Theoretical Evaluation on Terahertz Source Generators from Ternary

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Theoretical Evaluation on Terahertz Source Generator from Ternary Metal Chalcogenides of PbMTe (M = Ga, In) 6

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Wendan Cheng, Chen-Sheng Lin, Hao Zhang, and Guo-Liang Chai J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.7b10972 • Publication Date (Web): 03 Feb 2018 Downloaded from http://pubs.acs.org on February 3, 2018

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The Journal of Physical Chemistry

Theoretical Evaluation on Terahertz Source Generator from Ternary Metal Chalcogenides of PbM6Te10 (M = Ga, In) Wen-Dan Cheng,* Chen-Sheng Lin, Hao Zhang, and Guo-Liang Chai* State Key Laboratory of Structural Chemistry, Fujian Institute of Research on the Structure of Matter, Chinese Academy of Sciences, Fuzhou, China. KEYWORDS: Nonlinear optical susceptibility, Performance evaluation, Terahertz source, Metal chalcogenides.

ABSTRACT: We develop a new method to calculate nonlinear optical susceptibility, and give a definition of the extended figure of merit (EFOM) contributing from optical susceptibility, refractive index and absorptions to evaluate the material intrinsic property. The calculated phonon frequency determines the infrared absorption coefficient and transparent cutoff edge. We calculate the conversion efficiencies of terahertz source generating from chalcogenides PbM6Te10 (M = Ga, In), based on difference frequency generation of optical process in term of the EFOM and experiment parameters. The calculated terahertz light conversion efficiencies of PbGa6Te10 and PbIn6Te10 are in the order of 10-3 to 10-2 at low side of THz wavelengths, and the

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conversion efficiency of PnIn6Te10 is larger than that of PbGa6Te10 at the same conditions. A small terahertz wavelength and absorption coefficient, and large nonlinear susceptibility, i.e. a large EFOM will result in a large conversion efficiency. These studies give an indication that the chalcogenides with heavy element composites are the desired candidates as terahertz source generation. The present work will give contributions to evaluate and search new NLO materials as terahertz source generation.

1. Introduction Terahertz (THz) source plays prominent roles not only in the basic theory of modern science but also in the application of innovative technology. The wavelength of THz source localizes between microwave and infrared sources. THz has many important applications in current society based on the following factors. First, the low photon energy of THz waves cannot lead to photoionization in biological tissues, which makes them safe for medical diagnosis and health monitoring of human body.1-6 Second, it can be used for homeland safety check, such as identification of weapons and explosives concealed under cloth or package, as it is transparent to cloth, paper, wood, and plastic etc.7-10 In addition, the THz waves can also be applied for information and communication technologies, non-destructive evaluation of materials and constructors, quality control of food and agricultural products, global environmental monitoring etc.10-15 High quality THz radiation sources are urgently needed to ensure the above mentioned applications. Difference-frequency generation (DFG) or optical parametric process by using nonlinear optical (NLO) crystals is one of the important methods to generate high quality THz


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sources. Although this technique provides broadly tunable THz radiation by using relatively compact portable laser, it is still suffered from low conversion efficiencies . At presently, high efficient NLO materials for more efficient THz source generation are urgently needed. Fortunately, heavy-metal chalcogenides are favored candidates as THz-DFG materials16-21 due to their small band gap and lattice vibration frequency, and inactive constituent element compared to the other THz materials. By compared with experiments, first-principles simulations is a non-destructive and economic technique to evaluate and test THz source generation properties for new chalcogenide materials to determine whether these materials are valuable for further research and market production.22 The figure of merit (FOM) is defined as deff2/nxnynz, and is employed to evaluate property of transparent material, where d eff is nonlinear optical coefficient and nx,ny,nz are linear refractive index that only depend on the structure of material. After we obtained FOM, we could get the conversion efficiency of THz-DFG materials under experimental conditions.23, 24 In this work, we will develop a new method to calculate nonlinear optical susceptibility, and give a definition of the extended figure of merit (EFOM) contributing from nonlinear optical (NLO) susceptibility, refractive index and absorption to evaluate the material intrinsic property. We will calculate the conversion efficiencies of terahertz source generating from chalcogenides PbM6Te10 (M = Ga, In), based on difference frequency generation (DFG) of optical process in term of the EFOM and experiment parameters.

2. Simulation Models and Theoretical Calculations 2.1 Geometry structures of simulation models The Te2- anionic arrangement in PGT and PIT crystals are in the topology of filled -Mn structure.25 This term is used for the description that the tellurium anions of these two solids form a -Mn like arrangement with Ga atoms (PGT) and In atoms (PIT) localized in some


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tetrahedral hollows, respectively. The Te sublattice of the crystals can be regarded as being composed of two interpenetrating polyhedral of vertex- and edge-sharing tetrahedral and vertexsharing octahedral. The complex three-dimensional arrangements of PGT and PIT crystals are formed by the connections among the tetrahedral and the connections between the tetrahedron and octahedron, in which two (three) of each four distorted octahedral holes are completely (part) occupied by Pb atoms for PGT (for PIT), and 12% distorted tetrahedral holes are occupied by Ga or In atoms in one unit cell.26, 27 For the PGT compound, the X-ray crystal structure data26, 27

was used for the energy band calculations. For the PIT compound, experimental crystal

structure shows that there are nine distorted octahedral holes and are partly occupied by Pb atoms, i.e. each hole occupied by only 2/3 Pb atom in a unit cell (Z = 6).26, 27 In fact, there are six Pb atoms (9 x 2/3 = 6) in a unit cell (Z = 6). The optimized structure constructed by 6 Pb, 36 In, and 60 Te atoms with hexagonal symmetry was used for the calculations of optical properties, 28 as shown in Figure 1. The optimized and experimental structure parameters are listed in Tables S1 and S2 of Supporting Information for PGT and PIT crystals.

Figure 1. The PbIn6Te10 (PIT) unit cell with hexagonal symmetry.


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2.2 Calculation of refractive index and nonlinear optical coefficient The interaction between electrons and ion cores was represented by the norm-conserving pseudopotentials.29 The valence electronic configurations for the component elements are Pb5s25p65d106s26p2, Ga-4s24p1, In-5s25p1and Te-5s25p4, respectively. The local density approximation (LDA) was used as exchange-correlation functional. The cut-off energy of 820 eV, the convergence criteria of 1.0 × 10–6 eV/atom and total energy difference less than 2.1 x 10-7 eV in consecutive iteration were employed in density functional theory (DFT) calculations, respectively. The

wavefunction was represented by using a Monkhorst-Pack mesh of 1 x 1 x 2 and there were 500 bands (480 valence bands and 20 conduction bands) in energy band calculations at any given kvector in the Brillouin zone. The energy convergence tolerance was set to be 2.125 x 10 -7 eV, and there were 480 valence bands and 999 conduction bands in the optical property calculations. The latter calculations were accomplished by using the first principles plane-wave pseudopotential method with the CASTEP code provided by Material Studio package. 29,30 The refractive index of n and first-order susceptibility of (1) depend on the dielectric function of , and they show the relations of n2 =  and (1)()ii = [()i – 1]/4. The complex dielectric function is () = 1() + i2(), where the imaginary part is given by:  2ij ( ) 

p i ( k ) p j (k ) 8 2  2 e2  k  cv ( f c  f v ) cv 2 vc  [ Ecv ( k )   ] (1.1) 2 m Veff Evc

The real part 1() and imaginary part 2() are linked by a Kramers-Kronig transform, and the ε1(ω) is obtained by this transform. Here, [Ecv(k) – ħ] = [Ec(k) – Ev(k) – ħ] indicates that the energy difference between the conduction bands (CB) and valence bands (VB) at the k point with absorption of a quantum ħ. The fc and fv represent the Fermi distribution functions of the CB and VB, respectively. The term pcvi(k) denotes the momentum matrix element transition


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from the energy level c of CB to the level v of VB at the k point in the BZ and Veff is the volume of the unit cell. The m, e and ħ are the electron mass, charge and Plank's constant, respectively. We employ -function properties to derive the formula of frequency-dependence nonlinear susceptibility at the different optical processes of SHG and DFG, as shown in the Supporting Information (SI). The SHG susceptibility formula in Lin’s paper

31

only makes the calculations

of static SHG susceptibility and is not suitable for the calculation of frequency-dependence susceptibility, and the formula in Sharma’s paper

32

does not give the treatments of resonance

divergence in denominator although it is suitable for the calculation of frequency-dependence SHG susceptibility. By the comparisons with the previously presented expressions of SHG susceptibility,31,32 our method can eliminate resonance divergence between the applied frequency or generated frequency and transition frequencies, and makes calculations of dependent frequency SHG susceptibility. In particular, until now there is no formula to directly calculate the frequency-dependence DFG susceptibility of solid state materials, as far as we know. The second-order NLO susceptibilities based on the SHG and DFG processes are calculated by formula (S4, S5) and (S9, S10) in the SI, respectively, the NLO d-coefficient is obtained by the real and imaginary parts of the second-order NLO susceptibility (see SI).

2.3 Calculation of phonon frequency The crystallographic data

26, 27

of PGT and PIT compounds determined by X-ray single crystal

diffraction was used for the input structures of geometry optimization, in which the initial structure of PIT was selected to complete occupied octahedral holes by six Pb atoms, in order to make successful calculation of vibration properties. During the geometrical optimization, we employed the DFT-LDA method embedded the Vienna ab initio simulation package (VASP). 33-36 In this processes, we used k-mesh 3 x 3 x 2 and the cut-off energy of 368 eV and precision of 1.0


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× 10–8 eV/atom and forces of 0.01 eV/Å on the atoms, the valence electronic configurations of Pb-5d106s26p2, Ga-3d104s24p1, In-4d105s25p1, Te-5s25p4 and the PAW (projector augmented wave) potentials.35 The optimized unit-cell structure with Gamma k-point was employed to calculate phonon properties. The small displacement structures (102 and 612 structures) at the equilibrium position of each atom were generated by Phonopy code

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for PGT and PIT crystals,

respectively. The energies and atomic force constants were calculated by the VASP code, and the phonon frequencies were obtained from atomic force constants by the Phonopy code. 37 We obtain the phonon band structure, phonon density of state and infrared absorption spectra while the phonon frequencies were calculated in PGT and PIT crystals.

2.4 Calculation of conversion efficiency For the DFG process, the conversion efficiency including the effects of linear absorption in the infinite plane wave and nondepleted pump approximation can be written as formula (1.2a) in cgs unit.24 Under the conditions of phase-matching (i.e. K0), the DFG conversion efficiency d in formula (1.2a) can be abbreviated as formula (1.2b), and A = 1 while the linear absorption of crystal does not appear. Here, d eff is the effective nonlinear coefficient, I is the intensity of the incident light, c for the velocity of light in vacuum, L for the length of the nonlinear crystal, d is the wavelength of generate wave, and ni is the light refraction index in the formulas (1.2a, 1.2b). In fact, the conversion efficiency d is the dependence on the properties of material self, i.e.d∝ Adeff2/n3 = EFOM while the crystal is optical phase matching, where n 3= nxnynz and EFOM is extended figure of merit, and the parameter A is relative with absorption (formula 1.2b); d∝ deff2/n3 = FOM while the crystal is transparent (A=1). The d is also dependent on the conditions


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of experiments and devices, d ∝L2Ip/(cd2) = FOC. The formula is defined as the factor of condition (FOC). Hence, the equation can be rewrites as d= C.EFOM.FOC, here C=5125.  d   d0 exp[  ( 1 ) L / 2 ]

sin 2 (  kl / 2)  sinh 2 ( 2 L / 4) (  kl / 2) 2  ( 2 L / 4 ) 2

(1.2a)

 d   d0 A (1.2b)  d0 

2 512 5 d eff L2 I p1

n p1n p 2 n d cd d2

A  exp[(1 ) L / 2]

sinh 2 ( 2 L / 4) ( 2 L / 4) 2

1   p1   p 2   d  2   p1   p 2   d

,

3. Results and Discussions 3.1 Refractive index and DFG susceptibility in THz zone The EFOM or conversion efficiency of material depends on the refractive index, nonlinear susceptibility and absorption. And small refractive index and large susceptibility will result in large EFOM. The calculated refractive indexes n x (=ny) and nz dispersion curves of PGT and PIT crystals are plotted in Figure 2, which are localized in the wavelengths of 10 – 125 m or frequencies of 30 – 2.40 THz range, respectively. The calculated refractive indexes of n 3= nxnynz are 29.4585 and 28.9562, and average refractive indexes are 3.0895 and 3.0723; the average refractive index of experimental determination38 is 3.06 and 3.03 at the wavelength of 10 µm for PGT and PIT crystals, respectively. The average refractive index is larger for PGT (cal. 3.09, expt.3.06) than for PIT (cal.3.07, expt. 3.03). By the comparison between them, it is shown that the theoretical and experiment values are consistent.


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3.149

3 .1 4 1

3.148

3 .1 4 0

PGT nx

3.147

3 .1 3 9

(a)

Refractive index

Refractive index

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


3.146 2.972

x

2 .9 3 6

PGT nz

2.971

P IT n

(b ) 3 .1 3 8

P IT n 2 .9 3 5

z

2.970 0

20

40

60

80

100

120

2 .9 3 4 0

Wavelength  (m)

2 0

4 0

6 0

8 0

10 0

1 2 0

W a v e le n g t h  (  m )

Figure 2. The refractive index nx (= ny) and nz dispersions within wavelengths of 10 – 125 m for crystals (a) PGT and (b) PIT.

The PGT and PIT crystals belong to the crystal class 32, and there are five non-zero secondorder nonlinear susceptibilities of dij tensors. Under the constraints of Kleinman symmetry, and only three dependent tensor components

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d11 = -d12 = -d26. By using formulas (S9) and (S10)

and their relations, we can obtain the susceptibility of (2) and NLO parameter d in terms of relation of 2d = (2) based on the DFG optical process. The calculated dynamic d 11 component is plotted in Figure 3 with the wavelengths d from 5 to 125 m for the PGT and PIT crystals, in which the dynamic d values of DFG processes are obtained while the input wavelengths 1 from 1.10 to 1.53m and the 2 is at a given value of 1.55 m. It is found from Figure 3 that the d11 value (～deff value) is larger for the PIT crystal than that for the PGT crystal. For an example, d 11 of PGT is 51.24 pm/V and d11 of PIT is 80.02 pm/V at THz wavelength of 62 m. It is also found that the variations of NLO parameters d11 of DFG optical processes vs. wavelengths (or frequency) are very small within the THz zone (the zone localized at larger than wavelength of 30 µm) for these two crystals. The measured SHG NLO coefficient d11 of PIT were about 51


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pm/V at the wavelength of 4.7 µm.40 The calculated dispersions of SHG d11 are plotted in the Figure S1 of SI for the PGT and PIT crystals, respectively. The calculated d11 coefficients of PIT based on the SHG and DFG processes are 51.58 and 95.37 pm/V at the wavelengths of 5.0 µm in this work. By the comparisons between the experimental and calculated results, the calculation results of SHG and DFG d coefficients are reasonable. Here, we noted that the SHG and DFG are different optical processes and the DFG susceptibility is about two times as the SHG susceptibility.41 The refractive index and second-order nonlinear susceptibility can be used to evaluate the NLO material property described as EFOM = Adeff2/(nxnynz) while NLO material appears at transparent zone (A = 1), and they are not independently controllable to material property due to both are dependence with band gap of material. The refractive index and nonlinear susceptibility show the opposite contribution to EFOM, and they are the greatest contribution to EFOM (i.e. to conversion efficiency) only when the refractive index and nonlinear susceptibility reach the competitive balance. The EFOM [222.30 (pm/V)2] of PIT is larger than that [89.41 (pm/V)2] of PGT at the wavelength of 41 µm by DFG process. The reason results from a large In ionic size of PIT crystal, and it results in a small band gap and large polarization of PIT crystal.


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1.10 1.15 1.20 1.25 1.30 1.35 1.40 1.45 1.50  (m)

58 56

DFG NLO coefficient d11 (pm/V)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


54

(a) PGT 52

50 105

DFG: 1/d= 1/1-1/2 (2 > 1)

100

2 = 1.55m

95 90 85

(b) PIT

80

20

40

60

80

100

120

Wavelength d (m)

Figure 3. The dynamic nonlinear susceptibilities d11 based on DFG process within wavelengths of 5– 125 m for crystals (a) PGT and (b) PIT.

3.2 Phonon dispersion spectrum and phonon density of states We only use the 1x1x1 supercell (102 atoms) in the phonon calculations of PGT and PIT crystals. Finite displacement approach was employed to construct dynamical matrices, and we obtained frequency in terms of relation between the vibration frequency and force constant. Then, the phonon dispersion spectra were obtained from the calculations of frequencies vary between two points in the Brillouin zone, and the phonon densities of states were obtained from the plots of the phonon state numbers versus frequency value (i.e. phonon state numbers of unit frequency). Figures 4a and 4b give phonon dispersion curves along high symmetry direction of PGT and PIT crystals, in which the figures show break plots (the complete plots are given at


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Figure S2 in SI). It is shown that the largest phonon frequencies of about 7.0 and 6.2 THz are localized at -point within the top phonon dispersion curves for PGT and PIT crystals, and they give the information of the cutoff edge of infrared transparency, respectively. The absorption of PGT appears at less than 7.0 THz of phonon frequency, in other word, the infrared light is transparency within wavelength of < 43 m (> 7.0 THz) for the PGT crystal (Figure 4a). From Figure 4b we also can get information of infrared light transparency within < 44 m (> 6.2 THz) for PIT crystal. The information is concerned to the performance of mid/far infrared NLO crystals. Additionally, figures 4a and 4b also give the acoustic branches in views of discontinuous curve at -point in the lowest frequency phonon dispersion curve. By the comparisons between the two absorption frequencies (or absorption wavelengths), we find that the infrared transparency is wider for PIT than for PGT crystals, and a heavier atom (In > Ga) is of smaller phonon frequency in PMT (M= Ga, In) system.


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(a)

Frequency (THz)

7.0

6.5

6.0 1.0 0.5 0.0 

H

A



K

M

L

H

L

H

q-point

(b)

6.0

Phonon frequency (THz)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


5.5

5.0

1.0

0.5

0.0 

A

H

K



M

q-ponit

Figure 4. Phonon frequency dispersion curves of PGT (a) and PIT (b).

The phonon densities of states (total and part) calculated by Phonopy code

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are plot in

Figures 5a and 5b, and they give the evidence of lattice vibration contributions at specially designated frequency. Figures 5a and 5b show three zones of bands. The broad band localized at about 0.25—3.25 THz (wavelengths 1200—92 m) and 0.25—3.10 THz (1200—88 m) frequencies contribute from mixings of Pb, Ga or In and Te lattice vibrations, and Te vibrations


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give the largest contribution to this frequency zone and the lowest phonon frequency contributes from the Pb vibration in the PGT and PIT crystals, respectively. The narrow band localized at about 3.25—4.25 THz frequencies (wavelengths 92—71 m) for PGT, and 3.10—4.10 THz frequencies (88—74 m) for PIT are the contributions from Te lattice vibrations as shown in phonon PDOS of Figures 5a and 5b, respectively. The bands localized at about 4.25—7.0 THz frequencies (wavelengths 71—43 m) and 4.10—6.20 THz frequencies (wavelengths 74—44 m) are the mixing contributions from Ga (In) and Te lattice vibrations, but the peaks come from contribution of Ga or In within the PGT and PIT crystals, respectively. These findings again give the information that a heavier atom would lead to smaller phonon frequency. The cutoff edges of mid/far infrared transparent range are at the frequency of 7.0 and 6.2 THz, and they dependent on the band localized at largest vibration frequency for PGT and PIT crystals, respectively. Accordingly, the cutoff edges of infrared transparency are determined on Ga-Te and In-Te mixing phonon at high frequency zone in the PGT and PIT crystals. This finding is extracted from the phonon dispersion spectra and phonon density of states. We can find from formula (1.2b) that the linear absorption is very detrimental to frequency conversion processes. Accordingly, the incident and generation lights will avoid localized at an infrared absorption zone in order to improve the THz light conversion efficiency. 23


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(a)

100

120

PbGa6Te10 TDOS

(b)

PbIn6Te10 TDOD

100

80

80

60 Phonon Density of States (states/THz)

Phonon Density of States (states/THz)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


40 20 0 70

PDOS

60

Te

50 40 Ge

30 20 10

2

20 0 80 Te

PDOS

60 In 40

Pb

0 1

40

20

Pb

0

60

3 4 5 6 Frequency (THz)

7

8

0 0

1

2 3 4 Frequency (THz)

5

6

7

Figure 5. Phonon density of states of PGT (a) and PIT (b) crystals.

3.3 Conversion efficiency of THz wave The conversion efficiency is an important evaluation criterion while one selects an NLO crystal as frequency conversion devices with a certain laser wavelength. The conversion efficiency of DFG optical process lies on two factors: 1) material-self properties including the phase mismatch, absorption, refractive index and NLO coefficient (when NLO material is phase matching, we only consider the last three contributions, i.e. EFOM = Adeff2/n3); 2) the experimental and device conditions including the length of light pass (crystal size), intensity of incident light and wavelength of generate light. For the PGT and PIT crystals, we have EFOM=5125Adeff2/n3 = 0.3118 x 10-10 and 1.9851 x 10-10 (cm3/erg) at wavelengths of 41 m (THz transparency zone, A=1), respectively. Here, deff  d11 and n3 = nxnynz. If we set the pump


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intensity of 10 MW/cm2 [10 x 1013 (erg/cm2s)] and optical path length of 0.5 cm (crystal size), and the DFG wavelength of 41 m, we obtain the values of FOC of 4.9607 x 107 (erg/cm3) for crystals of PGS and PIT, respectively. Accordingly, the DFG conversion efficiencies of d (=EFOM.FOC) are about 1.5467 x 10-3 and 9.8476 x 10-3 at the THz wavelengths of 41 m for the PGS and PIT crystals, respectively. The zero-level transmission limit of about 31 m was reported in reference.40 Accordingly, the DFG output wavelength is set at 31 m and by the same experimental conditions as the simulation ones. Following the previous process, the calculated DFG conversion efficiency of d is about 2.7103 x 10-3 for PGT and 17.292 x 10-3 for PIT crystals at the THz wavelength of 31 m, respectively. These results are listed in Table 1, and it is shown that a small THz wavelength will result in a larger DFG conversion efficiency while there are the same conditions of experiment and device. Now we consider the influence of THz light absorption on the conversion efficiency. The phonon dispersion spectra (Figures 4a and 4b) and lattice vibration infrared absorption spectra (Figures 6a and 6b) show that the infrared light is transparency within infrared wavelength ranges of < 43 m and < 44 m for the PGT and PIT crystals, respectively. In terms of the relation between the absorption coefficient  and infrared intensity I,

23,42

we obtain the

absorption coefficient (in Table 1) at designed wavelengths ( or frequencies) of 85 and 125 m from Figures 6a and 6b. Then, we can calculate the absorption factor A by the formula (1.2b). The obtained A factor is listed in Table 1 at THz wavelengths of 85 and 125 m for the PGT and PIT crystals, respectively. It is found from Table 1 that a larger absorption coefficient will result in a smaller A factor, furthermore, result in a smaller THz conversion efficiency for the PGT and PIT crystals, respectively. From Table 1, we also find that a large NLO coefficient will obtain a large efficiency for different materials under the same experimental conditions; a low


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wavelength of THz source (DFG output wavelength) will result in a large efficiency for the designed material; the THz conversion efficiency of PIT is larger than that of PGT crystals at the same experimental conditions. Light conversion efficiency depends on material property, i.e. EFOM, at constant condition and device. Accordingly, the EFOM can be employed to evaluate performance of NLO material.

Figure 6. Infrared absorption spectra of PGT (a) and PIT (b) crystals.

The reported conversion efficiencies of GaSe crystal were 1.77 x 10 -5 (4 mm, 106 µm), 4.5 x 10-5 (7 mm, 146 µm), 1.8 x 10-4 (15 mm, 196 µm) for the different crystal size and output wavelengths.43 For PIT crystal, our calculated conversion efficiencies are 1.73 x 10-2 and 9.85 x 10-3 at wavelengths of 31 and 41 m, and are 6.71 x 10-4 and 0.57 x 10-5 at wavelengths of 85 and 125 m, respectively. The latter two values are comparable in magnitude to that of GaSe crystals, and the PIT crystal appears with very large light conversion efficiency at the low side of THz wavelength.


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Table 1.The calculated parameters and conversion efficiencies for (PGT) and (PIT).* species WL

deff

PGT

31

PIT

R(n3)

abs.

A

CF

32.07 29.4040 trans.

1.0

2.7103

41

32.04 29.3992 trans.

1.0

1.5467

85

32.02 29.3987 2.8684 0.50943 0.1831

125

32.01 29.3978 23.860 0.02788 0.0046

31

80.30 28.8939 trans.

1.0

17.292

41

80.14 28.8905 trans.

1.0

9.8476

85

79.99 28.8878 5.5206 0.29402 0.6712

125

79.95 28.8867 16.991 0.05382 0.0057

*

size L=0.5 cm; incident light intensity I = 10 MW/cm2 for PGT and PIT crystals.

Units: WL (m); deff (pm/V); abs. (cm-1); CF ( 10-3)

3. Conclusion In

this work, we have calculated the light-light conversion efficiencies of THz source based on

the DFG process for ternary metal chalcogenides PGT and PIT. The conversion efficiency is a comprehensive index to evaluate performance of the THz source. It depends on EFOM that including the NLO coefficient, refractive index, and infrared absorption under the phasematching and constancy experimental condition. The NLO coefficients and refractive indexes are obtained by through the calculations of electronic structure information. The cut-off edge of infrared transparency and absorption coefficient are obtained in terms of the calculated phonon frequency. The calculated phonon density of states determines the individual phonon frequency. It is shown that the lowest phonon frequency contributes from the Pb lattice vibrations and the largest phonon frequency comes from Te-Ga or Te-In mixing lattice vibrations for the studied species, and that a heavier atom (In > Ga) possess smaller phonon frequency in PMT system (M


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= Ga, In). The calculated conversion efficiencies are in magnitude order of 10 -3 to 10-2 at the low side of THz wavelengths (31 and 41 m), and in magnitude order of 10-5 to 10-4 at the THz wavelengths of 85 and 125 m. The latter is comparable in magnitude to that of commercial GaSe crystals, and the PIT crystal appears with unusually large light conversion efficiency at the low side of THz wavelength. In views of the evaluations of physical behavior in this study, we find that a large THz wavelength and absorption coefficient will result in small conversion efficiency. It concludes that THz source generator would like constructions by the metal chalcogenides having a small energy gap, a large density of states at gap edges and a small phonon frequency. The first two will result in a large NLO coefficient for THz-DFG process, and the last will result in a wide infrared transparent zone for THz source. Our study gives an indicator to design a high efficiency THz source generator in metal chalcogenide systems.

ASSOCIATED CONTENT The following files are available free of charge. Formula derivations and calculations of secondorder NLO coefficients based on SHG and DFG processes in Supporting Information.

AUTHOR INFORMATION Corresponding Author * [email protected]; * [email protected].


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Author Contributions ‡These authors contributed equally.

Notes (i) = I(i)C/(10i), here C is the concentration (mol/L),and it is related to the density (g/cm 3) and weight (g) of the unit cell, and the factor of 10 in the denominator is an experience correction (listed in references 42). ACKNOWLEDGMENT This investigation was based on work supported by the National Basic Research Program of China (grant no.2014CB845605), the National Natural Science Foundation of China under projects 91222204, and 21473203, and Fujian Provincial Key Laboratory of Theoretical and Computational Chemistry. Funding Sources National Basic Research Program of China (No.2014CB845605), the National Natural Science Foundation of China under projects 91222204, and 21473203. REFERENCES (1) Wang, S.; Zhang, X.-C. Tomographic imaging with a terahertz binary lens. Appl. Phys. Lett., 2003, 82, 1821-1823. (2) Shen, Y. C.; Lo, T.; Taday, P. F.; Cole, B. E.; Tribe, W. R.; Kemp, M. C. Detection and identification of explosives using terahertz pulsed spectroscopic imaging. Appl. Phys. Lett. 2005, 86, 241116-241118.


20

Page 21 of 27 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(3) Markelz, A. G.; Roitberg, A.; Heilweil, E. J. Pulsed terahertz spectroscopy of DNA, bovine serum albumin and collagen between 0.1 and 2.0 THz. Chem. Phys. Lett. 2000, 320, 42-48. (4) Xie, A.; van der Meer, A. F. G.; Austin, R. H. Excited-state lifetimes of far-infrared collective modes in proteins. Phys. Rev. Lett, 2002, 88, 018102. (5) Dai, J.; Xie, X.; Zhang, X.-C. Detection of broadband terahertz waves with a laser-induced plasma in gases. Phys. Rev. Lett. 2006, 97, 103903. (6) Humphreys, K.; Loughran, J. P.; Gradziel, M.; Lanigan, W.; Ward, T.; Murphy, J. A.; O'Sullivan, C. Proceedings of Anuuual International Conference of The IEEE Engineering in Medicine and Biology Society. 2006, 26, 1302-1305. (7) Borak, A. Toward bridging the terahertz gap with silicon-based lasers. Science, 2005, 308, 638-639. (8) Corsi, C. New frontiers for infrared. Opto−Electron. Rev. 2015, 23, 1–23. (9) Ferguson, B.; Zhang, X.-C. Materials for terahertz science and technology. Nature Materials, 2002, 1, 26-33. (10) Zhang, X.-C.; Xu, J. Introduction to THz Wave Photonics, Springer Science+Business Media, LLC, New York, USA, 2010. (11) Dong, J.; Locquet, A.; Citrin, D. S. Terahertz Quantitative Nondestructive Evaluation of Failure Modes in Polymer-Coated Steel. IEEE J. Select. Topics in Quant. Electro. 2017, 23 (4), 8400207. (12) Shi, S.-C.; Paine, S.; Yao, Q.-J.; Lin, Z.-H.; Li, X.-X.; Duan, W.-Y.; Matsuo, H.; Zhang, Q.; Yang, J.; Ashley, M. C. B.; Shang, Z.; Hu, Z..-W. Terahertz and far-infrared windows opened at Dome A in Antarctica. Nature Astronomy, 2016, 1, 1-7.


21


Page 22 of 27

(13) Rakshit, R.; Serita, K.; Tonouchi, M.; Mandal, K. THz conductivity of semi-insulating and magnetic CoFe2O4 nano-hollow structures through thermally activated polaron. J. Appl. Phys. 2016, 120, 203901-11. (14) Nakanishi, H.; Ito, A.; Takayama, K.; Kawayama, I.; Murakami, H.; Tonouchi, M. Visualization of Photoexcited Carrier Responses in a Solar Cell Using Optical Pump-Terahertz Emission Probe Technique. J. Infrared Millimeter and Terahertz Waves, 2016, 37, 498-506. (15) Wu, J. B.; Zhang, X.; Jin, B. B.; Liu, H. T.; Chen, Y. H.; Zhang, C. H.; Kang, L.; Xu, W. W.; Chen, J.; Wang, H. B.; Tonouchi, M.; Wu, P. H. The dynamic process and microscopic mechanism of extraordinary terahertz transmission through perforated superconducting films. Sci. Rep. 2015, 5, 15588. (16) Chung, I.; Kanatzidis, M. G. A rich source of nonlinear optical materials. Chem. Mater. 2014, 26, 849-869. (17) Luo, Z.-Z.; Lin, C.-S.; Cui, H.-H.; Zhang, W.-L.; Zhang, H.; Chen, H.; He, Z.-Z,; Cheng, W.-D. PbGa2MSe6 (M = Si, Ge): Two exceptional Infrared nonlinear optical crystals. Chem. Mater., 2015, 27, 914-922. (18) Luo, Z.-Z.; Lin, C.-S.; Cui, H.-H.; Zhang, W.-L.; Zhang, H.; He, Z.-Z,; Cheng, W.-D. SHG materials SnGa4Q7 (Q = S, Se) appearing with large conversion efficiencies, high damage thresholds, and wide transparencies in the mid-infrared region. Chem. Mater., 2014, 26, 2743−2749. (19) Petrov, V. Parametric down-conversion devices: The coverage of the mid-infrared spectral range by solid-state laser sources. Opt. Mater., 2012, 34, 536-554.


22

Page 23 of 27 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(20) Mei, J.; Zhong, K.; Wang, M.; Liu, Y.; Xu, D.; Shi, W.; Wang, Y.; Yao, J.; Norwood, R. A.; Peyghambarian, N. Widely-tunable high-repetition-rate terahertz generation in GaSe with a compact dual-wavelength KTP OPO around 2 m. Opt. Express 2016, 24, 23369-23375. (21) Xu, J.; Knippels, G. M. H.; Oepts, D.; van der Meer, A. F. G. A far-infrared broadband (8.5-37 m) autocorrelator with sub-picosecond time resolution based on cadmium telluride. Opt. Commun. 2001, 197, 379–383. (22) Augustyniak, M.; Usarek, Z. Finite element method applied in electromagnetic NDTE: A review. J. Nondestruct. Eval. 2016, 35, 39-54. (23) Cheng, W.-D.; Lin, C.-S.; Zhang, H.; Huang, Y.-Z.; Chai, G.-L. Theoretical evaluation of terahertz sources generated from SnGa4Q7 (Q=S, Se) as infrared nonlinear optical materials. ChemPhysChem 2017, 18, 519 – 525. (24) Rutherland, R. L. in Handbook of Nonlinear Optics, 2nd ed., Marcel Dekker, New York, 2003, pp. 33–100. (25) Shoemaker, C. B.; PShoemaker, D.; Hopkins, T.E.; Yindepit, S. Refinement of the structure of beta-manganese and of a related phase in the Mn-Ni-Si system Acta Crystallogr. 1978, B34, 3573-3576. (26) Kienle, L.; Deiserou, H. J. SnAl6Te10, SnGa6Te10 and PbGa6Te10: Superstructures, symmetry relations and structural chemistry of filled beta-manganese phases. Z. Kristallogr. 1998, 213, 569-574. (27) Deiserou, H. J.; Muller, H. D. Structural relations in the family of nonmetallic filled betamanganese Phases: The new members AGa6Te10 (A: Sn, Pb) and PbIn6Te10. Z. Anorg. Allg. Chem. 1996, 622, 405–410.


23


Page 24 of 27

(28) Reshak, A. H.; Parasyuk, Oleg.V.; Kamarudin, H.; Kityk, I.V.; Alahmed, Zeyad A.; Al Zayed, Nasser S.; Auluck, Sushil; Fedorchuk, Anatolii O.; Chysky, J. Experimental and theoretical study of the electronic structure and optical spectral features of PbIn 6Te10. RSC Advance 2016, 6, 73107-731. (29) Clark, S. J.; Segall, M. D.;.Pickard, C. J.; Hasnip, P. J.; Probert, M. J.; Refson, K.; Payne, M. C., First principles methods using CASTEP. Z. Kristallogr. 2005, 220, 567-570. (30) Refson, K.; Clark, S. J.; Tulip, P. R. Variational density-functional perturbation theory for dielectrics and lattice dynamics. Phys. Rev. B 2006, 73, 155114-12. (31) Lin, Jiao; Lee, Ming-Hsien; Liu, Zhi-Ping; Chen, Chuangtian; Pickard, Chris J. Mechanism for linear and nonlinear optical effects in b-BaB2O4 crystals. Phys. Rev. B 1990, 60, 1338013389. (32) Sharma, S.; Ambrosch-Draxl, C. Second-harmonic optical response from first principles. Physica Scripta 2004, T109, 128-134. (33) Hafner, J.； Hafner, J. Ab-initio simulations of materials using VASP: Density-functional theory and beyond. J. Comput. Chem. 2008, 29, 2044-2078. (34) Kresse, G.; Furthmüller, J. Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set. Phys. Rev. B 1996, 54, 11169-11186. (35) Kresse, G.; Joubert, D. From ultrasoft pseudopotentials to the projector augmented-wave method. Phys. Rev. B 1999, 59, 1758-1775. (36) Perdew, J. P.; Zunger, A. Self-interaction correction on density-functional approximations for many-electron systems. Phys. Rev. B 1981, 23, 5048-5079. (37) Togo, A.; Oba, F.; Tanaka, I. First-principles calculations of the ferroelastic transition between rutile-type and CaCl2-type SiO2 at high pressures. Phys. Rev. B 2008, 78, 134106.


24

Page 25 of 27 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(38) Avanesov, S. A.; Badikov, D. V.; Badikov, V. V.; Panyutin, V. L.; Petrov, V.; Shevyrdyaeva, G. S.; Martynov, A. A.; Mitin, K. V. Phase equilibrium studies in the PbTeGa2Te3 and PbTe-In2Te3 systems for growing new nonlinear optical crystals of PbGa6Te10 and PbIn6Te10 with transparency extending into the far-IR. J. Alloys and Compounds 2014, 612, 386-391. (39) Boyd, R. W. in Nonlinear Optics Third Edit., Academic Press INC. San Diego USA, 2008 pp. 46-50. (40) Avanesov, S.; Badikov, V.;

Tyazhev, A.; Badikov, D.; Panyutin, V.; Marchev, G.;

Shevyrdyaeva, G.; Mitin, K.; Noack, F.; Vinogradova, P.;

Schebetova, N.; Petrov, V.;

Kwasniewski, A. PbIn6Te10: new nonlinear crystal for three-wave interactions with transmission extending from 1.7 to 25 m. Opt. Mater. Express 2011, 1, 1286-1291. (41) Orr, B. J.; Ward, J. F. Perturbation theory of non-linear optical polarization of isolated system. Mol. Phys. 1971, 20, 513-526. (42) (i) = I(i)C/(10i), here C is the concentration (mol/L),and it is related to the density (g/cm3) and weight (g) of theunit cell, and the factor of 10 in the denominator is an experience correction. (43) Shi, W.; Ding, Y. J.; Fernelius,N.; Vodopyanov, K. Efficient, tunable, and coherent 0.185.27-THz source based on GaSe crystal. Opt. Letters 2002, 27, 1454-1456.


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Theoretical Evaluation on Terahertz Source Generators from Ternary

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