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Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 21, Iss. 19 — Sep. 23, 2013
  • pp: 22937–22961
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Silicon nitride microwave photonic circuits

Chris G. H. Roeloffzen, Leimeng Zhuang, Caterina Taddei, Arne Leinse, René G. Heideman, Paulus W. L. van Dijk, Ruud M. Oldenbeuving, David A. I. Marpaung, Maurizio Burla, and Klaus -J. Boller  »View Author Affiliations


Optics Express, Vol. 21, Issue 19, pp. 22937-22961 (2013)
http://dx.doi.org/10.1364/OE.21.022937


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Abstract

We present an overview of several microwave photonic processing functionalities based on combinations of Mach-Zehnder and ring resonator filters using the high index contrast silicon nitride (TriPleXTM) waveguide technology. All functionalities are built using the same basic building blocks, namely straight waveguides, phase tuning elements and directional couplers. We recall previously shown measurements on high spurious free dynamic range microwave photonic (MWP) link, ultra-wideband pulse generation, instantaneous frequency measurements, Hilbert transformers, microwave polarization networks and demonstrate new measurements and functionalities on a 16 channel optical beamforming network and modulation format transformer as well as an outlook on future microwave photonic platform integration, which will lead to a significantly reduced footprint and thereby enables the path to commercially viable MWP systems.

© 2013 OSA

1. Introduction

Microwave photonic (MWP) signal processing enables RF/microwave processing functionalities unreachable with conventional all-electronic signal processing solutions [1

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

,2

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

]. In integrated MWP the RF/microwave signals are first frequency up-converted to optical frequencies where they are processed in an optical chip. Exploiting the advantages inherent to integrated photonic devices, such as large instantaneous bandwidth, low loss transmission, easy implementation of tunability and re-configurability, electromagnetic inference insensitivity, as well as small size, low weight and power consumption. However, to become a disruptive technology to improve the mature RF/microwave electronics industry for both niche and consumer markets, MWP signal processing solutions still require effective reduction on the system cost, which is mostly limited by the use of non-integrated discrete optical devices. Its evolution is largely determined by the progress of on-chip MWP signal processing functionality [3

3. D. A. I. Marpaung, C. G. H. Roeloffzen, R. G. Heideman, A. Leinse, S. Sales, and J. Capmany, “Integrated microwave photonics,” Laser Photon. Rev.7(1), 1–33 (2013).

].

In this paper we present the key aspects of MWP signal processing in silicon nitride TriPleXTM waveguide platform. We will show that fairly high complexity, tunable MWP circuits for numerous MWP functionalities can be implemented using a set of standard building blocks, such as MZIs and ORRs, fabricated in this high performance waveguide technology. We briefly present the transfer functions of the elementary building block in its z-transform, highlight the key technological issues in the silicon nitride chip fabrication, and revisit the key functionalities achieved with these circuits. We will show the most recent MWP results, a 16 × 1 beamformer and a modulation format transformer, accomplished using this waveguide platform. Finally, we will discuss the prospect of these circuits for future MWP applications.

2. Theory

2.1 Microwave photonic link

2.2 Building blocks

The fundamental building blocks for realizing on chip microwave photonic functionalities in TriPleXTM waveguide technology are the optical waveguide, tuning element and directional coupler as shown in Table 1

Table 1. Basic building blocks and their transfer functions (back scattering, non-linearity’s, common path lengths and non-idealities are neglected)

table-icon
View This Table
.

In order to obtain a framework for describing these building blocks and the more advanced variations to be discussed later, we will first introduce the concepts of the transfer matrix, the normalized frequency and the z-transform [16

16. C. K. Madsen and J. H. Zhao, Optical Filter Design and Analysis: A Signal Processing Approach. (Wiley-Interscience, 1999).

,17

17. A. V. Oppenheim, and R. W. Schafer, Digital Signal Processing (Prentice-Hall, 1975).

]. The overall transfer matrix of the MZI and ORR will be calculated in terms of the z-parameter.

Transfer matrix method and z-transform description of a waveguide

The transfer of a single mode waveguide (delay-section), as shown in Table 1(a) with a length L can be described as
Hwg=eαLejk0neff(ω)Lejφ=γejωτejφ,
(1)
where j is the imaginary unit, L is length of the waveguide, k0 = ω/c is the vacuum wave number, ω the angular frequency of the guided wave, and c the speed of light in vacuum. The loss is given by γ = exp(-αL), is the attenuation (loss in decibels: A = −20log∣γ∣). In order to model, e.g., thermo-optic tuning, we do allow for a small deviation from the average effective index neff, leading to an additional tuning phase delay φ . The building block is shown in Table 1(b) and when required can be placed atop the waveguide. The group delay τ of this waveguide is given as
τ=Lngc,
(2)
where ng is the group index defined as
ng=neff(ω)+ωneff(ω)ω.
(3)
This delay-section has a periodic angular frequency response with period Δω = 2π/τ (or in temporal frequency Δf = 1/τ)

In interferometric structures it is useful to normalize the angular frequency with respect to a fixed unit delay τu (with waveguide length Lu), so that the transfer function in terms of the normalized angular frequency ω = ωτu (i.e. f = u) will be periodic with period Δω = 2π (i.e. Δf = 1). In digital filter theory the so-called z-transform is widely used in order to simplify mathematics [17

17. A. V. Oppenheim, and R. W. Schafer, Digital Signal Processing (Prentice-Hall, 1975).

]. Then, by making the substitution
ejω=z1,
(4)
the frequency transfer becomes a polynomial in z. Applying this z-transform, we arrive at the following transfer for a waveguide and tuning element
Hwg=γz1ejφ.
(5)
The transfer of a single waveguide can be extended to the matrix transfer of two parallel uncoupled waveguides with equal length as show in Table 1(c)

Group delay is a measure of linearity of the phase response with respect to the frequency. The group delay is the local slope of the phase response curve, i.e., the slope of the phase at the frequency being evaluated. A filter’s group delay or envelope delay is defined as the negative derivative of the phase response with respect to angular frequency ω as follows [16

16. C. K. Madsen and J. H. Zhao, Optical Filter Design and Analysis: A Signal Processing Approach. (Wiley-Interscience, 1999).

]
τg(ω)=dθ(ω)dω=ddωarg(H(z))|z=ejω.
(6)
The normalized group delay τg′ is given in number of unit delays τu, leading to:

τg(ω)=τgτu=dθ(ω)dω=ddωarg(H(z))|z=eiω.
(7)

Directional coupler (2 × 2)

Couplers are among the most elementary building blocks in planar light wave circuits, performing the functions of splitting and combining guided optical waves. Directional couplers (DCs) consist of two optical waveguides in close proximity to each other, see Table 1(d). Light will be coupled by the evanescent field of the mode, and power will be exchanged between the waveguides. Arbitrary power splitting ratios can be obtained by simply choosing the length of the DC. The equation in the table gives a shorthand notation for the transfer matrix of a DC, where c = (1 - κ)1/2 is the bar transfer function, and –js = –j (κ)1/2 is the cross transfer function, and κ is the cross power coupling coefficient.

Differential delay section (two waveguides with different lengths) (2 × 2)

The delay section of an asymmetric MZI is formed by two independent waveguides having different lengths L1 and L2 respectively (we assume L2 > L1). The 2 × 2 port z-transfer is shown in Table 1(e) with upper branch as a reference. The differential loss γΔL = exp(-αΔL) is the loss along the path length difference ΔL. The common length loss has been neglected in this equation. A tuning element has been placed on the upper waveguide.

Symmetric Mach-Zehnder Interferometer (2 × 2)

The symmetric MZI consists of two (assumed equal) DCs with power coupling ratios κ interconnected by two waveguides of equal length, where one can be phase tuned by the tuning element. The transfer matrix of the MZI, is shown in Table 1(f). The common path length has been neglected, since it adds only a constant loss and a linear phase to the frequency response. Since the power coupling of the MZI can be changed by tuning the phase of the tuning element it is a good candidate for a tunable coupling element.

Asymmetric Mach-Zehnder Interferometer (2 × 2)

The difference of the asymmetric Mach-Zehnder Interferometer (aMZI) as shown in Table 1(g) with respect to the symmetric MZI described above is the differential delay section, rendering its response frequency dependent. The bar and cross transfer are complementary sine-shaped functions. In terms of signal processing, such a device manifests a discrete-time finite impulse response. Figure 1(a)
Fig. 1 (a) Magnitude response for the asymmetric Mach-Zehnder interferometer filter with differential loss of 0, 0.5 and 1 dB respectively. (b) Group delay transfer of the MZI for various coupling constants.
shows the frequency response of the aMZI filter for several values of the differential loss. Note that the filter curve has a very narrow stopband having a bandwidth of only 4% of the free spectral range (FSR) at −25 dB suppression. Figure 1(b) shows the normalized group delay of the aMZI for different coupling constants, where the bell-shaped profile results from the fast phase change transition around the stopband center. Note that the ideal aMZI (κ = 0.5 → c = s = (0.5)1/2 has a constant group delay in the passband and thus allows dispersion-free transmission.

Ring resonator (1 × 1)

The waveguide implementation of a basic ring resonator (RR) with one input and one output is constructed by feeding one output of a 2 × 2 power coupler to the input of the same arm by means of a feedback loop (ring-shaped path). A schematic of this structure and the corresponding z-transform are given in Table 1(h). Inherent to the feedback mechanism, such a device is characterized by a discrete-time infinite impulse response [16

16. C. K. Madsen and J. H. Zhao, Optical Filter Design and Analysis: A Signal Processing Approach. (Wiley-Interscience, 1999).

]. Figure 2
Fig. 2 Frequency responses of a ring resonator with one input and one output for different values of κ and PL: (a) phase responses, (b) group delay and power transmissions.
depicts the frequency responses of a RR for different values of power coupling coefficient κr (cr = (1-κr)1/2) and roundtrip loss PL. Evidently, although the overall phase change over one FSR is a constant of 2π, the steepness of the phase change transition around the resonance frequency can be varied by changing κr. For the power transmission, the total loss of the device scales proportionally with the group delay and the waveguide propagation loss. Moreover, in practice, the resonance frequency of the device can be shifted by changing the additional roundtrip phase shift φr in the feedback loop.

Ring resonator (2 × 2)

The waveguide implementation of a ring resonator with two couplers, featuring two inputs and two outputs, is constructed using two times 2 × 2 couplers with one arm of a coupler joint to that of the other in a closed loop. A schematic of this structure and the corresponding z-transform are given in Table 1(i). Similar to MZIs, such devices also feature two power-complementary outputs and manifest better frequency selectivity inherent to the resonance mechanism. Hence, they are a good candidate for the add-drop functionality for wavelength (frequency) multiplexed signals. In addition to that, the sharp passband-stopband transition is also a useful property for many signal processing functionalities. The frequency responses of a ring resonator with two couplers are depicted in Fig. 3
Fig. 3 Frequency responses of a ring resonator with two couplers for different settings of coupling coefficients: (a) power transmissions, (b) phase responses.
for different setting of the coupling coefficients.

3. Chip realization (Technology)

To fabricate functional microwave photonic circuits in planar waveguide technology, multiple building blocks as described in Section 2 have to be connected in series or parallel. Such circuits have a typical footprint of several square centimeters [7

7. L. Zhuang, C. G. H. Roeloffzen, A. Meijerink, M. Burla, D. A. I. Marpaung, A. Leinse, M. Hoekman, R. G. Heideman, and W. C. van Etten, “Novel ring resonator-based integrated photonic beamformer for broadband phased-array antennas-Part II: experimental prototype,” J. Lightwave Technol. 28(1), 19–31 (2010). [CrossRef]

,10

10. L. Zhuang, D. A. I. Marpaung, M. Burla, W. P. Beeker, A. Leinse, and C. G. H. Roeloffzen, “Low-loss, high-index-contrast Si₃N₄/SiO₂ optical waveguides for optical delay lines in microwave photonics signal processing,” Opt. Express 19(23), 23162–23170 (2011). [CrossRef] [PubMed]

]. In order to transmit optical signals with high enough power for easy detection through such a circuit, the optical propagation loss of the waveguides should be minimized. Previously, planar waveguides of different materials were realized with very low loss. As noticeable examples we mention waveguides with a core of phosphorus-doped silicon dioxide and silicon oxinitride, both with a low optical propagation loss of <0.05 dB/cm [18

18. R. Adar, M. Serbin, and V. Mizrahi, “Less than 1 dB per meter propagation loss of silica waveguides measured using a ring resonator,” J. Lightwave Technol. 12(8), 1369–1372 (1994). [CrossRef]

,19

19. B. Larsen, L. Nielsen, K. Zenth, L. Leick, C. Laurent-Lund, L. Andersen, and K. Mattsson, “A low-loss, silicon-oxynitride process for compact optical devices,” in Proceedings of ECOC (Rimini, Italy, 2003).

]. In general, waveguides that exhibit low propagation loss, also have a low refractive index contrast between core and cladding [20

20. J. F. Bauters, M. J. R. Heck, D. John, D. Dai, M. C. Tien, J. S. Barton, A. Leinse, R. G. Heideman, D. J. Blumenthal, and J. E. Bowers, “Ultra-low-loss high-aspect-ratio Si3N4 waveguides,” Opt. Express 19(4), 3163–3174 (2011). [CrossRef] [PubMed]

]. This can, e.g., be seen in the mentioned examples, where the refractive index contrasts are 0.6-0.7% and 2.5% respectively [18

18. R. Adar, M. Serbin, and V. Mizrahi, “Less than 1 dB per meter propagation loss of silica waveguides measured using a ring resonator,” J. Lightwave Technol. 12(8), 1369–1372 (1994). [CrossRef]

,19

19. B. Larsen, L. Nielsen, K. Zenth, L. Leick, C. Laurent-Lund, L. Andersen, and K. Mattsson, “A low-loss, silicon-oxynitride process for compact optical devices,” in Proceedings of ECOC (Rimini, Italy, 2003).

]. However, such low values of index contrast, via radiation loss, limit the waveguide’s minimum bend radius. As a rule of thumb, the minimum bend radius in micrometer is given by Rmin = 5Δn-1.5, for 0.1 dB/rad radiation loss [21

21. A. Melloni, R. Costa, G. Cusmai, and F. Morichetti, “The role of index contrast in dielectric optical waveguides,” Int. J. Mater. Prod. Technol. 34(4), 421–437 (2009). [CrossRef]

]. This causes the footprint of functional structures to be rather large. For the mentioned examples, the minimum bend radii were several millimeter. Therefore, a solution that optimizes this tradeoff, i.e., which provides a low loss and high index contrast, is preferred. Recently, silicon nitride waveguides with a silicon oxide cladding with a high index contrast (which can be tailored up to 20-30% [22

22. F. Morichetti, A. Melloni, M. Martinelli, R. G. Heideman, A. Leinse, D. H. Geuzebroek, and A. Borreman, “Box-shaped dielectric waveguides: A new concept in integrated optics?” J. Lightwave Technol. 25(9), 2579–2589 (2007). [CrossRef]

]) have been shown to exhibit low optical loss (0.095 dB/cm), for small waveguide bend radii of 70 μm [10

10. L. Zhuang, D. A. I. Marpaung, M. Burla, W. P. Beeker, A. Leinse, and C. G. H. Roeloffzen, “Low-loss, high-index-contrast Si₃N₄/SiO₂ optical waveguides for optical delay lines in microwave photonics signal processing,” Opt. Express 19(23), 23162–23170 (2011). [CrossRef] [PubMed]

]. For the last-mentioned low optical loss measurements, the reader is referred to Section 4.2. The main contributor of optical propagation loss is scattering due to waveguide roughness [20

20. J. F. Bauters, M. J. R. Heck, D. John, D. Dai, M. C. Tien, J. S. Barton, A. Leinse, R. G. Heideman, D. J. Blumenthal, and J. E. Bowers, “Ultra-low-loss high-aspect-ratio Si3N4 waveguides,” Opt. Express 19(4), 3163–3174 (2011). [CrossRef] [PubMed]

]. By choosing the proper fabrication processes, waveguide roughness can be minimized. The latter mentioned results were obtained in waveguides that were produced using a technology with minimized waveguide roughness, called Si3N4/SiO2 TriPleXTM waveguide technology. In the following section the benefits of TriPleXTM technology, the fabrication process, possibilities and recent results are discussed.

The TriPleXTM waveguides described in this paper are fabricated using a Low Pressure Chemical Vapor Deposition (LPCVD) processes in which stoichiometric silicon nitride (Si3N4) and silicon oxide (SiO2) are grown as superposing layers on a silicon wafer. The Si3N4 layers have a large tensile stress, whereas the SiO2 layers have a large compressive stress, resulting in an overall low-stress layer stack. Using the LPCVD technique to deposit different layers has two main advantages. First it allows for thickness control on a nanometer scale, whereas the surface roughness is less than 0.4 nm, as measured by atomic force microscopy. This results in very low propagation losses, while maintaining high index contrast [20

20. J. F. Bauters, M. J. R. Heck, D. John, D. Dai, M. C. Tien, J. S. Barton, A. Leinse, R. G. Heideman, D. J. Blumenthal, and J. E. Bowers, “Ultra-low-loss high-aspect-ratio Si3N4 waveguides,” Opt. Express 19(4), 3163–3174 (2011). [CrossRef] [PubMed]

]. Secondly, it allows for mass-volume scaling because LPCVD is CMOS compatible [23

23. M. Asghari, “Silicon Photonics: A low cost integration platform for datacom and telecom applications,” in Proc. OFC/NFOEC (San Diego, Calif., USA, 2008). [CrossRef]

].

An important issue for commercial microwave photonic circuits is power consumption. As example, let us consider an 8 × 1 optical beam forming network (OBFN) as described by Zhuang et al. [7

7. L. Zhuang, C. G. H. Roeloffzen, A. Meijerink, M. Burla, D. A. I. Marpaung, A. Leinse, M. Hoekman, R. G. Heideman, and W. C. van Etten, “Novel ring resonator-based integrated photonic beamformer for broadband phased-array antennas-Part II: experimental prototype,” J. Lightwave Technol. 28(1), 19–31 (2010). [CrossRef]

]. The fabricated circuits are optically tuned by means of refractive index changes induced by local heating. A tuning element capable of performing such local heating, has a typical average power consumption of about 350 mW. A π phase tuning is required on average. For a heater length of 2 mm the change in temperature underneath is approximately 40° C. The chip needs to be temperature stabilized within 0.1° C for stable operation of the RRs and MZIs. So for the described 8x1 OBFN, to which 8 antennas can be connected for conversion into a single output beam with tunable direction, the total power consumption is only several Watts. However, for functional designs in, e.g., satellites, many more beams and many more antennas are required. To give an example, the KaSat launched in 2010 [31

31. Website of Eutelsat, a satellite operator, www.eutelsat.com/en/satellites/the-fleet/EUTELSAT-KA-SAT.html, visited May 28 2013.

], has a total number of 1900 antenna elements, and is capable of producing 82 separate beams. This means that if an OBFN as mentioned above would be used as beam forming network, the total power consumption for the heaters alone would be in the order of kilowatts to megawatts. Obviously, for use in a satellite this is too high. However, a recent publication [32

32. S. R. Davis, G. Farca, S. D. Rommel, S. Johnson, and M. H. Anderson, “Liquid crystal waveguides: new devices enabled by > 1000 waves of optical phase control,” Proc. SPIE 7618, 76180E (2010). [CrossRef]

], on the use of liquid crystal as top cladding for TriPleXTM waveguides has shown a dramatic decrease in power consumption per tuning element. By applying a voltage of only 5 V to the liquid crystal cladding, the refractive index of the waveguide is changed accordingly. This achieved similar tuning as attained with the above mentioned heaters, however with a dramatically lower power consumption by a factor of 80.000. This means that for future application of OBFNs in highly complex, high performance systems such as, e.g., satellite communication systems, the OBFN has to be equipped with a liquid crystal top cladding.

4. Chip characterization

4.1 Measurement setup

The experimental setup depicted in Fig. 5
Fig. 5 Measurement setup for the characterizations of the fabricated optical chips. MZM is Mach-Zehnder modulator, PMF is polarization maintaining fiber, SMF is single mode fiber.
is used to fully characterize the frequency responses of the components on the chip. When RF frequency sweeping and single-sideband full-carrier modulation to a CW light is performed (e.g., by using dual-parallel Mach-Zehnder modulator), this setup functions as an optical vector analyzer, which measures the amplitude and phase responses over the bandwidth allowed by the network analyzer. Besides, it can also be used to perform the direct group delay measurement using the well-known phase-shift method, where laser frequency sweeping and a fixed low frequency RF are employed instead and the measurement bandwidth is only determined by the frequency sweeping range of the laser. Moreover, the reconfiguration of the chips under test are performed by applying proper DC voltages to the tuning elements (heaters) on the chip. In practice, a dedicated channel-scalable control subsystem is preferred for characterization efficiency and setup complexity, especially when a large number of tuning elements are designed on the chip to support complex functionalities.

The RF frequency modulating the optical carrier can be adjusted according to the spectral resolution requirement (minimum 10 MHz with the used network analyzer).

A dedicated 12-bit control subsystem was used to drive the heaters on the chip, where the control information for each tuning element is read from a custom generated lookup table. Owing to the properties of the used waveguide (Si3N4) and heater material (chromium) issues regarding to drift are not observed.

4.2 Measurements of common PIC functionalities

Waveguide

In terms of PICs, the systematic propagation loss is the most important performance metric of a waveguide-based device. For the TriPleXTM waveguide geometry described in Section 3, the waveguide propagation loss has been characterized in a group of ring resonator-based delay lines, which are the most common building block of PICs. For the sake of comparison, the delay lines were fabricated with a common ring circumference of 8783 μm (corresponding to a FSR of 20 GHz) and ring-loop bend radii varying from 50 μm to 125 μm [10

10. L. Zhuang, D. A. I. Marpaung, M. Burla, W. P. Beeker, A. Leinse, and C. G. H. Roeloffzen, “Low-loss, high-index-contrast Si₃N₄/SiO₂ optical waveguides for optical delay lines in microwave photonics signal processing,” Opt. Express 19(23), 23162–23170 (2011). [CrossRef] [PubMed]

]. The device layout is depicted in Fig. 6(a)
Fig. 6 (a) device layout and (b) measured systematic propagation loss of ring resonator-based delay lines in TriPleXTM technology (from [10]).
, where the power coupler is implemented using an MZI coupler equipped with coupling-coefficient tunability by means of resistor-based heaters. The measurement results are depicted in Fig. 6(b). As shown in the result, the maximum system propagation loss was measured to be 0.12 dB/cm in the ORR with a bend radius of 50 µm, and an average waveguide propagation loss as low as 0.095 dB/cm was achieved for the bend radii ≥ 70 µm where the loss contribution of the bend radiation is negligible compared to the scattering loss of the waveguide. Besides, the small measurement deviations of the different devices also indicate good fabrication uniformity.

Arbitrary splitters and combiners

Two most fundamental and also critical PIC functionalities are the arbitrary splitter and combiner. In practice, both can be implemented using 2 × 2 MZI-based tunable couplers [7

7. L. Zhuang, C. G. H. Roeloffzen, A. Meijerink, M. Burla, D. A. I. Marpaung, A. Leinse, M. Hoekman, R. G. Heideman, and W. C. van Etten, “Novel ring resonator-based integrated photonic beamformer for broadband phased-array antennas-Part II: experimental prototype,” J. Lightwave Technol. 28(1), 19–31 (2010). [CrossRef]

]. Beside the tunability in splitting/combining ratio, such MZI-based couplers can also be concatenated to construct binary-tree splitting/combining circuits, which features easy scalability. Figure 7(a)
Fig. 7 (a) schematic and (b) measurements of a 4 × 1 combiner constructed using three times 2 × 2 MZI-based tunable couplers, where modulated optical signals with equal amplitude and synchronized phase are applied to the four inputs, and all the couplers are set to 50/50 status (from [7]).
depicts the schematic of a 4 × 1 combiner constructed using three 2 × 2 MZI-based tunable couplers in a binary tree configuration, and Fig. 7(b) demonstrates the combining functionality of the device. For this demonstration, a CW laser was externally modulated by a RF signal with frequency range of 1 to 2 GHz, and subsequently split into four equal portions. Mutually synchronized, the four splits were applied to the four inputs of the device, where all the MZI-based couplers are set to 50/50 status. In agreement with the theory, the combining of every two inputs results in a 6 dB enhancement of the detected signals. Besides, background ripples exhibit in the measurement results, which are mainly due to the Fabry-Perot effect caused by the light reflections at the waveguide facets. However, this can be effectively reduced by optimizing the waveguide design.

Tunable delay lines

Tunable delay lines can be implemented using fully-programmable RRs, namely, equipped with tunability in both coupling coefficient and additional roundtrip phase shift [8

8. L. Zhuang, C. G. H. Roeloffzen, R. G. Heideman, A. Borreman, A. Meijerink, and W. van Etten, “Single-chip ring resonator-based 1x8 optical beam forming network in CMOS-compatible waveguide technology,” IEEE Photon. Technol. Lett. 19(15), 1130–1132 (2007). [CrossRef]

]. When using multiple RRs in cascade configurations, the maximum delay line bandwidth for a certain target delay value increases approximately in linear relation with the number of RRs. Besides, inherent to the linear system properties, a larger delay can be achieved by means of adding up multiple smaller delays which are generated by separate delay lines in a serial cascade. When this delay functionality is incorporated in a binary-tree architecture, simultaneous generation of incremental delays can be realized. Figure 8
Fig. 8 (a) schematic of a delay line circuit with a 1 × 8 port configuration, (b)-(d) measured group delay responses of different output ports, where the ring resonators (RRs) are set such that incremental delays of different ports are aligned to a common center frequency (from [8]).
depicts a schematic of such a circuit with a 1 × 8 port configuration and RRs with a FSR of 14 GHz.

5. Construction of complex MWP signal processors

5.1 On-chip 16 × 1 optical beam former

Employing the proven PIC functionalities previously constructed, and using the waveguide basic building blocks, an example of complex, on-chip MWP signal processors, namely an optical beamformer chip for Ku-band phased array antennas [33

33. D. Marpaung, L. Zhuang, M. Burla, C. Roeloffzen, J. Verpoorte, H. Schippers, A. Hulzinga, P. Jorna, W. P. Beeker, A. Leinse, R. Heideman, B. Noharet, Q. Wang, B. Sanadgol, and R. Baggen, “Towards a broadband and squint-free Ku-band phased array antenna system for airborne satellite communications,” in Proc. of the Fifth European Conference on Antennas and Propagation EuCAP (Rome, Italy, 2011).

] has been designed and fabricated. The full functionalities of such an optical beamformer chip have been elaborated on in [6

6. A. Meijerink, C. G. H. Roeloffzen, R. Meijerink, L. Zhuang, D. A. I. Marpaung, M. J. Bentum, M. Burla, J. Verpoorte, P. Jorna, A. Hulzinga, and W. C. van Etten, “Novel ring resonator-based integrated photonic beamformer for broadband phased-array antennas-Part I: design and performance analysis,” J. Lightwave Technol. 28(1), 3–18 (2010). [CrossRef]

,7

7. L. Zhuang, C. G. H. Roeloffzen, A. Meijerink, M. Burla, D. A. I. Marpaung, A. Leinse, M. Hoekman, R. G. Heideman, and W. C. van Etten, “Novel ring resonator-based integrated photonic beamformer for broadband phased-array antennas-Part II: experimental prototype,” J. Lightwave Technol. 28(1), 19–31 (2010). [CrossRef]

], where an optical sideband filter (OSBF) and an optical carrier reinsertion coupler are incorporated together with the primary signal-combining circuit using RR-based delay lines. The intention is to apply the optical beam former in a Ku-band phased array antenna system to enable mobile broadband satellite communications. The chip is required to support 16 inputs, 4.5 GHz optical bandwidth, and a maximum delay of 290 ps. Correspondingly, this is translated into a functional design which consists of a 16 × 1 binary-tree combining circuit inserted symmetrically with a total of 40 RR-based delay lines, an OSBF using the MZI-double-RR architecture, and a flexible optical carrier reinsertion circuit allowing the optical carrier to be inserted from both sides of the chip. The schematic of the beam former architecture is depicted in Fig. 9(a)
Fig. 9 (a) schematic of the designed 16 × 1 optical beamforming network (OBFN) chip; (b) chip mask layout using waveguide bend radius of 125 µm; (c) a photo of a processed wafer; (d) a photo of a packaged chip with electrical connections and fiber pigtailing.
, which is the most complex on-chip MWP signal processor to date. Using the waveguide bend radius of 125 µm, a chip mask layout has been generated as shown in Fig. 9(b), which has a footprint as small as 0.7 × 2.2 cm. Figure 9(c)-9(d) exhibit the photos of a processed wafer and a packaged chip, respectively.

Several measurements have been performed on the fabricated 16 × 1 beamformer chip to verify the delay functionality. The used delay line configurations are shown in Fig. 10
Fig. 10 Measured group delay responses of a cascade of (a) 2 RRs, (b) 3 RRs, (c) 4 RRs and (d) 6 RRs
together with the measured group delay responses over one FSR of 25 GHz. By using the tunable elements of each RR, i.e., a coupler and a phase shifter, different delays were obtained over a defined bandwidth. As shown in the results, the delay dynamic tuning range scales with the number of RRs in the cascade. For a cascade of 6 RRs, a maximum delay of 650 ps is achieved for a bandwidth of 4.5 GHz, which is in good agreement with the functional design.

5.2 Integrated phase-shifter and true-time-delay on a single chip based on separate carrier tuning

Tunable delay lines and phase shifters have a primary role in the implementation of multiple signal processing functionalities. The realization of continuously tunable delays with large tuning range (in the order of nanoseconds) and broadband performance (tens to hundreds of GHz) is highly desired for a number of functionalities, for example the realization of reconfigurable and highly selective microwave photonic filters, or for control of broadband phased array antennas. Several optical solutions have been proposed over the years to overcome the limited performance of purely-electronic true time delay (TTD) and phase shifting (PS), allowing to increase the amount of delay (almost 13 ns demonstrated in [34

34. R. L. Moreira, J. Garcia, W. Li, J. Bauters, J. S. Barton, M. J. R. Heck, J. E. Bowers, and D. J. Blumenthal, “Integrated ultra-low-loss 4-bit tunable delay for broadband phased array antenna applications,” IEEE Photon. Technol. Lett. 25(12), 1165–1168 (2013). [CrossRef]

]) with bandwidths of hundreds of GHz and continuous tunability, and phase shifters with full-360° tunability in mm-wave band [35

35. W. Li, W. Zhang, and J. Yao, “An ultra-wideband 360° photonic-assisted microwave phase shifter,” in Proc. of OFC/NFOEC (Anaheim, Calif., USA, 2013).

]. In [9

9. M. Burla, D. A. I. Marpaung, L. Zhuang, C. G. H. Roeloffzen, M. R. Khan, A. Leinse, M. Hoekman, and R. G. Heideman, “On-chip CMOS compatible reconfigurable optical delay line with separate carrier tuning for microwave photonic signal processing,” Opt. Express 19(22), 21475–21484 (2011). [CrossRef] [PubMed]

] we have shown a broadband (1 GHz) processor that includes delaying, phase shifting and single sideband filtering functionalities in a single unit. The delay module is based on the separate carrier tuning technique [36

36. P. A. Morton and J. B. Khurgin, “Microwave photonic delay line with separate tuning of the optical carrier,” IEEE Photon. Technol. Lett. 21(22), 1686–1688 (2009). [CrossRef]

,37

37. S. Chin, L. Thévenaz, J. Sancho, S. Sales, J. Capmany, P. Berger, J. Bourderionnet, and D. Dolfi, “Broadband true time delay for microwave signal processing, using slow light based on stimulated Brillouin scattering in optical fibers,” Opt. Express 18(21), 22599–22613 (2010). [CrossRef] [PubMed]

].The processor consists of a reconfigurable optical delay line, a separate carrier tuning unit and an optical sideband filter. The optical sideband filter is an MZI with an optical ring resonator in one of its arms (Fig. 11
Fig. 11 Schematic layout of the separate carrier tuning (SCT) unit (top) and principle of operation (bottom) (from [9]).
, top). This filter is used to remove one of the RF sidebands of a double sideband plus carrier (DSB + C) signal previously generated using a Mach-Zehnder intensity modulator. Optical delay and carrier tuning are implemented using a pair of cascaded optical ring resonators each (Fig. 11, bottom). The group delay can be varied between 0 and approx. 400 ps by tuning the coupling factor of the optical ring resonators of the delay line, while simultaneously applying a full 0 – 360° phase shift to the carrier using the carrier tuning unit (Fig. 12
Fig. 12 Generation of tunable group delay (a) and of full-360° phase shift (b) using the integrated photonic processor (from [9]).
).

5.3 Microwave photonics filters

Fig. 14 Demonstration of the full tunability of the microwave photonics filter (MPF) based on separate carrier tuning (SCT). (a) shift of the resonance frequency. (b) Tuning of the FSR. (c) Simultaneous tuning of notch frequency and FSR (from [9]).

5.4 Spectral filters based on RR-assisted MZI architectures

Spectral filters are a widely required functionality for signal processing. Various well-known digital filter concepts can be implemented on-chip using waveguide analogies. For example, Chebyshev II filters featuring flat passband and sharp transition band are good candidates for optical sideband filtering. A practical way to construct this type of filter is to use RR-assisted MZI architectures [14

14. L. Zhuang, W. P. Beeker, A. Leinse, R. G. Heideman, P. van Dijk, and C. Roeloffzen, “Novel wideband microwave polarization network using a fully-reconfigurable photonic waveguide interleaver with a two-ring resonator-assisted asymmetric Mach-Zehnder structure,” Opt. Express 21(3), 3114–3124 (2013). [CrossRef] [PubMed]

]. Figure 15(a)
Fig. 15 (a) Schematics of waveguide implementations of 3-order and 5-order Chebyshev II filters using MZI-single-RR and MZI-double-RR architecture, respectively. (b) Comparison between the optimized filter transmissions. (c)-(d) Measured complementary outputs, phase and group delay responses of the MZI-double-RR filter (from [14] and [10]).
depicts the schematics of waveguide implementations of 3rd-order and 5th-order Chebyshev II filters which use MZI-single-RR and MZI-double-RR architectures, respectively. The fabricated devices are characterized by a FSR of 19.6 GHz, and the filter coefficients are reconfigurable by means of the heaters. The optimized filter transmissions are depicted in Fig. 15(b), where the transition band improvement by increasing the filter order is demonstrated. Moreover, the measured complementary outputs, phase and group delay responses of the MZI-double-RR filter are also depicted in Fig. 15(c)-15(e) in contrast with the simulations, which verify the device functionality and design accuracy.

5.5 Frequency discriminator chip

5.5.1 High SFDR MWP link

5.6 Ultrawideband pulse generation

Ultra-wideband (UWB) signal generation is one of the key applications of MWP, because it clearly highlights the advantage of wide bandwidth of photonics. Flexible generation and spectrum shaping of RF pulses with multiple-gigahertz bandwidth has been proven challenging for traditional RF techniques. In MWP, successive temporal differentiation has been shown effective to shape the power spectrum of UWB pulses. The frequency discriminator chip in Fig. 16 can be programmed to synthesize a first-order and a second-order temporal differentiators simultaneously from both outputs. In this case, UWB pulses coded in the phase of the optical carrier will be converted to variations of pulsed intensity with shaped power spectrum. The experiment setup for the UWB pulse shaping is shown in Fig. 18(a)
Fig. 18 (a) Schematic of the measurement setup used to demonstrate the pulse shaping. The discriminator chip is configured to shape the Gaussian pulses modulated onto the phase of the optical carrier into a monocycle or a doublet. (b) Simulated (left) and measured (right) ring responses for modified doublet generation. (c) Waveforms (left) and power spectrum (right) of the modified doublets (from [12]).
. An example of a result is shown in Fig. 18(b). The top left figure depicts the simulated response synthesized to generate modified UWB doublets. Here, the cascade of drop response from Ring 1 and the through response from Ring 2 was synthesized from Out 1, while the cascade of the through responses from Ring 1 and Ring 3 was obtained from Out 2. The UWB pulses from these outputs, together with their power spectrum, are depicted in Fig. 18(c).

5.7 Instantaneous frequency measurement

5.8 Hilbert transformer

Besides being applied as delay lines, another interesting signal processing functionality is the fractional Hilbert transformer (FHT), or in other words, the stand-alone arbitrary phase shift [15

15. L. Zhuang, M. R. Khan, W. P. Beeker, A. Leinse, R. G. Heideman, and C. G. H. Roeloffzen, “Novel microwave photonic fractional Hilbert transformer using a ring resonator-based optical all-pass filter,” Opt. Express 20(24), 26499–26510 (2012). [CrossRef] [PubMed]

]. Similar to the arbitrary phase shifter principle mentioned earlier, a RR as depicted in Fig. 6(a) can provide a tunable phase shift to the RF signals modulated on the optical carrier by making use of its sharp phase transitions around the resonance frequencies and quasi-linear phase responses around the off-resonance frequencies. However, in this case, the optical carrier is always aligned with one resonance frequency of the RR, so that the RR phase response has an anti-symmetric profile with respect to the carrier frequency and therefore allows the regular double-sideband modulated optical signals. Figure 20
Fig. 20 (a) Measured RF phase response of a waveguide realization of a RR for different values of power coupling coefficient κ and the curve-fittings to the target fractional Hilbert transformer (FHT) specifications; (b) demonstration of the resulting FHT phase shift by removing the delay effect (linear phase) from the measured phase responses (from [15]).
depicts the measurements of this FHT functionality of a RR with a FSR of 15 GHz. As it appears, the FHT phase shift can be varied by means of changing the RR coupling coefficient κ. However, a limited phase shift tuning range is exhibited. In practice, this phase tuning range can be linearly extended to 2π by using a cascade of multiple RRs.

5.9 RF phase control in optical heterodyne-based RF signal generation

5.10 Microwave polarization network

5.11 Modulation-format transparent MWP signal processors

6. Conclusions

In this paper multiple integrated microwave photonic processing functionalities using high contrast silicon nitride (TriPleXTM) waveguide technology have been presented. The TriPleXTM technology is especially suited for microwave photonics applications mainly due to the combination of low propagation losses in the optical waveguides and high refractive index contrast between core and cladding, allowing for small bend radii. Consequently, this technology allows for very complex optical circuits to be realized by combining the building blocks on a system level. However, to realize microwave photonic functionalities with ultimate performance, the conversion from RF signals to optical and back requires the active components -such as lasers, modulators and detectors- to be integrated on the platform as well. Despite featuring higher optical propagation losses, InP waveguide technology is prone to provide those active functionalities. Moreover, hybrid integration between InP and TriPleXTM waveguides allows for functionalities using the best of both worlds: active components on InP and low optical propagation loss on TriPleXTM. For future work, a schematic of a state of art hybrid-platform solution is shown in Fig. 25
Fig. 25 InP and SiN platform solution for complex microwave photonic processing. Example of an optical beamformer chip for transmit phased array antennas.
, where an InP chip is directly butt-coupled to a TriPleXTM chip. On-chip spot size converters (achieved by tapering waveguides) will ensure low transfer loss between the two platforms, assuming that the waveguides have been aligned properly.

Another important criterion is the total power consumption of the MWP chip which is, in the system depicted in Fig. 25, given by the resistive heater used as tuning elements on the TriPleXTM chip. As example the 16x1 OBFN chip, from Fig. 8 has 120 heaters with an average total power consumption of 20 W. Alternative tuning solutions, such as those employing liquid crystal claddings, will reduce the total power consumption by many orders of magnitude.

Microwave photonics is a rapidly developing field enabled by advancements in low-loss waveguide and hybrid integration technologies. The enabler to merge these technologies successfully lies within the ability to use optimized technology building blocks which allow creation of on-chip integrated photonic systems and the used packaging and assembly approach. To achieve reliable and robust packaging, developments in industry will play a crucial role. The combination of on-chip manufacturing and automated high-volume assembly and packaging capability will then secure that this technology can be introduced in novel applications at competitive cost levels.

Acknowledgment

The research described in this paper is partly funded by the Dutch Point One R&D Innovation Project: Broadband Satellite Communication Services on High-Speed Vehicles, with project number PNE101008, the IOP Photonic Devices Promis2day project IPD12009, and by the European Commission in the 7th Framework Program. The SANDRA project is a Large Scale Integrating Project for the FP7 Topic AAT.2008.4.4.2 (Integrated approach to network centric aircraft communications for global aircraft operations).

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6.

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8.

L. Zhuang, C. G. H. Roeloffzen, R. G. Heideman, A. Borreman, A. Meijerink, and W. van Etten, “Single-chip ring resonator-based 1x8 optical beam forming network in CMOS-compatible waveguide technology,” IEEE Photon. Technol. Lett. 19(15), 1130–1132 (2007). [CrossRef]

9.

M. Burla, D. A. I. Marpaung, L. Zhuang, C. G. H. Roeloffzen, M. R. Khan, A. Leinse, M. Hoekman, and R. G. Heideman, “On-chip CMOS compatible reconfigurable optical delay line with separate carrier tuning for microwave photonic signal processing,” Opt. Express 19(22), 21475–21484 (2011). [CrossRef] [PubMed]

10.

L. Zhuang, D. A. I. Marpaung, M. Burla, W. P. Beeker, A. Leinse, and C. G. H. Roeloffzen, “Low-loss, high-index-contrast Si₃N₄/SiO₂ optical waveguides for optical delay lines in microwave photonics signal processing,” Opt. Express 19(23), 23162–23170 (2011). [CrossRef] [PubMed]

11.

D. Marpaung, C. Roeloffzen, A. Leinse, and M. Hoekman, “A photonic chip based frequency discriminator for a high performance microwave photonic link,” Opt. Express 18(26), 27359–27370 (2010). [CrossRef] [PubMed]

12.

D. A. I. Marpaung, L. Chevalier, M. Burla, and C. G. H. Roeloffzen, “Impulse radio ultrawideband pulse shaper based on a programmable photonic chip frequency discriminator,” Opt. Express 19(25), 24838–24848 (2011). [CrossRef] [PubMed]

13.

D. Marpaung, “On-chip photonic-assisted instantaneous microwave frequency measurement system,” IEEE Photon. Technol. Lett. 25(9), 837–840 (2013). [CrossRef]

14.

L. Zhuang, W. P. Beeker, A. Leinse, R. G. Heideman, P. van Dijk, and C. Roeloffzen, “Novel wideband microwave polarization network using a fully-reconfigurable photonic waveguide interleaver with a two-ring resonator-assisted asymmetric Mach-Zehnder structure,” Opt. Express 21(3), 3114–3124 (2013). [CrossRef] [PubMed]

15.

L. Zhuang, M. R. Khan, W. P. Beeker, A. Leinse, R. G. Heideman, and C. G. H. Roeloffzen, “Novel microwave photonic fractional Hilbert transformer using a ring resonator-based optical all-pass filter,” Opt. Express 20(24), 26499–26510 (2012). [CrossRef] [PubMed]

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B. Larsen, L. Nielsen, K. Zenth, L. Leick, C. Laurent-Lund, L. Andersen, and K. Mattsson, “A low-loss, silicon-oxynitride process for compact optical devices,” in Proceedings of ECOC (Rimini, Italy, 2003).

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34.

R. L. Moreira, J. Garcia, W. Li, J. Bauters, J. S. Barton, M. J. R. Heck, J. E. Bowers, and D. J. Blumenthal, “Integrated ultra-low-loss 4-bit tunable delay for broadband phased array antenna applications,” IEEE Photon. Technol. Lett. 25(12), 1165–1168 (2013). [CrossRef]

35.

W. Li, W. Zhang, and J. Yao, “An ultra-wideband 360° photonic-assisted microwave phase shifter,” in Proc. of OFC/NFOEC (Anaheim, Calif., USA, 2013).

36.

P. A. Morton and J. B. Khurgin, “Microwave photonic delay line with separate tuning of the optical carrier,” IEEE Photon. Technol. Lett. 21(22), 1686–1688 (2009). [CrossRef]

37.

S. Chin, L. Thévenaz, J. Sancho, S. Sales, J. Capmany, P. Berger, J. Bourderionnet, and D. Dolfi, “Broadband true time delay for microwave signal processing, using slow light based on stimulated Brillouin scattering in optical fibers,” Opt. Express 18(21), 22599–22613 (2010). [CrossRef] [PubMed]

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OCIS Codes
(060.2360) Fiber optics and optical communications : Fiber optics links and subsystems
(070.6020) Fourier optics and signal processing : Continuous optical signal processing
(130.3120) Integrated optics : Integrated optics devices
(350.4010) Other areas of optics : Microwaves
(060.5625) Fiber optics and optical communications : Radio frequency photonics

ToC Category:
Integrated Microwave Photonics

History
Original Manuscript: June 4, 2013
Revised Manuscript: August 22, 2013
Manuscript Accepted: August 22, 2013
Published: September 23, 2013

Virtual Issues
Microwave Photonics (2013) Optics Express

Citation
Chris G. H. Roeloffzen, Leimeng Zhuang, Caterina Taddei, Arne Leinse, René G. Heideman, Paulus W. L. van Dijk, Ruud M. Oldenbeuving, David A. I. Marpaung, Maurizio Burla, and Klaus -J. Boller, "Silicon nitride microwave photonic circuits," Opt. Express 21, 22937-22961 (2013)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-19-22937


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References

  1. J. Capmany and D. Novak, “Microwave photonics combines two worlds,” Nat. Photonics1(6), 319–330 (2007). [CrossRef]
  2. J. Yao, “Microwave photonics,” J. Lightwave Technol.27(3), 314–335 (2009). [CrossRef]
  3. D. A. I. Marpaung, C. G. H. Roeloffzen, R. G. Heideman, A. Leinse, S. Sales, and J. Capmany, “Integrated microwave photonics,” Laser Photon. Rev.7(1), 1–33 (2013).
  4. M. Burla, C. G. H. Roeloffzen, L. Zhuang, D. Marpaung, M. R. Khan, P. Maat, K. Dijkstra, A. Leinse, M. Hoekman, and R. Heideman, “System integration and radiation pattern measurements of a phased array antenna employing an integrated photonic beamformer for radio astronomy applications,” Appl. Opt.51(7), 789–802 (2012). [CrossRef] [PubMed]
  5. M. Burla, D. Marpaung, L. Zhuang, A. Leinse, M. Hoekman, R. Heideman, and C. Roeloffzen, “Integrated photonic Ku-band beamformer chip with continuous amplitude and delay control,” IEEE Photon. Technol. Lett.25(12), 1145–1148 (2013). [CrossRef]
  6. A. Meijerink, C. G. H. Roeloffzen, R. Meijerink, L. Zhuang, D. A. I. Marpaung, M. J. Bentum, M. Burla, J. Verpoorte, P. Jorna, A. Hulzinga, and W. C. van Etten, “Novel ring resonator-based integrated photonic beamformer for broadband phased-array antennas-Part I: design and performance analysis,” J. Lightwave Technol.28(1), 3–18 (2010). [CrossRef]
  7. L. Zhuang, C. G. H. Roeloffzen, A. Meijerink, M. Burla, D. A. I. Marpaung, A. Leinse, M. Hoekman, R. G. Heideman, and W. C. van Etten, “Novel ring resonator-based integrated photonic beamformer for broadband phased-array antennas-Part II: experimental prototype,” J. Lightwave Technol.28(1), 19–31 (2010). [CrossRef]
  8. L. Zhuang, C. G. H. Roeloffzen, R. G. Heideman, A. Borreman, A. Meijerink, and W. van Etten, “Single-chip ring resonator-based 1x8 optical beam forming network in CMOS-compatible waveguide technology,” IEEE Photon. Technol. Lett.19(15), 1130–1132 (2007). [CrossRef]
  9. M. Burla, D. A. I. Marpaung, L. Zhuang, C. G. H. Roeloffzen, M. R. Khan, A. Leinse, M. Hoekman, and R. G. Heideman, “On-chip CMOS compatible reconfigurable optical delay line with separate carrier tuning for microwave photonic signal processing,” Opt. Express19(22), 21475–21484 (2011). [CrossRef] [PubMed]
  10. L. Zhuang, D. A. I. Marpaung, M. Burla, W. P. Beeker, A. Leinse, and C. G. H. Roeloffzen, “Low-loss, high-index-contrast Si₃N₄/SiO₂ optical waveguides for optical delay lines in microwave photonics signal processing,” Opt. Express19(23), 23162–23170 (2011). [CrossRef] [PubMed]
  11. D. Marpaung, C. Roeloffzen, A. Leinse, and M. Hoekman, “A photonic chip based frequency discriminator for a high performance microwave photonic link,” Opt. Express18(26), 27359–27370 (2010). [CrossRef] [PubMed]
  12. D. A. I. Marpaung, L. Chevalier, M. Burla, and C. G. H. Roeloffzen, “Impulse radio ultrawideband pulse shaper based on a programmable photonic chip frequency discriminator,” Opt. Express19(25), 24838–24848 (2011). [CrossRef] [PubMed]
  13. D. Marpaung, “On-chip photonic-assisted instantaneous microwave frequency measurement system,” IEEE Photon. Technol. Lett.25(9), 837–840 (2013). [CrossRef]
  14. L. Zhuang, W. P. Beeker, A. Leinse, R. G. Heideman, P. van Dijk, and C. Roeloffzen, “Novel wideband microwave polarization network using a fully-reconfigurable photonic waveguide interleaver with a two-ring resonator-assisted asymmetric Mach-Zehnder structure,” Opt. Express21(3), 3114–3124 (2013). [CrossRef] [PubMed]
  15. L. Zhuang, M. R. Khan, W. P. Beeker, A. Leinse, R. G. Heideman, and C. G. H. Roeloffzen, “Novel microwave photonic fractional Hilbert transformer using a ring resonator-based optical all-pass filter,” Opt. Express20(24), 26499–26510 (2012). [CrossRef] [PubMed]
  16. C. K. Madsen and J. H. Zhao, Optical Filter Design and Analysis: A Signal Processing Approach. (Wiley-Interscience, 1999).
  17. A. V. Oppenheim, and R. W. Schafer, Digital Signal Processing (Prentice-Hall, 1975).
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