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Photonic generation of microwave waveforms with wide chirp tuning range
Optics Communications 304 (2013) 102–106
Contents lists available at SciVerse ScienceDirect
Optics Communications journal homepage: www.elsevier.com/locate/optcom
Discussion
Photonic generation of microwave waveforms with wide chirp tuning range Jia Haur Wong a,n, Huan Huan Liu a, Huy Quoc Lam b, Sheel Aditya a, Junqiang Zhou a, Peng Huei Lim a, Kenneth Eng Kian Lee b, Kan Wu a, Kin Kee Chow a, Perry Ping Shum a a OPTIMUS, Photonics Centre of Excellence, School of Electrical & Electronic Engineering, Nanyang Technological University, 50 Nanyang Drive, 637553, Singapore b Temasek Laboratories, Nanyang Technological University, 637553, Singapore
art ic l e i nf o
a b s t r a c t
Article history: Received 3 September 2012 Received in revised form 16 April 2013 Accepted 17 April 2013 Available online 9 May 2013
We show analytically as well as demonstrate experimentally an approach to generate microwave waveforms with wide chirp tuning range. The approach is based on the interference of two temporallystretched pulses which are time-delayed with respect to each other and having different frequency chirp. This approach is realized by an unbalanced Mach Zehnder Interferometer (MZI) incorporating a linearlychirped fiber-Bragg-grating (LCFBG) whose group-delay-dispersion (GDD) can be tuned across a wide range. In general, tuning the GDD of the LCFBG changes the chirp rate of the generated microwave waveform and tuning the relative time-delay between the interferometer arms changes the center frequency of the generated microwave waveform. Balanced photodetection is also implemented to obtain DC-free microwave waveforms. Based on this approach, we demonstrate the generation of microwave waveforms with different center frequencies and with the chirp rates ranging from∼−126.7 GHz/ns to ∼+120.8 GHz/ns, including the zero-chirp case. & 2013 Elsevier B.V. All rights reserved.
Keywords: Microwave photonics Chirped pulse generation Fiber-Bragg-gratings Frequency-to-time mapping Dispersion
1. Introduction Leveraging on the advantageous features offered by photonic components, such as low loss, broad bandwidth, immunity to electromagnetic interference and high rate-distance product, the area of microwave photonics has attracted extensive research interest over the past few years [1–3]. With the motivation to improve the performance of existing radio-frequency (RF) systems, this has led to the development of various photonic techniques for analog-to-digital conversion [4–6], microwave filtering [7–9], instantaneous frequency measurement [10,11] and generation of high frequency continuous-wave microwave signals [12,13]. Furthermore, the area of photonic generation of arbitrary microwave waveforms has also become increasingly important due to its diverse applications such as fiber wireless communication, pulsed radar as well as electronic countermeasures. With conventional electronic arbitrary waveform generators limited to relatively low frequencies, much effort has been put into developing photonic techniques which have the capability to generate microwave waveforms at frequencies ranging from tens to hundreds of gigahertz (GHz). Some of these techniques include optical spectral
n
Corresponding author. Tel.: +65 67904527. E-mail address: [email protected] (J.H. Wong).
0030-4018/$ - see front matter & 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.optcom.2013.04.045
shaping of a broadband optical pulse followed by frequency-totime mapping through a dispersive medium [14,15], manipulating the phase and amplitude of the longitudinal modes of a modelocked laser [16,17], direct space-to-time optical pulse shaping [18,19] as well as temporal pulse shaping [20]. In most of the aforementioned techniques, the upper-end frequencies of the generated microwave waveforms are generally limited by the bandwidth of the photodetector used. In recent years, the spectral shaping and frequency-to-time mapping technique has shown promise in generating microwave waveforms with complex arbitrary profiles, such as linearlychirped waveforms that are typically characterized with a large time bandwidth product (TBWP) and widely used in modern radar, computed tomography and spread-spectrum communication systems [21]. Proposed and demonstrated in [22], Zeitouny et al. generated linearly-chirped microwave waveforms by implementing two LCFBG with different chirp rates in an unbalanced MZI based on the spectral shaping and linear frequency-to-time mapping technique. As the fabricated LCFBGs possessed a fixed second-order dispersion term, it was shown that tuning the relative time-delay between the interferometer arms would change the center frequency while keeping the chirp rate constant for the microwave waveform. Later, an alternative approach to generate linearly-chirped microwave waveforms was demonstrated by Wang et al. [23]. Unlike [22], spectral shaping is
J.H. Wong et al. / Optics Communications 304 (2013) 102–106
accomplished by a LCFBG-incorporated Sagnac loop mirror (spectral filter), which has a spectral response with an increasing or decreasing free spectral range (FSR), while linear frequency-totime mapping is realized by a dispersive medium. It was shown that by tuning the time-delay in the Sagnac loop mirror, the center frequency and chirped profile of the generated microwave waveform can be controlled. Specifically, depending on the polarity of the time-delay in the Sagnac loop mirror, the chirp rate can be tuned to either negative or positive values but its absolute value is kept constant. This limitation is clearly attributed to the nontunable nature of the spectral filter's spectral response. Besides linear frequency-to-time mapping, Ashrafi et al. have shown that nonlinear frequency-to-time mapping together with spectral shaping can also be implemented in an unbalanced MZI setup to generate linearly-chirped microwave waveforms [24]. Essentially, the nonlinear frequency-to-time mapping is induced by a dispersive medium having both the second and the third-order dispersion terms. More importantly, it has been demonstrated that by varying the relative time-delay between the interferometer arms, this scheme permits the generation of microwave waveforms whose chirp rate can be tuned to negative, zero or positive values. Despite the tunability of the chirp rate, the center frequency of the generated microwave waveforms however will change when the chirp rate is tuned. Recently, Li et al. proposed and demonstrated the generation of microwave waveforms with continuously tunable linear chirp rate [25] based on the spectral shaping and linear frequency-to-time mapping technique. In contrast to [23], the spectral filter is realized by an unbalanced MZI incorporating an optically pumped LCFBG whose spectral response can be tuned to have increasing or decreasing FSR. As the optically pumped LCFBG is written in an Erbium–Ytterbium co-doped fiber, pumping it with different pump power changes its group-delay response and this leads to a shift in the FSR. It should be emphasized that, unlike all the previously aforementioned schemes, the center frequency and chirp rate can be tuned independently. In general, for a fixed value of the second-order dispersion term of the dispersive medium which induces the linear frequency-to-time mapping, the center frequency of the microwave waveform changes with the relative time-delay between the interferometer arms, while the chirp rate is dependent on both the polarity of the relative time-delay as well as the GDD induced by the optically pumped LCFBG. It is shown experimentally that the chirp rate of the generated microwave waveforms changes from 79 to 64 GHz/ns when the injection current to the pumping laser diode increases from 0 to 100 mA. In this paper, we show analytically and experimentally the generation of linearly-chirped microwave waveforms based on an approach similar to that proposed in [25]. But instead of an optically pumped LCFBG, a LCFBG which has a programmable GDD is implemented in our scheme. Our scheme also employs balanced photodetection and offers the following advantages. The dispersion of the LCFBG can be tuned from −900 ps/nm to +900 ps/nm, enabling the generation of linearly-chirped microwave waveforms with a wider chirp tuning range. The tuning range in our scheme also covers the zero-chirp case and the generated microwave waveforms are DC-free due to the implementation of balanced photodetection. The principle of operation of our scheme and its governing mathematics is presented in Section 2, following which the measured results are presented in Section 3. Finally, we summarize the conclusions in Section 4.
2. Principle of operation Fig. 1 illustrates a schematic of the proposed scheme. An ultrashort pulse g(t) is first propagated through a length L of single-mode€ S ¼ β2 L, where β2 is the fiber (SMF) whose GDD is defined as Φ
103
Fig. 1. Basic principle of operation of the proposed scheme for generating linearly chirped microwave pulses. SMF: single-mode-fiber; LCFBG: linearly chirped fiber Bragg grating; OTDL: optical tunable delay line; and BPD: balanced photodetector.
second-order dispersion term. The temporally-stretched and linearly chirped pulse is then fed to an unbalanced MZI which splits the pulse into two independent paths. As depicted in Fig. 1, the pulse propagating in the upper arm is further chirped by a LCFBG which has a magnitude response (reflection) jrðωÞj as well as a program€ F . On the other hand, after passing through an optical mable GDD of Φ tunable delay line (OTDL), the pulse propagating in the lower arm experiences a tunable time-delay Δt relative to the pulse in the upper arm. When the output pulses E1(t) and E2(t) from both arms combine, a temporal interference pattern with increasing or decreasing FSR will be generated. With the interference patterns having a phase difference of π=2 for the outputs of the MZI, followed by optical-to-electrical (OE) conversion by a balanced photodetector, a DC-free chirped microwave waveform can be obtained and observed on a sampling oscilloscope. Assuming the initial pulse to be Gaussian-shaped, so that gðtÞ ¼ expð−t 2 =2τ2o Þ, τo ¼ half pulsewidth at 1/e maximum, and following the detailed derivation in [25], the individual photocurrents I1(t) and E2(t) as illustrated in Fig. 1 are expressed as 2 2 t1 t2 t1 þ A2 G I 1 ðtÞ∝ A1 r G € € €S ΦT ΦT Φ 2 t t t t2 t2 1 1 2 þA1 A2 r − 1 G 2 cos ð1Þ G € S 2Φ €T €T €T €S 2Φ Φ Φ Φ 2 2 t1 t2 t1 þ A2 G I 2 ðtÞ∝ A1 r G €T €T €S Φ Φ Φ 2 t t t t2 t2 1 1 2 G 2 sin þA1 A2 r − 1 G € S 2Φ €T €T €T €S 2Φ Φ Φ Φ
ð2Þ
where A1 ðtÞ and A2 ðtÞ are the amplitudes of E1 ðtÞ and E2 ðtÞ, GðωÞis the Fourier transform of gðtÞ, t 1 ¼ t−Δt=2, t 2 ¼ t−Δt=2 and €T ¼Φ €F þΦ € S . Here, it should be noted that gðtÞ is real-time Φ Fourier-transformed under the assumption that the condition € T j⪡1 is satisfied. The output photocurrent Iout ðtÞ is given as jτ2o =2Φ I out ðtÞ ¼ I 1 ðtÞ−I 2 ðtÞ 2 2 t t t t2 t2 t2 t2 1 1 2 G cos ∝A1 A2 r − 1 − sin − 1 G € S 2Φ €T € S 2Φ €T €T €T €S 2Φ 2Φ Φ Φ Φ 2 t t t t2 t2 π 1 1 2 − 1 þ G cos G € S 2Φ €T 4 €T €T €S 2Φ Φ Φ Φ
∝A1 A2 r
ð3Þ
where it is observed that the instantaneous level of the generated microwave waveform oscillates according to the cos ðt 22 = € S −t 2 =2Φ € T þ π=4Þ term while its envelope is dependent on the 2Φ 1 remaining terms. The instantaneous frequency of the microwave waveform can be derived by differentiating the phase of the cosine € S −t 2 =2Φ € T þ π=4 w.r.t. time and is expressed as term ϕRF ¼ t 22 =2Φ 1 €T € T Δt € S −Φ €S þΦ 1 δϕRF 1 Φ Φ ð4Þ ¼ t− f RF ¼ € SΦ €T € SΦ €T 2π δt 2π 2 Φ Φ Clearly, fRF is observed to be linearly proportional to time and therefore the generated microwave waveform is linearly-chirped. Furthermore, the center frequency of the waveform can be
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calculated when t¼ 0 and expressed as 1 Δt Δt fo ¼ þ €S Φ €F þΦ €S 4π Φ
J.H. Wong et al. / Optics Communications 304 (2013) 102–106
ð5Þ
€S From Eq. (5), it is evident that f o is proportional to Δt. Since Φ is generally fixed, tuning Δt would change the f o of the linearlychirped microwave waveform. Furthermore, the chirp rate of the microwave waveform can be written as €F δf 1 Φ sgnðΔtÞ CR ¼ RF ¼ ð6Þ €F þΦ € S ÞΦ €S 2π δt ðΦ Unlike f o , the absolute value of the chirp rate is independent of € F. the magnitude of Δt but tunable by changing the value of Φ Moreover, both up-chirp and down-chirp are obtainable as the polarity of the chirp rate is dependent on the sign of Δt. Tuning the € F of the programmable LCFBG to zero would also enable the Φ generation of zero-chirp microwave waveforms in the proposed scheme. As the bandwidth of the LCFBG is generally narrower than the bandwidth of the pulse source, the time aperture τTA of the generated chirped microwave waveform is largely dependent on € T Þ term. Here, τTA is defined as twice the duration in the rðt 1 =Φ which the intensity increases from 0.1% to its peak value ( −30 dB) and can be calculated as € T ωo Þð−2lnð0:001ÞÞ1=2m τTA ≈2ðΦ
ð7Þ
In (7), we have assumed the LCFBG to have a 2mth order superGaussian profile whose half bandwidth at 1/e maximum is expressed ωo . Further, the TBWP of the generated chirped microwave waveform can be estimated as € FΦ €T 2ω2 ð−2lnð0:001ÞÞ1=m Φ TBWP≈ðτTA Þ2 CR≈ o ð8Þ €S π Φ Considering all other parameters as fixed and ignoring any bandwidth constraint imposed by the photodetector or the sampling oscilloscope, the value of the TBWP varies accordingly to the € F . Thus, the maximum TBWP that can be tunable parameter Φ achieved through our scheme depends on the maximum GDD that the implemented LCBG can provide.
3. Measured results Fig. 2 illustrates the experimental setup for realization of the proposed scheme. In the experiments, the initial pulse source is implemented by a homemade 68 MHz mode-locked laser which is characterized to have a full-width half-maximum (FWHM) pulsewidth of 2.5 ps, a FWHM bandwidth of 2 nm and a center wavelength of 1565.3 nm. A readily-available 27 km long SMF with standard dispersion parameterDλ ¼ ð2πc=λ2 Þβ2 ¼ 17 ps=nm=km is utilized to temporally-stretch as well as linearly chirp the pulse€ S can be calculated to be∼−596.63 ps2. Next, the train. Hence, Φ temporally-stretched pulse-train is fed to an unbalanced MZI. For the realization of the programmable LCFBG in arm 1, a single channel
Fig. 2. Experimental setup of the proposed scheme for generating linearly chirped microwave pulses. SMF: single-mode-fiber; LCFBG: linearly chirped fiber Bragg grating; OTDL: optical tunable delay line; OATT: optical attenuator; OBPF: optical bandpass filter; TDCM: tunable dispersion compensation module; and BPD: balanced photodetector.
is bandpass filtered from a commercially available tunable dispersion compensation module (TDCM) which comprises multiple-channels of similar group-delay characteristics. The magnitude response of the filtered channel which has a 1-dB bandwidth of 0.5 nm and centered at 1565.3 nm is depicted in Fig. 3. Based on two superimposed fiberBragg-gratings (FBGs) connected to an optical circulator, the disper€ F of the implemented TDCM can be tuned from sion DF ¼ ð2πc=λ2 ÞΦ −900 ps/nm to +900 ps/nm with a minimum resolution of 1 ps/nm. € F can be tuned from −1169.99 ps2 to +1169.99 ps2. In other words, Φ As for arm 2, the OTDL is used to control the tunable relative timedelay between the interferometer arms, while the tunable optical attenuator is used to maximize the fringe visibility of the interference pattern at the outputs of the MZI. The MZI outputs are sent to a balanced photodetector with a 42 GHz bandwidth for OE conversion and removal of any DC component. Finally, the generated DC-free linearly-chirped microwave waveform is RF amplified and observed using a 70 GHz sampling oscilloscope. In the first experiment, we target the generation of a zero chirp € F ¼ 0 ps2 . The microwave waveform by setting Δt ¼ 100 ps and Φ center frequency and chirp rate are calculated as 27.2 GHz and 0 GHz/ns from Eqs. (5) and (6), respectively. Fig. 4(a) illustrates the generated microwave waveform which can be observed to be DCfree. Based on the Hilbert-transform method, the corresponding instantaneous frequency is calculated and also plotted in Fig. 4(a) wherein the center frequency and chirp rate are clearly indicated. It can be observed that the generated microwave waveform has nearly zero chirp and its center frequency of ∼27.24 GHz is in close agreement with the theoretically calculated center frequency. Besides this, for comparison, a numerically simulated result based on the values of the experimental parameters is presented in Fig. 4(b), where we have assumed the LCFBG to have a 6th order super-Gaussian profile and a 1-dB bandwidth of 0.5 nm. It is seen that, in terms of the generated waveform profile, center frequency and chirp rate, the experimental and simulated results are in good agreement. Next, generation of linearly-chirped microwave waveforms based on the proposed scheme is investigated. Fig. 5(a) illustrates the experimentally generated microwave waveform when we set € F ¼ −519:94 ps2 . It can be seen that the generated Δt ¼ 0 ps and Φ microwave waveform has a nearly symmetrical profile centered at 0 GHz while its instantaneous frequency changes linearly from down-chirp (∼−126.7 GHz/ns) to up-chirp (∼+120.8 GHz/ns). Again, our experimental results agree well with the simulation results shown in Fig. 5(b). In order to generate a microwave waveform which is either linearly up-chirped or down-chirped, Δt has to be set to an appropriate value such that the zero instantaneous frequency is shifted out of the waveform's mainlobe. This is exemplified in Fig. 6(a) when we set Δt ¼ −100 ps and € F ¼ −194:98 ps2 in which a linearly down-chirped microwave Φ waveform is generated. With a center frequency of ∼26.46 GHz, the instantaneous frequency of the waveform decreases linearly from ∼41 GHz to ∼10 GHz., equivalent to a down-chirp rate
Fig. 3. Magnitude response (reflection) of the filtered channel serving as the programmable LCFBG in the proposed approach.
J.H. Wong et al. / Optics Communications 304 (2013) 102–106
Fig. 4. (a) Experimental and (b) simulated results for generation of zero chirp € F ¼ 0 ps2 ). Green/Red line: amplitude of the microwave waveform (Δt ¼ 100 ps, Φ generated microwave waveform. Blue line: instantaneous frequency of the generated microwave waveform. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
Fig. 5. (a) Experimental and (b) simulated results for generation of linearly chirped € F ¼ −519:94 ps2 ). Green/Red line: amplitude of microwave waveform (Δt ¼ 0 ps,Φ the generated microwave waveform. Blue line: instantaneous frequency of the generated microwave waveform. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
of∼−67.37 GHz/ns. According to the experimental result, the generated waveform has an time aperture of ∼473.6 ps and correspondingly, achieved a TBWP of ∼15.11. Lastly, Fig. 7(a) illustrates a generated microwave waveform which has a center frequency of 25.42 GHz and is observed to
105
Fig. 6. (a) Experimental and (b) simulated results for generation of linearly chirped € F ¼ −194:98ps2 ). Green/Red line: amplitude microwave waveform (Δt ¼ −100 ps,Φ of the generated microwave waveform. Blue line: instantaneous frequency of the generated microwave waveform. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
have a linear up-chirp of ∼94.1 GHz, with the instantaneous frequency increasing from ∼4 GHz to ∼43 GHz. This is realized € F ¼ −324:96 ps2 . The time aperture when we set Δt ¼ 100 ps and Φ of the generated waveform is observed to be ∼517.2 ps, leading to a TBWP of ∼25.17. In the last two examples, the center frequency and chirp rate are again in good agreement with the corresponding simulation results shown in Figs. 6 and 7 (b), respectively. It is pertinent to mention here that, the mismatch in the amplitude between the experimental and simulated results at high instantaneous frequencies is mainly attributed to the frequency response of the RF link (comprised of the balanced photodetector, RF amplifier and RF cables) as well as the limited bandwidth of the sampling oscilloscope. Consequently, this also led to a significant mismatch in the time aperture (and TBWP) between the experimental and simulated results. Use of an RF link with a high roll-off frequency as well as a higher sampling rate oscilloscope would provide a more accurate measurement of the microwave waveform in terms of its amplitude at high frequencies as well as its corresponding time aperture (and TBWP). Furthermore, it should be emphasized that based on the LCFBG which we have used in the experiments, the chirp rate of the generated microwave waveform can be tuned continuously across a wide range, extending from ∼−176.66 GHz/ ns to ∼+176.66 GHz/ns with a minimum resolution of ∼5.69 GHz/ns. Assuming no limited bandwidth constraints and using our experimental parameters' values in Eq. (8), we can obtain a theoretically calculated maximum TBWP of ∼270.73 based on our proposed scheme. As we have implemented a fiber-based structure for our MZI and used a long length of SMF in our experiment, the stability of the generated microwave waveforms is observed to be sensitive to environmental perturbations. A potential improvement to the current scheme is to replace the fiber-based MZI with an integrated MZI incorporating a linearly chirped waveguide grating as well as using a shorter length of dispersion compensation fiber (DCF) whose β2 can be larger than a typical SMF over the same length.
106
J.H. Wong et al. / Optics Communications 304 (2013) 102–106
photodetection has also been proposed for the removal of DC components in the generated microwave waveform. Experimentally, we have shown the generation of several microwave waveforms with different center frequencies, chirp rates ranging from ∼−126.7 GHz/ns to ∼+120.8 GHz/ns, and no DC component. Based on the specifications of the LCFBG which we have used, our scheme has the potential to tune the chirp rate of the generated microwave waveforms continuously from ∼−176.66 GHz/ ns to ∼+176.66 GHz/ns with a minimum resolution of ∼5.69 GHz/ns. References [1] [2] [3] [4] [5]
[6] [7] [8] [9] [10] Fig. 7. (a) Experimental and (b) simulated results for generation of linearly chirped € F ¼ −324:96 ps2 ). Green/Red line: amplitude of microwave waveform (Δt ¼ 100 ps,Φ the generated microwave waveform. Blue line: instantaneous frequency of the generated microwave waveform. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
4. Conclusion In this paper, we have shown analytically and demonstrated experimentally a scheme for the generation of microwave waveforms of zero-chirp, up-chirp and down-chirp based on the temporal interference of two temporally- stretched pulses which are relatively time-delayed and have different frequency chirps. The scheme makes use of an unbalanced MZI, incorporating a tunable time delay and a LCFBG with tunable group-delay-dispersion (GDD). Through analytically derived equations, it has been shown that by tuning to appropriate values the relative time-delay between the two arms of the MZI as well as the GDD of the LCFBG, one can generate a microwave waveform with desired chirp rate and center frequency. The chirp rate can be tuned by changing the GDD of the LCFBG, while the center frequency can be tuned by changing the relative time-delay. Balanced
[11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25]
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Contents lists available at SciVerse ScienceDirect
Optics Communications journal homepage: www.elsevier.com/locate/optcom
Discussion
Photonic generation of microwave waveforms with wide chirp tuning range Jia Haur Wong a,n, Huan Huan Liu a, Huy Quoc Lam b, Sheel Aditya a, Junqiang Zhou a, Peng Huei Lim a, Kenneth Eng Kian Lee b, Kan Wu a, Kin Kee Chow a, Perry Ping Shum a a OPTIMUS, Photonics Centre of Excellence, School of Electrical & Electronic Engineering, Nanyang Technological University, 50 Nanyang Drive, 637553, Singapore b Temasek Laboratories, Nanyang Technological University, 637553, Singapore
art ic l e i nf o
a b s t r a c t
Article history: Received 3 September 2012 Received in revised form 16 April 2013 Accepted 17 April 2013 Available online 9 May 2013
We show analytically as well as demonstrate experimentally an approach to generate microwave waveforms with wide chirp tuning range. The approach is based on the interference of two temporallystretched pulses which are time-delayed with respect to each other and having different frequency chirp. This approach is realized by an unbalanced Mach Zehnder Interferometer (MZI) incorporating a linearlychirped fiber-Bragg-grating (LCFBG) whose group-delay-dispersion (GDD) can be tuned across a wide range. In general, tuning the GDD of the LCFBG changes the chirp rate of the generated microwave waveform and tuning the relative time-delay between the interferometer arms changes the center frequency of the generated microwave waveform. Balanced photodetection is also implemented to obtain DC-free microwave waveforms. Based on this approach, we demonstrate the generation of microwave waveforms with different center frequencies and with the chirp rates ranging from∼−126.7 GHz/ns to ∼+120.8 GHz/ns, including the zero-chirp case. & 2013 Elsevier B.V. All rights reserved.
Keywords: Microwave photonics Chirped pulse generation Fiber-Bragg-gratings Frequency-to-time mapping Dispersion
1. Introduction Leveraging on the advantageous features offered by photonic components, such as low loss, broad bandwidth, immunity to electromagnetic interference and high rate-distance product, the area of microwave photonics has attracted extensive research interest over the past few years [1–3]. With the motivation to improve the performance of existing radio-frequency (RF) systems, this has led to the development of various photonic techniques for analog-to-digital conversion [4–6], microwave filtering [7–9], instantaneous frequency measurement [10,11] and generation of high frequency continuous-wave microwave signals [12,13]. Furthermore, the area of photonic generation of arbitrary microwave waveforms has also become increasingly important due to its diverse applications such as fiber wireless communication, pulsed radar as well as electronic countermeasures. With conventional electronic arbitrary waveform generators limited to relatively low frequencies, much effort has been put into developing photonic techniques which have the capability to generate microwave waveforms at frequencies ranging from tens to hundreds of gigahertz (GHz). Some of these techniques include optical spectral
n
Corresponding author. Tel.: +65 67904527. E-mail address: [email protected] (J.H. Wong).
0030-4018/$ - see front matter & 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.optcom.2013.04.045
shaping of a broadband optical pulse followed by frequency-totime mapping through a dispersive medium [14,15], manipulating the phase and amplitude of the longitudinal modes of a modelocked laser [16,17], direct space-to-time optical pulse shaping [18,19] as well as temporal pulse shaping [20]. In most of the aforementioned techniques, the upper-end frequencies of the generated microwave waveforms are generally limited by the bandwidth of the photodetector used. In recent years, the spectral shaping and frequency-to-time mapping technique has shown promise in generating microwave waveforms with complex arbitrary profiles, such as linearlychirped waveforms that are typically characterized with a large time bandwidth product (TBWP) and widely used in modern radar, computed tomography and spread-spectrum communication systems [21]. Proposed and demonstrated in [22], Zeitouny et al. generated linearly-chirped microwave waveforms by implementing two LCFBG with different chirp rates in an unbalanced MZI based on the spectral shaping and linear frequency-to-time mapping technique. As the fabricated LCFBGs possessed a fixed second-order dispersion term, it was shown that tuning the relative time-delay between the interferometer arms would change the center frequency while keeping the chirp rate constant for the microwave waveform. Later, an alternative approach to generate linearly-chirped microwave waveforms was demonstrated by Wang et al. [23]. Unlike [22], spectral shaping is
J.H. Wong et al. / Optics Communications 304 (2013) 102–106
accomplished by a LCFBG-incorporated Sagnac loop mirror (spectral filter), which has a spectral response with an increasing or decreasing free spectral range (FSR), while linear frequency-totime mapping is realized by a dispersive medium. It was shown that by tuning the time-delay in the Sagnac loop mirror, the center frequency and chirped profile of the generated microwave waveform can be controlled. Specifically, depending on the polarity of the time-delay in the Sagnac loop mirror, the chirp rate can be tuned to either negative or positive values but its absolute value is kept constant. This limitation is clearly attributed to the nontunable nature of the spectral filter's spectral response. Besides linear frequency-to-time mapping, Ashrafi et al. have shown that nonlinear frequency-to-time mapping together with spectral shaping can also be implemented in an unbalanced MZI setup to generate linearly-chirped microwave waveforms [24]. Essentially, the nonlinear frequency-to-time mapping is induced by a dispersive medium having both the second and the third-order dispersion terms. More importantly, it has been demonstrated that by varying the relative time-delay between the interferometer arms, this scheme permits the generation of microwave waveforms whose chirp rate can be tuned to negative, zero or positive values. Despite the tunability of the chirp rate, the center frequency of the generated microwave waveforms however will change when the chirp rate is tuned. Recently, Li et al. proposed and demonstrated the generation of microwave waveforms with continuously tunable linear chirp rate [25] based on the spectral shaping and linear frequency-to-time mapping technique. In contrast to [23], the spectral filter is realized by an unbalanced MZI incorporating an optically pumped LCFBG whose spectral response can be tuned to have increasing or decreasing FSR. As the optically pumped LCFBG is written in an Erbium–Ytterbium co-doped fiber, pumping it with different pump power changes its group-delay response and this leads to a shift in the FSR. It should be emphasized that, unlike all the previously aforementioned schemes, the center frequency and chirp rate can be tuned independently. In general, for a fixed value of the second-order dispersion term of the dispersive medium which induces the linear frequency-to-time mapping, the center frequency of the microwave waveform changes with the relative time-delay between the interferometer arms, while the chirp rate is dependent on both the polarity of the relative time-delay as well as the GDD induced by the optically pumped LCFBG. It is shown experimentally that the chirp rate of the generated microwave waveforms changes from 79 to 64 GHz/ns when the injection current to the pumping laser diode increases from 0 to 100 mA. In this paper, we show analytically and experimentally the generation of linearly-chirped microwave waveforms based on an approach similar to that proposed in [25]. But instead of an optically pumped LCFBG, a LCFBG which has a programmable GDD is implemented in our scheme. Our scheme also employs balanced photodetection and offers the following advantages. The dispersion of the LCFBG can be tuned from −900 ps/nm to +900 ps/nm, enabling the generation of linearly-chirped microwave waveforms with a wider chirp tuning range. The tuning range in our scheme also covers the zero-chirp case and the generated microwave waveforms are DC-free due to the implementation of balanced photodetection. The principle of operation of our scheme and its governing mathematics is presented in Section 2, following which the measured results are presented in Section 3. Finally, we summarize the conclusions in Section 4.
2. Principle of operation Fig. 1 illustrates a schematic of the proposed scheme. An ultrashort pulse g(t) is first propagated through a length L of single-mode€ S ¼ β2 L, where β2 is the fiber (SMF) whose GDD is defined as Φ
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Fig. 1. Basic principle of operation of the proposed scheme for generating linearly chirped microwave pulses. SMF: single-mode-fiber; LCFBG: linearly chirped fiber Bragg grating; OTDL: optical tunable delay line; and BPD: balanced photodetector.
second-order dispersion term. The temporally-stretched and linearly chirped pulse is then fed to an unbalanced MZI which splits the pulse into two independent paths. As depicted in Fig. 1, the pulse propagating in the upper arm is further chirped by a LCFBG which has a magnitude response (reflection) jrðωÞj as well as a program€ F . On the other hand, after passing through an optical mable GDD of Φ tunable delay line (OTDL), the pulse propagating in the lower arm experiences a tunable time-delay Δt relative to the pulse in the upper arm. When the output pulses E1(t) and E2(t) from both arms combine, a temporal interference pattern with increasing or decreasing FSR will be generated. With the interference patterns having a phase difference of π=2 for the outputs of the MZI, followed by optical-to-electrical (OE) conversion by a balanced photodetector, a DC-free chirped microwave waveform can be obtained and observed on a sampling oscilloscope. Assuming the initial pulse to be Gaussian-shaped, so that gðtÞ ¼ expð−t 2 =2τ2o Þ, τo ¼ half pulsewidth at 1/e maximum, and following the detailed derivation in [25], the individual photocurrents I1(t) and E2(t) as illustrated in Fig. 1 are expressed as 2 2 t1 t2 t1 þ A2 G I 1 ðtÞ∝ A1 r G € € €S ΦT ΦT Φ 2 t t t t2 t2 1 1 2 þA1 A2 r − 1 G 2 cos ð1Þ G € S 2Φ €T €T €T €S 2Φ Φ Φ Φ 2 2 t1 t2 t1 þ A2 G I 2 ðtÞ∝ A1 r G €T €T €S Φ Φ Φ 2 t t t t2 t2 1 1 2 G 2 sin þA1 A2 r − 1 G € S 2Φ €T €T €T €S 2Φ Φ Φ Φ
ð2Þ
where A1 ðtÞ and A2 ðtÞ are the amplitudes of E1 ðtÞ and E2 ðtÞ, GðωÞis the Fourier transform of gðtÞ, t 1 ¼ t−Δt=2, t 2 ¼ t−Δt=2 and €T ¼Φ €F þΦ € S . Here, it should be noted that gðtÞ is real-time Φ Fourier-transformed under the assumption that the condition € T j⪡1 is satisfied. The output photocurrent Iout ðtÞ is given as jτ2o =2Φ I out ðtÞ ¼ I 1 ðtÞ−I 2 ðtÞ 2 2 t t t t2 t2 t2 t2 1 1 2 G cos ∝A1 A2 r − 1 − sin − 1 G € S 2Φ €T € S 2Φ €T €T €T €S 2Φ 2Φ Φ Φ Φ 2 t t t t2 t2 π 1 1 2 − 1 þ G cos G € S 2Φ €T 4 €T €T €S 2Φ Φ Φ Φ
∝A1 A2 r
ð3Þ
where it is observed that the instantaneous level of the generated microwave waveform oscillates according to the cos ðt 22 = € S −t 2 =2Φ € T þ π=4Þ term while its envelope is dependent on the 2Φ 1 remaining terms. The instantaneous frequency of the microwave waveform can be derived by differentiating the phase of the cosine € S −t 2 =2Φ € T þ π=4 w.r.t. time and is expressed as term ϕRF ¼ t 22 =2Φ 1 €T € T Δt € S −Φ €S þΦ 1 δϕRF 1 Φ Φ ð4Þ ¼ t− f RF ¼ € SΦ €T € SΦ €T 2π δt 2π 2 Φ Φ Clearly, fRF is observed to be linearly proportional to time and therefore the generated microwave waveform is linearly-chirped. Furthermore, the center frequency of the waveform can be
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calculated when t¼ 0 and expressed as 1 Δt Δt fo ¼ þ €S Φ €F þΦ €S 4π Φ
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ð5Þ
€S From Eq. (5), it is evident that f o is proportional to Δt. Since Φ is generally fixed, tuning Δt would change the f o of the linearlychirped microwave waveform. Furthermore, the chirp rate of the microwave waveform can be written as €F δf 1 Φ sgnðΔtÞ CR ¼ RF ¼ ð6Þ €F þΦ € S ÞΦ €S 2π δt ðΦ Unlike f o , the absolute value of the chirp rate is independent of € F. the magnitude of Δt but tunable by changing the value of Φ Moreover, both up-chirp and down-chirp are obtainable as the polarity of the chirp rate is dependent on the sign of Δt. Tuning the € F of the programmable LCFBG to zero would also enable the Φ generation of zero-chirp microwave waveforms in the proposed scheme. As the bandwidth of the LCFBG is generally narrower than the bandwidth of the pulse source, the time aperture τTA of the generated chirped microwave waveform is largely dependent on € T Þ term. Here, τTA is defined as twice the duration in the rðt 1 =Φ which the intensity increases from 0.1% to its peak value ( −30 dB) and can be calculated as € T ωo Þð−2lnð0:001ÞÞ1=2m τTA ≈2ðΦ
ð7Þ
In (7), we have assumed the LCFBG to have a 2mth order superGaussian profile whose half bandwidth at 1/e maximum is expressed ωo . Further, the TBWP of the generated chirped microwave waveform can be estimated as € FΦ €T 2ω2 ð−2lnð0:001ÞÞ1=m Φ TBWP≈ðτTA Þ2 CR≈ o ð8Þ €S π Φ Considering all other parameters as fixed and ignoring any bandwidth constraint imposed by the photodetector or the sampling oscilloscope, the value of the TBWP varies accordingly to the € F . Thus, the maximum TBWP that can be tunable parameter Φ achieved through our scheme depends on the maximum GDD that the implemented LCBG can provide.
3. Measured results Fig. 2 illustrates the experimental setup for realization of the proposed scheme. In the experiments, the initial pulse source is implemented by a homemade 68 MHz mode-locked laser which is characterized to have a full-width half-maximum (FWHM) pulsewidth of 2.5 ps, a FWHM bandwidth of 2 nm and a center wavelength of 1565.3 nm. A readily-available 27 km long SMF with standard dispersion parameterDλ ¼ ð2πc=λ2 Þβ2 ¼ 17 ps=nm=km is utilized to temporally-stretch as well as linearly chirp the pulse€ S can be calculated to be∼−596.63 ps2. Next, the train. Hence, Φ temporally-stretched pulse-train is fed to an unbalanced MZI. For the realization of the programmable LCFBG in arm 1, a single channel
Fig. 2. Experimental setup of the proposed scheme for generating linearly chirped microwave pulses. SMF: single-mode-fiber; LCFBG: linearly chirped fiber Bragg grating; OTDL: optical tunable delay line; OATT: optical attenuator; OBPF: optical bandpass filter; TDCM: tunable dispersion compensation module; and BPD: balanced photodetector.
is bandpass filtered from a commercially available tunable dispersion compensation module (TDCM) which comprises multiple-channels of similar group-delay characteristics. The magnitude response of the filtered channel which has a 1-dB bandwidth of 0.5 nm and centered at 1565.3 nm is depicted in Fig. 3. Based on two superimposed fiberBragg-gratings (FBGs) connected to an optical circulator, the disper€ F of the implemented TDCM can be tuned from sion DF ¼ ð2πc=λ2 ÞΦ −900 ps/nm to +900 ps/nm with a minimum resolution of 1 ps/nm. € F can be tuned from −1169.99 ps2 to +1169.99 ps2. In other words, Φ As for arm 2, the OTDL is used to control the tunable relative timedelay between the interferometer arms, while the tunable optical attenuator is used to maximize the fringe visibility of the interference pattern at the outputs of the MZI. The MZI outputs are sent to a balanced photodetector with a 42 GHz bandwidth for OE conversion and removal of any DC component. Finally, the generated DC-free linearly-chirped microwave waveform is RF amplified and observed using a 70 GHz sampling oscilloscope. In the first experiment, we target the generation of a zero chirp € F ¼ 0 ps2 . The microwave waveform by setting Δt ¼ 100 ps and Φ center frequency and chirp rate are calculated as 27.2 GHz and 0 GHz/ns from Eqs. (5) and (6), respectively. Fig. 4(a) illustrates the generated microwave waveform which can be observed to be DCfree. Based on the Hilbert-transform method, the corresponding instantaneous frequency is calculated and also plotted in Fig. 4(a) wherein the center frequency and chirp rate are clearly indicated. It can be observed that the generated microwave waveform has nearly zero chirp and its center frequency of ∼27.24 GHz is in close agreement with the theoretically calculated center frequency. Besides this, for comparison, a numerically simulated result based on the values of the experimental parameters is presented in Fig. 4(b), where we have assumed the LCFBG to have a 6th order super-Gaussian profile and a 1-dB bandwidth of 0.5 nm. It is seen that, in terms of the generated waveform profile, center frequency and chirp rate, the experimental and simulated results are in good agreement. Next, generation of linearly-chirped microwave waveforms based on the proposed scheme is investigated. Fig. 5(a) illustrates the experimentally generated microwave waveform when we set € F ¼ −519:94 ps2 . It can be seen that the generated Δt ¼ 0 ps and Φ microwave waveform has a nearly symmetrical profile centered at 0 GHz while its instantaneous frequency changes linearly from down-chirp (∼−126.7 GHz/ns) to up-chirp (∼+120.8 GHz/ns). Again, our experimental results agree well with the simulation results shown in Fig. 5(b). In order to generate a microwave waveform which is either linearly up-chirped or down-chirped, Δt has to be set to an appropriate value such that the zero instantaneous frequency is shifted out of the waveform's mainlobe. This is exemplified in Fig. 6(a) when we set Δt ¼ −100 ps and € F ¼ −194:98 ps2 in which a linearly down-chirped microwave Φ waveform is generated. With a center frequency of ∼26.46 GHz, the instantaneous frequency of the waveform decreases linearly from ∼41 GHz to ∼10 GHz., equivalent to a down-chirp rate
Fig. 3. Magnitude response (reflection) of the filtered channel serving as the programmable LCFBG in the proposed approach.
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Fig. 4. (a) Experimental and (b) simulated results for generation of zero chirp € F ¼ 0 ps2 ). Green/Red line: amplitude of the microwave waveform (Δt ¼ 100 ps, Φ generated microwave waveform. Blue line: instantaneous frequency of the generated microwave waveform. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
Fig. 5. (a) Experimental and (b) simulated results for generation of linearly chirped € F ¼ −519:94 ps2 ). Green/Red line: amplitude of microwave waveform (Δt ¼ 0 ps,Φ the generated microwave waveform. Blue line: instantaneous frequency of the generated microwave waveform. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
of∼−67.37 GHz/ns. According to the experimental result, the generated waveform has an time aperture of ∼473.6 ps and correspondingly, achieved a TBWP of ∼15.11. Lastly, Fig. 7(a) illustrates a generated microwave waveform which has a center frequency of 25.42 GHz and is observed to
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Fig. 6. (a) Experimental and (b) simulated results for generation of linearly chirped € F ¼ −194:98ps2 ). Green/Red line: amplitude microwave waveform (Δt ¼ −100 ps,Φ of the generated microwave waveform. Blue line: instantaneous frequency of the generated microwave waveform. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
have a linear up-chirp of ∼94.1 GHz, with the instantaneous frequency increasing from ∼4 GHz to ∼43 GHz. This is realized € F ¼ −324:96 ps2 . The time aperture when we set Δt ¼ 100 ps and Φ of the generated waveform is observed to be ∼517.2 ps, leading to a TBWP of ∼25.17. In the last two examples, the center frequency and chirp rate are again in good agreement with the corresponding simulation results shown in Figs. 6 and 7 (b), respectively. It is pertinent to mention here that, the mismatch in the amplitude between the experimental and simulated results at high instantaneous frequencies is mainly attributed to the frequency response of the RF link (comprised of the balanced photodetector, RF amplifier and RF cables) as well as the limited bandwidth of the sampling oscilloscope. Consequently, this also led to a significant mismatch in the time aperture (and TBWP) between the experimental and simulated results. Use of an RF link with a high roll-off frequency as well as a higher sampling rate oscilloscope would provide a more accurate measurement of the microwave waveform in terms of its amplitude at high frequencies as well as its corresponding time aperture (and TBWP). Furthermore, it should be emphasized that based on the LCFBG which we have used in the experiments, the chirp rate of the generated microwave waveform can be tuned continuously across a wide range, extending from ∼−176.66 GHz/ ns to ∼+176.66 GHz/ns with a minimum resolution of ∼5.69 GHz/ns. Assuming no limited bandwidth constraints and using our experimental parameters' values in Eq. (8), we can obtain a theoretically calculated maximum TBWP of ∼270.73 based on our proposed scheme. As we have implemented a fiber-based structure for our MZI and used a long length of SMF in our experiment, the stability of the generated microwave waveforms is observed to be sensitive to environmental perturbations. A potential improvement to the current scheme is to replace the fiber-based MZI with an integrated MZI incorporating a linearly chirped waveguide grating as well as using a shorter length of dispersion compensation fiber (DCF) whose β2 can be larger than a typical SMF over the same length.
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photodetection has also been proposed for the removal of DC components in the generated microwave waveform. Experimentally, we have shown the generation of several microwave waveforms with different center frequencies, chirp rates ranging from ∼−126.7 GHz/ns to ∼+120.8 GHz/ns, and no DC component. Based on the specifications of the LCFBG which we have used, our scheme has the potential to tune the chirp rate of the generated microwave waveforms continuously from ∼−176.66 GHz/ ns to ∼+176.66 GHz/ns with a minimum resolution of ∼5.69 GHz/ns. References [1] [2] [3] [4] [5]
[6] [7] [8] [9] [10] Fig. 7. (a) Experimental and (b) simulated results for generation of linearly chirped € F ¼ −324:96 ps2 ). Green/Red line: amplitude of microwave waveform (Δt ¼ 100 ps,Φ the generated microwave waveform. Blue line: instantaneous frequency of the generated microwave waveform. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
4. Conclusion In this paper, we have shown analytically and demonstrated experimentally a scheme for the generation of microwave waveforms of zero-chirp, up-chirp and down-chirp based on the temporal interference of two temporally- stretched pulses which are relatively time-delayed and have different frequency chirps. The scheme makes use of an unbalanced MZI, incorporating a tunable time delay and a LCFBG with tunable group-delay-dispersion (GDD). Through analytically derived equations, it has been shown that by tuning to appropriate values the relative time-delay between the two arms of the MZI as well as the GDD of the LCFBG, one can generate a microwave waveform with desired chirp rate and center frequency. The chirp rate can be tuned by changing the GDD of the LCFBG, while the center frequency can be tuned by changing the relative time-delay. Balanced
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