Supercontinuum Generation in Silica-Based Photonic Crystal Fibers for High-Resolution Ophthalmic Optical Coherence Tomography

Supercontinuum Generation in Silica-Based Photonic Crystal Fibers for High-Resolution Ophthalmic Optical Coherence Tomography | 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 Supercontinuum Generation in Silica-Based Photonic Crystal Fibers for High-Resolution Ophthalmic Optical Coherence Tomography Udayakumar Arunkumar, Hassan Pakarzadeh, Zahrasadat Fatemipanah This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-2100413/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract Optical coherence tomography (OCT) is a new technology for high-resolution cross-sectional images of biological tissues. In this paper, we design photonic crystal fibers (PCFs) made of silica with proper dispersion characteristics about the center wavelength of 800 nm to simulate supercontinuum generation (SCG) which is desired for high-resolution OCT in ophthalmology. Several types of PCFs with different air-hole diameters are designed where squared hyperbolic secant pulses are input to simulate SCG by solving generalized nonlinear Schrodinger equation (GNLSE) via split-step Fourier method. To obtain more accurate SCG, dispersion coefficients up to the 9th order, Raman scattering and self-steepening are taken into account. We examine impacts of air-hole diameter, input pulse width and pulse peak power on the SCG bandwidth as well as the OCT resolution through which suitable parameters for maximum axial resolution in ophthalmology are determined. photonic crystal fiber optical coherence tomography supercontinuum generation axial resolution ophthalmology Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Introduction Photonic crystal fibers (PCFs) as a new generation of optical fibers have attracted great attention in recent years[ 1 , 2 ]. PCFs have different cladding structures compared with the standard optical fibers where there is an arranged air holes running parallel to the fiber axis[ 3 , 4 ]. The size of air-holes is about the micrometer that is comparable with the wavelength of the light wave guided in the PCF[ 5 ]. The advantages of PCFs can be attributed to their high flexibility in design which means that by varying their geometrical parameters such as the cross-sectional area, size or arrangement of the air holes, different optical characteristics can be obtained for various applications [ 2 , 6 – 9 ]. High mode confinement in the PCFs and enhanced nonlinearity make them very good candidates for observation of nonlinear phenomena specially production of new frequency components[ 10 ] which has been the subject of extensive research since 1990s[ 6 , 11 ]. The process in which the narrow-bandwidth input pulse undergoes nonlinear spectral broadening to spectrally generate a wide-bandwidth output is called supercontinuum generation (SCG). SCG is a complex nonlinear phenomenon that results from the expansion of the main spectrum of a laser pulse propagating in a dispersive nonlinear medium[ 12 ]. The widest spectrum is obtained when the pump pulse wavelength is set very close to the zero-dispersion wavelength (ZDW) of the PCF[ 13 ]. By using a PCF as a nonlinear medium with a longer interaction length and a higher nonlinear parameter compared to standard fibers, it is possible to dramatically reduce the input peak power required for SCG observation [ 14 ]. Light sources based on SCG provide a combination of desirable features including: high output power[ 15 ], wide and controlled spectrum and high degree of flexibility. These features make SCG sources ideal for many applications such as frequency metrology[ 16 ], ultra-short pulse compression[ 17 ], spectroscopy of materials and photonic structures[ 18 ], and optical coherence tomography (OCT)[ 19 ]. OCT is a new technology for obtaining high-resolution cross-sectional imaging. OCT was introduced first in 1991 by David Huang and named by Fujimoto[ 20 , 21 ]. The advantage of OCT is that it can act as a non-destructive biopsy and provide information of pathological sample at the exact time and space domains with micrometer resolution[ 20 , 22 ]. OCT generally uses broadband light sources in various wavelength regions such as super luminescent diode, Ti: Al 2 O 3 lasers, femtosecond Kerr-lens mode locked (KLM) lasers, infrared lasers, etc.[ 20 , 23 ]. OCT systems operate based on low-coherence interferometry and require broadband light sources to produce high-resolution images[ 24 ]. Among the different sources used for OCT, the PCF-based SCG is one of the most promising sources that can provide wide and flat spectrum for high-resolution OCT images [ 25 ]. As the eye is fundamentally transparent around the wavelength of 800nm, the light can be easily transmitted with minimal loss to access the retina layers [ 24 , 25 ]. The ophthalmic OCT systems at the center wavelength of 800nm have been optimum since they fulfill the imaging criteria due to the accessibility of Ti:Sapphire lasers with a very broad bandwidth resulting in a significant resolution ~ 3µm. Also, super luminescent diodes (SLDs) were mainly utilized in the commercial ophthalmic OCT systems owing to their good output characteristics and cost-effective price. Therefore, OCT systems operating around 800nm are very good candidates to resolve all essential intra-retinal layers and provide high-resolution images of small morphological changes in these layers [ 25 ]. In this paper, PCFs are designed with proper dispersion characteristics around the center wavelength of 800 nm which is desired for ophthalmic OCT. Several designs of PCFs with different air-hole diameters are simulated and then short/ultra-short pulses are input into the PCFs to generate supercontinuum by solving generalized nonlinear Schrodinger equation (GNLSE) via split-step Fourier method. Impacts of air-hole diameter, input pulse width and pulse peak power on the SCG bandwidth as well as the OCT resolution are investigated and finally suitable parameters for maximum axial resolution in ophthalmology are determined. It should be noted that our proposed PCF design at 800 nm center wavelength is innovative compared with other PCF designs operating at different wavelengths of 1.0 µm, etc. [ 26 , 27 ]. Theory And Simulation Method In order to design PCFs, we start out from one of the relatively accurate methods which is known as the finite-difference time-domain (FDTD) method, since it solves the Maxwell equations with the least approximation and high accuracy[ 26 , 27 ]. In fact, the FDTD method is a common method for electromagnetic numerical simulation in an optical environment. When the PCF is designed and its dispersion curve is plotted for given parameters, then it is used as a dispersive nonlinear medium for pulse propagation and supercontinuum generation. The famous equation governing the pulse propagation in optical fibers is GNLSE which is[ 11 ]: $$\frac{\partial A\left(z\text{,}T\right)}{\partial \text{z}}=-\left(\sum _{m=2}{\beta }_{m}\frac{{i}^{m-1}}{m!}\frac{{\partial }^{m}}{{\partial T}^{m}}+\frac{\alpha }{2}\right)A\left(z\text{,}T\right)+i\gamma \left(1+\frac{i}{{\omega }_{0}}\frac{\partial }{\partial T}\right)\left(A\left(z\text{,}T\right)\underset{-\infty }{\overset{+\infty }{\int }}R\left({t}^{{\prime }}\right){\left|A\left(z\text{,}T-{t}^{{\prime }}\right)\right|}^{2}dt{\prime }\right)$$ 1 where A(z,T), β m (m = 2 to 9), α, γ and R(t) are pulse envelope, dispersion coefficients of m th order, loss coefficient, nonlinear parameter and Raman response function, respectively. Also, \({{\omega }}_{0}\) is the center frequency of pump pulse and T is the retarded time measured in the reference frame moving with pulse. The terms in the first parentheses on the right-hand side is related to the linear effects (dispersion and loss) while the remaining terms correspond to the nonlinear effects such self-steepening, Raman scattering, self-phase modulation and cross-phase modulation. Equation ( 1 ) is a nonlinear partial differential equation that generally does not have algebraic solutions except in some specific situations, so a numerical solution is often required. Split-step Fourier (SSF) is a method often used in nonlinear dispersive environments to solve the pulse propagation problem[ 28 ]. This means that in SSF method it is assumed that dispersion and nonlinearity act independently along the length of the fiber. Here, the fiber length is divided into several sections each of them with small distance of h where propagation from z to z + h is carried out in two steps so that in the first step, the nonlinearity acts alone and in the second step, dispersion acts alone. When the simulation of SCG is accomplished and the output spectrum is obtained; one should evaluate the output spectal width which is used for OCT axial resolution. The OCT axial resolution l c is determined by the coherent length of the light source (here is the PCF-based SCG) [ 29 ] which is given by [ 20 , 29 ]: $${\text{l}}_{\text{c}}={\Delta }\text{z}=\frac{2\text{ln}2}{{\pi }} \frac{{{{\lambda }}_{0}}^{2}}{{\Delta }{\lambda }}$$ 2 where \({{\lambda }}_{0}\) is the center wavelength of the SCG (here for ophthalmology \({{\lambda }}_{0}\) is about 800nm) and \({\Delta }{\lambda }\) corresponds to the 10-dB spectral width of output SCG. Therefore, as it is obvious, for obtaining higher OCT resolution, a wider and flatter SCG source is needed. Results And Discussion In this section, we perform simulations for a 10m-long PCF and the input squared hyperbolic secant pulse with the envelope of \(\text{A}\left(0\text{,}\text{t}\right)=\sqrt{{\text{P}}_{0}}{\text{sech}}^{2}(\frac{t}{{T}_{0}})\) . Here, T 0 is the pulse width and P 0 is the peak power. The central wavelength of the pulse is set at 800 nm which is desired for OCT in ophthalmology[ 30 ]. Figure 1 shows the cross section of the designed silica-based PCF used for generation of supercontinuum for OCT in ophthalmology. The air–hole diameters of the first, second, third, fourth and fifth ring are d 1 = 0.26µm, 0.31µm, 0.36µm and 0.41µm, respectively. Also, the lattice pitch is 0.85µm. Dispersion curves of the designed PCF for different values of first ring air-hole diameters d 1 are shown in Fig. 2 . We have used the dispersion relation as \(D=-\frac{\lambda }{c}\frac{{d}^{2}{n}_{eff}}{d{\lambda }^{2}}\) to plot dispersion curves where \({n}_{eff}\) is the effective refractive index of the fundamental mode [ 11 ]. As it is seen, by changing d 1 , the dispersion curve is changed where the flattest curve around 0.8µm is obtained for d 1 =0.41µm. By taking successive derivatives of each dispersion curve in Fig. 2 , one can obtain the curves for different orders of the dispersion coefficients ( \({\beta }_{m}={\left(\frac{{d}^{m}\beta }{d{\omega }^{m}}\right)}_{\omega ={\omega }_{0}}\) ) versus the wavelength for the given d 1 as shown in Fig. 3. However, for sake of brevity, only the curves for d 1 =0.41µm are shown in Fig. 3. Since the pump wavelength is chosen at 0.8 µm, the values of dispersion coefficients at this specific wavelength are required for simulation of GNLSE. Therefore, the linear and nonlinear parameters of the PCF calculated at 0.8µm for each air-hole diameter are listed in Table 1. Using these parameters and solving GNLSE via SSF method, one can simulate the SCG spectra as shown in Fig. 4 . The pump peak power is P 0 =150W and pulse width is T 0 =1.5ps. As it is evident, the spectra depend on the air-hole diameter where the widest spectrum is achieved for d 1 =0.41µm. This is in consistent with the result obtained from Fig. 2 where the flattest dispersion curve was obtained for d 1 =0.41µm. The 10-dB width is usually used as a measure of the spectral width which is given in Table. 2. As it is obvious, the 10-dB width for the PCF with d 1 =0.41µm is maximum. According to Table 2, the best bandwidth and resolution are obtained for the PCF with d 1 =0.41µm; therefore, we fix the air-hole diameter at d 1 =0.41µm for following simulations. In Fig. 5 , the SCG spectra are shown when the pump width T 0 is changed. Evidently, as the pulse width decreases, the spectrum is widened so that the widest spectrum is obtained for T 0 =30fs.This means that for T 0 =30fs, the 10-dB spectrum bandwidth is Δλ =62.0 nm which corresponds to the highest axial resolution of l c =4.5µm. Table 3 lists the 10-dB bandwidths as well as the OCT axial resolutions calculated at each pump width T 0 for the fixed air-hole diameter of d 1 = 0.41µm. As it is seen the best bandwidth and resolution are obtained for the pulse width of T 0 = 30fs; therefore, we fix the simulation parameters at T 0 = 30fs and d 1 = 0.41µm and then examine the role of pulse peak power in SCG spectrum and its 10-dB bandwidth. This is shown in Fig. 6 where the SCG spectra are plotted when the pump peak power is changed from P 0 = 150W to P 0 = 750W. Table 4 lists the 10-dB bandwidths Δλ as well as the OCT resolutions l c calculated at different pump peak powers P 0 . It can be seen that by increasing the peak power, the SCG bandwidth and the OCT resolution are improved so that the best bandwidth and resolution are obtained for the pump with the peak power of P 0 =750W. Therefore, totally the best SCG bandwidth and OCT resolution are achieved when the squared hyperbolic secant pump pulse with P 0 =750W and T 0 =30fs is input into the PCF with d 1 =0.41µm. Obviously, this best bandwidth results in the best OCT resolution of 2.6µm for ophthalmology. This means that the supercontinuum generated from the designed PCF (see Fig. 1 ) is a very good candidate as a OCT source for ophthalmology since it can provide high quality images with resolutions as high as 2.6µm. Conclusion We have designed for the first time, silica-based PCFs with a cladding consists of 5 rings of air holes where the hole diameter of the first ring d1 was changed to obtain suitable dispersion characteristics around 0.8 µm. We have simulated SCG in the designed PCFs to obtain a wide and flat spectrum to be used as a source of OCT for application in ophthalmology. By solving the GNLSE and using the SSF method, the SCG bandwidths as well as the OCT resolutions were calculated for different effective parameters including the air-hole diameter, pulse width and peak powers. The results showed that, in general, the best SCG bandwidth of 109.0nm and equivalent OCT resolution of 2.6µm were achieved when a squared hyperbolic secant pump pulse with P0 = 750W and T0 = 30fs was input into the 10-m long PCF with d1 = 0.41µm. To the best of our knowledge, this is the maximum bandwidth and the highest OCT resolution obtained for ophthalmology via the PCF-based SCG. Therefore, the proposed PCF may be considered as a very good candidate for the SCG to obtain high-resolution images in the ophthalmic OCT systems. Declarations Acknowledgement Authors would like to thank Dr. Michael Frosz from Max Planck Institute for the Science of Light for his assistance with developing GNLSE code. Funding No funding was received for this work. Competing Interest The authors declare that they have no potential conflicts of interests. Author’s Contributions All authors contributed to the study conception and design. Material preparation, simulation results and analysis were performed by H. Pakarzadeh, and Z. Fatemipanah. The first draft of the manuscript was written by Z. Fatemipanah and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript. Ethics approval Compliance with ethical standards is followed by authors. Informed Consent Not applicable. Consent to Participate Not applicable. Consent for Publication Not applicable. Research Involving Human Participants and/or Animals Not applicable. Data Availability Statement Data sharing not applicable to this article as no datasets were generated or analyzed during the current study. References Broeng, J., et al., Photonic crystal fibers: A new class of optical waveguides. Optical fiber technology, 1999. 5 (3): p. 305-330. Singla, S. and P. Singal, Photonic crystal fiber: construction, properties, developments and applications. International Journal of Electronics Engineering, 2017. 9 (1). Knight, J., et al., All-silica single-mode optical fiber with photonic crystal cladding. Optics letters, 1996. 21 (19): p. 1547-1549. Russell, P., Photonic crystal fibers. science, 2003. 299 (5605): p. 358-362. Poli, F., A. Cucinotta, and S. Selleri, Photonic crystal fibers: properties and applications . Vol. 102. 2007: Springer Science & Business Media. Pakarzadeh, H., R. Derakhshan, and S. Hosseinabadi, Tunable wavelength conversion based on optofluidic infiltrated photonic crystal fibers. 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Tables TABLE I Dispersion coefficients and nonlinear parameter of the PCF calculated at 0.8 µm for different air-hole diameter d1. β 2 (ps 2 /km) β 3 (ps 3 /km) β 4 (ps 4 /km) β 5 (ps 5 /km) β 6 (ps 6 /km) β 7 (ps 7 /km) β 8 (ps 8 /km) β 9 (ps 9 /km) γ (1/ W.km ) d 1 =0.26 µm 25.1 0.02205 -7.868e-6 1.307e-7 3.689e-9 -8.73e-12 -3.206e-12 -6.98e-14 93.1 d 1 =0.31 µm 24.25 0.009306 3.09e-5 5.88e-8 3.997e-9 -8.994e-12 -3.412e-12 -7.422e-14 104.6 d 1 =0.36 µm 2.042 0.0007783 7.226e-5 -5.708e-8 4.504e-9 -9.67e-12 -3.632e-12 -7.894e-14 117.9 d 1 =0.41 µm 14.74 -0.003818 0.000118 -2.198e-7 5.371e-9 -1.217e-11 -3.865e-12 -8.416e-14 133.2 TABLE II The 10-dB bandwidths Δλ of SCG as well as the OCT axial resolutions l c calculated at each air-hole diameter d1. d 1 ( µm ) Δλ(nm) l c (µm) 0.26 µm 27.2 10.4 0.31 µm 29.3 9.6 0.36 µm 33.7 8.4 0.41 µm 41.5 6.8 TABLE III The 10-dB bandwidths of SCG as well as the OCT axial resolutions calculated at each pump width T0. The air-hole diameter is d1=0.41µm. T 0 Δλ(nm) l c (µm) 1.5ps 41.5 6.8 1.0ps 43.0 6.6 0.5ps 44.5 6.3 200fs 45.3 6.2 100fs 46.7 6.0 80fs 47.7 5.9 50fs 51.8 5.4 30fs 62.0 4.5 TABLE IV The 10-dB bandwidths of SCG as well as the OCT axial resolutions calculated at different pump peak powers. The air-hole diameter and the pump width are fixed at d1=0.41µm and T0=30fs, respectively. P 0 (W) Δλ(nm) l c (µm) 150 41.5 6.8 300 76.5 3. 7 450 88.8 3.2 600 99.5 2.8 750 109.0 2.6 Additional Declarations No competing interests reported. Cite Share Download PDF Status: Posted Version 1 posted 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-2100413","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":141308238,"identity":"74fc0414-115b-4a56-a04a-3f4b3b2dc463","order_by":0,"name":"Udayakumar Arunkumar","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA5UlEQVRIiWNgGAWjYJACxgYQyd4GYklAhBKI0sJzjIHhIGlaJNJAWohwFP/sM2YPZ7Ztkzef+Szx88cdFvkM7IcfMDzcgVuLxLkcc8ONbbcN59xOOyxx8IyEZQNPmgFD4hk81pzhMZN82HabcYZ0eoPEwTYJAwaGHAaGxDbcOuShWuxnSB5v/gHWwv8GvxYDkBagwxJnSLAdg9giQcAWwzNsZZIzzt1OnsGTlmZxFqiFTeKZwQF8WuTOMG+T7Cm7bTuD/Zjxjcq2OgN+/uSHD3/i0YIJ2ID4ACkaRsEoGAWjYBRgAgBoQ1CkDR/iKQAAAABJRU5ErkJggg==","orcid":"","institution":"Kathir College of Engineering","correspondingAuthor":true,"submittingAuthor":false,"prefix":"","firstName":"Udayakumar","middleName":"","lastName":"Arunkumar","suffix":""},{"id":141308240,"identity":"62e07618-4e2f-4fce-8ea2-aa26b98cf305","order_by":1,"name":"Hassan Pakarzadeh","email":"","orcid":"","institution":"Shiraz University of Technology","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Hassan","middleName":"","lastName":"Pakarzadeh","suffix":""},{"id":141308242,"identity":"0b043348-a88d-4014-9a41-87bf4951a3c6","order_by":2,"name":"Zahrasadat Fatemipanah","email":"","orcid":"","institution":"Shiraz University of Technology","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Zahrasadat","middleName":"","lastName":"Fatemipanah","suffix":""}],"badges":[],"createdAt":"2022-09-25 03:59:11","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-2100413/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-2100413/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":27567318,"identity":"0de55e5d-051a-4fd2-acc8-dab1a47abcdb","added_by":"auto","created_at":"2022-10-10 16:38:34","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":429267,"visible":true,"origin":"","legend":"\u003cp\u003eThe cross section of the designed silica-based PCF for the ophthalmology OCT. d\u003csub\u003e1\u003c/sub\u003e=0.26µm (can be varied), d\u003csub\u003e2\u003c/sub\u003e=0.31µm, d\u003csub\u003e3\u003c/sub\u003e=0.36µm, d\u003csub\u003e4\u003c/sub\u003e=d\u003csub\u003e5\u003c/sub\u003e=0.41µm, Λ=0.85µm. PML is perfectly matched layer.\u003c/p\u003e","description":"","filename":"1.png","url":"https://assets-eu.researchsquare.com/files/rs-2100413/v1/fddd93cb63e57845379339c3.png"},{"id":27567051,"identity":"14633761-4120-4576-b78e-15d2715cfee2","added_by":"auto","created_at":"2022-10-10 16:33:33","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":211435,"visible":true,"origin":"","legend":"\u003cp\u003eDispersion curves of the designed PCF for different values of first ring air-hole diameters d\u003csub\u003e1\u003c/sub\u003e.\u003c/p\u003e","description":"","filename":"2.png","url":"https://assets-eu.researchsquare.com/files/rs-2100413/v1/df765233b98922cfd665988a.png"},{"id":27567052,"identity":"be95fe2b-a0ce-41f3-8dbb-fa162e27764a","added_by":"auto","created_at":"2022-10-10 16:33:33","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":338149,"visible":true,"origin":"","legend":"\u003cp\u003eVarious dispersion coefficients of the PCF as a function of wavelength for d\u003csub\u003e1\u003c/sub\u003e=0.41µm.\u003c/p\u003e","description":"","filename":"3.png","url":"https://assets-eu.researchsquare.com/files/rs-2100413/v1/94e794114ea66b852c4501bc.png"},{"id":27567317,"identity":"87cba4f0-d2f9-4a9f-a901-8727dd58656b","added_by":"auto","created_at":"2022-10-10 16:38:33","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":251868,"visible":true,"origin":"","legend":"\u003cp\u003eSCG spectra simulated at different air-hole diameter d\u003csub\u003e1\u003c/sub\u003e. The pump peak power is 150W and pulse width is 1.5ps.\u003c/p\u003e","description":"","filename":"4.png","url":"https://assets-eu.researchsquare.com/files/rs-2100413/v1/54ca22413606f833cf489dd7.png"},{"id":27567054,"identity":"37fc54f7-2cc1-4ce4-a753-f127815b0228","added_by":"auto","created_at":"2022-10-10 16:33:34","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":355214,"visible":true,"origin":"","legend":"\u003cp\u003eThe SCG spectra for different pump widths \u003cem\u003eT\u003c/em\u003e\u003csub\u003e\u003cem\u003e0\u003c/em\u003e\u003c/sub\u003e and fixed air-hole diameter d\u003csub\u003e1\u003c/sub\u003e=0.41µm.\u003c/p\u003e","description":"","filename":"5.png","url":"https://assets-eu.researchsquare.com/files/rs-2100413/v1/cbdc281f967d5de77c318f45.png"},{"id":27567055,"identity":"e1391776-49b2-48b3-befa-6a5b921abc9d","added_by":"auto","created_at":"2022-10-10 16:33:34","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":393968,"visible":true,"origin":"","legend":"\u003cp\u003eThe SCG spectra for different pump peak powers P\u003csub\u003e0\u003c/sub\u003e. The air-hole diameter and the pump width are fixed at d\u003csub\u003e1\u003c/sub\u003e=0.41µm and T\u003csub\u003e0\u003c/sub\u003e=30fs, respectively.\u003c/p\u003e","description":"","filename":"6.png","url":"https://assets-eu.researchsquare.com/files/rs-2100413/v1/63b92be0c6552833d445445f.png"},{"id":28103074,"identity":"b98d2efa-c3f8-4161-abd2-aa5cf30ca1e5","added_by":"auto","created_at":"2022-10-21 17:44:35","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":2038577,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-2100413/v1/cffa41cf-c5f3-48ba-9bdc-23620a76e5a5.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Supercontinuum Generation in Silica-Based Photonic Crystal Fibers for High-Resolution Ophthalmic Optical Coherence Tomography","fulltext":[{"header":"Introduction","content":"\u003cp\u003ePhotonic crystal fibers (PCFs) as a new generation of optical fibers have attracted great attention in recent years[\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e, \u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e]. PCFs have different cladding structures compared with the standard optical fibers where there is an arranged air holes running parallel to the fiber axis[\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e, \u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e]. The size of air-holes is about the micrometer that is comparable with the wavelength of the light wave guided in the PCF[\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e]. The advantages of PCFs can be attributed to their high flexibility in design which means that by varying their geometrical parameters such as the cross-sectional area, size or arrangement of the air holes, different optical characteristics can be obtained for various applications [\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e, \u003cspan additionalcitationids=\"CR7 CR8\" citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eHigh mode confinement in the PCFs and enhanced nonlinearity make them very good candidates for observation of nonlinear phenomena specially production of new frequency components[\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e] which has been the subject of extensive research since 1990s[\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e, \u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e]. The process in which the narrow-bandwidth input pulse undergoes nonlinear spectral broadening to spectrally generate a wide-bandwidth output is called supercontinuum generation (SCG). SCG is a complex nonlinear phenomenon that results from the expansion of the main spectrum of a laser pulse propagating in a dispersive nonlinear medium[\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e]. The widest spectrum is obtained when the pump pulse wavelength is set very close to the zero-dispersion wavelength (ZDW) of the PCF[\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e]. By using a PCF as a nonlinear medium with a longer interaction length and a higher nonlinear parameter compared to standard fibers, it is possible to dramatically reduce the input peak power required for SCG observation [\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e]. Light sources based on SCG provide a combination of desirable features including: high output power[\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e], wide and controlled spectrum and high degree of flexibility. These features make SCG sources ideal for many applications such as frequency metrology[\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e], ultra-short pulse compression[\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e], spectroscopy of materials and photonic structures[\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e], and optical coherence tomography (OCT)[\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eOCT is a new technology for obtaining high-resolution cross-sectional imaging. OCT was introduced first in 1991 by David Huang and named by Fujimoto[\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e, \u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e]. The advantage of OCT is that it can act as a non-destructive biopsy and provide information of pathological sample at the exact time and space domains with micrometer resolution[\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e, \u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e]. OCT generally uses broadband light sources in various wavelength regions such as super luminescent diode, Ti: Al\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003e lasers, femtosecond Kerr-lens mode locked (KLM) lasers, infrared lasers, etc.[\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e, \u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e]. OCT systems operate based on low-coherence interferometry and require broadband light sources to produce high-resolution images[\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e]. Among the different sources used for OCT, the PCF-based SCG is one of the most promising sources that can provide wide and flat spectrum for high-resolution OCT images [\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eAs the eye is fundamentally transparent around the wavelength of 800nm, the light can be easily transmitted with minimal loss to access the retina layers [\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e, \u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e]. The ophthalmic OCT systems at the center wavelength of 800nm have been optimum since they fulfill the imaging criteria due to the accessibility of Ti:Sapphire lasers with a very broad bandwidth resulting in a significant resolution\u0026thinsp;~\u0026thinsp;3\u0026micro;m. Also, super luminescent diodes (SLDs) were mainly utilized in the commercial ophthalmic OCT systems owing to their good output characteristics and cost-effective price. Therefore, OCT systems operating around 800nm are very good candidates to resolve all essential intra-retinal layers and provide high-resolution images of small morphological changes in these layers [\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eIn this paper, PCFs are designed with proper dispersion characteristics around the center wavelength of 800 nm which is desired for ophthalmic OCT. Several designs of PCFs with different air-hole diameters are simulated and then short/ultra-short pulses are input into the PCFs to generate supercontinuum by solving generalized nonlinear Schrodinger equation (GNLSE) via split-step Fourier method. Impacts of air-hole diameter, input pulse width and pulse peak power on the SCG bandwidth as well as the OCT resolution are investigated and finally suitable parameters for maximum axial resolution in ophthalmology are determined. It should be noted that our proposed PCF design at 800 nm center wavelength is innovative compared with other PCF designs operating at different wavelengths of 1.0 \u0026micro;m, etc. [\u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e, \u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e27\u003c/span\u003e].\u003c/p\u003e"},{"header":"Theory And Simulation Method","content":"\u003cp\u003eIn order to design PCFs, we start out from one of the relatively accurate methods which is known as the finite-difference time-domain (FDTD) method, since it solves the Maxwell equations with the least approximation and high accuracy[\u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e, \u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e27\u003c/span\u003e]. In fact, the FDTD method is a common method for electromagnetic numerical simulation in an optical environment. When the PCF is designed and its dispersion curve is plotted for given parameters, then it is used as a dispersive nonlinear medium for pulse propagation and supercontinuum generation. The famous equation governing the pulse propagation in optical fibers is GNLSE which is[\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e]:\u003cdiv id=\"Equ1\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ1\" name=\"EquationSource\"\u003e\n$$\\frac{\\partial A\\left(z\\text{,}T\\right)}{\\partial \\text{z}}=-\\left(\\sum _{m=2}{\\beta }_{m}\\frac{{i}^{m-1}}{m!}\\frac{{\\partial }^{m}}{{\\partial T}^{m}}+\\frac{\\alpha }{2}\\right)A\\left(z\\text{,}T\\right)+i\\gamma \\left(1+\\frac{i}{{\\omega }_{0}}\\frac{\\partial }{\\partial T}\\right)\\left(A\\left(z\\text{,}T\\right)\\underset{-\\infty }{\\overset{+\\infty }{\\int }}R\\left({t}^{{\\prime }}\\right){\\left|A\\left(z\\text{,}T-{t}^{{\\prime }}\\right)\\right|}^{2}dt{\\prime }\\right)$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e1\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003ewhere \u003cem\u003eA(z,T), β\u003c/em\u003e\u003csub\u003e\u003cem\u003em\u003c/em\u003e\u003c/sub\u003e\u003cem\u003e(m\u0026thinsp;=\u0026thinsp;2 to 9), α, γ\u003c/em\u003e and \u003cem\u003eR(t)\u003c/em\u003e are pulse envelope, dispersion coefficients of m\u003csup\u003eth\u003c/sup\u003e order, loss coefficient, nonlinear parameter and Raman response function, respectively. Also, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({{\\omega }}_{0}\\)\u003c/span\u003e\u003c/span\u003e is the center frequency of pump pulse and \u003cem\u003eT\u003c/em\u003e is the retarded time measured in the reference frame moving with pulse. The terms in the first parentheses on the right-hand side is related to the linear effects (dispersion and loss) while the remaining terms correspond to the nonlinear effects such self-steepening, Raman scattering, self-phase modulation and cross-phase modulation.\u003c/p\u003e \u003cp\u003eEquation (\u003cspan refid=\"Equ1\" class=\"InternalRef\"\u003e1\u003c/span\u003e) is a nonlinear partial differential equation that generally does not have algebraic solutions except in some specific situations, so a numerical solution is often required. Split-step Fourier (SSF) is a method often used in nonlinear dispersive environments to solve the pulse propagation problem[\u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e28\u003c/span\u003e]. This means that in SSF method it is assumed that dispersion and nonlinearity act independently along the length of the fiber. Here, the fiber length is divided into several sections each of them with small distance of h where propagation from z to z\u0026thinsp;+\u0026thinsp;h is carried out in two steps so that in the first step, the nonlinearity acts alone and in the second step, dispersion acts alone.\u003c/p\u003e \u003cp\u003eWhen the simulation of SCG is accomplished and the output spectrum is obtained; one should evaluate the output spectal width which is used for OCT axial resolution. The OCT axial resolution \u003cem\u003el\u003c/em\u003e\u003csub\u003e\u003cem\u003ec\u003c/em\u003e\u003c/sub\u003e is determined by the coherent length of the light source (here is the PCF-based SCG) [\u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e] which is given by [\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e, \u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e]:\u003cdiv id=\"Equ2\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ2\" name=\"EquationSource\"\u003e\n$${\\text{l}}_{\\text{c}}={\\Delta }\\text{z}=\\frac{2\\text{ln}2}{{\\pi }} \\frac{{{{\\lambda }}_{0}}^{2}}{{\\Delta }{\\lambda }}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e2\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003ewhere \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({{\\lambda }}_{0}\\)\u003c/span\u003e\u003c/span\u003e is the center wavelength of the SCG (here for ophthalmology \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({{\\lambda }}_{0}\\)\u003c/span\u003e\u003c/span\u003e is about 800nm) and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\Delta }{\\lambda }\\)\u003c/span\u003e\u003c/span\u003e corresponds to the 10-dB spectral width of output SCG. Therefore, as it is obvious, for obtaining higher OCT resolution, a wider and flatter SCG source is needed.\u003c/p\u003e"},{"header":"Results And Discussion","content":"\u003cp\u003eIn this section, we perform simulations for a 10m-long PCF and the input squared hyperbolic secant pulse with the envelope of\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\text{A}\\left(0\\text{,}\\text{t}\\right)=\\sqrt{{\\text{P}}_{0}}{\\text{sech}}^{2}(\\frac{t}{{T}_{0}})\\)\u003c/span\u003e\u003c/span\u003e. Here, T\u003csub\u003e0\u003c/sub\u003e is the pulse width and P\u003csub\u003e0\u003c/sub\u003e is the peak power. The central wavelength of the pulse is set at 800 nm which is desired for OCT in ophthalmology[\u003cspan class=\"CitationRef\"\u003e30\u003c/span\u003e].\u003c/p\u003e\n\u003cp\u003eFigure \u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003e shows the cross section of the designed silica-based PCF used for generation of supercontinuum for OCT in ophthalmology. The air\u0026ndash;hole diameters of the first, second, third, fourth and fifth ring are d\u003csub\u003e1\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;0.26\u0026micro;m, 0.31\u0026micro;m, 0.36\u0026micro;m and 0.41\u0026micro;m, respectively. Also, the lattice pitch is 0.85\u0026micro;m.\u003c/p\u003e\n\u003cp\u003eDispersion curves of the designed PCF for different values of first ring air-hole diameters d\u003csub\u003e1\u003c/sub\u003e are shown in Fig. \u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003e. We have used the dispersion relation as \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(D=-\\frac{\\lambda }{c}\\frac{{d}^{2}{n}_{eff}}{d{\\lambda }^{2}}\\)\u003c/span\u003e\u003c/span\u003e to plot dispersion curves where \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({n}_{eff}\\)\u003c/span\u003e\u003c/span\u003e is the effective refractive index of the fundamental mode [\u003cspan class=\"CitationRef\"\u003e11\u003c/span\u003e]. As it is seen, by changing d\u003csub\u003e1\u003c/sub\u003e, the dispersion curve is changed where the flattest curve around 0.8\u0026micro;m is obtained for d\u003csub\u003e1\u003c/sub\u003e=0.41\u0026micro;m. By taking successive derivatives of each dispersion curve in Fig. \u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003e, one can obtain the curves for different orders of the dispersion coefficients (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\beta }_{m}={\\left(\\frac{{d}^{m}\\beta }{d{\\omega }^{m}}\\right)}_{\\omega ={\\omega }_{0}}\\)\u003c/span\u003e\u003c/span\u003e) versus the wavelength for the given d\u003csub\u003e1\u003c/sub\u003e as shown in Fig. 3. However, for sake of brevity, only the curves for d\u003csub\u003e1\u003c/sub\u003e=0.41\u0026micro;m are shown in Fig. 3. Since the pump wavelength is chosen at 0.8 \u0026micro;m, the values of dispersion coefficients at this specific wavelength are required for simulation of GNLSE. Therefore, the linear and nonlinear parameters of the PCF calculated at 0.8\u0026micro;m for each air-hole diameter are listed in Table 1. Using these parameters and solving GNLSE via SSF method, one can simulate the SCG spectra as shown in Fig. \u003cspan class=\"InternalRef\"\u003e4\u003c/span\u003e. The pump peak power is P\u003csub\u003e0\u003c/sub\u003e=150W and pulse width is T\u003csub\u003e0\u003c/sub\u003e=1.5ps. As it is evident, the spectra depend on the air-hole diameter where the widest spectrum is achieved for d\u003csub\u003e1\u003c/sub\u003e=0.41\u0026micro;m. This is in consistent with the result obtained from Fig. \u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003e where the flattest dispersion curve was obtained for d\u003csub\u003e1\u003c/sub\u003e=0.41\u0026micro;m. The 10-dB width is usually used as a measure of the spectral width which is given in Table. 2. As it is obvious, the 10-dB width for the PCF with d\u003csub\u003e1\u003c/sub\u003e=0.41\u0026micro;m is maximum.\u003c/p\u003e\n\u003cp\u003eAccording to Table 2, the best bandwidth and resolution are obtained for the PCF with d\u003csub\u003e1\u003c/sub\u003e=0.41\u0026micro;m; therefore, we fix the air-hole diameter at d\u003csub\u003e1\u003c/sub\u003e=0.41\u0026micro;m for following simulations. In Fig. \u003cspan class=\"InternalRef\"\u003e5\u003c/span\u003e, the SCG spectra are shown when the pump width T\u003csub\u003e0\u003c/sub\u003e is changed. Evidently, as the pulse width decreases, the spectrum is widened so that the widest spectrum is obtained for T\u003csub\u003e0\u003c/sub\u003e=30fs.This means that for T\u003csub\u003e0\u003c/sub\u003e=30fs, the 10-dB spectrum bandwidth is \u0026Delta;\u0026lambda; =62.0 nm which corresponds to the highest axial resolution of l\u003csub\u003ec\u003c/sub\u003e=4.5\u0026micro;m.\u003c/p\u003e\n\u003cp\u003eTable\u0026nbsp;3 lists the 10-dB bandwidths as well as the OCT axial resolutions calculated at each pump width T\u003csub\u003e0\u003c/sub\u003e for the fixed air-hole diameter of d\u003csub\u003e1\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;0.41\u0026micro;m. As it is seen the best bandwidth and resolution are obtained for the pulse width of T\u003csub\u003e0\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;30fs; therefore, we fix the simulation parameters at T\u003csub\u003e0\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;30fs and d\u003csub\u003e1\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;0.41\u0026micro;m and then examine the role of pulse peak power in SCG spectrum and its 10-dB bandwidth. This is shown in Fig. \u003cspan class=\"InternalRef\"\u003e6\u003c/span\u003e where the SCG spectra are plotted when the pump peak power is changed from P\u003csub\u003e0\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;150W to P\u003csub\u003e0\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;750W.\u003c/p\u003e\n\u003cp\u003eTable 4 lists the 10-dB bandwidths \u0026Delta;\u0026lambda; as well as the OCT resolutions l\u003csub\u003ec\u003c/sub\u003e calculated at different pump peak powers P\u003csub\u003e0\u003c/sub\u003e. It can be seen that by increasing the peak power, the SCG bandwidth and the OCT resolution are improved so that the best bandwidth and resolution are obtained for the pump with the peak power of P\u003csub\u003e0\u003c/sub\u003e=750W. Therefore, totally the best SCG bandwidth and OCT resolution are achieved when the squared hyperbolic secant pump pulse with P\u003csub\u003e0\u003c/sub\u003e=750W and T\u003csub\u003e0\u003c/sub\u003e=30fs is input into the PCF with d\u003csub\u003e1\u003c/sub\u003e=0.41\u0026micro;m. Obviously, this best bandwidth results in the best OCT resolution of 2.6\u0026micro;m for ophthalmology. This means that the supercontinuum generated from the designed PCF (see Fig. \u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003e) is a very good candidate as a OCT source for ophthalmology since it can provide high quality images with resolutions as high as 2.6\u0026micro;m.\u003c/p\u003e\n\u003cp\u003e\u003cbr\u003e\u003c/p\u003e"},{"header":"Conclusion","content":"\u003cp\u003eWe have designed for the first time, silica-based PCFs with a cladding consists of 5 rings of air holes where the hole diameter of the first ring d1 was changed to obtain suitable dispersion characteristics around 0.8 \u0026micro;m. We have simulated SCG in the designed PCFs to obtain a wide and flat spectrum to be used as a source of OCT for application in ophthalmology. By solving the GNLSE and using the SSF method, the SCG bandwidths as well as the OCT resolutions were calculated for different effective parameters including the air-hole diameter, pulse width and peak powers. The results showed that, in general, the best SCG bandwidth of 109.0nm and equivalent OCT resolution of 2.6\u0026micro;m were achieved when a squared hyperbolic secant pump pulse with P0\u0026thinsp;=\u0026thinsp;750W and T0\u0026thinsp;=\u0026thinsp;30fs was input into the 10-m long PCF with d1\u0026thinsp;=\u0026thinsp;0.41\u0026micro;m. To the best of our knowledge, this is the maximum bandwidth and the highest OCT resolution obtained for ophthalmology via the PCF-based SCG. Therefore, the proposed PCF may be considered as a very good candidate for the SCG to obtain high-resolution images in the ophthalmic OCT systems.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003eAcknowledgement \u003c/strong\u003eAuthors would like to thank Dr. Michael Frosz from Max Planck Institute for the Science of Light for his assistance with developing GNLSE code.\u003c/p\u003e\n\n\u003cp\u003e\u003cstrong\u003eFunding \u003c/strong\u003eNo funding was received for this work.\u003c/p\u003e\n\n\u003cp\u003e\u003cstrong\u003eCompeting Interest \u003c/strong\u003eThe authors declare that they have no potential conflicts of interests.\u003c/p\u003e\n\n\u003cp\u003e\u003cstrong\u003eAuthor\u0026rsquo;s Contributions\u003c/strong\u003e All authors contributed to the study conception and design. Material preparation, simulation results and analysis were performed by H. Pakarzadeh, and Z. Fatemipanah. The first draft of the manuscript was written by Z. Fatemipanah and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript.\u003c/p\u003e\n\n\u003cp\u003e\u003cstrong\u003eEthics approval \u003c/strong\u003eCompliance with ethical standards is followed by authors.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eInformed Consent\u003c/strong\u003e Not applicable.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eConsent to Participate\u003c/strong\u003e Not applicable.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eConsent for Publication\u003c/strong\u003e Not applicable.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eResearch Involving Human Participants and/or Animals\u003c/strong\u003e Not applicable.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eData Availability Statement \u003c/strong\u003eData sharing not applicable to this article as no datasets were generated or analyzed during the current study. \u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n\u003cli\u003eBroeng, J., et al., \u003cem\u003ePhotonic crystal fibers: A new class of optical waveguides.\u003c/em\u003e Optical fiber technology, 1999. \u003cstrong\u003e5\u003c/strong\u003e(3): p. 305-330.\u003c/li\u003e\n\u003cli\u003eSingla, S. and P. 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Optical Society of America.\u003c/li\u003e\n\u003cli\u003eAmiot, C.G., et al., \u003cem\u003eGhost optical coherence tomography.\u003c/em\u003e Optics express, 2019. \u003cstrong\u003e27\u003c/strong\u003e(17): p. 24114-24122.\u003c/li\u003e\n\u003cli\u003eFujimoto, J.G., \u003cem\u003eOptical coherence tomography.\u003c/em\u003e Comptes Rendus de l\u0026apos;Acad\u0026eacute;mie des Sciences-Series IV-Physics, 2001. \u003cstrong\u003e2\u003c/strong\u003e(8): p. 1099-1111.\u003c/li\u003e\n\u003cli\u003eHuang, D., et al., \u003cem\u003eOptical coherence tomography.\u003c/em\u003e science, 1991. \u003cstrong\u003e254\u003c/strong\u003e(5035): p. 1178-1181.\u003c/li\u003e\n\u003cli\u003eYu, Y., et al., \u003cem\u003eOptical Coherence Tomography in Fingertip Biometrics.\u003c/em\u003e Optics and Lasers in Engineering, 2022. \u003cstrong\u003e151\u003c/strong\u003e: p. 106868.\u003c/li\u003e\n\u003cli\u003eHartl, I., et al., \u003cem\u003eUltrahigh-resolution optical coherence tomography using continuum generation in an air\u0026ndash;silica microstructure optical fiber.\u003c/em\u003e Optics letters, 2001. \u003cstrong\u003e26\u003c/strong\u003e(9): p. 608-610.\u003c/li\u003e\n\u003cli\u003eBezerra, H.G., et al., \u003cem\u003eIntracoronary optical coherence tomography: a comprehensive review: clinical and research applications.\u003c/em\u003e JACC: Cardiovascular Interventions, 2009. \u003cstrong\u003e2\u003c/strong\u003e(11): p. 1035-1046.\u003c/li\u003e\n\u003cli\u003eFerhat, M.L., L. 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Bononi, \u003cem\u003eOn the accuracy of split-step Fourier simulations for wideband nonlinear optical communications.\u003c/em\u003e Journal of Lightwave Technology, 2018. \u003cstrong\u003e36\u003c/strong\u003e(23): p. 5669-5677.\u003c/li\u003e\n\u003cli\u003eFercher, A.F., et al., \u003cem\u003eOptical coherence tomography-principles and applications.\u003c/em\u003e Reports on progress in physics, 2003. \u003cstrong\u003e66\u003c/strong\u003e(2): p. 239.\u003c/li\u003e\n\u003cli\u003eLeitgeb, R., et al., \u003cem\u003eEnhanced medical diagnosis for dOCTors: a perspective of optical coherence tomography.\u003c/em\u003e Journal of Biomedical Optics, 2021. \u003cstrong\u003e26\u003c/strong\u003e(10): p. 100601.\u003c/li\u003e\n\u003c/ol\u003e"},{"header":"Tables","content":"\u003cp style=\"text-align: center;\"\u003e\u003cem\u003eTABLE I\u003c/em\u003e\u003c/p\u003e\n\u003cp style=\"text-align: center;\"\u003e\u003cem\u003eDispersion coefficients and nonlinear parameter of the PCF calculated at 0.8 \u0026micro;m for different air-hole diameter d1.\u003c/em\u003e\u003cem\u003e\u0026nbsp;\u003c/em\u003e\u003c/p\u003e\n\u003cdiv align=\"center\"\u003e\n \u003ctable border=\"1\" cellpadding=\"0\" cellspacing=\"0\" width=\"680\"\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd width=\"11.160058737151248%\"\u003e\n \u003cp\u003e\u003cem\u003e\u0026nbsp;\u003c/em\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"8.370044052863436%\"\u003e\n \u003cp\u003e\u003cem\u003e\u0026beta;\u003csub\u003e2\u003c/sub\u003e\u003c/em\u003e\u003c/p\u003e\n \u003cp\u003e\u003cem\u003e(ps\u003csup\u003e2\u003c/sup\u003e/km)\u003c/em\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.691629955947137%\"\u003e\n \u003cp\u003e\u003cem\u003e\u0026beta;\u003csub\u003e3\u003c/sub\u003e\u003c/em\u003e\u003c/p\u003e\n \u003cp\u003e\u003cem\u003e(ps\u003csup\u003e3\u003c/sup\u003e/km)\u003c/em\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.691629955947137%\"\u003e\n \u003cp\u003e\u003cem\u003e\u0026beta;\u003csub\u003e4\u003c/sub\u003e\u003c/em\u003e\u003c/p\u003e\n \u003cp\u003e\u003cem\u003e(ps\u003csup\u003e4\u003c/sup\u003e/km)\u003c/em\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.691629955947137%\"\u003e\n \u003cp\u003e\u003cem\u003e\u0026beta;\u003csub\u003e5\u003c/sub\u003e\u003c/em\u003e\u003c/p\u003e\n \u003cp\u003e\u003cem\u003e(ps\u003csup\u003e5\u003c/sup\u003e/km)\u003c/em\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.691629955947137%\"\u003e\n \u003cp\u003e\u003cem\u003e\u0026beta;\u003csub\u003e6\u003c/sub\u003e\u003c/em\u003e\u003c/p\u003e\n \u003cp\u003e\u003cem\u003e(ps\u003csup\u003e6\u003c/sup\u003e/km)\u003c/em\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"11.160058737151248%\"\u003e\n \u003cp\u003e\u003cem\u003e\u0026beta;\u003csub\u003e7\u003c/sub\u003e\u003c/em\u003e\u003c/p\u003e\n \u003cp\u003e\u003cem\u003e(ps\u003csup\u003e7\u003c/sup\u003e/km)\u003c/em\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"11.160058737151248%\"\u003e\n \u003cp\u003e\u003cem\u003e\u0026beta;\u003csub\u003e8\u003c/sub\u003e\u003c/em\u003e\u003c/p\u003e\n \u003cp\u003e\u003cem\u003e(ps\u003csup\u003e8\u003c/sup\u003e/km)\u003c/em\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"11.160058737151248%\"\u003e\n \u003cp\u003e\u003cem\u003e\u0026beta;\u003csub\u003e9\u003c/sub\u003e\u003c/em\u003e\u003c/p\u003e\n \u003cp\u003e\u003cem\u003e(ps\u003csup\u003e9\u003c/sup\u003e/km)\u003c/em\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"8.223201174743025%\"\u003e\n \u003cp\u003e\u003cem\u003e\u0026gamma;\u003c/em\u003e\u003c/p\u003e\n \u003cp\u003e\u003cem\u003e(1/\u003c/em\u003e\u003cem\u003eW.km\u003c/em\u003e\u003cem\u003e)\u003c/em\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"11.160058737151248%\"\u003e\n \u003cp\u003ed\u003csub\u003e1\u003c/sub\u003e=0.26 \u0026micro;m\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"8.370044052863436%\"\u003e\n \u003cp\u003e25.1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.691629955947137%\"\u003e\n \u003cp\u003e0.02205\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.691629955947137%\"\u003e\n \u003cp\u003e-7.868e-6\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.691629955947137%\"\u003e\n \u003cp\u003e1.307e-7\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.691629955947137%\"\u003e\n \u003cp\u003e3.689e-9\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"11.160058737151248%\"\u003e\n \u003cp\u003e-8.73e-12\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"11.160058737151248%\"\u003e\n \u003cp\u003e-3.206e-12\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"11.160058737151248%\"\u003e\n \u003cp\u003e-6.98e-14\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"8.223201174743025%\"\u003e\n \u003cp\u003e93.1\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"11.160058737151248%\"\u003e\n \u003cp\u003ed\u003csub\u003e1\u003c/sub\u003e=0.31 \u0026micro;m\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"8.370044052863436%\"\u003e\n \u003cp\u003e24.25\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.691629955947137%\"\u003e\n \u003cp\u003e0.009306\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.691629955947137%\"\u003e\n \u003cp\u003e3.09e-5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.691629955947137%\"\u003e\n \u003cp\u003e5.88e-8\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.691629955947137%\"\u003e\n \u003cp\u003e3.997e-9\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"11.160058737151248%\"\u003e\n \u003cp\u003e-8.994e-12\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"11.160058737151248%\"\u003e\n \u003cp\u003e-3.412e-12\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"11.160058737151248%\"\u003e\n \u003cp\u003e-7.422e-14\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"8.223201174743025%\"\u003e\n \u003cp\u003e104.6\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"11.160058737151248%\"\u003e\n \u003cp\u003ed\u003csub\u003e1\u003c/sub\u003e=0.36\u0026nbsp;\u0026micro;m\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"8.370044052863436%\"\u003e\n \u003cp\u003e2.042\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.691629955947137%\"\u003e\n \u003cp\u003e0.0007783\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.691629955947137%\"\u003e\n \u003cp\u003e7.226e-5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.691629955947137%\"\u003e\n \u003cp\u003e-5.708e-8\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.691629955947137%\"\u003e\n \u003cp\u003e4.504e-9\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"11.160058737151248%\"\u003e\n \u003cp\u003e-9.67e-12\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"11.160058737151248%\"\u003e\n \u003cp\u003e-3.632e-12\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"11.160058737151248%\"\u003e\n \u003cp\u003e-7.894e-14\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"8.223201174743025%\"\u003e\n \u003cp\u003e117.9\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"11.160058737151248%\"\u003e\n \u003cp\u003ed\u003csub\u003e1\u003c/sub\u003e=0.41\u0026nbsp;\u0026micro;m\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"8.370044052863436%\"\u003e\n \u003cp\u003e14.74\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.691629955947137%\"\u003e\n \u003cp\u003e-0.003818\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.691629955947137%\"\u003e\n \u003cp\u003e0.000118\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.691629955947137%\"\u003e\n \u003cp\u003e-2.198e-7\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.691629955947137%\"\u003e\n \u003cp\u003e5.371e-9\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"11.160058737151248%\"\u003e\n \u003cp\u003e-1.217e-11\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"11.160058737151248%\"\u003e\n \u003cp\u003e-3.865e-12\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"11.160058737151248%\"\u003e\n \u003cp\u003e-8.416e-14\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"8.223201174743025%\"\u003e\n \u003cp\u003e133.2\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003c/table\u003e\n\u003c/div\u003e\n\u003cp\u003e\u003cbr\u003e\u003c/p\u003e\n\u003cp style=\"text-align: center;\"\u003e\u003cem\u003eTABLE II\u003c/em\u003e\u003c/p\u003e\n\u003cp style=\"text-align: center;\"\u003e\u003cem\u003eThe 10-dB bandwidths \u0026Delta;\u0026lambda; of SCG as well as the OCT axial resolutions l\u003csub\u003ec\u003c/sub\u003e calculated at each air-hole diameter d1.\u003c/em\u003e\u0026nbsp;\u003c/p\u003e\n\u003cdiv align=\"center\"\u003e\n \u003ctable border=\"1\" cellpadding=\"0\" cellspacing=\"0\"\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" width=\"34.437086092715234%\"\u003e\n \u003cp\u003e\u003cem\u003ed\u003csub\u003e1\u003c/sub\u003e(\u003c/em\u003e\u003cem\u003e\u0026micro;m\u003c/em\u003e\u003cem\u003e)\u003c/em\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"34.437086092715234%\"\u003e\n \u003cp\u003e\u003cem\u003e\u0026Delta;\u0026lambda;(nm)\u003c/em\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"31.125827814569536%\"\u003e\n \u003cp\u003e\u003cem\u003el\u003csub\u003ec\u003c/sub\u003e(\u0026micro;m)\u003c/em\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" width=\"34.437086092715234%\"\u003e\n \u003cp\u003e0.26 \u0026micro;m\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"34.437086092715234%\"\u003e\n \u003cp\u003e27.2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"31.125827814569536%\"\u003e\n \u003cp\u003e10.4\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" width=\"34.437086092715234%\"\u003e\n \u003cp\u003e0.31 \u0026micro;m\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"34.437086092715234%\"\u003e\n \u003cp\u003e29.3\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"31.125827814569536%\"\u003e\n \u003cp\u003e9.6\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" width=\"34.437086092715234%\"\u003e\n \u003cp\u003e0.36 \u0026micro;m\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"34.437086092715234%\"\u003e\n \u003cp\u003e33.7\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"31.125827814569536%\"\u003e\n \u003cp\u003e8.4\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" width=\"34.437086092715234%\"\u003e\n \u003cp\u003e0.41 \u0026micro;m\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"34.437086092715234%\"\u003e\n \u003cp\u003e41.5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"31.125827814569536%\"\u003e\n \u003cp\u003e6.8\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003c/table\u003e\n\u003c/div\u003e\n\u003cp style=\"text-align: center;\"\u003e\u003cbr\u003e\u003c/p\u003e\n\u003cp style=\"text-align: center;\"\u003eTABLE III\u003c/p\u003e\n\u003cp style=\"text-align: center;\"\u003e\u003cem\u003eThe 10-dB bandwidths of SCG as well as the OCT axial resolutions calculated at each pump width T0. The air-hole diameter is d1=0.41\u0026micro;m.\u003c/em\u003e\u003c/p\u003e\n\u003cdiv align=\"center\"\u003e\n \u003ctable border=\"1\" cellpadding=\"0\" cellspacing=\"0\"\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" width=\"26.760563380281692%\"\u003e\n \u003cp style=\"text-align: center;\"\u003e\u003cem\u003eT\u003csub\u003e0\u003c/sub\u003e\u003c/em\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"36.61971830985915%\"\u003e\n \u003cp style=\"text-align: center;\"\u003e\u003cem\u003e\u0026Delta;\u0026lambda;(nm)\u003c/em\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"36.61971830985915%\"\u003e\n \u003cp style=\"text-align: center;\"\u003e\u003cem\u003el\u003csub\u003ec\u003c/sub\u003e(\u0026micro;m)\u003c/em\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" width=\"26.760563380281692%\"\u003e\n \u003cp style=\"text-align: center;\"\u003e1.5ps\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"36.61971830985915%\"\u003e\n \u003cp style=\"text-align: center;\"\u003e41.5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"36.61971830985915%\"\u003e\n \u003cp style=\"text-align: center;\"\u003e6.8\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" width=\"26.760563380281692%\"\u003e\n \u003cp style=\"text-align: center;\"\u003e1.0ps\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"36.61971830985915%\"\u003e\n \u003cp style=\"text-align: center;\"\u003e43.0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"36.61971830985915%\"\u003e\n \u003cp style=\"text-align: center;\"\u003e6.6\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" width=\"26.760563380281692%\"\u003e\n \u003cp style=\"text-align: center;\"\u003e0.5ps\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"36.61971830985915%\"\u003e\n \u003cp style=\"text-align: center;\"\u003e44.5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"36.61971830985915%\"\u003e\n \u003cp style=\"text-align: center;\"\u003e6.3\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" width=\"26.760563380281692%\"\u003e\n \u003cp style=\"text-align: center;\"\u003e200fs\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"36.61971830985915%\"\u003e\n \u003cp style=\"text-align: center;\"\u003e45.3\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"36.61971830985915%\"\u003e\n \u003cp style=\"text-align: center;\"\u003e6.2\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" width=\"26.760563380281692%\"\u003e\n \u003cp style=\"text-align: center;\"\u003e100fs\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"36.61971830985915%\"\u003e\n \u003cp style=\"text-align: center;\"\u003e46.7\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"36.61971830985915%\"\u003e\n \u003cp style=\"text-align: center;\"\u003e6.0\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" width=\"26.760563380281692%\"\u003e\n \u003cp style=\"text-align: center;\"\u003e80fs\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"36.61971830985915%\"\u003e\n \u003cp style=\"text-align: center;\"\u003e47.7\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"36.61971830985915%\"\u003e\n \u003cp style=\"text-align: center;\"\u003e5.9\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" width=\"26.760563380281692%\"\u003e\n \u003cp style=\"text-align: center;\"\u003e50fs\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"36.61971830985915%\"\u003e\n \u003cp style=\"text-align: center;\"\u003e51.8\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"36.61971830985915%\"\u003e\n \u003cp style=\"text-align: center;\"\u003e5.4\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" width=\"26.760563380281692%\"\u003e\n \u003cp style=\"text-align: center;\"\u003e30fs\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"36.61971830985915%\"\u003e\n \u003cp style=\"text-align: center;\"\u003e62.0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"36.61971830985915%\"\u003e\n \u003cp style=\"text-align: center;\"\u003e4.5\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003c/table\u003e\n\u003c/div\u003e\n\u003cp\u003e\u003cbr\u003e\u003c/p\u003e\n\u003cp style=\"text-align: center;\"\u003eTABLE IV\u003c/p\u003e\n\u003cp style=\"text-align: center;\"\u003e\u003cem\u003eThe 10-dB bandwidths of SCG as well as the OCT axial resolutions calculated at different pump peak powers. The air-hole diameter and the pump width are fixed at d1=0.41\u0026micro;m and T0=30fs, respectively.\u003c/em\u003e\u0026nbsp;\u003c/p\u003e\n\u003cdiv align=\"center\"\u003e\n \u003ctable border=\"1\" cellpadding=\"0\" cellspacing=\"0\"\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" width=\"27.60942760942761%\"\u003e\n \u003cp\u003eP\u003csub\u003e0\u0026nbsp;\u003c/sub\u003e(W)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"43.77104377104377%\"\u003e\n \u003cp\u003e\u0026Delta;\u0026lambda;(nm)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"28.61952861952862%\"\u003e\n \u003cp\u003el\u003csub\u003ec\u003c/sub\u003e(\u0026micro;m)\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" width=\"27.60942760942761%\"\u003e\n \u003cp\u003e150\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"43.77104377104377%\"\u003e\n \u003cp\u003e41.5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"28.61952861952862%\"\u003e\n \u003cp\u003e6.8\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" width=\"27.60942760942761%\"\u003e\n \u003cp\u003e300\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"43.77104377104377%\"\u003e\n \u003cp\u003e76.5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"28.61952861952862%\"\u003e\n \u003cp\u003e3. 7\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" width=\"27.60942760942761%\"\u003e\n \u003cp\u003e450\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"43.77104377104377%\"\u003e\n \u003cp\u003e88.8\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"28.61952861952862%\"\u003e\n \u003cp\u003e3.2\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" width=\"27.60942760942761%\"\u003e\n \u003cp\u003e600\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"43.77104377104377%\"\u003e\n \u003cp\u003e99.5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"28.61952861952862%\"\u003e\n \u003cp\u003e2.8\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" width=\"27.60942760942761%\"\u003e\n \u003cp\u003e750\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"43.77104377104377%\"\u003e\n \u003cp\u003e109.0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"28.61952861952862%\"\u003e\n \u003cp\u003e2.6\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003c/table\u003e\n\u003c/div\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"photonic crystal fiber, optical coherence tomography, supercontinuum generation, axial resolution, ophthalmology","lastPublishedDoi":"10.21203/rs.3.rs-2100413/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-2100413/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eOptical coherence tomography (OCT) is a new technology for high-resolution cross-sectional images of biological tissues. In this paper, we design photonic crystal fibers (PCFs) made of silica with proper dispersion characteristics about the center wavelength of 800 nm to simulate supercontinuum generation (SCG) which is desired for high-resolution OCT in ophthalmology. Several types of PCFs with different air-hole diameters are designed where squared hyperbolic secant pulses are input to simulate SCG by solving generalized nonlinear Schrodinger equation (GNLSE) via split-step Fourier method. To obtain more accurate SCG, dispersion coefficients up to the 9th order, Raman scattering and self-steepening are taken into account. We examine impacts of air-hole diameter, input pulse width and pulse peak power on the SCG bandwidth as well as the OCT resolution through which suitable parameters for maximum axial resolution in ophthalmology are determined.\u003c/p\u003e","manuscriptTitle":"Supercontinuum Generation in Silica-Based Photonic Crystal Fibers for High-Resolution Ophthalmic Optical Coherence Tomography","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2022-10-10 16:33:31","doi":"10.21203/rs.3.rs-2100413/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"ab321b66-4613-46f7-89b2-4610cb52f4e0","owner":[],"postedDate":"October 10th, 2022","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2023-01-02T13:44:27+00:00","versionOfRecord":[],"versionCreatedAt":"2022-10-10 16:33:31","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-2100413","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-2100413","identity":"rs-2100413","version":["v1"]},"buildId":"7rjqhiLT3MXkJMwkYKINL","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}