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Optical parametric generation with two pairs of gain bands based on a photonic crystal fiber
Optics Communications 300 (2013) 22–26
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Optics Communications journal homepage: www.elsevier.com/locate/optcom
Optical parametric generation with two pairs of gain bands based on a photonic crystal fiber Lei Zhang a, Si-Gang Yang a,n, Ying Han b, Hong-Wei Chen a, Ming-Hua Chen a, Shi-Zhong Xie a a Tsinghua National Laboratory for Information Science and Technology (TNList), Department of Electronic Engineering, Tsinghua University, Beijing 100084, China b Institute of Infrared Optical Fibers and Sensors, Physics Department, Yanshan University, Qinhuangdao 066004, China
art ic l e i nf o
a b s t r a c t
Article history: Received 23 December 2012 Received in revised form 4 March 2013 Accepted 5 March 2013 Available online 4 April 2013
An optical parametric amplifier with two pairs of gain bands is demonstrated based on a photonic crystal fiber (PCF) pumped with a Ti: sapphire pulse laser. A photonic crystal fiber with two zero-dispersion wavelengths is designed and fabricated, which can be expected to support phase matched wavelengths at the visible and infrared bands. The influences of the pump power and the pump wavelength on the phase-matching contours are investigated in detail. It predicts that two pairs of parametric gain bands can appear. In experiment, it benefits from the high peak pump power of the Ti: sapphire pulse laser, two pairs of parametric gain bands are observed. The signal band extends to the mid-infrared region of 2190 nm, and the idler band extends down to the ultraviolet region of 300 nm. The characteristics of the parametric gain bands agree well with the simulations. & 2013 Elsevier B.V. All rights reserved.
Keywords: Four-wave mixing Photonic crystal fiber Nonlinear optics
1. Introduction Fiber optical parametric amplifier (FOPA) has attracted considerable attentions recently due to its remarkable properties, such as high gain [1], wide band width [2,3], low noise figure, large tunable range [4,5] and so on. The even-order dispersion coefficients of optical fibers play an important role in the profile of the gain spectrum during the process of parametric amplification [6,7]. A 400-nm gain bandwidth has been obtained by using a pump from a C band tunable laser source in a highly nonlinear fiber (HNLF) [7]. Phase matched signal and idler wavelengths at 3.105 μm and 0.642 μm have been achieved based on a large mode area PCF pumped by a nanosecond Q-switched pulsed Nd:YAG laser [8]. A wavelength conversion from near-infrared to visible optical band has been demonstrated in a PCF pumped with a single frequency continue wave Ti: Sapphire laser [9,10]. A widely tunable parametric gain between 500 nm and 900 nm has been achieved by using a mode-locked cavity-dumped DCM-dye laser and pump in a 1.3-m PCF [3]. These studies are characterized by the pump wavelength operating near the zero dispersion wavelength of the gain fiber so as to realize the phase matching among the pump, signal and the idler. To the best of our knowledge, in these experiments, only one pair of parametric gain band is observed.
n
Corresponding author. E-mail address: [email protected] (S.-G. Yang).
0030-4018/$ - see front matter & 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.optcom.2013.03.006
Reeves et al. have predicted theoretically that two pairs of gain bands can be exist in particular dispersion-engineered PCFs [11]. However, they have not been observed experimentally yet. In this paper, we design and fabricate a PCF with two zero dispersion wavelengths. It can support two pairs of phase matched signal and idler at the visible and infrared bands. The dependence of the parametric gain profiles on the pump power and pump wavelength are analyzed. Specifically, a Ti: sapphire femtosecond pulse laser is used as the pump. Due to the walk-off among the pump, signal and idler waves, the effective interaction length is limited to several centimeters. In spite of the short interaction length, it benefits from the high peak pump power. In experiment, two pairs of gain bands are observed. The signal band extends to the midinfrared region of 2190 nm, and the idler band extends down to the ultraviolet region of 300 nm.
2. Theory and simulations The process of FOPA is substantially four-wave mixing (FWM) which is based on the third-order nonlinear effect. The efficiency of parametric amplification is mainly affected by the propagation parameter, the nonlinear coefficient, the pump wavelength and the pump power. During the process of FWM, the phase matching condition is [7]: Δβ þ 2γP ¼ 0
ð1Þ
L. Zhang et al. / Optics Communications 300 (2013) 22–26
where 2γP is the nonlinear phase mismatch term, γ is the nonlinear coefficient, P is the peak pump power, and Δβ is the linear phase mismatch term, which can be expressed as [7]: Δβ ¼ βs þ βi −2βp
ð2Þ
here βs, βi, and βp are the propagation constants of the signal, the idler, and the pump, respectively. When the linear phase mismatch is in the region of −4γPoΔβo0, a non-zero parametric gain can be obtained. It requires the group-velocity dispersion parameter β(2) at the pump wavelength approximately in the range of: −
4γP βð4Þ Ω2 βð4Þ Ω2 o βð2Þ o − − 12 12 Ω2
23
nonlinear mismatch term to the process of FWM. It would lead to a large distribution on the phase matching curve. The influence of pump power on the phase-matching contour needs to be studied in detail. In this paper, we use a Ti: sapphire femtosecond pulse laser as the pump, which is usually used for supercontinuum spectrum generation [15]. The peak power of the pulse can reach a high value of 1.2 105 W, which affords a freedom for us to
ð3Þ
β(4) is the fourth derivative of the propagation parameter β with respect to the pump wavelength. When β(4) o0, the parametric gain can be obtained with fiber pumped in the normal dispersion region of β(2) o−β(4)Ω2/12 which is near the zero dispersion wavelength or pumped in the anomalous dispersion region of β(2) 4−4γP/Ω2−β(4)Ω2/12. When β(4) 40, the parametric gain can be obtained with fiber pumped in the anomalous dispersion region of −4γP/Ω2−β(4)Ω2/12 oβ(2) o−β(4)Ω2/12. If the pump wave is in the normal dispersion region of β(2) 4 |β(4)Ω2/12| which is far away from the zero dispersion wavelength or in the huge negative dispersion region of β(2) o−4γP/Ω2−|β(4)Ω2/12|, the parametric amplification will not be observed. In this paper, we design and fabricate a highly nonlinear fused silica PCF. Its scanning electron microscope (SEM) image is shown in the inset of Fig. 1. The core diameter is about 1.55 μm, the air hole diameter is 0.755 μm, and the pitch of air holes is 1.15 μm. It exhibits slight birefringence in the order of 10−4. The properties of waveguide mode in the PCF are calculated by the Multi-pole method (MPM) [12,13]. Fig. 1 shows the evolution of β(2) and β(4) with respect to wavelength for the high group-index HE11 mode and the low group-index HE11 mode of the PCF. The calculated two zero dispersion wavelengths of the high group-index HE11 mode are at 723 nm and 1363 nm, respectively, and the two zero dispersion wavelengths of the low group-index HE11 mode are at 728 nm and 1373 nm, respectively. At wavelength of 800 nm, both the values of β(2) and β(4) are negative, the calculated nonlinear coefficient γ is about 160 km−1 W−1. The 800 nm pump from the Ti: sapphire laser locates in the anomalous dispersion regime between the two zero-dispersion wavelengths of the PCF. The pump power P is of key importance combined with the nonlinear coefficient γ during the FWM process. In the studies about FOPA and fiber optical parametric oscillator (FOPO) a pulse laser with a large peak power is often used as the pump source [4,14]. The large peak pump power will introduce a great
Fig. 2. (a) The phase-matching contour for the high group-index mode of the PCF with nonlinear mismatch term γP¼ 0. (b) The phase-matching contours for the high group-index mode of the PCF at several pump powers.
P P
6 54 1
Fig. 1. Variations of β(2) and β(4) with wavelength for the high group-index HE11 mode (solid lines) and the low group-index HE11 mode (dashed lines) of the PCF. The inset shows the scanning electron microscope (SEM) image of the highly nonlinear PCF.
2
3
4
5
6
Fig. 3. The Phase matching contours for the high group-index mode of the PCF with the linear phase mismatch Δβ of −4γP, −2γP and zero, respectively, when the pump power is 20,000 W.
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L. Zhang et al. / Optics Communications 300 (2013) 22–26
investigate the influence of the pump power on the parametric gain profile. As the transmission distance increases, the walk-off among the pump, signal and idler waves will increase too. Due to the ultrashort pulse width of the pump, the interaction length is limited to several centimeters. But benefitting from the large peak power, the efficiency of the parametric amplification is still very high. The phase-matching contour for the high group-index mode of the PCF with nonlinear mismatch term γP ¼0 is shown in Fig. 2(a). The range of the pump wavelength, in which phase matched signal and idler pair exists, is from 710 nm to 1346 nm, beginning at the normal dispersion regime near the first zero dispersion wavelength of 723 nm, and ending at the anomalous dispersion regime close to the second zero dispersion wavelength of 1363 nm. For each pump wave in the regions from 710 nm to 832 nm and from 1120 nm to 1346 nm, two groups of phase matched signal and idler pairs exist. For example, with the pump wavelength of 1200 nm, the outer pair of the phase matched points is consisted of 1 and 2, and the inner pair of the phase matched points is consisted of 3 and 4, as shown in the vertical solid line on Fig. 2(a). For each pump wave in the region from 832 nm to 1120 nm, only one group of phase matched signal and idler pair exists, and the
signal and the idler bands have a large interval. Fig. 2(b) shows the evolution of the phase matched sidebands versus the pump wavelength with different pump powers for the high groupindex mode. The black slant shows the location of the pump wavelength in the vertical coordinate. The curves above the slant indicate the wavelengths of the signal sidebands, and the curves below the slant indicate the wavelengths of the idler sidebands. When the peak pump power is 500 W, for each pump wavelength in the region from 711 nm to 1330 nm, two groups of phase matched signal and idler pairs exist. The inner and outer phase matched pairs constitute a shape of ring on each side of the slant of the pump wavelength. With the peak pump power increased, the nonlinear phase mismatch will seriously affect the phase matching condition. The pump wavelength region in which the phase matched waves pair can appear becomes smaller. The frequency detuning of the inner pair from the pump wave increases, and the frequency detuning of the outer pair from the pump wave decreases. The gain bandwidth is a critical parameter to the parametric amplification. The frequencies distributed in the region of −4γPoΔβ (Ω)o0 will experience a nonzero gain. Fig. 3 shows the phasematching contours for the high group-index mode of the PCF when
Fig. 4. The observed output spectra of idler waves, with the pump wavelengths of (a) 0.76 μm, (c) 0.8 μm and (e) 0.815 μm, respectively. The observed output spectra of signal waves, with the pump wavelengths of (b) 0.76 μm, (d) 0.8 μm and (f) 0.815 μm, respectively. The peak pump power is set to be P¼ 20,000 W.
L. Zhang et al. / Optics Communications 300 (2013) 22–26
the linear phase mismatch Δβ equals to −4γP, −2γP and zero, respectively, and the peak pump power P is 20,000 W. For a given pump wavelength, the gain band covers the wavelengths that satisfy the condition of −4γPoΔβ(Ω)o0. The phase matching curve with Δβ¼−2γP indicates the signals and idlers with the maximal gain. Based on the profiles of the gain spectrum, the pump wavelengths are divided into six regions. In the region 1, for a given pump wave, there are four separated gain bands, corresponding to the signal and idler gain bands of the inner and outer pairs, respectively. For example, with the pump wavelength of 800 nm, the four gain bands are a, b, c and d, which are signed in the Fig. 3. In the region 2, for a given pump, the signal and idler bands of the inner pair are connected to each other, and a broad band is formed near the pump wavelength except for two separated signal and idler bands of the outer pair. In the region 3, for a given pump, the four gain bands are all connected to each other, and form a super-broad gain band similar to a supercontinuum spectrum. In the region 4, for a given pump, the idler or signal of the outer and inner gain bands are combined together. Either the signal or the idler band includes two gain peaks since two fulfilled phase matching wavelengths are existed. In the region 5, the fulfilled phase matched wavelengths do not exist, and the parametric gain is very weak. The region 6 belongs to zero gain region, no parametric gain exist. It can be predicted that, according to band gain contours, various parametric gain shapes can be obtained by adjusting the pump wavelength.
25
Fig. 5. Sideband wavelength of the two pairs of FWM versus the pump wavelength, the peak pump power is set to be 20,000 W.
3. Experimental results and discussions Experimentally, a Ti: sapphire pulse laser can emit a pulse train with the full width at half maximum (FWHM) of 130 fs, at the repetition rate of 76 MHz. The pump pulse train is coupled into 1.0-m PCF mentioned above through a 40 microscope objective lens with the numerical aperture of 0.65. The central wavelength of the pump wave is set to be 800 nm. The pump power can be adjusted by a neutral-density filter wheel. The light emitting from the fiber is collimated by a 40 microscope objective lens and then sent to two optical fiber spectrometers (Avaspec-2048-2 and Avaspec-NIR-256-2.5) with the measurement scopes from 200 nm to 1100 nm and from 900 nm to 2500 nm. Since the signal band distributing in the wavelength region of 1000 nm to 2200 nm, a suitable signal source is not accessible. We use amplified spontaneous emission (ASE) from the pump laser as the seed source and infer the FOPA gain spectrum from the measurement of the output ASE spectrum. The experimentally observed spectra with the peak pump power of 20,000 W and the pump wavelengths of 760 nm, 800 nm and 815 nm are shown in Fig. 4. The idler bands are shown in Fig. 4(a), (c) and (e), in which two gain bands in visible region can be clearly seen. When the pump operates at 800 nm, the region of 550–730 nm corresponds to the idler wave of the inner pair (IWIP) of the sideband. And the region of 410–501 nm corresponds to the idler wave of the outer pair (IWOP) of the sideband. When the pump wavelength increases, both the IWIP and IWOP move to longer wavelength, which is shown in Fig. 5. Especially, when the pump wavelength is 760 nm, the idler wave extends down to the ultraviolet region of 300 nm. The signal waves are shown in Fig. 4(b), (d) and (f). Two gain bands corresponding to the signal waves of the inner and outer pairs (SWIP & SWOP) can be observed clearly. For example, when the pump wavelength is 800 nm, the two gain bands distribute in bands of 1010–1320 nm and 1805–2160 nm, respectively. Each band has two peaks resulted from the birefringence of the PCF, since only one half wave plate is used and the polarization state of pump is not aligned properly with the principle axis of the PCF. Theoretically, a half wave plate and two quarter wave plates should be used simultaneously so that all the polarization states
Fig. 6. The DW wavelength as a function of soliton wavelength, the peak pump power is set to be 20,000 W.
can be reached. The evolution of the signal band versus the pump wavelength is also shown in Fig. 5. When the pump wavelength is 815 nm, the signal band extends to the mid-infrared region of 2190 nm. The two pairs of gain bands are approximately in agreement with the simulation results in Fig. 3. Due to the effect of the Raman-induced frequency shift (RIFS), the pump soliton shifts to longer wavelength regions. After a short propagation distance of about 2 mm, the spectral peak of the pump soliton reaches the second zero dispersion wavelength of the PCF. Then the effect of RIFS is suppressed [19,20]. In the visible wavelength region, except for the two gain peaks, the dispersive waves (DW) are also generated. To some extent, they are overlapped with the idler gain bands. The wavelength of DW is governed by the phase-matching condition between the DW and soliton [16–18]. In the calculation, the dispersion parameters up to β(6), which is the sixth order derivative of the propagation parameter with respect to the pump wavelength, are considered. The simulated result is shown in Fig. 6. The experimentally measured DW wavelength is signed by red points. The maximal discrepancy with the simulated results is below 0.02 μm. In order to further study the evolution of the two pairs FWM gain bands versus the propagation distance, we simulate the sech2 pulses with peak power of 20,000 W and 130 fs FWHM propagating in 1 m of the PCF using the split-step Fourier method to solve the generalized nonlinear Schrödinger equation [20]. The spectral evolution is shown in Fig. 7. It is clear that two pairs of sideband
26
L. Zhang et al. / Optics Communications 300 (2013) 22–26 A
C
D
B
2190 nm, and the idler band extends down to the ultraviolet region of 300 nm.
0
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This work is supported by the National Basic Research Program of China (973 Program) under Contract 2010CB327606 and by the National Nature Science Foundation of China under Contract 61108007, 61090391.
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References
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Frequency [THz] Fig. 7. Simulated spectral evolution of a pulse launched at 800 nm with the peak pump power of 20,000 W.
are generated at the propagation distance of about 3 mm. As shown in Fig. 7, the outer pair of FWM gain bands is composed of A and B, and the inner pair is composed of C and D. The wavelengths of them remain relatively fixed with the increasing of the propagation distance to 1 m. 4. Conclusion In conclusion, a PCF is designed and fabricated for phase matching at the visible and infrared bands. The characteristics of the parametric gain versus the pump power and the pump wavelength are investigated. It predicts that two pairs of parametric gain bands exist, the possibility of the appearance of the outer phase matched pair increases with the increasing of the pump power, and various parametric gain shapes can be obtained by adjusting the pump wavelength. In experiment, two pairs of parametric gain bands corresponding to the signal and idler waves are observed with the PCF pumped with a Ti: sapphire pulse laser. The distribution of the gain bands agree well with the simulation results. The signal band extends to the mid-infrared region of
[1] T. Torounidis, P.A. Andrekson, B. –E. Olsson, IEEE Photonics Technology Letters 18 (2006) 1194. [2] Y. Deng, Q. Lin, F. Lu, G.P. Agrawal, W.H. Knox, Optics Letters 30 (2005) 1234. [3] K. K. Y. Wong, M. E. Marhic, G. Kalogerakis, L. G. Kazovsky, Fiber optical parametric amplifier and wavelength converter with record 360 nm gain bandwidth and 50 dB signal gain, in: Presented at the Conf. Lasers and ElectroOptics, Baltimore, MD, Postdeadline paper CThPDB6, (2003). [4] A.Y.H. Chen, G.K.L. Wong, S.G. Murdoch, R. Leonhardt, J.D. Harvey, J.C. Knight, W.J. Wadsworth, P.St.J. Russell, Optics Letters (2005)762. [5] S. Yang, K.K.Y. Cheung, Y. Zhou, K.K.Y. Wong, Optics Letters 35 (2010) 481. [6] J. Hansryd, P.A. Andrekson, M. Westlund, J. Li, P. –O. Hedekvist, IEEE Journal of Selected Topics in Quantum Electronics 8 (2002) 506. [7] M.E. Marhic, K.K.Y. Wong, L.G. Kazovsky, IEEE Journal of Selected Topics in Quantum Electronics 10 (2004) 1133. [8] A. Herzog, A. Shamir, A.A. Ishaaya, Optics Letters 37 (2012) 82. [9] T.V. Andersen, K.M. Hilligsøe, C.K. Nielsen, J. Thøgersen, K.P. Hansen S.R. Keiding, J.J. Larsen, Optics Express 12 (2004) 4113. [10] R. Jiang, R.E. Saperstein, N. Alic, M. Nezhad, C.J. Mckinstrie, J.E. Ford, Y. Fainman, S. Radic, Journal of Lightwave Technology 25 (2007) 58. [11] W.H. Reeves, D.V. Skryabin, F. Biancalana, J.C. Knight, P. St., J. Russell F.G. Omenetto, A. Efimov, A.J. Taylor, Nature 424 (2003) 511. [12] B.T. Kuhlmey, T.P. White, G. Renersez, D. Maystre, L.C. Botten, C.M. de Sterke R.C. McPhedran, Journal of the Optical Society of America B 19 (2002) 2331. [13] CUDOS MOF Utilities, available online: 〈http://www.physics.usyd.edu.au/ cudos/mofsoftware/〉. [14] S. Yang, K.K.Y. Cheung, Y. Zhou, K.K.Y. Wong, IEEE Photonics Technology Letters 22 (2010) 580. [15] J.M. Dudley, G. Genty, S. Coen, Reviews of Modern Physics 78 (2006) 1135. [16] I. Cristiani, R. Tediosi, L. Tartara, V. Degiorgio, Optics Express 12 (2003) 124. [17] J. Yuan, X. Sang, C. Yu, Y. Han, G. Zhou, S. Li, L. Hou, IEEE Photonics Technology Letters 23 (2011) 786. [18] H. Liu, Y. Dai, C. Xu, J. Wu, K. Xu, Y. Li, X. Hong, J. Lin, Optics Letters 35 (2010) 4042. [19] D.V. Skryabin, F. Luan, J.C. Knight, P. St., J. Russell, Science 301 (2003) 1705. [20] G.P. Agrawal, Nonlinear Fiber Optics, fourth ed., Academic Press, Boston, 2007.
Contents lists available at SciVerse ScienceDirect
Optics Communications journal homepage: www.elsevier.com/locate/optcom
Optical parametric generation with two pairs of gain bands based on a photonic crystal fiber Lei Zhang a, Si-Gang Yang a,n, Ying Han b, Hong-Wei Chen a, Ming-Hua Chen a, Shi-Zhong Xie a a Tsinghua National Laboratory for Information Science and Technology (TNList), Department of Electronic Engineering, Tsinghua University, Beijing 100084, China b Institute of Infrared Optical Fibers and Sensors, Physics Department, Yanshan University, Qinhuangdao 066004, China
art ic l e i nf o
a b s t r a c t
Article history: Received 23 December 2012 Received in revised form 4 March 2013 Accepted 5 March 2013 Available online 4 April 2013
An optical parametric amplifier with two pairs of gain bands is demonstrated based on a photonic crystal fiber (PCF) pumped with a Ti: sapphire pulse laser. A photonic crystal fiber with two zero-dispersion wavelengths is designed and fabricated, which can be expected to support phase matched wavelengths at the visible and infrared bands. The influences of the pump power and the pump wavelength on the phase-matching contours are investigated in detail. It predicts that two pairs of parametric gain bands can appear. In experiment, it benefits from the high peak pump power of the Ti: sapphire pulse laser, two pairs of parametric gain bands are observed. The signal band extends to the mid-infrared region of 2190 nm, and the idler band extends down to the ultraviolet region of 300 nm. The characteristics of the parametric gain bands agree well with the simulations. & 2013 Elsevier B.V. All rights reserved.
Keywords: Four-wave mixing Photonic crystal fiber Nonlinear optics
1. Introduction Fiber optical parametric amplifier (FOPA) has attracted considerable attentions recently due to its remarkable properties, such as high gain [1], wide band width [2,3], low noise figure, large tunable range [4,5] and so on. The even-order dispersion coefficients of optical fibers play an important role in the profile of the gain spectrum during the process of parametric amplification [6,7]. A 400-nm gain bandwidth has been obtained by using a pump from a C band tunable laser source in a highly nonlinear fiber (HNLF) [7]. Phase matched signal and idler wavelengths at 3.105 μm and 0.642 μm have been achieved based on a large mode area PCF pumped by a nanosecond Q-switched pulsed Nd:YAG laser [8]. A wavelength conversion from near-infrared to visible optical band has been demonstrated in a PCF pumped with a single frequency continue wave Ti: Sapphire laser [9,10]. A widely tunable parametric gain between 500 nm and 900 nm has been achieved by using a mode-locked cavity-dumped DCM-dye laser and pump in a 1.3-m PCF [3]. These studies are characterized by the pump wavelength operating near the zero dispersion wavelength of the gain fiber so as to realize the phase matching among the pump, signal and the idler. To the best of our knowledge, in these experiments, only one pair of parametric gain band is observed.
n
Corresponding author. E-mail address: [email protected] (S.-G. Yang).
0030-4018/$ - see front matter & 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.optcom.2013.03.006
Reeves et al. have predicted theoretically that two pairs of gain bands can be exist in particular dispersion-engineered PCFs [11]. However, they have not been observed experimentally yet. In this paper, we design and fabricate a PCF with two zero dispersion wavelengths. It can support two pairs of phase matched signal and idler at the visible and infrared bands. The dependence of the parametric gain profiles on the pump power and pump wavelength are analyzed. Specifically, a Ti: sapphire femtosecond pulse laser is used as the pump. Due to the walk-off among the pump, signal and idler waves, the effective interaction length is limited to several centimeters. In spite of the short interaction length, it benefits from the high peak pump power. In experiment, two pairs of gain bands are observed. The signal band extends to the midinfrared region of 2190 nm, and the idler band extends down to the ultraviolet region of 300 nm.
2. Theory and simulations The process of FOPA is substantially four-wave mixing (FWM) which is based on the third-order nonlinear effect. The efficiency of parametric amplification is mainly affected by the propagation parameter, the nonlinear coefficient, the pump wavelength and the pump power. During the process of FWM, the phase matching condition is [7]: Δβ þ 2γP ¼ 0
ð1Þ
L. Zhang et al. / Optics Communications 300 (2013) 22–26
where 2γP is the nonlinear phase mismatch term, γ is the nonlinear coefficient, P is the peak pump power, and Δβ is the linear phase mismatch term, which can be expressed as [7]: Δβ ¼ βs þ βi −2βp
ð2Þ
here βs, βi, and βp are the propagation constants of the signal, the idler, and the pump, respectively. When the linear phase mismatch is in the region of −4γPoΔβo0, a non-zero parametric gain can be obtained. It requires the group-velocity dispersion parameter β(2) at the pump wavelength approximately in the range of: −
4γP βð4Þ Ω2 βð4Þ Ω2 o βð2Þ o − − 12 12 Ω2
23
nonlinear mismatch term to the process of FWM. It would lead to a large distribution on the phase matching curve. The influence of pump power on the phase-matching contour needs to be studied in detail. In this paper, we use a Ti: sapphire femtosecond pulse laser as the pump, which is usually used for supercontinuum spectrum generation [15]. The peak power of the pulse can reach a high value of 1.2 105 W, which affords a freedom for us to
ð3Þ
β(4) is the fourth derivative of the propagation parameter β with respect to the pump wavelength. When β(4) o0, the parametric gain can be obtained with fiber pumped in the normal dispersion region of β(2) o−β(4)Ω2/12 which is near the zero dispersion wavelength or pumped in the anomalous dispersion region of β(2) 4−4γP/Ω2−β(4)Ω2/12. When β(4) 40, the parametric gain can be obtained with fiber pumped in the anomalous dispersion region of −4γP/Ω2−β(4)Ω2/12 oβ(2) o−β(4)Ω2/12. If the pump wave is in the normal dispersion region of β(2) 4 |β(4)Ω2/12| which is far away from the zero dispersion wavelength or in the huge negative dispersion region of β(2) o−4γP/Ω2−|β(4)Ω2/12|, the parametric amplification will not be observed. In this paper, we design and fabricate a highly nonlinear fused silica PCF. Its scanning electron microscope (SEM) image is shown in the inset of Fig. 1. The core diameter is about 1.55 μm, the air hole diameter is 0.755 μm, and the pitch of air holes is 1.15 μm. It exhibits slight birefringence in the order of 10−4. The properties of waveguide mode in the PCF are calculated by the Multi-pole method (MPM) [12,13]. Fig. 1 shows the evolution of β(2) and β(4) with respect to wavelength for the high group-index HE11 mode and the low group-index HE11 mode of the PCF. The calculated two zero dispersion wavelengths of the high group-index HE11 mode are at 723 nm and 1363 nm, respectively, and the two zero dispersion wavelengths of the low group-index HE11 mode are at 728 nm and 1373 nm, respectively. At wavelength of 800 nm, both the values of β(2) and β(4) are negative, the calculated nonlinear coefficient γ is about 160 km−1 W−1. The 800 nm pump from the Ti: sapphire laser locates in the anomalous dispersion regime between the two zero-dispersion wavelengths of the PCF. The pump power P is of key importance combined with the nonlinear coefficient γ during the FWM process. In the studies about FOPA and fiber optical parametric oscillator (FOPO) a pulse laser with a large peak power is often used as the pump source [4,14]. The large peak pump power will introduce a great
Fig. 2. (a) The phase-matching contour for the high group-index mode of the PCF with nonlinear mismatch term γP¼ 0. (b) The phase-matching contours for the high group-index mode of the PCF at several pump powers.
P P
6 54 1
Fig. 1. Variations of β(2) and β(4) with wavelength for the high group-index HE11 mode (solid lines) and the low group-index HE11 mode (dashed lines) of the PCF. The inset shows the scanning electron microscope (SEM) image of the highly nonlinear PCF.
2
3
4
5
6
Fig. 3. The Phase matching contours for the high group-index mode of the PCF with the linear phase mismatch Δβ of −4γP, −2γP and zero, respectively, when the pump power is 20,000 W.
24
L. Zhang et al. / Optics Communications 300 (2013) 22–26
investigate the influence of the pump power on the parametric gain profile. As the transmission distance increases, the walk-off among the pump, signal and idler waves will increase too. Due to the ultrashort pulse width of the pump, the interaction length is limited to several centimeters. But benefitting from the large peak power, the efficiency of the parametric amplification is still very high. The phase-matching contour for the high group-index mode of the PCF with nonlinear mismatch term γP ¼0 is shown in Fig. 2(a). The range of the pump wavelength, in which phase matched signal and idler pair exists, is from 710 nm to 1346 nm, beginning at the normal dispersion regime near the first zero dispersion wavelength of 723 nm, and ending at the anomalous dispersion regime close to the second zero dispersion wavelength of 1363 nm. For each pump wave in the regions from 710 nm to 832 nm and from 1120 nm to 1346 nm, two groups of phase matched signal and idler pairs exist. For example, with the pump wavelength of 1200 nm, the outer pair of the phase matched points is consisted of 1 and 2, and the inner pair of the phase matched points is consisted of 3 and 4, as shown in the vertical solid line on Fig. 2(a). For each pump wave in the region from 832 nm to 1120 nm, only one group of phase matched signal and idler pair exists, and the
signal and the idler bands have a large interval. Fig. 2(b) shows the evolution of the phase matched sidebands versus the pump wavelength with different pump powers for the high groupindex mode. The black slant shows the location of the pump wavelength in the vertical coordinate. The curves above the slant indicate the wavelengths of the signal sidebands, and the curves below the slant indicate the wavelengths of the idler sidebands. When the peak pump power is 500 W, for each pump wavelength in the region from 711 nm to 1330 nm, two groups of phase matched signal and idler pairs exist. The inner and outer phase matched pairs constitute a shape of ring on each side of the slant of the pump wavelength. With the peak pump power increased, the nonlinear phase mismatch will seriously affect the phase matching condition. The pump wavelength region in which the phase matched waves pair can appear becomes smaller. The frequency detuning of the inner pair from the pump wave increases, and the frequency detuning of the outer pair from the pump wave decreases. The gain bandwidth is a critical parameter to the parametric amplification. The frequencies distributed in the region of −4γPoΔβ (Ω)o0 will experience a nonzero gain. Fig. 3 shows the phasematching contours for the high group-index mode of the PCF when
Fig. 4. The observed output spectra of idler waves, with the pump wavelengths of (a) 0.76 μm, (c) 0.8 μm and (e) 0.815 μm, respectively. The observed output spectra of signal waves, with the pump wavelengths of (b) 0.76 μm, (d) 0.8 μm and (f) 0.815 μm, respectively. The peak pump power is set to be P¼ 20,000 W.
L. Zhang et al. / Optics Communications 300 (2013) 22–26
the linear phase mismatch Δβ equals to −4γP, −2γP and zero, respectively, and the peak pump power P is 20,000 W. For a given pump wavelength, the gain band covers the wavelengths that satisfy the condition of −4γPoΔβ(Ω)o0. The phase matching curve with Δβ¼−2γP indicates the signals and idlers with the maximal gain. Based on the profiles of the gain spectrum, the pump wavelengths are divided into six regions. In the region 1, for a given pump wave, there are four separated gain bands, corresponding to the signal and idler gain bands of the inner and outer pairs, respectively. For example, with the pump wavelength of 800 nm, the four gain bands are a, b, c and d, which are signed in the Fig. 3. In the region 2, for a given pump, the signal and idler bands of the inner pair are connected to each other, and a broad band is formed near the pump wavelength except for two separated signal and idler bands of the outer pair. In the region 3, for a given pump, the four gain bands are all connected to each other, and form a super-broad gain band similar to a supercontinuum spectrum. In the region 4, for a given pump, the idler or signal of the outer and inner gain bands are combined together. Either the signal or the idler band includes two gain peaks since two fulfilled phase matching wavelengths are existed. In the region 5, the fulfilled phase matched wavelengths do not exist, and the parametric gain is very weak. The region 6 belongs to zero gain region, no parametric gain exist. It can be predicted that, according to band gain contours, various parametric gain shapes can be obtained by adjusting the pump wavelength.
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Fig. 5. Sideband wavelength of the two pairs of FWM versus the pump wavelength, the peak pump power is set to be 20,000 W.
3. Experimental results and discussions Experimentally, a Ti: sapphire pulse laser can emit a pulse train with the full width at half maximum (FWHM) of 130 fs, at the repetition rate of 76 MHz. The pump pulse train is coupled into 1.0-m PCF mentioned above through a 40 microscope objective lens with the numerical aperture of 0.65. The central wavelength of the pump wave is set to be 800 nm. The pump power can be adjusted by a neutral-density filter wheel. The light emitting from the fiber is collimated by a 40 microscope objective lens and then sent to two optical fiber spectrometers (Avaspec-2048-2 and Avaspec-NIR-256-2.5) with the measurement scopes from 200 nm to 1100 nm and from 900 nm to 2500 nm. Since the signal band distributing in the wavelength region of 1000 nm to 2200 nm, a suitable signal source is not accessible. We use amplified spontaneous emission (ASE) from the pump laser as the seed source and infer the FOPA gain spectrum from the measurement of the output ASE spectrum. The experimentally observed spectra with the peak pump power of 20,000 W and the pump wavelengths of 760 nm, 800 nm and 815 nm are shown in Fig. 4. The idler bands are shown in Fig. 4(a), (c) and (e), in which two gain bands in visible region can be clearly seen. When the pump operates at 800 nm, the region of 550–730 nm corresponds to the idler wave of the inner pair (IWIP) of the sideband. And the region of 410–501 nm corresponds to the idler wave of the outer pair (IWOP) of the sideband. When the pump wavelength increases, both the IWIP and IWOP move to longer wavelength, which is shown in Fig. 5. Especially, when the pump wavelength is 760 nm, the idler wave extends down to the ultraviolet region of 300 nm. The signal waves are shown in Fig. 4(b), (d) and (f). Two gain bands corresponding to the signal waves of the inner and outer pairs (SWIP & SWOP) can be observed clearly. For example, when the pump wavelength is 800 nm, the two gain bands distribute in bands of 1010–1320 nm and 1805–2160 nm, respectively. Each band has two peaks resulted from the birefringence of the PCF, since only one half wave plate is used and the polarization state of pump is not aligned properly with the principle axis of the PCF. Theoretically, a half wave plate and two quarter wave plates should be used simultaneously so that all the polarization states
Fig. 6. The DW wavelength as a function of soliton wavelength, the peak pump power is set to be 20,000 W.
can be reached. The evolution of the signal band versus the pump wavelength is also shown in Fig. 5. When the pump wavelength is 815 nm, the signal band extends to the mid-infrared region of 2190 nm. The two pairs of gain bands are approximately in agreement with the simulation results in Fig. 3. Due to the effect of the Raman-induced frequency shift (RIFS), the pump soliton shifts to longer wavelength regions. After a short propagation distance of about 2 mm, the spectral peak of the pump soliton reaches the second zero dispersion wavelength of the PCF. Then the effect of RIFS is suppressed [19,20]. In the visible wavelength region, except for the two gain peaks, the dispersive waves (DW) are also generated. To some extent, they are overlapped with the idler gain bands. The wavelength of DW is governed by the phase-matching condition between the DW and soliton [16–18]. In the calculation, the dispersion parameters up to β(6), which is the sixth order derivative of the propagation parameter with respect to the pump wavelength, are considered. The simulated result is shown in Fig. 6. The experimentally measured DW wavelength is signed by red points. The maximal discrepancy with the simulated results is below 0.02 μm. In order to further study the evolution of the two pairs FWM gain bands versus the propagation distance, we simulate the sech2 pulses with peak power of 20,000 W and 130 fs FWHM propagating in 1 m of the PCF using the split-step Fourier method to solve the generalized nonlinear Schrödinger equation [20]. The spectral evolution is shown in Fig. 7. It is clear that two pairs of sideband
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L. Zhang et al. / Optics Communications 300 (2013) 22–26 A
C
D
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2190 nm, and the idler band extends down to the ultraviolet region of 300 nm.
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This work is supported by the National Basic Research Program of China (973 Program) under Contract 2010CB327606 and by the National Nature Science Foundation of China under Contract 61108007, 61090391.
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References
0.2 -60 0.1 0
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Frequency [THz] Fig. 7. Simulated spectral evolution of a pulse launched at 800 nm with the peak pump power of 20,000 W.
are generated at the propagation distance of about 3 mm. As shown in Fig. 7, the outer pair of FWM gain bands is composed of A and B, and the inner pair is composed of C and D. The wavelengths of them remain relatively fixed with the increasing of the propagation distance to 1 m. 4. Conclusion In conclusion, a PCF is designed and fabricated for phase matching at the visible and infrared bands. The characteristics of the parametric gain versus the pump power and the pump wavelength are investigated. It predicts that two pairs of parametric gain bands exist, the possibility of the appearance of the outer phase matched pair increases with the increasing of the pump power, and various parametric gain shapes can be obtained by adjusting the pump wavelength. In experiment, two pairs of parametric gain bands corresponding to the signal and idler waves are observed with the PCF pumped with a Ti: sapphire pulse laser. The distribution of the gain bands agree well with the simulation results. The signal band extends to the mid-infrared region of
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