Nonlinear fiber mirror based on kerr lens effect

Abstract

The application discloses a reflection type nonlinear fiber mirror based on Kerr lens effect, and relates to the technical field of nonlinear optics and fiber laser, which comprises a single-mode optical fiber, a lens group (containing a single lens or a lens group composed of multiple lenses) for collimation and focusing, a nonlinear wafer and a mirror; the light beam output by the single-mode optical fiber is collimated and focused by the lens group, is incident to the nonlinear wafer, and is reflected by the mirror to return to the single-mode optical fiber along the original light path; the nonlinear wafer has a very high nonlinear refractive coefficient, so that the Kerr self-focusing effect is generated when the incident light intensity increases. The application has the advantages of fast response, compact structure, easy integration with the fiber system and the like, improves the integration degree of the system, and is suitable for passive mode locking and intensity-dependent reflection modulation in an ultrafast fiber laser.

Description

Technical Field

[0001] This invention relates to the field of nonlinear optics and fiber laser technology, and in particular to a nonlinear fiber optic mirror based on the Kerr lens effect. Background Technology

[0002] Generating and controlling ultrafast laser pulses is a key technology driving precision measurement, advanced manufacturing, and cutting-edge scientific research. Passive mode-locking technology, due to its ability to generate ultrashort pulses on the femtosecond and even picosecond scales, has become one of the core solutions for achieving ultrafast laser output. The physical essence of this technology lies in introducing intensity-related losses or phase modulation within the laser resonant cavity through optical nonlinearity, thereby achieving the self-formation and stabilization of the pulse.

[0003] In the field of solid-state lasers, Kerr lens mode-locking (KLM) technology has been widely applied. This technology utilizes the self-focusing effect caused by the Kerr nonlinearity of the gain medium itself, combined with the cavity aperture, to achieve intensity-dependent loss modulation. Its greatest advantage lies in its extremely fast nonlinear response, reaching the femtosecond level, without involving slow processes such as carrier dynamics. However, KLM technology heavily relies on precise free-space confocal cavity design and spatial filtering, resulting in a complex system that is sensitive to mechanical vibrations. Furthermore, its spatial self-focusing physical mechanism is difficult to directly transfer to all-fiber systems that prioritize structural simplicity, compactness, and robustness.

[0004] Fiber passive mode-locking technology, through the deep synergy of waveguide nonlinearity and all-fiber architecture, overcomes the limitations of poor robustness and cumbersome maintenance of solid-state mode-locking systems; however, its inherent physical bottlenecks still restrict performance breakthroughs. Nonlinear polarization rotation technology utilizes the nonlinear birefringence effect in optical fibers to achieve mode-locking. While it can generate extremely short pulses, its traditional non-polarization-maintaining structure is extremely sensitive to environmental temperature and vibration, posing stability challenges. Nonlinear optical loop mirrors and their variants, based on the Sagnac interferometer structure and nonlinear phase shift, can achieve excellent environmental stability when designed with all-polarization-maintaining fibers, but often face difficulties in self-starting. The Mamyshev oscillator, developed in recent years, can generate extremely high pulse energies, but its self-starting usually relies on external pulse injection or complex preprocessing. Furthermore, semiconductor saturable absorbers, as a general-purpose discrete saturable absorber, are used in both solid-state and fiber lasers; however, their response speed is limited by the carrier lifetime of the semiconductor material, typically on the picosecond scale, and their interband absorption-based operating mechanism is prone to thermal damage at high power, limiting their power enhancement potential.

[0005] Therefore, existing technologies still lack a reflective nonlinear device capable of providing ultrafast intensity-dependent loss modulation in fiber-coupled structures without relying on traditional saturable absorbers and complex free-space KLM cavity designs. Based on this, this invention proposes a nonlinear fiber optic mirror that utilizes the Kerr lensing effect to modify the round-trip beam mode matching conditions, thus balancing response speed, structural compactness, tunability, and environmental stability. Summary of the Invention

[0006] The technical problem to be solved by the present invention is to provide a reflective nonlinear fiber optic device based on the Kerr lens effect, so as to achieve ultrafast and tunable intensity-dependent loss modulation without the need for traditional saturable absorbers and complex free-space KLM cavity structures, thereby improving the device's integration, parameter tunability and environmental stability.

[0007] To solve the above-mentioned technical problems, the technical solution of the present invention is as follows: A nonlinear fiber optic reflector based on the Kerr lens effect includes a single-mode fiber, a lens group, a nonlinear thin film, and a reflector. The beam output from the single-mode fiber is collimated and focused by the lens group, then incident on the nonlinear thin film, and reflected by the reflector back to the single-mode fiber along the original optical path. The nonlinear thin film has a positive nonlinear refractive index. When the incident light intensity increases, the nonlinear thin film induces self-focusing due to the Kerr effect, which can be equivalent to a lens whose focal length changes with light intensity. This causes the beam's focal point to shift forward, thereby changing the mode matching condition between the returning beam and the fundamental mode of the single-mode fiber. By adjusting the position of the reflector relative to the nonlinear thin film, the system exhibits an equivalent saturable absorption characteristic within a preset power range, where the back-coupling loss decreases with increasing incident power. The coupling efficiency reaches its peak at the corresponding incident power; further increasing the incident power reduces the coupling efficiency, exhibiting a reverse saturable absorption characteristic.

[0008] The above-described solutions of the present invention include at least the following beneficial effects.

[0009] This invention separates the core physical mechanism of Kerr lens mode-locking in solid-state lasers—the intensity-dependent lens effect—from the gain medium and reconstructs it into an independent reflective device that can be coupled to the fiber end face. This facilitates integration with fiber laser cavities, reduces the dependence of traditional KLM technology on complex free-space optical paths, and enables femtosecond-level fast nonlinear responses to be integrated into an all-fiber laser resonator in a simple and compact manner, greatly improving the system's integration and environmental stability.

[0010] The core working mechanism of the device is the optical Kerr lens effect, which does not rely on the carrier recovery process. Therefore, it has the potential for ultrafast response, possibly even reaching the femtosecond level, far faster than semiconductor saturable absorber mirrors based on carrier recombination. Meanwhile, its switching function is mainly achieved through beam mode mismatch caused by refractive index changes, rather than relying on the intrinsic strong absorption and saturation of the material. This theoretically avoids the thermal damage risk caused by interband absorption in SESAMs, providing a physical basis for handling higher peak and average power.

[0011] By systematically adjusting parameters such as the thickness of the nonlinear slab, the beam waist radius of the incident beam, and the axial position of the mirror, key performance indicators of the device can be optimized independently and collaboratively, allowing for the design of peak coupling power, modulation depth, and coupling efficiency curve shapes. This high degree of design flexibility enables the device to adapt to laser systems with different power levels and pulse dynamics requirements (such as continuous mode-locking or Q-switched mode-locking). Because the device employs a reflective common-path design, its core operating mechanism does not rely on nonlinear polarization rotation effects, thus effectively reducing the high sensitivity of traditional nonlinear polarization rotation techniques to environmental disturbances. Attached Figure Description

[0012] Figure 1 The present invention relates to a nonlinear fiber optic reflector based on the Kerr lens effect.

[0013] Figure 2 The simulation results are for the equivalent saturable absorption characteristics of the nonlinear reflector based on the 33Ge-12As-55Se glass nonlinear thin film of the present invention. Figure 2 In the figure (a), the coupling efficiency η and the mode field matching efficiency η are respectively. mode With loss efficiency η L With incident power P in The curve of change; Figure 2 (b) represents the positive direction f f With the opposite f b Evolution of the focal length of a Kerr lens within a thin film.

[0014] Figure 3 This demonstrates the relationship between the nonlinear sheet thickness d and the Rayleigh distance Z of the beam. R The influence of the equivalent saturable absorption characteristics of a nonlinear mirror based on chalcogenide glass (33Ge-12As-55Se) on the following: Figure 3 Figure (a) shows the curves of coupling efficiency η as a function of the thickness d of the nonlinear sheet (d = 100-500 μm, with 100 μm intervals). Figure 3 In the middle (b), the corresponding maximum coupling power P is... max (Blue curve) and modulation depth η max -η0 (red curve); Figure 3Figure (c) shows the coupling efficiency η as a function of the Rayleigh distance Z of the beam. R The curve of the variation of (waist ω0); Figure 3 In the middle (d), P is the corresponding P. max With modulation depth η max -η0.

[0015] Figure 4 The effect of the structural parameters (u and v) of the nonlinear mirror on the equivalent saturable absorption performance of the chalcogenide glass (33Ge-12As-55Se) nonlinear mirror is demonstrated. Figure 4 The effects of the normalized offset u were studied in (a) and (b); Figure 4 In (c) and (d), the effect of the normalized distance v was studied. Detailed Implementation

[0016] Exemplary embodiments of the present disclosure will now be described in more detail with reference to the accompanying drawings. While exemplary embodiments of the present disclosure are shown in the drawings, it should be understood that the present disclosure may be implemented in various forms and should not be limited to the embodiments set forth herein. Rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the scope of the disclosure to those skilled in the art.

[0017] This invention proposes a reflective nonlinear fiber optic mirror based on the Kerr lens effect, comprising a single-mode fiber, a lens group (including a single lens or a lens group composed of multiple lenses) for collimation and focusing, a nonlinear thin film, and a reflector. The beam output from the single-mode fiber is collimated and focused sequentially by the lens group, then incident on the nonlinear thin film, and reflected by the reflector back to the single-mode fiber along the original optical path. The nonlinear thin film has a positive nonlinear refractive index. When the incident light intensity increases, the Kerr effect induces self-focusing, making the nonlinear thin film equivalent to a lens whose focal length varies with the incident light intensity. This causes the beam focal point to shift forward. By adjusting the geometric position of the reflector, the system achieves corresponding mode field matching, and the coupling efficiency reaches its peak at the corresponding incident power, thus realizing the equivalent saturable absorption characteristic with reduced loss as power increases. The position of the reflector is adjustable along the optical axis. By adjusting it to the beam focal point position at a specific power, the coupling efficiency between the returned beam and the fiber reaches its peak at a preset incident power, thereby manifesting the equivalent saturable absorption function.

[0018] In this embodiment of the invention, the device relies on the optical Kerr effect to dynamically change the equivalent optical properties of the nonlinear thin film with the incident light intensity. As the incident light intensity increases, the thin film is equivalent to a lens with a focal length that changes with the light intensity. With the help of an adjustable mirror to precisely match the focal point, the coupling efficiency between the returned beam and the single-mode fiber can reach its peak under a specific incident power, thereby manifesting the equivalent saturable absorption function. The entire process does not require additional electronically controlled modulation elements, relying on a purely optical mechanism to achieve dynamic control. It has a fast response speed and does not depend on the carrier recovery process, thus possessing ultrafast response potential, especially suitable for the generation of ultrashort pulse lasers. At the same time, the adjustable design of the mirror along the optical axis can flexibly adapt to laser systems with different incident powers, achieving precise control of the equivalent saturable absorption threshold, solving the problems of fixed threshold and poor adaptability of traditional saturable absorbers.

[0019] The chalcogenide glass sheet used in the device has a high nonlinear refractive index and a high optical damage threshold, which can withstand long-term irradiation by high-power lasers and is suitable for high-power fiber laser systems. The lens group adopts a collimation and focusing structure. The lens group efficiently collimates the diverging beam output from the single-mode fiber into parallel light, and then accurately focuses the parallel light onto the surface of the nonlinear sheet. This greatly reduces the divergence loss during beam transmission, improves the interaction efficiency between light and nonlinear materials, and ensures that changes in incident light intensity can quickly and significantly trigger the Kerr lensing effect, thus guaranteeing the stability and reliability of the equivalent saturable absorption function.

[0020] The device employs a single-mode fiber direct access optical path design, allowing for seamless integration with existing fiber laser systems without the need for complex beam coupling and conversion devices, significantly reducing the difficulty and overall cost of laser system construction. Simultaneously, its compact structure and small size facilitate integration into miniaturized, portable laser devices, expanding its application scenarios in laser processing, laser communication, and laser ranging. The core control mechanism of the device is a purely optical process, without the involvement of electronic components, avoiding issues such as electronic component aging and response delays. The selected chalcogenide glass exhibits stable chemical properties, strong resistance to environmental interference, and a high optical damage threshold, enabling it to withstand long-term irradiation by high-power lasers, extending the device's lifespan and reducing the subsequent maintenance costs of the laser system.

[0021] In a preferred embodiment of the present invention, the light intensity-dependent transmission characteristics of the nonlinear thin sheet are analyzed using a piecewise model, specifically including: The thin film is divided into N segments along the optical axis, and each segment is equivalent to a combination of a thin lens with light intensity-dependent focal length and a linear dielectric layer. By sequentially calculating the nonlinear refractive index change, light intensity attenuation, and corresponding transmission matrix of the beam in each segment, and then multiplying the transmission matrices of all segments in sequence, the total transmission matrix of the nonlinear sheet is obtained, which is used to describe the transformation of the beam after passing through the nonlinear medium.

[0022] In this embodiment of the invention, the required core parameters are first clearly analyzed, including the material properties of the nonlinear thin sheet (such as refractive index, nonlinear refractive coefficient, linear absorption coefficient, and two-photon absorption coefficient), geometric parameters (total thickness of the medium), and initial parameters of the incident beam (such as the incident beam radius, initial light intensity, and center wavelength). The nonlinear thin sheet is uniformly divided into N segments along the optical axis, and the thickness of each segment is the ratio of the total thickness of the thin sheet to the number of segments N. The number of segments needs to be reasonably selected according to the thickness of the thin sheet (e.g., N=500 for thick sheets, and N=5 for nanoscale thin sheets) to ensure that the thickness of each segment is small enough to accurately capture the local light intensity-dependent nonlinear characteristics. Each segment of the nonlinear thin sheet is equivalent to a combination structure of a thin lens with light intensity-dependent focal length and a linear medium layer. The linear dielectric layer describes the linear propagation behavior of light within this segment, while the thin lens specifically characterizes the nonlinear focusing effect caused by the optical Kerr effect. For each segment, the average light intensity of the incident light and the outgoing light intensity (i.e., the average light intensity of the segment) are first obtained. Then, combined with the nonlinear refractive index of the material, the corresponding nonlinear refractive index change is calculated. This change directly reflects the modulation effect of light intensity on the optical properties of the material. Based on the nonlinear refractive index change, segment thickness, and the beam spot radius incident on the segment, the intensity-dependent focal length of the equivalent thin lens for that segment is determined. The higher the light intensity, the more significant the nonlinear refractive index change, and the shorter the focal length of the equivalent thin lens, reflecting the self-focusing characteristics of the Kerr lens. Considering the energy loss of the beam during its propagation in this segment, the outgoing light intensity after passing through the segment is calculated based on the linear absorption coefficient and two-photon absorption coefficient of the material, combined with the light intensity incident on the segment, thus quantifying the intensity attenuation.

[0023] The transmission matrix of the linear dielectric layer (describing the propagation transformation of light in a linear medium) and the transmission matrix of the thin lens (describing the nonlinear focusing transformation) are established separately. These two matrices are then multiplied in the order of beam propagation to obtain the total transmission matrix for that single segment, fully characterizing the light propagation and nonlinear modulation effects of that segment. Starting from the first segment at the incident end, the outgoing light intensity and spot radius of the previous segment are used as the incident parameters for the next segment. The nonlinear refractive index changes, light intensity attenuation, and transmission matrix calculations for all N segments are performed sequentially, ensuring that the calculation for each segment is based on the actual local light intensity after propagation, guaranteeing the accuracy of the results. The transmission matrices of all N segments are multiplied sequentially in segmental order (matrix product from the Nth segment to the first segment) to finally obtain the total transmission matrix of the entire nonlinear thin sheet. This total matrix can fully describe the comprehensive transformation effect of the beam after passing through the nonlinear thin sheet, including changes in key parameters such as spot radius and radius of curvature.

[0024] In a preferred embodiment of the present invention, the specific implementation process of the segmentation model is as follows: Based on the nonlinear refractive index of the nonlinear thin sheet and the average light intensity within the segment, the change in nonlinear refractive index caused by the optical Kerr effect in each segment of the medium is calculated. The intensity attenuation of the beam in each segment is calculated based on the linear absorption coefficient and two-photon absorption coefficient of the nonlinear thin sheet. Based on the nonlinear refractive index change and the beam spot radius before segmentation, the focal length of each equivalent thin lens is determined, and the transmission matrix of the segment is constructed in combination with the segment thickness. The beam is passed through the transmission matrices of all N segments in the order of light propagation, and the total transmission matrix of the beam for the nonlinear sheet is obtained. The total transmission matrix is ​​used to characterize the beam parameter transformation caused by the Kerr lensing effect.

[0025] In this embodiment of the invention, the core parameters of the nonlinear thin film are defined, including the nonlinear refractive index, linear absorption coefficient, and two-photon absorption coefficient of the material itself. At the same time, basic information such as the total thickness of the thin film, the initial light intensity of the incident beam, the spot radius, and the center wavelength are recorded. The nonlinear thin film is uniformly divided into N segments along the optical axis. The number of segments needs to be reasonably set in combination with the total thickness of the thin film to ensure that the thickness of each segment is small enough to accurately capture the influence of local light intensity on optical properties, while taking into account both computational efficiency and result accuracy.

[0026] For each segment of the medium, the initial incident light intensity and the outgoing light intensity after passing through the segment are first obtained, and the average of the two is taken as the average light intensity within the segment. Then, combined with the pre-determined nonlinear refractive index of the material, the nonlinear refractive index change caused by the light intensity in the medium segment is calculated by analyzing the effect of the optical Kerr effect, thus quantifying the degree of modulation of the optical properties of the medium by the light intensity. Based on the linear absorption coefficient and two-photon absorption coefficient of the thin film material, the energy loss of the beam by the two absorption mechanisms is analyzed. Linear absorption corresponds to the basic energy attenuation of the beam, while two-photon absorption is related to the light intensity and produces additional attenuation. Combining the incident light intensity and the segment thickness, the average light intensity after passing through the segment is calculated. The intensity attenuation after the incident light is determined to establish the output light intensity of each segment, providing incident light intensity parameters for the next segment calculation. First, based on the nonlinear refractive index change obtained in the previous step, combined with the beam spot radius before incident on that segment, the focal length of the equivalent thin lens for that segment is determined through optical characteristic analysis. The focal length is directly related to the nonlinear refractive index change and the spot radius, reflecting the intensity-dependent focusing characteristics. Then, each segment is equivalent to a combination structure of "equivalent thin lens + linear dielectric layer". Combined with the segment thickness, the nonlinear focusing transmission matrix of the thin lens and the optical transmission matrix of the linear dielectric layer are established respectively. The two matrices are then combined according to the beam propagation order to obtain the comprehensive transmission matrix of that segment, which fully characterizes the modulation and transmission effect of that segment on the beam.

[0027] According to the actual propagation order of the beam in the nonlinear thin plate, starting from the Nth segment to the first segment at the incident end, the transmission matrices of all N segments are multiplied in sequence to obtain the total transmission matrix of the entire nonlinear thin plate. This total transmission matrix can accurately characterize the beam parameter transformation caused by the Kerr lensing effect, including the variation law of key parameters such as beam spot radius and radius of curvature, providing core data support for subsequent analysis of the focusing characteristics of the beam after passing through the nonlinear thin plate and the coupling efficiency after reflection.

[0028] In a preferred embodiment of the present invention, the equivalent saturable absorption characteristics of the nonlinear fiber optic mirror are optimized synergistically by adjusting two independent geometric parameters, specifically including: By adjusting the initial position of the reflector and the first actual distance between the reflector and the rear surface of the nonlinear sheet, the beam waist position or spot size in front of the nonlinear sheet is adjusted, thereby changing the peak light intensity distribution entering the nonlinear sheet and adjusting the intensity of the Kerr lens effect. By adjusting the second actual distance between the target reflector position and the rear surface of the nonlinear sheet, the mode matching condition of the returned beam is set. This distance is the final coupling position corresponding to the manifestation of the equivalent saturable absorption function. Specifically, by reducing the first actual distance to decrease the initial spot size of the beam in the nonlinear medium W, the optical Kerr lensing effect is enhanced, effectively reducing the saturated incident power required to achieve peak coupling efficiency; by reducing the second actual distance to increase the modulation depth of the equivalent saturable absorption function; and by synergistically adjusting the first and second actual distances, the curve shape of the coupling efficiency versus incident power is changed, specifically including: Decreasing the second actual distance causes the curve to exhibit a bimodal structure within the corresponding power range, accompanied by a trough in coupling efficiency. Increasing the second actual distance causes the bimodal structure to gradually merge, eventually evolving into a curve with a single peak.

[0029] In this embodiment, the core reference parameters of the device are first defined, including the thickness of the nonlinear thin sheet, material properties (nonlinear refractive index, absorption coefficient), collimation and focusing parameters of the lens group (including a single lens or a lens group composed of multiple lenses), and the initial power and spot shape of the incident beam. Simultaneously, using the rear surface of the nonlinear thin sheet as a unified reference plane, a distance measurement and adjustment device is constructed to ensure the adjustment accuracy and reading accuracy of the two actual distances.

[0030] The first actual distance is defined as the gap between the initial position of the reflector and the rear surface of the nonlinear thin plate. Its core function is to control the beam waist position or spot size before the beam enters the nonlinear thin plate, thereby changing the peak intensity distribution upon entering the nonlinear thin plate and adjusting the intensity of the Kerr lensing effect. During operation, the initial position of the reflector is changed by a translation adjustment mechanism, which in turn changes this gap: when the first actual distance is decreased, the spot size before entering the nonlinear thin plate is smaller after the beam is focused by the lens group, the intensity distribution is more concentrated, and the intensity per unit area is increased, thus significantly enhancing the optical Kerr effect within the nonlinear thin plate. This makes the effect of moving the beam focus point forward more pronounced, ultimately reducing the saturation incident power required to reach the peak coupling efficiency, achieving downward control of the saturation threshold. Conversely, increasing the first actual distance will cause the incident spot to diffuse, the intensity to decrease, the Kerr effect to weaken, and the saturation incident power to increase accordingly. During the adjustment process, the spot shape and intensity distribution incident on the thin plate must be monitored in real time to ensure that the parameter adjustment meets the expected target.

[0031] The second actual distance is defined as the distance between the target mirror position and the rear surface of the nonlinear slab. Its core function is to set the final coupling position when the equivalent saturable absorption function is manifested, while simultaneously controlling the modulation depth and coupling efficiency curve shape of the equivalent saturable absorption. During adjustment, based on the light intensity determined by the first actual distance, the mirror is further translated to the target position, changing this distance: when the second actual distance is decreased, the mirror is closer to the rear surface of the nonlinear slab. At this time, the coupling matching state between the beam and the single-mode fiber after reflection changes, and the modulation depth of the equivalent saturable absorption function increases accordingly. This is manifested as a more significant difference between the peak and valley values ​​of the coupling efficiency, and the coupling efficiency curve in the corresponding power range will exhibit a double-peak structure with a significant coupling efficiency trough between the two peaks. Conversely, when the second actual distance is increased, the mirror moves away from the rear surface of the slab, the beam coupling matching state tends to be flat, the double-peak structure gradually merges towards the middle, and finally evolves into a single-peak curve shape, and the modulation depth also decreases accordingly.

[0032] Based on the independent action of the two distances, a coordinated adjustment is performed to achieve precise optimization of the equivalent saturable absorption characteristics. First, the first actual distance is adjusted according to the target saturated incident power: if low-power triggering of equivalent saturable absorption is required, the first actual distance is decreased to enhance the Kerr effect; if high-power triggering is required, the distance is increased. Then, the second actual distance is adjusted according to the target modulation depth and curve shape: if a strong modulation effect is required and a bi-peak characteristic is needed for specific pulse selection, the second actual distance is decreased; if a stable coupling effect with a single peak is required, the second actual distance is increased until the bi-peaks merge. During the adjustment process, the coupling efficiency curve as a function of incident power is monitored in real time, and the two distances are dynamically fine-tuned: if a peak position shift occurs, the first actual distance can be fine-tuned to calibrate the saturated power; if an abnormal peak shape occurs, the second actual distance can be fine-tuned to optimize the curve shape, ultimately ensuring that the coupling efficiency curve meets the requirements of the target application scenario, achieving the optimal configuration of the equivalent saturable absorption characteristics.

[0033] After adjustment, the coupling efficiency change curve was comprehensively tested by changing the incident beam power to verify whether the saturated incident power, modulation depth, and curve shape met the preset target. At the same time, the coupling stability of the beam returning to the single-mode fiber after reflection was checked to ensure that the equivalent saturable absorption characteristics after dual-parameter coordinated adjustment are stable and reliable, and meet the working requirements of the overall device.

[0034] The structure of a nonlinear fiber optic mirror based on the Kerr lens effect is as follows: Figure 1 As shown in (a) of the diagram, a Gaussian beam output from a single-mode fiber F is collimated and focused by a lens group L, followed by a highly nonlinear thin plate W. W has a refractive index of n, an extremely high nonlinear refractive index n² (n²>0), a linear absorption coefficient α, and a two-photon absorption coefficient β, where two-photon absorption is considered the primary nonlinear loss mechanism. After passing through W, the beam is focused onto a reflector M'. At lower incident light intensities, the beam propagates along the path F→L→W→M', and after reflection by M', returns to fiber F along the same path. Under ideal conditions, neglecting aberrations and absorption losses, the coupling efficiency of this structure is 1 at low incident power. However, as the power density incident on W increases, the optical Kerr effect makes W equivalent to a convex lens, causing the beam focal point to shift forward. For a specific power P0, the focal point is exactly at M; moving the reflector forward to this point, if the power deviates from P0, the focal point will fall between M' and M or between M and W, neither of which achieves the highest coupling efficiency. Therefore, as the incident power increases, the coupling efficiency first gradually increases and reaches a peak, which is equivalent to saturable absorption. If the incident power is further increased, the coupling efficiency decreases accordingly, which is a reverse saturable absorption.

[0035] Figure 1 This refers to a nonlinear fiber optic reflector based on the Kerr lens effect. Figure 1Figure (a) shows that the beam output from the single-mode fiber (F) is collimated and focused by the lens group L, and then reaches the reflector M' after passing through the nonlinear thin film (W). The figure also marks the position M of the target reflector and the feature points on the forward transmission path: the front surface C and the rear surface B of W; the corresponding points for the reverse transmission are C' and B'. At low power, the beam returns via reflection from M'; at high power, the Kerr effect makes W equivalent to a convex lens, causing the beam focus to shift forward, and achieving equivalent saturable absorption characteristics by adjusting the coupling efficiency. Figure 1 Figure (b) shows a schematic diagram of the piecewise thicklens model of the Kerr medium: this model divides a nonlinear medium W of thickness d into N segments along the optical axis for numerical analysis of intensity-dependent nonlinear propagation. The figure illustrates the beam parameters q and the equivalent thin lens focal length f of the m-th segment. m and its transmission matrix M m Its definition and role in the model, and its specific expression, are detailed in the main text.

[0036] The thickness of W is d, and the distances between its rear surface and M' and M are δ and s, respectively. Taking the beam return direction as the positive direction, the origin O is set at M'. At low power, the forward propagation path is F to M', with the beam passing sequentially through the front surface C and the rear surface B of W; the reverse propagation path is M' to F, with the positions corresponding to B and C denoted as B' and C', respectively. At power P0, the position of the reflector M is denoted as O'. Under low power conditions, the beam q parameter at position O satisfies: , where q0, q C The q parameters of the beams at points O and C are respectively. , These are the transmission matrices for propagation in W and from position B to M', respectively. Point O is the waist position, so the q parameter at that point is: ,in Let be the Rayleigh length of the beam, and λ and ω0 be the center wavelength and beam waist radius, respectively. Therefore, we can obtain: The radius of curvature R of C can be obtained from the following relationship between the q parameter, the radius of curvature R, and the spot radius ω. C With the light spot radius ω C : Where Re(1 / q) and Im(1 / q) represent the real and imaginary parts of 1 / q, respectively.

[0037] For conventional bulk materials, as the incident light intensity increases, the equivalent lens theory of W under the optical Kerr effect can be described by the aberration-free thicklens model of Sheik-Bahae et al., and its structure is as follows: Figure 1 As shown in (b), this Kerr medium can be considered as N thin lenses with a thickness of... A stack of thin dielectric materials. For the m-th dielectric segment, its transmission matrix is... ,in The focal length ω of the thin lens in this medium m-1 The radius of the light spot output by the previous thin film can be obtained from formula (1) q m-1 Extract, ∆n m It is a nonlinear change in refractive index, therefore of which Let I be the average light intensity of this segment of the medium and the previous segment. Considering linear absorption and two-photon absorption, I... m Transmission in the thin film is by The description is as follows: Considering the incident light is a Gaussian beam, its average power... The transmission matrix throughout the medium is the product of the matrices of each slice, i.e.: Under the action of a Kerr lens, the beam propagates from C, passes through B, O', B', and C', and returns to position C'. The transmission matrix is ​​as follows: Among them, M f With M b The Kerr lens matrices for forward and reverse transmission are respectively, and can be solved using formula (2). Let be the transfer matrix from B to B' in free space. Therefore, the q-parameter at position C is... Combining formula (1), the radius of curvature R at that point can be obtained. C’ With the light spot radius ω C’ .

[0038] Based on Gaussian beam mode matching theory, the coupling efficiency calculated at the F end face of the fiber is equivalent to the coupling efficiency of the two beams traveling to and from the W front surface. When the two Gaussian beams have coincident optical axes and no lateral or angular offset, the coupling efficiency is determined solely by their spot radii ω on the reference plane. c ω c’ and radius of curvature R C R C’ The formula for power coupling efficiency, i.e., mode-field matching coupling efficiency, is: The first and second terms in the denominator represent the effects of spot size matching and radius of curvature matching at positions C and C', respectively, on coupling efficiency. The sign of the radius of curvature R follows a unified geometric optics convention: for diverging beams, the radius of curvature is greater than 0; for converging beams, the radius of curvature is less than 0. In addition to mode-matching efficiency, the absorption loss of W must also be considered, including linear absorption, nonlinear absorption, and equivalent saturable absorption (for saturable absorbers). The round-trip loss efficiency is: Therefore, the overall coupling efficiency is: Figure 2 Numerical simulation results of the equivalent saturable absorption characteristics based on 33Ge-12As-55Se glass are presented. The specific material parameters are: refractive index n = 2.545, nonlinear refractive index n² = 1.5 × 10⁻⁶. -17 m 2 / W, linear absorption coefficient α = 3.25 / m, two-photon absorption coefficient β = 1.9 × 10 -8 m / W, medium thickness d = 500 μm, total number of segments N = 500. For ease of analysis, a normalized length is introduced. , The incident beam has a waist spot radius ω0 = 5 μm and a center wavelength λ = 1550 nm. The structural parameters are u = 3 and v = 2.5. Figure 2 Figure (a) gives the coupling efficiency η and the mode field matching efficiency η. mode With loss efficiency η L With incident power P in The curves representing the changes in η are represented by solid blue lines, dashed red lines, and dotted green lines, respectively. mode With P in The increase of η first increases and then decreases, with its rising phase exhibiting characteristics similar to saturable absorption; under lossless conditions, η mode The maximum value is 1. However, due to the increasing power loss caused by nonlinear absorption, the peak value of the actual coupling efficiency η decreases and shifts towards lower power, and its maximum value η... max Approximately 0.96, corresponding to the maximum coupling power P max =7.5kW. The inherent coupling efficiency η0 at zero power is approximately 0.8, and the modulation depth η max -η0 is approximately 0.16. Figure 2 (b) depicts the positive Kerr focal length f f With reverse Kerr focal length f b The evolution trend of the propagation distance within the nonlinear thin sheet W is represented by the blue and red curves, respectively. During forward propagation, the beam gradually converges, the spot radius ω decreases with increasing propagation distance, and the light intensity increases accordingly, leading to f f The beam gradually decreases; during reverse transmission, the beam gradually diverges, the spot radius ω increases with increasing transmission distance, and the light intensity decreases. b It increases with increasing transmission distance.

[0039] Figure 2 The simulation results represent the equivalent saturable absorption characteristics of a nonlinear mirror based on a nonlinear thin sheet of 33Ge-12As-55Se glass. Figure 2 In the middle (a), η represents the coupling efficiency η and the mode field matching efficiency η. mode With loss efficiency η L With incident power P in The curve showing the change. Figure 2 (b) represents the positive direction f f With the opposite f b Evolution of the focal length of a Kerr lens within a thin film.

[0040] Figure 3 This demonstrates the relationship between the nonlinear sheet thickness d and the Rayleigh length Z. R Numerical simulation results are presented to investigate the influence of nonlinear 33Ge-12As-55Se glass on the equivalent saturable absorption characteristics. Except for the variable, all other material parameters and beam parameters are consistent with... Figure 2 To maintain consistency. To study the effect of thickness d, Figure 3 Figure (a) shows the curve of coupling efficiency η as a function of nonlinear sheet thickness d (d = 100-500 μm, in 100 μm intervals). Figure 3 In the middle (b), the corresponding maximum coupling power P is... max (Blue curve) and modulation depth η max -η0 (red curve). The results show that as d increases, P max A significant nonlinear decrease occurs towards lower power (from 44kW@100μm to 7.5kW@500μm), implying a reduction in the incident power required for optimal coupling; while the modulation depth remains almost constant throughout. To investigate the impact on beam characteristics, Figure 3 Figure (c) shows the coupling efficiency η as a function of Rayleigh distance Z. R (This is achieved by changing the waist radius ω0, ranging from 4-8 μm with 1 μm intervals). Figure 3 In the middle (d), P is the corresponding P. max With modulation depth. The pattern shows that as Z... R (i.e., ω0) increases, P max The increase is approximately linear because, with the same power, the focal length of the Kerr lens decreases, requiring higher power to move the focus forward to the set M position; at the same time, the modulation depth also remains basically stable.

[0041] Figure 4 This study demonstrates the effect of nonlinear mirror structural parameters (u and v) on the equivalent saturable absorption performance of 33Ge-12As-55Se glass. Except for the variable, all other parameters are related to... Figure 2 Maintain consistency. Figure 4Images (a) and (b) in the figure investigated the effect of the normalized offset u (u = 2–6, with an interval of 1), while keeping uv = 0.5 to fix the relative positions of M and M'. The results show that as u decreases (i.e., the incident light spot ω...), the effect of the normalized offset u (u = 2–6, with an interval of 1) increases. C (Reduced), nonlinear effects are enhanced, and the focal length of the Kerr lens is shortened at the same power, making it easier to move the focal point forward to M. Therefore, the maximum coupling power P is reduced. max Significantly reduced ( Figure 4 (blue curve in (b)); while the modulation depth remains basically unchanged (red curve). Figure 4 In (c) and (d), the effect of the normalized distance v (v = 1.7–2.7, interval 0.2) was investigated, with u kept constant. A decrease in v means M moves further away from M', leading to a decrease in the background coupling efficiency η0, and requiring stronger nonlinearity (i.e., higher power) to move the focus forward. Therefore, P... max It increases as v decreases ( Figure 4 (The blue curve in (d)). Meanwhile, the modulation depth increases as v decreases, reaching η at v=1.7. max -η0 exceeds 0.4, corresponding to P max Only about 17kW Figure 4 (The purple curve in (c)). Figure 4 In (c), as v increases from 1.7 to 2.7, η-P in The curve exhibits a double peak accompanied by a deep valley (derived from the radii of curvature R of the forward and reverse light spots in formula (1)). C With R C’ The structure gradually evolved from multiple intersections (deep valleys to shallow valleys) to a single-peak structure, revealing the significant regulatory ability of structural parameters on the equivalent saturable absorption performance.

[0042] Figure 3 The nonlinear sheet thickness d and the Rayleigh distance Z to the beam are represented by... R The effect on the equivalent saturable absorption performance of nonlinear mirrors. Figure 3 Figure (a) shows the curve of coupling efficiency η as a function of the thickness d of the nonlinear sheet. Figure 3 In the diagram, (b) represents the corresponding maximum coupling power P. max With modulation depth η max The relationship between -η0. Figure 3 In the equation (c), the coupling efficiency η varies with the Rayleigh distance Z. R The curve showing the variation of (waist radius ω0) Figure 3 In this context, (d) represents the corresponding P. max With modulation depth η max The relationship between -η0.

[0043] Figure 4This represents the control of structural parameters (u,v) on the equivalent saturable absorption performance of the nonlinear mirror. Figure 4 In the middle (a), the coupling efficiency η varies with the incident power P. in The curves showing the variation of u at different values ​​(keeping uv=0.5). Figure 4 In the middle (b), the corresponding maximum coupling power P is represented. max With modulation depth η max -η0. Figure 4 In the figure (c), the coupling efficiency η varies with the incident power P. in Curves showing the variation of v at different values ​​(with u fixed). Figure 4 In the middle (d), it represents the corresponding P. max With modulation depth η max -η0.

[0044] This structure allows for precise performance design by adjusting the nonlinear intensity and mode-matching conditions. Increasing the thickness d of the nonlinear lamellae enhances the accumulation of nonlinear phase shift and significantly reduces P. max The modulation depth remains essentially unchanged, indicating that it only alters the sensitivity of the nonlinear response; the Rayleigh length Z R (Or) An increase in the waist radius ω0 leads to a decrease in light intensity, requiring a linear increase in P. max To compensate for the weakened Kerr effect and adapt to different power scenarios, the normalized parameters u and v can be adjusted synergistically, independently optimizing saturation power and modulation depth over a wide range, demonstrating high design flexibility. This structure is based on the Kerr lensing effect to change the mode matching degree to achieve its functional switching. Its mechanism is essentially independent of strong absorption, thus avoiding the risk of absorption-type damage in principle. In contrast, SESAM relies on the intrinsic absorption and saturation recovery of semiconductor materials, and its damage threshold is limited by the band gap and thermal damage of the material itself. When used in conjunction with large-mode-field fibers, this structure can provide a more promising solution for continuously increasing the power limit of laser resonators. In addition, the Kerr effect has ultrafast response characteristics on the femtosecond scale, making it exhibit superior speed potential compared to SESAM in the field of high-power ultrafast lasers.

[0045] Based on the aforementioned fundamental advantages, this nonlinear mirror has broad application prospects in multiple photonics fields. It is not only a highly promising mode-locking element in high-power femtosecond fiber lasers, but can also be used as a high-speed all-optical modulator or optical switch. The scalability of this structure is particularly outstanding: in terms of operating wavelength, the 33Ge-12As-55Se glass used in this invention can effectively operate in the mid-to-far infrared band of 2-10μm, filling the gap in high-performance equivalent saturable absorber devices in this band. However, current simulation results are based on an aberration-free theoretical model; lens aberrations, thermal effects, and other factors may affect the final performance. Future research needs to incorporate these practical constraints into the model and verify and optimize it through systematic experiments.

[0046] In summary, this invention proposes and theoretically studies a reflective nonlinear fiber optic mirror based on the Kerr lensing effect, based on transmission matrix theory and Gaussian beam mode matching analysis. This structure utilizes intensity-dependent modulation caused by the Kerr effect to dynamically control the beam mode matching degree, thereby achieving equivalent saturable absorption. Numerical analysis shows that by synergistically adjusting the nonlinear slab thickness, beam parameters, and normalized structural parameters, the peak coupling power, modulation depth, and coupling efficiency curve shapes can be effectively designed, exhibiting high flexibility. This device provides a new and feasible solution for the development of high-power, ultrafast fiber lasers and all-optical modulation devices.

[0047] The above description represents the preferred embodiments of the present invention. It should be noted that those skilled in the art can make various improvements and modifications without departing from the principles of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A nonlinear fiber optic reflector based on the Kerr lens effect, comprising a single-mode fiber, a lens group, a nonlinear thin film, and a reflector; the beam output from the single-mode fiber is collimated and focused by the lens group, incident on the nonlinear thin film, and then reflected by the reflector back to the single-mode fiber along the original optical path; characterized in that: The nonlinear thin film has a positive nonlinear refractive index. When the incident light intensity increases, the nonlinear thin film induces self-focusing due to the Kerr effect, which can be equivalent to a lens whose focal length changes with the light intensity. This causes the beam focal point to shift forward, thereby changing the mode matching condition between the returning beam and the fundamental mode of the single-mode fiber. By adjusting the position of the reflector relative to the nonlinear thin film, the system exhibits an equivalent saturable absorption characteristic within a preset power range, where the return loss decreases with increasing incident power. The coupling efficiency reaches its peak at the corresponding incident power. As the incident power continues to increase, the coupling efficiency decreases, exhibiting a reverse saturable absorption characteristic. The position of the reflector is adjustable along the optical axis. By adjusting it to the beam focal point position at a specific power, the coupling efficiency between the returning beam and the fiber reaches its peak at the preset incident power. The equivalent saturable absorption characteristic of the nonlinear fiber reflector is optimized synergistically by adjusting two independent geometric parameters, specifically including: By adjusting the initial position of the reflector and the first actual distance between the reflector and the rear surface of the nonlinear sheet, the beam waist position or spot size in front of the nonlinear sheet is adjusted, thereby changing the peak light intensity distribution entering the nonlinear sheet and adjusting the intensity of the Kerr lens effect. By adjusting the second actual distance between the target reflector position and the rear surface of the nonlinear sheet, the mode matching condition of the returned beam is set. This distance is the final coupling position corresponding to the manifestation of the equivalent saturable absorption function. Specifically, by reducing the first actual distance, the initial spot size of the beam at the nonlinear medium W is reduced to enhance the optical Kerr lens effect and effectively reduce the saturated incident power required to achieve peak coupling efficiency; by reducing the second actual distance, the modulation depth of the equivalent saturable absorption function is increased.

2. The nonlinear fiber optic reflector based on the Kerr lens effect according to claim 1, characterized in that, The nonlinear sheet is a chalcogenide glass sheet with high nonlinearity.

3. The nonlinear fiber optic reflector based on the Kerr lens effect according to claim 2, characterized in that, The lens group includes a single lens or a lens group consisting of multiple lenses arranged sequentially along the optical path for collimating or focusing the beam.

4. The nonlinear fiber optic reflector based on the Kerr lens effect according to claim 3, characterized in that, The intensity-dependent transmission characteristics of the nonlinear thin film are analyzed using a piecewise model, specifically including: The thin film is divided into N segments along the optical axis, and each segment is equivalent to a combination of a thin lens with light intensity-dependent focal length and a linear dielectric layer. By sequentially calculating the nonlinear refractive index change, light intensity attenuation, and corresponding transmission matrix of the beam in each segment, and then multiplying the transmission matrices of all segments in sequence, the total transmission matrix of the nonlinear sheet is obtained, which is used to describe the transformation of the beam after passing through the nonlinear medium.

5. The nonlinear fiber optic reflector based on the Kerr lens effect according to claim 4, characterized in that, The specific implementation process of the segmentation model is as follows: Based on the nonlinear refractive index of the nonlinear thin sheet and the average light intensity within the segment, the change in nonlinear refractive index caused by the optical Kerr effect in each segment of the medium is calculated. The intensity attenuation of the beam in each segment is calculated based on the linear absorption coefficient and two-photon absorption coefficient of the nonlinear thin sheet. Based on the nonlinear refractive index change and the beam spot radius before segmentation, the focal length of each equivalent thin lens is determined, and the transmission matrix of the segment is constructed in combination with the segment thickness. The total transmission matrix of the beam is obtained by multiplying the transmission matrices of all N segments in the order of light propagation. This total transmission matrix is ​​used to quantitatively characterize the beam propagation caused by the Kerr lensing effect. q Parameter transformation and evolution of spatial modulus.

6. The nonlinear fiber optic reflector based on the Kerr lens effect according to claim 5, characterized in that, By coordinating the adjustment of the first and second actual distances, the shape of the coupling efficiency curve as a function of incident power is altered, specifically including: Decreasing the second actual distance causes the curve to exhibit a bimodal structure within the corresponding power range, accompanied by a trough in coupling efficiency. Increasing the second actual distance causes the bimodal structure to gradually merge, eventually evolving into a curve with a single peak.

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