Holographic all-optical waveguide based on photoisomerization

Holographic all-optical waveguide based on photoisomerization | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Holographic all-optical waveguide based on photoisomerization Jianchu Liang, Dafeng Long, Tong Liu, Kai Wan, Weiping Gong, Na Qiang, and 2 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-2310112/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 9 You are reading this latest preprint version Abstract The all-optical waveguide theory based on photoisomerization nonlinear effects is systematically and deeply studied, and a nonlinear holographic all-optical waveguide scheme is proposed for the first time. It is found that the induction of a light with stronger isomerization activity on the material weakens the self-defocusing effects of the signal light. Especially, polarization states of both inducing light and signal light also unexpectedly affect propagation of signal light. Part of the theoretical results has been qualitatively confirmed by Z-scan experiments. The proposed holographic all-optical waveguide scheme means polarization information is applied in the all-optical waveguide besides intensity information. Compared with the traditional all-optical waveguide, the performance of holographic waveguide will be greatly improved, making the control of light more precise and easier. Such nonlinear waveguide scheme may find its application in the future all-optical net. Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Full Text It is the development trend of modern communication that optical communication replaces electrical communication, and all-optical waveguides, which include light-controlled optical waveguide (LCOW) and light-induced optical waveguide (LIOW), are key devices of all-optical network in the future. LCOW is a kind of simultaneous “light-controlling-light” technique, where the controlling light and the signal light act on the material at the same time. Generally LCOWs are nonlinear waveguides, because the controlling light and the signal light always influence each other. LCOW are widely used in so-called discrete solitons 1–4 . As a successive “light-controlling-light” technique, LIOW 5–9 means that the controlling light first induces a waveguide, and then the signal light propagates in it. LIOWs are mostly linear waveguides, as the inducing light is always not affected by the signal light. All-optical waveguides can also be used in all-optical switches 10,11 . We have previously studied LCOW based on photoisomerization of organic materials. Photoisomerization is a fascinating area of investigation because it leads to light-induced surface pattern of amorphous azo-containing polymer film and light-induced deformation of liquid crystal elastomers, some of them are completely unexpected and still unexplained 12 . There are countless review papaers on this topoic 13–15 . However, as a logical component of photoisomerization research, nonlinear effects associated with photoisomerization has not been adequately investigated, which can be seen from all these reviews. Related research area centers on micropic mechanism of second-order nonlinear optical polarizabilities, photoinduced poling, and photoswitching, etc 17,18 . Every step in the exploration process of photoisomerization nonlinear effects is helpful to systematization of photoisomerization research. Photoisomerization leads to extremely strong nonlinear effects, and we systematically explore nonlinear effects associated with photoisomerization in three steps. For the case of a single light beam, we 19,20 revealed polarization effects of nonlinearity associated with photoisomerization for the first time. For the case of two light beams, we systematically studied photoisomerization -related LCOW. We found successively that both intensity information 21,22 and polarization information 23 of the controlling light with stronger self-defocucing effects could be used to control the propagation of the signal light. Especially, we found that with the help of a controlling light, photoisomerization nonlinear effects can even be changed from a defocusing one to a focusing one, and we could achieve the conversion of dark solitons to bright solitons 21,22 . Because of the important theoretical and practical significance, the above work was picked by the editors of Optics Letters as an excellent contribution. Then how about the situation of LIOW based on photoisomerization? This is just what we study in this letter. The light wave information mainly includes amplitude (or intensity), phase and polarization. The polarization state of light was explored in photonic devices and other linear fields 24,25 . However, as far as we know, the optical nonlinear effect is only related to the light intensity, so the polarization information of light has not been used in the formation process of all-optical waveguide and optical spacial solitons. The more information that is utilized, the better the device performance. For example, plane image technology that only uses the amplitude information of light wave evolves into three-dimensional holographic image technology when phase information is utilized. We will propose a holographic all-optical waveguide based on photoisomerization nonlinear effects in this paper. Taking full advantage of the amplitude information and polarization information of light waves, the proposed holographic LIOW will make the propagation controlling of light beams more accurate and simpler. Suppose both inducing light and signal light are general elliptically-polarized (EP) light, which is formed by a linearly-polarized (LP) light passed through a quarter-wavelength slide, the angle \(\varphi\) between the polarization direction and the principal axis direction of the slide is called polarization angle and \({a_j}={\cos ^2}{\varphi _j}\) ( \(j=c,\;s\) ) is the polarization degree of the inducing light ( \(j=c\) ) or the signal light ( \(j=s\) ). The subscript " s " is omitted for simplicity in the context. In order to avoid the rotation of the polarization direction of the signal light during the propagation process due to the phenomenon of photo-induced birefringence, the direction of the main axis of the polarization ellipse of the signal light and the inducing light must be consistent, that is, the fast axis directions of the glass slides are parallel to each other. Firstly, according to the model of angular hole-burning 26 , stationary density distribution of molecules in the trans form is given by 20 $${N^{\prime}_T}=N\frac{{{I_c}{{\sigma ^{\prime}}_c}{{q^{\prime}}_c}+\gamma }}{{{I_c}{\sigma _c}{q_c}[{a_c}{{\cos }^2}\theta +(1 - {a_c}){{\sin }^2}\theta {{\cos }^2}\psi ]+{I_c}{{\sigma ^{\prime}}_c}{{q^{\prime}}_c}{\text{+}}\gamma }}$$ 1 where N is the total density of material molecules, \({I_c}\) is intensity of the inducing light, \({\sigma _c}\) and \({q_c}\) are the absorption cross section of inducing light and quantum yield of trans molecules respectively, \({\sigma ^{\prime}_c}\) and \({q^{\prime}_c}\) are the absorption cross section and quantum yield of cis molecules respectively, \(\gamma\) is the thermal relaxation rate from the cis to trans. \(\theta\) and \(\psi\) are polar angle and azimuthal angle of orientation of trans molecule respectively in the spherical coordinate system, whose z axis is the main axis of the polarization ellipse. Secondly, the density distribution function \({N^{\prime}_T}\) become the initial condition of optical chemistry process of the signal light, and the final density distribution of trans molecules under action of the signal light is $${N_T}={N^{\prime}_T}\frac{{I\sigma ^{\prime}q^{\prime}+\gamma }}{{I\sigma q[a{{\cos }^2}\theta +(1 - a){{\sin }^2}\theta {{\cos }^2}\psi ]+I\sigma ^{\prime}q^{\prime}+\gamma }}$$ 2 where is intensity of the signal light, \(\sigma\) and \(q\) are the absorption cross section of signal light and quantum yield of trans molecules respectively, \(\sigma ^{\prime}\) and \(q^{\prime}\) are the absorption cross section and quantum yield of cis molecules respectively. Finally, refractive index perturbation arises from photoisomerization of the signal light is 20 \(\Delta n=\int_{{\psi =0}}^{{2\pi }} {\int_{{\theta =0}}^{\pi } {a\alpha ({N_T} - {{N^{\prime}}_T})} } {\cos ^2}\theta \sin \theta d\theta d\psi\) \(+(1 - a)\int_{{\psi =0}}^{{2\pi }} {\int_{{\theta =0}}^{\pi } {\alpha ({N_T} - {{N^{\prime}}_T})} } {\cos ^2}\psi {\sin ^3}\theta d\theta d\psi\) . (3) It must be pointed out that the inducing light generates a nonlinear waveguide, which is related to the signal light. Exploring the effect of light intensity, we first consider the situation when both the inducing light and the signal light are LP light, which are of the same polarization direction. In this situation, \(a={a_c}=0\) . The relation between nonlinear refractive index perturbation \(\Delta n\) and intensities of signal light and of inducing light \({I_c}\) is shown in Fig. 1 (a). It can be seen from Fig. 1 (a) that the perturbation of refractive index is forever negative for LIOW, regardless of the intensity of the inducing light and the signal light. That’s to say, the inducing light affects the nonlinear effects of the signal light, it however never change the defocusing nature associated with photoisomerization. It is worthy of notice that as for the case of LCOW, the controlling light could turn the defocusing nonlinear effect to a focusing one under certain conditions. Moreover, intensities undergo similar influence on the nonlinear effects regardless of the polarization states of both the inducing light and the signal light; see Fig. 1 (b)(c), where the polarization degrees of signal light and inducing light are \(a=0,\ {a_c}=0.5\) and \(a=0.5,\ {a_c}=0\) , respectively. Figure 2 (a) reveals the influence of inducing light intensity on nonlinear effects of the signal light when intensities of uniform inducing lights are \({I_c}{\text{=}}0,\;\;0.1, \;\;1,\;\;10,\) respectively. The bigger the intensity of inducing light ( \({I_c}\) ), the smaller the absolute value of refractive index perturbation ( \(\left| {\Delta n} \right|\) ). So the inducing light weakens the self-defocusing effects. When \({I_c}\) increases, defocusing nonlinear effects become weaker. Figure 2 (b) reveals the influence of distribution of inducing light intensity by illustrating dependence of refractive index change on inducing light intensity when the signal light intensity is 0.1, 1, and 10, respectively. Here two LP light beams ( \(a={a_c}=0\) ) are considered. Apparently, \(\Delta n\) increases as \({I_c}\) increases. Assume that a light beam with Gaussian distribution \({I_c}={e^{ - {r^2}/{\omega ^2}}}\) ( \(\omega {\text{=1}}\) ) excites the material and then the signal light with uniform distribution propagate in the material. The LIOW shown as the relation of index change and the signal light intensity is illustrated by Fig. 3 (a). The nonlinear effect felt by signal light looks like a focusing one, although it essentially is not a nonlinear effect because refractive index change is not the function of the signal light. Nonlinear effects induced by the inducing light is some of a focusing one. A bright beam experiences self-defocusing effects itself, however induces a focusing waveguide. This is actually an interesting phenomenon. Considering that the signal light experiences self-defocusing effects, a bright inducing beam weakens the self-defocusing effects of signal light. Figure 3 (b) is the waveguide induced by a light with periodically distributed intensity, which is generated by an amplitude mask and is described as \({I_c}={I_0}\cos {x^2}{\cos ^2}y\) . So photonic crystals can be generated with periodic bright beams. When a light with uniform distribution pass through the photonic crystal, the focusing effect associated with the photonic crystal, the self-defocusing effect and natural diffraction of the signal light will achieve balance and discrete solitons may be formed. Figure 4 shows the polarization-dependence of nonlinear effects, where intensities are set as \({I_c}=0.3\) and \(I=1\) . It is seen that from Fig. 4 (a) the dependence of polarization is not always monotonous, and there is a twist in the \(\Delta n(a,\;\;{a_c})\) surface. Complicated polarization-dependence of nonlinear effects is elaborated as follows. Figure 4 (b) illustrates the influence of polarization of the inducing light on nonlinear effects. As for the circularly-polarized (CP) signal light ( \(a=0.5\) ), when the polarization degree of the inducing light turns smaller ( \({a_c}=0 \to 0.5\) , from linear polarization to circular polarization), \(\left| {\Delta n} \right|\) decreases, which denotes that the defocusing effect becomes weaker. As for a LP signal light ( \(a=0\) ), when the degree of polarization of the inducing light turns smaller, \(\left| {\Delta n} \right|\) increases, and the defocusing effect becomes stronger. Figure 4 (c) illustrates the influence of polarization of the signal light on nonlinear effects. As for the CP inducing light ( \({a_c}=0.5\) ), when the polarization degree of the signal light turns smaller, \(\left| {\Delta n} \right|\) decreases monotonically, which denotes that the effect becomes weaker gradually. As for the LP inducing light ( \({a_{\text{c}}}=0\) ), when the polarization degree of the signal light turns smaller, \(\left| {\Delta n} \right|\) first decreases until \(a \approx 3\) , and then increases, which denotes that the defocusing effect first becomes weaker and weaker, and then become stronger and stronger. Theoretically comparing the influence of intensity and polarization on index change, we find that effects of polarization is generally weaker than that of intensity; see Fig. 5 . Thus when inducing waveguide, we can coarsely control the waveguide by adjusting intensity and distribution of the inducing light, and then experience fine control by adjusting the polarization of the inducing light. thereupon, a holographic LIOW scheme is proposed. Holographic all-optical waveguide makes the guide of light beam more precise and more convenient. Moreover, influence of intensity of signal light is obviously greater then that of inducing light, from Fig. 5 and Fig. 6 . Now we give some of our qualitative experimental confirmation. The Z-scan experimental 12 setup is shown in Fig. 6 . The part enclosed by the dotted line is the inducing light path. The intensity of uniform inducing light with a wavelength of \({\lambda _2}{\text{=}}514.5nm\) emitted from the Ar + laser is controlled by the combination of two polarizers, P3 and P4. The LP light becomes EP light through the \({\lambda _1}{\text{/}}4\) ( \({\lambda _2}{\text{/}}4\) ) slide (quarter-wave plate). The concave lens X and the convex lens L2 are combined to expand the beam. Similarly, the intensity of the signal light with a wavelength of \({\lambda _1}{\text{=}}632.8nm\) is determined by polarizers P1 and P2. To avoid the change of the polarization state of the light in the sample due to the photo-induced birefringence (including the rotation of the polarization direction), keep the fast axis direction of the slide \({\lambda _1}{\text{/}}4\) and \({\lambda _2}{\text{/}}4\) parallel. P1 and P2 are fixed on a platform and by rotating the platform, the polarization state of the signal light can be changed without changing the intensity. A lens of focal length \(f=111mm\) provides a tight focus of the laser beam, whose spatial mode of the laser is close to Gaussian TEM00, and the beam-waist radius is \({\omega _0} \approx 62\mu m\) at the focal point. An aperture with a linear transmittance of 0.15 is fixed at the position about 70 cm from the focal plane. A photodetector (Field Master, Coherent Inc.) D is used to detect the light power behind the aperture. The sample is poly(methyl methacrylate) (PMMA) film doped with disperse red 13 (DR3) (1.6 % by weight), which was prepared from a solution containing an appropriate amount of dye, polymer, and chloroform. The thickness of the film is measured to be \(l \approx 52\mu m\) . Normalized transmittance of the signal light passing through the aperture is measured as the sample is moved along the propagation path z of the focused Gaussian beam. Peak-valley difference \(\Delta {T_{p - v}}\) of Z-scan curves denotes the magnitude of the refractive index perturbation. Experimental results are shown in Fig. 7 when central intensity of the signal light at the focal point is \({I_0}=0.80W/c{m^2}\) . Py3 is the Z-scan curve of signal CP light ( \(a=0.5\) ) before the sample is induced ( \({I_c}=0\) ). py1, py2 and py4 are the Z-scan curves of LP light ( \(a=0\) ), EP light ( \(a=0.25\) ) and CP light, respectively after the sample is induced by an uniform light with intensity of \({I_c}=0.42W/c{m^2}\) . \(\Delta {T_{p - v}}\) of py1-py4 are 0.39, 0.34, 0.23, 0.17, respectively. The above experimental results preliminarily and qualitatively confirm some of theoretical results. Comparing py3 with py4, \(\Delta {T_{p - v}}\) of the latter is smaller, which indicates that optical induction weakens the self-defocusing effects. This result is consistent with Fig. 1 and Fig. 2 (a). Comparing py1, py2 and py4, \(\Delta {T_{p - v}}\) decline in turn. That’s to say, as for the case of CP inducing light, nonlinear effects become weaker and weaker when signal light change gradually from LP lightto CPL. This is consistent with Fig. 4 (c) (the case of \({a_c}=0.5\) ). Moreover, the influence of intensity of inducing light is rather smaller than that of polarization information of the signal light. In this way, the dependence of nonlinear effects on intensity information of inducing light and on polarization information of signal light is qualitatively verified. However we failed to find obvious influence of polarization of the inducing light on nonlinear effects. Perhaps this dependence is too weak to be observed for the sample we used. Actually this is somehow consistent with Fig. 5 (a). In summary, the all-optical waveguide theory based on photoisomerization nonlinear effects is systematically and deeply studied, and a nonlinear holographic all-optical waveguide scheme is proposed for the first time. We find that LIOW based on photoisomerization weakens the defocusing effects, however never change the defocusing nature. Besides, a bright inducing light beam generates a focusing waveguide. Polarization states of both inducing light and signal light also affect propagation of signal light. For a CP signal light, when the polarization degree of the inducing light turns smaller, the defocusing effect becomes weaker; as for a LP signal light, when the polarization degree of the inducing light turns smaller, the defocusing effect becomes stronger. For the CP inducing light when the polarization degree of the signal light turns smaller, the defocing effect becomes weaker gradually; As for the LP inducing light, when the polarization degree of the signal light turns smaller, the defocusing effect first becomes weaker and weaker, and then become stronger and stronger. Part of the theoretical results has been qualitatively confirmed by Z-scan experiments. The more information a photonic device utilizes, the better its performance. For holographic imaging technology, by additional use of phase information besides amplitude information of light wave, the two-dimensional plane image can be evolved into a three-dimensional image. Similarly, the application of polarization information is joined to the proposed holographic all-optical waveguide scheme. Compared with the traditional all-optical waveguide, the performance of holographic waveguide will be greatly improved, making the control of light more precise and easier. The influence of the polarization degree on the beam propagation is much smaller than that of the light intensity, thus can be used for fine-tuning of the waveguide. In addition, the operation of changing the degree of polarization is simpler than changing the light intensity distribution. The former only needs to rotate the glass slide, while the latter requires complex operations such as beam shaping. Generally speaking, defocusing effects associated with photoisomerization is too strong to form dark solitons, only if in materials with weaker nonlinear effects,such as DR1/PMMA with low doping concentration and with red light. In order to form dark solitons in materials with strong defocusing effects such as DR13/PMMA, one should weaken defocusing effects by forming holographic waveguide. In order to precisely control the beam propagation, such as form optical spacial solitons, we can adjust the intensity and distribution of the signal light at first, and when the beam is close to the soliton form, we modify the intensity and polarization degree of the inducing light in turn to fine-tune the signal light, so that the optical solitons can be precisely and easily formed. Such nonlinear waveguide may find its application in the future all-optical net. Up to now, the role of polarization has been explored in three situations: polarization information of a signal light 6,7 , polarization information of the controlling light in a light-controlled waveguide 10 and polarization information of the inducing light in a light-inducing waveguide. This work deals with LIOW, while Ref.10 dealt with LCOW; they are two parallel works. The theoretical models and results of the two papers differ from each other. For example, for the case of LIOW, inducing light affects the nonlinear effects of the signal light, it however never change the defocusing nature associated with photoisomerization, while for the case of LCOW, the controlling light could turn the defocusing nonlinear effects to a focusing one under certain conditions. Declarations This work was supported by the Guangdong Provincial Basic and Applied Basic Research Fund Project (Grant Nos. 2021A1515010282 and 2114050002323), the National Natural Science Foundation of China (Grant Nos. 61372064 and 62103159), Special Projects in Key Fields of General Universities in Guangdong Province (Grant No. 2021ZDZX1012) and the Huizhou Science and Technology Program Project (Grant No. 2020SD0406034). Conflict of Interest The authors have no conflicts to disclose. DATA AVAILABILITY The data that support the findings of this study are available within the article. References Z. Chen, H. Martin, E. D. Eugenieva, J. Xu, and J. Yang, Opt. Express 13 , 1816 (2005). N. K. Efremidis, S. Sears, D. N. Christodoulides, J. W. Fleischer, and M. Segev, Phys. Rev. E. 66, 046602 (2002). J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, Nature, 422, 147 (2003) . Z. Chen, A. Bezryadina, I. Makasyuk, and J. Yang, Opt. Lett. 29, 1656 (2004). D. N. Christodoulides, F. Lederer, Y. Silberberg, Nature 424, 817 (2003). N. K. Efremidis, J. Hudock, D. N. Christodoulides, J. W. Fleischer, O. Cohen, and M. Segev, Phys. Rev. Lett. 91, 213906 (2003). J. Yang and Z. H. Musslimani, Opt. Lett. 28, 2094 (2003). J. W. Fleischer, G. Bartal, O. Cohen, O. Manela, M. Segev, J. Hudock, and D. N. Christodoulides, Phys. Rev. Lett. 92, 123904 (2004). D. Neshev, E. Ostrovskaya, Y. Kivshar, and W. Krolikowski, Opt. Lett. 28, 710 (2003). X. Hu, P. Jiang, C. Ding, H. Yang, Q. Gong, Nature Photon. 2, 185 (2008) . N. Li, J. Xu, G. Song, C. Zhu, S. Xie, Y. Yang, M. S.Zubairy, and S. Y. Zhu , Phys. Rev. A 93, 043819 (2016). S. De Martino ,F. Mauro, P. A. Netti, Photonic applications of azobenzene molecules embedded in amorphous polymer, La Rivista del Nuovo Cimento, 43, 599 (2020). Z. Sekkat, Model for athermal enhancement of molecular mobility in solid polymers by light, Phys. Rev. E 102, 032501 (2020). A. Natansohn, P. Rochon, Photoinduced motions in azo-containing polymers, Chem. Rev., 102, 4139 (2002). S. L. Oscurato, M. Salvatore, P. Maddalena, and A. Ambrosio, From nanoscopic to macroscopic photo-driven motion in azobenzene-containing materials, Nanophotonics, 2018, 7, 1387 (2018). S. Lee, H. S. Kang, J. K. Park, Directional photofluidization lithography: micro/ nanostructural evolution by photofluidic motions of azobenzene materials, Adv. Mater. 24, 2069 (2012). J. A. Delaire, K.Nakatani, Linear and nonlinear optical properties of photochromic molecules and materials, Chem. Rev. 100, 1817 (2000). M. Dudek, N. Tarnowicz-Staniak, M. Deiana, Z. Pokłade, M. Samoć and K. Matczyszyn, RSC Advances, 10, 40489 (2020). J. C. Liang and X. Q. Zhou, J. Opt. Soc. Am. B 22, 2468 (2005). J. C. Liang, H. Zhao, X. Zhou, and H. C. Wang, J. Appl. Phys. 101, 013106 (2007). J. C. Liang, Z. B. Cai, Y. Z. Sun, S. L. Xu, L. Yi, J. Opt. Soc. Am. B 26, 36 (2009). J. C. Liang, Opt. Lett. 35, 4081 (2010). J. C. Liang, and H. C. Wang, Opt. Lett. 42, 3654 (2017). H. Yuan, X. Liu, F. Afshinmanesh, W. Li, G. Xu, J. Sun, B. Lian, A. G. Curto, G. Ye, Y. Hikita, Z. Shen, S. C. Zhang, X. Chen, M. Brongersma, H. Y. Hwang, and Y. Cui, Nature Nanotech. 10, 707 (2015). P. Chen, C. Shu, X. Guo, M. M. T. Loy, and S. Du, Phys. Rev. Lett. 114, 010401 (2015). Additional Declarations No competing interests reported. Cite Share Download PDF Status: Under Review Version 1 posted Editorial decision: Major revision 17 Feb, 2023 Reviews received at journal 17 Feb, 2023 Reviewers agreed at journal 16 Feb, 2023 Reviewers agreed at journal 02 Jan, 2023 Reviewers agreed at journal 08 Dec, 2022 Reviewers invited by journal 05 Dec, 2022 Editor assigned by journal 28 Nov, 2022 Submission checks completed at journal 26 Nov, 2022 First submitted to journal 24 Nov, 2022 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-2310112","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":155283751,"identity":"e7294097-014b-4fde-b9a1-07f5ca3e0a95","order_by":0,"name":"Jianchu Liang","email":"","orcid":"","institution":"Huizhou University","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Jianchu","middleName":"","lastName":"Liang","suffix":""},{"id":155283754,"identity":"fdc29cbc-7fcf-4c24-8103-3d42def7f8d4","order_by":1,"name":"Dafeng Long","email":"","orcid":"","institution":"Huizhou University","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Dafeng","middleName":"","lastName":"Long","suffix":""},{"id":155283756,"identity":"d8abf42f-defc-4e44-8eed-44f54efcc91b","order_by":2,"name":"Tong Liu","email":"","orcid":"","institution":"Huizhou University","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Tong","middleName":"","lastName":"Liu","suffix":""},{"id":155283758,"identity":"86d0da95-1d1e-48e9-baa4-a1f468fc1348","order_by":3,"name":"Kai Wan","email":"","orcid":"","institution":"Huizhou University","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Kai","middleName":"","lastName":"Wan","suffix":""},{"id":155283760,"identity":"3b0eda7a-e104-424d-aae1-596f3d0bea0b","order_by":4,"name":"Weiping Gong","email":"","orcid":"","institution":"Huizhou University","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Weiping","middleName":"","lastName":"Gong","suffix":""},{"id":155283761,"identity":"25fbe66f-3d98-49a6-b101-a8b7baf63076","order_by":5,"name":"Na Qiang","email":"","orcid":"","institution":"Huizhou University","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Na","middleName":"","lastName":"Qiang","suffix":""},{"id":155283762,"identity":"99a0f35d-01ba-4515-9e60-0e185aeaf419","order_by":6,"name":"Kaijian Huang","email":"","orcid":"","institution":"Huizhou University","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Kaijian","middleName":"","lastName":"Huang","suffix":""},{"id":155283763,"identity":"83643444-4ce8-4824-ab4b-c17e88bb4dd8","order_by":7,"name":"Xiaohui Wei","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAyUlEQVRIiWNgGAWjYBAC+wMHEgw+/LCx42dvIFbPwQMPCmf2pCVL9hwgVsvhgw8+87AdZtwwI4FIHYxthxM38PAwMxtIPt54g6HGJpqgFmaeY8kGEhZsfObSacUWDMfSchsIaWGTOJNmYAC0xnJ2jpkEY8Nhwlp45N9//5HAJsG44eYZIrVIMAAD+QCbAeOGGzxEajEAajFs7EkABjLQLwnE+AWkxfjPj//AqDy88caHGhvCWlC0SySQohyihVQdo2AUjIJRMDIAAMo3Qz6iTOjUAAAAAElFTkSuQmCC","orcid":"","institution":"Huizhou University","correspondingAuthor":true,"submittingAuthor":false,"prefix":"","firstName":"Xiaohui","middleName":"","lastName":"Wei","suffix":""}],"badges":[],"createdAt":"2022-11-24 17:29:17","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-2310112/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-2310112/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":29741142,"identity":"230833dc-a464-4e6c-bd9d-22a3ff03afbb","added_by":"auto","created_at":"2022-11-30 20:17:03","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":199461,"visible":true,"origin":"","legend":"\u003cp\u003eSee image above for figure legend\u003c/p\u003e","description":"","filename":"1.png","url":"https://assets-eu.researchsquare.com/files/rs-2310112/v1/e0991ccdaf5bac18118f7707.png"},{"id":29741143,"identity":"09e58fe3-31b7-4dc5-a7e7-4b5b7329170d","added_by":"auto","created_at":"2022-11-30 20:17:03","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":100985,"visible":true,"origin":"","legend":"\u003cp\u003eThe relation between nonlinear refractive index perturbation and (a) signal light intensity under different uniform inducing light intensities; (b) inducing light intensity under different signal light intensities.\u003c/p\u003e","description":"","filename":"2.png","url":"https://assets-eu.researchsquare.com/files/rs-2310112/v1/244c67d7a41a19f14bbb96c9.png"},{"id":29741227,"identity":"1181a74b-7c7d-4dd4-ae1e-1e2331f73154","added_by":"auto","created_at":"2022-11-30 20:25:03","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":211934,"visible":true,"origin":"","legend":"\u003cp\u003e(a) waveguide induced by a Gaussian beam; (b) photonic crystal generated\u003c/p\u003e\n\u003cp\u003eby a uniform broad beam passed through an amplitude mask.\u003c/p\u003e","description":"","filename":"3.png","url":"https://assets-eu.researchsquare.com/files/rs-2310112/v1/7bec375c9d73d1068f77ca61.png"},{"id":29741146,"identity":"cf6acb76-e840-4f50-bd46-97c58343b46f","added_by":"auto","created_at":"2022-11-30 20:17:04","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":138833,"visible":true,"origin":"","legend":"\u003cp\u003e(a)The relation between nonlinear refractive index perturbation and polarization degree of signal light and inducing light; influence of polarization of inducing light (b) and signal light (self-modulation) (c).\u003c/p\u003e","description":"","filename":"4.png","url":"https://assets-eu.researchsquare.com/files/rs-2310112/v1/8520e40bff03f559872694fb.png"},{"id":29741149,"identity":"921057bf-f792-400a-a939-262ecd78b378","added_by":"auto","created_at":"2022-11-30 20:17:04","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":148487,"visible":true,"origin":"","legend":"\u003cp\u003eComparison of the influence of intensity and that of polarization on index change.\u003c/p\u003e","description":"","filename":"5.png","url":"https://assets-eu.researchsquare.com/files/rs-2310112/v1/4c4439281ac238222bb3d513.png"},{"id":29741228,"identity":"e25ad594-b9c4-437e-be7f-1d9e33d73a8c","added_by":"auto","created_at":"2022-11-30 20:25:04","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":81601,"visible":true,"origin":"","legend":"\u003cp\u003eSetup of Z-scan experiment.\u003c/p\u003e","description":"","filename":"6.png","url":"https://assets-eu.researchsquare.com/files/rs-2310112/v1/b2c3f537413ef32410ae8182.png"},{"id":29741147,"identity":"12251cc4-b97c-440d-b7c5-eb5f282b59c2","added_by":"auto","created_at":"2022-11-30 20:17:04","extension":"png","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":49926,"visible":true,"origin":"","legend":"\u003cp\u003eSee image above for figure legend\u003c/p\u003e","description":"","filename":"7.png","url":"https://assets-eu.researchsquare.com/files/rs-2310112/v1/6efb929633f79a34c54f09ad.png"},{"id":29741229,"identity":"c2a95b74-c09d-4871-9e34-a0e1968e3af4","added_by":"auto","created_at":"2022-11-30 20:25:10","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1043759,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-2310112/v1/4f918c46-a2fc-4130-acb3-9f4dc87b108c.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Holographic all-optical waveguide based on photoisomerization","fulltext":[{"header":"Full Text","content":"\u003cp\u003eIt is the development trend of modern communication that optical communication replaces electrical communication, and all-optical waveguides, which include light-controlled optical waveguide (LCOW) and light-induced optical waveguide (LIOW), are key devices of all-optical network in the future. LCOW is a kind of simultaneous \u0026ldquo;light-controlling-light\u0026rdquo; technique, where the controlling light and the signal light act on the material at the same time. Generally LCOWs are nonlinear waveguides, because the controlling light and the signal light always influence each other. LCOW are widely used in so-called discrete solitons\u003csup\u003e1\u0026ndash;4\u003c/sup\u003e.\u003c/p\u003e\n\u003cp\u003eAs a successive \u0026ldquo;light-controlling-light\u0026rdquo; technique, LIOW\u003csup\u003e5\u0026ndash;9\u003c/sup\u003e means that the controlling light first induces a waveguide, and then the signal light propagates in it. LIOWs are mostly linear waveguides, as the inducing light is always not affected by the signal light. All-optical waveguides can also be used in all-optical switches\u003csup\u003e10,11\u003c/sup\u003e.\u003c/p\u003e\n\u003cp\u003eWe have previously studied LCOW based on photoisomerization of organic materials. Photoisomerization is a fascinating area of investigation because it leads to light-induced surface pattern of amorphous azo-containing polymer film and light-induced deformation of liquid crystal elastomers, some of them are completely unexpected and still unexplained\u003csup\u003e12\u003c/sup\u003e. There are countless review papaers on this topoic\u003csup\u003e13\u0026ndash;15\u003c/sup\u003e. However, as a logical component of photoisomerization research, nonlinear effects associated with photoisomerization has not been adequately investigated, which can be seen from all these reviews. Related research area centers on micropic mechanism of second-order nonlinear optical polarizabilities, photoinduced poling, and photoswitching, etc\u003csup\u003e17,18\u003c/sup\u003e. Every step in the exploration process of photoisomerization nonlinear effects is helpful to systematization of photoisomerization research.\u003c/p\u003e\n\u003cp\u003ePhotoisomerization leads to extremely strong nonlinear effects, and we systematically explore nonlinear effects associated with photoisomerization in three steps. For the case of a single light beam, we\u003csup\u003e19,20\u003c/sup\u003e revealed polarization effects of nonlinearity associated with photoisomerization for the first time. For the case of two light beams, we systematically studied photoisomerization -related LCOW. We found successively that both intensity information\u003csup\u003e21,22\u003c/sup\u003e and polarization information\u003csup\u003e23\u003c/sup\u003e of the controlling light with stronger self-defocucing effects could be used to control the propagation of the signal light. Especially, we found that with the help of a controlling light, photoisomerization nonlinear effects can even be changed from a defocusing one to a focusing one, and we could achieve the conversion of dark solitons to bright solitons\u003csup\u003e21,22\u003c/sup\u003e. Because of the important theoretical and practical significance, the above work was picked by the editors of Optics Letters as an excellent contribution. Then how about the situation of LIOW based on photoisomerization? This is just what we study in this letter.\u003c/p\u003e\n\u003cp\u003eThe light wave information mainly includes amplitude (or intensity), phase and polarization. The polarization state of light was explored in photonic devices and other linear fields\u003csup\u003e24,25\u003c/sup\u003e. However, as far as we know, the optical nonlinear effect is only related to the light intensity, so the polarization information of light has not been used in the formation process of all-optical waveguide and optical spacial solitons. The more information that is utilized, the better the device performance. For example, plane image technology that only uses the amplitude information of light wave evolves into three-dimensional holographic image technology when phase information is utilized. We will propose a holographic all-optical waveguide based on photoisomerization nonlinear effects in this paper. Taking full advantage of the amplitude information and polarization information of light waves, the proposed holographic LIOW will make the propagation controlling of light beams more accurate and simpler.\u003c/p\u003e\n\u003cp\u003eSuppose both inducing light and signal light are general elliptically-polarized (EP) light, which is formed by a linearly-polarized (LP) light passed through a quarter-wavelength slide, the angle \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\varphi\\)\u003c/span\u003e\u003c/span\u003e between the polarization direction and the principal axis direction of the slide is called polarization angle and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({a_j}={\\cos ^2}{\\varphi _j}\\)\u003c/span\u003e\u003c/span\u003e(\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(j=c,\\;s\\)\u003c/span\u003e\u003c/span\u003e) is the polarization degree of the inducing light (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(j=c\\)\u003c/span\u003e\u003c/span\u003e) or the signal light (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(j=s\\)\u003c/span\u003e\u003c/span\u003e). The subscript \u0026quot;\u003cem\u003es\u003c/em\u003e\u0026quot; is omitted for simplicity in the context. In order to avoid the rotation of the polarization direction of the signal light during the propagation process due to the phenomenon of photo-induced birefringence, the direction of the main axis of the polarization ellipse of the signal light and the inducing light must be consistent, that is, the fast axis directions of the glass slides are parallel to each other. Firstly, according to the model of angular hole-burning\u003csup\u003e26\u003c/sup\u003e, stationary density distribution of molecules in the trans form is given by\u003csup\u003e20\u003c/sup\u003e\u003c/p\u003e\n\u003cdiv class=\"Equation\" id=\"Equ1\"\u003e\n \u003cdiv class=\"mathdisplay\" id=\"FileID_Equ1\" name=\"EquationSource\"\u003e$${N^{\\prime}_T}=N\\frac{{{I_c}{{\\sigma ^{\\prime}}_c}{{q^{\\prime}}_c}+\\gamma }}{{{I_c}{\\sigma _c}{q_c}[{a_c}{{\\cos }^2}\\theta +(1 - {a_c}){{\\sin }^2}\\theta {{\\cos }^2}\\psi ]+{I_c}{{\\sigma ^{\\prime}}_c}{{q^{\\prime}}_c}{\\text{+}}\\gamma }}$$\u003c/div\u003e\n \u003cdiv class=\"EquationNumber\"\u003e1\u003c/div\u003e\n\u003c/div\u003e\n\u003cp\u003ewhere \u003cem\u003eN\u003c/em\u003e is the total density of material molecules, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({I_c}\\)\u003c/span\u003e\u003c/span\u003eis intensity of the inducing light, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\sigma _c}\\)\u003c/span\u003e\u003c/span\u003eand \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({q_c}\\)\u003c/span\u003e\u003c/span\u003eare the absorption cross section of inducing light and quantum yield of trans molecules respectively, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\sigma ^{\\prime}_c}\\)\u003c/span\u003e\u003c/span\u003eand \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({q^{\\prime}_c}\\)\u003c/span\u003e\u003c/span\u003e are the absorption cross section and quantum yield of cis molecules respectively, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\gamma\\)\u003c/span\u003e\u003c/span\u003e is the thermal relaxation rate from the cis to trans. \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\theta\\)\u003c/span\u003e\u003c/span\u003e and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\psi\\)\u003c/span\u003e\u003c/span\u003e are polar angle and azimuthal angle of orientation of trans molecule respectively in the spherical coordinate system, whose z axis is the main axis of the polarization ellipse.\u003c/p\u003e\n\u003cp\u003eSecondly, the density distribution function \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({N^{\\prime}_T}\\)\u003c/span\u003e\u003c/span\u003e become the initial condition of optical chemistry process of the signal light, and the final density distribution of trans molecules under action of the signal light is\u003c/p\u003e\n\u003cdiv class=\"Equation\" id=\"Equ2\"\u003e\n \u003cdiv class=\"mathdisplay\" id=\"FileID_Equ2\" name=\"EquationSource\"\u003e$${N_T}={N^{\\prime}_T}\\frac{{I\\sigma ^{\\prime}q^{\\prime}+\\gamma }}{{I\\sigma q[a{{\\cos }^2}\\theta +(1 - a){{\\sin }^2}\\theta {{\\cos }^2}\\psi ]+I\\sigma ^{\\prime}q^{\\prime}+\\gamma }}$$\u003c/div\u003e\n \u003cdiv class=\"EquationNumber\"\u003e2\u003c/div\u003e\n\u003c/div\u003e\n\u003cp\u003ewhere \u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABIAAAAWCAYAAADNX8xBAAAAx0lEQVQ4je3UIQ6DQBCF4X8bDgEWPA6HgltguNDeZgUOhcXgUDgWSxZJMnVNmpZuQ2uadJJxL18yk8koERG+UJdvID8K1XWNUurWSZJgrX0MyhtljBFAtNaHmbdGG8eROI6pqur8aADDMJDnOVEUnYestXRdR5qmL3NeaFkWgiCgKIrPoLZt2fedMAzPQ9u20TSNdz9eyDnHNE3e/Xihvu9Z19W7H+D4IJ1zUpalZFkm8zx7j/YppLUW4K6NMS8hJfL/Rz8HXQEogPMcwV2NgQAAAABJRU5ErkJggg==\" width=\"18\" height=\"22\"\u003e is intensity of the signal light, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\sigma\\)\u003c/span\u003e\u003c/span\u003e and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(q\\)\u003c/span\u003e\u003c/span\u003e are the absorption cross section of signal light and quantum yield of trans molecules respectively, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\sigma ^{\\prime}\\)\u003c/span\u003e\u003c/span\u003e and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(q^{\\prime}\\)\u003c/span\u003e\u003c/span\u003e are the absorption cross section and quantum yield of cis molecules respectively.\u003c/p\u003e\n\u003cp\u003eFinally, refractive index perturbation arises from photoisomerization of the signal light is\u003csup\u003e20\u003c/sup\u003e\u003c/p\u003e\n\u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u0026nbsp;\u003cspan class=\"mathinline\"\u003e\\(\\Delta n=\\int_{{\\psi =0}}^{{2\\pi }} {\\int_{{\\theta =0}}^{\\pi } {a\\alpha ({N_T} - {{N^{\\prime}}_T})} } {\\cos ^2}\\theta \\sin \\theta d\\theta d\\psi\\)\u003c/span\u003e\u0026nbsp;\u003c/span\u003e \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(+(1 - a)\\int_{{\\psi =0}}^{{2\\pi }} {\\int_{{\\theta =0}}^{\\pi } {\\alpha ({N_T} - {{N^{\\prime}}_T})} } {\\cos ^2}\\psi {\\sin ^3}\\theta d\\theta d\\psi\\)\u003c/span\u003e\u003c/span\u003e. (3)\u003c/p\u003e\n\u003cp\u003eIt must be pointed out that the inducing light generates a nonlinear waveguide, which is related to the signal light.\u003c/p\u003e\n\u003cp\u003e\u003cimg 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\" width=\"637\" height=\"134\"\u003e\u003cbr\u003e\u003c/p\u003e\n\u003cp\u003eExploring the effect of light intensity, we first consider the situation when both the inducing light and the signal light are LP light, which are of the same polarization direction. In this situation, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(a={a_c}=0\\)\u003c/span\u003e\u003c/span\u003e. The relation between nonlinear refractive index perturbation \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\Delta n\\)\u003c/span\u003e\u003c/span\u003e and intensities of signal light \u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABIAAAAWCAYAAADNX8xBAAAAx0lEQVQ4je3UIQ6DQBCF4X8bDgEWPA6HgltguNDeZgUOhcXgUDgWSxZJMnVNmpZuQ2uadJJxL18yk8koERG+UJdvID8K1XWNUurWSZJgrX0MyhtljBFAtNaHmbdGG8eROI6pqur8aADDMJDnOVEUnYestXRdR5qmL3NeaFkWgiCgKIrPoLZt2fedMAzPQ9u20TSNdz9eyDnHNE3e/Xihvu9Z19W7H+D4IJ1zUpalZFkm8zx7j/YppLUW4K6NMS8hJfL/Rz8HXQEogPMcwV2NgQAAAABJRU5ErkJggg==\" width=\"18\" height=\"22\"\u003e and of inducing light \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({I_c}\\)\u003c/span\u003e\u003c/span\u003e is shown in Fig. \u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003e(a).\u003c/p\u003e\n\u003cp\u003eIt can be seen from Fig. \u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003e(a) that the perturbation of refractive index is forever negative for LIOW, regardless of the intensity of the inducing light and the signal light. That\u0026rsquo;s to say, the inducing light affects the nonlinear effects of the signal light, it however never change the defocusing nature associated with photoisomerization. It is worthy of notice that as for the case of LCOW, the controlling light could turn the defocusing nonlinear effect to a focusing one under certain conditions. Moreover, intensities undergo similar influence on the nonlinear effects regardless of the polarization states of both the inducing light and the signal light; see Fig. \u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003e(b)(c), where the polarization degrees of signal light and inducing light are \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(a=0,\\ {a_c}=0.5\\)\u003c/span\u003e\u003c/span\u003e and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(a=0.5,\\ {a_c}=0\\)\u003c/span\u003e\u003c/span\u003e, respectively.\u003c/p\u003e\n\u003cp\u003eFigure \u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003e(a) reveals the influence of inducing light intensity on nonlinear effects of the signal light when intensities of uniform inducing lights are \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({I_c}{\\text{=}}0,\\;\\;0.1, \\;\\;1,\\;\\;10,\\)\u003c/span\u003e\u003c/span\u003e respectively. The bigger the intensity of inducing light (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({I_c}\\)\u003c/span\u003e\u003c/span\u003e), the smaller the absolute value of refractive index perturbation (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\left| {\\Delta n} \\right|\\)\u003c/span\u003e\u003c/span\u003e). So the inducing light weakens the self-defocusing effects. When \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({I_c}\\)\u003c/span\u003e\u003c/span\u003eincreases, defocusing nonlinear effects become weaker. Figure \u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003e(b) reveals the influence of distribution of inducing light intensity by illustrating dependence of refractive index change on inducing light intensity when the signal light intensity is 0.1, 1, and 10, respectively. Here two LP light beams (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(a={a_c}=0\\)\u003c/span\u003e\u003c/span\u003e) are considered. Apparently, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\Delta n\\)\u003c/span\u003e\u003c/span\u003e increases as \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({I_c}\\)\u003c/span\u003e\u003c/span\u003eincreases. Assume that a light beam with Gaussian distribution \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({I_c}={e^{ - {r^2}/{\\omega ^2}}}\\)\u003c/span\u003e\u003c/span\u003e(\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\omega {\\text{=1}}\\)\u003c/span\u003e\u003c/span\u003e) excites the material and then the signal light with uniform distribution propagate in the material. The LIOW shown as the relation of index change and the signal light intensity is illustrated by Fig. \u003cspan class=\"InternalRef\"\u003e3\u003c/span\u003e(a). The nonlinear effect felt by signal light looks like a focusing one, although it essentially is not a nonlinear effect because refractive index change is not the function of the signal light. Nonlinear effects induced by the inducing light is some of a focusing one. A bright beam experiences self-defocusing effects itself, however induces a focusing waveguide. This is actually an interesting phenomenon. Considering that the signal light experiences self-defocusing effects, a bright inducing beam weakens the self-defocusing effects of signal light. Figure \u003cspan class=\"InternalRef\"\u003e3\u003c/span\u003e(b) is the waveguide induced by a light with periodically distributed intensity, which is generated by an amplitude mask and is described as \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({I_c}={I_0}\\cos {x^2}{\\cos ^2}y\\)\u003c/span\u003e\u003c/span\u003e. So photonic crystals can be generated with periodic bright beams. When a light with uniform distribution pass through the photonic crystal, the focusing effect associated with the photonic crystal, the self-defocusing effect and natural diffraction of the signal light will achieve balance and discrete solitons may be formed.\u003c/p\u003e\n\u003cp\u003eFigure \u003cspan class=\"InternalRef\"\u003e4\u003c/span\u003e shows the polarization-dependence of nonlinear effects, where intensities are set as \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({I_c}=0.3\\)\u003c/span\u003e\u003c/span\u003e and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(I=1\\)\u003c/span\u003e\u003c/span\u003e. It is seen that from Fig. \u003cspan class=\"InternalRef\"\u003e4\u003c/span\u003e(a) the dependence of polarization is not always monotonous, and there is a twist in the \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\Delta n(a,\\;\\;{a_c})\\)\u003c/span\u003e\u003c/span\u003esurface. Complicated polarization-dependence of nonlinear effects is elaborated as follows.\u003c/p\u003e\n\u003cp\u003eFigure \u003cspan class=\"InternalRef\"\u003e4\u003c/span\u003e(b) illustrates the influence of polarization of the inducing light on nonlinear effects. As for the circularly-polarized (CP) signal light (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(a=0.5\\)\u003c/span\u003e\u003c/span\u003e), when the polarization degree of the inducing light turns smaller (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({a_c}=0 \\to 0.5\\)\u003c/span\u003e\u003c/span\u003e, from linear polarization to circular polarization), \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\left| {\\Delta n} \\right|\\)\u003c/span\u003e\u003c/span\u003edecreases, which denotes that the defocusing effect becomes weaker. As for a LP signal light (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(a=0\\)\u003c/span\u003e\u003c/span\u003e), when the degree of polarization of the inducing light turns smaller, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\left| {\\Delta n} \\right|\\)\u003c/span\u003e\u003c/span\u003e increases, and the defocusing effect becomes stronger. Figure \u003cspan class=\"InternalRef\"\u003e4\u003c/span\u003e(c) illustrates the influence of polarization of the signal light on nonlinear effects. As for the CP inducing light (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({a_c}=0.5\\)\u003c/span\u003e\u003c/span\u003e), when the polarization degree of the signal light turns smaller, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\left| {\\Delta n} \\right|\\)\u003c/span\u003e\u003c/span\u003edecreases monotonically, which denotes that the effect becomes weaker gradually. As for the LP inducing light (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({a_{\\text{c}}}=0\\)\u003c/span\u003e\u003c/span\u003e), when the polarization degree of the signal light turns smaller, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\left| {\\Delta n} \\right|\\)\u003c/span\u003e\u003c/span\u003efirst decreases until \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(a \\approx 3\\)\u003c/span\u003e\u003c/span\u003e, and then increases, which denotes that the defocusing effect first becomes weaker and weaker, and then become stronger and stronger.\u003c/p\u003e\n\u003cp\u003eTheoretically comparing the influence of intensity and polarization on index change, we find that effects of polarization is generally weaker than that of intensity; see Fig. \u003cspan class=\"InternalRef\"\u003e5\u003c/span\u003e. Thus when inducing waveguide, we can coarsely control the waveguide by adjusting intensity and distribution of the inducing light, and then experience fine control by adjusting the polarization of the inducing light. thereupon, a holographic LIOW scheme is proposed. Holographic all-optical waveguide makes the guide of light beam more precise and more convenient. Moreover, influence of intensity of signal light is obviously greater then that of inducing light, from Fig. \u003cspan class=\"InternalRef\"\u003e5\u003c/span\u003e and Fig. \u003cspan class=\"InternalRef\"\u003e6\u003c/span\u003e.\u003c/p\u003e\n\u003cp\u003eNow we give some of our qualitative experimental confirmation. The Z-scan experimental\u003csup\u003e12\u003c/sup\u003e setup is shown in Fig. \u003cspan class=\"InternalRef\"\u003e6\u003c/span\u003e. The part enclosed by the dotted line is the inducing light path. The intensity of uniform inducing light with a wavelength of \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\lambda _2}{\\text{=}}514.5nm\\)\u003c/span\u003e\u003c/span\u003eemitted from the Ar\u0026thinsp;+\u0026thinsp;laser is controlled by the combination of two polarizers, P3 and P4. The LP light becomes EP light through the \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\lambda _1}{\\text{/}}4\\)\u003c/span\u003e\u003c/span\u003e (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\lambda _2}{\\text{/}}4\\)\u003c/span\u003e\u003c/span\u003e) slide (quarter-wave plate). The concave lens X and the convex lens L2 are combined to expand the beam. Similarly, the intensity of the signal light with a wavelength of \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\lambda _1}{\\text{=}}632.8nm\\)\u003c/span\u003e\u003c/span\u003eis determined by polarizers P1 and P2. To avoid the change of the polarization state of the light in the sample due to the photo-induced birefringence (including the rotation of the polarization direction), keep the fast axis direction of the slide \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\lambda _1}{\\text{/}}4\\)\u003c/span\u003e\u003c/span\u003e and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\lambda _2}{\\text{/}}4\\)\u003c/span\u003e\u003c/span\u003e parallel. P1 and P2 are fixed on a platform and by rotating the platform, the polarization state of the signal light can be changed without changing the intensity. A lens of focal length \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(f=111mm\\)\u003c/span\u003e\u003c/span\u003eprovides a tight focus of the laser beam, whose spatial mode of the laser is close to Gaussian TEM00, and the beam-waist radius is \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\omega _0} \\approx 62\\mu m\\)\u003c/span\u003e\u003c/span\u003eat the focal point. An aperture with a linear transmittance of 0.15 is fixed at the position about 70 cm from the focal plane. A photodetector (Field Master, Coherent Inc.) D is used to detect the light power behind the aperture. The sample is poly(methyl methacrylate) (PMMA) film doped with disperse red 13 (DR3) (1.6 % by weight), which was prepared from a solution containing an appropriate amount of dye, polymer, and chloroform. The thickness of the film is measured to be \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(l \\approx 52\\mu m\\)\u003c/span\u003e\u003c/span\u003e. Normalized transmittance of the signal light passing through the aperture is measured as the sample is moved along the propagation path \u003cem\u003ez\u003c/em\u003e of the focused Gaussian beam. Peak-valley difference \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\Delta {T_{p - v}}\\)\u003c/span\u003e\u003c/span\u003eof Z-scan curves denotes the magnitude of the refractive index perturbation.\u003c/p\u003e\n\u003cp\u003eExperimental results are shown in Fig. \u003cspan class=\"InternalRef\"\u003e7\u003c/span\u003e when central intensity of the signal light at the focal point is \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({I_0}=0.80W/c{m^2}\\)\u003c/span\u003e\u003c/span\u003e. Py3 is the Z-scan curve of signal CP light (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(a=0.5\\)\u003c/span\u003e\u003c/span\u003e) before the sample is induced (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({I_c}=0\\)\u003c/span\u003e\u003c/span\u003e). py1, py2 and py4 are the Z-scan curves of LP light (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(a=0\\)\u003c/span\u003e\u003c/span\u003e), EP light (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(a=0.25\\)\u003c/span\u003e\u003c/span\u003e) and CP light, respectively after the sample is induced by an uniform light with intensity of \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({I_c}=0.42W/c{m^2}\\)\u003c/span\u003e\u003c/span\u003e. \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\Delta {T_{p - v}}\\)\u003c/span\u003e\u003c/span\u003eof py1-py4 are 0.39, 0.34, 0.23, 0.17, respectively.\u003c/p\u003e\n\u003cp\u003eThe above experimental results preliminarily and qualitatively confirm some of theoretical results. Comparing py3 with py4, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\Delta {T_{p - v}}\\)\u003c/span\u003e\u003c/span\u003eof the latter is smaller, which indicates that optical induction weakens the self-defocusing effects. This result is consistent with Fig. \u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003e and Fig. \u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003e(a). Comparing py1, py2 and py4, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\Delta {T_{p - v}}\\)\u003c/span\u003e\u003c/span\u003e decline in turn. That\u0026rsquo;s to say, as for the case of CP inducing light, nonlinear effects become weaker and weaker when signal light change gradually from LP lightto CPL. This is consistent with Fig. \u003cspan class=\"InternalRef\"\u003e4\u003c/span\u003e(c) (the case of \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({a_c}=0.5\\)\u003c/span\u003e\u003c/span\u003e). Moreover, the influence of intensity of inducing light is rather smaller than that of polarization information of the signal light. In this way, the dependence of nonlinear effects on intensity information of inducing light and on polarization information of signal light is qualitatively verified. However we failed to find obvious influence of polarization of the inducing light on nonlinear effects. Perhaps this dependence is too weak to be observed for the sample we used. Actually this is somehow consistent with Fig. \u003cspan class=\"InternalRef\"\u003e5\u003c/span\u003e(a).\u003c/p\u003e\n\u003cp\u003eIn summary, the all-optical waveguide theory based on photoisomerization nonlinear effects is systematically and deeply studied, and a nonlinear holographic all-optical waveguide scheme is proposed for the first time. We find that LIOW based on photoisomerization weakens the defocusing effects, however never change the defocusing nature. Besides, a bright inducing light beam generates a focusing waveguide. Polarization states of both inducing light and signal light also affect propagation of signal light. For a CP signal light, when the polarization degree of the inducing light turns smaller, the defocusing effect becomes weaker; as for a LP signal light, when the polarization degree of the inducing light turns smaller, the defocusing effect becomes stronger. For the CP inducing light when the polarization degree of the signal light turns smaller, the defocing effect becomes weaker gradually; As for the LP inducing light, when the polarization degree of the signal light turns smaller, the defocusing effect first becomes weaker and weaker, and then become stronger and stronger. Part of the theoretical results has been qualitatively confirmed by Z-scan experiments. The more information a photonic device utilizes, the better its performance. For holographic imaging technology, by additional use of phase information besides amplitude information of light wave, the two-dimensional plane image can be evolved into a three-dimensional image. Similarly, the application of polarization information is joined to the proposed holographic all-optical waveguide scheme. Compared with the traditional all-optical waveguide, the performance of holographic waveguide will be greatly improved, making the control of light more precise and easier. The influence of the polarization degree on the beam propagation is much smaller than that of the light intensity, thus can be used for fine-tuning of the waveguide. In addition, the operation of changing the degree of polarization is simpler than changing the light intensity distribution. The former only needs to rotate the glass slide, while the latter requires complex operations such as beam shaping. Generally speaking, defocusing effects associated with photoisomerization is too strong to form dark solitons, only if in materials with weaker nonlinear effects,such as DR1/PMMA with low doping concentration and with red light. In order to form dark solitons in materials with strong defocusing effects such as DR13/PMMA, one should weaken defocusing effects by forming holographic waveguide. In order to precisely control the beam propagation, such as form optical spacial solitons, we can adjust the intensity and distribution of the signal light at first, and when the beam is close to the soliton form, we modify the intensity and polarization degree of the inducing light in turn to fine-tune the signal light, so that the optical solitons can be precisely and easily formed. Such nonlinear waveguide may find its application in the future all-optical net.\u003c/p\u003e\n\u003cp\u003eUp to now, the role of polarization has been explored in three situations: polarization information of a signal light\u003csup\u003e6,7\u003c/sup\u003e, polarization information of the controlling light in a light-controlled waveguide\u003csup\u003e10\u003c/sup\u003e and polarization information of the inducing light in a light-inducing waveguide. This work deals with LIOW, while Ref.10 dealt with LCOW; they are two parallel works. The theoretical models and results of the two papers differ from each other. For example, for the case of LIOW, inducing light affects the nonlinear effects of the signal light, it however never change the defocusing nature associated with photoisomerization, while for the case of LCOW, the controlling light could turn the defocusing nonlinear effects to a focusing one under certain conditions.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003eThis work was supported by the Guangdong Provincial Basic and Applied Basic Research Fund Project (Grant Nos. 2021A1515010282 and 2114050002323), the National Natural Science Foundation of China (Grant Nos. 61372064 and 62103159), Special Projects in Key Fields of General Universities in Guangdong Province (Grant No. 2021ZDZX1012) and the Huizhou Science and Technology Program Project (Grant No. 2020SD0406034).\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eConflict of Interest\u0026nbsp;\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe authors have no conflicts to disclose.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eDATA AVAILABILITY\u0026nbsp;\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe data that support the findings of this study are available within the article.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n \u003cli\u003eZ. Chen, H. Martin, E. D. Eugenieva, J. Xu, and J. Yang, Opt. Express \u003cstrong\u003e13 ,\u003c/strong\u003e1816 (2005).\u003c/li\u003e\n \u003cli\u003eN. K. Efremidis, S. Sears, D. N. Christodoulides, J. W. Fleischer, and M. Segev, Phys. Rev. E. \u003cstrong\u003e66,\u003c/strong\u003e 046602 (2002).\u0026nbsp;\u003c/li\u003e\n \u003cli\u003eJ. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, Nature, \u003cstrong\u003e422,\u003c/strong\u003e 147 (2003) .\u0026nbsp;\u003c/li\u003e\n \u003cli\u003eZ. Chen, A. Bezryadina, I. Makasyuk, and J. Yang, Opt. Lett.\u003cstrong\u003e\u0026nbsp;29,\u003c/strong\u003e 1656 (2004).\u0026nbsp;\u003c/li\u003e\n \u003cli\u003eD. N. Christodoulides, F. Lederer, Y. Silberberg, Nature \u003cstrong\u003e424,\u0026nbsp;\u003c/strong\u003e817 (2003).\u0026nbsp;\u003c/li\u003e\n \u003cli\u003eN. K. Efremidis, J. Hudock, D. N. Christodoulides, J. W. Fleischer, O. Cohen, and M. Segev, Phys. Rev. Lett. \u003cstrong\u003e91,\u003c/strong\u003e 213906 (2003).\u0026nbsp;\u003c/li\u003e\n \u003cli\u003eJ. Yang and Z. H. Musslimani, \u0026nbsp;Opt. Lett.\u003cstrong\u003e\u0026nbsp;28,\u003c/strong\u003e 2094 (2003).\u0026nbsp;\u003c/li\u003e\n \u003cli\u003eJ. W. Fleischer, G. Bartal, O. Cohen, O. Manela, M. Segev, J. Hudock, and D. N. Christodoulides, Phys. Rev. Lett. \u003cstrong\u003e92,\u0026nbsp;\u003c/strong\u003e123904 (2004).\u0026nbsp;\u003c/li\u003e\n \u003cli\u003eD. Neshev, E. Ostrovskaya, Y. Kivshar, and W. Krolikowski, Opt. Lett. \u003cstrong\u003e28,\u0026nbsp;\u003c/strong\u003e710 (2003).\u003c/li\u003e\n \u003cli\u003eX. Hu, P. Jiang, C. Ding, H. Yang, Q. Gong, Nature Photon. \u003cstrong\u003e2,\u003c/strong\u003e 185 (2008) .\u003c/li\u003e\n \u003cli\u003eN. Li, J. Xu, G. Song, C. Zhu, S. Xie, Y. Yang, M. S.Zubairy, and S. Y. Zhu , Phys. Rev. A \u003cstrong\u003e93,\u003c/strong\u003e 043819 (2016).\u003c/li\u003e\n \u003cli\u003eS. De Martino ,F. Mauro, P. A. Netti, Photonic applications of azobenzene molecules embedded in amorphous polymer, La Rivista del Nuovo Cimento, 43, 599 (2020).\u0026nbsp;\u003c/li\u003e\n \u003cli\u003eZ. Sekkat, Model for athermal enhancement of molecular mobility in solid polymers by light, \u0026nbsp;Phys. Rev. E 102, 032501 (2020).\u003c/li\u003e\n \u003cli\u003eA. Natansohn, P. Rochon, Photoinduced motions in azo-containing polymers, Chem. Rev., \u0026nbsp; 102, 4139 (2002).\u0026nbsp;\u003c/li\u003e\n \u003cli\u003eS. L. Oscurato, M. Salvatore, P. Maddalena, and\u0026nbsp;A. Ambrosio, From nanoscopic to macroscopic photo-driven motion in azobenzene-containing materials, Nanophotonics, 2018, 7, 1387 (2018).\u003c/li\u003e\n \u003cli\u003eS. Lee, H. S. Kang, J. K. Park, Directional photofluidization lithography: micro/ nanostructural evolution by photofluidic motions of azobenzene materials, Adv. Mater. 24, 2069 (2012).\u0026nbsp;\u003c/li\u003e\n \u003cli\u003eJ. A. Delaire, K.Nakatani, Linear and nonlinear optical properties of photochromic molecules and materials, Chem. Rev. 100, 1817 (2000).\u003c/li\u003e\n \u003cli\u003eM. Dudek, N. Tarnowicz-Staniak, M. Deiana, Z. Pokłade, M. Samoć and K. Matczyszyn, RSC Advances, 10, 40489 (2020).\u003c/li\u003e\n \u003cli\u003eJ. C. Liang and X. Q. Zhou, J. Opt. Soc. Am. B \u003cstrong\u003e22,\u003c/strong\u003e 2468 (2005).\u003c/li\u003e\n \u003cli\u003eJ. C. Liang, H. Zhao, X. Zhou, and H. C. Wang, J. Appl. Phys. \u003cstrong\u003e101,\u0026nbsp;\u003c/strong\u003e013106 (2007).\u003c/li\u003e\n \u003cli\u003eJ. C. Liang, Z. B. Cai, Y. Z. Sun, S. L. Xu, L. Yi, J. Opt. Soc. Am. B \u003cstrong\u003e26,\u0026nbsp;\u003c/strong\u003e36 (2009).\u003c/li\u003e\n \u003cli\u003eJ. C. Liang, Opt. Lett. \u003cstrong\u003e35,\u003c/strong\u003e 4081 (2010).\u003c/li\u003e\n \u003cli\u003eJ. C. Liang, and H. C. Wang, Opt. Lett.\u003cstrong\u003e\u0026nbsp;42,\u003c/strong\u003e 3654 (2017).\u0026nbsp;\u003c/li\u003e\n \u003cli\u003eH. Yuan, X. Liu, F. Afshinmanesh, W. Li, G. Xu, J. Sun, B. Lian, A. G. Curto, G. Ye, Y. Hikita, Z. Shen, S. C. Zhang, X. Chen, M. Brongersma, H. Y. Hwang, and Y. Cui, Nature Nanotech. \u003cstrong\u003e10,\u003c/strong\u003e 707 (2015).\u003c/li\u003e\n \u003cli\u003eP. Chen, C. Shu, X. Guo, M.\u0026thinsp;M.\u0026thinsp;T. Loy, and S. Du, Phys. Rev. Lett. \u003cstrong\u003e114,\u003c/strong\u003e 010401 (2015). \u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"applied-physics-b","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"aphb","sideBox":"Learn more about [Applied Physics B](http://link.springer.com/journal/340)","snPcode":"340","submissionUrl":"https://submission.nature.com/new-submission/340/3","title":"Applied Physics B","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"","lastPublishedDoi":"10.21203/rs.3.rs-2310112/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-2310112/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThe all-optical waveguide theory based on photoisomerization nonlinear effects is systematically and deeply studied, and a nonlinear holographic all-optical waveguide scheme is proposed for the first time. It is found that the induction of a light with stronger isomerization activity on the material weakens the self-defocusing effects of the signal light. Especially, polarization states of both inducing light and signal light also unexpectedly affect propagation of signal light. Part of the theoretical results has been qualitatively confirmed by Z-scan experiments. The proposed holographic all-optical waveguide scheme means polarization information is applied in the all-optical waveguide besides intensity information. Compared with the traditional all-optical waveguide, the performance of holographic waveguide will be greatly improved, making the control of light more precise and easier. Such nonlinear waveguide scheme may find its application in the future all-optical net.\u003c/p\u003e","manuscriptTitle":"Holographic all-optical waveguide based on photoisomerization","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2022-11-30 20:16:58","doi":"10.21203/rs.3.rs-2310112/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Major revision","date":"2023-02-17T21:13:07+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2023-02-17T05:13:24+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"fb9c5899-a66e-4513-9fab-75455d24350d","date":"2023-02-17T02:26:11+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"d386e476-bd23-4ef0-9cb2-9f19c120d590","date":"2023-01-02T12:35:56+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"73bdd0d0-7618-4a78-8198-d6fd5b03d90b","date":"2022-12-08T10:29:03+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2022-12-05T05:42:45+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2022-11-28T12:59:29+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2022-11-26T17:06:49+00:00","index":"","fulltext":""},{"type":"submitted","content":"Applied Physics B","date":"2022-11-24T17:24:51+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"applied-physics-b","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"aphb","sideBox":"Learn more about [Applied Physics B](http://link.springer.com/journal/340)","snPcode":"340","submissionUrl":"https://submission.nature.com/new-submission/340/3","title":"Applied Physics B","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false}}],"origin":"","ownerIdentity":"1cdbb236-75f4-43c5-bdb8-28a16186317f","owner":[],"postedDate":"November 30th, 2022","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"under-review","subjectAreas":[],"tags":[],"updatedAt":"2023-04-10T18:29:29+00:00","versionOfRecord":[],"versionCreatedAt":"2022-11-30 20:16:58","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-2310112","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-2310112","identity":"rs-2310112","version":["v1"]},"buildId":"WrCJVZZCHTDjtuVLN7oU0","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}