With the advent of advanced modulation formats, ultra-wideband (multi-GHz), and extremely high carrier frequencies (>90 GHz) in communication and radars systems, there is continual demand for microwave monitoring with increased bandwidths and enhanced performance. While electronic analog-to-digital converters (ADCs) have seen steady improvement in performance over the past several years, no single chip ADCs exist that can directly capture signals with 10 effective vertical bits of resolution beyond 2 GHz of bandwidth [1]. Only modest improvements in electronic ADC performance are expected in the near term [1]. Photonic based ADC systems have the potential to overcome the limits of electronic ADCs, due in particular to the capability to modulate high bandwidth (>10 GHz) electronic signals directly onto optical carriers with high signal fidelity [2].

Recently, time-stretched photonic-assisted ADCs have exploited the ability of dispersive elements to temporally stretch modulated broadband chirped optical pulses to reduce the necessary back-end electronic ADC bandwidth requirement [3]. Time-stretched ADCs have demonstrated effective sampling rates that exceed 1 terasample per second and effective resolutions of about 5 bits over a 10 GHz bandwidth, but their time apertures for single shot transient digitization are limited to on the order of nanoseconds and time-bandwidth products greater than 1000 are difficult to achieve with these systems [3].

Rather than stretching the time-domain representation of a signal-of-interest (SOI), the technique demonstrated here captures the signal in the frequency domain and stretches the frequency-domain representation of the SOI during readout [4]. The frequency-domain capture and readout is made possible by the unique properties of spatial-spectral holographic (SSH) materials [5]. Like time-stretch ADCs, the SSH-ADC acts to convert high bandwidth input signals into low bandwidth output signals (without loss of information) to take advantage of high performance, lower bandwidth back-end electronic ADCs. Some SSH materials have transition bandwidths over 100 GHz and single-shot time apertures greater than 10 µs, providing the potential for time-bandwidth products in excess of 10⁶ [6]. While the achievable vertical resolution of the SSH-ADC requires further experimental study, previous simulations have predicted greater than 10 effective resolution bits for a 10 GHz bandwidth with currently available optical components [4]. The SSH-ADC also allows the direct capture of signals modulated on a high frequency carrier, eliminating the inter-modulation spurs that can arise from down-conversion. This paper presents the first proof-of-concept demonstrations of a SSH-ADC and demonstrates the direct capture of a 1600 MHz SOI modulated on a 6.5 GHz microwave carrier.

 

Fig. 1. The SSH-ADC conceptual diagram. Waveform Capture: the SOI and reference waveform are converted into the optical domain and illuminate the SSH material to produce a spectral hologram. Readout: a chirped optical waveform reads the absorption profile, which is detected and digitized with high fidelity, low speed ADCs, and post processed to yield the digitized version of the SOI.

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The operation of the SSH-ADC is a two step process [4]. First, a broadband reference signal, V_R(t), and the SOI, V_S(t-τ), are modulated serially onto a single optical carrier. This requires that the time delay, τ, be larger than the durations of V_R(t) and V_S(t). Here, an electro-optic phase modulator (EOPM) and a collinear configuration for the reference and SOI beams were used. If the voltage applied to the EOPM, V(t)=V_R(t)+V_S(t-τ), is much less than the V_π of the EOPM, the resultant optical field is simply proportional to V(t), whereas for V(t) on the order of V _π, saturation and considerable distortion of the recorded SOI will occur. This modulated optical field then illuminates the SSH material, as shown in Fig. 1. The SSH material responds to a broadband optical signal by recording a high-fidelity replica of its power spectrum in the form of a modified absorption profile (i.e. a SSH). This absorption profile has an interference term that includes the Fourier transform (FT) of the SOI. Faithful capture of the SOI requires that the spectral content of the reference signal overlap that of the SOI. The average material absorption (over the crystal length, L) to first order can be shown to be proportional to the optical energy spectrum of the incident modulated light field, ε (f) [4], and is found to be

where V_S(f) and V _R(f) are the FTs of the SOI and reference waveforms, respectively, and f_L is the optical carrier frequency. The spectral interference terms in ε (f) separately contain all the information needed to reconstruct a time-domain representation of the SOI. Due to the coherence time in the material, the SOI duration is typically limited to less than 10 µs. The recorded spectrum lasts for the effective material’s upper state lifetime, which is typically several milliseconds in rare-earth doped crystals.

The second step is a spectral readout of the recorded optical spectrum utilizing a scanned optical source, as shown in Fig. 1. The readout duration depends on the frequency scan rate, κ, and is typically much longer than the duration of the SOI (τ_SOI) enabling the effective stretched processing of the frequency-domain representation of the SOI. Note that a spectral recovery technique is used to compensate for coherent distortions and allows for fast readout scan rates [7]. The transmitted time-domain optical signal is to first order proportional to the averaged material absorption, and the transmitted readout signal is detected, digitized, and high-pass-filtered to remove the terms |V_R(f′)|² and |V_R(f′)|² where f′=f-f_L=κt. This signal is then multiplied by the FT of the delayed reference signal and low pass filtered, yielding

provided the time interval between the end of the reference and the start of the SOI is greater than the duration of either signals. When the resultant signal is inverse FT, the result is

where ⊕ and ⊗ represent the operations of convolution and correlation, respectively. If the reference signal has a strong autocorrelation (i.e. low temporal sidelobe structure) then the time domain representation of the SOI is essentially recovered. These sidelobes act to limit the achievable vertical resolution of the recovered SOI. Complementary codes can be used as reference waveforms to reduce or eliminate the impact of the reference sidelobe structure, and is accomplished by capturing duplicate copies of the SOI in two parallel (or serial) processes. When the auto-correlations of the two complementary codes are added, their sidelobe structures (ideally) will cancel [8]. Similarly, by reading out the two results separately and adding the two resulting digitized outputs, the convolved sidelobe structures cancel, yielding a faithful reproduction of the SOI [4].

 

Fig. 2. The experimental setup for the SSH-ADC demonstrations. See text for discussion.

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Experiments were conducted to demonstrate the SSH-ADC concept utilizing a 7 mm long, 0.1% Tm:YAG crystal held at 4K in an optical cryostat as the SSH material. Fig. 2 shows the experimental setup. Light from a frequency stable laser was passed to an injection locked semiconductor amplifier (ILA) to increase power and was subsequently split into two paths, one for the recording of the reference and SOI, and the other for the readout of the material. The recording beam travels through EOPM1, where the reference and SOI are serially modulated onto the optical carrier, amplified with a semiconductor optical amplifier (SOA), and then focused along direction k⃗₁ into the SSH material. Optical powers for the record signals were 205 mW and focused to a ~65 µm beam waist (1/e ²) before the crystal.

The light from the readout path travels through EOPM2 where either a single sided or double sided microwave frequency sweep creates chirped optical sidebands for the readout of the recorded information [9]. After EOPM2, the light is amplified with an SOA and split into two paths so that balanced detection can be used to remove common mode noise and signals in the readout channel. After passing through the lens, one readout path overlaps with the recorded information in the crystal along direction k⃗₂. The other readout path travels in direction k⃗₃, such that it does not overlap with either k⃗₁ or k⃗₂ within the crystal and is used for background subtraction. These two readout paths were of equal power (~20 mW) and both were focused to roughly the same spot size as the signal beam. There is no spatial diffraction in this configuration because the difference in k-vectors between the SOI and the reference waveform are zero, thus any coherent emission travels in the direction of the readout beam (k⃗₂). The output light from the readout paths is detected with a custom, high-power balanced photodiode. The electrical output from the balanced photodiode is detected and digitized with a National Instruments 5122 14-bit 100 MSPS ADC. As described above, two complementary reference codes were used in a serial manner along with matching SOI, to reduce the impact of reference sidelobe structure on the recovered SOI. These two sequences were applied serially to the material after a suitable time to allow prior recordings to decay away and the resultant signals were added during post-processing. In practice, these complementary codes would be applied in parallel into separate spots in the material, allowing for single-shot capture of the signal of interest [4].

 

Fig. 3. (Left) Post processing results showing the demodulated, time-domain representation of the SOI for lengths of 1,2,4,8,16,32, and 64 bits. The SOI was a 50 MSPS BPSK modulated signal on a 100 MHz and mixed onto a 6.5 GHz microwave carrier. The reference signal was a 512 bit complementary code at 400 MSPS. (Right) A zoom of the first 10 bits and shows good agreement with a simple simulation.

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First, the basic functionality of the approach was proven at low-effective bandwidths. To do this, both the SOI and the reference code were created with an arbitrary waveform generator (Tektronix AWG610). The reference signals were two 512-bit baseband complementary codes at 400 MSPS (1280 ns duration). The SOI was a phase-shift keyed code with a bit rate of 50 MSPS on a 100 MHz carrier whose duration could range from a single bit (20 ns) to 64 bits (1280 ns). The SOI was delayed by 3 µs with respect to the reference code. Both signals were subsequently mixed onto a 6.5 GHz carrier, resulting in double-sided RF signals, which were amplified and applied to the EOPM. The microwave readout signal was created with another AWG610 and chirped from 0 to 400 MHz in 100 µs. This signal was mixed onto a 6.5 GHz carrier and amplified before being applied to the readout EOPM. The voltage applied to both EOPMs was initially optimized to provide the largest signal strength, which required a maximum signal in the first order optical sidebands and also caused some signal distortion.

Fig. 3 shows experimental results for this photonics assisted ADC approach. The time-domain representation of the captured SOI is shown and was calculated using a post-processing algorithm based on the theory outlined above. The waterfall plot shows demodulated SOI results for 1, 2, 4, 8, 16, 32, and 64 bit SOI durations from top to bottom. This plot shows that the time aperture can be large, although some decay is seen due to the decoherence time, T₂, which was measured to be 7 µs. The SOI can be seen to start at exactly the correct delay time of 3 µs. The inset in Fig. 3 shows a zoom of the first 10 bits in the SOI. For comparison, the original digital signal (red dotted line) and a simulation of the basic SSH-ADC process (blue dashed line) are shown alongside the SOI results. The simulation takes into account the transfer function of the complementary reference codes, utilizes the same post-processing routines, and includes the dephasing time of the material. The observed SOI and the simulation agree very well, even though the simulation did not include transfer functions for the microwave or optical components.

 

Fig. 4. (a) The post-processed results as the AWG voltages are reduced showing a corresponding reduction in amplitude in the captured SOI. (b) A plot of the measured standard deviation (STD) of the waveform versus the amplitude from the AWG shown as the dots. The blue line is a plot of the expected amplitude response calculated for the EOPM. (c) The captured SOI results (black line) and simulated SOI results (blue dashed line) for a 1600 MSPS, 2048 bit binary coded SOI showing the total SOI duration. (d) A zoom of (c) showing that single bits can still be detected.

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The system’s capability to record various amplitude signals was also explored. To do so, the amplitude of just the SOI was reduced in the AWG610 with all other voltages remaining the same. Fig. 4(a) shows the results. The captured SOI does show the correct general dependence on voltage. To analyze the results further, the standard deviation (STD) of the captured waveform was calculated for each amplitude and was plotted with respect to the actual AWG voltage and normalized to the maximum value. The results are shown in Fig. 4(b). The effective vertical resolution in bits is given by the full scale of the signal divided by the rms at zero voltage divided by √12 and is ~4.6 bits [1]. The measured values increase fairly linearly and then saturate, which is expected when operating near the EOPMs first order maximum. For comparison, the normalized first order response is plotted and was calculated assuming that 1 V from the AWG corresponds to the peak of the EOPM response. The comparison shows that the observed saturation is likely attributed to a combination of processes, including those from the EOPM, the electronics chain, and the SSH material itself. These saturation issues were not studied at the time of this experiment. Future systems should carefully examine the amplitude linearity of the electronics chain, the SOI modulation into the optical domain, and the field interaction with the material to calibrate the measured amplitude.

Higher bandwidth operation was also explored. For these demonstrations, an Advantest D3186 pulse pattern generator was used to create both the complementary reference code and the SOI. The system was tested at 1600 MHz. The reference code was 2048 bits in duration (1280 ns). Following this was a baseband 2048 bit binary SOI with a 3 µs delay. Both the reference and the SOI were then mixed up to 4.0 GHz, amplified, and applied to the EOPM. In order to readout these higher bandwidths, a larger bandwidth chirp than what the AWG610 could create was necessary. To accomplish this, a 500 MHz to 700 MHz chirp from the AWG610 was frequency doubled three times to create a 4.0 to 5.6 GHz chirp in 400 µs [10].

Fig. 4(c) shows the time-domain representation of the captured 1600 MSPS SOI using the same post-processing algorithm with the new reference codes (black line). For comparison, the result from the simple simulation is also shown (blue dashed line). The results show the full duration of the SOI and the correct 3 µs delay. The decay due to the coherence time is again apparent. Fig. 4(d) shows the first 70 ns of the SOI and provides a better view of the results. At this scale, the individual bits can be seen and there are strong similarities with the simulation. Note that it appears that higher frequency components have slightly less energy, leading to a loss of signal fidelity, especially when a single bit is isolated. This is likely due to frequency dependent losses in the system from the EOPM or other associated electronics.

Comparing Fig. 4(a) with Fig. 4(c) shows an overall loss in fidelity as signal bandwidth is increased, which is due to limited available laser power. To maintain constant signal to noise, the optical power must scale with bandwidth. In the unsaturated material regime, if the optical power is held constant, the output signal goes as ~1/B ², where B is the system’s bandwidth, but the shot noise limited noise spectral density remains constant. Under a constant optical power condition, the captured SOI loses 3.3 vertical resolution bits per decade increase in bandwidth. Our simulations verified this dependence. An experimental study of the bandwidth dependence showed a slightly larger loss of ~4.5 vertical bits per decade increase in bandwidth, which is likely due to increased population decay and instantaneous spectral diffusion on readout with increased bandwidth [11]. Thus, it is important to both scale optical power with bandwidth and minimize instantaneous spectral diffusion.

This paper has shown the first proof-of-concept demonstrations for a SSH-ADC based on frequency-domain stretched processing. Experiments at 50 MHz bandwidths demonstrated large time apertures, good agreement with predicted SOI shapes, and ~4.6 effective vertical bits of resolution. The recovered SOI amplitude showed the correct trend as the SOI voltage was increased and was ultimately observed to saturate due to EOPM, electronics chain, and material effects. Demonstrations also showed that the system was capable of recording signals up to 1600 MHz bandwidths. Several advantages of this photonic-assisted ADC were also shown including 1) the ability to directly record signals on microwave carriers, 2) the use of lower bandwidth ADCs in conjunction with the material to capture much larger signal bandwidths, and 3) the potential to scale the system to much higher bandwidths.