## Jammed-array wideband sawtooth filter |

Optics Express, Vol. 19, Issue 24, pp. 24563-24568 (2011)

http://dx.doi.org/10.1364/OE.19.024563

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### Abstract

We present an all-optical passive low-cost spectral filter that exhibits a high-resolution periodic sawtooth spectral pattern without the need for active optoelectronic components. The principle of the filter is the partial masking of a phased array of virtual light sources with multiply jammed diffraction orders. We utilize the filter’s periodic linear map between frequency and intensity to demonstrate fast sensitive interrogation of fiber Bragg grating sensor arrays and ultrahigh-frequency electrical sawtooth waveform generation.

© 2011 OSA

## 1. Introduction

2. G. Z. Xiao, P. Zhao, F. G. Sun, Z. G. Lu, Z. Zhang, and C. P. Grover, “Interrogating fiber Bragg grating sensors by thermally scanning a demultiplexer based on arrayed waveguide gratings,” Opt. Lett. **29**(19), 2222–2224 (2004). [CrossRef] [PubMed]

3. S. Baskar, P. N. Suganthan, N. Q. Ngo, A. Alphones, and R. T. Zheng, “Design of triangular FBG filter for sensor applications using covariance matrix adapted evolution algorithm,” Opt. Commun. **260**(2), 716–722 (2006). [CrossRef]

4. S. Bandyopadhyay, P. Biswas, A. Pal, S. K. Bhadra, and K. Dasgupta, “Empirical relations for design of linear edge filters using apodized linearly chirped fiber Bragg grating,” J. Lightwave Technol. **26**(24), 3853–3859 (2008). [CrossRef]

5. A. M. Weiner, “Femtosecond pulse shaping using spatial light modulators,” Rev. Sci. Instrum. **71**(5), 1929–1960 (2000). [CrossRef]

6. M. Shirasaki, “Large angular dispersion by a virtually imaged phased array and its application to a wavelength demultiplexer,” Opt. Lett. **21**(5), 366–368 (1996). [CrossRef] [PubMed]

8. K. Goda, K. K. Tsia, and B. Jalali, “Serial time-encoded amplified imaging for real-time observation of fast dynamic phenomena,” Nature **458**(7242), 1145–1149 (2009). [CrossRef] [PubMed]

## 2. Jammed-array wideband sawtooth (JAWS) filter

### 2.1 Theory

6. M. Shirasaki, “Large angular dispersion by a virtually imaged phased array and its application to a wavelength demultiplexer,” Opt. Lett. **21**(5), 366–368 (1996). [CrossRef] [PubMed]

*FSR*=

*c/(2d*cos

*θ*

_{1}

*-2dx*sin

*θ*

_{1}

*/f*

_{2}

*-dx*

^{2}cos

*θ*

_{1}

*/f*

_{2}

^{2}

*)*is the free spectral range (FSR) of the VIPA,

*f*

_{1}is the focal length of the cylindrical lens before the VIPA,

*f*

_{2}is the focal length of the Fourier lens,

*θ*

_{1}is the incident angle of the beam with respect to the VIPA,

*R*

_{1}and

*R*

_{2}are the reflectivity of the front and back surfaces of the VIPA,

*a*is the radius of the collimated beam prior to the cylindrical lens,

*d*is the thickness of the VIPA,

*a*is the angular frequency, and

*x*is the transverse displacement of the beam with respect to the position of the center wavelength in the plane of the intensity mask. Equation (1) is a Lorentzian function with resonance peaks when the following resonance conditions are satisfied:

*x*< 0) is covered so that only the upper part (

*x*> 0) is reflected back to the VIPA, the transfer function of the filter for the frequency within the range of one FSR is given bywhere we have only considered the dominant intensities at the resonance frequencies, used the approximate linear relation between

*x*and

*ω*from Eq. (2), assuming

*x*/

*f*

_{2}<< 1 and computed the summation by replacing it with an integral. Equation (3) repeats itself at every FSR, producing a periodic sawtooth spectral pattern with negative slopes (in the frequency domain while the sign is opposite in the wavelength domain) as shown in Fig. 1c. Likewise, if the upper part of the intensity mask (

*x*> 0) is covered, the transfer function of the filter for the frequency within the range of one FSR is given by

*T*(

*x*< 0,

*ω*) ∝ (

*da*/

*cf*

_{1})

*ω*, which gives a periodic sawtooth spectral pattern with positive slopes (in the frequency domain while the sign is opposite in the wavelength domain) as shown in Fig. 1c.

### 2.2 Experimental demonstration

*d*= 2.4 mm,

*f*

_{1}= 100 mm,

*f*

_{2}= 150 mm,

*θ*

_{1}= 4°,

*R*

_{1}= 99.5%,

*R*

_{2}= 95%, and

*a*= 1.2 mm. The measured filter response (transfer function) is shown in Fig. 2 , indicating that the experimental results are in good agreement with the aforementioned theoretical analysis. Broadband sawtooth filtration for more than 30 nm was achieved. The tooth size (bandwidth) and FSR are measured to be 0.4 nm and 0.5 nm, respectively, and hence the duty cycle of the sawtooth pattern is 80%. These parameters can easily be optimized by varying the thickness of the VIPA, depending on the requirements for various applications. While the optical loss in the filter is relatively large (~20 dB) due to aberrations in the free-space optics and inherent loss in the VIPA, it can easily be compensated by an optical amplifier such as an erbium-doped fiber amplifier (EDFA).

## 3. Utility of the JAWS filter

### 3.1 Application to fiber Bragg grating sensors

9. D. Chen, C. Shu, and S. He, “Multiple fiber Bragg grating interrogation based on a spectrum-limited Fourier domain mode-locking fiber laser,” Opt. Lett. **33**(13), 1395–1397 (2008). [CrossRef] [PubMed]

10. H. Xia, C. Wang, S. Blais, and J. Yao, “Ultrafast and precise interrogation of fiber Bragg grating sensor based on wavelength-to-time mapping incorporating higher order dispersion,” J. Lightwave Technol. **28**(3), 254–261 (2010). [CrossRef]

2. G. Z. Xiao, P. Zhao, F. G. Sun, Z. G. Lu, Z. Zhang, and C. P. Grover, “Interrogating fiber Bragg grating sensors by thermally scanning a demultiplexer based on arrayed waveguide gratings,” Opt. Lett. **29**(19), 2222–2224 (2004). [CrossRef] [PubMed]

10. H. Xia, C. Wang, S. Blais, and J. Yao, “Ultrafast and precise interrogation of fiber Bragg grating sensor based on wavelength-to-time mapping incorporating higher order dispersion,” J. Lightwave Technol. **28**(3), 254–261 (2010). [CrossRef]

### 3.2 Application to ultrahigh-frequency sawtooth waveform generation

## 4. Summary

## Acknowledgements

## References and links

1. | H. A. Macleod, |

2. | G. Z. Xiao, P. Zhao, F. G. Sun, Z. G. Lu, Z. Zhang, and C. P. Grover, “Interrogating fiber Bragg grating sensors by thermally scanning a demultiplexer based on arrayed waveguide gratings,” Opt. Lett. |

3. | S. Baskar, P. N. Suganthan, N. Q. Ngo, A. Alphones, and R. T. Zheng, “Design of triangular FBG filter for sensor applications using covariance matrix adapted evolution algorithm,” Opt. Commun. |

4. | S. Bandyopadhyay, P. Biswas, A. Pal, S. K. Bhadra, and K. Dasgupta, “Empirical relations for design of linear edge filters using apodized linearly chirped fiber Bragg grating,” J. Lightwave Technol. |

5. | A. M. Weiner, “Femtosecond pulse shaping using spatial light modulators,” Rev. Sci. Instrum. |

6. | M. Shirasaki, “Large angular dispersion by a virtually imaged phased array and its application to a wavelength demultiplexer,” Opt. Lett. |

7. | S. Xiao, A. M. Weiner, and C. L. Lin, “A dispersion law for virtually imaged phased array spectral dispersers based on paraxial wave theory,” IEEE J. Quantum Electron. |

8. | K. Goda, K. K. Tsia, and B. Jalali, “Serial time-encoded amplified imaging for real-time observation of fast dynamic phenomena,” Nature |

9. | D. Chen, C. Shu, and S. He, “Multiple fiber Bragg grating interrogation based on a spectrum-limited Fourier domain mode-locking fiber laser,” Opt. Lett. |

10. | H. Xia, C. Wang, S. Blais, and J. Yao, “Ultrafast and precise interrogation of fiber Bragg grating sensor based on wavelength-to-time mapping incorporating higher order dispersion,” J. Lightwave Technol. |

11. | J. H. Reed, |

12. | B. Jalali, P. V. Kelkar, and V. Saxena, “Photonic arbitrary waveform generator,” Proc. Lasers Electro-Opt. Soc. |

**OCIS Codes**

(120.2440) Instrumentation, measurement, and metrology : Filters

(280.0280) Remote sensing and sensors : Remote sensing and sensors

**ToC Category:**

Optical Devices

**History**

Original Manuscript: August 25, 2011

Revised Manuscript: October 7, 2011

Manuscript Accepted: October 9, 2011

Published: November 16, 2011

**Citation**

Zhongwei Tan, Chao Wang, Keisuke Goda, Omer Malik, and Bahram Jalali, "Jammed-array wideband sawtooth filter," Opt. Express **19**, 24563-24568 (2011)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-24-24563

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### References

- H. A. Macleod, Thin-film optical filters (CRC Press, 2010)
- G. Z. Xiao, P. Zhao, F. G. Sun, Z. G. Lu, Z. Zhang, and C. P. Grover, “Interrogating fiber Bragg grating sensors by thermally scanning a demultiplexer based on arrayed waveguide gratings,” Opt. Lett.29(19), 2222–2224 (2004). [CrossRef] [PubMed]
- S. Baskar, P. N. Suganthan, N. Q. Ngo, A. Alphones, and R. T. Zheng, “Design of triangular FBG filter for sensor applications using covariance matrix adapted evolution algorithm,” Opt. Commun.260(2), 716–722 (2006). [CrossRef]
- S. Bandyopadhyay, P. Biswas, A. Pal, S. K. Bhadra, and K. Dasgupta, “Empirical relations for design of linear edge filters using apodized linearly chirped fiber Bragg grating,” J. Lightwave Technol.26(24), 3853–3859 (2008). [CrossRef]
- A. M. Weiner, “Femtosecond pulse shaping using spatial light modulators,” Rev. Sci. Instrum.71(5), 1929–1960 (2000). [CrossRef]
- M. Shirasaki, “Large angular dispersion by a virtually imaged phased array and its application to a wavelength demultiplexer,” Opt. Lett.21(5), 366–368 (1996). [CrossRef] [PubMed]
- S. Xiao, A. M. Weiner, and C. L. Lin, “A dispersion law for virtually imaged phased array spectral dispersers based on paraxial wave theory,” IEEE J. Quantum Electron.40(4), 420–426 (2004). [CrossRef]
- K. Goda, K. K. Tsia, and B. Jalali, “Serial time-encoded amplified imaging for real-time observation of fast dynamic phenomena,” Nature458(7242), 1145–1149 (2009). [CrossRef] [PubMed]
- D. Chen, C. Shu, and S. He, “Multiple fiber Bragg grating interrogation based on a spectrum-limited Fourier domain mode-locking fiber laser,” Opt. Lett.33(13), 1395–1397 (2008). [CrossRef] [PubMed]
- H. Xia, C. Wang, S. Blais, and J. Yao, “Ultrafast and precise interrogation of fiber Bragg grating sensor based on wavelength-to-time mapping incorporating higher order dispersion,” J. Lightwave Technol.28(3), 254–261 (2010). [CrossRef]
- J. H. Reed, An introduction to ultra wideband communication systems (Prentice-Hall, 2005)
- B. Jalali, P. V. Kelkar, and V. Saxena, “Photonic arbitrary waveform generator,” Proc. Lasers Electro-Opt. Soc.1, 253–254 (2001).

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