- Email: [email protected]
Second harmonic generation by femtosecond Yb-doped fiber laser source based on PPKTP waveguide fabricated by femtosecond laser direct writing
Optics Communications 284 (2011) 455–459
Contents lists available at ScienceDirect
Optics Communications j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / o p t c o m
Second harmonic generation by femtosecond Yb-doped fiber laser source based on PPKTP waveguide fabricated by femtosecond laser direct writing Chenghou Tu a, Zhangchao Huang a, Shuanggen Zhang a, Minglie Hu b, Qingyue Wang b, Enbang Li b, Yongnan Li a, Fuyun Lu a,⁎ a b
School of Physics and The Key Laboratory of Weak Light Nonlinear Photonics, Nankai University, Tianjin 300071, Ministry of Education, People's Republic of China College of Precision Instrument and Optoelectronics Engineering, Tianjin University, Tianjin 300072, People's Republic of China
a r t i c l e
i n f o
Article history: Received 30 July 2010 Received in revised form 8 September 2010 Accepted 8 September 2010 Keywords: Second harmonic generation Femtosecond Fiber laser PPKTP waveguide Femtosecond laser direct writing
a b s t r a c t The frequency doubling of femtosecond pulses from an Yb-doped fiber laser source was demonstrated in a PPKTP waveguide fabricated by femtosecond laser direct writing. The PPKTP waveguide contains a fixed period of 8.9 μm and the feomtosecond fundamental pulses have a central wavelength of 1044 nm. A maximum SHG power of 406 mW was produced, yielding a conversion efficiency of 5.6%. Numerical simulations were carried out to investigate the property of frequency doubling for femtosecond pulses. The results show that the SHG process proceeds even the quasi-phase-matching (QPM) condition is not well satisfied, which is significantly different from that of “long” pulses or CW light and is accorded with the experimental results. © 2010 Elsevier B.V. All rights reserved.
1. Introduction Second harmonic generation (SHG) by quasi-phase-matching (QPM) [1] interaction is an attractive method to generate blue-green lights from infrared pump sources. Among the currently available QPM materials, periodically poled potassium titanyl phosphate (PPKTP) is an attractive one due to its increased resistance to photorefractive damage, high effective nonlinearity and wide transparency and low poling electric field [2]. Recently, periodically poled ferroelectric waveguides have attracted a lot of attention as higher conversion efficiencies are possible as a result of prolonged wave interaction at higher intensities [3–5]. Waveguides have the additional potential of being fiber pigtailed, allowing for efficient integration into compact configurations with fiber pump sources. KTP waveguide is normally fabricated by ion diffusion [6] which is only suitable for fabricating channel waveguides close to the surface, and in which high visible degradation has to be involved. Recently, femtosecond (fs) laser inscription has been applied successfully to create waveguides in a variety of optical materials including glasses [7], overcoming the limitations of waveguide fabricated by ion diffusion, and improving the optical quality of the inscribed waveguides. Frequency doubling with a conversion efficiency (CE) of ~0.002% has been achieved in femtosecond laser inscribed PPKTP waveguides from a continuous-wave (CW) Ti:sapphire laser [8]. Using a Q-switched Nd:
⁎ Corresponding author. Tel./fax: + 86 22 23509856. E-mail address: [email protected] (F. Lu). 0030-4018/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.optcom.2010.09.022
YAG laser as the pump source, we have demonstrated efficient 532 nm green light generations in a double line type II PPKTP waveguide with a CE of 39.6% [9]. Fiber laser sources are compact, robust, efficient, air-cooled, and do not require optical alignment. In this paper, using a high power femtosecond Ytterbium-doped fiber (YDF) laser with a central wavelength of 1044 nm, we demonstrated a femtosecond green light source at 523 nm by SHG in a PPKTP waveguide inscribed by fs laser pulses. A SHG power of 406 mW has been generated for a fundamental pump power of 7.3 W, yielding the total SHG CE of 5.6%. Numerical simulations were carried out to study the SHG characteristics of fs pulses, and to show the effect of the grating period of KTP crystal and cubic nonlinear effects on the SHG process. 2. PPKTP waveguide fabrication and its property Two types of waveguides can be fabricated by femtosecond laser direct writing [10,11]. For type I waveguides the guiding region is located at the trace of the femtosecond laser focus, and the thermal stability of such waveguide is not good [10]. This disadvantage can be overcome by double line written (type II) waveguides. In these structures the nonlinear coefficients are not affected [11], which allow high SHG efficiency. In this work, double line type II waveguides are designed and fabricated. A z-cut PPKTP sample with a dimension of 10 × 10 × 1 mm3 was fabricated by electrical poling technique. The PPKTP contains a grating with a period of 8.9 μm, an optical micrograph of the KTP crystal after periodically poled is shown in Fig. 1(a).
456
C. Tu et al. / Optics Communications 284 (2011) 455–459
(a)
(b)
oscillator and an ytterbium fiber amplifier. The oscillator operated as soliton-like mode-locking fiber laser using single-polarization large mode area (LMA) ytterbium-doped photonic crystal fiber (YD-PCF) as the gain medium, and directly generated 520 fs pulses with a repetition rate of 50 MHz and an average power of 300 mW. The pulses were then amplified in the LMA YD-PCF amplifier, and subsequently compressed by a pair of gratings. As a result, the YDF laser source produces pulses polarized linearly at 1044 nm with a maximum output power of 16 W, and the pulses have a full width at half maximum (FWHM) duration of 100 fs and a spectral width of 30 nm respectively, as shown in Fig. 3(a) and (b). To maintain stable output characteristics, we operated the YDF laser source at the maximum power and used an attenuator comprising a half-wave plate (HWP) and a polarizing beam splitter (PBS) to vary the input fundamental power. A second HWP was used to yield the correct pump polarization for phase matching. The fundamental beam was focused into the PPKTP waveguide by freespace coupling using a 10 × microscope objective (NA = 0.25). Both end-faces of the waveguide were polished but without anti-reflection coating. In order to detect the second harmonic light, an optical filter stopping 99.5% of the 1064 nm laser light and allowing 95% of the 532 nm light to pass through was placed after the collimating lens (f = 10 mm).
20μm
(c)
(d)
Fig. 1. (a) Optical micrograph of the KTP crystal after periodically poled, (b) the schematic diagram of PPKTP waveguide fabrication, (c) optical micrograph of the end facet of double line type II waveguide written with femtosecond pulses, and (d) the near filed guided mode profile at 532 nm.
To fabricate waveguides in the prepared PPKTP sample, we used an amplified Ti:sapphire laser system (HP-Spitfire, Spectra-Physics Inc.) operating at a central wavelength of 800 nm. The laser emitted linearly polarized femtosecond pulse trains with FWHM duration of 50 fs and maximum energy of 2 mJ at a repetition of 1 kHz. The laser beam was focused into the sample (along the z axis) with a 25 × microscope objective (NA = 0.4) at a depth of 300 μm beneath the sample surface, and the laser spot size was about 2.5 μm. A CCD (KA-320) detector was used to monitor the focusing condition. In order to produce a thermally stable double line written type waveguide, we consecutively wrote pairs of straight lines separated by 14.5 μm in the × direction of the sample. The sample was inscribed at a velocity of 200 μm/s perpendicular to the z axis by a computer-controlled positioner. The optimum pulse energy for the waveguide fabrication was investigated to be about 100 μJ. A schematic diagram of the waveguide fabrication system is shown in Fig. 1(b), and an optical micrograph of the waveguide's end facet and the corresponding near field image of the guided 532 nm mode are shown in Fig. 1(c) and (d) respectively.
3.2. Experimental results Based on the experimental setup shown in Fig. 2, we investigated the second harmonic generation in the PPKTP waveguide. To protect
3. Experiment for femtosecond green light generation 3.1. Experimental setup An experimental setup including a YDF femtosecond laser source and a PPKTP waveguide for green light generation is shown in Fig. 2. The fundamental pulses were generated by an fs YDF laser source which is composed of a passively mode-locked ytterbium fiber FW fs YDF laser source
SHG 1/2 λ
PBS
1/2 λ MO
PPKTP waveguide
lens
Filter
Fig. 2. Schematic of the experimental design for single-pass SHG of femtosecond YDF laser source in PPKTP waveguide fabricated by femtosecond laser pulses. YDF: ytterbium-doped fiber, 1/2λ: half-wave plate, PBS: polarizing beam splitter, MO: microscope objective, and FW: fundamental wave.
Fig. 3. (a) The spectrum and (b) the temporal shape (autocorrelation trace) of the out pulses from YDF amplifier.
C. Tu et al. / Optics Communications 284 (2011) 455–459
the PPKTP waveguide from being damaged, the power launched to the waveguide was controlled under 8 W. We measured the SHG power and the CE curve is shown in Fig. 4. It is clear that the SHG power and the corresponding CE increase as the pump power increased. For fundamental pump powers lower than 430 mW, no SHG signal can be detected. At a fundamental pump power of 7.3 W, the SHG power is 406 mW, corresponding to a conversion efficiency of 5.6% without considering the losses. A coupling loss of 1.1 dB/facet and a propagation loss of 1.0 dB/cm were measured at 1044 nm for TM polarization in PPKTP waveguide. If the losses are taken into account, the total conversion efficiency can be 9.1%. In our experiment, the fundamental wavelength is 1044 nm, while the first order QPM wavelength is 1052 nm for the grating period of 8.9 μm. That is to say, a CE of ~ 9% can be obtained for fs fundamental pulses even with a large phase mismatch, which indicates the SHG characteristic of fs pulses is different from that of long pulses or CW radiation [12]. The detailed discussion will be held in Section 4. Moreover, we expect that with the use of anti-reflectioncoated front and end facets, it is possible to further enhance the second harmonic output power and to increase the efficiency. In Fig. 5(a), we measured the SHG spectra at different fundamental powers. As the fundamental pump power increased, the SHG occurs towards both the longer and shorter wavelength sides of fundamental pulses, making the FWHM spectral width of SHG pulses broader. The phenomenon of the spectrum broadening is mainly because of the strong self-phase modulation (SPM) effect owing to such high peak power of fs pulses. Combining with the CE profile given in Fig. 4, we can view that high power (density) can also enhance the SHG process. Fig. 5(b) shows the SHG spectrum at a fundamental power of 4 W. The spectrum has an FWHM spectral width of 7.5 nm with a central wavelength of 523 nm, obviously its profile is almost the same as that of the fundamental pulses. To investigate the guiding property of the PPKTP waveguide, we measured the mode profile of SHG pulses using a mode profiler. Fig. 6 shows the mode profiles of both the fundamental and SHG pulses. In the figure SHG pulses have a good mode profile comparing with that of the fundamental pulses, and the spatial profile is very close to a Gaussian shape. A good guiding for the propagated pulses in the fabricated PPKTP waveguide was indicated. For comparison, the output power of second harmonic pulses in the bulk PPKTP crystal was also measured. We used the same PPKTP crystal and switched from the waveguide area to bulk crystal for this experiment. The laser beam was loosely focused into the PPKTP crystal by free-space coupling. The SHG output power at different fundamental pump power is shown in Fig. 7, from which we can see that the CE is smaller than that in the PPKTP waveguide. The higher CE implies that the propagated pulses are well confined in the waveguide, achieving a higher power density and better mode overlapping. Additionally,
457
Fig. 5. (a) The SHG spectra at different pump power levels and (b) the spectrum of the SHG and the fundamental pulses at a fundamental pump power of 4 W.
the SHG mode profile in waveguide is also better than that in bulk crystal. 4. Numerical simulation and discussions for SHG of fs pulses Based on the plane wave and slowly varying envelope approximations, the following coupled partial differential equations can be used to describe the evolution of the fundamental and the second harmonic pulses in PPKTP waveguide [13–15]: ∂ i ∂2 n k A = −iαdeff A2 A⁎1 expð−iΔkzÞ−i 2 1 A − β n0;1 ∂z 1 2 2;1 ∂τ2 1 h i 2 2 × jA1 j + 2jA2 j A1 ∂ A + ∂z 2
ð1Þ
1 1 ∂ i ∂2 2 − A2 − β2;2 2 A2 = −iαdeff A1 expðiΔkzÞ v2 v1 ∂τ 2 ∂τ n k 2 2 −i 2 2 jA2j + 2jA1j A2 n0;2 ð2Þ
Fig. 4. The SHG output power and the corresponding conversion efficiency vs. the fundamental pump power.
Where Ai is the envelope function of the electric field and vi is the group velocity. Here the indices 1 and 2 represent the fundamental and the second harmonic, respectively. β2, i is the group velocity dispersion (GVD) parameter. deff is the effective nonlinear coefficient, α is the coupling coefficient between the fundamental the second harmonic and is given by α = (2ω2 / ε0c3n201n02Seff)1/2. n0, i is the refractive index of the fundamental and second harmonic pulses, Seff is the effective waveguide cross section and n2 is the third order nonlinear refractive index. 1/ v2 − 1/ v1 is the group velocity mismatch
458
C. Tu et al. / Optics Communications 284 (2011) 455–459
Fig. 6. The spatial beam profile of the fundamental and SHG pulses, (a), (c) the fundamental pulse, (b), and (d) the SHG pulses.
GVM between the fundamental and the second harmonic pulses. Δk = k2 − 2k1 − 2π / Λ is the phase mismatch of the fundamental and second harmonic pulses at a given grating period Λ of a PPKTP crystal. Eqs. (1) and (2) include the effects of GVD, GVM, SPM and crossphase modulation (XPM), they are solved numerically by using a symmetrized split-step Fourier and Runge–Kutta method. The fundamental pulse is Gaussian shape: A1(0, t) = exp(− t 2 /2T02), T0 is the half width (at the 1/e intensity point) of the input pulse. The parameters used in simulations are: T0 = 60 fs (corresponds to an intensity profile with an FWHM duration of 100 fs), deff = 2d33 / π = 10.75 pm/V [16], n2 = 46 × 10−20 m2/W [17], Seff = 2 × 10−10 m2,β2, 1 = −0.013 ps2/m, β2, 2 = 0.070 ps2/m, n0, 1 = 1.8297 and n0, 2 = 1.8888 (at 20 °C) [18]. The grating period Λ of PPKTP crystal is 8.9 μm (phase matched for 1052 nm at 20 °C), and the waveguide length is 10 mm. Herein we set the peak power density in the PPKTP waveguide to be ~100 GW/cm2, which is the case in our experiments. For 100-fs pulses, the dispersion length (LD = T20/|β2|) is several times larger than our sample length. Thus GVD does not seem to be significant in our experiments. Nevertheless, it is included in the model for completeness.
Fig. 7. The SHG output vs. fundamental femtosecond pulse power in PPKTP waveguide and bulk PPKTP crystal.
From the expression of Δk we can see it is related to both the fundamental wavelength of fs pulses and the grating period Λ, here we illustrate how they affect the SHG CE of fs pulses. Just as above mentioned, the phase matching wavelength is 1052 nm at 20 °C for a grating period of 8.9 μm, while it is 1044 nm for the case of 8.83 μm. As shown in Fig. 8, the CE fluctuates and reduces with the central wavelength deviating from the phase matching wavelength, and the maximum CE is obtained near the phase matching wavelength. The trend of the CE curve remains almost the same but the peak wavelength (for the maximum CE) shifts when the grating period is changed. If phase matching is not well satisfied, then the CE will be almost zero [12]. However, it is not the case for fs pulses. Fig. 9 shows the wavelength tuning curves for pulses with durations of 100 fs and 100 ps respectively, herein we use the same pulse energy for them. The FWHM of the tuning curve is about 1 nm for 100 ps pulse. Compared with 100 ps pulses, 100 fs pulses have a much wider wavelength tuning range, which is 5 times of that for 100 ps pulses, meanwhile, the SHG CE of fs pulses is also higher than that of ps pulse within the tuning range. The results make the SHG process of fs pulses very different from that of “long” (picosecond and nanosecond)
Fig. 8. The variation of SHG CE with the central wavelength of fundamental pulse.
C. Tu et al. / Optics Communications 284 (2011) 455–459
459
see the CE is very small at lower pump power, however, it grows quickly with the pump power increasing. Obviously the numerical results give a good fit to the experimental results within a permitted accuracy. 5. Conclusions
Fig. 9. Picosecond pulse and femtosecond pulse wavelength tuning curve.
Based on a PPKTP waveguide inscribed by femtosecond laser, we have successfully generated 406 mW of fs pulses radiation at 523 nm with an efficiency of 5.6% in a highly compact and practical design using single-pass SHG of an fs YDF laser source. Numerical simulations are carried out to illustrate the SHG characteristics of fs pulses. The simulation results suggest that effective SHG of fs pulses can be obtained even under the non-QPM condition due to the cubic nonlinear effects originating from the high peak power density, which accords well with the experimental results. We have numerically studied the influences of the grating period, fundamental wavelength and the peak power density on the SHG CE. The unique characteristics imply that the SHG process of fs pulses is significantly different from that of the “long” pulses or CW light. Acknowledgements This work was supported by the National Natural Science Foundation of China (60677013, 60808003), the Specialized Research Fund for the Doctoral Program Foundation of Institute of Higher Education of China (20090031120004). References
Fig. 10. The SHG CE variation with the peak power density. The central wavelength of the femtosecond pump pulse is 1044 nm and Λ is 8.90 μm.
pulses [13]. If looking into the origin of the results in Fig. 9, we know it lies in the peak power and the spectrum width of these two pulses. As the interacting fs pulses have relatively broad bandwidths, the phase mismatch of interactions between different frequency components deviate from the phase mismatch Δk0 at the central wavelength [14], for some of the frequency components phase mismatch may be small, as a result, efficient SHG occurs. At the same time, the high peak power of fs pulses will induce strong SPM and XPM effects, and the phase mismatch due to cubic nonlinearity also influences the SHG CE [15]. Suppose the central wavelength of fs pulses is 1044 nm, we numerically studied the influence of the peak power density on the SHG CE for the grating period of 8.90 μm, the results are shown in Fig. 10. To make the simulation approach the experiment, we have considered the experimental loss in the numerical simulation. From Fig. 10 we can
[1] S. Somekh, A. Yariv, Opt. Commun. 6 (1972) 301. [2] M. Pierrou, F. Laurell, H. Karlsson, T. Kellner, C. Czeranowsky, G. Huber, Opt. Lett. 24 (1999) 205. [3] Y. Wang, V. Petrov, Y.J. Ding, Y. Zheng, J.B. Khurgin, W.P. Risk, Appl. Phys. Lett. 73 (1998) 873. [4] B. Agate, E.U. Rafailov, W. Sibbett, S.M. Saltiel, P. Battle, T. Fry, E. Noonan, Opt. Lett. 28 (2003) 1963. [5] S. Sinha, C. Langrock, M.J.F. Digonnet, M.M. Fejer, R.L. Byer, Opt. Lett. 31 (2006) 347. [6] J.-P. Ruske, M. Rottschalk, S. Steinberg, Opt. Commun. 120 (1995) 47. [7] K.M. Davis, K. Miura, N. Sugimoto, K. Hirao, Opt. Lett. 21 (1996) 1729. [8] S. Campbell, R.R. Thomson, D.P. Hand, A.K. Kar, D.T. Reid, C. Canalias, V. Pasiskevicius, F. Laurell, Opt. Express 15 (2007) 17146. [9] S.G. Zhang, J.H. Yao, W.W. Liu, Z.C. Huang, J. Wang, Y.N. Li, C.H. Tu, F.Y. Lu, Opt. Express 16 (2008) 14180. [10] R.R. Thomson, S. Campbell, I.J. Blewett, A.K. Kar, D.T. Reid, Appl. Phys. Lett. 88 (2006) 111109. [11] J. Burghoff, C. Grebing, S. Nolte, A. Tünnermann, Appl. Phys. Lett. 89 (2006) 081108. [12] M.M. Fejer, G.A. Magel, H.J. Dieter, L.B. Robert, J. Quantum Electron. 28 (1992) 2631. [13] Z.C. Huang, C.H. Tu, S.G. Zhang, Y.N. Li, F.Y. Lu, Y.X. Fan, E.B. Li, Opt. Lett. 35 (2010) 877. [14] Z. Zheng, A.M. Weiner, J. Opt. Soc. Am. B 19 (2002) 839. [15] T. Ditmire, A.M. Rubenchik, D. Eimerl, M.D. Perry, J. Opt. Soc. Am. B 13 (1996) 649. [16] A.A. Lagatsky, C.T.A. Brown, W. Sibbett, S.J. Holmgren, C. Canalias, V. Pasiskevicius, F. Laurell, E.U. Rafailov, Opt. Express 15 (2007) 1155. [17] B. Boulanger, J.P. Feve, P. Delarue, I. Rousseau, G. Marnier, J. Phys. B: At. Mol. Opt. Phys. 32 (1999) 475. [18] K. Kato, E. Takaoka, Appl. Opt. 41 (2002) 5040.
Contents lists available at ScienceDirect
Optics Communications j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / o p t c o m
Second harmonic generation by femtosecond Yb-doped fiber laser source based on PPKTP waveguide fabricated by femtosecond laser direct writing Chenghou Tu a, Zhangchao Huang a, Shuanggen Zhang a, Minglie Hu b, Qingyue Wang b, Enbang Li b, Yongnan Li a, Fuyun Lu a,⁎ a b
School of Physics and The Key Laboratory of Weak Light Nonlinear Photonics, Nankai University, Tianjin 300071, Ministry of Education, People's Republic of China College of Precision Instrument and Optoelectronics Engineering, Tianjin University, Tianjin 300072, People's Republic of China
a r t i c l e
i n f o
Article history: Received 30 July 2010 Received in revised form 8 September 2010 Accepted 8 September 2010 Keywords: Second harmonic generation Femtosecond Fiber laser PPKTP waveguide Femtosecond laser direct writing
a b s t r a c t The frequency doubling of femtosecond pulses from an Yb-doped fiber laser source was demonstrated in a PPKTP waveguide fabricated by femtosecond laser direct writing. The PPKTP waveguide contains a fixed period of 8.9 μm and the feomtosecond fundamental pulses have a central wavelength of 1044 nm. A maximum SHG power of 406 mW was produced, yielding a conversion efficiency of 5.6%. Numerical simulations were carried out to investigate the property of frequency doubling for femtosecond pulses. The results show that the SHG process proceeds even the quasi-phase-matching (QPM) condition is not well satisfied, which is significantly different from that of “long” pulses or CW light and is accorded with the experimental results. © 2010 Elsevier B.V. All rights reserved.
1. Introduction Second harmonic generation (SHG) by quasi-phase-matching (QPM) [1] interaction is an attractive method to generate blue-green lights from infrared pump sources. Among the currently available QPM materials, periodically poled potassium titanyl phosphate (PPKTP) is an attractive one due to its increased resistance to photorefractive damage, high effective nonlinearity and wide transparency and low poling electric field [2]. Recently, periodically poled ferroelectric waveguides have attracted a lot of attention as higher conversion efficiencies are possible as a result of prolonged wave interaction at higher intensities [3–5]. Waveguides have the additional potential of being fiber pigtailed, allowing for efficient integration into compact configurations with fiber pump sources. KTP waveguide is normally fabricated by ion diffusion [6] which is only suitable for fabricating channel waveguides close to the surface, and in which high visible degradation has to be involved. Recently, femtosecond (fs) laser inscription has been applied successfully to create waveguides in a variety of optical materials including glasses [7], overcoming the limitations of waveguide fabricated by ion diffusion, and improving the optical quality of the inscribed waveguides. Frequency doubling with a conversion efficiency (CE) of ~0.002% has been achieved in femtosecond laser inscribed PPKTP waveguides from a continuous-wave (CW) Ti:sapphire laser [8]. Using a Q-switched Nd:
⁎ Corresponding author. Tel./fax: + 86 22 23509856. E-mail address: [email protected] (F. Lu). 0030-4018/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.optcom.2010.09.022
YAG laser as the pump source, we have demonstrated efficient 532 nm green light generations in a double line type II PPKTP waveguide with a CE of 39.6% [9]. Fiber laser sources are compact, robust, efficient, air-cooled, and do not require optical alignment. In this paper, using a high power femtosecond Ytterbium-doped fiber (YDF) laser with a central wavelength of 1044 nm, we demonstrated a femtosecond green light source at 523 nm by SHG in a PPKTP waveguide inscribed by fs laser pulses. A SHG power of 406 mW has been generated for a fundamental pump power of 7.3 W, yielding the total SHG CE of 5.6%. Numerical simulations were carried out to study the SHG characteristics of fs pulses, and to show the effect of the grating period of KTP crystal and cubic nonlinear effects on the SHG process. 2. PPKTP waveguide fabrication and its property Two types of waveguides can be fabricated by femtosecond laser direct writing [10,11]. For type I waveguides the guiding region is located at the trace of the femtosecond laser focus, and the thermal stability of such waveguide is not good [10]. This disadvantage can be overcome by double line written (type II) waveguides. In these structures the nonlinear coefficients are not affected [11], which allow high SHG efficiency. In this work, double line type II waveguides are designed and fabricated. A z-cut PPKTP sample with a dimension of 10 × 10 × 1 mm3 was fabricated by electrical poling technique. The PPKTP contains a grating with a period of 8.9 μm, an optical micrograph of the KTP crystal after periodically poled is shown in Fig. 1(a).
456
C. Tu et al. / Optics Communications 284 (2011) 455–459
(a)
(b)
oscillator and an ytterbium fiber amplifier. The oscillator operated as soliton-like mode-locking fiber laser using single-polarization large mode area (LMA) ytterbium-doped photonic crystal fiber (YD-PCF) as the gain medium, and directly generated 520 fs pulses with a repetition rate of 50 MHz and an average power of 300 mW. The pulses were then amplified in the LMA YD-PCF amplifier, and subsequently compressed by a pair of gratings. As a result, the YDF laser source produces pulses polarized linearly at 1044 nm with a maximum output power of 16 W, and the pulses have a full width at half maximum (FWHM) duration of 100 fs and a spectral width of 30 nm respectively, as shown in Fig. 3(a) and (b). To maintain stable output characteristics, we operated the YDF laser source at the maximum power and used an attenuator comprising a half-wave plate (HWP) and a polarizing beam splitter (PBS) to vary the input fundamental power. A second HWP was used to yield the correct pump polarization for phase matching. The fundamental beam was focused into the PPKTP waveguide by freespace coupling using a 10 × microscope objective (NA = 0.25). Both end-faces of the waveguide were polished but without anti-reflection coating. In order to detect the second harmonic light, an optical filter stopping 99.5% of the 1064 nm laser light and allowing 95% of the 532 nm light to pass through was placed after the collimating lens (f = 10 mm).
20μm
(c)
(d)
Fig. 1. (a) Optical micrograph of the KTP crystal after periodically poled, (b) the schematic diagram of PPKTP waveguide fabrication, (c) optical micrograph of the end facet of double line type II waveguide written with femtosecond pulses, and (d) the near filed guided mode profile at 532 nm.
To fabricate waveguides in the prepared PPKTP sample, we used an amplified Ti:sapphire laser system (HP-Spitfire, Spectra-Physics Inc.) operating at a central wavelength of 800 nm. The laser emitted linearly polarized femtosecond pulse trains with FWHM duration of 50 fs and maximum energy of 2 mJ at a repetition of 1 kHz. The laser beam was focused into the sample (along the z axis) with a 25 × microscope objective (NA = 0.4) at a depth of 300 μm beneath the sample surface, and the laser spot size was about 2.5 μm. A CCD (KA-320) detector was used to monitor the focusing condition. In order to produce a thermally stable double line written type waveguide, we consecutively wrote pairs of straight lines separated by 14.5 μm in the × direction of the sample. The sample was inscribed at a velocity of 200 μm/s perpendicular to the z axis by a computer-controlled positioner. The optimum pulse energy for the waveguide fabrication was investigated to be about 100 μJ. A schematic diagram of the waveguide fabrication system is shown in Fig. 1(b), and an optical micrograph of the waveguide's end facet and the corresponding near field image of the guided 532 nm mode are shown in Fig. 1(c) and (d) respectively.
3.2. Experimental results Based on the experimental setup shown in Fig. 2, we investigated the second harmonic generation in the PPKTP waveguide. To protect
3. Experiment for femtosecond green light generation 3.1. Experimental setup An experimental setup including a YDF femtosecond laser source and a PPKTP waveguide for green light generation is shown in Fig. 2. The fundamental pulses were generated by an fs YDF laser source which is composed of a passively mode-locked ytterbium fiber FW fs YDF laser source
SHG 1/2 λ
PBS
1/2 λ MO
PPKTP waveguide
lens
Filter
Fig. 2. Schematic of the experimental design for single-pass SHG of femtosecond YDF laser source in PPKTP waveguide fabricated by femtosecond laser pulses. YDF: ytterbium-doped fiber, 1/2λ: half-wave plate, PBS: polarizing beam splitter, MO: microscope objective, and FW: fundamental wave.
Fig. 3. (a) The spectrum and (b) the temporal shape (autocorrelation trace) of the out pulses from YDF amplifier.
C. Tu et al. / Optics Communications 284 (2011) 455–459
the PPKTP waveguide from being damaged, the power launched to the waveguide was controlled under 8 W. We measured the SHG power and the CE curve is shown in Fig. 4. It is clear that the SHG power and the corresponding CE increase as the pump power increased. For fundamental pump powers lower than 430 mW, no SHG signal can be detected. At a fundamental pump power of 7.3 W, the SHG power is 406 mW, corresponding to a conversion efficiency of 5.6% without considering the losses. A coupling loss of 1.1 dB/facet and a propagation loss of 1.0 dB/cm were measured at 1044 nm for TM polarization in PPKTP waveguide. If the losses are taken into account, the total conversion efficiency can be 9.1%. In our experiment, the fundamental wavelength is 1044 nm, while the first order QPM wavelength is 1052 nm for the grating period of 8.9 μm. That is to say, a CE of ~ 9% can be obtained for fs fundamental pulses even with a large phase mismatch, which indicates the SHG characteristic of fs pulses is different from that of long pulses or CW radiation [12]. The detailed discussion will be held in Section 4. Moreover, we expect that with the use of anti-reflectioncoated front and end facets, it is possible to further enhance the second harmonic output power and to increase the efficiency. In Fig. 5(a), we measured the SHG spectra at different fundamental powers. As the fundamental pump power increased, the SHG occurs towards both the longer and shorter wavelength sides of fundamental pulses, making the FWHM spectral width of SHG pulses broader. The phenomenon of the spectrum broadening is mainly because of the strong self-phase modulation (SPM) effect owing to such high peak power of fs pulses. Combining with the CE profile given in Fig. 4, we can view that high power (density) can also enhance the SHG process. Fig. 5(b) shows the SHG spectrum at a fundamental power of 4 W. The spectrum has an FWHM spectral width of 7.5 nm with a central wavelength of 523 nm, obviously its profile is almost the same as that of the fundamental pulses. To investigate the guiding property of the PPKTP waveguide, we measured the mode profile of SHG pulses using a mode profiler. Fig. 6 shows the mode profiles of both the fundamental and SHG pulses. In the figure SHG pulses have a good mode profile comparing with that of the fundamental pulses, and the spatial profile is very close to a Gaussian shape. A good guiding for the propagated pulses in the fabricated PPKTP waveguide was indicated. For comparison, the output power of second harmonic pulses in the bulk PPKTP crystal was also measured. We used the same PPKTP crystal and switched from the waveguide area to bulk crystal for this experiment. The laser beam was loosely focused into the PPKTP crystal by free-space coupling. The SHG output power at different fundamental pump power is shown in Fig. 7, from which we can see that the CE is smaller than that in the PPKTP waveguide. The higher CE implies that the propagated pulses are well confined in the waveguide, achieving a higher power density and better mode overlapping. Additionally,
457
Fig. 5. (a) The SHG spectra at different pump power levels and (b) the spectrum of the SHG and the fundamental pulses at a fundamental pump power of 4 W.
the SHG mode profile in waveguide is also better than that in bulk crystal. 4. Numerical simulation and discussions for SHG of fs pulses Based on the plane wave and slowly varying envelope approximations, the following coupled partial differential equations can be used to describe the evolution of the fundamental and the second harmonic pulses in PPKTP waveguide [13–15]: ∂ i ∂2 n k A = −iαdeff A2 A⁎1 expð−iΔkzÞ−i 2 1 A − β n0;1 ∂z 1 2 2;1 ∂τ2 1 h i 2 2 × jA1 j + 2jA2 j A1 ∂ A + ∂z 2
ð1Þ
1 1 ∂ i ∂2 2 − A2 − β2;2 2 A2 = −iαdeff A1 expðiΔkzÞ v2 v1 ∂τ 2 ∂τ n k 2 2 −i 2 2 jA2j + 2jA1j A2 n0;2 ð2Þ
Fig. 4. The SHG output power and the corresponding conversion efficiency vs. the fundamental pump power.
Where Ai is the envelope function of the electric field and vi is the group velocity. Here the indices 1 and 2 represent the fundamental and the second harmonic, respectively. β2, i is the group velocity dispersion (GVD) parameter. deff is the effective nonlinear coefficient, α is the coupling coefficient between the fundamental the second harmonic and is given by α = (2ω2 / ε0c3n201n02Seff)1/2. n0, i is the refractive index of the fundamental and second harmonic pulses, Seff is the effective waveguide cross section and n2 is the third order nonlinear refractive index. 1/ v2 − 1/ v1 is the group velocity mismatch
458
C. Tu et al. / Optics Communications 284 (2011) 455–459
Fig. 6. The spatial beam profile of the fundamental and SHG pulses, (a), (c) the fundamental pulse, (b), and (d) the SHG pulses.
GVM between the fundamental and the second harmonic pulses. Δk = k2 − 2k1 − 2π / Λ is the phase mismatch of the fundamental and second harmonic pulses at a given grating period Λ of a PPKTP crystal. Eqs. (1) and (2) include the effects of GVD, GVM, SPM and crossphase modulation (XPM), they are solved numerically by using a symmetrized split-step Fourier and Runge–Kutta method. The fundamental pulse is Gaussian shape: A1(0, t) = exp(− t 2 /2T02), T0 is the half width (at the 1/e intensity point) of the input pulse. The parameters used in simulations are: T0 = 60 fs (corresponds to an intensity profile with an FWHM duration of 100 fs), deff = 2d33 / π = 10.75 pm/V [16], n2 = 46 × 10−20 m2/W [17], Seff = 2 × 10−10 m2,β2, 1 = −0.013 ps2/m, β2, 2 = 0.070 ps2/m, n0, 1 = 1.8297 and n0, 2 = 1.8888 (at 20 °C) [18]. The grating period Λ of PPKTP crystal is 8.9 μm (phase matched for 1052 nm at 20 °C), and the waveguide length is 10 mm. Herein we set the peak power density in the PPKTP waveguide to be ~100 GW/cm2, which is the case in our experiments. For 100-fs pulses, the dispersion length (LD = T20/|β2|) is several times larger than our sample length. Thus GVD does not seem to be significant in our experiments. Nevertheless, it is included in the model for completeness.
Fig. 7. The SHG output vs. fundamental femtosecond pulse power in PPKTP waveguide and bulk PPKTP crystal.
From the expression of Δk we can see it is related to both the fundamental wavelength of fs pulses and the grating period Λ, here we illustrate how they affect the SHG CE of fs pulses. Just as above mentioned, the phase matching wavelength is 1052 nm at 20 °C for a grating period of 8.9 μm, while it is 1044 nm for the case of 8.83 μm. As shown in Fig. 8, the CE fluctuates and reduces with the central wavelength deviating from the phase matching wavelength, and the maximum CE is obtained near the phase matching wavelength. The trend of the CE curve remains almost the same but the peak wavelength (for the maximum CE) shifts when the grating period is changed. If phase matching is not well satisfied, then the CE will be almost zero [12]. However, it is not the case for fs pulses. Fig. 9 shows the wavelength tuning curves for pulses with durations of 100 fs and 100 ps respectively, herein we use the same pulse energy for them. The FWHM of the tuning curve is about 1 nm for 100 ps pulse. Compared with 100 ps pulses, 100 fs pulses have a much wider wavelength tuning range, which is 5 times of that for 100 ps pulses, meanwhile, the SHG CE of fs pulses is also higher than that of ps pulse within the tuning range. The results make the SHG process of fs pulses very different from that of “long” (picosecond and nanosecond)
Fig. 8. The variation of SHG CE with the central wavelength of fundamental pulse.
C. Tu et al. / Optics Communications 284 (2011) 455–459
459
see the CE is very small at lower pump power, however, it grows quickly with the pump power increasing. Obviously the numerical results give a good fit to the experimental results within a permitted accuracy. 5. Conclusions
Fig. 9. Picosecond pulse and femtosecond pulse wavelength tuning curve.
Based on a PPKTP waveguide inscribed by femtosecond laser, we have successfully generated 406 mW of fs pulses radiation at 523 nm with an efficiency of 5.6% in a highly compact and practical design using single-pass SHG of an fs YDF laser source. Numerical simulations are carried out to illustrate the SHG characteristics of fs pulses. The simulation results suggest that effective SHG of fs pulses can be obtained even under the non-QPM condition due to the cubic nonlinear effects originating from the high peak power density, which accords well with the experimental results. We have numerically studied the influences of the grating period, fundamental wavelength and the peak power density on the SHG CE. The unique characteristics imply that the SHG process of fs pulses is significantly different from that of the “long” pulses or CW light. Acknowledgements This work was supported by the National Natural Science Foundation of China (60677013, 60808003), the Specialized Research Fund for the Doctoral Program Foundation of Institute of Higher Education of China (20090031120004). References
Fig. 10. The SHG CE variation with the peak power density. The central wavelength of the femtosecond pump pulse is 1044 nm and Λ is 8.90 μm.
pulses [13]. If looking into the origin of the results in Fig. 9, we know it lies in the peak power and the spectrum width of these two pulses. As the interacting fs pulses have relatively broad bandwidths, the phase mismatch of interactions between different frequency components deviate from the phase mismatch Δk0 at the central wavelength [14], for some of the frequency components phase mismatch may be small, as a result, efficient SHG occurs. At the same time, the high peak power of fs pulses will induce strong SPM and XPM effects, and the phase mismatch due to cubic nonlinearity also influences the SHG CE [15]. Suppose the central wavelength of fs pulses is 1044 nm, we numerically studied the influence of the peak power density on the SHG CE for the grating period of 8.90 μm, the results are shown in Fig. 10. To make the simulation approach the experiment, we have considered the experimental loss in the numerical simulation. From Fig. 10 we can
[1] S. Somekh, A. Yariv, Opt. Commun. 6 (1972) 301. [2] M. Pierrou, F. Laurell, H. Karlsson, T. Kellner, C. Czeranowsky, G. Huber, Opt. Lett. 24 (1999) 205. [3] Y. Wang, V. Petrov, Y.J. Ding, Y. Zheng, J.B. Khurgin, W.P. Risk, Appl. Phys. Lett. 73 (1998) 873. [4] B. Agate, E.U. Rafailov, W. Sibbett, S.M. Saltiel, P. Battle, T. Fry, E. Noonan, Opt. Lett. 28 (2003) 1963. [5] S. Sinha, C. Langrock, M.J.F. Digonnet, M.M. Fejer, R.L. Byer, Opt. Lett. 31 (2006) 347. [6] J.-P. Ruske, M. Rottschalk, S. Steinberg, Opt. Commun. 120 (1995) 47. [7] K.M. Davis, K. Miura, N. Sugimoto, K. Hirao, Opt. Lett. 21 (1996) 1729. [8] S. Campbell, R.R. Thomson, D.P. Hand, A.K. Kar, D.T. Reid, C. Canalias, V. Pasiskevicius, F. Laurell, Opt. Express 15 (2007) 17146. [9] S.G. Zhang, J.H. Yao, W.W. Liu, Z.C. Huang, J. Wang, Y.N. Li, C.H. Tu, F.Y. Lu, Opt. Express 16 (2008) 14180. [10] R.R. Thomson, S. Campbell, I.J. Blewett, A.K. Kar, D.T. Reid, Appl. Phys. Lett. 88 (2006) 111109. [11] J. Burghoff, C. Grebing, S. Nolte, A. Tünnermann, Appl. Phys. Lett. 89 (2006) 081108. [12] M.M. Fejer, G.A. Magel, H.J. Dieter, L.B. Robert, J. Quantum Electron. 28 (1992) 2631. [13] Z.C. Huang, C.H. Tu, S.G. Zhang, Y.N. Li, F.Y. Lu, Y.X. Fan, E.B. Li, Opt. Lett. 35 (2010) 877. [14] Z. Zheng, A.M. Weiner, J. Opt. Soc. Am. B 19 (2002) 839. [15] T. Ditmire, A.M. Rubenchik, D. Eimerl, M.D. Perry, J. Opt. Soc. Am. B 13 (1996) 649. [16] A.A. Lagatsky, C.T.A. Brown, W. Sibbett, S.J. Holmgren, C. Canalias, V. Pasiskevicius, F. Laurell, E.U. Rafailov, Opt. Express 15 (2007) 1155. [17] B. Boulanger, J.P. Feve, P. Delarue, I. Rousseau, G. Marnier, J. Phys. B: At. Mol. Opt. Phys. 32 (1999) 475. [18] K. Kato, E. Takaoka, Appl. Opt. 41 (2002) 5040.