Abstract

Third-order optical nonlinearities, χ (3) of GeS2-Ga2S3-AgCl chalcohalide glasses have been studied systematically utilizing the femtosecond time-resolved optical Kerr effect (OKE) technique at 820nm, showing that the value of χ (3) enhances with increasing atomic ratio of (S+Cl/2)/(Ge+Ga). From the compositional dependence of glass structure by Raman spectra, a strong dependence χ (3) upon glass structure has been found, i.e. compared with [ClxS3-xGe(Ga)-Ge(Ga)S3-xClx] ethane-like s.u. as the structural defectiveness, [Ge(Ga)S4-xClx] mixed tetrahedra make greater contribution to the enhancement of χ (3). The maximum χ (3) among the present glasses is as large as 5.26×10-13esu (A1 (80GeS2-10Ga2S3-10AgCl)), and the nonlinear refractive index (n2) of A1 glass is also up to 4.60×10-15 cm2/W. In addition, using Maker fringe technique, SHG was observed in the representative A1 glass poled by electron beam (25 kV, 25 nA, 15 min), and the second-order optical nonlinear susceptibility is estimated to be greater than 6.1 pm/V. There was no evident structural change detected in the as-prepared and after irradiated A1 glass by the Raman spectra, and maybe only electronic transition and distortion of electron cloud occurred in the glasses. The large third/second-order optical nonlinearities have made these GeS2-Ga2S3-AgCl chalcohalide glasses as promising materials applied in photoelectric fields.

©2007 Optical Society of America

1. Introduction

Third-order optical nonlinearity of glasses have been extensively investigated because of their potential applications in the optoelectronic field [1, 2]. However, in the case of the silica glass, the typical values of third-order optical nonlinearity (χ (3)) are not large enough for the design of devices in optical communication networks [3]. Chalcogenide glasses, which are the typical nonresonant materials, have attracted much attention for their large third-order optical nonlinear susceptibility and wide transmission [3, 4]. Recently, GeS2-based chalcogenide glasses have become one of the predominant candidates for all-optical switching applications at the telecommunication wavelength of 1.3μm due to their higher band-gap energy compared with Se- and As2S3-containing chalcogenide glasses [4, 5]. In addition, according to the Miller’s rule [6], χ (3) can be enhanced in the glasses doped with heavy-metal ions which exhibit higher linear refractive index (n). Consequently, the third-order optical nonlinearities of GeS2-Ga2S3-AgCl chalcohalide glasses were studied in this paper through femtosecond time-resolved optical Kerr effect (OKE) technique. Although some researches of GeS2-based chalcogenide glasses have been reported in our previous works [7, 8], the studies on the relationship between the structure and χ (3) are scarce. Therefore, in this paper, compositional and structural dependence of χ (3) of the GeS2-Ga2S3-AgCl chalcohalide glasses was also discussed in detail.

On the other side, materials with large second-order optical nonlinearity have attained wide applications in many fields such as frequency conversion, high density storage, speed modulators, etc. [9, 10]. Glasses, as one of inverse centrosymmetric materials, can not exhibit second-harmonic generation (SHG). However, SHG can be induced through specific treatment like electron beam irradiation, thermal-electric poling, laser irradiation and so on [11–13]. As one of the most convenient and effective poling means, electron beam irradiation has been utilized to induce SHG in some previous papers. And in this paper, SHG was observed in the electron beam irradiated A1 sample (80GeS2-10Ga2S3-10AgCl) using the Maker fringe method, and the poling mechanism was also discussed in this paper.

2. Experimental

2.1. Glass synthesis and characterization

Homogeneous GeS2-Ga2S3-AgCl glasses were obtained by melt-quenching technique using high-purity Ge, Ga, S (all of 5N) and AgCl (3N) as raw materials. Details of the preparations were similar to the procedure in our previous works [14]. The 10×10×1 mm3 glass plates were prepared from the bulk glasses and were optically double-faced polished. The compositions of the prepared glasses were analyzed by electron probing micro analysis (EPMA, JXA-8800R), indicating that the difference between theoretical and real composition was within reasonable range (±1.5 atom.%) except for the element of chlorine (losing almost 10 atom.% of the theoretical content), which is mainly due to the light-induced decomposition of AgCl in the process of glass preparation.

Optical transmission was recorded with a spectrophotometer (Shimadzu UV-1601) in the visible and near-IR region (Vis-NIR). To study the structure of these glasses, Raman spectroscopy was conducted by the micro Raman Spectrometer (Type: Renishaw inVia) using the back (180°) scattering configuration at room temperature. For the avoidance of local laser damage and crystallization, an Ar+ laser (λ=514nm) with a power less than 2 mW was used as an excitation source. The error was within the range of ± 1cm-1.

2.2 Third-order optical nonlinearity characterization

The third-order optical nonlinearity of the glasses was measured using standard femtosecond time-resolved optical Kerr effect technique (OKE). A Ti:Sapphire laser (Mira 900F, Coherent, USA) pumped by a CW Nd:YAG laser (Coherent, USA) was used as the light source. The laser pulse operated at 76MHz, and the wavelength was centered at 820nm with the pulse duration of 120fs. The laser output was split into two beams by a beamsplitter with an intensity ratio of 10:1. The strong beam acts as the pump one and the weak beam as the probe one. To obtain the time-resolved signal, the pump beam was set to pass through an optical delay line driven by a step-motor. Two beams were carefully adjusted parallel and then focused by a convex lens to overlap spatially inside the glass sample. After transmitting through the glass sample, the pump beam was blocked, while the probe beam passed through a polarizer whose transmission axis was strictly perpendicular to its original polarization. Therefore, only the generated orthogonal optical Kerr signal can enter into the analyzer. The gating pump power on the samples was set to be 76mW. Liquid CS2 in a quartz cell with a thickness of 1mm was used as a reference. For details see our previous paper [15].

2.3. Second-order optical nonlinearity characterization

The polished glass plate with representative composition A1 (80GeS2-10Ga2S3-10AgCl) was placed into EPMA (JXA-8800R) (the pressure of sample chamber is lower than 7×10-3 Pa), and then irradiated by electron beam (voltage: 25kV; current: 25nA) for 15min. No distinct physical damage was observed on the glassy surface after irradiation.

Second-order optical nonlinearity of the electron beam irradiated A1 chalcohalide glass was characterized with the standard Maker fringe method. A Q-switched Nd: YAG laser providing 10ns pulses of 1064nm radiation was used as the fundamental light. After attenuating, this fundamental light with a repetition rate of 10 Hz was focused onto the center of poled areas. The beam area was about 1mm in diameter. After transmitting from the glass sample, the light then passed through a IR cut off filter, and second harmonic (SH) wave was detected with a photomultiplier (PMT). The output signal was accumulated by a boxcar integrator. Z-cut quartz was used as a reference in this Maker fringe technique. For details see our previous work [16].

3. Results and Discussion

According to our previous work [17], the maximum content of dissolved AgCl is up to 65mol%. Differential scanning calorimetry (DSC) indicated that most of GeS2-Ga2S3-AgCl glasses had good glass-forming ability. In addition, in terms of transmission spectra, these chalcohalide glasses also exhibited broad region of transmission approximately from 0.45 to 12.5 μm. Figure 1 shows the optical linear absorption spectrum of the representative A1 glass (80GeS2-10Ga2S3-10AgCl) in the Visible and near-IR region (Vis-NIR). It distinctly indicates that almost no absorption exists at the laser operated wavelength (820nm) in OKE measurement, and the operated fundamental wavelength (1064nm) and SH wavelength (532nm) in Maker fringe measurement.

 

Fig. 1. Linear absorption spectrum of the representative A1 (80GeS2-10Ga2S3-10AgCl) glass

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3.1 Third-order optical nonlinearities (OKE) and their structural dependence (Raman spectroscopy)

Figure 2(a) shows the OKE signal of the standard reference (CS2). Its signal has an asymmetrical decay tail more than 1ps due to the molecular reorientation relaxation processes. The OKE signals of the representative GeS2-Ga2S3-AgCl glasses with the thickness of 1±0.02mm are illustrated in Fig. 2(b), and no decay tail can be observed. The solid lines are the Fit Gaussian curves which are symmetrical and the full width at half maximum is 160fs, indicating that the response time in the present glass is subpicosecond. Similarly, the third-order nonlinear optical responses of other compositions are also instantaneous and symmetrical.

 

Fig. 2. Time-resolved OKE signals of (a) a standard CS2 reference and (b) A1 (80GeS2-10Ga2S3-10AgCl) and B4 (64GeS2-16Ga2S3-20AgCl) glasses at a wavelength of 820nm

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For the amorphous materials, the ultrafast third-order nonlinear optical response mainly originates from the distortion of electron cloud and/or the motion of nuclei [18]. If the optical nonlinearity only originates from the former, the nonlinear response of glasses is expected to be less than 10 fs. However, the decay of this response will have the relaxation times between 100fs and 10ps if the nonlinear optical response originates from the motion of nuclei. Considering the longer pulse duration (120fs) used in this study which is too long to excite high-frequency Raman vibrations in our experiment and the better symmetry of the obtained OKE signals (no distinct decay tail), it can be deduced that the ultrafast third-order nonlinear optical response of GeS2-Ga2S3-AgCl glasses is predominantly attributed to the ultrafast distortion of the electron cloud. In addition, for the present chalcohalide glasses, the S atoms are only two-fold coordinated and possess lone pair electrons which are normally non-bonding. These non-bonding electrons lie at the top of the valence band. Therefore these lone pair electrons are preferentially excited when stimulated by the light and subsequently produce some short-lived free electrons plasma together with the band filling effects [19]. It is just the forming of the short-lived electrons that makes GeS2-Ga2S3-AgCl glasses show an ultrafast response time within 200fs.

Besides the ultrafast third-order nonlinear optical response, the value of third-order optical nonlinear susceptibility, χ (3) is another important parameter when evaluating the applications of materials in the photoelectric field. Using the standard procedure of measurement by keeping the CS2 reference medium and samples under the same condition, the value of χ (3) can be calculated by the following Eq. [20]:

χS(3)=χR(3)(ISIR)12(nSnR)2

where the subscript S and R represent the samples and the CS2 reference, respectively, I is the OKE signal intensity and n is the linear refractive index. The linear refractive index, nR and χ (3) of the reference CS2 are taken to be 1.62 and 1×10-13 esu, respectively [21]. Using the maximum values of the Fit Gaussian curves of OKE signals in CS2 reference and samples, the OKE signal intensity ratio of A1 (80GeS2-10Ga2S3-10AgCl) glass sample to CS2 reference, IS/IR is up to 9.09. Then χ (3) can be calculated to be as large as 5.26×10-13 esu according to the Eq. (1). With the conversion n2(cm2/W)≈0.04χ (3)(esu)/n2 which has been frequently employed by researchers[1], the nonlinear refractive index, n2, of A1 glass is estimated to be up to 4.60×10-15 cm2/W. The values of IS/IR, n2 and χ (3) of other samples are also listed in Table 1. For the (100-x)GeS2-xGa2S3 pseudo-binary glasses, the values of IS/IR decrease gradually when GeS2 is replaced by Ga2S3. On Series A (100-2x)GeS2-xGa2S3-xAgCl, where the ratio of Ga2S3 to AgCl is equal to 1, the values of IS/IR also decrease with the additions of Ga2S3 and AgCl. Lastly, for the glasses on Series B 0.8(100-x)GeS2-0.2(100-x)Ga2S3-xAgCl, where the ratio of GeS2 to Ga2S3 maintains as 4:1, the values of IS/IR increase tardily with the addition of AgCl.

Tables Icon

Table 1. Linear and third-order nonlinear optical properties of GeS2-Ga2S3-AgCl glasses

To study the structural dependence of third-order optical nonlinearities, Raman spectroscopy, which is one of the important means to study the structure of amorphous materials, was conducted. Figure 3 shows the Raman spectra of (100-x)GeS2-xGa2S3 pseudo-binary glasses. The spectra have the similar characters with previous works [22, 23]. In GeS2 glass, the basic structural unit (s.u.), i.e. [GeS4] tetrahedra form a three-dimensional glass network via bridging sulfur bonds. When GeS2 is replaced by Ga2S3, two changes are observed in the Raman spectra. Firstly, due to the similar atomic mass between Ge and Ga atoms, the strongest peak at 340cm-1, which is ascribed to the symmetrical stretching vibration (ν1) of [Ge(Ga)S4] tetrahedra, slightly broadens toward the higher frequency. Secondly, due to the formation of [GaS4] tetrahedra (S/Ga =2), [S3Ge(Ga)-Ge(Ga)S3] ethane-like s.u. (S/Ga =1.5) will be formed instead of [Ge(Ga)S4] tetrahedra to alleviate the shortage of sulfur atoms. Consequently, the peak at about 255cm-1 ascribed to the vibration of the [S3Ge(Ga)-Ge(Ga)S3] ethane-like s.u. appears gradually.

For samples on Series B 0.8(100-x)GeS2-0.2(100-x)Ga2S3-xAgCl, where the ratio of GeS2 to Ga2S3 maintains as 4:1. Two distinct changes can be observed in the Raman spectra (see Fig. 4) with the the addition of AgCl. Firstly, the peaks at 340cm-1 and 255cm-1 shift slightly toward the lower frequency respectively due to the formation of [Ge(Ga)S4-xClx] mixed tetrahedra and [ClxS3-xGe(Ga)-Ge(Ga)S3-xClx] mixed ethane-like s.u.. It can be interpreted by the theory of molecular vibration [23]. The vibrating frequency bears a relationship as follows:

vfμ

where f is a constant related to the bond strength, and μ is the reduced mass. Due to the larger atomic weight of chlorine comparing with that of sulfur, the vibrational frequency of Cl-mixed s.u. will be lower than that of pure S-containing s.u.. Another distinct spectral evolution about the gradual decrease of intensity of the peak at 255cm-1 with the addition of AgCl can also be successfully interpreted as follows. With the gradual replacement of GeS2 and Ga2S3 by AgCl, the ratio of (S+Cl/2)/(Ge+Ga) (listed in the last column in table 1) increases slowly and the added Cl atoms lead to the formation of [Ge(Ga)S4-xClx] mixed tetrahedra and [ClxS3-xGe(Ga)-Ge(Ga)S3-xClx] mixed ethane-like s.u.. Subsequently, [ClxS3-xGe(Ga)-Ge(Ga)S3-xClx] mixed ethane-like s.u. will gradually convert into [Ge(Ga)S4-xClx] mixed tetrahedra. Theoretically, the peak near 255cm-1 should vanished completely when the ratio of (S+Cl/2)/(Ge+Ga) exceeds 2 (Such as samples B6, B7 and B8). However, a weak peak at 255cm-1 still exists due to the local shortage of sulfur and chlorine atoms in the process of quenching in ice water and the loss of chlorine atoms due to the light-induced decomposition of AgCl during the process of glass preparation mentioned-above.

 

Fig. 3. Raman spectra of pseudo-binary (100-x)GeS2-xGa2S3 (x=0, 10, 20, 30) glasses

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Fig. 4. Raman spectra of the pseudo-ternary glasses on Series B

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Based on the structural evolution of the GeS2-Ga2S3-AgCl glasses, to further investigate the compositional and structural dependence of χ (3), the values of (S+Cl/2)/(Ge+Ga) which can reflect the structural integrity of glasses are listed in the last column in table 1. To our surprise, for all the samples on three Series, the value of χ (3) almost increases linearly with the value of (S+Cl/2)/(Ge+Ga). Take samples on Series B as an example, the values of (S+Cl/2)/(Ge+Ga) and IS/IR are collected with the content of AgCl in Fig. 5, which clearly shows that the values of (S+Cl/2)/(Ge+Ga) and χ (3) increase monotonously with the addition of AgCl, and the same phenomenon is observed on the other two Series as well. For more clearly, the value of IS/IR vs. (S+Cl/2)/(Ge+Ga) for all the samples on three Series are illustrated in Fig. 6, which indicates the strong dependence of the values of IS/IR upon (S+Cl/2)/(Ge+Ga).

This strong dependence can be interpreted as follows. Firstly, in the case of (100-x)GeS2-xGa2S3 pseudo-binary glasses, the values of (S+Cl/2)/(Ge+Ga) and IS/IR decrease when GeS2 is replaced by Ga2S3. Simultaneously, the peak at about 255cm-1 in Raman spectra (see Fig. 3) ascribed to the vibration of [S3Ge(Ga)-Ge(Ga)S3] ethane-like s.u. increases gradually due to the shortage of sulfur, which forces [Ge(Ga)S4] tetrahedra convert into [S3Ge(Ga)-Ge(Ga)S3] ethane-like s.u.. Secondly, the shortage of sulfur does not mitigate on Series A with the addition of Ga2S3 and AgCl in the same ratio, which is due to the decrease of (S+Cl/2)/(Ge+Ga). And at the same time, the magnitude of [Ge(Ga)S4-xClx] mixed tetrahedra decreases gradually. Subsequently, the values of IS/IR on Series A decrease with the addition of AgCl. However, for samples on Series B, the values of IS/IR increase tardily when GeS2 and Ga2S3 are replaced by AgCl. On this Series, the values of (S+Cl/2)/(Ge+Ga) increase with the addition of AgCl, which will result in the conversion from [ClxS3-xGe(Ga)-Ge(Ga)S3-xClx] mixed ethane-like s.u. to [Ge(Ga)S4-xClx] mixed tetrahedra and lead to the decrease of the peak at about 255cm-1 in Raman spectra (see Fig. 4).

Judging from the discussion mentioned above, it can be deduced that [Ge(Ga)S4] and [Ge(Ga)S4-xClx] mixed tetrahedra with high hyperpolarizability make greater contribution to the enhancement of χ (3) compared with the structural defectiveness of the present glasses such as [S3Ge(Ga)-Ge(Ga)S3] and [ClxS3-xGe(Ga)-Ge(Ga)S3-xClx] mixed ethane-like s.u. In addition, as the terminator of the glassy network, the addition of chlorine atoms originated from AgCl will induce the degradation of integrity of glassy network and more structural defectiveness may be formed, which will partially counteract the mitigation of the shortage of sulfur. These considerations can better interpret the sharp decrease of the values of IS/IR from A2 to A3 and the slow enhancement of the values from B1 to B6. To sum up, an integrated and homogeneous glassy network with less structural defectiveness is more beneficial to the enhancement of χ (3).

 

Fig. 5. The ratio of IS/IR and (S+Cl/2)/(Ge+Ga) collected as a function of the content of AgCl for the pseudo-ternary glasses on Series B

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Fig. 6. Optical Kerr signal ratio of IS/IR collected as a function of the values of (S+Cl/2)/(Ge+Ga) for the glasses on three Series

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3.2 Second-order optical nonlinearity (Maker fringe technique)

R.A. Myers, et al, [24] have provided that an effective second-order optical nonlinearity, χ (2) associated intimately with χ (3) via the Eq.: χ (2)=χ (3)Edc, which indicates that A1 glass possessing the largest χ (3) in this system may exhibit large second-order optical nonlinearity. In addition, high transmission at the operated fundamental wavelength (1064nm) and SH wavelength (532nm) (see Fig. 1) of this sample together with its better glass-forming ability [17] also enable A1 glass as the optimal composition of this glassy system for the study on second-order optical nonlinearity.

With the Maker fringe method, SHG was observed in the A1 glass irradiated by electron beam (see Fig. 7), which was attributed to the breakage of centrosymmetry in the glass after being irradiated by the electron beam with moderate energy. The poling mechanism was partially discussed in our previous paper [14]. In GeS2-Ga2S3-AgCl glasses, the S atoms are only two-fold coordinated and possess lone pair electrons, which can be preferentially excited by electron beam, etc.. When the electron beam irradiates on the glass surface, most of the incidence electrons collide with outer electrons of atomic nucleus and stimulate these outer electrons to become the secondary electrons. Residual incidence electrons collide with inner electrons and excite these inner electrons to lead to the generation of inner core holes and Auger electrons. The secondary electrons and Auger electrons possessing enough energy will emit from the surface, which will result in the formation of the region of positive charges near the poling surface. Simultaneously, due to the incessant collision, most of the incidence electrons will be out of energy and become the absorbed electrons, creating the region of negative charges beneath the positive one. Therefore, a strong perpendicular built-in space-charge electrostatic field, Edc, which results in generation of χ(2), is created. According to the Bohr-Bethe formula [25], it can be deduced that Edc is only a several micron thin layer approximately. In our previous work, the refractive index nω and n is equal to 2.17 and 2.28 at the fundamental (1064 nm) and its second harmonic wavelength (532 nm), respectively. Therefore, the coherence length, Lc defined as Lc=Λ/4(n-nω) (λ is the fundamental wavelength) is also up to 2.67μm of the electron beam irradiated A1 glass. In terms of the maximum value of the Maker fringe pattern, the SH intensity of the irradiated A1 (25 kV, 25 nA, 15 min) glass is about 1.5 times larger than that of Z-cut quartz as a reference, and the second-order optical nonlinear susceptibility is estimated to be greater than 6.1pm/V considering the higher attenuation of reflection of the light that occurs at the surfaces and the higher absorption coefficient of the present chalcohalide glasses compared with that of the Z-cut quartz reference, which is much larger than many other glasses [12,26].

 

Fig. 7. Maker fringe pattern of the A1 (80GeS2-10Ga2S3-10AgCl) glass poled by the electron beam

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As one of the important techniques to study the structure of glasses, Raman scattering measurement was conducted in this experiment. Figure 8 shows the Raman spectra of the as-prepared and after irradiated A1 (80GeS2-10Ga2S3-10AgCl) glass. No any obvious change is observed in the spectra, which indicates that no distinct structural change can be detected. Maybe it is only electronic transition and distortion of electron cloud that occurred within the irradiated A1 glass. It can be further deduced that no damage appeared about the structure of the glass.

 

Fig. 8. Raman spectra of the as-prepared 80GeS2-10Ga2S3-10AgCl glass and the irradiated one

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Furthermore, more detailed studies on the optimization of experimental conditions and compositions are necessary to make them perform high optical nonlinear susceptibility and meet the need of all-optical devices.

4. Conclusion

Third/second-order optical nonlinearities of GeS2-Ga2S3-AgCl chalcohalide glasses have been studied by OKE and Maker fringe technique, respectively. The maximum χ (3) within the present pseudo-ternary chalcogenide glasses, which is as large as 5.26×10-13esu, was obtained in the glass with the composition 80GeS2-10Ga2S3-10AgCl. Furthermore, through irradiating by electron beam upon this glass, a large second-order optical nonlinear susceptibility which is estimated to be greater than 6.1 pm/V was also obtained. The dependence of χ(3) upon structure of these glasses revealed by the experimental results indicates that an integrated and homogeneous glass network with less structural defectiveness such as [ClxS3-xGe(Ga)-Ge(Ga)S3-xClx] mixed ethane-like s.u. and larger number of [Ge(Ga)S4-xClx] mixed tetrahedra with high hyperpolarizability is more beneficial to the enhancement of χ (3). These GeS2-Ga2S3-AgCl chalcohalide glasses with large third/second-order optical nonlinearities are expected to be used as one of the most promising candidates in photoelectric fields.

Acknowledgment

This work was partially funded by the National Natural Science Foundation of China (No. 50125205, 10647142).

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26. M. Guignard, V. Nazabal, J. Troles, F. Smektala, H. Zeghlache, Y. Quiquempois, A. Kudlinski, and G. Martinelli, “Second-harmonic generation of thermally poled chalcogenide glass,” Opt. Express. 13, 789–795 (2005). [CrossRef]   [PubMed]  

References

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  1. K. Tanaka, “Optical nonlinearity in photonic glasses,” J. Mater. Sci. Mater. Electron. 16, 633–643 (2005).
    [Crossref]
  2. G. Boudebs, S. Cherukulappurath, H. Leblond, J. Troles, F. Smektala, and F. Sanchez, “Experimental and theoretical study of higher-order nonlinearities in chalcogenide glasses,” Opt. Commun. 219, 427–433 (2003).
    [Crossref]
  3. F. Smektala, J. Troles, V. Couderc, A. Barthelemy, G. Boudebs, F. Sanchez, H. Zeghlache, G. Martinelli, Y. Quiquempois, and S. Bailleux, “Third and second order nonlinear optical properties of Ge-Se-S-As chalcogenide glasses,” Proc SPIE 4628, 30–38 (2002).
    [Crossref]
  4. X. F. Wang, S. X. Gu, J. G. Yu, C. L. Liu, X. J. Zhao, and H. Z. Tao, “Formation and properties of chalcogenide glasses in the GeS2-Ga2S3-CdS system,” Mater. Chem. Phys. 83, 284–288 (2004).
    [Crossref]
  5. K. Ogusu, J. Yamasaki, S. Maeda, M. Kitao, and M. Minakata, “Linear and nonlinear optical properties of Ag-As-Se chalcogenide glasses for all-optical switching,” Opt. Lett. 29, 265–267 (2004).
    [Crossref] [PubMed]
  6. R. C. Miller, “Optical second harmonic generation in piezoelec-tric crystals,” Appl. Phys. Lett. 5, 17–19 (1964).
    [Crossref]
  7. H. Z. Tao, G. P. Dong, Y. B. Zhai, H. T. Guo, X. J. Zhao, Z. W. Wang, S. S. Chu, S. F. Wang, and Q. H. Gong, “Femtosecond third-order optical nonlinearity of the GeS2-Ga2S3-CdI2 new chalcohalide glasses,” Solid State Commun. 138, 485–488 (2006).
    [Crossref]
  8. X. F. Wang, Z. W. Wang, J. G. Yu, C. L. Liu, X. J. Zhao, and Q. H. Gong, “Large and ultrafast third-order optical nonlinearity of GeS2-Ga2S3-CdS chalcogenide glass,” Chem. Phys. Lett. 399, 230–233 (2004).
    [Crossref]
  9. A. Narazaki, K. Tanaka, and K. Hirao, “Surface structure and second-order nonlinear optical properties of thermally poled WO3-TeO2 glasses doped with Na+,” J. Opt. Soc. Am. B 19, 54–62 (2002).
    [Crossref]
  10. P. G. Kazansky, A. Kamal, and P. S. J. Russell, “Erasure of thermally poled second-order nonlinearity in fused silica by electron implantation,” Opt. Lett. 18, 1141–1143 (1993).
    [Crossref] [PubMed]
  11. T. Fujiwara, M. Talahashi, and A. J. Ikushima, “Second-harmonic generation in germanosilicate glass poled with ArF laser irradiation,” Appl. Phys. Lett. 71, 1032–1034 (1997).
    [Crossref]
  12. M. X. Qiu, F. Pi, and G. Orriols, “The role of lead component in second-harmnonic generation in lead silica by electron-beam irradiation,” Appl. Phys. Lett. 73, 3040–3042 (1998).
    [Crossref]
  13. I. V. Kityk, “IR-induced second harmonic generation in Sb2Te3-BaF2-PbCl2 glasses,” J. Phys. Chem. B 107, 10083–10087 (2003).
    [Crossref]
  14. H.Z. Tao, S. Mao, G.P. Dong, H.Y. Xiao, and X.J. Zhao, “Raman scattering studies of the Ge-In sulfide glasses,” Solid State Commun. 137, 408–412 (2006).
    [Crossref]
  15. G. P. Dong, H. Z. Tao, S. S. Chu, S. F. Wang, X. J. Zhao, Q. H. Gong, X. D. Xiao, and C. G. Lin, “Study on the structure dependent ultrafast third-order optical nonlinearity of GeS2-In2S3 chalcogenide glasses,” Opt. Commun. 270, 373–378 (2007).
    [Crossref]
  16. G.P. Dong, H.Z. Tao, X.D. Xiao, C.G. Lin, X.J. Zhao, and S. Mao, “Mechanism of electron beam poled SHG in 0.95GeS2∙0.05In2S3 chalcogenide glasses,” J. Phys. Chem. Solids (doi:10.1016/j.jpcs.2006.10.002).
  17. G. P. Dong, H. Z. Tao, X. D. Xiao, C. G. Lin, and X. J. Zhao, “Study on the formation, thermal, optical and physical properties of GeS2-Ga2S3-AgCl novel chalcohalide glasses,” J. Phys. Chem. Solids (Submit).
  18. J. E. Aber, M. C. Newstein, and B. A. Garetz, “Femtosecond optical kerr effect measurement in silicate glasses,” J. Opt. Soc. Am. B 17, 120–127 (2000).
    [Crossref]
  19. Q. M. Liu, X. J. Zhao, F. X. Gan, J. Mid, and S. X. Qian, “Femtosecond optical Kerr effect study of Ge10As40S30Se20 film,” Solid State Commun. 134, 513–517 (2005)
    [Crossref]
  20. M. K. Casstevens, M. Samoc, J. Pfleger, and P. N. Prasad, “Dynamics of third-order nonlinear optical processes in Langmuir-Blodgett and evaporated films of phthalocyanines,” J. Chem. Phys. 92, 2019–2024 (1990).
    [Crossref]
  21. K. Minoshima, M. Taiji, and T. Kobayashi, “Femtosecond time-resolved interferometry for the determination of complex nonlinear susceptibility,” Opt. Lett. 16, 1683–1685 (1991).
    [Crossref] [PubMed]
  22. G. Lucovsky, F. L. Galeener, R. C. Kezer, R. H. Geils, and H. A. Six, “Structural interpretation of the infrared and raman spectra of glasses in the alloy system Ge1-x Sx,” Phys. Rev. B 10, 5134–5146 (1974).
    [Crossref]
  23. H. Z. Tao, X. J. Zhao, C. B. Jing, H. Yang, and S. Mao, “Raman scattering studies of the GeS2-Ga2S3-CsCl glassy system,” Solid State Commun. 133, 327–332 (2005).
    [Crossref]
  24. R. A. Myers, N. Mukherjee, and S. R. J. Brueck, “Large second-order nonlinearity in poled fused silica,” 16, 1732–1734 (1991).
  25. T. E. Everhart and P. H. Hoff, “Determination of kilovolt electron energy dissipation vs penetration distance in solid materials,” J. Appl. Phys. 42, 5837–5846 (1971).
    [Crossref]
  26. M. Guignard, V. Nazabal, J. Troles, F. Smektala, H. Zeghlache, Y. Quiquempois, A. Kudlinski, and G. Martinelli, “Second-harmonic generation of thermally poled chalcogenide glass,” Opt. Express. 13, 789–795 (2005).
    [Crossref] [PubMed]

2007 (1)

G. P. Dong, H. Z. Tao, S. S. Chu, S. F. Wang, X. J. Zhao, Q. H. Gong, X. D. Xiao, and C. G. Lin, “Study on the structure dependent ultrafast third-order optical nonlinearity of GeS2-In2S3 chalcogenide glasses,” Opt. Commun. 270, 373–378 (2007).
[Crossref]

2006 (2)

H.Z. Tao, S. Mao, G.P. Dong, H.Y. Xiao, and X.J. Zhao, “Raman scattering studies of the Ge-In sulfide glasses,” Solid State Commun. 137, 408–412 (2006).
[Crossref]

H. Z. Tao, G. P. Dong, Y. B. Zhai, H. T. Guo, X. J. Zhao, Z. W. Wang, S. S. Chu, S. F. Wang, and Q. H. Gong, “Femtosecond third-order optical nonlinearity of the GeS2-Ga2S3-CdI2 new chalcohalide glasses,” Solid State Commun. 138, 485–488 (2006).
[Crossref]

2005 (4)

K. Tanaka, “Optical nonlinearity in photonic glasses,” J. Mater. Sci. Mater. Electron. 16, 633–643 (2005).
[Crossref]

Q. M. Liu, X. J. Zhao, F. X. Gan, J. Mid, and S. X. Qian, “Femtosecond optical Kerr effect study of Ge10As40S30Se20 film,” Solid State Commun. 134, 513–517 (2005)
[Crossref]

H. Z. Tao, X. J. Zhao, C. B. Jing, H. Yang, and S. Mao, “Raman scattering studies of the GeS2-Ga2S3-CsCl glassy system,” Solid State Commun. 133, 327–332 (2005).
[Crossref]

M. Guignard, V. Nazabal, J. Troles, F. Smektala, H. Zeghlache, Y. Quiquempois, A. Kudlinski, and G. Martinelli, “Second-harmonic generation of thermally poled chalcogenide glass,” Opt. Express. 13, 789–795 (2005).
[Crossref] [PubMed]

2004 (3)

X. F. Wang, S. X. Gu, J. G. Yu, C. L. Liu, X. J. Zhao, and H. Z. Tao, “Formation and properties of chalcogenide glasses in the GeS2-Ga2S3-CdS system,” Mater. Chem. Phys. 83, 284–288 (2004).
[Crossref]

K. Ogusu, J. Yamasaki, S. Maeda, M. Kitao, and M. Minakata, “Linear and nonlinear optical properties of Ag-As-Se chalcogenide glasses for all-optical switching,” Opt. Lett. 29, 265–267 (2004).
[Crossref] [PubMed]

X. F. Wang, Z. W. Wang, J. G. Yu, C. L. Liu, X. J. Zhao, and Q. H. Gong, “Large and ultrafast third-order optical nonlinearity of GeS2-Ga2S3-CdS chalcogenide glass,” Chem. Phys. Lett. 399, 230–233 (2004).
[Crossref]

2003 (2)

G. Boudebs, S. Cherukulappurath, H. Leblond, J. Troles, F. Smektala, and F. Sanchez, “Experimental and theoretical study of higher-order nonlinearities in chalcogenide glasses,” Opt. Commun. 219, 427–433 (2003).
[Crossref]

I. V. Kityk, “IR-induced second harmonic generation in Sb2Te3-BaF2-PbCl2 glasses,” J. Phys. Chem. B 107, 10083–10087 (2003).
[Crossref]

2002 (2)

F. Smektala, J. Troles, V. Couderc, A. Barthelemy, G. Boudebs, F. Sanchez, H. Zeghlache, G. Martinelli, Y. Quiquempois, and S. Bailleux, “Third and second order nonlinear optical properties of Ge-Se-S-As chalcogenide glasses,” Proc SPIE 4628, 30–38 (2002).
[Crossref]

A. Narazaki, K. Tanaka, and K. Hirao, “Surface structure and second-order nonlinear optical properties of thermally poled WO3-TeO2 glasses doped with Na+,” J. Opt. Soc. Am. B 19, 54–62 (2002).
[Crossref]

2000 (1)

1998 (1)

M. X. Qiu, F. Pi, and G. Orriols, “The role of lead component in second-harmnonic generation in lead silica by electron-beam irradiation,” Appl. Phys. Lett. 73, 3040–3042 (1998).
[Crossref]

1997 (1)

T. Fujiwara, M. Talahashi, and A. J. Ikushima, “Second-harmonic generation in germanosilicate glass poled with ArF laser irradiation,” Appl. Phys. Lett. 71, 1032–1034 (1997).
[Crossref]

1993 (1)

1991 (1)

1990 (1)

M. K. Casstevens, M. Samoc, J. Pfleger, and P. N. Prasad, “Dynamics of third-order nonlinear optical processes in Langmuir-Blodgett and evaporated films of phthalocyanines,” J. Chem. Phys. 92, 2019–2024 (1990).
[Crossref]

1974 (1)

G. Lucovsky, F. L. Galeener, R. C. Kezer, R. H. Geils, and H. A. Six, “Structural interpretation of the infrared and raman spectra of glasses in the alloy system Ge1-x Sx,” Phys. Rev. B 10, 5134–5146 (1974).
[Crossref]

1971 (1)

T. E. Everhart and P. H. Hoff, “Determination of kilovolt electron energy dissipation vs penetration distance in solid materials,” J. Appl. Phys. 42, 5837–5846 (1971).
[Crossref]

1964 (1)

R. C. Miller, “Optical second harmonic generation in piezoelec-tric crystals,” Appl. Phys. Lett. 5, 17–19 (1964).
[Crossref]

Aber, J. E.

Bailleux, S.

F. Smektala, J. Troles, V. Couderc, A. Barthelemy, G. Boudebs, F. Sanchez, H. Zeghlache, G. Martinelli, Y. Quiquempois, and S. Bailleux, “Third and second order nonlinear optical properties of Ge-Se-S-As chalcogenide glasses,” Proc SPIE 4628, 30–38 (2002).
[Crossref]

Barthelemy, A.

F. Smektala, J. Troles, V. Couderc, A. Barthelemy, G. Boudebs, F. Sanchez, H. Zeghlache, G. Martinelli, Y. Quiquempois, and S. Bailleux, “Third and second order nonlinear optical properties of Ge-Se-S-As chalcogenide glasses,” Proc SPIE 4628, 30–38 (2002).
[Crossref]

Boudebs, G.

G. Boudebs, S. Cherukulappurath, H. Leblond, J. Troles, F. Smektala, and F. Sanchez, “Experimental and theoretical study of higher-order nonlinearities in chalcogenide glasses,” Opt. Commun. 219, 427–433 (2003).
[Crossref]

F. Smektala, J. Troles, V. Couderc, A. Barthelemy, G. Boudebs, F. Sanchez, H. Zeghlache, G. Martinelli, Y. Quiquempois, and S. Bailleux, “Third and second order nonlinear optical properties of Ge-Se-S-As chalcogenide glasses,” Proc SPIE 4628, 30–38 (2002).
[Crossref]

Brueck, S. R. J.

R. A. Myers, N. Mukherjee, and S. R. J. Brueck, “Large second-order nonlinearity in poled fused silica,” 16, 1732–1734 (1991).

Casstevens, M. K.

M. K. Casstevens, M. Samoc, J. Pfleger, and P. N. Prasad, “Dynamics of third-order nonlinear optical processes in Langmuir-Blodgett and evaporated films of phthalocyanines,” J. Chem. Phys. 92, 2019–2024 (1990).
[Crossref]

Cherukulappurath, S.

G. Boudebs, S. Cherukulappurath, H. Leblond, J. Troles, F. Smektala, and F. Sanchez, “Experimental and theoretical study of higher-order nonlinearities in chalcogenide glasses,” Opt. Commun. 219, 427–433 (2003).
[Crossref]

Chu, S. S.

G. P. Dong, H. Z. Tao, S. S. Chu, S. F. Wang, X. J. Zhao, Q. H. Gong, X. D. Xiao, and C. G. Lin, “Study on the structure dependent ultrafast third-order optical nonlinearity of GeS2-In2S3 chalcogenide glasses,” Opt. Commun. 270, 373–378 (2007).
[Crossref]

H. Z. Tao, G. P. Dong, Y. B. Zhai, H. T. Guo, X. J. Zhao, Z. W. Wang, S. S. Chu, S. F. Wang, and Q. H. Gong, “Femtosecond third-order optical nonlinearity of the GeS2-Ga2S3-CdI2 new chalcohalide glasses,” Solid State Commun. 138, 485–488 (2006).
[Crossref]

Couderc, V.

F. Smektala, J. Troles, V. Couderc, A. Barthelemy, G. Boudebs, F. Sanchez, H. Zeghlache, G. Martinelli, Y. Quiquempois, and S. Bailleux, “Third and second order nonlinear optical properties of Ge-Se-S-As chalcogenide glasses,” Proc SPIE 4628, 30–38 (2002).
[Crossref]

Dong, G. P.

G. P. Dong, H. Z. Tao, S. S. Chu, S. F. Wang, X. J. Zhao, Q. H. Gong, X. D. Xiao, and C. G. Lin, “Study on the structure dependent ultrafast third-order optical nonlinearity of GeS2-In2S3 chalcogenide glasses,” Opt. Commun. 270, 373–378 (2007).
[Crossref]

H. Z. Tao, G. P. Dong, Y. B. Zhai, H. T. Guo, X. J. Zhao, Z. W. Wang, S. S. Chu, S. F. Wang, and Q. H. Gong, “Femtosecond third-order optical nonlinearity of the GeS2-Ga2S3-CdI2 new chalcohalide glasses,” Solid State Commun. 138, 485–488 (2006).
[Crossref]

G. P. Dong, H. Z. Tao, X. D. Xiao, C. G. Lin, and X. J. Zhao, “Study on the formation, thermal, optical and physical properties of GeS2-Ga2S3-AgCl novel chalcohalide glasses,” J. Phys. Chem. Solids (Submit).

Dong, G.P.

H.Z. Tao, S. Mao, G.P. Dong, H.Y. Xiao, and X.J. Zhao, “Raman scattering studies of the Ge-In sulfide glasses,” Solid State Commun. 137, 408–412 (2006).
[Crossref]

G.P. Dong, H.Z. Tao, X.D. Xiao, C.G. Lin, X.J. Zhao, and S. Mao, “Mechanism of electron beam poled SHG in 0.95GeS2∙0.05In2S3 chalcogenide glasses,” J. Phys. Chem. Solids (doi:10.1016/j.jpcs.2006.10.002).

Everhart, T. E.

T. E. Everhart and P. H. Hoff, “Determination of kilovolt electron energy dissipation vs penetration distance in solid materials,” J. Appl. Phys. 42, 5837–5846 (1971).
[Crossref]

Fujiwara, T.

T. Fujiwara, M. Talahashi, and A. J. Ikushima, “Second-harmonic generation in germanosilicate glass poled with ArF laser irradiation,” Appl. Phys. Lett. 71, 1032–1034 (1997).
[Crossref]

Galeener, F. L.

G. Lucovsky, F. L. Galeener, R. C. Kezer, R. H. Geils, and H. A. Six, “Structural interpretation of the infrared and raman spectra of glasses in the alloy system Ge1-x Sx,” Phys. Rev. B 10, 5134–5146 (1974).
[Crossref]

Gan, F. X.

Q. M. Liu, X. J. Zhao, F. X. Gan, J. Mid, and S. X. Qian, “Femtosecond optical Kerr effect study of Ge10As40S30Se20 film,” Solid State Commun. 134, 513–517 (2005)
[Crossref]

Garetz, B. A.

Geils, R. H.

G. Lucovsky, F. L. Galeener, R. C. Kezer, R. H. Geils, and H. A. Six, “Structural interpretation of the infrared and raman spectra of glasses in the alloy system Ge1-x Sx,” Phys. Rev. B 10, 5134–5146 (1974).
[Crossref]

Gong, Q. H.

G. P. Dong, H. Z. Tao, S. S. Chu, S. F. Wang, X. J. Zhao, Q. H. Gong, X. D. Xiao, and C. G. Lin, “Study on the structure dependent ultrafast third-order optical nonlinearity of GeS2-In2S3 chalcogenide glasses,” Opt. Commun. 270, 373–378 (2007).
[Crossref]

H. Z. Tao, G. P. Dong, Y. B. Zhai, H. T. Guo, X. J. Zhao, Z. W. Wang, S. S. Chu, S. F. Wang, and Q. H. Gong, “Femtosecond third-order optical nonlinearity of the GeS2-Ga2S3-CdI2 new chalcohalide glasses,” Solid State Commun. 138, 485–488 (2006).
[Crossref]

X. F. Wang, Z. W. Wang, J. G. Yu, C. L. Liu, X. J. Zhao, and Q. H. Gong, “Large and ultrafast third-order optical nonlinearity of GeS2-Ga2S3-CdS chalcogenide glass,” Chem. Phys. Lett. 399, 230–233 (2004).
[Crossref]

Gu, S. X.

X. F. Wang, S. X. Gu, J. G. Yu, C. L. Liu, X. J. Zhao, and H. Z. Tao, “Formation and properties of chalcogenide glasses in the GeS2-Ga2S3-CdS system,” Mater. Chem. Phys. 83, 284–288 (2004).
[Crossref]

Guignard, M.

M. Guignard, V. Nazabal, J. Troles, F. Smektala, H. Zeghlache, Y. Quiquempois, A. Kudlinski, and G. Martinelli, “Second-harmonic generation of thermally poled chalcogenide glass,” Opt. Express. 13, 789–795 (2005).
[Crossref] [PubMed]

Guo, H. T.

H. Z. Tao, G. P. Dong, Y. B. Zhai, H. T. Guo, X. J. Zhao, Z. W. Wang, S. S. Chu, S. F. Wang, and Q. H. Gong, “Femtosecond third-order optical nonlinearity of the GeS2-Ga2S3-CdI2 new chalcohalide glasses,” Solid State Commun. 138, 485–488 (2006).
[Crossref]

Hirao, K.

Hoff, P. H.

T. E. Everhart and P. H. Hoff, “Determination of kilovolt electron energy dissipation vs penetration distance in solid materials,” J. Appl. Phys. 42, 5837–5846 (1971).
[Crossref]

Ikushima, A. J.

T. Fujiwara, M. Talahashi, and A. J. Ikushima, “Second-harmonic generation in germanosilicate glass poled with ArF laser irradiation,” Appl. Phys. Lett. 71, 1032–1034 (1997).
[Crossref]

Jing, C. B.

H. Z. Tao, X. J. Zhao, C. B. Jing, H. Yang, and S. Mao, “Raman scattering studies of the GeS2-Ga2S3-CsCl glassy system,” Solid State Commun. 133, 327–332 (2005).
[Crossref]

Kamal, A.

Kazansky, P. G.

Kezer, R. C.

G. Lucovsky, F. L. Galeener, R. C. Kezer, R. H. Geils, and H. A. Six, “Structural interpretation of the infrared and raman spectra of glasses in the alloy system Ge1-x Sx,” Phys. Rev. B 10, 5134–5146 (1974).
[Crossref]

Kitao, M.

Kityk, I. V.

I. V. Kityk, “IR-induced second harmonic generation in Sb2Te3-BaF2-PbCl2 glasses,” J. Phys. Chem. B 107, 10083–10087 (2003).
[Crossref]

Kobayashi, T.

Kudlinski, A.

M. Guignard, V. Nazabal, J. Troles, F. Smektala, H. Zeghlache, Y. Quiquempois, A. Kudlinski, and G. Martinelli, “Second-harmonic generation of thermally poled chalcogenide glass,” Opt. Express. 13, 789–795 (2005).
[Crossref] [PubMed]

Leblond, H.

G. Boudebs, S. Cherukulappurath, H. Leblond, J. Troles, F. Smektala, and F. Sanchez, “Experimental and theoretical study of higher-order nonlinearities in chalcogenide glasses,” Opt. Commun. 219, 427–433 (2003).
[Crossref]

Lin, C. G.

G. P. Dong, H. Z. Tao, S. S. Chu, S. F. Wang, X. J. Zhao, Q. H. Gong, X. D. Xiao, and C. G. Lin, “Study on the structure dependent ultrafast third-order optical nonlinearity of GeS2-In2S3 chalcogenide glasses,” Opt. Commun. 270, 373–378 (2007).
[Crossref]

G. P. Dong, H. Z. Tao, X. D. Xiao, C. G. Lin, and X. J. Zhao, “Study on the formation, thermal, optical and physical properties of GeS2-Ga2S3-AgCl novel chalcohalide glasses,” J. Phys. Chem. Solids (Submit).

Lin, C.G.

G.P. Dong, H.Z. Tao, X.D. Xiao, C.G. Lin, X.J. Zhao, and S. Mao, “Mechanism of electron beam poled SHG in 0.95GeS2∙0.05In2S3 chalcogenide glasses,” J. Phys. Chem. Solids (doi:10.1016/j.jpcs.2006.10.002).

Liu, C. L.

X. F. Wang, S. X. Gu, J. G. Yu, C. L. Liu, X. J. Zhao, and H. Z. Tao, “Formation and properties of chalcogenide glasses in the GeS2-Ga2S3-CdS system,” Mater. Chem. Phys. 83, 284–288 (2004).
[Crossref]

X. F. Wang, Z. W. Wang, J. G. Yu, C. L. Liu, X. J. Zhao, and Q. H. Gong, “Large and ultrafast third-order optical nonlinearity of GeS2-Ga2S3-CdS chalcogenide glass,” Chem. Phys. Lett. 399, 230–233 (2004).
[Crossref]

Liu, Q. M.

Q. M. Liu, X. J. Zhao, F. X. Gan, J. Mid, and S. X. Qian, “Femtosecond optical Kerr effect study of Ge10As40S30Se20 film,” Solid State Commun. 134, 513–517 (2005)
[Crossref]

Lucovsky, G.

G. Lucovsky, F. L. Galeener, R. C. Kezer, R. H. Geils, and H. A. Six, “Structural interpretation of the infrared and raman spectra of glasses in the alloy system Ge1-x Sx,” Phys. Rev. B 10, 5134–5146 (1974).
[Crossref]

Maeda, S.

Mao, S.

H.Z. Tao, S. Mao, G.P. Dong, H.Y. Xiao, and X.J. Zhao, “Raman scattering studies of the Ge-In sulfide glasses,” Solid State Commun. 137, 408–412 (2006).
[Crossref]

H. Z. Tao, X. J. Zhao, C. B. Jing, H. Yang, and S. Mao, “Raman scattering studies of the GeS2-Ga2S3-CsCl glassy system,” Solid State Commun. 133, 327–332 (2005).
[Crossref]

G.P. Dong, H.Z. Tao, X.D. Xiao, C.G. Lin, X.J. Zhao, and S. Mao, “Mechanism of electron beam poled SHG in 0.95GeS2∙0.05In2S3 chalcogenide glasses,” J. Phys. Chem. Solids (doi:10.1016/j.jpcs.2006.10.002).

Martinelli, G.

M. Guignard, V. Nazabal, J. Troles, F. Smektala, H. Zeghlache, Y. Quiquempois, A. Kudlinski, and G. Martinelli, “Second-harmonic generation of thermally poled chalcogenide glass,” Opt. Express. 13, 789–795 (2005).
[Crossref] [PubMed]

F. Smektala, J. Troles, V. Couderc, A. Barthelemy, G. Boudebs, F. Sanchez, H. Zeghlache, G. Martinelli, Y. Quiquempois, and S. Bailleux, “Third and second order nonlinear optical properties of Ge-Se-S-As chalcogenide glasses,” Proc SPIE 4628, 30–38 (2002).
[Crossref]

Mid, J.

Q. M. Liu, X. J. Zhao, F. X. Gan, J. Mid, and S. X. Qian, “Femtosecond optical Kerr effect study of Ge10As40S30Se20 film,” Solid State Commun. 134, 513–517 (2005)
[Crossref]

Miller, R. C.

R. C. Miller, “Optical second harmonic generation in piezoelec-tric crystals,” Appl. Phys. Lett. 5, 17–19 (1964).
[Crossref]

Minakata, M.

Minoshima, K.

Mukherjee, N.

R. A. Myers, N. Mukherjee, and S. R. J. Brueck, “Large second-order nonlinearity in poled fused silica,” 16, 1732–1734 (1991).

Myers, R. A.

R. A. Myers, N. Mukherjee, and S. R. J. Brueck, “Large second-order nonlinearity in poled fused silica,” 16, 1732–1734 (1991).

Narazaki, A.

Nazabal, V.

M. Guignard, V. Nazabal, J. Troles, F. Smektala, H. Zeghlache, Y. Quiquempois, A. Kudlinski, and G. Martinelli, “Second-harmonic generation of thermally poled chalcogenide glass,” Opt. Express. 13, 789–795 (2005).
[Crossref] [PubMed]

Newstein, M. C.

Ogusu, K.

Orriols, G.

M. X. Qiu, F. Pi, and G. Orriols, “The role of lead component in second-harmnonic generation in lead silica by electron-beam irradiation,” Appl. Phys. Lett. 73, 3040–3042 (1998).
[Crossref]

Pfleger, J.

M. K. Casstevens, M. Samoc, J. Pfleger, and P. N. Prasad, “Dynamics of third-order nonlinear optical processes in Langmuir-Blodgett and evaporated films of phthalocyanines,” J. Chem. Phys. 92, 2019–2024 (1990).
[Crossref]

Pi, F.

M. X. Qiu, F. Pi, and G. Orriols, “The role of lead component in second-harmnonic generation in lead silica by electron-beam irradiation,” Appl. Phys. Lett. 73, 3040–3042 (1998).
[Crossref]

Prasad, P. N.

M. K. Casstevens, M. Samoc, J. Pfleger, and P. N. Prasad, “Dynamics of third-order nonlinear optical processes in Langmuir-Blodgett and evaporated films of phthalocyanines,” J. Chem. Phys. 92, 2019–2024 (1990).
[Crossref]

Qian, S. X.

Q. M. Liu, X. J. Zhao, F. X. Gan, J. Mid, and S. X. Qian, “Femtosecond optical Kerr effect study of Ge10As40S30Se20 film,” Solid State Commun. 134, 513–517 (2005)
[Crossref]

Qiu, M. X.

M. X. Qiu, F. Pi, and G. Orriols, “The role of lead component in second-harmnonic generation in lead silica by electron-beam irradiation,” Appl. Phys. Lett. 73, 3040–3042 (1998).
[Crossref]

Quiquempois, Y.

M. Guignard, V. Nazabal, J. Troles, F. Smektala, H. Zeghlache, Y. Quiquempois, A. Kudlinski, and G. Martinelli, “Second-harmonic generation of thermally poled chalcogenide glass,” Opt. Express. 13, 789–795 (2005).
[Crossref] [PubMed]

F. Smektala, J. Troles, V. Couderc, A. Barthelemy, G. Boudebs, F. Sanchez, H. Zeghlache, G. Martinelli, Y. Quiquempois, and S. Bailleux, “Third and second order nonlinear optical properties of Ge-Se-S-As chalcogenide glasses,” Proc SPIE 4628, 30–38 (2002).
[Crossref]

Russell, P. S. J.

Samoc, M.

M. K. Casstevens, M. Samoc, J. Pfleger, and P. N. Prasad, “Dynamics of third-order nonlinear optical processes in Langmuir-Blodgett and evaporated films of phthalocyanines,” J. Chem. Phys. 92, 2019–2024 (1990).
[Crossref]

Sanchez, F.

G. Boudebs, S. Cherukulappurath, H. Leblond, J. Troles, F. Smektala, and F. Sanchez, “Experimental and theoretical study of higher-order nonlinearities in chalcogenide glasses,” Opt. Commun. 219, 427–433 (2003).
[Crossref]

F. Smektala, J. Troles, V. Couderc, A. Barthelemy, G. Boudebs, F. Sanchez, H. Zeghlache, G. Martinelli, Y. Quiquempois, and S. Bailleux, “Third and second order nonlinear optical properties of Ge-Se-S-As chalcogenide glasses,” Proc SPIE 4628, 30–38 (2002).
[Crossref]

Six, H. A.

G. Lucovsky, F. L. Galeener, R. C. Kezer, R. H. Geils, and H. A. Six, “Structural interpretation of the infrared and raman spectra of glasses in the alloy system Ge1-x Sx,” Phys. Rev. B 10, 5134–5146 (1974).
[Crossref]

Smektala, F.

M. Guignard, V. Nazabal, J. Troles, F. Smektala, H. Zeghlache, Y. Quiquempois, A. Kudlinski, and G. Martinelli, “Second-harmonic generation of thermally poled chalcogenide glass,” Opt. Express. 13, 789–795 (2005).
[Crossref] [PubMed]

G. Boudebs, S. Cherukulappurath, H. Leblond, J. Troles, F. Smektala, and F. Sanchez, “Experimental and theoretical study of higher-order nonlinearities in chalcogenide glasses,” Opt. Commun. 219, 427–433 (2003).
[Crossref]

F. Smektala, J. Troles, V. Couderc, A. Barthelemy, G. Boudebs, F. Sanchez, H. Zeghlache, G. Martinelli, Y. Quiquempois, and S. Bailleux, “Third and second order nonlinear optical properties of Ge-Se-S-As chalcogenide glasses,” Proc SPIE 4628, 30–38 (2002).
[Crossref]

Taiji, M.

Talahashi, M.

T. Fujiwara, M. Talahashi, and A. J. Ikushima, “Second-harmonic generation in germanosilicate glass poled with ArF laser irradiation,” Appl. Phys. Lett. 71, 1032–1034 (1997).
[Crossref]

Tanaka, K.

Tao, H. Z.

G. P. Dong, H. Z. Tao, S. S. Chu, S. F. Wang, X. J. Zhao, Q. H. Gong, X. D. Xiao, and C. G. Lin, “Study on the structure dependent ultrafast third-order optical nonlinearity of GeS2-In2S3 chalcogenide glasses,” Opt. Commun. 270, 373–378 (2007).
[Crossref]

H. Z. Tao, G. P. Dong, Y. B. Zhai, H. T. Guo, X. J. Zhao, Z. W. Wang, S. S. Chu, S. F. Wang, and Q. H. Gong, “Femtosecond third-order optical nonlinearity of the GeS2-Ga2S3-CdI2 new chalcohalide glasses,” Solid State Commun. 138, 485–488 (2006).
[Crossref]

H. Z. Tao, X. J. Zhao, C. B. Jing, H. Yang, and S. Mao, “Raman scattering studies of the GeS2-Ga2S3-CsCl glassy system,” Solid State Commun. 133, 327–332 (2005).
[Crossref]

X. F. Wang, S. X. Gu, J. G. Yu, C. L. Liu, X. J. Zhao, and H. Z. Tao, “Formation and properties of chalcogenide glasses in the GeS2-Ga2S3-CdS system,” Mater. Chem. Phys. 83, 284–288 (2004).
[Crossref]

G. P. Dong, H. Z. Tao, X. D. Xiao, C. G. Lin, and X. J. Zhao, “Study on the formation, thermal, optical and physical properties of GeS2-Ga2S3-AgCl novel chalcohalide glasses,” J. Phys. Chem. Solids (Submit).

Tao, H.Z.

H.Z. Tao, S. Mao, G.P. Dong, H.Y. Xiao, and X.J. Zhao, “Raman scattering studies of the Ge-In sulfide glasses,” Solid State Commun. 137, 408–412 (2006).
[Crossref]

G.P. Dong, H.Z. Tao, X.D. Xiao, C.G. Lin, X.J. Zhao, and S. Mao, “Mechanism of electron beam poled SHG in 0.95GeS2∙0.05In2S3 chalcogenide glasses,” J. Phys. Chem. Solids (doi:10.1016/j.jpcs.2006.10.002).

Troles, J.

M. Guignard, V. Nazabal, J. Troles, F. Smektala, H. Zeghlache, Y. Quiquempois, A. Kudlinski, and G. Martinelli, “Second-harmonic generation of thermally poled chalcogenide glass,” Opt. Express. 13, 789–795 (2005).
[Crossref] [PubMed]

G. Boudebs, S. Cherukulappurath, H. Leblond, J. Troles, F. Smektala, and F. Sanchez, “Experimental and theoretical study of higher-order nonlinearities in chalcogenide glasses,” Opt. Commun. 219, 427–433 (2003).
[Crossref]

F. Smektala, J. Troles, V. Couderc, A. Barthelemy, G. Boudebs, F. Sanchez, H. Zeghlache, G. Martinelli, Y. Quiquempois, and S. Bailleux, “Third and second order nonlinear optical properties of Ge-Se-S-As chalcogenide glasses,” Proc SPIE 4628, 30–38 (2002).
[Crossref]

Wang, S. F.

G. P. Dong, H. Z. Tao, S. S. Chu, S. F. Wang, X. J. Zhao, Q. H. Gong, X. D. Xiao, and C. G. Lin, “Study on the structure dependent ultrafast third-order optical nonlinearity of GeS2-In2S3 chalcogenide glasses,” Opt. Commun. 270, 373–378 (2007).
[Crossref]

H. Z. Tao, G. P. Dong, Y. B. Zhai, H. T. Guo, X. J. Zhao, Z. W. Wang, S. S. Chu, S. F. Wang, and Q. H. Gong, “Femtosecond third-order optical nonlinearity of the GeS2-Ga2S3-CdI2 new chalcohalide glasses,” Solid State Commun. 138, 485–488 (2006).
[Crossref]

Wang, X. F.

X. F. Wang, Z. W. Wang, J. G. Yu, C. L. Liu, X. J. Zhao, and Q. H. Gong, “Large and ultrafast third-order optical nonlinearity of GeS2-Ga2S3-CdS chalcogenide glass,” Chem. Phys. Lett. 399, 230–233 (2004).
[Crossref]

X. F. Wang, S. X. Gu, J. G. Yu, C. L. Liu, X. J. Zhao, and H. Z. Tao, “Formation and properties of chalcogenide glasses in the GeS2-Ga2S3-CdS system,” Mater. Chem. Phys. 83, 284–288 (2004).
[Crossref]

Wang, Z. W.

H. Z. Tao, G. P. Dong, Y. B. Zhai, H. T. Guo, X. J. Zhao, Z. W. Wang, S. S. Chu, S. F. Wang, and Q. H. Gong, “Femtosecond third-order optical nonlinearity of the GeS2-Ga2S3-CdI2 new chalcohalide glasses,” Solid State Commun. 138, 485–488 (2006).
[Crossref]

X. F. Wang, Z. W. Wang, J. G. Yu, C. L. Liu, X. J. Zhao, and Q. H. Gong, “Large and ultrafast third-order optical nonlinearity of GeS2-Ga2S3-CdS chalcogenide glass,” Chem. Phys. Lett. 399, 230–233 (2004).
[Crossref]

Xiao, H.Y.

H.Z. Tao, S. Mao, G.P. Dong, H.Y. Xiao, and X.J. Zhao, “Raman scattering studies of the Ge-In sulfide glasses,” Solid State Commun. 137, 408–412 (2006).
[Crossref]

Xiao, X. D.

G. P. Dong, H. Z. Tao, S. S. Chu, S. F. Wang, X. J. Zhao, Q. H. Gong, X. D. Xiao, and C. G. Lin, “Study on the structure dependent ultrafast third-order optical nonlinearity of GeS2-In2S3 chalcogenide glasses,” Opt. Commun. 270, 373–378 (2007).
[Crossref]

G. P. Dong, H. Z. Tao, X. D. Xiao, C. G. Lin, and X. J. Zhao, “Study on the formation, thermal, optical and physical properties of GeS2-Ga2S3-AgCl novel chalcohalide glasses,” J. Phys. Chem. Solids (Submit).

Xiao, X.D.

G.P. Dong, H.Z. Tao, X.D. Xiao, C.G. Lin, X.J. Zhao, and S. Mao, “Mechanism of electron beam poled SHG in 0.95GeS2∙0.05In2S3 chalcogenide glasses,” J. Phys. Chem. Solids (doi:10.1016/j.jpcs.2006.10.002).

Yamasaki, J.

Yang, H.

H. Z. Tao, X. J. Zhao, C. B. Jing, H. Yang, and S. Mao, “Raman scattering studies of the GeS2-Ga2S3-CsCl glassy system,” Solid State Commun. 133, 327–332 (2005).
[Crossref]

Yu, J. G.

X. F. Wang, S. X. Gu, J. G. Yu, C. L. Liu, X. J. Zhao, and H. Z. Tao, “Formation and properties of chalcogenide glasses in the GeS2-Ga2S3-CdS system,” Mater. Chem. Phys. 83, 284–288 (2004).
[Crossref]

X. F. Wang, Z. W. Wang, J. G. Yu, C. L. Liu, X. J. Zhao, and Q. H. Gong, “Large and ultrafast third-order optical nonlinearity of GeS2-Ga2S3-CdS chalcogenide glass,” Chem. Phys. Lett. 399, 230–233 (2004).
[Crossref]

Zeghlache, H.

M. Guignard, V. Nazabal, J. Troles, F. Smektala, H. Zeghlache, Y. Quiquempois, A. Kudlinski, and G. Martinelli, “Second-harmonic generation of thermally poled chalcogenide glass,” Opt. Express. 13, 789–795 (2005).
[Crossref] [PubMed]

F. Smektala, J. Troles, V. Couderc, A. Barthelemy, G. Boudebs, F. Sanchez, H. Zeghlache, G. Martinelli, Y. Quiquempois, and S. Bailleux, “Third and second order nonlinear optical properties of Ge-Se-S-As chalcogenide glasses,” Proc SPIE 4628, 30–38 (2002).
[Crossref]

Zhai, Y. B.

H. Z. Tao, G. P. Dong, Y. B. Zhai, H. T. Guo, X. J. Zhao, Z. W. Wang, S. S. Chu, S. F. Wang, and Q. H. Gong, “Femtosecond third-order optical nonlinearity of the GeS2-Ga2S3-CdI2 new chalcohalide glasses,” Solid State Commun. 138, 485–488 (2006).
[Crossref]

Zhao, X. J.

G. P. Dong, H. Z. Tao, S. S. Chu, S. F. Wang, X. J. Zhao, Q. H. Gong, X. D. Xiao, and C. G. Lin, “Study on the structure dependent ultrafast third-order optical nonlinearity of GeS2-In2S3 chalcogenide glasses,” Opt. Commun. 270, 373–378 (2007).
[Crossref]

H. Z. Tao, G. P. Dong, Y. B. Zhai, H. T. Guo, X. J. Zhao, Z. W. Wang, S. S. Chu, S. F. Wang, and Q. H. Gong, “Femtosecond third-order optical nonlinearity of the GeS2-Ga2S3-CdI2 new chalcohalide glasses,” Solid State Commun. 138, 485–488 (2006).
[Crossref]

H. Z. Tao, X. J. Zhao, C. B. Jing, H. Yang, and S. Mao, “Raman scattering studies of the GeS2-Ga2S3-CsCl glassy system,” Solid State Commun. 133, 327–332 (2005).
[Crossref]

Q. M. Liu, X. J. Zhao, F. X. Gan, J. Mid, and S. X. Qian, “Femtosecond optical Kerr effect study of Ge10As40S30Se20 film,” Solid State Commun. 134, 513–517 (2005)
[Crossref]

X. F. Wang, S. X. Gu, J. G. Yu, C. L. Liu, X. J. Zhao, and H. Z. Tao, “Formation and properties of chalcogenide glasses in the GeS2-Ga2S3-CdS system,” Mater. Chem. Phys. 83, 284–288 (2004).
[Crossref]

X. F. Wang, Z. W. Wang, J. G. Yu, C. L. Liu, X. J. Zhao, and Q. H. Gong, “Large and ultrafast third-order optical nonlinearity of GeS2-Ga2S3-CdS chalcogenide glass,” Chem. Phys. Lett. 399, 230–233 (2004).
[Crossref]

G. P. Dong, H. Z. Tao, X. D. Xiao, C. G. Lin, and X. J. Zhao, “Study on the formation, thermal, optical and physical properties of GeS2-Ga2S3-AgCl novel chalcohalide glasses,” J. Phys. Chem. Solids (Submit).

Zhao, X.J.

H.Z. Tao, S. Mao, G.P. Dong, H.Y. Xiao, and X.J. Zhao, “Raman scattering studies of the Ge-In sulfide glasses,” Solid State Commun. 137, 408–412 (2006).
[Crossref]

G.P. Dong, H.Z. Tao, X.D. Xiao, C.G. Lin, X.J. Zhao, and S. Mao, “Mechanism of electron beam poled SHG in 0.95GeS2∙0.05In2S3 chalcogenide glasses,” J. Phys. Chem. Solids (doi:10.1016/j.jpcs.2006.10.002).

Appl. Phys. Lett. (3)

R. C. Miller, “Optical second harmonic generation in piezoelec-tric crystals,” Appl. Phys. Lett. 5, 17–19 (1964).
[Crossref]

T. Fujiwara, M. Talahashi, and A. J. Ikushima, “Second-harmonic generation in germanosilicate glass poled with ArF laser irradiation,” Appl. Phys. Lett. 71, 1032–1034 (1997).
[Crossref]

M. X. Qiu, F. Pi, and G. Orriols, “The role of lead component in second-harmnonic generation in lead silica by electron-beam irradiation,” Appl. Phys. Lett. 73, 3040–3042 (1998).
[Crossref]

Chem. Phys. Lett. (1)

X. F. Wang, Z. W. Wang, J. G. Yu, C. L. Liu, X. J. Zhao, and Q. H. Gong, “Large and ultrafast third-order optical nonlinearity of GeS2-Ga2S3-CdS chalcogenide glass,” Chem. Phys. Lett. 399, 230–233 (2004).
[Crossref]

J. Appl. Phys. (1)

T. E. Everhart and P. H. Hoff, “Determination of kilovolt electron energy dissipation vs penetration distance in solid materials,” J. Appl. Phys. 42, 5837–5846 (1971).
[Crossref]

J. Chem. Phys. (1)

M. K. Casstevens, M. Samoc, J. Pfleger, and P. N. Prasad, “Dynamics of third-order nonlinear optical processes in Langmuir-Blodgett and evaporated films of phthalocyanines,” J. Chem. Phys. 92, 2019–2024 (1990).
[Crossref]

J. Mater. Sci. Mater. Electron. (1)

K. Tanaka, “Optical nonlinearity in photonic glasses,” J. Mater. Sci. Mater. Electron. 16, 633–643 (2005).
[Crossref]

J. Opt. Soc. Am. B (2)

J. Phys. Chem. B (1)

I. V. Kityk, “IR-induced second harmonic generation in Sb2Te3-BaF2-PbCl2 glasses,” J. Phys. Chem. B 107, 10083–10087 (2003).
[Crossref]

Mater. Chem. Phys. (1)

X. F. Wang, S. X. Gu, J. G. Yu, C. L. Liu, X. J. Zhao, and H. Z. Tao, “Formation and properties of chalcogenide glasses in the GeS2-Ga2S3-CdS system,” Mater. Chem. Phys. 83, 284–288 (2004).
[Crossref]

Opt. Commun. (2)

G. Boudebs, S. Cherukulappurath, H. Leblond, J. Troles, F. Smektala, and F. Sanchez, “Experimental and theoretical study of higher-order nonlinearities in chalcogenide glasses,” Opt. Commun. 219, 427–433 (2003).
[Crossref]

G. P. Dong, H. Z. Tao, S. S. Chu, S. F. Wang, X. J. Zhao, Q. H. Gong, X. D. Xiao, and C. G. Lin, “Study on the structure dependent ultrafast third-order optical nonlinearity of GeS2-In2S3 chalcogenide glasses,” Opt. Commun. 270, 373–378 (2007).
[Crossref]

Opt. Express. (1)

M. Guignard, V. Nazabal, J. Troles, F. Smektala, H. Zeghlache, Y. Quiquempois, A. Kudlinski, and G. Martinelli, “Second-harmonic generation of thermally poled chalcogenide glass,” Opt. Express. 13, 789–795 (2005).
[Crossref] [PubMed]

Opt. Lett. (3)

Phys. Rev. B (1)

G. Lucovsky, F. L. Galeener, R. C. Kezer, R. H. Geils, and H. A. Six, “Structural interpretation of the infrared and raman spectra of glasses in the alloy system Ge1-x Sx,” Phys. Rev. B 10, 5134–5146 (1974).
[Crossref]

Proc SPIE (1)

F. Smektala, J. Troles, V. Couderc, A. Barthelemy, G. Boudebs, F. Sanchez, H. Zeghlache, G. Martinelli, Y. Quiquempois, and S. Bailleux, “Third and second order nonlinear optical properties of Ge-Se-S-As chalcogenide glasses,” Proc SPIE 4628, 30–38 (2002).
[Crossref]

Solid State Commun. (4)

H. Z. Tao, G. P. Dong, Y. B. Zhai, H. T. Guo, X. J. Zhao, Z. W. Wang, S. S. Chu, S. F. Wang, and Q. H. Gong, “Femtosecond third-order optical nonlinearity of the GeS2-Ga2S3-CdI2 new chalcohalide glasses,” Solid State Commun. 138, 485–488 (2006).
[Crossref]

Q. M. Liu, X. J. Zhao, F. X. Gan, J. Mid, and S. X. Qian, “Femtosecond optical Kerr effect study of Ge10As40S30Se20 film,” Solid State Commun. 134, 513–517 (2005)
[Crossref]

H.Z. Tao, S. Mao, G.P. Dong, H.Y. Xiao, and X.J. Zhao, “Raman scattering studies of the Ge-In sulfide glasses,” Solid State Commun. 137, 408–412 (2006).
[Crossref]

H. Z. Tao, X. J. Zhao, C. B. Jing, H. Yang, and S. Mao, “Raman scattering studies of the GeS2-Ga2S3-CsCl glassy system,” Solid State Commun. 133, 327–332 (2005).
[Crossref]

Other (3)

R. A. Myers, N. Mukherjee, and S. R. J. Brueck, “Large second-order nonlinearity in poled fused silica,” 16, 1732–1734 (1991).

G.P. Dong, H.Z. Tao, X.D. Xiao, C.G. Lin, X.J. Zhao, and S. Mao, “Mechanism of electron beam poled SHG in 0.95GeS2∙0.05In2S3 chalcogenide glasses,” J. Phys. Chem. Solids (doi:10.1016/j.jpcs.2006.10.002).

G. P. Dong, H. Z. Tao, X. D. Xiao, C. G. Lin, and X. J. Zhao, “Study on the formation, thermal, optical and physical properties of GeS2-Ga2S3-AgCl novel chalcohalide glasses,” J. Phys. Chem. Solids (Submit).

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Figures (8)

Fig. 1.
Fig. 1. Linear absorption spectrum of the representative A1 (80GeS2-10Ga2S3-10AgCl) glass
Fig. 2.
Fig. 2. Time-resolved OKE signals of (a) a standard CS2 reference and (b) A1 (80GeS2-10Ga2S3-10AgCl) and B4 (64GeS2-16Ga2S3-20AgCl) glasses at a wavelength of 820nm
Fig. 3.
Fig. 3. Raman spectra of pseudo-binary (100-x)GeS2-xGa2S3 (x=0, 10, 20, 30) glasses
Fig. 4.
Fig. 4. Raman spectra of the pseudo-ternary glasses on Series B
Fig. 5.
Fig. 5. The ratio of IS/IR and (S+Cl/2)/(Ge+Ga) collected as a function of the content of AgCl for the pseudo-ternary glasses on Series B
Fig. 6.
Fig. 6. Optical Kerr signal ratio of IS/IR collected as a function of the values of (S+Cl/2)/(Ge+Ga) for the glasses on three Series
Fig. 7.
Fig. 7. Maker fringe pattern of the A1 (80GeS2-10Ga2S3-10AgCl) glass poled by the electron beam
Fig. 8.
Fig. 8. Raman spectra of the as-prepared 80GeS2-10Ga2S3-10AgCl glass and the irradiated one

Tables (1)

Tables Icon

Table 1. Linear and third-order nonlinear optical properties of GeS2-Ga2S3-AgCl glasses

Equations (2)

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χ S ( 3 ) = χ R ( 3 ) ( I S I R ) 1 2 ( n S n R ) 2
v f μ

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