Simulated pressure-induced blue-shift of phase-matching
region and nonlinear optical
mechanism for K3B6O10X
(X=Cl,Br)
Bingbing Zhang(张兵兵),1,2 Ming-Hsien Lee(李明憲),1,3 Zhihua Yang(杨志
华),1,a) Qun Jing(井群) 1, Shilie Pan(潘世烈),1,a) Min Zhang(张敏),1 Hongping
Wu(吴红萍), 1 Xin Su(苏欣),1,2 and Cheng-Shun Li(李政勛)3
1Key
Laboratory of Functional Materials and Devices for Special Environments of CAS; Xinjiang
Key Laboratory of Electronic Information Materials and Devices; Xinjiang Technical Institute of
Physics & Chemistry of CAS, 40-1 South Beijing Road, Urumqi 830011, China.
2University
of Chinese Academy of Sciences, Beijing 100049, China;
3Department
a)
of Physics, Tamkang University, New Taipei City 25137, Taiwan
Electronic mail: zhyang@ms.xjb.ac.cn (Zhihua Yang); slpan@ms.xjb.ac.cn (Shilie Pan)
The expression of Two-Band (TB) processes in the equation given by Lin et al.1 is
（TwoBands）=
Im[ pvc pcv ( pvv  pcc )]
e3
d 3k
. (1)
P
(

)
2 3 
m vc 4 3
vc5
Where, α, β, γ are Cartesian components, v and v′ denote valence bands, c and c′ refer to
conduction bands, and P(αβγ) denotes full permutation. The band energy difference and
momentum matrix elements are denoted as ℏωij and Pijα, respectively.
In Equation (1),
Im[ pvc pcv ( pvv  pcc )] 
i   
 
{ pvc pcv ( pvv  pcc )  [ pvc
pcv ( pvv  pcc )]*} .
2
 *



For （pvc）=pcv , and pvc  imvc rvc ,
Im[ pvc pcv ( pvv  pcc )] 

i
[imvc rvc  imcv rcv  mvc  imcv rcv  imvc rvc  mvc ]
2
im3
(vc  cv )(rvc rcv vc  rcv rvc vc )
2

 pcc  mvc , the equation (1)
Where pvv
（TwoBands）=
（TwoBands）= 

ie3
2 2
ie3
2 2
ie3
2 2
(   )
d 3k
P( )[ vc 5 cv (rvc rcv vc  rcv rvc vc )] (2)

3

4
vc
vc
d 3k 1
P ( )[rvc rcv vc  rcv rvc cv ]

3
3

4


vc
vc
d 3k 1
[(rvc rcv vc  rvc rcv  vc  rvc rcv vc  rvc rcv vc  rvc rcv  vc  rvc rcv vc )

3
3

4 vc
vc


(rcv rvc cv  rcv rvc  cv
 rcv rvc cv  rcv rvc cv  rcv rvc  cv
 rcv rvc cv )]

ie3
2 2
d 3k 1




[(rvc rcv (vc  cv )  rvc rcv（
 vc
+ cv
） rvc rcv（
vc +cv）

3
3

4


vc
vc





 rvc rcv
（
vc +cv） rvc rcv（
 vc
+ cv
） rvc rcv（
vc +cv )]
=0
For determining the cutting radius of specific ion, we investigated the charge-density
distribution of KBOC and KBOB. The charge-distribution of the B 6O10 unit is relatively
nonlocal due to the covalent properties of B-O bonding. While the charge-distribution of
Cl, Br and K is spherelike that show more ionic properties. Therefore, the B 6O10 units are
treated as a whole, Cl, Br and K cut as an isolated atom. We first determine the cutting
radius of K and O by searching the minimum points of charge density between K and the
nearest O. Thus, the cutting radius of K and O is 1.308 and 1.370 Å, respectively.
Considering the nonlocal charge-distribution of B6O10, the cutting radius of B is set to the
covalent radius (0.82 Å) in order to cover the nonlocal electrons. The cutting radius of Cl
and Br is set as 1.468 Å. The contribution of an ion or an ion group is extracted by indirect
stratage, i.e., the contribution of ion A is obtained by substracting the χ(2) contribution of
other ions except A from the origin χ(2) value, that is, χ(2)(A) = χ(2)(origin) − χ(2)(cut A).
Figure S1. The calculated polarizabilities α∕∕ and α┴ of (B6O13)−2 group in free and under 10 GPa
z-direction pressure, respectively.
Table SI. Sellmeier coefficients derived from the measured and calculated refractive indices.
Sellmeier equation: n  A 
B
 F2
 C
Crystal
n
A
B
C
F
no
2.47524
0.01450
0.01667
-0.01249
ne
2.33147
0.01264
0.01634
-0.00879
no
2.58462
0.01574
0.01865
-0.00125
ne
2.43277
0.01298
0.01802
-0.00120
no
2.49322
0.01325
0.01589
-0.00068
ne
2.34857
0.01091
0.01510
-0.00063
no
2.69556
0.01565
0.01808
-0.00134
ne
2.42929
0.01090
0.01627
-0.00119
no
2.63985
0.01370
0.01453
-0.00058
ne
2.45767
0.01080
0.01330
-0.00050
KBOB
Exp.
Cal.
KBOC
Cal. free
z-pressure
h-pressure
2
Reference
1.
Lin, J.; Lee, M.-H.; Liu, Z.-P.; Chen, C.; Pickard, C. J. Mechanism for linear and nonlinear optical
effects in β-BaB3O4 crystals. Phys. Rev. B 1999, 60 (19), 13380-13389.