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This paper reports the demonstration of a continuously-tunable true-time delay line for microwave photonics and optical communications capable of high-resolution phase control throughout the 1-100 GHz modulation range. A fiber-coupled device is demonstrated with 75 ps of continuous delay tuning range, 3 dB optical insertion loss, and minimal RF amplitude and phase variation over the 4-18 GHz band. Measured delay ripple was less than 0.2 ps. Theoretical analysis is also presented which indicates scalability to delay tuning ranges over 1000 ps and modulation bandwidths over 10 THz.
©2011 Optical Society of America
1. Introduction
Optical-domain, radio-frequency (RF) true-time-delay (TTD) lines with programmable time delays, wide bandwidth and low optical loss are key components of microwave photonic signal processing systems [1,2] and future optical communications networks [3]. Their unique advantages, including low loss (independent of RF frequency), large instantaneous bandwidth, immunity to electromagnetic interference, and parallel signal processing capability, have led to the realization of high-performance, tunable microwave filters, phased array beamformers, fast analog-to-digital converters, arbitrary waveform generators, signal correlators, and frequency converters and mixers [1,2]. For such applications, it is critical that the delay lines exhibit low loss, wide RF bandwidth, minimal frequency-dependent loss and dispersion, as well as achievable time delays at least on the order of the RF period. In addition, rapid tuning speed and fine delay resolution are of interest for enabling higher-performance, more agile photonic systems.
Although a wide variety of optical-domain, RF TTD lines have been demonstrated, relatively few are currently capable of fine-resolution tuning over an entire RF period at 10 GHz and above. Discrete fiber Bragg grating (FBG) delay lines, for example, are limited to minimum delay increments of 10 ps [2], which translates to a coarse 36° RF phase step at 10 GHz. Integrated-optic switch delay lines [4], on the other hand, suffer from prohibitive optical loss at large bit-depths, and are challenging to phase-trim to 1 ps. Piezoelectric fiber stretchers can provide both fine delay resolution and low optical loss, but are currently limited to tuning ranges on the order of 10 ps, over which the tuning is rather slow [5]. Delay lines based on chirped FBGs also suffer from group delay ripple (non-linear variations in group delay across the optical bandwidth) at high frequencies, typically on the order of 10 ps, which limits the achievable phase and amplitude control [6,7].
More realizable approaches for finely-tunable TTD at 10 GHz include linearly-translated mirror, 3D linear switch array [8] and highly-dispersive fiber [9] delay lines, the latter of which allows continuously-tunable time delay via either a tunable laser [9] or nonlinear optical wavelength conversion process [10]. The 3D linear switch approach is expensive, however, because at least N switchable, phase-trimmed paths are required to realize N programmable delay levels (a linear architecture is necessitated by the small incremental delay). Translated mirrors, on the other hand, are relatively slow. Dispersive fiber delay lines also suffer from poor tuning speed when using high-performance, tunable distributed-feedback (DFB) lasers, because temperature stabilization within a small fraction of the full temperature tuning range is rather slow. Rapidly-tunable lasers can be substituted to provide faster tuning, but this comes at the expense of increased laser noise and reduced power, which ultimately impacts system performance. For reasons such as these, there is continued interest in developing optical TTD delay lines capable of rapid tuning and fine delay resolution at 10 GHz and beyond.
This paper reports the demonstration of a continuously-tunable TTD line for microwave photonics and optical communications developed to address such needs. It is shown schematically in Fig. 1(a) , and utilizes a beam deflector to scan an optical beam across a stationary diffraction grating. In form it is similar to a scanning delay line developed for optical coherence tomography (OCT) [11,12], with the notable exceptions that (1) our implementation images, rather than collimates, the optical beam onto the beam deflector, and (2) in its operation produces a RF TTD for modulated signals on an optical carrier, as opposed to an optical delay for optical coherence measurements. The significance of the latter point is that OCT measurements cannot sample the optical frequency in steps less than 1/Δτmax (100 GHz in [11,12]), where Δτmax is the total delay tuning range, and therefore do not adequately characterize delay line frequency variations across a typical RF bandwidth. As such, this work represents the first proposal and demonstration of a beam-scanned diffraction grating (BSG) delay line for true-time delay of coherent, modulated optical signals. Specifically, we demonstrate a fiber-coupled device providing 75 ps of continuous tuning range, 3 dB optical insertion loss, and minimal RF amplitude and group delay variation across the 4-18 GHz modulation range. Theoretical analysis is also presented which shows that the BSG delay line is feasible for high-resolution tuning over at least one RF period at modulation frequencies from 1 to 100 GHz. Lower-resolution phase control is also possible well into the THz. Although the beam deflector used in this work was a manually-rotated mirror, the design is compatible with rapid-scanning mirror and other fast beam deflector technologies, to enable high-speed, continuously-tunable TTD.
Fig. 1 (a) Schematic diagram of the beam-scanned grating delay line studied in this work, and (b) the theoretical relationship between the lens clear aperture and the maximum delay tuning range, assuming a Littrow configuration. In (a), a rotatable mirror served as a beam deflector, which scanned the optical beam across a stationary diffraction grating to produce a variable delay.
2. Experimental results
A schematic diagram of the delay line presented in this work is shown in Fig. 1(a). The output of a single-mode optical fiber was first imaged onto the face of a rotatable gold-surface mirror, aligned such that its rotation axis coincided with the mirror reflection point. The deflected beam was then redirected by a lens, positioned with focal point coincident with the mirror reflection point, such that the beam was parallel to the optical axis, but offset by
where F is the focal length of the lens and θ the beam deflection angle. The beam was then reflected back along its original path by a reflective diffraction grating placed at the back focal point of the lens, aligned in Littrow configuration at the angle ψ. At the end of the device a fiber-optic circulator was used to separate the input and output optical beams. Due to the angle of the grating, rotating the mirror changed the round-trip optical path length through the system, which resulted in a mirror-controlled relative phase delaywhere c is the vacuum speed of light. The corresponding relative group delay, τg = τ + f∂τ/∂f, was essentially identical to the phase delay, due to negligible frequency dependence of Eq. (2) (the focal length did not vary significantly with frequency, and other parameters remained fixed). Thus, the device provided a controllable, optical true-time-delay, and as such, also provided a true-time-delay of the modulated RF signal. Distinctions between phase and group delay have therefore been neglected throughout the paper, and the term “delay” used as appropriate. It is also worth noting that the tunable TTD delay was produced without introducing significant optical dispersion, which degrades modulated signals by introducing AM-PM conversion [13,14] and/or pulse broadening [15].Figure 1(b) plots the relationship between the maximum delay tuning range Δτmax and the lens clear aperture Δymax for common grating reflectance angles at the optical wavelength 1.55 µm. Based on these predictions, a 50 mm diameter achromatic doublet lens with 40 mm clear aperture and 100 mm focal length, and a 50 mm wide diffraction grating with 600 grooves/mm, aligned at 27.7°, were selected to provide up to 140 ps of delay tuning range.
In order to characterize the RF response of the BSG delay line, a 26 GHz vector network analyzer and microwave photonic link were utilized as shown in Fig. 2 . The photonic link consisted of a 16 GHz Mach-Zehnder intensity modulator, 1.55 µm wavelength DFB laser, fiber-loop polarization controller, and reverse-biased 18 GHz photodiode. A 6-18 GHz low noise RF amplifier was also included for measurements ranging from 4 to 18 GHz, but removed for lower-frequency tests below 4 GHz. For both sets of measurements, a calibration run was first performed through the photonic link, and then the BSG delay line was added to the system in order to test its RF response. Figure 3(a) plots the measured RF phase ΦRF versus frequency for various beam deflection angles, after adjusting for a common 7.8558 ns phase delay (that measured at θ = 0). The corresponding relative RF phase delay is also plotted in Fig. 3(b), calculated using
As shown, the RF phase delay was independent of frequency (within the measurement accuracy), which indicates that the delay line provided a true RF time delay as the beam was deflected. Furthermore, the standard deviation of the delay ranged from 60 to 160 fs for the various curves in Fig. 3(b), when calculated over the 6-18 GHz amplifier bandwidth. Although such values include measurement error due to imperfect network analyzer calibration, taken as an upper bound they represent a 1-2 order of magnitude improvement in delay ripple compared to chirped FBGs. They also demonstrate the potential of the BSG delay line to provide high-resolution time delay control well into the high GHz.Fig. 2 Experimental setup used to test the RF response of the BSG delay line. The network analyzer was first calibrated with the connectorized fibers from the polarization controller and photodiode directly connected. The delay line was then inserted into the system for testing via its connectorized fibers.
Fig. 3 (a) Measured RF phase for various beam deflection adjusted for a common 7.8558 ns delay, and (b) resulting RF phase delay. The flat response in (b) indicates a true RF time delay.
The relationship between the measured relative RF phase delay and the beam deflection angle is plotted in Fig. 4(a) . A linear least-squares fit of the data gave a slope of 5.96 ps/°, which was in good agreement with Eq. (2). Figure 4(b) plots the variation in both measured RF power transmission |S21|2 and derived optical power transmission (calculated as |S21|) with the beam deflection angle. Data for two different lens-to-mirror distances are shown, one near the paraxial focal length of the lens, and the other adjusted slightly to focus non-paraxial rays. These data demonstrate significant spherical aberration in the system, which ultimately limited the useful delay tuning range to less than the theoretical limit of 140 ps, but which could have presumably been mitigated with better optics. Nonetheless, Fig. 4(b) demonstrates RF power ripple less than 3 dB over a 12.8° beam deflection range, and less than 6 dB over 15.8°, corresponding to the delay tuning ranges 76.3 ps and 94.2 ps, respectively. Figure 4(b) also indicates that the optical insertion loss of the delay line was 2.95 dB (5.9 dB RF). Of this, 1.25 dB was attributed to losses in the fiber-optic circulator and mirror, determined by measuring the back-reflected signal with the mirror rotated to normal incidence. The remaining 1.7 dB was attributed to imperfect grating efficiency and reflections from the improperly antireflection-coated lens. In addition, 2.35 dB of optical polarization-dependent loss was observed as the fiber polarization controller was varied. However, this loss could have been avoided using polarization maintaining fiber. The RF power transmission is plotted versus frequency in Fig. 5 , for the representative case θ = 0. As shown, the RF transmission was independent of frequency (within the measurement accuracy), which indicates that in addition to providing true RF time delay, the BSG delay line provided a flat amplitude response throughout the 4-18 GHz measurement range.
Fig. 4 Measured relationships between (a) the RF delay and (b) the RF and optical transmission with beam deflection angle. Data in (b) are for lens-to-mirror distances (●) close to the paraxial focal length, and (■) adjusted to focus non-paraxial rays. The tendency for loss to vary significantly with deflection angle, and to improve at large angles as the lens was defocused, is indicative of significant lens spherical aberration.
Fig. 5 Measured RF transmission versus frequency at θ = 0, indicating a flat amplitude response. Similarly flat response was observed for all beam deflection angles.
3. Theoretical limits
The range of frequencies over which the BSG delay line design remains feasible, and the range of time delays it can realistically provide, are potentially limited by spectral beam broadening at the diffraction grating, inherent variations in the optical path length resulting from the tunable delay, and practical device size. Each of these effects can be conveniently analyzed in the framework of Gaussian beam optics. In this framework, the output of the optical fiber is approximated as a Gaussian beam, with waist ω0fiber located at the fiber end face. The beam is then imaged onto the face of the mirror, forming a waist of size ω0mirror. The reflected beam then passes through the lens and is projected to a waist with size ω0grating at the back focal plane of the lens. The relationship between the latter two beam waists is given by
where λ is the optical wavelength.Spectral beam broadening originates at the diffraction grating, which converts the nonzero wavelength spread Δλ of the optical beam (and corresponding frequency spread 2fRF) to the angular spread
where m is the grating diffraction order and fcarrier the optical carrier frequency. The lens converts this angular spread to a spatial variation, Δymirror = FΔα, at the mirror. This spatial spread must be small compared to the beam diameter at the mirror to prevent substantial optical loss. Taking Δymirror ≤ 2ω0mirror as a practical limit, and making use of Eqs. (4) and (5), leads to the simple restrictionon the size of the beam waist at the grating. The corresponding maximum beam diameter, 2ω0grating(max), is plotted versus RF frequency in Fig. 6(a) . This plot shows that spectral broadening does not place any fundamental restriction on modulation frequency until over 10 THz. Similar curves plotted for the minimum beam diameter at the mirror (not shown) did not provide additional insight, except to highlight that the beam waist at the grating, which controls the frequency cutoff of the delay line, is directly linked to the size of the beam waist at the mirror. By imaging the fiber output onto the mirror, the size of both waists can be appropriately controlled.Fig. 6 Maximum beam diameter at the grating (a), due to spectral beam broadening, and minimum beam diameter at the grating (b), due to the changing system optical path length.
Varying the optical path length of the system to impart a time delay can also affect the optical throughput. Its impact can be gauged by noting that although the beam waist ω0grating is initially projected to the back focal point of the lens, upon reflection its (virtual) distance from the lens will vary by the amount Δzgrating, where
It can easily be shown that this variation in waist position at the grating produces a corresponding variation in waist position at the fiber, Δzfiber, given bywhere z0fiber and z0grating are the Rayleigh ranges at the fiber and grating, respectively. Although the variation in waist position at the grating also produces some lateral beam broadening, as shown in the Appendix this effect is unsubstantial. The variation in the waist position at the fiber must be small compared to the Rayleigh range to prevent substantial optical loss. Taking Δzfiber ≤ 2z0fiber as a practical limit, and making use of the definition z0 = πω02/λ leads to the simple restrictionon the size of the beam waist at the grating. The corresponding minimum beam diameter, 2ω0grating(min), is plotted in Fig. 6(b) versus RF frequency. This plot demonstrates that the restriction placed on beam size is significant, and must be taken into account. However, it is also easily satisfied with proper system design for the tuning ranges shown.The most significant restrictions on time delay tuning range are therefore based on overall device size. Figure 1(b) indicates that a delay tuning range of 1000 ps should be possible with a 60 mm clear aperture. Scaling to much larger tuning ranges, however, would require large optics and long focal lengths, which places practical limitations on the achievable delay tuning range.
4. Conclusions
In summary, this paper demonstrates the feasibility of the beam-scanned diffraction grating delay line for high-resolution RF phase control over the 1-100 GHz modulation frequency range, as well as lower-resolution control well into the THz. The observed 75 ps of continuously-tunable RF true-time-delay provided full-cycle tuning of the RF phase at 13.3 GHz and beyond. Predictions show that the tuning range could potentially be scaled to 1000 ps. Although the beam deflector used in this work was a manually-rotated mirror, the design is compatible with rapid-scanning mirror and other fast beam deflector technologies, to enable high-speed, continuously-tunable optical and RF TTD.
Appendix
Using the Fig. 1(a) as a guide, the output of the optical fiber will be reflected off the mirror, approach the lens at angle θ, and then be imaged at the back focal plane of the lens, at the distance y=Ftanθ from the optical axis. Since the light will not be reflected from the back focal plane of the lens, but instead at the grating, located the distance ytanψ past the back focal plane, the reflected beam will appear to issue from a virtual source located 2ytanψ past the back focal plane. The effect of this shift in z is to shift the image in z at the mirror, an effect which has been accounted for in Eq. (8) and leads directly to Eq. (9). If one considers the spectral width of the beam as well, reflection from the grating will induce the angular spread Δα, which serves to spread the location of the virtual source by a maximum amount Δy’grating=Δα|ytanψ|max. The prime here is used to distinguish this effect, denoted geometric beam broadening [12], from that of spectral beam broadening discussed in Section 3. By substituting Eq. (1), (2) and (5), and making use of the simplifying assumption Δτmax =2|τ|max, this expression reduces to
The transverse beam spread at the grating in turn translates to a beam spread at the mirror Δy’mirror according to
Next, applying the condition Δy’mirror≤ 2ω’0mirror introduced in Section 3 leads to the restriction
The ratio of the minimum beam waist allowed by Eq. (12) to that allowed by Eq. (9) is
With the aid of Eq. (5) and (6), this reduces to
where n is the optical refractive index. For any useful implementation of the device, this ratio will be less than one. Thus, the restriction on waist size at the grating due to geometric beam broadening, given by Eq. (12), will inherently be satisfied by Eq. (9).
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