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Phase-matching properties of nonlinear crystals in deep ultraviolet
Optics & Laser Technology 33 (2001) 611–615
www.elsevier.com/locate/optlastec
Phase-matching properties of nonlinear crystals in deep ultraviolet Kenji Nagashimaa; ∗ , Liqiang Liub a Department
b Institute
of Visual Communication Design, Kyushu Institute of Design, 9-1 Siobaru 4, Minami-ku, Fukuoka 815-8540, Japan of Optoelectronic Technology, Shandong University of Science and Technology, Taian Shandong 271019, China Received 24 April 2001; received in revised form 31 July 2001; accepted 30 August 2001
Abstract We at present, can use a few nonlinear crystals such as LiB3 O5 (LBO), CsLiB6 O10 (CLBO), KBe2 BO3 F2 (KBBF) in deep ultraviolet (DUV) below 200 nm. Since the properties of these crystals have not been theoretically investigated in deep ultraviolet, we have performed the calculations of the frequency doubling, sum frequency phase matching and e9ective nonlinear coe:cients of LBO, CLBO and KBBF c 2001 Elsevier Science crystals in DUV waveband. We have also investigated the possibility of DUV output generation in these crystals. Ltd. All rights reserved. Keywords: LBO; CLBO; KBBF; Deep ultraviolet; Sum phase matching; E9ective nonlinear coe:cient
1. Introduction Deep ultraviolet lasers attract interest in many technical
Corresponding author. E-mail address: [email protected] (K. Nagashima).
DUV output was achieved by the direct frequency doubling of KBBF crystal [4]. This is the lowest wavelength that is attained by the direct frequency doubling of nonlinear crystals. CLBO also produced a 289 nm ultraviolet output by the direct frequency doubling [5]. Properties of these crystals in DUV region have been investigated, but detailed analyses of the DUV properties have not been conducted. Consequently, we have calculated the frequency doubling, the sum frequency phase matching and the e9ective nonlinear coe:cients of LBO, CLBO and KBBF crystals. We have also numerically analyzed the properties of these crystals in DUV output below 200 nm.
2. LBO, CLBO and KBBF phase-matching properties LBO, CLBO and KBBF crystals are all designed to be nonlinear chemical crystals with absorption band in DUV wavelength range in accordance with the anion group theory. The basic structural unit of LBO and CLBO is (B3 O7 )5− , and that of KBBF is (BO3 )3− , which have greater second nonlinear polarizability. Their ultraviolet cut-o9 wavelengths are 160 [6], 180 [7] and 155 nm [8], respectively. The three crystals possess cut-o9 wavelengths suitable for production of DUV light, and the possibility of the DUV output especially depends on whether the crystals can achieve the phase matching or not in DUV waveband.
c 2001 Elsevier Science Ltd. All rights reserved. 0030-3992/01/$ - see front matter PII: S 0 0 3 0 - 3 9 9 2 ( 0 1 ) 0 0 0 8 4 - 6
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K. Nagashima, L. Liu / Optics & Laser Technology 33 (2001) 611–615
Fig. 1. Type I phase-matching angles of LBO, CLBO and KBBF crystals versus doubling output wavelength.
Fig. 2. Type II phase-matching angles of LBO, CLBO and KBBF crystals versus doubling output wavelength.
LBO is an orthorhombic negative biaxial crystal, and the theoretical calculations of the phase-matching angles have been investigated in a previous study [9]. While CLBO and KBBF belong to tetragonal and trigonal structures, respectively, they are both negative uniaxial crystals. For type I phase matching of the negative uniaxial crystals, the interacting light wave is o+o → e. For type II it is e+o → e. For uniaxial crystals, the condition for type I phase matching is
Table 1 Properties of optical crystals
!1 no (!1 ; ) + !2 no (!2 ; ) = !3 ne (!3 ; ):
(1)
For type II !1 ne (!1 ; ) + !2 no (!2 ; ) = !3 ne (!3 ; ):
(2)
In Eq. (2), no and ne are no (!; ) = no (!) ne (!; ) =
n2o (!)n2e (!) n2o (!) sin2 + n2e (!) cos2
(3) 1=2 :
(4)
Phase-matching angles can be calculated by the above equations and the Sellmier equation of the crystals. In this work, the Sellmier equation used is quoted from other papers [4,10,11]. From the above equations, we calculated the type I phase matching curve and the type II phase-matching curve of the frequency doubling of LBO, CLBO and KBBF crystals. In order to clarify the di9erence of phase-matching properties in LBO, CLBO and KBBF, the phase-matching angles were calculated and the results are shown in Figs. 1 (type I) and 2 (type II), respectively. We can see from Fig. 1 that the shortest phase-matching wavelength of LBO is 555 nm whose second harmonic output wavelength is 277:5 nm, so that it cannot realize the DUV output below 200 nm by the direct frequency doubling. The shortest phase-matching wavelength of CLBO is 470:4 nm, and from this result, the shortest output
Crystals
Transparent range (nm)a
Nonlinear coe:cient (pm=V)a
Shortest SHG (nm)
LiB3 O5 (LBO)
160 –2600
277,a 277b
KBe2 BO3 F2 (KBBF) Sr 2 Be2 B2 O7 (SBBO) CsLiB6 O10 (CLBO) a Ref. [12]. b Our results.
155 –1660 155 –3780 180 –2750
d31 = 0:94; d32 = 1:13 d33 = 0:256 d11 = 0:8 d15 = 2 d36 = 0:95
185,a 164.4b 200a 237,a 235.2b
wavelength becomes 235:2 nm. Therefore, DUV output below 200 nm also cannot be obtained by the direct frequency doubling. Only KBBF having the lowest phase-matching wavelength of 328:7 nm whose doubling output wavelength is 164:4 nm can generate a DUV output below 200 nm by the direct frequency doubling. Fig. 2 indicates that the shortest wavelengths of the three crystals in type II phase-matching are higher than type I phase-matching wavelengths. Our results are shown in Table 1 together with a reference [12]. Next, we have calculated and analyzed the optical properties of three crystals in DUV wavelength in detail. First, we calculated the sum frequency phase-matching characteristics of LBO, CLBO and KBBF. For negative uniaxial crystals we can calculate the phase matching of the sum frequency by using Eqs. (1) – (4). The calculation method of biaxial crystals is similar to that of uniaxial crystals. Calculation methods were shown in previous papers [9,13]. In the calculation, the
K. Nagashima, L. Liu / Optics & Laser Technology 33 (2001) 611–615
Fig. 3. Type I phase-matching angles of LBO, CLBO and KBBF crystals versus sum frequency output wavelength. 1 is
Fig. 4. Type II phase-matching angles of LBO, CLBO and KBBF crystals versus sum frequency output wavelength. 1 is
613
Fig. 5. The shortest output wavelength of LBO versus sum frequency input wavelength.
Fig. 6. Type I phase-matching angles of LBO, CLBO and KBBF crystals versus sum frequency output wavelength. 1 is
following relation: 1= 1 + 1= 2 = 1= 3 ;
(5)
where 2 is the second mixing wavelength. From Figs. 3 and 4 we can see that the sum frequency output wavelength curves show similar properties with frequency doubling, but for LBO in type I phase matching, the shortest output wavelength is longer than 200 nm and in the crystals of CLBO and KBBF, it is shorter than 200 nm. The shortest output wavelength of KBBF crystal can reach almost 155 nm in type I phase matching and that of CLBO can reach 185:5 nm. In order to investigate further the DUV output of the LBO crystal, we calculated the shortest sum frequency output wavelength when 1 is varied from 1 to 2:1 m and 2 is varied from 173 to 316 nm. The result is shown in Fig. 5. It is obvious from Fig. 5 that if the input sum frequency light wavelength 1 exceeds 1:45 m, it can actualize DUV output below 200 nm. On the other hand, the
2:1 m wavelength corresponds to the emission wavelength of Ho : YAG [14], but in general, 1:064 m wavelength is used as 1 , so that it may be di:cult to achieve a DUV output below 200 nm as long as Nd laser is used. Fig. 6 shows type I phase-matching curves of LBO, CLBO and KBBF crystals in sum frequency output wavelength from 150 to 500 nm when 2 is varied from 162 to 656 nm. We have not calculated the type II phase matching, since the output wavelength is relatively long and the e9ective nonlinear coe:cient is low. Phase-matching properties of LBO, CLBO and KBBF crystals show that they may be all excellent crystal materials to generate a DUV output below 200 nm in 1 of 2:1 m, but it is di:cult to estimate the generation of DUV light from phase-matching property alone, since it may depend on the e9ective nonlinear coe:cient.
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K. Nagashima, L. Liu / Optics & Laser Technology 33 (2001) 611–615
Fig. 7. E9ective nonlinear coe:cients of LBO, CLBO and KBBF crystal versus frequency doubling output wavelength.
Fig. 8. E9ective nonlinear coe:cients of LBO, CLBO and KBBF crystals versus sum frequency output wavelength. 1 is
3. E ective nonlinear coe#cients of LBO,CLBO and KBBF We have calculated the e9ective nonlinear coe:cients (de9 ) of some crystals by using the nonlinear polarized coe:cients and the phase-matching angles of the crystals [9,12,13]. The equations used are as follows: LBO:
de9 = d32 cos ’ for type I, de9 = d31 cos for type II; CLBO: de9 = d36 sin sin 2’ for type I, de9 = d36 sin 2 cos 2’; d36 = d14 for type II; KBBF: de9 = d11 cos cos 3’ for type I, de9 = d11 cos2 sin 3’ for type II.
E9ective nonlinear coe:cients of LBO, CLBO and KBBF are shown in Fig. 7. In the calculation, phase-matching angles corresponding to those in Fig. 1 were used. From the curves shown in Fig. 7, it is obvious in doubling output wavelength that the magnitudes of the e9ective nonlinear coe:cients of LBO and KBBF crystals decrease together with the wavelength shift toward shorter wavelength side, and the e9ective nonlinear coe:cient of LBO becomes 0 at the wavelength over 270 nm. An e9ective nonlinear coe:cient of 0, which is the end point of phase matching, cor◦ responds to a phase angle of 90 . From this point of view, use of LBO may be a disadvantage for the doubling conversion at a wavelength of 200 nm though LBO crystal possesses good transparency in the DUV range between 160 and 200 nm from Table 1. Conversely, CLBO crystal possesses rather high e9ective nonlinear coe:cients in the range of shorter wavelength than 250 nm and the coe:cients increase with decreasing wavelength. Thus, CLBO may attain higher conversion ef
Fig. 9. E9ective nonlinear coe:cients of LBO, CLBO and KBBF crystals versus sum frequency output wavelength. 1 is
and the output wavelength is 235:2 nm, and the application of the CLBO to the DUV region below 200 nm is forbidden in direct frequency doubling. As to the e9ective nonlinear coe:cients, KBBF crystal is the optimal material to attain direct DUV output by frequency doubling. The calculations for type I sum frequency e9ective nonlinear coe:cients of LBO, CLBO and KBBF are the same as that in frequency doubling and were performed by using the data shown in Fig. 3. The result is shown in Fig. 8. Evidently, CLBO and KBBF crystals have good properties in the sum frequency output at 1 of 1064 nm. The sum frequency e9ective nonlinear coe:cient of CLBO and KBBF increases with decreasing the output wavelength. Therefore, CLBO and KBBF can produce higher conversion e:ciency in generation of DUV output below 200 nm but the coe:cient of LBO is decreased to 0 at 230 nm as well as that in frequency doubling. Fig 9 shows the relation between the e9ective nonlinear coe:cient and the sum frequency output wavelength at 1 of
K. Nagashima, L. Liu / Optics & Laser Technology 33 (2001) 611–615
2:1 m. In the calculation, wavelengths and phase-matching angles used for calculations were obtained from Fig. 6. It is obvious from Fig. 9 that all crystals can maintain high effective nonlinear coe:cients till the wavelength of 180 nm, and the coe:cients are larger than 0:7 pm=V at 180 nm. This result indicates that the DUV output below 200 nm may be e9ectively obtained by the sum frequency of LBO, CLBO and KBBF using proper laser pumping sources. However, the details remain unknown, since the experiments have not been performed. 4. Conclusion We have performed the numerical analyses of the frequency doublings, the sum frequency phase-matching properties and the e9ective nonlinear coe:cients of LBO, CLBO and KBBF crystals. Results of the calculations show that KBBF can generate a DUV output below 200 nm by the frequency doubling or the sum frequency. CLBO also has a relatively high e9ective nonlinear coe:cient in the lower wavelength region. It cannot achieve the phase matching by frequency doubling at an output wavelength below 200 nm, but the phase matching can be achieved by the sum frequency. As a result, it is concluded that LBO, CLBO and KBBF have a possibility of generating a DUV output below 200 nm in frequency doubling or sum frequency phase matching with suitable pumping sources. References [1] Watanabe M, Hayasaka K, Imajo H. Generation of continuous-wave coherent radiation tunable down to 190:8 nm in beta-BaB2 O4 . Appl Phys 1991;B53(1):11–5.
615
[2] Wu B, Xie F, Chen C, Deng D, Xu Z. Generation of tunable coherent vacuum ultraviolet radiation in LiB3 O5 crystal. Opt Commun 1992;88(4 – 6):451–4. [3] Seifert F, Ringling J, Noack F, Peirov V, Kittelmann O. Generation of tunable femtosecond pulses to as low as 172.7 nm by sum-frequency mixing in lithium triborate. Opt Lett 1994;19(19): 1538–40. [4] Chen C, Xu Z, Deng D, Zhang J, Wong GKL, Wu B, Ye N, Tang D. The vacuum ultraviolet phase-matching characteristics of nonlinear optical Kbe2 BO3 F2 crystal. Appl Phys Lett 1996;68(21): 2930–2. [5] Chandra S, Allik TA, Hutchinson JA, Fox J, Swin C. Tunable ultraviolet laser source based on solid-state dye laser technology and CsLiB6 O10 harmonic generation. Opt Lett 1997;22(4): 209–11. [6] Chen C, Wu Y, Jiang A, Wu B, You G, Li R, Lin S. New nonlinear-optical crystal: LiB3 O5 . J Opt Soc Am B 1989;6(4): 616–21. [7] Mori Y, Kuroda I, Nakajima S, Sasaki T, Nakai S. New nonlinear optical crystal: cesium lithium borate. Appl Phys Lett 1995;67(13):1818–20. [8] Chen C, Xu Z, Deng D, Zhang J, Wong GKL. The vacuum ultraviolet phase-matching characteristics of nonlinear optical Kbe2 BO3 F2 crystal. Appl Phys Lett 1996;68(21):2930–2. [9] Liu L, Nagashima K. Optimum phase matching and e9ective nonlinear coe:cients of LBO and KTP for continuously changing wavelength. Opt Laser Technol 1999;31:283–7. [10] Mao H, Wu B, Chen C. Broadband optical parametric ampli
www.elsevier.com/locate/optlastec
Phase-matching properties of nonlinear crystals in deep ultraviolet Kenji Nagashimaa; ∗ , Liqiang Liub a Department
b Institute
of Visual Communication Design, Kyushu Institute of Design, 9-1 Siobaru 4, Minami-ku, Fukuoka 815-8540, Japan of Optoelectronic Technology, Shandong University of Science and Technology, Taian Shandong 271019, China Received 24 April 2001; received in revised form 31 July 2001; accepted 30 August 2001
Abstract We at present, can use a few nonlinear crystals such as LiB3 O5 (LBO), CsLiB6 O10 (CLBO), KBe2 BO3 F2 (KBBF) in deep ultraviolet (DUV) below 200 nm. Since the properties of these crystals have not been theoretically investigated in deep ultraviolet, we have performed the calculations of the frequency doubling, sum frequency phase matching and e9ective nonlinear coe:cients of LBO, CLBO and KBBF c 2001 Elsevier Science crystals in DUV waveband. We have also investigated the possibility of DUV output generation in these crystals. Ltd. All rights reserved. Keywords: LBO; CLBO; KBBF; Deep ultraviolet; Sum phase matching; E9ective nonlinear coe:cient
1. Introduction Deep ultraviolet lasers attract interest in many technical
Corresponding author. E-mail address: [email protected] (K. Nagashima).
DUV output was achieved by the direct frequency doubling of KBBF crystal [4]. This is the lowest wavelength that is attained by the direct frequency doubling of nonlinear crystals. CLBO also produced a 289 nm ultraviolet output by the direct frequency doubling [5]. Properties of these crystals in DUV region have been investigated, but detailed analyses of the DUV properties have not been conducted. Consequently, we have calculated the frequency doubling, the sum frequency phase matching and the e9ective nonlinear coe:cients of LBO, CLBO and KBBF crystals. We have also numerically analyzed the properties of these crystals in DUV output below 200 nm.
2. LBO, CLBO and KBBF phase-matching properties LBO, CLBO and KBBF crystals are all designed to be nonlinear chemical crystals with absorption band in DUV wavelength range in accordance with the anion group theory. The basic structural unit of LBO and CLBO is (B3 O7 )5− , and that of KBBF is (BO3 )3− , which have greater second nonlinear polarizability. Their ultraviolet cut-o9 wavelengths are 160 [6], 180 [7] and 155 nm [8], respectively. The three crystals possess cut-o9 wavelengths suitable for production of DUV light, and the possibility of the DUV output especially depends on whether the crystals can achieve the phase matching or not in DUV waveband.
c 2001 Elsevier Science Ltd. All rights reserved. 0030-3992/01/$ - see front matter PII: S 0 0 3 0 - 3 9 9 2 ( 0 1 ) 0 0 0 8 4 - 6
612
K. Nagashima, L. Liu / Optics & Laser Technology 33 (2001) 611–615
Fig. 1. Type I phase-matching angles of LBO, CLBO and KBBF crystals versus doubling output wavelength.
Fig. 2. Type II phase-matching angles of LBO, CLBO and KBBF crystals versus doubling output wavelength.
LBO is an orthorhombic negative biaxial crystal, and the theoretical calculations of the phase-matching angles have been investigated in a previous study [9]. While CLBO and KBBF belong to tetragonal and trigonal structures, respectively, they are both negative uniaxial crystals. For type I phase matching of the negative uniaxial crystals, the interacting light wave is o+o → e. For type II it is e+o → e. For uniaxial crystals, the condition for type I phase matching is
Table 1 Properties of optical crystals
!1 no (!1 ; ) + !2 no (!2 ; ) = !3 ne (!3 ; ):
(1)
For type II !1 ne (!1 ; ) + !2 no (!2 ; ) = !3 ne (!3 ; ):
(2)
In Eq. (2), no and ne are no (!; ) = no (!) ne (!; ) =
n2o (!)n2e (!) n2o (!) sin2 + n2e (!) cos2
(3) 1=2 :
(4)
Phase-matching angles can be calculated by the above equations and the Sellmier equation of the crystals. In this work, the Sellmier equation used is quoted from other papers [4,10,11]. From the above equations, we calculated the type I phase matching curve and the type II phase-matching curve of the frequency doubling of LBO, CLBO and KBBF crystals. In order to clarify the di9erence of phase-matching properties in LBO, CLBO and KBBF, the phase-matching angles were calculated and the results are shown in Figs. 1 (type I) and 2 (type II), respectively. We can see from Fig. 1 that the shortest phase-matching wavelength of LBO is 555 nm whose second harmonic output wavelength is 277:5 nm, so that it cannot realize the DUV output below 200 nm by the direct frequency doubling. The shortest phase-matching wavelength of CLBO is 470:4 nm, and from this result, the shortest output
Crystals
Transparent range (nm)a
Nonlinear coe:cient (pm=V)a
Shortest SHG (nm)
LiB3 O5 (LBO)
160 –2600
277,a 277b
KBe2 BO3 F2 (KBBF) Sr 2 Be2 B2 O7 (SBBO) CsLiB6 O10 (CLBO) a Ref. [12]. b Our results.
155 –1660 155 –3780 180 –2750
d31 = 0:94; d32 = 1:13 d33 = 0:256 d11 = 0:8 d15 = 2 d36 = 0:95
185,a 164.4b 200a 237,a 235.2b
wavelength becomes 235:2 nm. Therefore, DUV output below 200 nm also cannot be obtained by the direct frequency doubling. Only KBBF having the lowest phase-matching wavelength of 328:7 nm whose doubling output wavelength is 164:4 nm can generate a DUV output below 200 nm by the direct frequency doubling. Fig. 2 indicates that the shortest wavelengths of the three crystals in type II phase-matching are higher than type I phase-matching wavelengths. Our results are shown in Table 1 together with a reference [12]. Next, we have calculated and analyzed the optical properties of three crystals in DUV wavelength in detail. First, we calculated the sum frequency phase-matching characteristics of LBO, CLBO and KBBF. For negative uniaxial crystals we can calculate the phase matching of the sum frequency by using Eqs. (1) – (4). The calculation method of biaxial crystals is similar to that of uniaxial crystals. Calculation methods were shown in previous papers [9,13]. In the calculation, the
K. Nagashima, L. Liu / Optics & Laser Technology 33 (2001) 611–615
Fig. 3. Type I phase-matching angles of LBO, CLBO and KBBF crystals versus sum frequency output wavelength. 1 is
Fig. 4. Type II phase-matching angles of LBO, CLBO and KBBF crystals versus sum frequency output wavelength. 1 is
613
Fig. 5. The shortest output wavelength of LBO versus sum frequency input wavelength.
Fig. 6. Type I phase-matching angles of LBO, CLBO and KBBF crystals versus sum frequency output wavelength. 1 is
following relation: 1= 1 + 1= 2 = 1= 3 ;
(5)
where 2 is the second mixing wavelength. From Figs. 3 and 4 we can see that the sum frequency output wavelength curves show similar properties with frequency doubling, but for LBO in type I phase matching, the shortest output wavelength is longer than 200 nm and in the crystals of CLBO and KBBF, it is shorter than 200 nm. The shortest output wavelength of KBBF crystal can reach almost 155 nm in type I phase matching and that of CLBO can reach 185:5 nm. In order to investigate further the DUV output of the LBO crystal, we calculated the shortest sum frequency output wavelength when 1 is varied from 1 to 2:1 m and 2 is varied from 173 to 316 nm. The result is shown in Fig. 5. It is obvious from Fig. 5 that if the input sum frequency light wavelength 1 exceeds 1:45 m, it can actualize DUV output below 200 nm. On the other hand, the
2:1 m wavelength corresponds to the emission wavelength of Ho : YAG [14], but in general, 1:064 m wavelength is used as 1 , so that it may be di:cult to achieve a DUV output below 200 nm as long as Nd laser is used. Fig. 6 shows type I phase-matching curves of LBO, CLBO and KBBF crystals in sum frequency output wavelength from 150 to 500 nm when 2 is varied from 162 to 656 nm. We have not calculated the type II phase matching, since the output wavelength is relatively long and the e9ective nonlinear coe:cient is low. Phase-matching properties of LBO, CLBO and KBBF crystals show that they may be all excellent crystal materials to generate a DUV output below 200 nm in 1 of 2:1 m, but it is di:cult to estimate the generation of DUV light from phase-matching property alone, since it may depend on the e9ective nonlinear coe:cient.
614
K. Nagashima, L. Liu / Optics & Laser Technology 33 (2001) 611–615
Fig. 7. E9ective nonlinear coe:cients of LBO, CLBO and KBBF crystal versus frequency doubling output wavelength.
Fig. 8. E9ective nonlinear coe:cients of LBO, CLBO and KBBF crystals versus sum frequency output wavelength. 1 is
3. E ective nonlinear coe#cients of LBO,CLBO and KBBF We have calculated the e9ective nonlinear coe:cients (de9 ) of some crystals by using the nonlinear polarized coe:cients and the phase-matching angles of the crystals [9,12,13]. The equations used are as follows: LBO:
de9 = d32 cos ’ for type I, de9 = d31 cos for type II; CLBO: de9 = d36 sin sin 2’ for type I, de9 = d36 sin 2 cos 2’; d36 = d14 for type II; KBBF: de9 = d11 cos cos 3’ for type I, de9 = d11 cos2 sin 3’ for type II.
E9ective nonlinear coe:cients of LBO, CLBO and KBBF are shown in Fig. 7. In the calculation, phase-matching angles corresponding to those in Fig. 1 were used. From the curves shown in Fig. 7, it is obvious in doubling output wavelength that the magnitudes of the e9ective nonlinear coe:cients of LBO and KBBF crystals decrease together with the wavelength shift toward shorter wavelength side, and the e9ective nonlinear coe:cient of LBO becomes 0 at the wavelength over 270 nm. An e9ective nonlinear coe:cient of 0, which is the end point of phase matching, cor◦ responds to a phase angle of 90 . From this point of view, use of LBO may be a disadvantage for the doubling conversion at a wavelength of 200 nm though LBO crystal possesses good transparency in the DUV range between 160 and 200 nm from Table 1. Conversely, CLBO crystal possesses rather high e9ective nonlinear coe:cients in the range of shorter wavelength than 250 nm and the coe:cients increase with decreasing wavelength. Thus, CLBO may attain higher conversion ef
Fig. 9. E9ective nonlinear coe:cients of LBO, CLBO and KBBF crystals versus sum frequency output wavelength. 1 is
and the output wavelength is 235:2 nm, and the application of the CLBO to the DUV region below 200 nm is forbidden in direct frequency doubling. As to the e9ective nonlinear coe:cients, KBBF crystal is the optimal material to attain direct DUV output by frequency doubling. The calculations for type I sum frequency e9ective nonlinear coe:cients of LBO, CLBO and KBBF are the same as that in frequency doubling and were performed by using the data shown in Fig. 3. The result is shown in Fig. 8. Evidently, CLBO and KBBF crystals have good properties in the sum frequency output at 1 of 1064 nm. The sum frequency e9ective nonlinear coe:cient of CLBO and KBBF increases with decreasing the output wavelength. Therefore, CLBO and KBBF can produce higher conversion e:ciency in generation of DUV output below 200 nm but the coe:cient of LBO is decreased to 0 at 230 nm as well as that in frequency doubling. Fig 9 shows the relation between the e9ective nonlinear coe:cient and the sum frequency output wavelength at 1 of
K. Nagashima, L. Liu / Optics & Laser Technology 33 (2001) 611–615
2:1 m. In the calculation, wavelengths and phase-matching angles used for calculations were obtained from Fig. 6. It is obvious from Fig. 9 that all crystals can maintain high effective nonlinear coe:cients till the wavelength of 180 nm, and the coe:cients are larger than 0:7 pm=V at 180 nm. This result indicates that the DUV output below 200 nm may be e9ectively obtained by the sum frequency of LBO, CLBO and KBBF using proper laser pumping sources. However, the details remain unknown, since the experiments have not been performed. 4. Conclusion We have performed the numerical analyses of the frequency doublings, the sum frequency phase-matching properties and the e9ective nonlinear coe:cients of LBO, CLBO and KBBF crystals. Results of the calculations show that KBBF can generate a DUV output below 200 nm by the frequency doubling or the sum frequency. CLBO also has a relatively high e9ective nonlinear coe:cient in the lower wavelength region. It cannot achieve the phase matching by frequency doubling at an output wavelength below 200 nm, but the phase matching can be achieved by the sum frequency. As a result, it is concluded that LBO, CLBO and KBBF have a possibility of generating a DUV output below 200 nm in frequency doubling or sum frequency phase matching with suitable pumping sources. References [1] Watanabe M, Hayasaka K, Imajo H. Generation of continuous-wave coherent radiation tunable down to 190:8 nm in beta-BaB2 O4 . Appl Phys 1991;B53(1):11–5.
615
[2] Wu B, Xie F, Chen C, Deng D, Xu Z. Generation of tunable coherent vacuum ultraviolet radiation in LiB3 O5 crystal. Opt Commun 1992;88(4 – 6):451–4. [3] Seifert F, Ringling J, Noack F, Peirov V, Kittelmann O. Generation of tunable femtosecond pulses to as low as 172.7 nm by sum-frequency mixing in lithium triborate. Opt Lett 1994;19(19): 1538–40. [4] Chen C, Xu Z, Deng D, Zhang J, Wong GKL, Wu B, Ye N, Tang D. The vacuum ultraviolet phase-matching characteristics of nonlinear optical Kbe2 BO3 F2 crystal. Appl Phys Lett 1996;68(21): 2930–2. [5] Chandra S, Allik TA, Hutchinson JA, Fox J, Swin C. Tunable ultraviolet laser source based on solid-state dye laser technology and CsLiB6 O10 harmonic generation. Opt Lett 1997;22(4): 209–11. [6] Chen C, Wu Y, Jiang A, Wu B, You G, Li R, Lin S. New nonlinear-optical crystal: LiB3 O5 . J Opt Soc Am B 1989;6(4): 616–21. [7] Mori Y, Kuroda I, Nakajima S, Sasaki T, Nakai S. New nonlinear optical crystal: cesium lithium borate. Appl Phys Lett 1995;67(13):1818–20. [8] Chen C, Xu Z, Deng D, Zhang J, Wong GKL. The vacuum ultraviolet phase-matching characteristics of nonlinear optical Kbe2 BO3 F2 crystal. Appl Phys Lett 1996;68(21):2930–2. [9] Liu L, Nagashima K. Optimum phase matching and e9ective nonlinear coe:cients of LBO and KTP for continuously changing wavelength. Opt Laser Technol 1999;31:283–7. [10] Mao H, Wu B, Chen C. Broadband optical parametric ampli