Photonic Image Rejection Mixer Based on Polarization Manipulation of a Broadband Optical Source

We propose a photonic mixer with image rejection capability using a broadband optical source (BOS) and polarization processing. Intermediate frequency (IF) signals with image rejection are generated from the local oscillator-modulated and the time-delayed radio frequency (RF)-modulated BOS light. The RF operating frequency is flexibly tunable over a wide range by simply adjusting the time delay. In addition, the proposed system is free from dispersion-induced mixing power fading and bias drift problem. Experimental results exhibit an image rejection ratio of more than 44.6 dB for RF signals from 2 to 18 GHz, while the IF signal is fixed at 800 MHz. Image rejection mixing operation at different IF frequencies and signal power is also confirmed.


Introduction
Frequency down-conversion of radio frequency (RF) signals is of critical importance for signal processing in microwave systems such as electronic warfare, wireless communication and radar [1]- [3]. Photonic microwave mixers have attracted increasing attention in recent years for its low loss, flexible tunability, electromagnetic interference immunity and compatibility with radio-over-fiber systems [4]- [6]. However, the image interference and the desired RF signal, which are located symmetrically with respect to the local oscillator (LO) signal, are down-converted to the identical intermediate frequency (IF) band, thus a deteriorated IF signal is generated and the performance of the system is degraded.
The first well-known approach to accomplishing image rejection mixing is the phase-cancellation technology based on Hartley architecture, where parallel quadrature IF signals are combined via a 90°electrical hybrid, thus the two IF components originated from the image are out of phase and can be suppressed [7]- [19]. Quadrature IF signals can be acquired through a pair of quadrature RF [8] or LO [9] signals generated from an electrical hybrid. The image rejection performance of these schemes depends on the electrical hybrid, which means an electrical hybrid with a precise 90°phase difference over a wide frequency range is required. In [10]- [12], a 90°optical hybrid has been introduced to generate quadrature LO-modulated sidebands, which faces the same challenge as the case of using electrical hybrids. A promising method for precise phase shift is to construct a microwave photonic phase shifter based on single sideband (SSB) modulation [13]- [19]. Unfortunately, the systems employing optical filters to select the desired sidebands [13]- [18] are sensitive to the wavelength fluctuation of the optical carrier and suffer from the constrained RF operating range. Recently, filter-free image rejection mixing has been successfully realized by the joint use of a polarization division multiplexing dual-parallel Mach-Zehnder modulator and three electrical hybrids [19]. However, sophisticated controls of bias voltages are required for carrier-suppressed SSB modulation. In addition, the phase cancellation-based schemes are sensitive to the imbalances of length and amplitude between parallel signal paths.
Another method of realizing image rejection mixing is pre-filtering the image from RF signals. For instance, the image component has been rejected by an electrical bandpass filter in [20], where multiple-stage frequency conversion has been utilized to realize a wide RF operating range, yet at the expense of a complex structure. A Fabry-Perot filter has been employed to accurately remove the image-modulated sidebands without affecting the RF-modulated sidebands [21], which may not be suitable for relatively low IF band due to the limited roll-off factor of the optical filter. In this context, stimulated Brillouin scattering (SBS) gain and loss spectrum with wide tunability and narrow bandwidth has been utilized in photonic mixing operation to process optical sidebands induced by RF or LO signals [22]- [24]. IF signals at hundreds of megahertz were successfully acquired with effective image suppression as expected. Nevertheless, an extra wideband microwave source is indispensable to generation of pump signals, which increases the complexity and cost of the SBS-based schemes.
In this paper, we propose a photonic microwave image rejection mixer (IRM) based on polarization manipulation of a broadband optical source (BOS). Thanks to the frequency selectivity provided by tunable time delay and non-coherent property of the BOS light [25], the desired RF signals are down-converted with image suppression through properly adjusting the time delay difference between the RF-and the LO-modulated signals. It is noted that most of previous laser-based photonic image rejection schemes require SSB modulation, which is implemented by optical filters or electrical hybrids in conjunction with complicated bias control [10]- [19]. In our work, SSB modulation is no more necessary, which ensures a comparatively convenient operation and a wide operating frequency range. Moreover, power fading of mixing outputs, which normally exists under circumstance of the combination of chromatic dispersion and double sideband modulation [26], is removed in our scheme. A proof-of-concept experiment confirms an effective image suppression across a wide frequency range.

Principle
The proposed IRM is schematically illustrated in Fig. 1. The spectrally shaped BOS light is polarization modulated by the RF signal and sent to a polarization beam splitter (PBS) through a dispersive element (DE). The modulated signal is polarization demultiplexed into two branches by the PBS, where the upper one is phase-modulated by the LO signal, and the lower one is time delayed. The two branches are subsequently coupled together with the same polarization, and the IF signal with image suppression can be acquired after photodetection.
The BOS light consists of continuously distributed frequency components which are incoherent to each other. The shaped signal in frequency domain can be described as a stochastic process E A ( ), whose statistical property is mathematically given by [25] where is the angular frequency and N( ) is the power spectral density of the BOS light. A polarization modulator (PolM) is utilized to achieve phase modulation with opposite modulation indices at the two orthogonal principal axes. A polarizer is integrated at front of the PolM, and aligned at 45 • to its principal axes. Thus, the BOS signal after polarization modulation can be expressed as where ⊗ and F[·] are convolution and Fourier transform operators, respectively. ω RF is the angular frequency of the RF signal to be down-converted. m RF = πV RF /V π is the modulation index of the PolM, where V RF and V π are the amplitude of the driven RF signal and the half-wave voltage of the modulator, respectively. Jacob-Anger expansion is also applied, and J k (m RF ) is the Bessel function of the first kind of order k. It is noted that even-order sidebands including optical carrier and odd-order sidebands can be respectively generated at two orthogonal polarization states, which show ±45 • off relative to the x axis of the PolM. The polarization-multiplexed optical signal can be expressed as The modulated signal is fed to the DE characterized by a group time delay of β 1 and a total dispersion of β 2 . Its transmission function is given by Taylor expansion as where β 0 is a constant and C is the central angular frequency of the shaped spectrum. The two polarization states are aligned with two principal axes of the PBS by adjusting the polarization controller (PC), and thus odd-order and even-order sidebands are separately acquired at two outputs of the PBS. A phase modulator (PM) is located at the upper branch to allow the even-order sidebands to be modulated by the LO signal, while a variable delay line (VDL) is utilized to introduce a tunable time delay T to the odd-order sidebands at the lower branch. The LO-modulated signal and the time-delayed signal are respectively given by Similar to (2), ω LO and m LO are the angular frequency of the LO signal and modulation index of the PM, respectively. With the assistance of an optical coupler, a PC and a polarizer, the two optical signals are recombined together at the same polarization. Under small signal modulation, the signal injected into the photodetector (PD) is expressed by Accordingly, the generated IF signal after photodetection can be given by where γ denotes the influence of the link loss and the responsivity of the PD. As can be seen from (1) and (8), the generated IF signal is the accumulation of beats between the RF-and LOmodulated sidebands originated from the identical frequency component of the BOS due to its incoherent characteristic. Spectra of the optical sidebands and IF signals corresponding to a single frequency component k are schematically shown in Figs. 1(a)-1(g), where ϕ ( · ) denotes the phase shift induced by the DE. Therefore, the IF signal down-converted from the desired RF signal can be given by where H b (ω) is a baseband response given by For the image with an angular frequency of ω IM , the mathematical deduction is similar to the case of the RF signal illustrated in (2)- (8). The IF signal generated from the image is given as follows (11) As can be seen from (9) and (11), a bandpass filter centered at T /β 2 is equivalently constructed at the front of the system. The inherent filtering characteristic can be attributed to the continuous impulse response, which is provided by continuously distributed frequency components of the BOS light with different complex coefficients given by dispersion.
The image rejection ratio (IRR), which is defined as the power ratio between the IF signal downconverted from the RF signal and from the image, is given by It indicates that the IRR in the proposed scheme depends on the suppression effect of the filter response on the RF signal and the image. Fortunately, a tunable filter with narrow bandwidth can be realized by adjusting the waveshaper (WS) since the filter characterize a proportional version of the Fourier transformation of the shaped BOS light, which is indicated by (10). Consequently, the image can be successfully suppressed even for the comparatively low IF. Furthermore, RF signals with different frequencies can be conveniently down-converted with image suppression by adjusting the VDL.
It is worth noting that in (9), the dispersion-induced phase shift (i.e., ϕ dis = 1/2β 2 ω 2 RF ) manipulates the phase rather than amplitude of the IF signal, which indicates that the power fading resulted from double sideband modulation and chromatic dispersion is avoided. It can be further illustrated by the electrical spectra shown in Fig. 1(g). The phase difference between the two IF signals, which are respectively originated from the two upper sidebands and the two lower sidebands, is determined by the frequency dependent phase shift induced by time delay (i.e., k T ) besides ϕ dis . As a consequent, the amplitude of the interference signal between the two IF photocurrents varies periodically versus the optical carrier frequency, and ϕ dis eventually makes no influence on the IF amplitude after accumulation among those frequency components.

Experiments and Results
A proof-of-concept experiment based on the configuration shown in Fig. 1 was carried out to verify the feasibility of the proposed image-reject mixer. A BOS light provided by an amplified spontaneous emission light source (Lightcomm) was filtered by a WS (Finisar 4000S), which was programmed as a Gaussian filter with a center wavelength of 1555 nm and a full width at half maximum (FWHM) of 8 nm. The shaped BOS light measured by an optical spectrum analyzer (YOKOGAWA AQ6370D) is shown in Fig. 2(a). After compensation for the insertion loss of the WS by an erbium-doped fiber amplifier (EDFA, KEOPSYS), the BOS light was coupled to a PolM (Versawave), which was driven by the RF signal or image generated by a vector network analyzer (VNA, Rohde & Schwarz ZVA40). The DE used in the experiment was a 5 km dispersion compensating fiber with a total dispersion of −803 ps/nm. A PM (EOSpace) driven by a LO signal from an analog signal generator (Keysight N5183B) was located at the upper branch, while a tunable optical delay line (TODL, OZ Optics Ltd) with 330 ps tunable range was placed at the lower branch. A PD (Agilent 11982A) was utilized to convert the polarized signal after another EDFA (JDS Uniphase). The generated IF signal was boosted by an electrical amplifier (EA, SHF) with a gain of 11.5 dB, and subsequently measured by a spectrum analyzer (Rohde & Schwarz).
Firstly, the RF signal was fixed at 6 GHz with a power of 5 dBm to demonstrate the performance of image suppression. A bandpass filter (i.e., H b (ω − T /β 2 )) centered at 6 GHz was realized by adjusting the TODL. Fig. 2(b) shows the transfer function of the filter measured by the VNA.  It is characterized by a Gaussian profile with a 3-dB bandwidth of 131 MHz, which agrees well with the theoretical analysis. It is noted that the 3-dB bandwidth of the bandpass filter limits the instantaneous bandwidth of the proposed IRM, which may not be suitable for processing broadband RF signals. Though the instantaneous bandwidth can be improved through reducing the FWHM of the Gaussian filter provided by the WS, a microwave photonic bandpass filter with broaden bandwidth may lead to a worsen IRR. Therefore, the bandwidth of the shaped BOS light should be carefully selected to make the instantaneous bandwidth and the IRR appropriate for specific applications. A LO signal with a frequency of 5.2 GHz and a power of 5 dBm was fed to the PM for frequency down-conversion. The 800 MHz IF signal with a power of −3.4 dBm was generated accordingly, whose spectrum is shown in Fig. 2(c). The conversion efficiency (CE), which is defined as the power ratio between the IF signal and the RF signal, is calculated to be −8.4 dB. The signal from the VNA was subsequently switched to 4.4 GHz to serve as the image. The corresponding IF signal shown in Fig. 2(c) is suppressed to be 48.3 dB lower than the desired one, which confirms the image rejection mixing operation.
As discussed in the theoretical part, the IRR is dependent on the suppression effect of the filter function on the image, which means the IRR may be influenced by the frequency of the IF signal. Thus the variation of the IRR versus the IF signal was experimentally investigated. The IF signal was swept from 50 to 300 MHz with a step of 50 MHz in sequence, and the frequencies of LO signals and image changed accordingly. The power of IF signals originated from RF signals and image, as well as the corresponding IRR, are shown in Figs. 3(a), 3(b) and 3(c), respectively. It is noted that an IRR of over 43.8 dB was achieved for frequencies ranging from 150 to 300 MHz, whereas the IF signals at 50 and 100 MHz revealed a relatively deteriorative IRR. It can be ascribed to the decreasing interval between the image and the center of the filter response, which also set the lower limit of the IF signal. To further verify the tunability of the IF, signals with frequencies from 400 to 1000 MHz and an interval of 100 MHz were generated as shown in Figs. 4(a) and 4(b),  which exhibits an effective suppression on the IF from image. Figs. 3(c) and 4(c) indicate that a CE of more than −9.2 dB is obtained with a slight fluctuation over the mentioned IF range.
To demonstrate that the image rejection mixing operation can be realized over a wide RF regime, the RF signal was tuned from 2 to 18 GHz with a step of 2 GHz while the IF signal was fixed at 800 MHz. As shown in Fig. 5(a), the corresponding bandpass response centered at 2-18 GHz was constructed by tunning the TODL, and an obvious decline of magnitude response is observed as the center frequency is switched to 18 GHz. The decline can be mainly attributed to the limited bandwidth of the PD utilized in our experiment. Figs. 5(b) and 5(c) show the electrical spectra of the IF signals generated from RF signals and the image, which demonstrates an IRR of more than 44.6 dB across the RF range from 2 to 18 GHz. It is noted that the CE displayed in Fig. 5(d) decreases by 9.4 dB with the RF signal varying from 2 to 18 GHz. It primarily results from the frequency dependent response of the modulators, and the bandwidth of the modulators determines the RF operating range of the proposed system. In addition, dispersion-induced power fading was eliminated for the above RF frequencies as discussed in the theoretical part.
The performance of the proposed mixer was further evaluated with respect to different signal power. The RF signal, the LO signal and the image were maintained at 6, 5.6 and 5.2 GHz, respectively. The RF power was swept from −5 to 15 dBm with an interval of 2 dB, while the LO tone was fixed at 5 dBm. As can be seen from Fig. 6(a), the power of the IF signals increases linearly with the RF power on the condition that the RF power is less than 7 dBm, and an almost constant CE with a fluctuation of about ±0.1 dB is observed. Fig. 6(a) also exhibits a 1 dB compression point of about 14.1 dBm. Fig. 6(b) shows the variation of the IF power and the CE versus LO power while the RF signal was fixed at 5 dBm. The power of the desired IF signal, as well as the CE, increases linearly with the LO power under small signal modulation, and the LO power at the 1 dB compression point is about 11.3 dBm. The IRR exhibited in Figs. 6(a) and 6(b) remains more than 47.6 dB, which illustrates that the disturbing IF components were efficiently rejected over the mentioned power range.
The higher-order RF-and LO-modulated optical sidebands are neglected in the previous theoretical derivation. To analyze the influence of the higher-order sidebands on the generated IF signal, the modulated optical sidebands up to the third-order ones are considered, in which case the optical field after the PM and the VDL can be respectively expressed as