Expand this Topic clickable element to expand a topic
Skip to content
Optica Publishing Group

Dual-polarization RF channelizer based on microcombs

Open Access Open Access

Abstract

We report a dual-polarization radio frequency (RF) channelizer based on microcombs. Two high-Q micro-ring resonators (MRRs) with slightly different free spectral ranges (FSRs) are used: one MRR is pumped to yield soliton crystal microcombs (“active”), and the other MRR is used as a “passive” periodic optical filter supporting dual-polarization operation to slice the RF spectrum. With the tailored mismatch between the FSRs of the active and passive MRRs, wideband RF spectra can be channelized into multiple segments featuring digital-compatible bandwidths via the Vernier effect. Due to the use of dual-polarization states, the number of channelized spectral segments, and thus the RF instantaneous bandwidth (with a certain spectral resolution), can be doubled. In our experiments, we used 20 microcomb lines with ∼ 49 GHz FSR to achieve 20 channels for each polarization, with high RF spectra slicing resolutions at 144 MHz (TE) and 163 MHz (TM), respectively; achieving an instantaneous RF operation bandwidth of 3.1 GHz (TE) and 2.2 GHz (TM). Our approach paves the path towards monolithically integrated photonic RF receivers (the key components — active and passive MRRs are all fabricated on the same platform) with reduced complexity, size, and unprecedented performance, which is important for wide RF applications with digital-compatible signal detection.

© 2024 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement

1. Introduction

Channelized receivers are key building blocks of modern radio frequency (RF) systems including the fifth-generation mobile networks, communication satellites, radar and modern electronic warfare systems [16], as they enable to divide the wideband RF spectra into multiple narrowband segments that can be detected by digital-compatible device with much lower bandwidths (such as generic analog-to-digital converters at hundreds of MHz). However, multi-format, multi-frequency and wideband signals pose challenges to present electronic processing systems. While electronic RF channelizers (generally formed by filter banks) are subject to the bandwidth bottleneck, mainly analog-to-digital converters (ADCs) performance limitations, and the operating bandwidth is limited to a few GHz [7,8]. Photonic approaches are promising since they can offer ultra-large bandwidths, low transmission loss and strong immunity to electromagnetic interference.

Photonic RF channelizers can generally be divided into three categories. The first category depends on the spectral-to-spatial conversion performed by a diffraction grating or an integrated Fresnel lens, yielding multiple parallel channels containing different frequency components in free space [9,10]. Similarly, narrowband optical filters, such as acousto-optic crystals [11], phase-shifted gratings [12], Fabry-Perot etalons [13,14] or commercial WaveShaper [15], physically separate the RF spectrum into several sub-channels. This method, while advantageous in terms of instantaneous bandwidth, poses limitations in terms of the system’s overall footprint and resolution. The second category of photonic RF channelizers is more compact, which employs the Vernier effect between a multi-wavelength source and a periodic filter array to achieve high-resolution wideband RF spectral channelization. Several types of devices and platforms have been utilized for this purpose, such as discrete laser arrays [16], stimulated Brillouin scattering [17], parametric processes in nonlinear fiber [18], cascaded electro-optic modulators [1922] and so on. However, the above approaches are restricted in channel number, spectral resolution, and compatibility for monolithic integration. The last solution is based on a frequency-to-time mapping, where the RF spectra are mapped to the time domain by using wavelength scanning or frequency shifting [2326]. Each wavelength is marked with a specific channel at the corresponding time slot, and only one photodetector (PD) is required to obtain the RF signal at a fast scan rate. Yet those approaches face limitations in one form or another — the scanning frequency step determines final channel number and operating bandwidth, even the serial detected results are non-contiguous.

Recently, microcombs, especially CMOS-compatible microcombs [27,28], have shown unique advantages over conventional mode-locked fiber combs [29] and electro-optical combs [30,31] as they provide massively coherent wavelength channels at the chip-scale size and have proven to be widely used in microwave photonics, such as true-time-delay beamforming [32,33], transversal filters [34,35], frequency conversion [36], microwave signal generators [37], and RF channelizers [38,39]. In previous work [39], we have reported a photonic RF channelizer using microcombs and passive micro-ring resonators (MRRs), which, although demonstrating a large number of wavelength channels and wide instantaneous operating bandwidths, facing limitations in two aspects: on one hand, the RF channelization step (87.5 MHz) is smaller than the spectral resolution (121.4 MHz), indicating high crosstalk between adjacent channels (-6.9 dB); on the other hand, the polarization division of optics was not sufficiently used to further enhance the performance, as only a single polarization state was used for RF channelization.

Here, we first leverage the polarization division of integrated photonics for RF channelization, and report a dual-polarization photonic RF channelizer, achieved with two MRRs with slightly different free spectral ranges (FSRs) at ∼ 49 GHz. The first MRR is used to generate optical comb lines (over 80 in the C band and 20 were used in this work), while the second acts as dual narrowband notch filters in two polarization states to slice the RF spectrum. The high Q passive MRR offers narrow resonance linewidths of 144 MHz (TE) and 163 MHz (TM), enabling high-resolution RF channelization and thus lowered requirements of subsequential ADCs for digital processing; in addition, with tailored FSR mismatch between the active and passive MRRs, the RF channelization steps (∼163 MHz for TE and ∼117 MHz for TM) are closer to the slicing resolution, leading to an improved channel crosstalk of ∼12 dB. Most importantly, the use of dual polarization modes doubled the number of channels (40 in total, 20 for each polarization state) and instantaneous bandwidth (3.1 GHz for TE and 2.2 GHz for TM in this work) in contrast to those using a single polarization mode, with wideband operation verified via thermal tuning of the passive MRR. By further increasing the channel number or adjusting the chip temperature, higher frequency and wider bandwidth signals up to tens of GHz can be processed. This approach explores the polarization division of optics using integrated devices, further demonstrating the potentials of photonic channelizers for wideband RF signal processing.

2. Principle

Figure 1 depicts the schematic of the 40-channel dual-polarization RF channelizer that consists of three modules. The first module achieves microcomb generation and flattening, where an active MRR is pumped by a continuous-wave (CW) laser and amplified by an erbium-doped fiber amplifier (EDFA) to excite intracavity parametric oscillations. The MRR features a high Q-factor of over 1 million, high nonlinear coefficients and designed anomalous dispersion, providing sufficient parametric gain to generate a Kerr frequency comb. Here, we utilize the soliton crystal combs and perform spectral shaping by a commercially available WaveShaper to achieve equalized channel power.

 figure: Fig. 1.

Fig. 1. Schematic diagram of 40-channel dual-polarization RF channelizer based on microcomb. EDFA: erbium-doped fibre amplifier. PC: polarization controller. MRR: micro-ring resonator. OC: optical coupler. OPM: optical powermeter. WS: WaveShaper. PM: phase modulator. TEC: temperature controller. PBS: polarization beam splitter. DEMUX: demultiplexer. PD: photodetector.

Download Full Size | PDF

Assuming the pre-shaped lines are generated with a spacing of δOFC, the optical frequency of the kth (k = 1, 2, 3, …, 20) comb line can be written as

$${f_{OFC}}(k )= {f_{OFC}}(1 )+ ({k - 1} ){\delta _{OFC}}$$
where fOFC(1) is the frequency of the first comb line.

In the second module, the flattened comb lines are fed into an electro-optic phase modulator, where the broadband RF spectra are multicast onto each wavelength channel. Next, the copied RF signals are sliced into segments by a dual-polarization passive MRR with FSRs of δMRR-TE and δMRR-TM for TE and TM polarization, respectively, where the channel resolution is determined by the 3 dB bandwidth of the TE- and TM-polarization resonances, denoted as ΔfTE and ΔfTM.

The kth centre frequency of the passive MRR’s resonance follows

$${f_{MRR - TE}}(k )= {f_{MRR - TE}}(1 )+ ({k - 1} ){\delta _{MRR - TE}}$$
$${f_{MRR - TM}}(k )= {f_{MRR - TM}}(1 )+ ({k - 1} ){\delta _{MRR - TM}}$$
where fMRR-TE(1) and fMRR-TM(1) are the frequency of the first filtering transmission lines of two polarizations, δMRR-TE and δMRR-TM denote the FSRs of passive MRR at TE- and TM-polarization.

The detailed mechanism of the dual polarization RF photonic channelizer is described in right part of Figure 1. For each wavelength channel, the microcomb line is phase-modulated by RF signals to produce counter-phase sidebands whose offset angle from the TE polarization is marked as θ (Fig. 1(i)). The components of modulated signal falling in TE- and TM-planes are filtered by the orthogonally-polarized notch filters (i.e., the TE- and TM-resonances of the passive MRR), respectively (Fig. 1(ii)), which break the balance between the inverted sidebands and enable the phase-to-intensity modulation conversion.

Finally, the dual polarization modes are separated by a polarization beam splitter (PBS), followed by wavelength-division demultiplexers to separate the wavelength channels for photodetection separately. After parallel detection, the channelized RF signals are each centered at fRF-TE(k) (or fRF-TM(k)) with a spectral bandwidth of ΔfTE (or ΔfTM), within the operation bandwidth of generic ADCs (Fig. 1(iii)).

Therefore, the progressive RF centre frequencies of the RF spectra on the TE- and TM-channel, respectively, are given by

$$\begin{aligned}{f_{RF - TE}}(k )&= {f_{MRR - TE}}(k )- {f_{OFC}}(k )\\& = [{{f_{MRR - TE}}(1 )- {f_{OFC}}(1 )} ]+ ({k - 1} )({{\delta_{MRR - TE}} - {\delta_{OFC}}} )\end{aligned}$$
$$\begin{aligned}{f_{RF - TM}}(k )&= {f_{MRR - TM}}(k )- {f_{OFC}}(k )\\& = [{{f_{MRR - TM}}(1 )- {f_{OFC}}(1 )} ]+ ({k - 1} )({{\delta_{MRR - TM}} - {\delta_{OFC}}} )\end{aligned}$$
where fRF-TE(k) and fRF-TM(k) are the kth channelized RF centre frequencies of TE- and TM-channel, [fMRR-TE(1) – fOFC(1)] and [fMRR-TM(1) – fOFC(1)] denote the relative spacing between the first comb and the adjacent dual polarization resonances, namely, the offset of the channelized RF frequency. And (δMRR-TEδOFC) and (δMRR-TMδOFC) represent the channelized RF frequency step between adjacent wavelength channels for TE- and TM-channel, respectively.

We further analyzed the operation of the dual-polarization passive MRR using the Jones matrix [40], and the through-port transmission can be written by

$$R = \left[ {\begin{array}{{cc}} {{T_{TE}}}&0\\ 0&{{T_{TM}}} \end{array}} \right]$$
where TTE and TTM are the through-port transfer functions of the passive MRR given by
$${T_{TE}} = \frac{{t({1 - a{e^{i{\phi_{TE}}}}} )}}{{1 - {t^2}a{e^{i{\phi _{TE}}}}}}$$
$${T_{TM}} = \frac{{t({1 - a{e^{i{\phi_{TM}}}}} )}}{{1 - {t^2}a{e^{i{\phi _{TM}}}}}}$$
where t is the transmission coefficient between the bus waveguide and the passive MRR, a is the round-trip transmission factor, ϕTE = 2πL × neff_TE / λ and ϕTM = 2πL × neff_TM / λ are the single-pass phase shifts of TE and TM modes, respectively, L denotes the round-trip length, neff_TE and neff_TM denote the effective indices of TE and TM modes, and λ represents the wavelength.

The phase-modulated optical signal can be given as

$${E_0}\left[ {\begin{array}{{c}} {\cos \theta }\\ {\sin \theta } \end{array}} \right]$$
where E0 denotes the modulated optical signal, θ is the polarization angle relative to the TE-axis, so the output field of the passive MRR can be written as
$${E_{out}} = R{E_0}\left[ {\begin{array}{{c}} {\cos \theta }\\ {\sin \theta } \end{array}} \right] = {E_0}\left[ {\begin{array}{{c}} {{T_{TE}} \cdot \cos \theta }\\ {{T_{TM}} \cdot \sin \theta } \end{array}} \right].$$

According to the above equation, the optical power of TE- and TM-polarized optical signals are proportional to cos2θ and sin2θ, respectively. Hence the extinction ratio between the channelized RF spectral segments of TE- and TM-resonances is given by

$$ER(\theta )\propto {\cot ^2}\theta.$$

ER(θ) can be continuously adjusted by changing θ, limited only by the performance of the polarization controller. Moreover, cot2θ can infinitely approach 0 or infinity as θ approaches 90° or 0°, thus theoretically an ultra-large dynamic tuning range of the extinction ratio for dual polarization states can be expected. Specifically, when θ = 45°, the amplitude of TE and TM polarization is equal.

3. Experimental results

Both active and passive MRRs are fabricated on a high-index doped silica glass platform through a CMOS compatible fabrication process [41]. The two MRRs featured similar characteristics with radii of ∼ 592 µm, corresponding to a FSR of ∼ 0.4 nm (∼ 49 GHz), with Q factors over one million. The intra-cavity power and comb spectra as the detuning varies are shown in Fig. 2. As the intracavity power exceeds the threshold to excite the homogeneous CW background power fluctuation, modulation instability (MI) is presented, which induces the appearance of primary combs (state (i)). Upon further manual control of the pump-resonance detuning, the pattern evolves to one that consists of multiple, smaller-spacing sub-combs (state (ii)), and finally reached soliton crystal combs (state (iii)) where laser tuning stopped. Eventually, the microcombs span over 150 nm, covering four optical bands including the S-, C-, L-, and U-bands. Due to the programmable optical filter (WaveShaper 4000A) operates in C-band, considering the requirement of signal-to-noise ratio (SNR), we selected only 20 optical combs located in 1557-1566 nm for flattening, and obtained flat microcombs as the wavelength channels for RF channelization with SNRs greater than 25 dB, as depicted in Fig. 3.

 figure: Fig. 2.

Fig. 2. Experimental demonstration of soliton crystal comb formation. (a) The transmission of a single resonance near the pump wavelength. (b) A zoom-in view of blue dashed box in (a), corresponding to different evolutionary states in the scan. (c) Optical power spectrum of the evolution, states (i-iii) represent the primary combs, transition of multiple sub-combs and soliton crystal combs, respectively.

Download Full Size | PDF

 figure: Fig. 3.

Fig. 3. (a) Optical spectrum of the soliton crystal combs with 150 nm span. (b) Flattened 20 comb lines.

Download Full Size | PDF

To demonstrate the analysis above regarding the dual-polarization passive MRR, we measured its transmission spectra with different polarization angles θ, as shown in Fig. 4. Meanwhile, we did a lot of work to stabilize the polarization state, such as gluing the PC to the bottom of a custom-made vibration-isolating iron box with an outer cover, which was done for both MRRs in the experiment. In addition, as many polarization-maintaining devices as possible were used in the optical link, and the non-polarization-maintaining optical fibers were fixed to the optical platform to isolate them as much as possible from external environmental influences. We note that the MRR exhibits higher order modes, which is an inherent feature determined during the fabrication process. As θ varies from 0° to 90°, the transmission spectra evolution of the passive MRR (with TE and TM resonances) and extinction ratios between the orthogonally polarized resonances are shown in Fig. 5. We note that the polarization angle θ is deferred by comparing measured and simulated results. As for the extinction ratio of dual modes (TE2-to-TM1 and TE2-to-TM2), the former varies from 34 dB to -35 dB, which indicates a continuously tunable extinction ratio of over 69 dB. As shown in Figs. 4 and 5(a), the higher order modes of the MRR have the same trend of amplitude change as the fundamental TE mode when the polarization angle θ is varied. Here, the effect of the higher-order modes is negligible, which is also confirmed from the recovered RF spectrum on the vector network analyzer (measured in the following experiments). Note that we actually used the through-port transmission of the passive MRR to achieve the channelizer, although here we plotted the drop-port transmission spectra to reveal the relationships between θ and the extinction ratio between the orthogonally polarized resonances.

 figure: Fig. 4.

Fig. 4. Measured transmission spectra of the passive MRR drop-port with (a) θ = 86.6°, (b) θ = 46.3°, (c) θ = 2.6°, where θ denotes the polarization angle.

Download Full Size | PDF

 figure: Fig. 5.

Fig. 5. (a) Measured transmission spectra of the drop-port with θ varying from 0° to 90°. (b) The fitted curves of extinction ratio between the TE and TM resonances as θ varies.

Download Full Size | PDF

The measured drop-port transmission spectra at dual polarization of the passive MRR and 20 microcomb lines are shown in Fig. 6(a). The microcombs are pre-shaped by an optical programmable processor. Proper control of the polarization state allows both TE and TM mode resonances to be observed simultaneously, as marked by the blue lines, while the orange lines denote the flattened comb spectra. The zoom-in views show the details near the second and the 20th comb lines. We note that the combs’ linewidths are much smaller (potentially at kHz level) than those shown in the figure (limited by the resolution of the optical spectrum analyzer at 0.02 nm). As Fig. 6(b) depicts, the full-width at half-maximum (FWHM) of TE and TM resonance are ∼ 144 MHz and ∼ 163 MHz, respectively, corresponding to a high Q factor over 1.2 million, and a 20 dB bandwidth of ∼ 1.2 GHz, which leads a high RF spectral resolution for the channelizer and thus reduced bandwidth requirements to ADCs (<200 MHz).

 figure: Fig. 6.

Fig. 6. (a) The experimental 40-channel channelizer of 20 microcombs optical spectrum (orange lines) and drop-port dual-polarization transmission spectrum (blue lines) of passive MRR. The zoom-in views of the shaded areas indicate the relative frequency spacing between the comb and adjacent transmission resonance, where the combs are rendered with a wider linewidth limited by the spectrometer resolution. (b) Drop-port transmission spectrum of the active MRR showing TE and TM resonances with FWHM of 144 MHz and 163 MHz, respectively, corresponding to Q factors over 1.2 × 106. (c) The channelized RF frequency of 20 channels, measured by the spacing between the comb lines and the passive resonances in (a). The fitted channelization slopes are 160 MHz (TE) and 110 MHz (TM) per comb wavelength.

Download Full Size | PDF

The channelized RF frequencies fRF(k) of dual polarization are derived, corresponding to the spacing between the comb and adjacent TE and TM resonances, showing an upward trend from red to blue in Fig. 6(c). Due to the insufficient resolution of the spectrometer, here the peak wavelength of each comb is calculated using the inherent FSR of the MRR. The fitted results indicate that the channelized RF frequencies increase at 160 MHz and 110 MHz per channel for TE and TM resonances respectively, eventually achieving instantaneous operating bandwidths of 3.04 GHz (TE) and 2.1 GHz (TM), 5.14 GHz in total. We note that a wider instantaneous bandwidth can be achieved with more wavelength channels, for example, with 80 wavelength channels the instantaneous bandwidths can be increased by 4 times to over 20 GHz, sufficient for general RF applications.

Next, the frequency responses of the 40 channels under dual polarization are verified by a vector network analyzer (VNA) in the RF domain, as shown in Figure 7. Herein, the 3 dB bandwidth of measured RF channels, or the average RF channelizing resolution is ∼ 115 MHz, as shown in Fig. 7(c), which is also a slight advantage over the previous one (∼120 MHz) [39]. This advantage can be further optimized by improving the chip fabrication, to increase the Q factor of the MRR and ultimately to increase the channelizing resolution. However, this involves a trade-off, the instantaneous RF bandwidth is given by the product of channel number and the channelizing resolution, so the channelizing resolution should be carefully designed according to the practical RF signals bandwidth (discussed in the following section). We note that due to imperfections of devices across a broad optical bandwidth, the measured RF channels can have power fluctuations, although they can be equalized straightforwardly by adjust the optical power of each comb line during the flattening process. As shown in Fig. 7(c), the channelized RF frequencies (i.e., the center frequencies of each RF channel) indicate instantaneous operation bandwidths of 3.1 GHz and 2.2 GHz for TE and TM polarization, respectively, with RF channelization steps of 163 MHz (TE) and 117 MHz (TM), which closely matches with the results in Fig. 6(c). We note that, due to the relatively close match between the channelized RF frequencies’ step and the resolution, the crosstalk between adjacent RF channels is further reduced (∼12 dB as shown in Fig. 7(b)), in contrast to our previous work [39]. In addition, we note that the crosstalk arose from the phase characteristics of the passive MRR, rather than random noises/instabilities of the system—this was verified by repetitive measurements of the vector network analyzer. To further reduce the crosstalk, several solutions can be adopted [39]: (i) tailored passive MRR’s FSR via accurate design and nanofabrication allows matching between the RF channelization step and resolution; (ii) passive optical filters with higher roll-offs and flat passbands, which can be achieved by high-order cascaded MRRs with negligible phase jumps in the resonance [42].

 figure: Fig. 7.

Fig. 7. Experimental RF transmission spectra of (a) the dual-polarization 40 channels and (b) a zoom-in view of the shaded area in (a). The first channel of TM mode with a 3 dB bandwidth of 122 MHz, and the adjacent channel crosstalk over 10 dB. (c) Derived channelized RF frequency of TE and TM passbands and RF resolution of the channelizer.

Download Full Size | PDF

To further verify the tunability of the proposed RF channelizer for spectral analysis at diverse RF bands (such as frequency-upconverted baseband RF signals), we thermally tuned the passive MRR to change the offset or spectral interval between a comb line and its adjacent passive resonances. Figure 8 shows the measured RF transmission spectra. The thermal tuning efficiencies of TE and TM channels are -1.59 GHz/°C and 1.65 GHz/°C, respectively, as shown in Fig. 8(b), indicating a wide tuning range up to >60 GHz with ∼ 40 °C temperature variation, well within the capability of external or on-chip heaters and sufficient for wideband RF applications. It’s worth noting that the two MRRs used in our experiments are controlled separately by two TECs placed under the chip and kept at a constant temperature. As this scheme moves towards integration, thermal crosstalk occurs during operation, with localized heat leakage into the surroundings, leading to resonance shifts in neighbouring MRR. Recently, thermal crosstalk can readily be diminished via deep trench processes [43], or dynamically compensated for [44], to achieve desired operation—both techniques are readily verified on chips with similar architectures.

 figure: Fig. 8.

Fig. 8. (a) Experimental RF transmission spectra of a dual-polarization channel with adjusting the passive chip temperature. (b) Derived centre frequencies of TE- and TM-channel with varying temperature.

Download Full Size | PDF

Furthermore, to verify the flexibility in the extinction ratio between TE- and TM-polarized channels, which can be used to equalize the channels’ power, we continuously adjusted the polarization angle θ via a polarization controller. By varying from 0 to 90 degree, the extinction ratio between the TE- and TM- RF channels varies from -25.1 to 25.4 dB, as shown in Fig. 9. This result indicates that the TE- and TM- RF channels can be equalized or switched on/off, bringing additional flexibilities for post sub-bands receiving and processing. We noted that here an external polarization controller adjusts the polarization state of the on-chip MRR, and for further integration, an active on-chip polarization control scheme can be considered, using two thermo-optic phaseshifters for phase manipulation [45] or utilizing Berry’s phase assisted by electrical control [46].

 figure: Fig. 9.

Fig. 9. (a) Experimental RF transmission spectra with varying polarization angle θ between TE- and TM-channel, resulting in varying extinction ratio.

Download Full Size | PDF

We note that the instantaneous RF operation bandwidth is given by the product of channel number and the channelizing resolution, as shown in Fig. 6(c) and Fig. 7(c), thus it can be further increased by: a) increasing the number of channels within available optical bands — this can be achieved by using active/passive MRRs with wider optical bandwidths and smaller FSRs, although we note that smaller FSRs introduces tradeoffs with the Nyquist bandwidth (i.e., half of the MRR’s FSR); b) decreasing the channelizing resolution — this can be achieved by using passive MRRs with lower Q factor (ideally high-order MRRs with wider passbands), although this imposes higher requirements on the performance of ADCs, thus needs to be chose upon the practical systems’ requirements of the instantaneous bandwidth, cost and size; c) the optical spectral interval between adjacent resonances of the passive MRR/the FSR of the comb source — this can be enlarged by using MRRs with higher FSRs [47,48], nonetheless, this brings about tradeoffs that larger FSRs lead to less channels within a certain optical bandwidth.

4. Noise performance analysis

In this section we analyze and discuss the noise performance of the photonic channelized receiver. We note that, here we focus on the analysis of noises arising from the light source, rather than the passive MRR — which operated with relatively input power and thus its contribution to the overall noise performance is negligible (only losses). We assume that: the phase noise of the kth comb line is comb(t), as the phase noise scales linearly with the number of tones counted from the pump line [49]; the modulator operates in the linear region and multicasts a single-tone signal with angular frequency ωin to every microcomb line. Thus, we can derive that the output of the photodetector corresponding to the kth comb line (TE-channel) is

$${I_{out,k}}(t )= R{P_{comb,k}}\frac{{\pi {A_{in}}}}{{{V_\pi }}}\exp ({i({{\omega_{in}}t + {\phi_0}(t )+ k{\phi_{comb}}(t )} )} )$$
where R is the responsivity of the photodiodes, Pcomb,k is the power of the kth microcomb line, Ain is the input RF signal amplitude, Vπ is the half-wave voltage of modulator, ϕ0(t) is the phase noise of pump laser. As shown in the above equation, the phase noise of the output signal is mainly subject to the pump laser and the microcomb, given as
$${\phi _{out,k}}(t )= {\phi _0}(t )+ k{\phi _{comb}}(t ).$$

As such, the single-sideband (SSB) phase noise power spectral density can be denoted by

$${L_{out,k}}(f )= {L_0}(f )+ {k^2}{L_{comb}}(f )$$
where L0(f) and Lcomb(f) are the SSB phase noise power spectral density of pump laser and comb modes, respectively.

We analyze and discuss the dominant noises of the microcomb — the relative intensity noise (RIN) of the laser and the thermorefractive noise (TRN) in the microresonator, as follows.

4.1 RIN-induced phase noise

The FSR fluctuations of the microresonator are related to the circulating optical power, so the RIN noise of the pump laser leads to time jitter of the repetition frequency [50]. When the laser is on resonance, the frequency shift caused by self-phase modulation is denoted as

$$\frac{{\delta {D_1}(\omega )}}{{2\pi }} = \left( {\frac{{{D_1}}}{{2\pi }}\frac{{4\eta c{n_2}}}{{\kappa {V_{eff}}n_0^2}}} \right)\delta {P_{in}}(\omega )$$
where D1 / 2π = 48.97 GHz is the FSR of microring resonator, η = κex / κ ≈ 0.94 is the coupling impedance of the MRR (κex is the coupling rate), Veff ≈ 8.07 × 10−15 m3 is the mode volume, n2= 1.15 × 10−19 m2/W is the Kerr nonlinear index and n0 = 1.65 is the refractive index, Pin ≈ 2W is the optical power coupled to the MRR. Based on the RIN noise of the pump laser measured in ref [50], we estimated the induced phase noise of the system (free-running, without any frequency and phase stabilization loops) utilizing the following equation:
$$S_{{D_1}/2\pi }^\phi (f )= {\left( {\frac{\alpha }{f}{P_{in}}} \right)^2}{S_{RIN}}(f )$$
where α = (D1 / 2π)4ηcn2 / κVeff n02 is the conversion coefficient.

The modelling results are shown in Fig. 10, where the yellow curve represents the RIN noise of the laser and the violet curve represents the estimated phase noise, which is ∼-85 dBc/Hz at 10kHz frequency offset. As the figure depicts, at lower offset frequencies, the phase noise is dominated by the thermal effect of the microresonator; at higher offset frequencies, the laser RIN noise becomes to be a dominant limitation.

 figure: Fig. 10.

Fig. 10. Single-sideband (SSB) phase noise power spectral density of the channelizer, including pump relative intensity noise (RIN) (yellow line), RIN-induced phase noise (violet line), thermorefractive noise (green line) and shot noise (red dashed line). Note that the RIN noise is measured in ref. [50] and the remaining noise is estimated.

Download Full Size | PDF

4.2 Thermorefractive noise

In a microresonator, thermal noise consists of thermorefractive noise (largest), thermoelastic, and elasto-optic [51]. Thermorefractive noise causes fluctuations in the refractive index n, leading to fluctuations in the resonance frequency, which is essentially caused by temperature variations,

$$\left\langle {\delta {T^2}} \right\rangle = \frac{{{k_B}{T^2}}}{{\rho CV}}$$
where T is the temperature of the heat bath, kB is the Boltzmann constant, ρ is the density, C is the specific heat capacity and V is the volume.

Assuming a homogeneous microresonator in an infinite heat bath, we model the thermorefractive noise by the following equation [51]:

$${S_{\delta T}}(\omega )= \frac{{{k_B}{T^2}}}{{\sqrt {{\pi ^3}\mu \rho C\omega } }}\sqrt {\frac{1}{{2p + 1}}} \frac{1}{{R\sqrt {d_r^2 - d_z^2} }}\frac{1}{{{{[{1 + {{({\omega {\tau_d}} )}^{3/4}}} ]}^2}}}$$
where µ is the thermal conductivity, R is the MRR radius, dz and dr are halfwidths of the fundamental mode with respect to the intensity, with orbital number l, azimuthal number m, meridional mode number p = l - m, τd = (π/4)1/3ρCdr2 / µ. To obtain the phase noise power spectral density, we perform a transformation of the equation for temperature fluctuation with frequency as follows
$${S_{\delta f}}(\omega )= {\left( {{f_0}\frac{1}{{{n_0}}}\frac{{dn}}{{dT}}} \right)^2}{S_{\delta T}}(\omega )$$
where f0 is the resonance frequency, n0 is the refractive index, dn / dT is the thermo-optic coefficient, and the detailed simulation parameters are listed in Table 1.

Tables Icon

Table 1. Physical properties for theoretical simulation of the thermorefractive noise of MRR

The green curve in Fig. 10 is the simulation result of the thermorefractive noise of the microring, and its trend agrees well with the experimental results in [52]. Here we have simulated the fundamental mode of the microresonator with l = m (p = 0). For the same microresonator, different values of l - m correspond to different levels of thermorefractive noise [53] and different orders of comb lines [52]. It can be seen that for the microresonator at tens of GHz, the thermorefractive noise dominates the overall system, and the induced phase noise deteriorates quadratically with the increase in the number of microcomb harmonics, which is also confirmed by the experiments in [52].

4.3 Shot noise and thermal noise

As for the shot noise caused by the photodiodes, we calculated the shot noise floor to be -165 dBc/Hz, with a responsivity of 0.8 A/W and an optical input power of 3 dBm. The thermal noise floor of the overall system, which includes both thermoelastic noise and thermal noise within the device in addition to the thermorefractive noise, is difficult to quantify individually and is therefore not shown in Fig. 10.

As predicted, the thermorefractive noise from the microring resonator is a major limit to the phase noise performance of our channelizer, thus needs to be suppressed to achieve microwave signal receiving with high signal-to-noise ratio (SNR) and spectral purity. At present, the thermorefractive noise can be suppressed by blue-detuned auxiliary CW laser [54] or reducing the operating temperature [55]. In addition, feedback loops can also be employed to further optimize the entire link noise, such as phase-locked loops and ultra-stable optical reference frequency combs for frequency and phase stabilization.

5. Conclusion

In this work, we report a dual-polarization photonic RF channelizer using two MRRs with slightly different FSRs. The first MRR is used to generate optical comb lines, while the second acts as dual narrowband notch filters in two polarization states to slice the RF spectrum. We achieved high RF channelization resolution of 144 MHz (TE), and 163 MHz (TM), and doubled instantaneous bandwidth (3.1 GHz for TE and 2.2 GHz for TM) due to the use of dual polarization states. The tunability of the proposed RF channelizer in terms of the operation bandwidth and extinction ratio between TE- and TM- channels are also experimentally verified, offering additional flexibilities for tailored practical RF systems. Finally, we analyze the overall noise in the system, with thermorefractive noise having the largest effect, pointing the way to optimization of the channelized receivers performance limits in the future. This approach explores the polarization division of integrated devices for photonic RF channelizers, which has the full potential to be monolithically integrated with ADCs and enables unprecedented performances of RF systems. As we know, active and passive MRRs both can be integrated monolithically. For other optics devices, such as lasers, EDFAs, modulators, PDs, microheaters, PBSs, etc. have already achieved on-chip integration [5661]. Recently, hybrid integration and heterogeneous integration processing have been developed to achieve a complete system on the same platform, such as soliton microcomb generation [62,63], SiPh optoelectronic systems [43,44]. Commercially available WSs also play a key role in our channelized scheme, and for bulky programmable optical filters, our alternatives are the chip-scale add-drop MRR array [43,44] or the MZI waveguide mesh [64]. Thus, we believe that our demonstration is an important step towards the monolithic integration of photonic channelized receivers.

Funding

Open Fund of IPOC (IPOC2022A01); National Natural Science Foundation of China (62105291).

Disclosures

The authors declare no conflicts of interest.

Data availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

References

1. G. W. Anderson, D. C. Webb, A. E. Spezio, et al., “Advanced channelization for RF, microwave, and millimeterwave applications,” Proc. IEEE 79(3), 355–388 (1991). [CrossRef]  

2. J. Capmany and D. Novak, “Microwave photonics combines two worlds,” Nat. Photonics 1(6), 319–330 (2007). [CrossRef]  

3. J. Yao, “Microwave Photonics,” J. Lightwave Technol. 27(3), 314–335 (2009). [CrossRef]  

4. S. Pan and J. Yao, “Photonics-Based Broadband Microwave Measurement,” J. Lightwave Technol. 35(16), 3498–3513 (2017). [CrossRef]  

5. X. Zou, B. Lu, W. Pan, et al., “Photonics for microwave measurements: Photonics for microwave measurements,” Laser Photonics Rev. 10(5), 711–734 (2016). [CrossRef]  

6. K. Xu, R. Wang, Y. Dai, et al., “Microwave photonics: radio-over-fiber links, systems, and applications [Invited],” Photonics Res. 2(4), B54 (2014). [CrossRef]  

7. H. Shin and R. Harjani, “Low-Power Wideband Analog Channelization Filter Bank Using Passive Polyphase-FFT Techniques,” IEEE J. Solid-State Circuits 52(7), 1753–1767 (2017). [CrossRef]  

8. H.-N. Nguyen, K.-S. Kim, S.-H. Han, et al., “A Low-Power Interference-Tolerance Wideband Receiver for 802.11af/ah Long-Range Wi-Fi With Post-LNA Active N -Path Filter,” IEEE Trans. Microwave Theory Tech. 66(5), 2287–2298 (2018). [CrossRef]  

9. W. Wang, R. L. Davis, T. J. Jung, et al., “Characterization of a coherent optical RF channelizer based on a diffraction grating,” IEEE Trans. Microwave Theory Tech. 49(10), 1996–2001 (2001). [CrossRef]  

10. S. T. Winnall, A. C. Lindsay, M. W. Austin, et al., “A microwave channelizer and spectroscope based on an integrated optical Bragg-grating Fabry-Perot and integrated hybrid Fresnel lens system,” IEEE Trans. Microwave Theory Tech. 54(2), 868–872 (2006). [CrossRef]  

11. R. E. Brooks and J. Z. Wilcox, “SAW RF Spectrum Analyzer/Channelizer Using a Focusing, Phased Array Transducer,” in IEEE 1985 Ultrasonics Symposium (IEEE, 1985), pp. 91–95.

12. D. B. Hunter, L. G. Edvell, and M. A. Englund, “Wideband Microwave Photonic Channelised Receiver,” in 2005 International Topical Meeting on Microwave Photonics (IEEE, 2005), pp. 249–252.

13. S. T. Winnall and A. C. Lindsay, “A Fabry-Perot scanning receiver for microwave signal processing,” IEEE Trans. Microwave Theory Tech. 47(7), 1385–1390 (1999). [CrossRef]  

14. E. M. Alexander and R. W. Gammon, “The Fabry-Perot Etalon As An Rf Frequency Channelizer,” in Solid-State Optical Control Devices, P. Yeh, ed. (SPIE, 1984), Vol. 0464, pp. 45–52.

15. C. Wang and J. Yao, “Ultrahigh-Resolution Photonic-Assisted Microwave Frequency Identification Based on Temporal Channelization,” IEEE Trans. Microwave Theory Tech. 61(12), 4275–4282 (2013). [CrossRef]  

16. S. J. Strutz and K. J. Williams, “An 8-18-GHz all-optical microwave downconverter with channelization,” IEEE Trans. Microwave Theory Tech. 49(10), 1992–1995 (2001). [CrossRef]  

17. X. Zou, W. Li, W. Pan, et al., “Photonic-Assisted Microwave Channelizer With Improved Channel Characteristics Based on Spectrum-Controlled Stimulated Brillouin Scattering,” IEEE Trans. Microwave Theory Tech. 61(9), 3470–3478 (2013). [CrossRef]  

18. C.-S. Brès, S. Zlatanovic, A. O. J. Wiberg, et al., “Reconfigurable parametric channelized receiver for instantaneous spectral analysis,” Opt. Express 19(4), 3531 (2011). [CrossRef]  

19. Z. Li, H. Chi, X. Zhang, et al., “A reconfigurable photonic microwave channelized receiver based on an optical comb,” in 2011 International Topical Meeting on Microwave Photonics Jointly Held with the 2011 Asia-Pacific Microwave Photonics Conference (IEEE, 2011), pp. 296–299.

20. X. Xie, Y. Dai, Y. Ji, et al., “Broadband Photonic Radio-Frequency Channelization Based on a 39-GHz Optical Frequency Comb,” IEEE Photon. Technol. Lett. 24(8), 661–663 (2012). [CrossRef]  

21. Z. Tang, D. Zhu, and S. Pan, “Coherent Optical RF Channelizer With Large Instantaneous Bandwidth and Large In-Band Interference Suppression,” J. Lightwave Technol. 36(19), 4219–4226 (2018). [CrossRef]  

22. X. Xie, Y. Dai, K. Xu, et al., “Broadband Photonic RF Channelization Based on Coherent Optical Frequency Combs and I/Q Demodulators,” IEEE Photonics J. 4(4), 1196–1202 (2012). [CrossRef]  

23. W. Gou, J. Zhang, Z. Zhang, et al., “Microwave photonics scanning channelizer with digital image-reject mixing and linearization,” Opt. Commun. 528, 129055 (2023). [CrossRef]  

24. L. Zhao, W. Gou, Z. Zhang, et al., “Deep-learning-assisted linearization for the broadband photonic scanning channelized receiver,” Opt. Lett. 47(22), 6021 (2022). [CrossRef]  

25. X. Xue, Y. Zhang, B. Chen, et al., “Microwave Photonic Channelizer With Large Instantaneous Bandwidth Based on AOFS,” IEEE Photonics J. 13(5), 1–7 (2021). [CrossRef]  

26. R. Li, H. Chen, Y. Yu, et al., “Multiple-frequency measurement based on serial photonic channelization using optical wavelength scanning,” Opt. Lett. 38(22), 4781 (2013). [CrossRef]  

27. A. Pasquazi, M. Peccianti, L. Razzari, et al., “Micro-combs: A novel generation of optical sources,” Phys. Rep. 729, 1–81 (2018). [CrossRef]  

28. P. Del’Haye, A. Schliesser, O. Arcizet, et al., “Optical frequency comb generation from a monolithic microresonator,” Nature 450(7173), 1214–1217 (2007). [CrossRef]  

29. N. R. Newbury and W. C. Swann, “Low-noise fiber-laser frequency combs (Invited),” J. Opt. Soc. Am. B 24(8), 1756 (2007). [CrossRef]  

30. C. Chen, C. He, D. Zhu, et al., “Generation of a flat optical frequency comb based on a cascaded polarization modulator and phase modulator,” Opt. Lett. 38(16), 3137 (2013). [CrossRef]  

31. R. Wu, V. R. Supradeepa, C. M. Long, et al., “Generation of very flat optical frequency combs from continuous-wave lasers using cascaded intensity and phase modulators driven by tailored radio frequency waveforms,” Opt. Lett. 35(19), 3234 (2010). [CrossRef]  

32. X. Xu, J. Wu, T. G. Nguyen, et al., “Photonic microwave true time delays for phased array antennas using a 49 GHz FSR integrated optical micro-comb source [Invited],” Photonics Res. 6(5), B30 (2018). [CrossRef]  

33. X. Xue, Y. Xuan, C. Bao, et al., “Microcomb-Based True-Time-Delay Network for Microwave Beamforming With Arbitrary Beam Pattern Control,” J. Lightwave Technol. 36(12), 2312–2321 (2018). [CrossRef]  

34. X. Xue, Y. Xuan, H.-J. Kim, et al., “Programmable Single-Bandpass Photonic RF Filter Based on Kerr Comb from a Microring,” J. Lightwave Technol. 32(20), 3557–3565 (2014). [CrossRef]  

35. X. Xu, M. Tan, J. Wu, et al., “Advanced Adaptive Photonic RF Filters with 80 Taps Based on an Integrated Optical Micro-Comb Source,” J. Lightwave Technol. 37(4), 1288–1295 (2019). [CrossRef]  

36. X. Xu, J. Wu, M. Tan, et al., “Broadband Microwave Frequency Conversion Based on an Integrated Optical Micro-Comb Source,” J. Lightwave Technol. 38(2), 332–338 (2020). [CrossRef]  

37. X. Xu, M. Tan, J. Wu, et al., “Photonic RF Phase-Encoded Signal Generation With a Microcomb Source,” J. Lightwave Technol. 38(7), 1722–1727 (2020). [CrossRef]  

38. X. Xu, J. Wu, T. G. Nguyen, et al., “Broadband RF Channelizer Based on an Integrated Optical Frequency Kerr Comb Source,” J. Lightwave Technol. 36(19), 4519–4526 (2018). [CrossRef]  

39. X. Xu, M. Tan, J. Wu, et al., “Broadband Photonic RF Channelizer With 92 Channels Based on a Soliton Crystal Microcomb,” J. Lightwave Technol. 38(18), 5116–5121 (2020). [CrossRef]  

40. P. Bianucci, C. R. Fietz, J. W. Robertson, et al., “Whispering gallery mode microresonators as polarization converters,” Opt. Lett. 32(15), 2224 (2007). [CrossRef]  

41. D. J. Moss, R. Morandotti, A. L. Gaeta, et al., “New CMOS-compatible platforms based on silicon nitride and Hydex for nonlinear optics,” Nat. Photonics 7(8), 597–607 (2013). [CrossRef]  

42. B. E. Little, S. T. Chu, P. P. Absil, et al., “Very High-Order Microring Resonator Filters for WDM Applications,” IEEE Photon. Technol. Lett. 16(10), 2263–2265 (2004). [CrossRef]  

43. H. Shu, L. Chang, Y. Tao, et al., “Microcomb-driven silicon photonic systems,” Nature 605(7910), 457–463 (2022). [CrossRef]  

44. B. Bai, Q. Yang, H. Shu, et al., “Microcomb-based integrated photonic processing unit,” Nat. Commun. 14(1), 66 (2023). [CrossRef]  

45. Y. Huo, J. Niu, X. Fu, et al., “Active polarization controller based on micro-ring resonators,” Opt. Lett. 48(21), 5491–5494 (2023). [CrossRef]  

46. Q. Xu, L. Chen, M. G. Wood, et al., “Electrically tunable optical polarization rotation on a silicon chip using Berry’s phase,” Nat. Commun. 5(1), 5337 (2014). [CrossRef]  

47. L. Razzari, D. Duchesne, M. Ferrera, et al., “CMOS-compatible integrated optical hyper-parametric oscillator,” Nat. Photonics 4(1), 41–45 (2010). [CrossRef]  

48. J. S. Levy, A. Gondarenko, M. A. Foster, et al., “CMOS-compatible multiple-wavelength oscillator for on-chip optical interconnects,” Nat. Photonics 4(1), 37–40 (2010). [CrossRef]  

49. C. Deakin and Z. Liu, “Noise and distortion analysis of dual frequency comb photonic RF channelizers,” Opt. Express 28(26), 39750 (2020). [CrossRef]  

50. E. Lucas, P. Brochard, R. Bouchand, et al., “Ultralow-noise photonic microwave synthesis using a soliton microcomb-based transfer oscillator,” Nat. Commun. 11(1), 374 (2020). [CrossRef]  

51. G. Huang, E. Lucas, J. Liu, et al., “Thermorefractive noise in silicon-nitride microresonators,” Phys. Rev. A 99(6), 061801 (2019). [CrossRef]  

52. K. Nishimoto, K. Minoshima, T. Yasui, et al., “Investigation of the phase noise of a microresonator soliton comb,” Opt. Express 28(13), 19295 (2020). [CrossRef]  

53. M. L. Gorodetsky and I. S. Grudinin, “Fundamental thermal fluctuations in microspheres,” J. Opt. Soc. Am. B 21(4), 697–705 (2004). [CrossRef]  

54. T. E. Drake, J. R. Stone, T. C. Briles, et al., “Thermal decoherence and laser cooling of Kerr microresonator solitons,” Nat. Photonics 14(8), 480–485 (2020). [CrossRef]  

55. G. Moille, X. Lu, A. Rao, et al., “Kerr-Microresonator Soliton Frequency Combs at Cryogenic Temperatures,” Phys. Rev. Appl. 12(3), 034057 (2019). [CrossRef]  

56. C. Xiang, J. Guo, W. Jin, et al., “High-performance lasers for fully integrated silicon nitride photonics,” Nat. Commun. 12(1), 6650 (2021). [CrossRef]  

57. Y. Liu, Z. Qiu, X. Ji, et al., “A photonic integrated circuit–based erbium-doped amplifier,” Science 376(6599), 1309–1313 (2022). [CrossRef]  

58. C. Op de Beeck, F. M. Mayor, S. Cuyvers, et al., “III/V-on-lithium niobate amplifiers and lasers,” Optica 8(10), 1288–1289 (2021). [CrossRef]  

59. A. Liu, R. Jones, L. Liao, et al., “A high-speed silicon optical modulator based on a metal–oxide–semiconductor capacitor,” Nature 427(6975), 615–618 (2004). [CrossRef]  

60. J. Michel, J. Liu, and L. C. Kimerling, “High-performance Ge-on-Si photodetectors,” Nat. Photonics 4(8), 527–534 (2010). [CrossRef]  

61. B. Shen, P. Wang, R. Polson, et al., “An integrated-nanophotonics polarization beamsplitter with 2.4 × 2.4 µm2 footprint,” Nat. Photonics 9(6), 378–382 (2015). [CrossRef]  

62. B. Shen, L. Chang, J. Liu, et al., “Integrated turnkey soliton microcombs,” Nature 582(7812), 365–369 (2020). [CrossRef]  

63. C. Xiang, J. Liu, J. Guo, et al., “Laser soliton microcombs heterogeneously integrated on silicon,” Science 373(6550), 99–103 (2021). [CrossRef]  

64. X. Xu, G. Ren, T. Feleppa, et al., “Self-calibrating programmable photonic integrated circuits,” Nat. Photonics 16(8), 595–602 (2022). [CrossRef]  

Data availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

Cited By

Optica participates in Crossref's Cited-By Linking service. Citing articles from Optica Publishing Group journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (10)

Fig. 1.
Fig. 1. Schematic diagram of 40-channel dual-polarization RF channelizer based on microcomb. EDFA: erbium-doped fibre amplifier. PC: polarization controller. MRR: micro-ring resonator. OC: optical coupler. OPM: optical powermeter. WS: WaveShaper. PM: phase modulator. TEC: temperature controller. PBS: polarization beam splitter. DEMUX: demultiplexer. PD: photodetector.
Fig. 2.
Fig. 2. Experimental demonstration of soliton crystal comb formation. (a) The transmission of a single resonance near the pump wavelength. (b) A zoom-in view of blue dashed box in (a), corresponding to different evolutionary states in the scan. (c) Optical power spectrum of the evolution, states (i-iii) represent the primary combs, transition of multiple sub-combs and soliton crystal combs, respectively.
Fig. 3.
Fig. 3. (a) Optical spectrum of the soliton crystal combs with 150 nm span. (b) Flattened 20 comb lines.
Fig. 4.
Fig. 4. Measured transmission spectra of the passive MRR drop-port with (a) θ = 86.6°, (b) θ = 46.3°, (c) θ = 2.6°, where θ denotes the polarization angle.
Fig. 5.
Fig. 5. (a) Measured transmission spectra of the drop-port with θ varying from 0° to 90°. (b) The fitted curves of extinction ratio between the TE and TM resonances as θ varies.
Fig. 6.
Fig. 6. (a) The experimental 40-channel channelizer of 20 microcombs optical spectrum (orange lines) and drop-port dual-polarization transmission spectrum (blue lines) of passive MRR. The zoom-in views of the shaded areas indicate the relative frequency spacing between the comb and adjacent transmission resonance, where the combs are rendered with a wider linewidth limited by the spectrometer resolution. (b) Drop-port transmission spectrum of the active MRR showing TE and TM resonances with FWHM of 144 MHz and 163 MHz, respectively, corresponding to Q factors over 1.2 × 106. (c) The channelized RF frequency of 20 channels, measured by the spacing between the comb lines and the passive resonances in (a). The fitted channelization slopes are 160 MHz (TE) and 110 MHz (TM) per comb wavelength.
Fig. 7.
Fig. 7. Experimental RF transmission spectra of (a) the dual-polarization 40 channels and (b) a zoom-in view of the shaded area in (a). The first channel of TM mode with a 3 dB bandwidth of 122 MHz, and the adjacent channel crosstalk over 10 dB. (c) Derived channelized RF frequency of TE and TM passbands and RF resolution of the channelizer.
Fig. 8.
Fig. 8. (a) Experimental RF transmission spectra of a dual-polarization channel with adjusting the passive chip temperature. (b) Derived centre frequencies of TE- and TM-channel with varying temperature.
Fig. 9.
Fig. 9. (a) Experimental RF transmission spectra with varying polarization angle θ between TE- and TM-channel, resulting in varying extinction ratio.
Fig. 10.
Fig. 10. Single-sideband (SSB) phase noise power spectral density of the channelizer, including pump relative intensity noise (RIN) (yellow line), RIN-induced phase noise (violet line), thermorefractive noise (green line) and shot noise (red dashed line). Note that the RIN noise is measured in ref. [50] and the remaining noise is estimated.

Tables (1)

Tables Icon

Table 1. Physical properties for theoretical simulation of the thermorefractive noise of MRR

Equations (19)

Equations on this page are rendered with MathJax. Learn more.

f O F C ( k ) = f O F C ( 1 ) + ( k 1 ) δ O F C
f M R R T E ( k ) = f M R R T E ( 1 ) + ( k 1 ) δ M R R T E
f M R R T M ( k ) = f M R R T M ( 1 ) + ( k 1 ) δ M R R T M
f R F T E ( k ) = f M R R T E ( k ) f O F C ( k ) = [ f M R R T E ( 1 ) f O F C ( 1 ) ] + ( k 1 ) ( δ M R R T E δ O F C )
f R F T M ( k ) = f M R R T M ( k ) f O F C ( k ) = [ f M R R T M ( 1 ) f O F C ( 1 ) ] + ( k 1 ) ( δ M R R T M δ O F C )
R = [ T T E 0 0 T T M ]
T T E = t ( 1 a e i ϕ T E ) 1 t 2 a e i ϕ T E
T T M = t ( 1 a e i ϕ T M ) 1 t 2 a e i ϕ T M
E 0 [ cos θ sin θ ]
E o u t = R E 0 [ cos θ sin θ ] = E 0 [ T T E cos θ T T M sin θ ] .
E R ( θ ) cot 2 θ .
I o u t , k ( t ) = R P c o m b , k π A i n V π exp ( i ( ω i n t + ϕ 0 ( t ) + k ϕ c o m b ( t ) ) )
ϕ o u t , k ( t ) = ϕ 0 ( t ) + k ϕ c o m b ( t ) .
L o u t , k ( f ) = L 0 ( f ) + k 2 L c o m b ( f )
δ D 1 ( ω ) 2 π = ( D 1 2 π 4 η c n 2 κ V e f f n 0 2 ) δ P i n ( ω )
S D 1 / 2 π ϕ ( f ) = ( α f P i n ) 2 S R I N ( f )
δ T 2 = k B T 2 ρ C V
S δ T ( ω ) = k B T 2 π 3 μ ρ C ω 1 2 p + 1 1 R d r 2 d z 2 1 [ 1 + ( ω τ d ) 3 / 4 ] 2
S δ f ( ω ) = ( f 0 1 n 0 d n d T ) 2 S δ T ( ω )
Select as filters


Select Topics Cancel
© Copyright 2024 | Optica Publishing Group. All rights reserved, including rights for text and data mining and training of artificial technologies or similar technologies.