Procedia Engineering 140 ( 2016 ) 171 – 175

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1877-7058 © 2016 Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).Selection and/or peer-review under responsibility of the scientific committee of Symposium 2015 ICMATdoi: 10.1016/j.proeng.2016.07.341

ScienceDirect

MRS Singapore – ICMAT Symposia Proceedings

8th International Conference on Materials for Advanced Technologies

Wavelength Corrected Ultrafast Pulse Characterization Using Frequency Resolved Optical Gating

Jiayun Liua,*, Biao Suna,b, Jiaqi Luoa,b, Xia Yua, Hao Lia aSingapore Institute of ManufacturingTtechnology,71 Nanyang Drive, Singapore 638075, Singapore

bNanyang Technological University,50 Nanyang Avenue, Singapore 639798, Singapore

Abstract

Frequency Resolved Optical Gating (FROG) has been used extensively for ultrafast pulse characterization. While the reconstructed electric field can be uniquely determined from the FROG trace, there is no real time calibration of wavelength dependent nonlinearity that affects the FROG trace in the reconstruction algorithm. This modifies the measured FROG trace which ultimately affects the reconstructed electric field. In this paper, we proposed an extension to the FROG setup through an optical spectrum analyser (OSA) for real time calibration. Through the addition of an OSA, the nonlinearity can be compensated to get the original FROG trace which allows for the accurate reconstruction of the ultrafast pulse. © 2015 The Authors. Published by Elsevier Ltd. Selection and/or peer-review under responsibility of the scientific committee of Symposium 2015 ICMAT.

Keywords: Autocorrelation;ultrashort;phase-retrevial;auto-spectrogram

1. Introduction

Femtosecond laser has seen wide applications in the field of biomedical which uses ultrafast pulse for deep tissue imaging and in vivo brain imaging [1]. In such applications, the pulse width is of paramount importance which greatly affects the performance of these applications. Therefore, the maintenance and characterization of the pulse

* Corresponding author. Tel.: +65-67932126; fax: +65-67916377.

E-mail address: liujy@SIMTech.edu.sg

© 2016 Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).Selection and/or peer-review under responsibility of the scientific committee of Symposium 2015 ICMAT

172 Jiayun Liu et al. / Procedia Engineering 140 ( 2016 ) 171 – 175

shape is crucial for ultrafast laser applications. Ultrafast pulse width measurement can be achieved through the use of an autocorrelator while Frequency Resolved Optical Gating (FROG) is capable of phase measurement which allows for full pulse characterization [2].

FROG is commonly used for pulse characterization due to the capability of uniquely determine an ultrashort pulse. Despite the capability of FROG, the wavelength range of the pulse is limited due to phase matching conditions [3]. In this paper, we showed that the wavelength dependent nonlinearity of the crystal causes the measured spectrogram to differ which affects the result of the reconstructed pulse. We further proposed a feedback mechanism by measuring the spectrum of the pulse which correlates this information into the reconstruction algorithm.

2. Wavelength Dependent Nonlinearity

2.1. Second Harmonic Generation (SHG) in crystal

In the perturbative regime, the polarization density due to an external electric field can be expressed as

(1)

where is the permittivity of free space, E is the applied external field and corresponds to the different nonlinearity order [4]. Using equation 1, the wave equation of the generated second harmonic can be expressed as

(2)

where E is the incident electric field, is the permittivity of the material, is the permittivity of free space, c is the speed of light and is the nonlinear part of the polarization density [4]. Using (2) and the slowly varying amplitude approximation, the intensity of the SHG can be expressed as

(3)

where is the second order susceptibility tensor, is the angular frequency of the generated second harmonic, L is the length of the nonlinear crystal and is the phase difference. is the intensity and is the refractive index where the subscript denotes the quantity associated to the fundamental and SHG [4]. The response curve of the crystal expressed by (3) is plotted in figure 1. The generated second harmonic spectrum is the product of the response curve of the crystal and the field spectrum. Therefore the generated second harmonic spectrum is modified by the response curve of the crystal.

Fig. 1. SHG response curve of crystal.

173 Jiayun Liu et al. / Procedia Engineering 140 ( 2016 ) 171 – 175

2.2. FROG trace

In SHG-FROG, a pulse is split using a beam splitter and one of the pulse travels through a variable delay line and the pulses are subsequently focused into a nonlinear crystal for SHG. The generated harmonic is detected by an optical spectrum analyzer (OSA) which measures the spectrum of the SHG at different time delay. The resulting spectrogram or FROG trace allows for reconstruction of the original electric field [5].

The FROG reconstruction algorithm [6] allows for unique reconstruction of the electric field due to the property of the 2D phase retrieval [7]. However, due to this wavelength dependent response curve of the crystal, the measured FROG trace will differ from that of the original FROG trace. This effect is illustrated in figure 2 where an original FROG trace depicted by figure 2 (a) is assumed and the FROG trace is multiplied by the response curve in figure 1. The modified FROG trace is shown in figure 2 (b) where additional peak intensity appears which is not present in the original FROG trace.

Fig. 2. (a) Original FROG trace. (b) FROG trace of modified field.

2.3. Electric field reconstruction

The electric field is reconstructed using the reconstruction algorithm based on the two previous FROG traces and the calculated electric field is shown in figure 3. From figure 3, the electric field reconstructed based on the modified FROG trace is represented in solid while the electric field reconstructed by the original FROG trace is shown in dotted line. Therefore, the response curve of the crystal affects the measured FROG trace which eventually affects the reconstruction electric field. The effect of the response curve on the spectrum is clearly depicted in figure 3 b where the original spectrum is denoted by dotted line and the modified spectrum is denoted by the solid line. The drop in spectra intensity at shorter wavelength is due to the lower SHG conversion efficiency of the crystal according to figure 1.

Fig. 3. (a) Reconstructed original (solid line) and modified (dotted line) electric field. (b) Spectrum of original (dotted line) and

modified spectrum (solid line).

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3. Proposed experimental setup

As mentioned previously, the nonlinearity affects the FROG trace and this problem is especially prominent if the field to be characterized has a broad spectrum. We proposed to include an additional OSA before the FROG to measure the spectrum of the pulse as shown in figure 4. This allows for real time calibration of the nonlinearity effect induced by the crystal mentioned previously.

Fig.4. Proposed setup with OSA measurement incorporated into FROG trace.

The OSA will measure the spectrum of the pulse while FROG will acquire the spectrogram of the pulse . By obtaining the spectrum information from both the OSA and FROG, the response curve of the crystal can be characterized. The response curve is calculated by dividing the spectrum measured by FROG with that measured by the OSA.

By acquiring the response curve, the FROG trace can be corrected by including the response curve into the reconstruction algorithm [7] as shown in figure 5. Additionally, by allowing FROG to characterize broadband spectrum pulse, the sensitivity of FROG can be increased as it allows for a thicker nonlinear crystal to be used. Due to the quadratic dependence of the SHG intensity to the crystal length, the minimum pulse energy required can also be quadratically reduced.

Fig. 5. FROG reconstruction algorithm with crystal’s response curve.

4. Conclusion

In this paper, we showed that the response curve of the nonlinear crystal used in FROG affects the FROG trace which ultimately affects the reconstructed electric field. We proposed to correct for this effect by measuring the spectrum of the pulse with an OSA and calculate the response curve. Therefore, by knowing the response curve, we can compensate for this effect and reconstruct the original electric field. By knowing the response curve and compensate the measured FROG trace correspondingly, the minimum required pulse energy can be reduced due to stronger SHG signal generated using a thicker crystal.

175 Jiayun Liu et al. / Procedia Engineering 140 ( 2016 ) 171 – 175

Acknowledgements

This research is funded by A*STAR SERC Advanced Optics Engineering TSRP research grant 1223600011.

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