## Photonic arbitrary waveform generation based on crossed frequency to time mapping |

Optics Express, Vol. 21, Issue 5, pp. 6488-6496 (2013)

http://dx.doi.org/10.1364/OE.21.006488

Acrobat PDF (1170 KB)

### Abstract

Microwave photonic arbitrary waveform generation based on incoherent frequency-to-time-mapping (FTTM) accompanied by intersymbol interference, so called crossed FTTM (CFTTM). The pulse shape can be defined and tuned by properly adjusting the spectrum shaper (symbol shape) and the degree of intersymbol interference. UWB-, triangular-, rectangle-, comb- and user-defined pulse shapes are experimentally obtained.

© 2013 OSA

## 1. Introduction

1. I.-S. Lin, J.-D. McKinney, and A.-M. Weiner, “Photonic synthesis of broadband microwave arbitrary waveforms applicable to ultra-wide-band communication,” IEEE Microw. Wirel. Compon. Lett. **15**(4), 226–228 (2005). [CrossRef]

2. S. Cundiff and A.-M. Weiner, “Optical arbitrary waveform generation,” Nat. Photonics **4**(11), 760–766 (2010). [CrossRef]

3. M.-H. Khan, H. Shen, Y. Xuan, L. Zhao, S.-J. Xiao, D.-E. Leaird, A.-M. Weiner, and M.-H. Qi, “Ultrabroad bandwidth arbitrary radio frequency waveform generation with a silicon photonic chip-based spectral shaper,” Nat. Photonics **4**(2), 117–122 (2010). [CrossRef]

4. C. Wang and J.-P. Yao, “Large time-bandwidth product microwave arbitrary waveform generation using spatially discrete chirped fiber Bragg grating,” J. Lightwave Technol. **28**(11), 1652–1660 (2010). [CrossRef]

5. N.-K. Fontaine, D.-J. Geisler, R.-P. Scott, T. He, J.-P. Heritage, and S.-J.-B. Yoo, “Demonstration of high-fidelity dynamic optical arbitrary waveform generation,” Opt. Express **18**(22), 22988–22995 (2010). [CrossRef] [PubMed]

6. J.-T. Willits, A.-M. Weiner, and S.-T. Cundiff, “Theory of rapid-update line-by-line pulse shaping,” Opt. Express **16**(1), 315–327 (2008). [CrossRef] [PubMed]

7. C. Dorrer, “Statistical analysis of incoherent pulse shaping,” Opt. Express **17**(5), 3341–3352 (2009). [CrossRef] [PubMed]

8. V. Torres-Company, J. Lancis, P. Andrés, and L. R. Chen, “20 GHz arbitrary radio-frequency waveform generator based on incoherent pulse shaping,” Opt. Express **16**(26), 21564–21569 (2008). [CrossRef] [PubMed]

9. Z. Jiang, C. Huang, D.-E. Leaird, and A.-M. Weiner, “Optical arbitrary waveform processing of more than 100 spectral comb lines,” Nat. Photonics **1**(8), 463–467 (2007). [CrossRef]

11. A.-L. Zhang and C.-X. Li, “Dynamic optical arbitrary waveform generation with amplitude controlled by interference of two FBG arrays,” Opt. Express **20**(21), 23074–23081 (2012). [CrossRef] [PubMed]

12. M. Bolea, J. Mora, B. Ortega, and J. Capmany, “Nonlinear dispersion-based incoherent photonic processing for microwave pulse generation with full reconfigurability,” Opt. Express **20**(6), 6728–6736 (2012). [CrossRef] [PubMed]

13. M.-A. Muriel, J. Azaña, and A. Carballar, “Real-time Fourier transformer based on fiber gratings,” Opt. Lett. **24**(1), 1–3 (1999). [CrossRef] [PubMed]

16. C. Wang, M. Li, and J.-P. Yao, “Continuously tunable photonic microwave frequency multiplication by use of an unbalanced temporal pulse shaping system,” IEEE Photon. Technol. Lett. **22**(17), 1285–1287 (2010). [CrossRef]

## 2. Principle of crossed frequency to time mapping

17. V. Torres-Company, J. Lancis, P. Andres, and L.-R. Chen, “Reconfigurable RF-waveform generation based on incoherent-filter design,” J. Lightwave Technol. **26**(15), 2476–2483 (2008). [CrossRef]

18. C. Dorrer, “Temporal van Cittert-Zernike theorem and its application to the measurement of chromatic dispersion,” J. Opt. Soc. Am. B **21**(8), 1417–1423 (2004). [CrossRef]

20. Y. Park and J. Azaña, “Optical signal processors based on a time-spectrum convolution,” Opt. Lett. **35**(6), 796–798 (2010). [CrossRef] [PubMed]

*Ф*is the total group delay dispersion (GDD) parameter(ps/nm),

_{2}*σ*and

_{ω}*Δω*is the bandwidth of the spectrally incoherent light source and the external modulator for time-gating function respectively .

*S(ω)*is the energy spectrum of the incoherent source (e.g. ASE) centered at the baseband,

*F(ω)*denotes the complex transfer function of the TFM and

*M(ω)*is the spectral complex transfer function of the external modulator for time-gating. When Eq. (1) is satisfied, the output intensity can be written as

*ΔT*) is proportional to the frequency bandwidth (

*Δλ*) of the spectral shape as

*1/B)*has to be limited by using the criterion

*BΔT<1*(similar to the concept of bit-rate capacity). The dispersion coefficient

*Ф*has to satisfy

_{2}*BΔT>1*, we have

*BΔT*. Note that the value of

*ΔT*is fixed once the spectrum shape and the dispersion parameter is pre-defined, and the degree of ISI can be determined by the parameter of

*B*. Obviously, when the parameter

*B*of the FTTM is set as

*B*, the output pulse shape would be quite different. The output pulse shape of the CFTTM is the superposition of several symbol shapes (spectrum shape of the input). Meanwhile the shape of an arbitrary signal can be regarded as the synthesis of certain basic shapes with different combinations, therefore photonic arbitrary waveform generation based on the CFTTM could be achieved with simplified spectrum manipulation in conventional FTTM-based schemes.

_{1}>B_{2}## 3. Waveform synthesis

*BΔT*). Figure 2 show typical configurations to tune the pulse shape. The solid lines of Fig. 2(a) are the synthetic waveforms of two triangle-shaped symbols with different degree of ISI (

*B*and

_{1}ΔT, 2/B_{1}ΔT*3/B*). Therefore the output pulse shape can be tuned by adjusting the period of the pulse source (i.e.

_{1}ΔT*1/B*). Assuming that the shape of the symbol is merely changed into notch-shape, we could obtain totally different synthetic waveforms as shown Fig. 2(b). Therefore, by adjusting the spectrum shaper to filter out different symbol shape, the output pulse shape could be tuned. Note that the bandwidth of the spectrum (

*Δλ)*could affect the degree of ISI through the parameter of

*ΔT*. Moreover, if

*B*as illustrated in Fig. 2(c)

_{1}≠B_{2}_{,}the non-uniform degree of ISI could be introduced to facilitate the arbitrary pulse shaping. The synthesis of three triangle-shaped symbols with uniform (left) and nonuniform (right) distributions of ISI could end with two different pulse shapes. Therefore the period of pulse (

*1/B*) might also be set as unequal to introduce the non-uniform ISI for the pulse shaping. Such approaches could be utilized either individually or by combinations for arbitrary waveform generation in accordance with specific environment requirements.

## 4. Experiment

*1/B*. The symbol shaper is composed of an array of FBGs with different characteristics (e.g. the central-wavelength of 1555.3, 1556.2 nm; the bandwidth of 0.1, 0.2 nm and the reflectivity of 85%, 70%, respectively) and an optical tunable bandpass filter (TBF). By varying the parameters of the TBF (i.e. the bandwidth and central wavelength), the symbol shape could be tuned. Here, a 10-km SMF is used as the first-order linear dispersive element with the total GDD (

*Ф*) value of 220 ps/nm

_{2}_{.}In our experiment, the light from the ASE source is intensity-modulated by a Mach-Zehnder modulator (MZM) driven by a user-defined RF signal, and then launched into the tunable spectrum shaper to filter out the desired spectrum shape. After the CFTTM process in the SMF, an arbitrary-shaped waveform can be generated at the output of PD. A sampling oscilloscope (Agilent 86100C)with eight-time averaging is used to measure the generated waveforms. In addition, an EDFA is used to compensate the power loss of the system.

*1/B = 400 ps*) and the TBF with its central wavelength of ~1556.3 nm and its bandwidth of ~1.3 nm is chosen. Figure 4(a) is obtained symbol shape (left) and the corresponding averaged notch-shaped electrical pulse (right). It can be observed that the generated temporal pulse shape is similar to the spectrum shape and its full width (

*ΔT*) after a 10-km SMF is ~286 ps. Thus, the corresponding value of

*BΔT*is ~0.71. The requirement of CFTTM (

*BΔT >1*) can’t be met, therefore the obtained optical pulse in average is a scaled copy of the spectrum based on the conventional FTTM process.

*1/B = 200 ps)*, Fig. 4(b) shows the measured optical spectrum after the spectrum shaper (left) and the generated triangle-shaped electrical pulse with averaged (right). As indicated in the insets of the left figure, the corresponding degree of ISI (

*BΔT)*is about 1.43, meeting the requirements for CFTTM, therefore the output pulse shape is not only determined by the spectrum shape, but also the degree of ISI. In addition to the results in Fig. 4(b), if we slightly adjust the central wavelength of the TBF to left or right (e.g. ~0.2 nm), we could easily obtain electrical averaged sawtooth-shaped pulses with positive ramp and negative ramp as shown in Figs. 5(a) and 5(b), respectively.

*BΔT*) for all cases is ~1.1 using different combinations of the period of the pulse source (

*1/B)*and the bandwidth of the TBF (i.e.

*Δλ,*which has a fixed relationship with the pulse width

*ΔT*): (i) For the monocycle-shaped pulse generation, we adjust the full-bandwidth of the TBF to be ~2 nm and the central wavelength to be ~1556.5 nm (positive) and ~1555.8 nm (negative). The period of the pulse source (

*1/B)*is ~400 ps while the symbol shapes are different. (ii) For the doublet-shaped pulse generation, we adjust the bandwidth of symbol to be ~2.2 nm (the corresponding value of

*ΔT*is ~440 ps), and tune the bit-rate of the driving RF signal to be 9 Gbit/s (the corresponding period of the pulse source

*1/B*is 484 ps).

*1/B*) with the same symbol shape (spectrum shape) for pulse shaping is verified. Figure 7 is the measured spectrum shape with full-bandwidth of ~1.9 nm for all cases (

*ΔT≈418 ps*). Three output signals with different shapes in average are generated: (i) if we fix the driving RF signal of MZM at 10 Gbit/s with the pattern of “100100”, a rectangle-shaped electrical pulse train could be obtained [Fig. 8(a) ], here

*1/B≈300 ps and BΔT≈1.4*; (ii) if the RF pattern is adjust to be “101010” (

*1/B≈200 ps, BΔT≈2.1)*, the shape of generated pulse is changed into the comb one as shown in Fig. 8(b). Note that both cases are still under a uniform ISI distribution. (iii) If we set the driving RF signal at 10-Gbit/s with a fixed pattern of “10011000”, there will be a relatively weak ISI (

*1/B*,

_{1}≈200 ps*B*) for the first two pulses and a strong ISI

_{1}ΔT≈2.1*(*1/B

*for the last two pulses. i.e. the ISI distribution is not uniform any more. The generated electrical pulses are illustrated in Fig. 8(c). Therefore, it is feasible to introduce the non-uniform distribution of ISI for the arbitrary waveform generation by proper selection of the ISI distribution and the driving signals.*

_{1}≈100 ps,B_{2}ΔT≈4.2)## 5. Analysis of key parameters

*ΔT*(

*ΔT = χΔλ*) and the ISI (

*BΔT*). Once the pulse shape is defined, the values of

*Δλ*and

*BΔT*are fixed. In order to tune the pulse width, we have to properly adjust the dispersion element (GDD) and the

*1/B*value at the same time. The adjustment of the GDD value is for the pulse width, and varying the 1/B value is for the shape preserving (i.e. fixed

*BΔT*). For example, under the same experimental parameters in Figs. 7 and 8 except that the pattern is set as “100010000000000”, the pulse width of generated doublet-like pulse is

*2ΔT-1/B*with the ISI (

*BΔT≈2*) fixed (see the inserts of Fig. 9 ). By properly adjusting the values of the total GDD amount and the 1/B period, we could demonstrate the tunability of the pulse width for the doublet-like pulse as shown in Fig. 9. The inserts of Fig. 9 are waveforms and electrical spectra of two generated doublet-like pulses with the pulse-width of ~780(a-1, a-2) and ~1100 (b-1, b-2) ps, respectively. Due to the limitation of modulated RF signal (the maximum bit-rate of 12.5 Gbit/s) and the bandwidth of the MZM, the available maximum RF bandwidth is ~10 GHz [17

17. V. Torres-Company, J. Lancis, P. Andres, and L.-R. Chen, “Reconfigurable RF-waveform generation based on incoherent-filter design,” J. Lightwave Technol. **26**(15), 2476–2483 (2008). [CrossRef]

## 6. Discussion

*ΔT*, as well as the bandwidth of the light source and the dispersion amount; iii) although we demonstrate such approach based on incoherent light source due to the advantages of simplicity and low cost [8

8. V. Torres-Company, J. Lancis, P. Andrés, and L. R. Chen, “20 GHz arbitrary radio-frequency waveform generator based on incoherent pulse shaping,” Opt. Express **16**(26), 21564–21569 (2008). [CrossRef] [PubMed]

## 7. Conclusion

*BΔT*(the degree of intersymbol interference) and the spectrum shape (the shape of symbol).

## Acknowledgments

## References and links

1. | I.-S. Lin, J.-D. McKinney, and A.-M. Weiner, “Photonic synthesis of broadband microwave arbitrary waveforms applicable to ultra-wide-band communication,” IEEE Microw. Wirel. Compon. Lett. |

2. | S. Cundiff and A.-M. Weiner, “Optical arbitrary waveform generation,” Nat. Photonics |

3. | M.-H. Khan, H. Shen, Y. Xuan, L. Zhao, S.-J. Xiao, D.-E. Leaird, A.-M. Weiner, and M.-H. Qi, “Ultrabroad bandwidth arbitrary radio frequency waveform generation with a silicon photonic chip-based spectral shaper,” Nat. Photonics |

4. | C. Wang and J.-P. Yao, “Large time-bandwidth product microwave arbitrary waveform generation using spatially discrete chirped fiber Bragg grating,” J. Lightwave Technol. |

5. | N.-K. Fontaine, D.-J. Geisler, R.-P. Scott, T. He, J.-P. Heritage, and S.-J.-B. Yoo, “Demonstration of high-fidelity dynamic optical arbitrary waveform generation,” Opt. Express |

6. | J.-T. Willits, A.-M. Weiner, and S.-T. Cundiff, “Theory of rapid-update line-by-line pulse shaping,” Opt. Express |

7. | C. Dorrer, “Statistical analysis of incoherent pulse shaping,” Opt. Express |

8. | V. Torres-Company, J. Lancis, P. Andrés, and L. R. Chen, “20 GHz arbitrary radio-frequency waveform generator based on incoherent pulse shaping,” Opt. Express |

9. | Z. Jiang, C. Huang, D.-E. Leaird, and A.-M. Weiner, “Optical arbitrary waveform processing of more than 100 spectral comb lines,” Nat. Photonics |

10. | V. Torres-Company, J. Lancis, and P. Andrés, “Arbitrary waveform generator based on all-incoherent pulse shaping,” IEEE Photon. Technol. Lett. |

11. | A.-L. Zhang and C.-X. Li, “Dynamic optical arbitrary waveform generation with amplitude controlled by interference of two FBG arrays,” Opt. Express |

12. | M. Bolea, J. Mora, B. Ortega, and J. Capmany, “Nonlinear dispersion-based incoherent photonic processing for microwave pulse generation with full reconfigurability,” Opt. Express |

13. | M.-A. Muriel, J. Azaña, and A. Carballar, “Real-time Fourier transformer based on fiber gratings,” Opt. Lett. |

14. | H.-Y. Jiang, L.-S. Yan, J. Ye, W. Pan, B. Luo, Z.-Y. Chen, X.-H. Zou, and X.-S. Yao, “Photonic generation of impulse ultrawideband signal with switchable shapes and polarities based on frequency to time mapping,” Opt. Lett. |

15. | J. Ye, L.-S. Yan, W. Pan, B. Luo, X. Zou, A.-L. Yi, and S. Yao, “Photonic generation of triangular-shaped pulses based on frequency-to-time conversion,” Opt. Lett. |

16. | C. Wang, M. Li, and J.-P. Yao, “Continuously tunable photonic microwave frequency multiplication by use of an unbalanced temporal pulse shaping system,” IEEE Photon. Technol. Lett. |

17. | V. Torres-Company, J. Lancis, P. Andres, and L.-R. Chen, “Reconfigurable RF-waveform generation based on incoherent-filter design,” J. Lightwave Technol. |

18. | C. Dorrer, “Temporal van Cittert-Zernike theorem and its application to the measurement of chromatic dispersion,” J. Opt. Soc. Am. B |

19. | V. Torres-Company, J. Lancis, and P. Andrés, “Incoherent frequency-to-time mapping: application to incoherent pulse shaping,” J. Opt. Soc. Am. A |

20. | Y. Park and J. Azaña, “Optical signal processors based on a time-spectrum convolution,” Opt. Lett. |

**OCIS Codes**

(230.0250) Optical devices : Optoelectronics

(350.4010) Other areas of optics : Microwaves

(060.5625) Fiber optics and optical communications : Radio frequency photonics

**ToC Category:**

Fiber Optics and Optical Communications

**History**

Original Manuscript: January 8, 2013

Revised Manuscript: February 23, 2013

Manuscript Accepted: February 25, 2013

Published: March 7, 2013

**Citation**

H.-Y. Jiang, L.-S. Yan, Y.-F. Sun, J. Ye, W. Pan, B. Luo, and X.-H. Zou, "Photonic arbitrary waveform generation based on crossed frequency to time mapping," Opt. Express **21**, 6488-6496 (2013)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-5-6488

Sort: Year | Journal | Reset

### References

- I.-S. Lin, J.-D. McKinney, and A.-M. Weiner, “Photonic synthesis of broadband microwave arbitrary waveforms applicable to ultra-wide-band communication,” IEEE Microw. Wirel. Compon. Lett.15(4), 226–228 (2005). [CrossRef]
- S. Cundiff and A.-M. Weiner, “Optical arbitrary waveform generation,” Nat. Photonics4(11), 760–766 (2010). [CrossRef]
- M.-H. Khan, H. Shen, Y. Xuan, L. Zhao, S.-J. Xiao, D.-E. Leaird, A.-M. Weiner, and M.-H. Qi, “Ultrabroad bandwidth arbitrary radio frequency waveform generation with a silicon photonic chip-based spectral shaper,” Nat. Photonics4(2), 117–122 (2010). [CrossRef]
- C. Wang and J.-P. Yao, “Large time-bandwidth product microwave arbitrary waveform generation using spatially discrete chirped fiber Bragg grating,” J. Lightwave Technol.28(11), 1652–1660 (2010). [CrossRef]
- N.-K. Fontaine, D.-J. Geisler, R.-P. Scott, T. He, J.-P. Heritage, and S.-J.-B. Yoo, “Demonstration of high-fidelity dynamic optical arbitrary waveform generation,” Opt. Express18(22), 22988–22995 (2010). [CrossRef] [PubMed]
- J.-T. Willits, A.-M. Weiner, and S.-T. Cundiff, “Theory of rapid-update line-by-line pulse shaping,” Opt. Express16(1), 315–327 (2008). [CrossRef] [PubMed]
- C. Dorrer, “Statistical analysis of incoherent pulse shaping,” Opt. Express17(5), 3341–3352 (2009). [CrossRef] [PubMed]
- V. Torres-Company, J. Lancis, P. Andrés, and L. R. Chen, “20 GHz arbitrary radio-frequency waveform generator based on incoherent pulse shaping,” Opt. Express16(26), 21564–21569 (2008). [CrossRef] [PubMed]
- Z. Jiang, C. Huang, D.-E. Leaird, and A.-M. Weiner, “Optical arbitrary waveform processing of more than 100 spectral comb lines,” Nat. Photonics1(8), 463–467 (2007). [CrossRef]
- V. Torres-Company, J. Lancis, and P. Andrés, “Arbitrary waveform generator based on all-incoherent pulse shaping,” IEEE Photon. Technol. Lett.18(24), 2626–2628 (2006). [CrossRef]
- A.-L. Zhang and C.-X. Li, “Dynamic optical arbitrary waveform generation with amplitude controlled by interference of two FBG arrays,” Opt. Express20(21), 23074–23081 (2012). [CrossRef] [PubMed]
- M. Bolea, J. Mora, B. Ortega, and J. Capmany, “Nonlinear dispersion-based incoherent photonic processing for microwave pulse generation with full reconfigurability,” Opt. Express20(6), 6728–6736 (2012). [CrossRef] [PubMed]
- M.-A. Muriel, J. Azaña, and A. Carballar, “Real-time Fourier transformer based on fiber gratings,” Opt. Lett.24(1), 1–3 (1999). [CrossRef] [PubMed]
- H.-Y. Jiang, L.-S. Yan, J. Ye, W. Pan, B. Luo, Z.-Y. Chen, X.-H. Zou, and X.-S. Yao, “Photonic generation of impulse ultrawideband signal with switchable shapes and polarities based on frequency to time mapping,” Opt. Lett.37(24), 5052–5054 (2012).
- J. Ye, L.-S. Yan, W. Pan, B. Luo, X. Zou, A.-L. Yi, and S. Yao, “Photonic generation of triangular-shaped pulses based on frequency-to-time conversion,” Opt. Lett.36(8), 1458–1460 (2011). [CrossRef] [PubMed]
- C. Wang, M. Li, and J.-P. Yao, “Continuously tunable photonic microwave frequency multiplication by use of an unbalanced temporal pulse shaping system,” IEEE Photon. Technol. Lett.22(17), 1285–1287 (2010). [CrossRef]
- V. Torres-Company, J. Lancis, P. Andres, and L.-R. Chen, “Reconfigurable RF-waveform generation based on incoherent-filter design,” J. Lightwave Technol.26(15), 2476–2483 (2008). [CrossRef]
- C. Dorrer, “Temporal van Cittert-Zernike theorem and its application to the measurement of chromatic dispersion,” J. Opt. Soc. Am. B21(8), 1417–1423 (2004). [CrossRef]
- V. Torres-Company, J. Lancis, and P. Andrés, “Incoherent frequency-to-time mapping: application to incoherent pulse shaping,” J. Opt. Soc. Am. A24(3), 888–894 (2007). [CrossRef] [PubMed]
- Y. Park and J. Azaña, “Optical signal processors based on a time-spectrum convolution,” Opt. Lett.35(6), 796–798 (2010). [CrossRef] [PubMed]

## Cited By |
Alert me when this paper is cited |

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article | Next Article »

OSA is a member of CrossRef.