Applying universal scaling laws to identify the best molecular design paradigms for second-order nonlinear optics

Javier Perez-Moreno; Shoresh Shafei; Mark G. Kuzyk

doi:10.1364/JOSAB.33.000E45

Journal of the Optical Society of America B
Vol. 33,
Issue 12,
pp. E45-E56
(2016)
•https://doi.org/10.1364/JOSAB.33.000E45

Applying universal scaling laws to identify the best molecular design paradigms for second-order nonlinear optics

Javier Perez-Moreno, Shoresh Shafei, and Mark G. Kuzyk

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Javier Perez-Moreno, Shoresh Shafei, and Mark G. Kuzyk, "Applying universal scaling laws to identify the best molecular design paradigms for second-order nonlinear optics," J. Opt. Soc. Am. B 33, E45-E56 (2016)

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About this Article
History
- Original Manuscript: April 29, 2016
- Revised Manuscript: August 18, 2016
- Manuscript Accepted: August 19, 2016
- Published: September 26, 2016

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Abstract

We apply scaling and the theory of the fundamental limits of the second-order molecular susceptibility to identify material classes with ultralarge nonlinear optical response. Size effects are removed by normalizing all nonlinearities to get intrinsic values so that the scaling behavior of a series of molecular homologues can be determined. Several new figures of merit are proposed that quantify the desirable properties for molecules that can be designed by adding a sequence of repeat units, and used in the assessment of the data. Three molecular classes are found. They are characterized by subscaling, nominal scaling, or superscaling. Superscaling homologues most efficiently take advantage of increased size. We apply our approach to data currently available in the literature to identify the best superscaling molecular paradigms with the aim of identifying desirable traits of new materials.

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Class	$E_{10}$ (eV)	$n^{'}$	$N$	$a \times 10^{- 3}$	$b \times 10^{- 3}$	$β_{int}^{\max} \times 10^{- 3}$	$n_{\max}$	$c ({esu}^{- 1} \times 10^{27})$	$d \times 10^{- 3}$	$β_{n = 1} \times 10^{- 30} esu$	$β_{SAT} \times 10^{- 28} esu$	$FOM \times 10^{- 30} esu$	$Δ β_{\exp} \times 10^{- 30} esu$
B01 [30]	3.351	1	8	$- 5 \pm 1$	$21 \pm 3$	$12 \pm 2$	2	$2.0 \pm 0.2$	$- 8 \pm 2$	4.5	–	–
B02 [30]	4.106	1	8	$- 6 \pm 1$	$23 \pm 3$	$17 \pm 3$	1	$- 5.00 \pm 0.02$	$31.0 \pm 0.1$	3.2	–	–
B03 [31]	4.429	0	8	$2 \pm 3$	$17 \pm 5$	$24 \pm 5$	3	$0.4 \pm 0.5$	$16 \pm 6$	7	–	–
B04 [31]	3.229	0	8	$- 1.0 \pm 0.3$	$17.0 \pm 0.7$	$16 \pm 3$	1	$- 0.20 \pm 0.07$	$18 \pm 1$	12.5	–	–
B05 [30]	3.647	1	16	$- 1.0 \pm 0.2$	$13.0 \pm 0.4$	$12 \pm 3$	1	$- 0.30 \pm 0.09$	$15 \pm 1$	10.1	–	–
B06 [30]	3.483	1	16	$- 1.0 \pm 0.8$	$10.0 \pm 0.2$	$9 \pm 2$	1	$- 0.40 \pm 0.06$	$12 \pm 6$	8.8	–	–
B07 [30]	3.298	1	16	$- 0.9 \pm 0.3$	$13.0 \pm 0.1$	$13 \pm 3$	1	$- 0.20 \pm 0.08$	$15 \pm 2$	14.9	–	–
B08 [30]	2.884	1	16	$- 0.9 \pm 0.4$	$12 \pm 1$	$11 \pm 2$	1	$- 0.1 \pm 0.1$	$14 \pm 4$	21.2	–	–
B09 [32]	2.768	0	12.7	$22 \pm 5$	$21 \pm 12$	$90 \pm 20$	3	$0.080 \pm 0.005$	$25 \pm 2$	150	122	273	275
B10 [32]	2.375	0	12.7	$19 \pm 3$	$16 \pm 6$	$77 \pm 15$	3	$0.06 \pm 0.02$	$20 \pm 1$	186	163	315	317
B11 [32]	2.460	0	12	$14 \pm 4$	$16 \pm 9$	$55 \pm 10$	3	$0.09 \pm 0.02$	$20 \pm 6$	100	109	155	156
B12 [33]	2.510	1	13.42	$- 1 \pm 1$	$14 \pm 3$	$13 \pm 3$	1	$- 0.01 \pm 0.05$	$13 \pm 3$	31	–	–
B13 [34]	2.510	1	4	$90 \pm 10$	$23 \pm 30$	$378 \pm 80$	4	$0.30 \pm 0.03$	$118 \pm 17$	66.8	29	271	300
B14 [34]	2.2828	1	4	$65 \pm 5$	$28 \pm 11$	$220 \pm 44$	3	$0.40 \pm 0.09$	$84 \pm 21$	46.8	23	153	162
B15 [35]	4.106	1	8	$- 9 \pm 2$	$35 \pm 3$	$27 \pm 5$	1	$- 3.00 \pm 0.02$	$41.0 \pm 0.1$	5.1	–	–
B16 [35]	2.799	0	12	$27 \pm 5$	$43 \pm 13$	$160 \pm 30$	4	$0.090 \pm 0.003$	$53 \pm 2$	195	105	297	300
B17 [35]	–	0	10	$22 \pm 2$	$59 \pm 8$	$170 \pm 30$	5	$0.070 \pm 0.009$	$68 \pm 9$	195	133	311	314
B18 [1]	3.41	1	38	$- 5 \pm 3$	$63 \pm 6$	60	1	$- 0.01 \pm 0.01$	$61 \pm 7$	248	–	–

Compound	$E_{10} (eV)$	$n$ (repeat units)	$β_{\exp} (10^{- 30} esu)$	$β_{int} (10^{- 2})$	$X$	$G (X)$	$f (E)$	Predicted $E_{20} (eV)$	Experimental $E_{20} (eV)$
A1	2.1	0	$123 \pm 18$	$3.3 \pm 0.5$	$0.268 \pm 0.004$	$0.431 \pm 0.007$	$0.07 \pm 0.01$	2.29	4.6
A2	2.08	1	$142 \pm 21$	$3.0 \pm 0.4$	$0.255 \pm 0.004$	$0.441 \pm 0.007$	$0.07 \pm 0.01$	2.26	3.9
A3	2.1	2	$372 \pm 56$	$6.6 \pm 1.0$	$0.263 \pm 0.004$	$0.423 \pm 0.006$	$0.16 \pm 0.03$	2.46	3.5
A4	2.18	3	$131 \pm 20$	$2.2 \pm 0.3$	$0.249 \pm 0.004$	$0.401 \pm 0.006$	$0.06 \pm 0.01$	2.33	3.2
C1	2.06	0	$100 \pm 15$	$2.5 \pm 0.4$	$0.274 \pm 0.004$	$0.441 \pm 0.007$	$0.06 \pm 0.01$	2.21	4.6
C2	2.05	1	$168 \pm 25$	$3.3 \pm 0.5$	$0.262 \pm 0.004$	$0.421 \pm 0.007$	$0.08 \pm 0.01$	2.34	3.9
C3	2.09	2	$237 \pm 36$	$4.1 \pm 0.6$	$0.268 \pm 0.004$	$0.459 \pm 0.006$	$0.09 \pm 0.01$	2.29	3.5
C4	2.18	3	$175 \pm 26$	$3.0 \pm 0.4$	$0.290 \pm 0.004$	$0.466 \pm 0.006$	$0.06 \pm 0.01$	2.35	3.1

Class	$E_{10}$ (eV)	$n^{'}$	$N$	$a \times 10^{- 3}$	$b \times 10^{- 3}$	$β_{int}^{\max} \times 10^{- 3}$	$n_{\max}$	$c ({esu}^{- 1} \times 10^{27})$	$d \times 10^{- 3}$	$β_{n = 1} \times 10^{- 30} esu$	$β_{SAT} \times 10^{- 28} esu$	$FOM \times 10^{- 30} esu$	$Δ β_{\exp} \times 10^{- 30} esu$
B01 [30]	3.351	1	8	$- 5 \pm 1$	$21 \pm 3$	$12 \pm 2$	2	$2.0 \pm 0.2$	$- 8 \pm 2$	4.5	–	–
B02 [30]	4.106	1	8	$- 6 \pm 1$	$23 \pm 3$	$17 \pm 3$	1	$- 5.00 \pm 0.02$	$31.0 \pm 0.1$	3.2	–	–
B03 [31]	4.429	0	8	$2 \pm 3$	$17 \pm 5$	$24 \pm 5$	3	$0.4 \pm 0.5$	$16 \pm 6$	7	–	–
B04 [31]	3.229	0	8	$- 1.0 \pm 0.3$	$17.0 \pm 0.7$	$16 \pm 3$	1	$- 0.20 \pm 0.07$	$18 \pm 1$	12.5	–	–
B05 [30]	3.647	1	16	$- 1.0 \pm 0.2$	$13.0 \pm 0.4$	$12 \pm 3$	1	$- 0.30 \pm 0.09$	$15 \pm 1$	10.1	–	–
B06 [30]	3.483	1	16	$- 1.0 \pm 0.8$	$10.0 \pm 0.2$	$9 \pm 2$	1	$- 0.40 \pm 0.06$	$12 \pm 6$	8.8	–	–
B07 [30]	3.298	1	16	$- 0.9 \pm 0.3$	$13.0 \pm 0.1$	$13 \pm 3$	1	$- 0.20 \pm 0.08$	$15 \pm 2$	14.9	–	–
B08 [30]	2.884	1	16	$- 0.9 \pm 0.4$	$12 \pm 1$	$11 \pm 2$	1	$- 0.1 \pm 0.1$	$14 \pm 4$	21.2	–	–
B09 [32]	2.768	0	12.7	$22 \pm 5$	$21 \pm 12$	$90 \pm 20$	3	$0.080 \pm 0.005$	$25 \pm 2$	150	122	273	275
B10 [32]	2.375	0	12.7	$19 \pm 3$	$16 \pm 6$	$77 \pm 15$	3	$0.06 \pm 0.02$	$20 \pm 1$	186	163	315	317
B11 [32]	2.460	0	12	$14 \pm 4$	$16 \pm 9$	$55 \pm 10$	3	$0.09 \pm 0.02$	$20 \pm 6$	100	109	155	156
B12 [33]	2.510	1	13.42	$- 1 \pm 1$	$14 \pm 3$	$13 \pm 3$	1	$- 0.01 \pm 0.05$	$13 \pm 3$	31	–	–
B13 [34]	2.510	1	4	$90 \pm 10$	$23 \pm 30$	$378 \pm 80$	4	$0.30 \pm 0.03$	$118 \pm 17$	66.8	29	271	300
B14 [34]	2.2828	1	4	$65 \pm 5$	$28 \pm 11$	$220 \pm 44$	3	$0.40 \pm 0.09$	$84 \pm 21$	46.8	23	153	162
B15 [35]	4.106	1	8	$- 9 \pm 2$	$35 \pm 3$	$27 \pm 5$	1	$- 3.00 \pm 0.02$	$41.0 \pm 0.1$	5.1	–	–
B16 [35]	2.799	0	12	$27 \pm 5$	$43 \pm 13$	$160 \pm 30$	4	$0.090 \pm 0.003$	$53 \pm 2$	195	105	297	300
B17 [35]	–	0	10	$22 \pm 2$	$59 \pm 8$	$170 \pm 30$	5	$0.070 \pm 0.009$	$68 \pm 9$	195	133	311	314
B18 [1]	3.41	1	38	$- 5 \pm 3$	$63 \pm 6$	60	1	$- 0.01 \pm 0.01$	$61 \pm 7$	248	–	–

Compound	$E_{10} (eV)$	$n$ (repeat units)	$β_{\exp} (10^{- 30} esu)$	$β_{int} (10^{- 2})$	$X$	$G (X)$	$f (E)$	Predicted $E_{20} (eV)$	Experimental $E_{20} (eV)$
A1	2.1	0	$123 \pm 18$	$3.3 \pm 0.5$	$0.268 \pm 0.004$	$0.431 \pm 0.007$	$0.07 \pm 0.01$	2.29	4.6
A2	2.08	1	$142 \pm 21$	$3.0 \pm 0.4$	$0.255 \pm 0.004$	$0.441 \pm 0.007$	$0.07 \pm 0.01$	2.26	3.9
A3	2.1	2	$372 \pm 56$	$6.6 \pm 1.0$	$0.263 \pm 0.004$	$0.423 \pm 0.006$	$0.16 \pm 0.03$	2.46	3.5
A4	2.18	3	$131 \pm 20$	$2.2 \pm 0.3$	$0.249 \pm 0.004$	$0.401 \pm 0.006$	$0.06 \pm 0.01$	2.33	3.2
C1	2.06	0	$100 \pm 15$	$2.5 \pm 0.4$	$0.274 \pm 0.004$	$0.441 \pm 0.007$	$0.06 \pm 0.01$	2.21	4.6
C2	2.05	1	$168 \pm 25$	$3.3 \pm 0.5$	$0.262 \pm 0.004$	$0.421 \pm 0.007$	$0.08 \pm 0.01$	2.34	3.9
C3	2.09	2	$237 \pm 36$	$4.1 \pm 0.6$	$0.268 \pm 0.004$	$0.459 \pm 0.006$	$0.09 \pm 0.01$	2.29	3.5
C4	2.18	3	$175 \pm 26$	$3.0 \pm 0.4$	$0.290 \pm 0.004$	$0.466 \pm 0.006$	$0.06 \pm 0.01$	2.35	3.1

Abstract

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Tables (2)

Equations (18)

Journal of the Optical Society of America B