connected in a way that it undergoes a double-pass modulation.

In those configurations, complicated structures and extra active or passive components are required. In this paper, we propose a novel method to implement microwave bandpass filters with a simple structure. It is different from the negative coefficient bandpass filters proposed in [5–7]; the bandpass filter proposed here is realized by eliminating the baseband resonance of a typical lowpass filter using a phase modulator combined with a dispersive device. In the proposed configuration, an array of laser diodes emitting at different optical wavelengths with identical wavelength spacing are phase modulated by the microwave signal to be filtered; two sidebands with *π* phase difference are generated for each optical carrier. The phase modulated signal is then applied to a length of standard single mode fiber serving as a dispersive medium. The filtered microwave signal is obtained at the output of a photodetector. A two-tap bandpass transversal microwave filter is implemented. A null is always observed at the dc frequency, which ensures a bandpass operation. The filter with a null-to-null bandwidth of 8.8 GHz with a 35-dB notch rejection level is demonstrated.

## 2. Principle of operation

Figure 1 shows a block diagram of the experimental setup of the all-optical bandpass microwave transversal filter. An array of tunable lasers emitting at different wavelength with identical wavelength spacing of Δ*λ* are fed to an electro-optic phase modulator via a star coupler. The phase modulator is driven by the microwave signal to be processed. The dispersive medium in the experiment is a coil of single mode fiber. To reduce the size of the system, the single mode fiber can be replaced by high dispersion fiber or a linear chirped fiber Bragg grating (LCFBG). The signal after the dispersive device is fed to a photodiode. A vector network analyzer is used to measure the frequency response of the proposed bandpass microwave filter.

The phase modulated optical spectrum is illustrated in Fig. 2(a), which consists of an optical carrier and two first-order sidebands. In general, the modulation process of a phase modulator generates a series of sidebands with Bessel function amplitude coefficients. However, when the modulation depth is small the higher-order sidebands can be neglected, and only the first-order upper and lower sidebands need to be considered. It is different from an intensity modulation where the two sidebands at the output are in phase. At the output of the phase modulator, the two sidebands are *π* out of phase. If this signal is directly detected using a photodiode, the RF signal cannot be recovered because beating between the carrier and the upper sideband exactly cancels the beating between the carrier and the lower sideband. However, as shown in Fig. 2(a), if the modulated optical signal passes through a dispersive device, the phase difference of the two sidebands can be effectively rotated to be totally or partially in phase thanks to the dispersion induced by the dispersive device. Then the modulating RF signal may be recovered when this dispersed optical signal is fed to a photodetector. Mathematically, the recovered microwave signal can be expressed by Eq. (1), which shows that the amplitude of the recovered RF signal, denoted as *E*_{RF}
(*t*), is the function of the system-induced dispersion as well as the modulating frequency,

where *c* is the optical wave propagation velocity in free space; *χ* is the accumulated dispersion of the dispersive device; *λ*
_{0} is the central wavelength of the carrier; *f*_{m}
is the frequency of the modulation signal; and *φ* is the phase delay of the recovered microwave signal, which is also determined by *χ* and *f*_{m}
. Based on Eq. (1), the frequency response of this phase modulation and intensity-detection operation is denoted as *H*
_{1} (*ω*) and is drawn in Fig. 2(b). We can see that there is a notch at the dc frequency; the first peak and the second notch can be calculated by letting ${\pi \chi \lambda}_{0}^{2}$
${f}_{m}^{2}$
/*c*=*π*/2 and *π*, respectively.

Let us again consider the configuration shown in Fig. 1, in which an array of laser diodes are phase modulated via the phase modulator. Each laser source can be considered as an independent optical carrier. If we assume that the wavelength spacing between any adjacent laser diode is very small and all the laser diodes have identical input power at the phase modulator, the dispersion effects induced frequency response se (*H*
_{1} (*ω*) for each carrier can be considered identical. But the phase *φ*_{n}
of the *n*-th RF signal recovered from the *n*-th modulated optical signal is not identical because different carrier travels at different velocity in this dispersive device. Then the summation of all the recovered RF signals will induce another frequency response *H*
_{2} (*ω*), which can be expressed as

where *N* is the number of the laser diodes or the number of the filter taps, *φ*_{n}
is the phase of the *n*-th recovered RF signal, *ω*_{m}
is the modulating angle frequency, and *T*=*χ*·Δ*λ* is the time interval of any two adjacent taps.

The effective transfer function of this phase-modulation-based microwave filter can be expressed as the multiplication of the two responses,

Based on the characteristics of *H*
_{1} (*ω*) and *H*
_{2} (*ω*) discussed earlier, we may conclude that the baseband resonance of the lowpass filtering function due to the conventional intensity-modulation direct-detection (IM-DD) scheme can be eliminated; and an all-optical equivalent bandpass microwave filter is consequently achieved.

## 3. Experimental setup and results

An experiment based on the configuration shown in Fig. 2(a) is carried to verify the dispersion effects in the phase modulated optical link. A tunable laser with a tuning range from 1520 nm to 1620 nm is used as an optical source. A 25-km standard single-mode SMF-28 fiber is employed as the dispersive device. The fiber shows a chromatic dispersion of 17 ps/nm/km at 1550 nm, which provides an accumulated dispersion of *χ*=425 ps/nm. By sweeping the modulating frequency from 45 MHz (which is limited by minimum measurement frequency of the vector network analyzer) up to 25 GHz, at the same output power of 3 dBm, the corresponding output of the photodiode is observed by the vector network analyzer, which is shown in Fig. 3.

Owing to the different propagation velocities of the different spectral components, a quasi-periodic change of the RF power can be observed from Fig. 3. We can see that a notch at the dc frequency is observed. When the carrier wavelength is 1550 nm (solid line), the second notch is located at 17.2 GHz. By use of Eq. (1), the theoretical value is calculated to be 17.1 GHz, which shows a good agreement between the two values. From Fig. 3, we can also see that the curve is squeezed or stretched when the carrier wavelength is tuned towards longer (dashed line) or shorter (dotted line) wavelength. This feature indicates that by varying the carrier frequency or the dispersion of the dispersive medium, the frequency response *H*
_{1} (*ω*) can be changed.

The overall filter frequency response is the multiplication of the *H*
_{1} (*ω*) and *H*
_{2} (*ω*), as shown in Eq. (3). To implement *H*
_{2} (*ω*), in the experiment two tunable laser sources emitting at *λ*
_{1}=1550.078 nm and *λ*
_{2}=1550.212 nm are combined via a 3-dB optical coupler to feed the phase modulator. The pumping current and the polarization state of each light source are carefully adjusted to obtain the same average output power from the phase modulator. The wavelength spacing between the two laser sources is 0.134 nm, which gives a time delay of 57 ps or a free spectral range (FSR) of 17.5 GHz. This value is equal to the frequency of the second notch of *H*
_{1} (*ω*). The effective transfer function of the microwave filter *H* (*ω*) measured using the vector network analyzer is shown in Fig. 4. From Fig. 4, we can see that although the lowest measurement frequency is 45 MHz, it can be extrapolated that the filter response has a notch at the dc frequency, which indicates clearly the function of an equivalent bandpass filter. As expected, the filter response consists of a number of notches located at the frequencies determined by the effective transfer function *H* (*ω*), which gives an equivalent bandpass filter with null-to-null bandwidth of 8.8 GHz and a 35-dB notch rejection level. The degradation of the magnitude response shown in higher frequencies is due to the unflat responses of the phase modulator and the photodetector.

The proposed scheme here has certain advantages compared with some earlier approaches. First, it has a simpler structure with less optical components. In the proposed structure, only an electro-optic phase modulator, a laser array and a dispersive device are required; whereas in other approaches complicated structure and additional components are required, i.e., SOAs in cross-gain modulation approach, a second EOM, or a special dual-output EOM, are required to implement bandpass filters with negative coefficients. Another important advantage provided by this approach is that it has the potential to be reconfigurable and tunable. The output power of each laser diode in the laser array can be adjusted independently, which means that different window functions can be easily applied to the filter and therefore the frequency response can be reconfigured. Furthermore, the same dispersive device is used to synthesize both the transfer functions of *H*
_{1} (*ω*) and *H*
_{2} (*ω*), which implies that by adopting more taps, and carefully selecting the carrier wavelengths or the dispersive medium with proper chromatic dispersion, the synthesis of some practical and tunable bandpass filters is possible.

## 4. Conclusions

A novel all-optical equivalent bandpass microwave transversal filter has been proposed and demonstrated. The proposed filter had a simple structure, in which the bandpass operation was implemented using a phase modulator combined with a dispersive device, to eliminate the resonance at the baseband. A notch at the dc frequency was observed. A two-tap bandpass filter with a null-to-null bandwidth of 8.8 GHz and a 35-dB notch rejection level was demonstrated.

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