1
|
Algorithm for Solving a System of Coupled Nonlinear Schrödinger Equations by the Split-Step Method to Describe the Evolution of a High-Power Femtosecond Optical Pulse in an Optical Polarization Maintaining Fiber. FIBERS 2022. [DOI: 10.3390/fib10030022] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
Abstract
This article proposes an advanced algorithm for the numerical solution of a coupled nonlinear Schrödinger equations system describing the evolution of a high-power femtosecond optical pulse in a single-mode polarization-maintaining optical fiber. We use the algorithm based on a variant of the split-step method with the Madelung transform to calculate the complex amplitude when executing a nonlinear operator. In contrast to the known solution, the proposed algorithm eliminates the need to numerically solve differential equations directly, concerning the phase of complex amplitude when executing the nonlinear operator. This made it possible, other things being equal, to reduce the computation time by more than four times.
Collapse
|
2
|
Original Solution of Coupled Nonlinear Schrödinger Equations for Simulation of Ultrashort Optical Pulse Propagation in a Birefringent Fiber. FIBERS 2020. [DOI: 10.3390/fib8060034] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
Abstract
This paper discusses approaches to the numerical integration of the coupled nonlinear Schrödinger equations system, different from the generally accepted approach based on the method of splitting according to physical processes. A combined explicit/implicit finite-difference integration scheme based on the implicit Crank–Nicolson finite-difference scheme is proposed and substantiated. It allows the integration of a nonlinear system of equations with a choice of nonlinear terms from the previous integration step. The main advantages of the proposed method are: its absolute stability through the use of an implicit finite-difference integration scheme and an integrated mechanism for refining the numerical solution at each step; integration with automatic step selection; performance gains (or resolutions) up to three or more orders of magnitude due to the fact that there is no need to produce direct and inverse Fourier transforms at each integration step, as is required in the method of splitting according to physical processes. An additional advantage of the proposed method is the ability to calculate the interaction with an arbitrary number of propagation modes in the fiber.
Collapse
|
3
|
Andreana M, Le T, Drexler W, Unterhuber A. Ultrashort pulse Kagome hollow-core photonic crystal fiber delivery for nonlinear optical imaging. OPTICS LETTERS 2019; 44:1588-1591. [PMID: 30933097 DOI: 10.1364/ol.44.001588] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/12/2023]
Abstract
We report ultrashort pulse delivery through a hypocycloid-core inhibited-coupling Kagome hollow-core photonic crystal fiber (HC-PCF). Undistorted 10 fs and 6.6 nJ pulses were launched through 1 m long fiber without fiber dispersion pre-compensation and 80% efficiency. The performance of this technology for biomedical imaging is demonstrated on a biological sample by incorporating the fiber into a two-photon excited fluorescence (TPEF) laser scanning microscope (LSM) achieving a pulse width of 15 fs at the sample location. To the best of our knowledge, this is the first report on undistorted TPEF imaging in a LSM with 15 fs pulses delivered through a 1 m long Kagome HC-PCF with high throughput.
Collapse
|
4
|
Tu H, Boppart SA. Coherent fiber supercontinuum for biophotonics. LASER & PHOTONICS REVIEWS 2013; 7:10.1002/lpor.201200014. [PMID: 24358056 PMCID: PMC3864867 DOI: 10.1002/lpor.201200014] [Citation(s) in RCA: 41] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/30/2012] [Accepted: 07/05/2012] [Indexed: 05/17/2023]
Abstract
Biophotonics and nonlinear fiber optics have traditionally been two independent fields. Since the discovery of fiber-based supercontinuum generation in 1999, biophotonics applications employing incoherent light have experienced a large impact from nonlinear fiber optics, primarily because of the access to a wide range of wavelengths and a uniform spatial profile afforded by fiber supercontinuum. However, biophotonics applications employing coherent light have not benefited from the most well-known techniques of supercontinuum generation for reasons such as poor coherence (or high noise), insufficient controllability, and inadequate portability. Fortunately, a few key techniques involving nonlinear fiber optics and femtosecond laser development have emerged to overcome these critical limitations. Despite their relative independence, these techniques are the focus of this review, because they can be integrated into a low-cost portable biophotonics source platform. This platform can be shared across many different areas of research in biophotonics, enabling new applications such as point-of-care coherent optical biomedical imaging.
Collapse
Affiliation(s)
- Haohua Tu
- Biophotonics Imaging Laboratory, Beckman Institute for Advanced Science and Technology, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA
| | - Stephen A Boppart
- Biophotonics Imaging Laboratory, Beckman Institute for Advanced Science and Technology, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA
| |
Collapse
|
5
|
Pawłowska M, Patas A, Achazi G, Lindinger A. Parametrically shaped femtosecond pulses in the nonlinear regime obtained by reverse propagation in an optical fiber. OPTICS LETTERS 2012; 37:2709-11. [PMID: 22743503 DOI: 10.1364/ol.37.002709] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/09/2023]
Abstract
We present the experimental realization of a method to generate predetermined, arbitrary pulse shapes after transmission through an optical fiber in the nonlinear regime. The method is based on simulating the reverse propagation of the desired pulse shape in the fiber. First, linear and nonlinear parameters of a single-mode step-index fiber required for the simulation are determined. The calculated pulse shapes are then generated in a pulse shaper.
Collapse
Affiliation(s)
- Monika Pawłowska
- Institut für Experimentalphysik, Freie Universität Berlin, Arnimallee 14, D-14195 Berlin, Germany. monika.pawlowska@fu‐berlin.de
| | | | | | | |
Collapse
|
6
|
Wang W, Liu Y, Xi P, Ren Q. Origin and effect of high-order dispersion in ultrashort pulse multiphoton microscopy in the 10 fs regime. APPLIED OPTICS 2010; 49:6703-6709. [PMID: 21151226 DOI: 10.1364/ao.49.006703] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/30/2023]
Abstract
Short pulses can induce high nonlinear excitation, and thus they should be favorable for use in multiphoton microscopy. However, the large spectral dispersion can easily destroy the advantages of the ultrashort pulse if there is no compensation. The group delay dispersion (GDD), third-order dispersion, and their effects on the intensity and bandwidth of second-harmonic generation (SHG) signal were analyzed. We found that the prism pair used for compensating the GDD of the two-photon microscope actually introduces significant negative high-order dispersion (HOD), which dramatically narrowed down the two-photon absorption probability for ultrashort pulses. We also investigated the SHG signal after GDD and HOD compensation for different pulse durations. Without HOD compensation, the SHG efficiency dropped significantly for a pulse duration below 20 fs. We experimentally compared the SHG and two-photon excited fluorescence (TPEF) signal intensity for 11 fs versus 50 fs pulses, a pulse duration close to that commonly used in conventional multiphoton microscopy. The result suggested that after adaptive phase compensation, the 11fs pulse can yield a 3.2- to 6.0-fold TPEF intensity and a 5.1-fold SHG intensity, compared to 50 fs pulses.
Collapse
Affiliation(s)
- Weichao Wang
- Department of Biomedical Engineering, School of Life Sciences and Biotechnology, Shanghai Jiao Tong University, No. 800 Dong-Chuan Road, Shanghai 200240, China
| | | | | | | |
Collapse
|
7
|
Liang X, Hu W, Fu L. Pulse compression in two-photon excitation fluorescence microscopy. OPTICS EXPRESS 2010; 18:14893-14904. [PMID: 20639976 DOI: 10.1364/oe.18.014893] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/29/2023]
Abstract
The use of shorter pulses is a practical way to improve the signal in two-photon excitation fluorescence microscopy. We report on the theoretical and experimental results of pulse compression in a two-photon excitation fluorescence microscope by using approximately 100-fs Ti:Sapphire laser and highly nonlinear photonic crystal fiber. Effects of the fiber parameters, transmitted power, and group-delay dispersion provided by the gratings have been investigated to optimize the compressor performance. By using a 20-mm-long photonic crystal fiber with a zero dispersion wavelength of 850 nm, a compressed pulse of 23.6 fs starting from 94 fs at 790 nm is experimentally demonstrated as a verification of our simulations. By integrating the compressor with a two-photon excitation fluorescence microscope, 5.6 times increase in autofluorescence intensity of NAD(P)H in Nasopharyngeal carcinoma cells is demonstrated, showing its potential in enhanced imaging and sensing for disease diagnosis.
Collapse
Affiliation(s)
- Xiaobao Liang
- Britton Chance Center for Biomedical Photonics, Wuhan National Laboratory for Optoelectronics, Huazhong University of Science and Technology, Wuhan 430074, China
| | | | | |
Collapse
|
8
|
Kang JW, Kim P, Alonzo CA, Park H, Yun SH. Two-photon microscopy by wavelength-swept pulses delivered through single-mode fiber. OPTICS LETTERS 2010; 35:181-3. [PMID: 20081961 PMCID: PMC2884992 DOI: 10.1364/ol.35.000181] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/21/2023]
Abstract
Nonlinear microscopy through flexible fiber-optic catheters has potential in clinical diagnostic applications. Here, we demonstrate a new approach based on wavelength-swept narrowband pulses that permits simple fiber-optic delivery without need of the dispersion management and allows nonmechanical beam scanning. Using 0.86 ps pulses rapidly tuned from 789 nm to 822 nm at a sweep rate of 200 Hz, we demonstrate two-photon fluorescence and second-harmonic generation imaging through a 5-m-long standard single-mode fiber.
Collapse
Affiliation(s)
- Jeon Woong Kang
- Harvard Medical School and Wellman Center for Photomedicine, Massachusetts General Hospital, 50 Blossom Street, BAR-8, Boston, Massachusetts 02114, USA
| | - Pilhan Kim
- Harvard Medical School and Wellman Center for Photomedicine, Massachusetts General Hospital, 50 Blossom Street, BAR-8, Boston, Massachusetts 02114, USA
| | - Carlo Amadeo Alonzo
- Harvard Medical School and Wellman Center for Photomedicine, Massachusetts General Hospital, 50 Blossom Street, BAR-8, Boston, Massachusetts 02114, USA
| | - Hyunsung Park
- Harvard Medical School and Wellman Center for Photomedicine, Massachusetts General Hospital, 50 Blossom Street, BAR-8, Boston, Massachusetts 02114, USA
- Graduate School of Nanoscience and Technology and WCU Program, KAIST, 335 Gwahak-ro, Yuseong-gu, Daejeon 305-701, Korea
| | - Seok H. Yun
- Harvard Medical School and Wellman Center for Photomedicine, Massachusetts General Hospital, 50 Blossom Street, BAR-8, Boston, Massachusetts 02114, USA
- Graduate School of Nanoscience and Technology and WCU Program, KAIST, 335 Gwahak-ro, Yuseong-gu, Daejeon 305-701, Korea
- Corresponding author:
| |
Collapse
|
9
|
Le T, Tempea G, Cheng Z, Hofer M, Stingl A. Routes to fiber delivery of ultra-short laser pulses in the 25 fs regime. OPTICS EXPRESS 2009; 17:1240-1247. [PMID: 19188951 DOI: 10.1364/oe.17.001240] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/26/2023]
Abstract
Femtosecond laser pulses came of age and found applications in many fields of life-sciences that call for dispersion-managed guiding of very short optical pulses. We investigate the potential for delivering 25-fs, nanojoule pulses from a Ti:Sapphire laser through optical fibers with lengths of up to 2m.
Collapse
Affiliation(s)
- Tuan Le
- Femtolasers Produktions GmbH, Vienna, Austria.
| | | | | | | | | |
Collapse
|