A photothermal vortex interferometer (PTVI) is proposed to fill the gap of full-field measurement of the laser-induced nanoscale thermal lens dynamics of optical elements. The PTVI produces a multi-ring petal-like interferogram by the coaxial coherent superposition of the high-order conjugated Laguerre–Gaussian beams. The non-uniform optical path change (OPC) profile resulting from the thermal lens causes the petals of the interferogram at the different radii to shift by the different azimuths. To demodulate such an interferogram, an azimuthal complex spectra analysis is presented by using a camera with a pixelated multi-ring pattern written on its sensor to extract multiple azimuthal intensity profiles synchronously from the interferogram. Therefore, the OPC profile can be determined dynamically from the complex spectra of the azimuthal intensity profiles at the main frequency components. An analytical thermophysical model of the thermal lens is given, and the basic principle of the azimuthal complex spectra analysis is revealed. A proof-of-concept experiment is demonstrated using a N-BK7 glass sample heated by a pump laser. The results verified that the PTVI achieves the measurement accuracy of 47 pm with a standard deviation of 358 pm (3σ) and can be used for full-field measurement of the nanoscale OPC profile caused by the thermal lens dynamics. Due to the picometer-scale accuracy of the PTVI, the absorption coefficient and thermal diffusivity of the glass sample were determined to be A0 = 0.126 m−1 and D = 5.63 × 10−7 m2 s−1, respectively, which agree with the nominal ones of A0 = 0.129 m−1 and D = 5.17 × 10−7 m2 s−1. Although the PTVI is only suitable for measuring the rotationally symmetric OPC, it shows less computation burden and hardware complexity, and it is proved to be a highly sensitive and effective tool in studying optical, thermo-physical, and mechanical properties of optical elements.

1.
S.
Bialkowski
,
N.
Astrath
, and
M.
Proskurnin
,
Photothermal Spectroscopy Methods
, 2nd ed. (
John Wiley & Sons, Inc.
,
2019
).
2.
D.
Bričkus
and
A. S.
Dement’ev
, “
Modeling of thermal lensing in a [1 1 1]-cut Nd:YAG rod with temperature-dependent parameters and different pumping profiles
,”
Laser Phys.
27
(
5
),
055002
(
2017
).
3.
M. A.
Isidro-Ojeda
,
J. J.
Alvarado-Gil
,
V. S.
Zanuto
,
M. L.
Baesso
,
N. G. C.
Astrath
, and
L. C.
Malacarne
,
Opt. Mater.
75
,
574
579
(
2018
).
4.
W.
Liu
,
Y.
Niu
,
H.
Liu
,
C.
Wang
,
S.
Hu
,
C.
Zhang
,
H.
Niu
, and
J.
Li
,
Opt. Eng.
53
(
2
),
026102
(
2014
).
5.
L. C.
Malacarne
,
N. G. C.
Astrath
, and
M. L.
Baesso
,
J. Opt. Soc. Am. B
29
(
7
),
1772
1777
(
2012
).
6.
L. C.
Malacarne
,
N. G. C.
Astrath
, and
L. S.
Herculano
,
J. Opt. Soc. Am. B
29
(
12
),
3355
3359
(
2012
).
7.
E.
Dy
,
C.
Gu
,
J.
Shen
,
W.
Qu
,
Z.
Xie
,
X.
Wang
,
M. L.
Baesso
, and
N. G. C.
Astrath
,
J. Appl. Phys.
131
(
6
),
063102
(
2022
).
8.
K. V.
Vlasova
,
A. I.
Makarov
, and
N. F.
Andreev
,
J. Appl. Phys.
129
(
4
),
043101
(
2021
).
9.
A.
Rahman
,
H.
Cabrera
,
M.
Usman Malik
, and
I.
Ashraf
,
J. Opt. Soc. Am. B
38
(
1
),
52
59
(
2021
).
10.
V.
Raj
,
M. N. S.
Swapna
, and
S. I.
Sankararaman
,
Eur. Phys. J. Appl. Phys.
90
(
1
),
11001
(
2020
).
11.
K. V.
Vlasova
,
A. I.
Makarov
,
N. F.
Andreev
, and
A. Y.
Konstantinov
,
Appl. Opt.
57
(
22
),
6318
6328
(
2018
).
12.
G. V. B.
Lukasievicz
,
L. S.
Herculano
,
E.
Sehn
,
M. P.
Belançon
,
S. E.
Bialkowski
,
O. A.
Capeloto
,
N. G. C.
Astrath
, and
L. C.
Malacarne
,
Appl. Spectrosc.
74
,
1274
1279
(
2020
).
13.
T. P.
Rodrigues
,
V. S.
Zanuto
,
R. A.
Cruz
,
T.
Catunda
,
M. L.
Baesso
,
N. G. C.
Astrath
, and
L. C.
Malacarne
,
Opt. Lett.
39
(
13
),
4013
(
2014
).
14.
G.
Kim
,
D.
Kim
,
S.
Kang
,
J.
Yoo
, and
H.
Kim
,
Appl. Sci.
11
(
4
),
1535
(
2021
).
15.
D. K.
Kobylińska
,
R. J.
Bukowski
,
J.
Bodzenta
,
S.
Kochowski
, and
A.
Kaźmierczak-Balata
,
Appl. Opt.
47
(
10
),
1559
1566
(
2008
).
16.
R. S.
Fontenot
,
V. K.
Mathur
, and
J. H.
Barkyoumb
,
J. Quant. Spectrosc. Radiat. Transfer
204
,
1
6
(
2018
).
17.
M.
Eskef
,
Y.
Jlailaty
, and
K.
Alnama
,
Rev. Sci. Instrum.
90
(
4
),
044902
(
2019
).
18.
S.
Kazemian
,
P.
Bazylewski
,
R.
Bauld
, and
G.
Fanchini
,
J. Chem. Phys.
150
(
18
),
184201
(
2019
).
19.
N.
Shiokawa
and
E.
Tokunaga
,
Opt. Express
24
(
11
),
11961
11974
(
2016
).
20.
G. A. S.
Flizikowski
,
O. A.
Capeloto
,
V. G.
Camargo
,
B.
Anghinoni
,
M. L.
Baesso
,
L. C.
Malacarne
,
M. P.
Belançon
,
T.
Požar
, and
N. G. C.
Astrath
,
Opt. Express
28
(
5
),
7116
7124
(
2020
).
21.
G. A. S.
Flizikowski
,
B.
Anghinoni
,
J. H.
Rohling
,
M. P.
Belançon
,
R. S.
Mendes
,
M. L.
Baesso
,
L. C.
Malacarne
,
T.
Požar
,
S. E.
Bialkowski
, and
N. G. C.
Astrath
,
J. Appl. Phys.
128
(
4
),
044509
(
2020
).
22.
H.
Piombini
,
A.
Guediche
, and
G.
Dammame
,
Opt. Lett.
45
(
2
),
519
522
(
2020
).
23.
L.
Rodriguez
and
M.
Chiesa
, “
Photothermal phase shift interferometry: an approach for nonlinear absorption measurements
,”
J. Opt.
14
(
1
),
015204
(
2011
).
24.
J.
Dong
,
P.
Yan
,
L.
Yang
,
Y.
Zhang
,
T.
Zhang
,
L.
Zhang
,
S.
Zhou
, and
J.
Li
,
Opt. Express
28
(
20
),
29865
29875
(
2020
).
25.
J.
Dong
,
X.
Xie
,
L.
Yang
,
X.
Lang
,
R.
Lu
,
T.
Zhang
,
L.
Zhang
,
S.
Zhou
, and
J.
Li
,
Opt. Lett.
46
(
12
),
2976
2979
(
2021
).
26.
M.
Takeda
,
H.
Ina
, and
S.
Kobayashi
,
J. Opt. Soc. Am.
72
(
1
),
156
160
(
1982
).
27.
Z.
Zheng
,
J.
Gao
,
J.
Mo
,
L.
Zhang
, and
Q.
Zhang
,
IEEE Trans. Instrum. Meas.
70
,
1006509
(
2021
).
28.
S.
Wu
,
Y.
Yao
,
B.
Wang
,
Y.
Wang
, and
F.
Yang
,
IEEE Trans. Instrum. Meas.
71
,
7004308
(
2022
).
29.
X.
Liu
,
P.
Yan
, and
Y.
Wang
,
Light: Adv. Manuf.
4
(
1
),
7
(
2023
).
30.
H.
Hooshmand-Ziafi
,
M.
Dashtdar
,
K.
Hassani
, and
M.
Motallebi-Araghi
,
Rev. Sci. Instrum.
90
(
10
),
105105
(
2019
).
31.
M.
Novak
,
J.
Millerd
,
N.
Brock
,
M.
North-Morris
,
J.
Hayes
, and
J.
Wyant
,
Appl. Opt.
44
(
32
),
6861
6868
(
2005
).
32.
Q.
Lu
,
S.
Liu
,
J.
Shao
,
Y.
Zhou
,
T.
Xu
,
J.
Pan
,
S.
Wang
,
Y.
Bai
, and
X.
Xu
,
Rev. Sci. Instrum.
90
(
7
),
075109
(
2019
).
33.
X.
Xu
,
M.
Wan
,
J.
Ge
,
H.
Chen
,
X.
Zhu
,
X.
Zhang
,
Q.
Chen
, and
G.
Gu
,
IEEE Trans. Instrum. Meas.
71
,
1
10
(
2022
).
35.
E.
Bolduc
,
N.
Bent
,
E.
Santamato
,
E.
Karimi
, and
R. W.
Boyd
,
Opt. Lett.
38
(
18
),
3546
3549
(
2013
).
36.
N.
Matsumoto
,
T.
Ando
,
T.
Inoue
,
Y.
Ohtake
,
N.
Fukuchi
, and
T.
Hara
,
J. Opt. Soc. Am. A
25
(
7
),
1642
1651
(
2008
).
37.
J.
Pinnell
,
V.
Rodríguez-Fajardo
, and
A.
Forbes
,
J. Opt.
23
(
1
),
015602
(
2021
).
38.
A.
Jesacher
,
A.
Schwaighofer
,
S.
Fürhapter
,
C.
Maurer
,
S.
Bernet
, and
M.
Ritsch-Marte
,
Opt. Express
15
(
9
),
5801
5808
(
2007
).
39.
J.
Pinnell
,
I.
Nape
,
B.
Sephton
,
M. A.
Cox
,
V.
Rodríguez-Fajardo
, and
A.
Forbes
,
J. Opt. Soc. Am. A
37
(
11
),
C146
C160
(
2020
).

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