Fully programmable spectrum sliced chirped microwave photonic filter

Peter Leitner; Xiaoke Yi; Liwei Li; Thomas X. H. Huang

doi:10.1364/OE.23.004033

1. Introduction

Microwave photonics is a cross disciplinary research field concerned with the development of photonic structures to perform equivalent tasks to traditional microwave electronics, bringing the well known benefits of optical communication systems to radio frequency (RF) technology, including high bandwidth, low loss and immunity to electro-magnetic interference (EMI) [1]. Microwave photonic filters (MPF) are able to achieve invariant tunability, the ability to tune the filter centre frequency over a wide range without altering the amplitude and phase response, and independent reconfigurability, the ability to alter the amplitude and phase response independently of each other, both of which are limited in electronic RF filters. Increasingly compact photonic structures have been recently proposed to improve their ease of integration as compared with electronic structures [2]. Spectrum sliced filters, where a broadband incoherent light source is optically filtered to generate an effective number of taps, were initially proposed as an alternative to coherent optical sources for high resolution finite impulse response filters requiring a large number of taps [3]. While much previous work on spectrum sliced microwave photonic filters has been focused on optimization of amplitude response characteristics [3,4], recent interest has arisen in chirped RF filters, which exhibit a quadratic phase response or linear group delay within the filter passband. Chirped microwave filters are typically employed due to their ability to compress or expand the bandwidth occupied by the signal, with the achievable RF group delay slope referred to as the chirp parameter. They have extensive application in high performance radar [5], antenna phase distortion compensation for ultra-wide band (UWB) radio systems [6], radio over fibre systems [7], real-time spectral analysis [8] and clinical diagnosis for microwave computed tomography systems [9]. Whilst applications typically require a large in-band chirp, electronic chirped filter structures have been limited in the maximum achievable group delay slope, operating bandwidth and reconfigurability of both the amplitude and phase response [10]. For instance, a tuneable chirped RF filter based upon an electromagnetic-bandgap (EBG) structure in microstrip lines was proposed in [11], achieving operation to 18 GHz with a maximum group delay slope of ~−0.4 ns/GHz.

A chirped spectrum sliced MPF utilizing a delay line with non-zero second order dispersion to generate a linear RF group delay was reported in [12], with an extension presented in [10] using a balanced photodetector (BPD) to eliminate the carrier suppression effect (CSE). Whilst a single passband response and in-band RF chirp values of up to ~18 ns/GHz were demonstrated, for a given delay line length, the chirp magnitude was inversely proportional to the filter centre frequency. This limited the invariant tunability and reconfigurability of the filter without manual adjustment. In [13], a slicing structure based on a phase modulator combined with a linearly chirped fibre Bragg grating (L-CFBG) was used to generate a chirped MPF. Whilst the device amplitude and phase response were invariantly tuneable, the demonstrated group delay slope was limited to −0.68 ns/GHz, a value comparable to electrical approaches. A structure incorporating an optical programmable filter to replace the L-CFBG was subsequently proposed in [14], yielding a tuneable RF chirp value up to −10 ns/GHz. However, the structure still required manual adjustment of the VDL to tune the filter passband and polarization control in the Mach-Zehnder Interferometer (MZI) structure. Moreover, the aforementioned chirped MPF proposals did not include a theoretical characterization of the device noise performance. The noise performance is a key consideration as the slicing of a broadband optical source produces a thermal like intensity noise due to the finite bandwidth of the optical source [15]. This results in excess noise in the RF response that is typically the dominant performance limitation in spectrum sliced filters. Furthermore, the effect of tuning on the passband noise performance of shifted RF fading based spectrum sliced MPFs has not been previously reported.

In this paper, a novel chirped MPF structure is presented based on an incoherent source, a Fourier domain optical processor (FD-OP) and an external single sideband (SSB) intensity modulator. The system simultaneously achieves a large in-band RF chirp, invariant tuning free from CSE and high frequency roll-off, independent reconfiguration of the RF amplitude and phase response and low passband noise. The FD-OP is utilized to generate both constant group delay to tune the filter and first order dispersion to induce a linear RF group delay. This allows for full software control of the device without the need for manual adjustment of the optical system after setup, with the slicing structure not requiring polarization control. An optimized parameter region is introduced that allows the generation of a large in-band RF chirp by substantially increasing the optical bandwidth, simultaneously benefitting the RF amplitude, phase and noise performance. Additionally, a stochastic analysis of the device noise performance is developed to study the RF noise of the new structure under chirped operation, tuning and reconfiguration.

The remainder of this paper is structured as follows. In section II, a theoretical analysis of the new structure and resulting RF transfer function are detailed, and the stochastic model for the filter noise is introduced. A full parameter space exploration is undertaken in section III to determine the optimal broadband source width and slicing dispersion to generate a large linear RF group delay slope, as well as the optimal apodization profile to minimize the ripple of the generated RF chirp. The experimental setup is discussed in section IV. The experimental results, including frequency invariant tuning and independent reconfiguration of the RF group delay and passband width are presented in section V. In addition, the noise performance of the RF filter when tuning the centre frequency, adjusting the chirp and reconfiguring the passband width is analyzed and measured. Finally, concluding remarks are given in section VI.

2. Theoretical analysis

The structure of the spectrum sliced chirped MPF is shown in Fig. 1, where an incoherent broadband optical source (BOS) is cascaded with a dual output FD-OP and a single sideband electro-optic modulator (EOM). The FD-OP is based on a two dimensional liquid crystal on silicon (LCoS) pixel array [16]. In the newly proposed design, the FD-OP performs the following optical signal processing functions; a 3 dB y-branch to split or route the broadband source spectrum into two separately programmable outputs, apodization of the broadband source spectrum, adjustable constant delay in the lower arm to tune the filter centre frequency, and adjustable first order dispersion in the upper arm to induce the RF chirp. A 3 dB y-branch coupler is utilized to complete the slicing.

Fig. 1 Schematic of the proposed chirped filter structure. VNA – vector network analyzer, LOA – linear optical amplifier, PD – photodetector, ω – optical frequency.

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The optical filtering function H_up(ω) of the upper output of the FD-OP is modelled as a unity magnitude filter with quadratic phase Φ_up(ω) [3],

H_{u p} (ω) = e^{j Φ_{u p} (ω)} = e^{\frac{j}{2} β_{S} {(ω - ω_{0})}^{2}},

where β_S is the first order dispersion coefficient [s²/rad]. The lower output is a linear phase filter H_lo(ω) modelled by,

H_{l o} (ω) = e^{j ω Δ τ},

where Δτ is the time delay between the upper and lower arms generated by the FD-OP, with corresponding optical slicing frequency given by Δω = 2π/Δτ. As will be detailed in section IV, the output power of each FD-OP port is equal. The optical power transfer function T_MZI(ω) of the FD-OP based MZI structure is given by,

T_{M Z I} (ω) = \frac{T_{A P} (ω)}{2} [1 - V \cos (ω Δ τ - \frac{1}{2} β_{S} {(ω - ω_{0})}^{2}) ​],

where V is the visibility of the MZI to account for the depth of the interferometer notches. The optical apodization profile T_AP(ω) dictates the un-sliced shape of the optical spectrum and the overall optical extinction ratio, defined as the ratio of the optical filter passband to stopband. The corresponding power spectral density (PSD) functions of the apodized P_AP(ω) and spectrum sliced P_S(ω) fields are respectively given as,

P_{A P} (ω) = T_{A P} (ω) {| E_{B O S} (ω) |}^{2},

P_{S} (ω) = T_{M Z I} (ω) {| E_{B O S} (ω) |}^{2} .

where E_BOS(ω) is the broadband source field.

For an incoherent source undergoing intensity modulation prior to propagation through a dispersive phase filter and square law detection as shown in Fig. 1, the RF photocurrent I(t) is expressed as [17],

I (t) = R \int_{- \infty}^{+ \infty} P_{S} (ω') {| \int_{- \infty}^{+ \infty} S (ω - ω') e^{j [(ω - ω') t - Φ_{D} (ω) + Φ_{D} (ω')]} d ω |}^{2} d ω',

where ω' is the optical convolution variable, Φ_D(ω) is the phase response of the L-CFBG delay line given by Eq. (1) with first order dispersion coefficient β_D, R is the responsivity of the photodetector and S(ω) is the Fourier transform of the single sideband time domain modulation signals

\sqrt{s (t)} = 1 + m e^{j 2 π f_{m} t}

with modulation frequency f_m and small signal modulation index m. The use of single sideband intensity modulation ensures that the response is free from CSE, and that polarization controllers are not required.

Evaluation of Eq. (6) yields the filter RF transfer function,

H (f_{m}) \propto \int_{ω_{\min}}^{ω_{\max}} [1 - V \cos (ω' Δ τ - \frac{1}{2} β_{S} {(ω' - ω_{0})}^{2}) ​] P_{A P} (ω') e^{- j β_{D} 2 π f_{m} (ω' - ω_{0})} d ω',

where ω_max and ω_min are respectively the maximum and minimum optical frequency utilized in the photonic system. Equation (7) can be rewritten in the form,

H (f_{m}) = B (f_{m}) - \frac{V}{2} (M_{+} (f_{m}) + M_{-} (f_{m})),

where the baseband response B(f_m), positive M₊(f_m) and negative sidebands M₋(f_m) are respectively given by,

B (f_{m}) = e^{j 2 π β_{D} f_{m} ω_{0}} \int_{ω_{\min}}^{ω_{\max}} P_{A P} (ω') e^{- j 2 π β_{D} f_{m} ω'} d ω',

M_{\pm} (f_{m}) = e^{j 2 π β_{D} f_{m} ω_{0}} \int_{ω_{\min}}^{ω_{\max}} P_{A P} (ω') e^{\pm j Δ τ ω'} e^{\mp \frac{j}{2} β_{S} {(ω' - ω_{0})}^{2}} e^{- j 2 π β_{D} f_{m} ω'} d ω' .

Recognizing the Fourier transform from the ω' to the β_Df_m domain, Eq. (9) and (10) can be rewritten respectively as,

B (f_{m}) = e^{j 2 π β_{D} f_{m} ω_{0}} p_{A P} (β_{D} f_{m}),

M_{\pm} (f_{m}) = e^{j 2 π β_{D} f_{m} ω_{0}} (p_{A P} (β_{D} f_{m}) * F {e^{\pm j Δ τ ω'}} * F {e^{\mp \frac{j}{2} β_{S} {(ω' - ω_{0})}^{2}}}),

where F is the forward, unitary and ordinary Fourier transform, p_AP(β_Dfm) is the Fourier transform of P_AP(ω'), and * denotes the convolution operation. Further simplifying Eq. (12) yields,

M_{\pm} (f_{m}) = e^{j 2 π β_{D} f_{m} ω_{0}} (p_{A P} (β_{D} f_{m} \mp \frac{Δ τ}{2 π}) * F {e^{\mp \frac{j}{2} β_{S} {(ω' - ω_{0})}^{2}}}) .

The baseband resonance in Eq. (11) is the Fourier transform of the apodized optical PSD and is equivalent to the RF fading characteristic in [3]. The passband response in Eq. (13) is the convolution of the shifted baseband resonance with the Fourier transform of the quadratic optical phase filter in the MZI slicing structure. Examining Eq. (13) reveals that the optical phase filter is equivalent to a complex Gaussian. Noting that that the Fourier transform operation on a complex Gaussian results in a complex Gaussian in the transform domain, a quadratic phase filter in the RF domain is generated which convolves with the shifted baseband resonance. The convolution operation is the fundamental mechanism via which the RF chirp is generated, whereby the quadratic phase in the slicing structure is imprinted on the RF spectrum after photodetection. For both the baseband and passband response, the broadband source will be mapped to the RF domain, dictating the shape of the RF resonance. However, the convolution with the quadratic phase increases the bandwidth of the passband, indicating that the baseband and passband resonances do not have the same profile. As the chirping of the passband response in Eq. (13) is independent of the modulation frequency, the passband amplitude and group delay response may be tuned invariantly. This is in contrast to the design presented in [10,12], where the third order optical phase yields a passband characteristic dependent on the filter centre frequency [4,18].

In the case where the slicing dispersion in the upper arm is set to zero, the convolution in Eq. (13) is performed with a baseband Dirac delta function, resulting in a single passband linear phase filter response. The baseband and passband exhibit the same shape and increasing optical bandwidth yields a narrower passband as in [4,18], which is in contrast to when the slicing dispersion is non-zero. Additionally, whilst the absolute passband power is constant and 6 dB lower than the baseband for a fixed optical bandwidth in single passband operation, decreasing the optical slicing dispersion will increase the absolute power of the passband in chirped operation. The central RF frequency f_c of the filter passband in chirped or single passband configuration is found from Eq. (13) as,

f_{c} = \frac{Δ τ}{2 π β_{D}} .

The noise performance of the chirped MPF structure is investigated based on the theoretical framework provided in [15]. Considering the small signal modulation employed and the slow autocorrelation roll-off of the optical spectrum relative to the photodetection and modulation bandwidths, the relative intensity noise (RIN) of the chirped filter at RF frequency f_RF is given by,

R I N (f_{R F}) = \frac{\int_{- \infty}^{+ \infty} P_{S} (ω' - ω_{0}) P_{S} (ω' - ω_{0} - 2 π f_{R F}) d ω'}{{(\int_{- \infty}^{+ \infty} P_{S} (ω' - ω_{0}) d ω')}^{2}} .

The corresponding noise spectral density of the photocurrent N_I(f) [A²/Hz] is expressed as,

N_{I} (f_{R F}) = {(R P_{o p t})}^{2} R I N (f_{R F}),

where the total power of the sliced field is given by

P_{o p t} = \frac{1}{2 π} \int_{- \infty}^{+ \infty} P_{S} (ω' - ω_{0}) d ω'

.

3. Optimized parameter space

An exploration of the available optical parameter space based on the filter transfer function in Section II was undertaken to determine the optimal source width and slicing dispersion to generate a large RF chirp. As the filter amplitude and phase response is invariantly tuneable, the generated RF properties are identical over the photodetection bandwidth in all cases where the passband is sufficiently separated from the baseband resonance. For ease of comparison, the simulations were undertaken at a fixed filter centre frequency of 10 GHz, requiring a delay of 24 ps when using a 300 ps/nm L-CFBG as the delay line. The impact of the visibility of the MZI structure was explored using Eq. (7). When decreasing the visibility from unity to −6 dB with the overall optical system extinction ratio set to ϵ_r = 15 dB, simulations indicated that whilst the power of the passband was lowered for reduced visibility, no change in the passband shape, in-band RF chirp or excess ripple in the group delay response was induced. Hence, in the simulations presented in this section, the visibility of the MZI structure was set to unity with ϵ_r = 15 dB.

Figures 2(a) and (b) respectively show the RF 3 dB passband width and chirp in the 3 dB bandwidth achieved by the MPF against the dispersion in the slicing structure β_s and the width of the broadband optical source BOS_3dB, indicating two distinct parameter regions for the device operation. When the 3 dB bandwidth of the optical source was lower than 750 GHz, the RF chirp was extremely limited to ~0.1 ns/GHz, an order of magnitude lower than the previous MPF proposals detailed in section I. However, by increasing BOS_3dB beyond 750 GHz and reducing β_s to less than −1 ps/nm, a large increase in the group delay slope was evident as shown in Fig. 2(b). The newly identified area of the parameter space enables generation of RF chirp values up to ± 8 ns/GHz, and is henceforth referred to as the high chirp region as shown in red in Fig. 2. This new design strategy additionally benefits the filter noise, as the enlarged optical bandwidth employed lowers the filter RIN.

Fig. 2 The RF (a) 3 dB passband width and (b) group delay slope against the dispersion in the slicing structure and the width of the broadband optical source, with the high chirp region shown in red.

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Within the high chirp region, the relations between the sliced optical spectrum and the RF passband width BW_RF and group delay slope C_RF are respectively expressed as,

B W_{R F} \propto B O S \times β_{S},

C_{R F} \propto \frac{1}{β_{S}} .

The observed relationships allow for independent reconfigurability of the in-band RF chirp and passband width via software control of the FD-OP, by setting the slicing dispersion to achieve the desired RF chirp, and adjusting the optical bandwidth to set the necessary passband width. For example, when the RF chirp requires doubling and passband width remains constant, β_S is halved and BOS doubled. Altering the sign of the slicing dispersion allows controlling the direction of the RF chirp. As the power of the passband is increased by increasing BOS and decreasing β_S, the optimized parameter space improves the passband power under highly chirped operation. Furthermore, the inverse proportionality of the RF chirp to the optical dispersion benefits the implementation presented, due to the limited dispersion bandwidth product of the FD-OP [19]. This indicates that a compromise does not exist between the delay available to tune the filter to high frequency and induce the RF chirp.

The effect of the broadband source apodization profile on the group delay linearity was explored by fitting a linear trend line to the simulated RF group delay and calculating the root mean square error (RMSE) within the filter 3 dB bandwidth in the high chirp region. The 3 dB bandwidths of each apodization profile were matched to achieve equal RF passband widths, with V = 1, ϵ_r = 15 dB and the filter centre frequency fixed at 10 GHz. The resulting RMSE plots for a Gaussian, Super Gaussian (~ $\exp (- ω^{4})$ ) and Rectangular profiles are shown in Figs. 3(a), (b) and (c) respectively, indicating that the Gaussian profile achieved approximately one and two orders of magnitude lower RMSE than the Super Gaussian and Rectangular profiles respectively. Additionally, only the Gaussian offered consistent performance in the high chirp region. As the shape of the apodization profile determines the RF fading characteristic and hence the passband shape as in Eq. (12), this reveals that for increasingly flat passbands, the linearity of the filter group delay is compromised. Hence, a Gaussian profile was utilized in all experimental work due to the superior chirp linearity and well known increase in sidelobe suppression. The significance of the overall extinction ratio of the photonic system on the group delay ripple was also investigated, with the RMSE in the high chirp region simulated for a Gaussian with ϵ_r = 25 dB in Fig. 3(d). Comparing with Fig. 3(a), it was evident that increasing the extinction ratio by an order of magnitude decreased the RMSE by approximately an order of magnitude, highlighting the importance of the extinction ratio of the slicing filters, optical amplifiers and L-CFBG.

Fig. 3 Root mean square error performance when changing windowing profiles for (a) Gaussian with ϵ_r = 15 dB (b) Super Gaussian with ϵ_r = 15 dB (c) Rectangular with ϵ_r = 15 dB and (d) Gaussian with ϵ_r = 25 dB.

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4. Experimental setup

In the experimental demonstration, a C-band Erbium-doped fibre amplifier (EDFA) (Amonics) was utilized as the optical source and connected to the LCoS based FD-OP (Finisar Waveshaper 4000S) as illustrated in Fig. 1. The optical amplitude and phase data for each port of the FD-OP are loaded via software [16], enabling the RF properties to be tuned and reconfigured without manual adjustment of the optical components. The dual output of the FD-OP was connected to a 2 by 1 coupler (y-branch) to form the MZI slicing structure prior to an SSB + C modulator (EOSpace). The modulator was biased at quadrature point for optimum linearity and amplitude of the filter passband, after which a linear optical amplifier (LOA) was used to increase the optical power prior to the delay line. An optical circulator was employed to connect a 300 ps/nm L-CFBG (Teraxion), after which the RF signal was detected by a 0-20 GHz photodiode (u2t) and the generated RF transfer function measured using a vector network analyzer (VNA) (Agilent N5230A). The notch depth of the MZI slicing structure and overall optical extinction ratio achieved by the configuration were ~1 and ~15 dB respectively. In order to measure the device noise performance, the noise spectral current was measured on an electrical spectrum analyzer (ESA) (Agilent E4466A).

The FD-OP exhibits a delay dependent attenuation A_FD-OP [dB] of the optical spectrum modelled as,

A_{F D - O P} = 0.0048 τ^{2},

where τ is the generated group delay [ps] [20]. As tuning the filter to higher frequency requires a larger constant time delay, a roll-off of the RF amplitude response at high frequency will occur due to the increased attenuation of the optical field. In order to retain the theoretically derived invariant tuning property of the filter, the optical power of all output ports was compensated via software control to equalize the power for all possible generated time delay and dispersion profiles. The compensation profile C_FD-OP(ω) was given by,

C_{F D - O P} (ω) = - 0.0048 ({(τ_{\max})}^{2} - τ^{2} (ω)),

with τ(ω) [ps] in the upper port given by integrating the exponent of Eq. (1) and in the lower port by the time delay for the desired centre frequency in Eq. (2), where τ_max is the delay at the maximum measured passband. Whilst the VNA available in the setup was limited to 20 GHz, the 80 ps maximum time delay of the FD-OP allows operation to 33.4 GHz.

5. Results and discussion

The ability of the device to generate a large RF group delay slope with invariant tunability of the amplitude and phase response was experimentally verified. Using optical parameters of BOS_3dB = 1.25 THz and β_S = 0.125 ps/nm in the high chirp region, the FD-OP constant delay was varied to tune the filter centre frequency from 2.0 GHz to 18 GHz in steps of 2.0 GHz. Examining the measured data in Fig. 4, a single passband response with a large linear group delay slope was evident, being the first demonstration of a shifted RF fading MPF with full software control. Considering the amplitude response in Fig. 4(a), the measurements exhibited a mean BW_RF,3dB = 0.42 GHz, indicating excellent agreement with the simulated mean BW_RF,3dB = 0.41 GHz. The worst case attenuation of a passband from the simulated value was 2.4 dB at the 12 GHz passband, indicating that the programmed compensation for the optical attenuation of the FD-OP system allowed for the invariant tuning property of the amplitude response to be well observed in experiment. Additionally, no high frequency attenuation or CSE was observed in the chirped filter response, nor passband broadening due to a non-zero dispersion slope. The baseband and passband showed a different shape and bandwidth, which occurred as the baseband response is not convolved with the chirped optical phase as in Eq. (11).

Fig. 4 The centre frequency invariant RF (a) amplitude and (b) group delay response with BW_RF,3dB = 0.42 GHz and C_RF = −4.2 ns/GHz. Measured – solid, Simulated – dotted. Group delay results out of the 15 dB filter bandwidth were curtailed to allow for clarity of the presented data. The decrease in the RF extinction ratio at high frequency in (a) arose due to the VNA calibration for the roll-off of the electronic components.

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Considering the group delay data shown in Fig. 4(b), within the 3 dB filter bandwidth the mean measured RF group delay slope was C_RF = −4.2 ns/GHz, which showed strong agreement with the simulated mean C_RF = −4.3 ns/GHz. This proved both the fundamental design concept of the high chirp region whereby a large optical bandwidth combined with a low slicing dispersion induces a large RF group delay slope, and the predicted centre frequency invariant tunability of the group delay. In order to examine the linearity of the experimentally generated chirp, a linear trend line was fit to the data. The RMSE was examined within the 3 dB passband width, with the experimental and simulation results yielding a mean RMSE of 0.15 ns and 0.017 ns respectively. The increased RMSE in the experimental implementation and small reduction in side lobe suppression in the amplitude response at high frequency may be attributed to the group delay ripple of the L-CFBG ( ± 15 ps/nm), as well as non-constant LOA gain characteristics affecting the uniformity of the slicing profile. The results additionally indicated that the group delay linearity was not significantly altered within the 10 dB bandwidth of the filter, avoiding distortion of the filtered pulse.

The passband RIN of the configuration in Fig. 4 was explored, with corresponding BW_RF,3dB = 0.42 GHz and C_RF = −4.2 ns/GHz. Measurements were taken until 10 GHz due to the substantial increase in the ESA noise floor. The results are shown in Fig. 5(a), indicating strong agreement between experimental and simulated data, where in all cases the passband RIN remained below −122.0 dB/Hz. This is an excellent achievement for a spectrum sliced MPF [15], demonstrating the combined low noise and high RF chirp achieved by the novel structure and optimized parameter space. In order to explore the effect of adjusting the RF chirp on the noise, the FD-OP dispersion was set to 0.25 ps/nm without changing the optical bandwidth, corresponding to simulated BW_RF,3dB = 0.76 GHz and C_RF = −2.7 ns/GHz. The experimental and simulated data showed strong agreement as in Fig. 5(b). Furthermore, comparing Figs. 5(a) and (b), the results agree within 0.4 dB and 0.1 dB in the measured and simulated cases respectively. This indicated that in the high chirp region, where the slicing dispersion was kept small, the passband noise was independent from the value of the slicing dispersion. Hence, the magnitude of the RF chirp can be adjusted without affecting the passband noise performance. The simulation data indicated that for tuning the device up to 32 GHz, the passband noise varied within ± 3 dB, indicating a consistent noise performance under tuning. The noise variation was caused by the altered autocorrelation overlap of the optical spectrum when the filter was tuned by changing the slicing frequency, leading to an altered passband RIN value. Due to the independence of the passband noise from the chirp value, these results are also applicable for single passband RF fading filters.

Fig. 5 The passband RIN performance for the novel chirped filter achieving (a) BW_RF,3dB = 0.42 GHz and C_RF = −4.2 ns/GHz and (b) BW_RF,3dB = 0.76 GHz and C_RF = −2.7 ns/GHz. Measured, Simulated.

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The ability of the structure to achieve independent reconfiguration of the amplitude and group delay response was experimentally confirmed. The default filter response is shown in Fig. 6(a) with BOS_3dB = 0.90 THz and β_S = 0.3 ps/nm, achieving measured BW_RF,10dB = 1.2 GHz and C_RF = −2.1 ns/GHz at 10 GHz. Figures 6(b), (c) and (d) show the independent reconfigurability of the filter, where it was desired to respectively; reverse the sign of the group delay slope, increase C_RF by 50% with BW_RF constant and increase BW_RF by 50% without altering C_RF. The device potential to alter the sign of the RF chirp was shown in Fig. 6(b) by reversing the sign of the FD-OP dispersion. The RF chirp was increased by 52% to C_RF = −3.2 ns/GHz whilst holding the RF bandwidth fixed at BW_RF,10dB = 1.2 GHz in Fig. 6(c), with the optical parameters set to BOS_3dB = 1.35 THz and β_S = 0.2 ps/nm. Finally, setting the optical parameters to BOS_3dB = 1.35 THz and β_S = 0.3 ps/nm, the 10 dB passband width was increased by 58% to BW_RF,10dB = 1.9 GHz with C_RF = −2.2 ns/GHz in Fig. 6(d). The excess ripple and small asymmetry in the measured results occurred due to the group delay ripple of the L-CFBG and non-uniform gain characteristics of the LOA about the central frequency of the optical system.

Fig. 6 The independent reconfiguration properties of the novel filter tuned to 10 GHz with (a) BW_{RF, 10dB} = 1.2 GHz, C_RF = −2.1 ns/GHz; (b) BW_{RF, 10dB} = 1.3 GHz, C_RF = 1.9 ns/GHz; (c) BW_{RF, 10dB} = 1.2 GHz, C_RF = −3.2 ns/GHz; (d) BW_{RF, 10dB} = 1.9 GHz, C_RF = −2.2 ns/GHz. (blue line) Measured amplitude response, (pink line) Simulated amplitude response, (black line) Measured group delay, (red line) Simulated group delay.

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The effect of reconfiguring the RF chirp sign, RF chirp magnitude and passband width as in Fig. 6 on the filter noise performance was investigated. The measured and simulated RIN values of Fig. 6(a) were −121.2 dB/Hz and −124.0 dB/Hz respectively, remaining constant when changing the RF group delay slope sign in Fig. 6(b). Decreasing β_S and increasing BOS_3dB in Fig. 6(c), yielded a decrease in the RIN from Fig. 6(a) by 1.6 dB and 0.6 dB in the measured and simulated cases respectively. In Fig. 6(d), setting β_S to that in (a) with BOS_3dB as in (c), yielded identical noise results to Fig. 6(c), again indicating the independence of the filter noise from the FD-OP dispersion. These results highlight that by increasing the spectral bandwidth to achieve a wider passband, the passband noise will be decreased. This indicates that for chirped filter applications that require a large RF bandwidth, the increased optical bandwidth employed in the high chirp region improves both the in-band chirp magnitude, passband power and passband noise performance.

The configuration presented in this paper was limited in the maximum operating frequency, achievable group delay slope and passband width due to the delay dependent attenuation of the FD-OP. For instance, Fig. 6(c) demonstrated C_RF = −3.2 ns/GHz and BW_RF,10dB = 1.2 GHz, as compared with C_RF = −5.61 ns/GHz and BW_RF,10dB = 11.7 GHz in [10] and C_RF = −10 ns/GHz and BW_RF,10dB ~4.0 GHz in [14]. The difference is attributable to the manually tuned VDL devices capable of >250 ps delay and large fibre delay lines utilized in the previous photonic approaches, as opposed to the software controlled FD-OP and compact grating utilized in the design presented here. Introducing a fixed time delay at an output of the FD-OP to create an unbalanced MZI slicing structure enables doubling the maximum operating frequency without compromising the FD-OP attenuation or achievable RF parameters. More significantly, enlarging the dispersion of the delay line to 600 ps/nm will double the RF chirp bandwidth product without altering the full software controllability, tunability and reconfigurability advantages relative to the previous electric and photonic chirped filter proposals.

6. Conclusion

A novel chirped microwave photonic filter structure has been proposed that achieves a large RF group delay slope, a single passband response, invariant tunability and independent reconfigurability of the amplitude and phase response. The new design is based upon an incoherent source, programmable FD-OP optical filter and single sideband intensity modulator, and is free from CSE and high frequency attenuation. The FD-OP was utilized to generate both constant delay and first order dispersion in the optical domain, yielding a linear RF group delay. A full theoretical analysis was developed to derive the device transfer function. The simulation results identified an optimal region of the optical parameter space based upon an optical bandwidth sufficiently >750 GHz and slicing dispersion < ± 1 ps/nm. This benefitted the RF chirp magnitude, passband power and noise performance achieved by the new structure. Furthermore, it has been determined that a Gaussian apodization profile yields superior group delay linearity, with approximately one and two orders of magnitude lower RMSE than a Super Gaussian and Rectangular profile respectively. Experimental results confirmed the device properties of a high RF chirp of −4.2 ns/GHz, invariant tunability and independent reconfigurability of the RF amplitude and group delay response. To the author’s best knowledge, this is the first chirped spectrum sliced MPF filter to achieve tunability and reconfigurability by software control without the need for manual tuning. Additionally, a systematic study of the device noise performance has been presented, indicating that the novel design achieved low noise <−120 dB/Hz. The passband noise was independent from the generated RF chirp, with < ± 4 dB fluctuation of the RIN under tuning and reconfiguration.

Acknowledgments

This work was supported by the Australian Research Council (ARC). Thanks are extended to Dr. Cibby Pulikkaseril and Mr. Patrick Blown from Finisar Australia.

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Fully programmable spectrum sliced chirped microwave photonic filter

Abstract

1. Introduction

2. Theoretical analysis

3. Optimized parameter space

4. Experimental setup

5. Results and discussion

6. Conclusion

Acknowledgments

References and Links

Cited By

Figures (6)

Equations (20)

Optics Express