Numerical study on the efficient generation of 351 nm broadband pulses by frequency mixing of broadband and narrowband Nd: glass lasers

Optics Communications 283 (2010) 2737–2741

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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

Numerical study on the efficient generation of 351 nm broadband pulses by frequency mixing of broadband and narrowband Nd: glass lasers Ying Chen, Peng Yuan, Liejia Qian ⁎, Heyuan Zhu, Dianyuan Fan Department of Optical Science and Engineering, Laboratory for Advanced Materials, Fudan University, Shanghai 200433, China

a r t i c l e

i n f o

Article history: Received 12 October 2009 Received in revised form 6 March 2010 Accepted 6 March 2010 Keywords: Third-harmonic generation Broadband frequency conversion Fusion lasers

a b s t r a c t Efficient frequency-tripling of phase-modulated broadband Nd:glass laser pulses is of interest to inertial confinement fusion. We report and theoretically study an efficient frequency-tripling scheme for 351 nm broadband pulses generation by use of broadband and narrowband Nd:glass lasers. Based on the conventional two-crystal doubling and tripling baseline configuration, employing an additional narrowband laser can increase the bandwidth acceptance of Nd:glass up to 320 GHz, which is 3.5 times larger than that of using the conventional configuration. The proposed scheme may also dramatically reduce the conversion of amplitude modulation from the frequency modulation. The efficiency sensitivities on both the fundamental intensity and the doubler orientation are discussed for practical applications. © 2010 Elsevier B.V. All rights reserved.

1. Introduction Third-harmonic component of Nd:glass laser radiation is thought to be an ideal wavelength for inertial confinement fusion (ICF), and thus frequency tripler has become a standard auxiliary device in the highpower laser facilities [1]. Conversion efficiencies of ∼80% for the thirdharmonic generation (THG) were confirmed with narrowband pulses from high-energy Nd:glass lasers [2–4]. A broader bandwidth for the third harmonic is favored both in ICF experiments and Nd:glass laser system itself: (1) It may suppress the transverse stimulated Brillouin scattering within large-size optics, where bandwidth larger than 30 GHz, depending on the working intensity and the size of optics, is required [5]; (2) For the purpose of smooth irradiation on the target, the optical spectrum has to be broadened to a moderate bandwidth of ∼300 GHz [6,7]. Such a broad bandwidth is normally obtained through phase modulation by an electronic modulator [8], whose bandwidth is beyond the bandwidth acceptance of conventional THG configuration. Our study in this paper will primarily focus on such a moderate bandwidth; (3) Since a typical Nd:glass patawatt laser delivers laser pulses with a bandwidth as large as ∼5 nm [9], the ultimate solution for THG needs to exploit the whole bandwidth of ∼5 nm efficiently. Conventional THG of high-energy laser pulses at 1 μm involves frequency doubling and sum-frequency mixing in sequence using KDP or KD*P crystals [10]. Efficient THG is limited to narrow bandwidth cases because of the dispersion of KDP crystal. Several approaches have been tried to broaden the bandwidth acceptance in the broadband THG process, including angular spectral dispersion and chirp-adapted ⁎ Corresponding author. Fax: + 86 21 65643264. E-mail addresses: [email protected] (Y. Chen), [email protected] (L. Qian). 0030-4018/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.optcom.2010.03.008

broadband phase-matching [11,12]. Eimerl et al. proposed that a broader bandwidth acceptance of fundamental can be achieved by using a dual-tripler, i.e., two mixing crystals in series with proper opposite angular detunings from phase matching and thicknesses as well [13]. However, Babushkin et al. pointed out that the THG efficiency is quite sensitive to the spacing between the two mixers [14]. Yuan et al. proposed a broadband THG scheme based on a single mixer using segmented partially-deuterated KDP crystal [15]. Unfortunately, the growth of such a subtle crystal seems to be tough at present. Under the condition of phase-matching at central wavelength, the bandwidth acceptance is basically determined by the first-order wavelength-sensitivity parameter of phase-mismatching, namely, the group-velocity mismatch (GVM). The GVMs between the interacting waves in KDP crystal for Type I-SHG and Type II-SFG processes of Nd: glass laser are given in Table 1, which shows that the GVMs in SFG process dominate and thus are the main factors in limiting the bandwidth acceptance of the resultant THG.. Besides, in the SFG process, the GVM between the ω and 3ω waves is about 5 times larger than that between the 2ω and 3ω waves. We can expect that the conversion efficiency of broadband lasers will be dramatically increased if the larger GVM does not play the role. Recently, we have experimentally demonstrated an efficient broadband SFG scheme by using a narrowband pulsed Nd:YLF laser and a femtosecond chirped-pulse Ti:sapphire regenerative amplifier [16]. The experimental results imply that only the GVM between the incident and generated broadband pulses acts while the narrowband pulse-related GVMs have little effect and thus an improved upconversion efficiency can be achieved. To exploit the novel THG scheme supporting a moderate Nd:glass laser bandwidth of ∼300 GHz, in this paper we will theoretically study the broadband THG process based on the broadband/narrowband SFG scheme. We consider the type I/type II matching process, as it was

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Table 1 Group-velocity mismatches of frequency doubling and tripling processes for Nd:glass laser in KDP. GVM31 (GVM32) is defined as GVM between 1054 nm and 351 nm pulses (1054 nm and 527 nm pulses). Frequency converter

GVM (fs/mm)

Doubler (Tye I) 1ω(o) + 1ω(o) → 2ω(e)

− 5.0

Tripler(Type II)

GVM31

GVM31

1ω(e) + 2ω(o) → 3ω(e)

250

50

adopted in National Ignition Facility (NIF) [1]. This scheme involves frequency-doubling of a broadband fundamental pulse, followed by frequency-mixing between the generated broadband second-harmonic pulse and an additional narrowband pulse, different from the conventional scheme in which all the incidences on the tripler are from the frequency-doubling process. In such a way, the larger GVM value between broadband and narrowband lasers takes little affect on the SFG process, and the dominate obstacle of efficient THG will be alleviated. As a consequence, the proposed scheme enhances the bandwidth acceptance of Nd:glass laser by a factor of 3.5 compared to that of the conventional scheme, and supports a bandwidth up to ∼ 320 GHz. 2. The THG scheme with broadband/narrowband pulses The basic principle of mixing broadband and narrowband pulses is schematically shown in Fig. 1. For comparison, the conventional schemes with a single-tripler or a dual-tripler are also presented. In the conventional THG scheme, the doubling-efficiency is restricted to ∼67% (i.e., lower than its potentiality) to satisfy the optimal photon-number-matching between the SH and residual fundamental components. In our proposed scheme, however, no restriction on the doubling-efficiency is required, and the higher the better. The required optimal 2:1 ratio of SHG and fundamental intensities is realized by using half of a narrowband fundamental Nd:glass laser, assuming that the Nd:glass lasers may produce similar output energies for both narrowband and broadband pulse spectra. In a real Nd:glass laser system with multiple beams, two broadband beams and one narrowband beam, assuming they are synchronized, may be regarded as a basic group. Thus two broadband THG laser beams at 351 nm can be produced by a single group if the narrowband beam is divided equally into two. For instance, the NIF facility with 192 laser beams could be composed by 64 such laser bundles.

Fig. 1. Configurations for THG of Nd:glass laser. The conventional single-source scheme with (a) a single-tripler and (b) a dual-tripler. (c) The proposed scheme based on mixing of broadband and narrowband laser pulses.

The time-dependent nonlinear coupled-wave equations are used to simulate the processes of frequency doubling and mixing [3,15]. To the first order in quadratic susceptibility and neglecting all derivatives of refraction index beyond the second order, the equations that govern the envelopes E1 and E2 of the fundamental and secondharmonic pulses in the process of doubling, respectively, are ∂E1 ðz; t Þ 1 iω d * = − γ1 E1 ðz; t Þ− 1 1 E2 ðz; t ÞE1 ðz; t Þ exp ð−iΔk1 zÞ; 2 n1 c ∂z

ð1Þ

∂E2 ðz; t Þ ∂E ðz; t Þ 1 iω d 2 + GVM21 2 = − γ2 E2 ðz; t Þ− 2 1 E1 ðz; t Þ expðiΔk1 zÞ; n2 c 2 ∂z ∂t ð2Þ

where GVM21, ω1(ω2) and n1 (n2) are the GVM between the secondharmonic and fundamental waves, the central frequency and the refractive index, respectively. d1 is the effective nonlinear coefficient, γi's are absorption coefficients, and Δk = 2 k1 − k2 is the phasemismatch at the central wavelengths. With similar notations for the parameters, except phase-mismatch Δk2 = k1 − k2 − k3, the equations that govern the envelopes E1, E2 and E3 of the fundamental, secondharmonic and third-harmonic pulses in the process of mixing, respectively, are ∂E1 ðz; t Þ 1 iω d * = − γ1 E1 ðz; t Þ− 1 2 E3 ðz; t ÞE2 ðz; t Þ exp ð−iΔk2 zÞ; 2 n1 c ∂z

ð3Þ

∂E2 ðz; t Þ ∂E ðz; t Þ 1 iω d * + GVM21 2 = − γ2 E2 ðz; t Þ− 2 2 E3 ðz; t ÞE1 ðz; t Þ expð−iΔk2 zÞ; 2 n2 c ∂z ∂t

ð4Þ ∂E3 ðz; t Þ ∂E ðz; t Þ 1 iω d + GVM31 3 = − γ3 E3 ðz; t Þ− 3 2 E1 ðz; t ÞE2 ðz; t Þ expðiΔk2 zÞ: n3 c 2 ∂z ∂t

ð5Þ In the above equations the transverse spatial effects (i.e., diffraction and beam walk-off) are neglected for simplicity. In our simulations, all the crystal parameters are directly adopted from or calculated based on the data in references [13,15,17] and [18]. The incident broadband fundamental is assumed to be a phase-modulated 40th-order super-Gaussian pulse with central wavelength of 1054 nm and duration of 2 ns. The electro-optical phase modulator produces broad frequency spectrum with a bandwidth (FWHM) of 2δΩ, and the phase modulation is characterized by ϕ(t) = δsin2πΩt [8]. A 20-mmthick KDP crystal is adopted as the doubler to obtain high conversion efficiency over a wide intensity range, an 8-mm-thick KD*P crystal is used as the tripler. In the simulations, the fundamental laser intensity was fixed at a typical value, i.e., 3 GW/cm2, which compromises the damage problem and optics (beam) size. Fig. 2 (a) shows the effects of fundamental-wavelength detuning on the efficiency of THG for monochromatic waves. It clearly suggests that the acceptance bandwidth (FWHM) of the proposed THG scheme is over 2 nm (solid curve). The acceptance bandwidth for the conventional THG scheme with a single tripler (dashed curve) or a dual-tripler (dotted curve), on the other hand, are only ∼0.6 nm and 1.2 nm, respectively. Our proposed THG scheme broadens the acceptance bandwidth by a factor of about 3.5 compared with that of the conventional THG scheme with a single tripler. Actually, acceptance bandwidth for THG of Nd:glass laser is primarily limited by the GVM-caused phase-mismatches in the SFG process that are proportional to the product of GVM and spectral bandwidth. Specifically, there are two GVM values in the SFG process, i.e., the GVM between ω and 3ω and that between 2ω and 3ω, and the magnitude of the former is five times larger than that of the latter one. For phase modulated pulse, the spectral bandwidth of SHG is approximately twice as broad as that of the fundamental. Thus, in

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however, may not be so straightforward. Though the overall walk-off time is only 2 picosecond in the SFG process, which is much smaller than nanosecond pulses, its impact on the SFG process cannot be ignored. Since the second-harmonic pulse is highly chirped, the generated third-harmonic pulse will also be chirped. The locally generated third-harmonic component will interfere with the existing one that reaches that position. The two components will have the same instantaneous frequency for all positions if GVM is absent and will be coherently added in phase. If GVM caused temporal walk-off exists, the two components will have different instantaneous frequencies, which may result in beating, and hence a reduced conversion efficiency. From this physical picture, we may conclude that the beating effect can be ignored only when the overall GVMs-caused walk-off time is much smaller than the coherence time of the involved broadband laser pulses, which is quite similar to the case of using transform-limited pulses. The increased phase-matching bandwidth will result in an improved tripling efficiency for the broadband pulse, i.e., an improved bandwidth acceptance of fundamental (theoretical efficiency ∼ 80%), which is shown by Fig. 2(b). For example, the bandwidth acceptance

Fig. 2. Dependence of tripling-efficiency on (a) the wavelength detunings of fundamental and (b) the fundamental bandwidth. Solid curve, the proposed scheme based on mixing broadband 2ω and narrow ω laser pulses in the SFG process; dashed and dotted curves, the conventional THG schemes with a single and a dual-tripler (see Fig. 1 in Ref. [10]), respectively.

the conventional THG scheme for all-broadband pulses, the magnitude of phase-mismatch due to the GVM between 2ω and 3ω is only about two-sevenths of that of the overall GVMs resulted phasemismatches. By using the proposed narrowband/broadband scheme, only the GVM between the broadband 2ω and the generated broadband 3ω is important, which results in a small GVM-caused phase-mismatch, i.e., only about two-sevenths of that in the conventional all-broadband SFG process. As a result, the proposed THG scheme can increases acceptance bandwidth by a factor of 3.5. As discussed above, the THG acceptance bandwidth is inversely proportional to the GVM, thus smaller GVM in our THG scheme results in a larger acceptance bandwidth. The role of GVM in time domain,

Fig. 3. Dependence of tripling-efficiency on the bandwidth of the fundamental. Solid curve, mixing between broadband ω and narrowband 2ω laser pulses; dashed curve, all-broadband mixing.

Fig. 4. Dependence of tripling efficiency on the fundamental laser intensity for different bandwidths (a) 0 GHz, (b) 320 GHz, (c) 600 GHz. Solid curves, the proposed scheme with a 20 mm/0 μrad doubler followed by an 8 mm/0 μrad tripler; dashed curves, the conventional scheme with an 11 mm/250 μrad doubler followed by a 9 mm/0 μrad tripler.

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is only ∼ 90 GHz for the conventional scheme with a single tripler (dashed curve) and ∼ 250 GHz by use of a dual-tripler (dotted curve), while it increases to ∼ 320 GHz for the proposed scheme (solid curve). More importantly, the mechanism of increasing THG bandwidth in our proposed scheme is independent with that of a dual-tripler design, which suggests that much larger THG bandwidth may be anticipated if combining these two schemes together. We can infer, by analogy, that the bandwidth acceptance will only be enhanced by a factor of ∼ 1.4 if SFG occurs between narrowband 2ω and broadband ω laser pulses. The simulation results confirm this prediction, i.e., the bandwidth acceptance of fundamental for efficient THG is only ∼ 125 GHz, as shown in Fig. 3. 3. Intensity and crystal-orientation sensitivities In practice, pulse shapes may not be as uniform as super-Gaussian. It is therefore desirable to obtain efficient THG with large intensity variations. A wide dynamic range of THG efficiency depends largely on the optimal 2:1 ratio between the fundamental and second-harmonic

Fig. 5. Dependence of tripling efficiency on detuning angles of the doubler for different fundamental bandwidths (a) 0 GHz, (b) 320 GHz, (c) 600 GHz. The zero of the abscissa corresponds to the perfect phase matching angle for the proposed scheme (solid curve) and an angular offset of 250 μrad from phase matching angle for the conventional scheme (dashed curve). The input intensity is 3 GW/cm2.

intensities over a broad intensity range. To this end such as in the NIF design, the doubler (KDP crystal with thickness of 11 mm) is offset by an angle of 250 μrad from the perfect phase-matching. For the proposed THG scheme, the optimal 2:1 ratio is satisfied by efficient doubling approaching 100%. Thus we may use a thicker doublingcrystal to maintain a high doubling-efficiency over a broad intensity range. The intensity dynamic ranges for the two tripling schemes with different incident bandwidths are shown in Fig. 4. Compared with the conventional THG scheme, the proposed scheme has a wider dynamic range. Especially for small spectral bandwidth, the proposed THG scheme shows higher tripling efficiency with larger incident intensities. In the case of moderate spectral bandwidth (320 GHz), the proposed scheme maintains a high tripling efficiency over a broad intensity range, and the numerical simulation clearly shows that the THG is optimally designed at incident intensity ∼3 GW/cm2. For the broader input bandwidth (600 GHz), a lower input intensity and/or a thinner tripler will be better for the frequency tripling. We also study the sensitivity of tripling efficiency on the detuning angles. The low sensitivity on the detuning angle is beneficial since the laser beam might have pointing jitter and/or not be diffraction-

Fig. 6. Temporal profiles of input and output beams for the conventional scheme with (a) a single-tripler and (b) a dual-tripler, and (c) the proposed THG scheme. Dashed curves, fundamental incident on doubler; solid curves, output third-harmonic wave; dotted curves, fundamental incident on tripler. The input fundamental bandwidth is 320 GHz.

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limited. The proposed scheme is more sensitive to the angular offset for narrower bandwidth, opposite to the case of intensity sensitivity, which is shown by Fig. 5(a). From Fig. 5, we can conclude that the tripling frequency is less sensitive to the angular offset with the increase of input bandwidth for both the conventional scheme (dashed line) and the proposed one (solid line). In fact, broader bandwidth means that more frequency components involve in the tripling process, which will reduce the sensitivity of conversion efficiency on the phase mismatch at a price of lower efficiency. 4. Frequency-modulation to amplitude-modulation conversion Smooth profiles in both temporal and spatial domains are also crucial for ICF physical experiments and the laser system itself. In broadband THG of Nd:glass laser, e.g., a bandwidth of 320 GHz, the frequency modulation (FM) of fundamental pulse can be converted to a strong amplitude modulation (AM) on the output third-harmonic pulse for the conventional scheme with a single tripler (Fig. 6(a)). The addition of a second tripler may reduce but not substantially suppress the FM-to-AM conversion, as shown by Fig. 6(b). In fact, the origin of the FM-to-AM conversion is the spectral filtering due to the limited phase-matching bandwidth [19]. By use of the proposed scheme, the FM-to-AM conversion is greatly reduced due to the alleviation of the GVM effects, as shown by Fig. 6(c). We also study the influence of the residual broadband fundamental from the doubler on the succeeding process of SFG. Simulation results show that the tripling efficiency will decrease if the residual broadband fundamental involves in the SFG process though its energy is much less than that of the narrowband fundamental, as shown in Fig. 7(a). Actually, the residual broadband fundamental beam will coherently superpose on the narrowband fundamental beam due to the same wavelength and polarization. The superposition of the broadband beam with phase-modulation and the narrowband beam

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without phase-modulation leads to a substantial intensity modulation, which is shown in Fig. 7(b). As a result, the tripling efficiency will decrease obviously and the temporal profile of the output THG is strongly modulated. Thus the residual broadband fundamental should be removed before entering the tripler crystal, which can be realized by a dichroic mirror. Finally, it is important to point out that all the laser techniques and crystal materials adopted in our broadband THG scheme are currently available. The required pulse synchronization might be the only possible difficulty when two independent broadband and narrowband laser sources are involved. This problem can be solved at the front-end of the whole laser system if both the broadband and narrowband seeding pulses are obtained by electronically modulating a common single longitudinal-mode laser with required corresponding phase-modulation speeds. 5. Conclusion In this paper we have proposed and numerically studied a simple and efficient broadband THG scheme for Nd:glass laser system based on mixing narrowband and broadband laser pulses in the SFG process. The GVM effects of the SFG process is substantially alleviated with the assist of a narrowband laser, which is the dominate obstacle to efficient broadband THG. As a result, the bandwidth acceptance of fundamental can be increased by a factor of 3.5, compared with that of the conventional scheme. The FM-to-AM conversion may also be reduced significantly in the broadband THG process due to the alleviation of GVM effects. Acknowledgements This work was partially supported by the Natural Science Foundation of China (grant Nos. 10776005, 60890202 and 60725418), and National Basic Research Program of China (973 Program) (Grant No. 2007CB815104). References [1] [2] [3] [4] [5] [6] [7]

[8] [9]

[10] [11] [12] [13] [14] [15] [16] [17] [18] [19] Fig. 7. (a) Dependence of tripling efficiency on crystal length for the proposed scheme with (solid curve) or without (dashed curve) the residual broadband fundamental. (b) The temporal profile of the resultant fundamental pulse. The fundamental incident upon the doubler is the same as that in Fig. 6.

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