Photonic microwave and radio frequency (RF) signal processing^[1-4] has attracted substantial attention for a wide range of applications because of the broad RF bandwidths that it can achieve, its high overall performance, its intrinsically lower loss, its very high reconfigurability and versatility, and finally its extremely high level of insensitivity to electro-magnetic interference. Its main applications lie in the areas of radar, communications and sensing. Many different capabilities have been achieved, such as advanced encoding format modulators^[5-10], devices for RF beam shaping^[11], RF signal processors based on transverse filtering^[12-14], RF channelizers^[15] and spectrum analysis^[16-18], and much more^[19-37].

For RF photonic-based systems, the optical RF signal modulation format directly impacts its transmission capacity as well as its spectral efficiency. Hence, this is a key factor in the design of state-of-the-art photonic RF transmitters^[38]. One advanced modulation format, optical single sideband (OSSB) modulation, has attracted significant attention because of its high spectral efficiency as well as its immunity to distortion induced by dispersion. Recently, a variation on this, termed orthogonally polarized OSSB modulation, has been proposed to increase the system flexibility as well as spectral efficiency. In this approach, the optical sideband and the carrier are polarized in orthogonal directions. Another big advantage of orthogonally polarized OSSB modulation is that it allows the individual control of both the optical sideband and the carrier by using polarization selective components. Hence, it has been employed in many applications from photonic microwave signal processing to antenna beamforming systems^[38-42]. Many methods have been proposed to realize orthogonally polarized OSSB modulation, such as a differential group delay module^[41], acousto-optic modulation^[42], modulators based on Sagnac-loops^[43], quadrature phase shift keying dual-polarization modulation^[44], and polarization-based modulation^{[45, 46]}. Stimulated Brillouin scattering in optical fibers has been reported, in order to control the optical signal polarization^{[47, 48]}. Many of these methods, however, are limited in some respect. RF hybrid couplers create a bottleneck in the system bandwidth, while fiber devices are bulky and limited in size reduction and stability for practical real-world applications.

Other key components for RF systems are RF equalizers, which compensate any imbalance in passive component frequency responses or variations in the gain profile of RF amplifiers^{[49, 50]}. Significant work has been done on photonic-based RF equalizers including devices based on substrate-integrated waveguides^{[51, 52]}. However, these methods have some limitations, including, again, a limited electronic bandwidth, and equalization resolution (minimum equalizing RF bandwidth), lack of RF frequency tunability, and limited transmission spectrum dynamic range. Thus, for advanced RF systems that need high-resolution, wideband RF equalization, and a large dynamic-range, more work is needed. A promising technique that can address these challenges is through the use of integrated microwave photonics^[53]. Our approach also offers all of the attractions of photonic integrated devices, which include a very small size, mass producibility, low power consumption, and high reliability^[54].

We review recent work on orthogonally polarized OSSB generation and a dual-channel RF equalizer^{[19, 20]} achieved through the use of integrated dual-polarization micro-ring resonators (DP-MRR). This work involves both fixed^[19] RF frequency and tuneable RF frequency devices^[20]. For fixed devices, a spectral interval of ~16.6 and ~32.2 GHz between the TE and TM polarized resonances of the DP-MRR is achieved. Lithographic control of the DP-MRR orthogonally polarized resonant mode refractive indices can realize waveguides that have a virtually symmetric cross section, supporting both TM and TE polarizations, yet at the same time displaying quite wide TE to TM polarized spectral intervals of ~16.6 or ~32.2 GHz in the C-band. Hence, the optical sideband and carrier can be separated by looking at the drop-port of the orthogonally polarized resonances, which achieves orthogonally polarized OSSB modulation. Further, we convert the signal automatically from phase modulation to intensity modulation by using the notches at the resonator through-port to suppress one of the sidebands, thus enabling dual-channel RF filtering and equalization. Finally, a large dynamic tuning range of over 55 dB for both the optical carrier-to-sideband ratio of the OSSB signal can be achieved by controlling the polarization angle and extinction ratio of the dual-channel RF equalizer. Subsequently, a continuously RF frequency tunable OP-OSSB generator was reported^[20], based on two different cascaded dual integrated MRRs. The operation RF frequency of the tuneable OP-OSSB generator was determined by the TE to TM resonance spectral interval, which could be tuned dynamically using individually controlled thermo-optical elements for each of the MRRs. This resulted in an operation bandwidth with a very wide RF tuning range. Further, by controlling the input light polarization angle, we achieved a large optical carrier-to-sideband ratio (OCSR) dynamic tuning range of 57.3 dB. These results emphasize the attractiveness of using polarization selective integrated micro-ring resonators to realize orthogonally polarized optical single sideband modulators for RF signals at frequencies as high as 100 GHz.

The integrated micro-ring resonators (Fig. 1) that formed the core components of the system were based on Hydex glass, a high-index doped silica platform that features CMOS compatible processes^[55–72]. First, a high refractive index (n = ~1.70 at 1550 nm) Hydex core was grown via PECVD (plasma-enhanced chemical vapour deposition), followed by patterning via a UV stepper mask aligner-based lithographically. Waveguides were then formed by dry etching (RIE - reactive ion etching) that achieved very low surface roughness. Finally, an upper cladding consisting of silica glass (n = ~1.44 at 1550 nm) was grown. The radius of the ring with the lower FSR of 49 GHz (or 0.4 nm), used for the fixed RF frequency device, was 592 μm. The insertion loss of the through-port was 1.5 dB, via butt coupling with fiber pigtails and on-chip mode converters. The waveguide was almost symmetric in cross-section (1.5 × 2 μm²) so that the MRRs could exhibit TM and TE polarization modes. The theoretical TM and TE modes [Figs. 1(b) and 1(c)] had effective indices n_{eff_TM} = 1.624 and n_{eff_TE} = 1.627, which produced marginally different FSRs for the two polarizations, and with a comparatively wide TE/TM offset of δ_TE//TM = ~16.6 GHz (Fig. 2) at 1550 nm. The two polarizations had comparable linewidths of ~ 140 MHz, or Q factors of about 1.2 million^[61-65], and with a –20 dB bandwidth of ~ 1 GHz [Fig. 2(b)]. This narrow optical linewidth resulted in a very narrowband RF operation and provided a very sharp optical filtering slope. This enabled operation as low as 500 MHz, with a suppression of better than –20 dB for unwanted sidebands. The RF frequency can be varied by changing the TE/TM mode separation during fabrication by the lithographic design of the waveguide ring radius and cross-section. Hence, the frequency that was demonstrated here at 16.6-GHz is not a limitation of the orthogonally polarized OSSB generator or of the RF equalizer either. Moreover, by using the complementary resonance, a second frequency of operation at 32.4 GHz (= FSR − δ_TE//TM) can also be realized. In general, ring resonators having FSRs of 200 GHz or even larger^[73] can be achieved, thus yielding operation at even higher RF frequency.

The ring resonators can be tuned thermally to match any optical carrier wavelength, to a resolution of less than 0.01 °C, equivalent to megahertz level resolution, and with a response time on the order of milliseconds^[74]. The DP-MRR transmission spectra were measured as a function of temperature to illustrate the ability to achieve thermal tunability. The transmission spectra are shown in Figs. 3(a) and 3(b), for temperature tuning from 23 to 30 °C, showing the corresponding two TM resonances (covering one FSR) and one TE resonance (marked as “TM1”, “TE” and “TM2” in Fig. 3(b), respectively). As shown in Fig. 3(c), the resonance center wavelength redshifted at a rate of ~1.67 GHz/°C for TM and ~1.77 GHz/°C for TE polarization. Therefore, the TE/TM mode offset, or birefringence, δ_TE//TM varies with temperature slightly. Fig. 3(d) shows the TE/TM mode splitting (“TE”, “TM1” and “TM2”) versus temperature, revealing that the ~90 MHz/°C rate is much smaller than the −20 dB bandwidth of the MRR (~1 GHz), but regardless can be compensated for by appropriate design of the waveguides (dispersion engineering).

For the orthogonally polarized OSSB system that was continuously tunable^[20], we fabricated both 49 GHz FSR and 200 GHz FSR integrated MRRs, such that each ring exhibited both TM and TE polarizations. We used TM polarization for the first ring that had the low FSR (49 GHz), and TE polarization for the second ring with the large FSR of 200 GHz. As before, both waveguides were nearly symmetric (49 GHz FSR at 1.5 × 2 μm² and 200 GHz FSR 1.45 × 1.5 μm²), enabling both MRRs to support both polarizations. The difference in the effective indices between polarizations (49 GHz MRR: TE: n_eff = 1.627 TE mode and TM: n_eff = 1.624, 200 GHz: TE: n_eff = 1.643 and TM n_eff = 1.642) produced only a very small difference in FSRs between the polarizations, while still showing a comparatively large TE/TM separation in absolute frequency in the C-band of ~16.8 GHz for the 49 GHz FSR ring and ~41.2 GHz for the 200 GHz MRR. The 49 GHz ring radius was ~592 μm as before, with Q = 1.5 × 10⁶, while the radius of the 200 GHz MRR was ~135 μm, with Q = 1.2 × 10⁶. This reduced the leakage of the undesired sideband from the 200 GHz MRR’s unused resonances. The measured transmission spectra are shown in Fig. 4 for both MRRs in which the FSRs and RF frequencies are clearly illustrated.

The architecture of the orthogonally polarized OSSB generator is shown in Fig. 5. As discussed, the rings were designed to support both polarizations, and yet still with a significant mode refractive index difference between them. We modulated a tunable CW laser to produce double sidebands (DSB). The signal was then coupled into the DP-MRR with a polarization angle of 45° to the TE-axis [Fig. 5(i)]. When the wavelength of the pump and the RF frequency of the signal were each equal to one of the two orthogonally polarized DP-MRR resonances, one generated DSB sideband together with the optical carrier signal were dropped by the TE/TM resonances, thus producing orthogonally polarized OSSB modulated signals [Fig. 5(ii)]. Further, we controlled the relative fraction of TE versus TM light for the orthogonally polarized OSSB signal by passing the signal through a polarizer and adjusting the polarization angle. This had the effect of tuning the optical carrier to sideband ratio (OCSR) for the single polarization OSSB modulated signal.

The effective index difference between the polarizations yielded a strong dependence on polarization in the DP-MRR transmission spectrum. We employed the Jones matrix approach, where the eigenmodes of the DP-MRR are the polarization states that provide a natural basis. Hence, the drop-port transmission of the DP-MRR becomes

 (1)

where D_TM and D_TE and are the drop-port transfer functions of the TM and TE modes given by

 (2)

 (3)

where k and t are the cross-coupling and transmission coefficients between the micro-ring and bus waveguide (t² + k² = 1 for zero loss coupling), a is the transmission for a round-trip, ϕ_TM = 2πLn_{eff_TM}/λ and ϕ_TE = 2πLn_{eff_TE}/λ are phase shifts for a single-pass of the TM and TE modes, respectively, and L is the length of the round-trip, and n_{eff_TM} and n_{eff_TE} are the effective indices for the TM and TE modes.

The polarizer Jones matrix is

 (4)

with θ being the angle between the TM axis and the direction of the polarize. For a general input field , the output field after the polarizer is , or an output intensity of^[75]

 (5)

where the input φ_TM and φ_TE are the complex phase angles of D_TM and D_TE.

Hence, the dropped optical output power or induced loss due to polarization conversion by the TM and TE resonances is ~ cos²θ or sin²θ, respectively. Specifically, when θ = 45°, the polarization conversion induced loss is 3 dB for both polarizations. The OCSR (with the carrier using the TM resonance and upper sideband the TE resonance) is

 (6)

which can be tuned continuously by varying θ. Further, since cot²θ can be adjusted arbitrarily close to 0 or 1 as θ approaches π/2 or 0, a very high OCSR dynamic tuning range is obtained.

For the experiments, we tuned the laser to the 1550.47 nm TE resonance and modulated it in intensity at frequencies of 16.6 or 32.4 GHz with an RF signal generator, so that both the lower and upper sidebands could be filtered out by the adjacent TM resonance on the carrier’s long (red) or short (blue) wavelength sides. The orthogonally polarized carrier and the sidebands were both obtained from the drop-port of the DP-MRR, with the optical power of the discarded sideband being attenuated by > 35 dB in comparison with the signal sideband ( Fig. 6).

Next, we converted the orthogonally polarized OSSB signal to a single polarized OSSB signal via a polarizer, and by adjusting the polarizer angle we were able to vary the OCSR. The transmission spectra of the OSSB generator with tunable OCSR is shown in Fig. 7. As θ was tuned from 2° to 92°, the TE and TM extinction ratio varied from 30 to –29 dB, yielding a tuning range for the OCSR of 59.3 dB. The extinction ratios [Figs. 7(d)–7(f)] clearly show that an RF operation frequency as high as 32.4 GHz was achieved. The resulting extinction ratios and transmission spectra (Fig. 8) for RF operation at 16.6 and 32.4 GHz, show that with a polarization angle varied from 2° to 92°, good agreement was achieved with the theory. From Fig. 8(b), a large dynamic range of 80 dB is anticipated and this can be accomplished by varying θ with a much finer resolution.

The generated 16.6 and 32.4 GHz single-polarization OSSB optical spectra signals (Fig. 9) show that a continuously tunable OCSR is achieved, with a range of −22.7 to 41.4 dB and −27.1 to 52.2 dB. This illustrates the high performance and practicality of the OSSB generator that features a tunable OCSR. Finally, carrier to sideband shifts of greater than one FSR can result in larger RF frequencies with the same device, which in our case correspond to 65.6 GHz = 16.6 GHz + FSR and 81.4 GHz = 32.4 GHz + FSR, and so on for higher frequencies.

The fact that the ring resonators had quite a high Q of over a million meant that the device achieved a high RF selectivity for the OSSB generation. In principle this could yield a self-oscillating source at high frequency that operates through optoelectronic oscillation, which is a powerful approach to obtain a very low phase noise. This is important for many applications, such as delivery of RF standards over long-distances. In this regard, the OSSB modulation format excels since it is immune to RF power fading arising from all dispersion effects. Hence our device can be applied to a very wide range of technical fields including even telescope arrays for radio astronomy.

Here we turn to the RF photonic equalizer that was also based on the DP-MRRs (Fig. 10). For this device, an RF signal was used to phase modulate a CW tunable laser, which produced dual sidebands that had opposite phases, and with an angle of θ between the TE-axis and polarization direction [Fig. 10(i)]. Next, the TE and TM phase-modulated signal components were filtered out by the two orthogonally polarized ring resonances (notches) [Fig. 10(ii)], where the imbalance between the two oppositely phased sidebands was produced in order to convert from phase to intensity modulation. Following this, the filtered orthogonally polarized optical signals were converted to RF signals and then combined after photodetection. Effectively, therefore, the high-Q orthogonally polarized optical resonances were translated into the RF domain [Fig. 10(iii)], which resulted in a high RF frequency selective filter with dual passbands and with a bandwidth determined by the Q factor of the DP-MRR. The center frequencies were given by the relative spacing of the optical carrier to the adjacent resonance. By varying the polarization angle θ, the fraction of TM to TE light was varied continuously, with an extinction ratio between the dual RF passbands able to be tuned to perform RF equalization after mapping the optical signal to the RF domain^[76].

The DP-MRR transmission through-port is

 (7)

where T_TE and T_TM are the through-port transfer functions of the DP-MRR given by

 (8)

 (9)

For a phase modulated optical signal , the DP-MRR output fields are

 (10)

This equation shows that the RF passband center frequencies supported by the TE/TM resonances are determined by the relative frequency gap between the MRR resonances and the optical carrier, thus yielding tunable operation regions for the RF equalizer. Moreover, the TE and TM polarized optical signal power is ~ cos²θ or sin²θ, respectively. Hence, after being detected, the RF passband extinction ratio (corresponding to the DP-MRR’s TE- and TM-polarized resonances) is given by

 (11)

Similarly to the tunable OCSR for OSSB generation, the ER(θ) can be continuously varied by adjusting θ, and since cot²θ can get arbitrarily, close to 1 or 0 as θ nears 0 or π/2 (limited only by the polarizer performance), the result is a large extinction ratio tuning range results, reflecting a very large RF equalization dynamic range.

The experiments first investigated the tunability and resolution of a single RF passband by setting the input optical signal to be TM-polarized (θ = 90°). The RF transmission spectra is shown in Fig. 11, measured with a vector network analyser. The 3 dB-bandwidth of the passband is 137.1 MHz, which defines the resolution of the RF equalizer. The passband’s centre frequency tunability was accomplished via adjusting the carrier wavelength [Figs. 12(a) and 12(b)], the DP-MRR chip temperature [Figs. 12(c) and 12(d)], and optical power [Figs. 12(e) and 12(f)]. As seen, all these methods of tuning can readily shift the RF passband central frequency (3 dB-bandwidth of ~140 MHz), thus achieving tunability of the RF high-resolution equalizer.

We varied the operation frequency of the RF equalizer by tuning the carrier wavelength [Figs. 13(a) and 13(b)] as well as the temperature of the ring [Figs. 13(c) and 13(d)]. This yielded a continuous frequency range coverage of more than 14.6 GHz. The TM and TE resonances supported the extracted RF passband centre frequencies [the TM and TE centre frequencies in Figs. 13(b) and 13(d)], showing the effectiveness of each approach to tuning. Tuning the RF TE to TM passband extinction ratios was accomplished by adjusting the angle of the polarized light θ (Fig. 10). The measured optical drop-port and through-port transmission spectra of the DP-MRR are shown versus θ in Fig. 14(a). Due to a limited resolution for the tuning angle, the TM and TE through-port transmission notches could not be properly resolved, and so we also measured the drop-port transmission. We achieved an extinction ratio between the two RF dual-channel equalizer passbands with a wide tuning range [Fig. 14(b)] of −27.4 to 28.2 dB, equivalent to a dynamic range > 55 dB. This demonstrates the very high-performance capability of our device.

The work that we review here focused on narrowband signals for optical single sideband generation as well as RF equalisation with a high-resolution. However, in many cases, signals that have a broad RF bandwidth need to be processed, and in this case either lower Q factor MRRs^[75] or higher order filters^[76-80] could be used instead of the high Q rings. The first method can achieve a 3 dB bandwidth of 2 to 12 GHz, equating to Q factors of 60 000 to 10 000, while higher order filters have easily achieved bandwidths greater than 100 GHz. Finally, recently^[20] a device with dynamic RF tunability has been reported that used cascaded MRRs supporting both polarizations and with a temperature tunable relative TE/TM spectral shift. We turn to this work next.

In this section we review our work based on a wideband tunable OP-OSSB generator^[20]. Fig. 15 shows the principle of operation of the device. A tunable CW laser is intensity modulated by an RF signal to produce a double sideband signal with a polarization angle θ relative to the TE-axis [Fig. 15(i)]. This is then coupled into two cascaded MRRs that both support both polarizations. When the RF frequency and optical carrier wavelength both match the orthogonally polarized MRRs resonance frequency difference, the optical carrier as well as one sideband of the double sideband signal are dropped [Fig. 15(ii)]. Next, the dropped optical carrier and sideband are combined by connecting the second resonator (200 GHz, TE pol.) drop-port to the add-port of the first ring (49 GHz, TM) [Fig. 15(iii)], thus generating OP-OSSB modulation.

We use the Jones matrix formalism to analyze our device polarization states rather than other methods, such as the Stokes parameters or Poincaré sphere^[81], for simplicity since the MRR polarization eigenmodes serve as a natural basis. The dual MRRs transmission can be written as

 (12)

where D_TE and D_TM are the drop-port transfer functions of the 49 GHz (TE) MRR and 200 GHz (TM) MRR given by

 (13)

 (14)

where t_TE, t_TM, k_TE and k_TM are the field transmission and cross-coupling coefficients between the bus waveguide and the ring (t² + k² = 1 for lossless coupling), a_TE and a_TM represent the round-trip transmission factors, ϕ_TE = 2πL_TEn_{eff_TE}/λ and ϕ_TM = 2πL_TMn_{eff_TM}/λ are the single-pass phase shifts of the TE-MRR and TM-MRR, respectively, with L_TE and L_TM denoting the round-trip length, n_{eff_TE} and n_{eff_TM} representing the effective indices, with λ the wavelength.

For a general optical input field , the dual MRRs output field is

 (15)

From this equation, the optical power of the spectral components dropped by the 49 GHz (TE) MRR and 200 GHz (TM) MRR are proportional to cos²θ and sin²θ, respectively. Thus, the OCSR (with the 49 GHz MRR for the carrier and the 200 GHz MRR for the sideband) is given by

 (16)

which can be continuously tuned by adjusting θ. Since cot²θ can get arbitrarily close to 1 or 0 as θ approaches 0 or π/2, a large OCSR tuning range can be achieved. Moreover, the generated OP-OSSB signal can be converted back into an RF signal by passing it through an optical polarizer [Fig. 15(iv)]. The RF frequency of the OP-OSSB generator is given by the spectral gap between adjacent resonances of the 49 and 200 GHz MRR. Thus, by separately controlling the MRRs, a tunable OP-OSSB generation can be realized over a large RF tuning range.

The two ring resonators were connected via polarization maintaining fiber pigtails, with the 49 GHz MRR through-port connected to the 200 GHz MRR input. Both ring’s drop-ports were then combined by connecting the 200 GHz (TE) MRR drop-port to the 49 GHz (TM) MRR add-port. Fig. 16 shows the experimental transmission spectra of the dual MRRs. As reflected by the dual resonances, both MRRs supported two polarizations. The 49 GHz spaced ring (first) and the 200 GHz FSR ring (second) acted as TM and TE filters for the OP-OSSB generation, respectively. The RF operation frequency was determined by the spectral interval between orthogonally polarized adjacent resonances [Fig. 16(b)]. The 49 GHz MRR had a high Q, with a 1.04 GHz bandwidth at –20 dB [Fig. 16(b)] for the OP-OSSB generator, reflecting a very high optical carrier rejection ratio and lower accessible RF frequency down below a Gigahertz.

For this device the carrier wavelength was tuned to one of the TE 200 GHz MRR resonances at ~1549.78 nm, and then the RF signal was used to drive the intensity modulator so that the adjacent TM resonance of the 49 GHz MRR dropped the lower sideband. The orthogonally polarized carrier and lower sideband were extracted at the output of the dual MRRs, where the upper sideband optical power was suppressed by > 35 dB in comparison with the lower sideband ( Fig. 17).

The orthogonally polarized optical carrier to lower sideband ratio could be adjusted by varying the polarization input angle (θ in Fig. 15). The measured dual MRR transmission [Fig. 18(a)] versus polarization angle θ shows that the TE to TM extinction ratio varied from 20.5 dB to –31.1 dB, equating to a dynamic OSCR tuning range of 51.1 dB. The generated OP-OSSB signal optical spectra with at RF frequencies of 19.7 and 26.6 GHz is shown in Figs. 18(b) and 18(c). An OCSR that is continuously variable from −21.1 to 36.2 dB and −18.1 to 38.9 dB was obtained, respectively, for the 19.7 and 26.6 GHz RF inputs, yielding a large OCSR tuning range of 57.3 dB. The cascaded MRR orthogonal polarization modes could also potentially offer an extra control mechanism for optical logic gates as an innovative approach to optical computing^{[82, 83]}.

To achieve wide RF tunability, the frequency difference between the TM 49 GHz ring resonances and the TE 200 GHz MRR resonances were tuned via separate thermal control^[74]. The 200 GHz (TE) MRR temperature was kept constant at 25 °C while the 49 GHz (TM) MRR temperature was varied from 20 to 36 °C. Fig. 19(a) shows the measured transmission spectra of the dual MRRs as a function of temperature, where the 49 GHz MRR TM polarized resonance was thermally tuned over a range of 0.2 nm while the 200 GHz MRR TE-polarized resonance was fixed, thus leading to a RF tuning range of > 20 GHz for the OP-OSSB generator. To reflect the wide RF operation range achievable with our approach, the OP-OSSB signal was converted into a single polarization with a polarizer and then detected. The RF system transmission response was characterized with a vector network analyzer. Wideband RF operation up to 23.14 GHz was achieved [ Fig. 19(b)]. The optical spectra of the OP-OSSB signals are shown in Fig. 20(a) for tuneable RF operation. As the TM 49 GHz MRR temperature was increased from 22 to 35 °C, the RF frequency of the OP-OSSB generator varied from 1.81 to 23.27 GHz with a −1.66 GHz/°C slope [Fig. 20(b)], thus illustrating the wide tuning range of our device. The OP-OSSB generator’s RF bandwidth was limited by the temperature controller’s tuning range of only 15 °C. Covering the entire TM-MRR FSR bandwidth of 49 GHz would require a temperature range of only 29.5 °C, which is easily achievable^{[74, 42]}. Small changes in the FSR with temperature can easily be calibrated. Finally, by using multiply spaced TM resonances greater than an FSR apart, the RF tuning range can be increased arbitrarily, even into the THz regime, which is well beyond the capacity of electronics^[84].

Because the cascaded micro-ring resonators are passive, they did not have any impact on the system performance regarding coherence or dephasing time. The generated signal dephasing time was mainly determined by the coherence length of our laser L_coh, which is given by^[85]

 (17)

where λ is the source wavelength (~1550 nm), n is the fiber refractive index (~1.45), and Δλ is the FWHM of the source spectral width. Our laser had a 400 kHz FWHM spectral width, yielding a coherence length of ~414 m.

For this tuneable OP-OSSB generator, the ring resonators that we used had quite high Q factors, suitable for generating relatively narrow band (albeit high frequency) RF signals. For applications to RF broadband signals, one can either use lower Q factor ring resonators^[75] or use higher order filters^{[77-80, 86]} instead of the high-Q resonators used here. The first approach can produce a 3 dB bandwidth spanning anywhere from 2 to 12 GHz for ring resonators with Q factors ranging from 60 000 to 10 000, while the latter can achieve a 3dB bandwidth > 100 GHz. Finally, the two MRRs can be easily be integrated onto the same chip, with the frequency difference tuned by separate on-chip thermal micro-heater controls ^[87].

In terms of fabrication tolerances and manufacturability, we note that the Hydex platform is CMOS compatible and was originally developed for extremely demanding applications in commercial wavelength division multiplexed optical communications systems for advanced filter design^[77]. Fabrication issues have been discussed at length in Refs. [55, 58, 77, 78] including the high Q factor ring resonators, where resonators with Q factors > 1 million can be routinely fabricated. For the specific applications here, to orthogonally polarized single sideband generation, the issues are the same and in fact are more forgiving. For the fixed RF frequency device where only one ring resonator is used, the TE to TM birefringent splitting determines the RF frequency and so this parameter would need to be engineered to adjust the frequency. However, in fact the preferred approach is actually to avoid this entire issue by adopting the tunable RF device that employs 2 ring resonators, and in this case the TE/TM mode splitting is irrelevant since this is controlled thermally. Finally, as mentioned above, for wideband RF signals, either low Q factor resonators or more preferably higher order filters should be used to achieve bandwidths of 100 GHz or higher. Again, these structures can be fabricated reliably in this CMOS compatible platform and have been discussed at length elsewhere^{[77, 78]}.

We review recent work on fixed and tunable orthogonally polarized optical single sideband (OSSB) generators as well as a dual-channel RF equalizer, both based on integrated dual polarization micro-ring resonators. By controlling the fabrication of the micro-rings, the refractive index of the ring resonator TE and TM polarized modes were engineered to produce a spacing of 16.6 GHz in the C-band. At the drop-port, the optical carrier and sideband were separated by the orthogonally polarized resonances to achieve orthogonally-polarized OSSB modulation. At the through-port, on the other hand, the transmission notches allowed dual-channel RF filtering via phase-to-intensity modulation conversion for equalization. We achieved a large dynamic tuning range of the optical carrier-to-sideband ratio of the OSSB signal and the dual-channel RF equalization by controlling the polarization angle. Our method represents a novel way of achieving OSSB generation as well as photonic RF equalization, while offering a compact footprint and high performance. This approach is promising for radar and communications systems RF photonic signal processing.