A method and a system for gain-equalized broadband amplification using few mode fibers

Abstract

The present disclosure discloses a method and a system for generating a gain-equalised amplified broadband signal using few mode fibers (FMFs). The method comprises amplifying, by a first amplification (FA) unit (102), an input signal to generate a first amplified signal. The input signal is a multi-mode broadband optical signal. Further, the method comprises receiving, by a spatial-spectral filtering (SSF) unit (104), the first amplified signal. Further, the method comprises determining, by the SSF unit (104), a transmission coefficient matrix associated with a target gain value. The method further comprises selectively attenuating power intensity of the first amplified signal. The method further comprises amplifying, by a second amplification (SA) unit (106), the second signal, based on a gain guiding mechanism to generate a second amplified signal as a gain-equalized output signal if the second amplified signal corresponds to the target gain value. [Figure 1]

Description

FIELD OF INVENTION

[0001] The present disclosure relates to the field of optical fiber technologies, specificallyto few mode fiber-based amplifiers. More particularly, the present disclosure relates to amethod and a system for gain-equalized broadband amplification using few mode fibers.BACKGROUND OF THE INVENTION

[0002] The following description of the related art is intended to provide backgroundinformation pertaining to the field of the disclosure. This section may include certain aspectsof the art that may be related to various features of the present disclosure. However, it shouldbe appreciated that this section is used only to enhance the understanding of the reader withrespect to the present disclosure, and not as admissions of the prior art.

[0003] As global demand for high-capacity communication rises, optical networks mustsupport progressively higher data rates, wider operational bandwidths, and improved energyefficiency. The development of new amplifier architectures capable of supportingmultimode signal propagation while maintaining uniform performance across spatial andspectral dimensions represents a significant technological challenge in modern opticalcommunication research.

[0004] Over the past time, single-mode fiber (SMF) systems have been extensively used inlong-haul communication networks. sophisticated multiplexing techniques such aswavelength-division multiplexing (WDM), and polarization-division multiplexing (PDM),have been developed to increase the data carrying capacity of the existing fiber systems.Further, the techniques have also been implemented in combination of each other to furtherincrease the capacity of the existing fiber systems. However, fundamental physical limitsnow constrain further expansion of the existing SMF-based systems. For example, theShannon capacity limit, with Kerr nonlinearities, creates an upper bound on the amount ofinformation that can be transmitted through a SMF-based system. Even with sophisticatedcoherent detection and digital signal processing (DSP), the achievable capacity of an SMFis approaching saturation at approximately 100 Tbit / s. Additionally, the usable spectralwindow for amplification is limited by the bandwidth of rare-earth-doped amplifiers, whichare currently used in long-haul telecommunications in the C- and L-bands. Attempts to scalecapacity by deploying additional parallel SMFs significantly increase infrastructure costs,power consumption, and operational complexity, making such approaches unsustainable forfuture network demands.

[0005] In response to these limitations, space-division multiplexing (SDM) utilizes multiplespatial channels within a single fiber to dramatically increase per-fiber data capacity. SDMmay be realized through multicore fibers (MCFs), in which several independent corescoexist within a common cladding, or through few-mode fibers (FMFs) and multimodefibers (MMFs), where multiple spatial modes propagate simultaneously within a single core.Each spatial mode acts as an independent information channel, thereby enabling substantialcapacity gains without proportional increases in physical fiber count.

[0006] Among SDM approaches, few-mode fibers (FMF) have been used due to theircompatibility with conventional fiber fabrication processes, ability to support a limitednumber of well-defined modes, and reduced losses and noise through larger mode areas ascompared to SMFs. However, practical implementation of FMF-based SDM networksdepends on the availability of few-mode fiber amplifiers (FMFAs) capable of amplifyingmultiple spatial modes simultaneously with minimal distortion, stable performance, and lownoise.

[0007] A major challenge in FMFA development is differential modal gain (DMG) or mode dependent gain (MDG). DMG is the phenomenon in which different spatial modesexperience unequal levels of amplification. DMG arises primarily from differences in modaloverlap with the doped region of the amplifier fiber, as well as variations in pump-signalinteractions across the supported modes. Higher-order modes typically exhibit reducedoverlap with the doped core and consequently receive less gain than lower-order modes.This leads to power difference among modes, increased noise figure, degraded signal-to-noise ratio (SNR), and limits system performance. In some cases, high DMG renders certainmodes practically unusable, thereby reducing effective system capacity.

[0008] Moreover, achieving broadband multimode amplification remains difficult due tothe inherent wavelength-dependent nature of rare-earth-doped fibers. Various researchefforts have attempted to mitigate DMG and improve the uniformity of few-mode fiberamplifiers. For example, few of the known techniques include: (a) Successive InterferenceCancellation (SIC) which reduces capacity loss induced by DMG through frequencydiversity, allowing the outage capacity to approach the average channel capacity, (b)Adaptive modal gain equalization which uses spatial light modulators (SLMs) in multimodeerbium-doped fiber amplifiers, wherein either the pump or signal modal powers aredynamically adjusted to achieve low root-mean-square DMG values (below 0.5-1 dB) withminimal penalty in mode-averaged gain, (c) few-mode chirped fiber Bragg gratings (FMCFBGs), which utilize mode-dependent reflectivity for gain equalization, achieving lowlevels of DMG.

[0009] Beyond the C-band, the advancements have extended broadband amplification intolonger wavelength regions, including the L-band (1570-1625 nm) and the S-band. Newtechniques, and fibers such as the erbium (Er3+) / ytterbium (Yb3+) co-doped fibers and few mode fibers have achieved bandwidths on the order of 30-40 nm. However, the existingtechniques fall short of the broadband amplification needed for future terabit-per-secondSDM systems. Even when modal gain uniformity is achieved over narrow bands, limitationspertaining to maintaining uniformity over the required broadband range remainunaddressed. Thus, despite significant development in multimode or few mode fiberamplifiers, several issues still persist. The existing issues / challenges include: (a) complexityand scalability issues (methods such as SLM-based adaptive control and SIC equalizationrequire intricate feedback mechanisms and high computational resources, which increasessystem complexity and limits their scalability, particularly for broadband multimodeamplifier operation), (b) fabrication and stability issues (optimized doping profile designsare highly sensitive to fabrication precision, and even minor imperfections can lead toinconsistent gain performance), (c) efficiency losses in multi-pump configurations(techniques employing multiple pump paths and beam combination through phase masksand beam splitters suffer from cumulative insertion losses, leading to reduced overall systemefficiency as the number of modes increases), (d) wavelength-specific limitations (mode dependent reflectivity of FM-CFBG-based equalization methods is wavelength-dependent,restricting their applicability for broadband amplification).

[0010] The above-mentioned limitations underscore the need for a simple, scalable, andefficient multimode amplification method that can simultaneously address the above andother related challenges existing in the art. There is, therefore, a need in the art to providean improved amplification technique that mitigates mode-dependent and wavelength dependent gain fluctuations, reduces system complexity, supports wideband / broadbandoperation, and enables the stable, high-capacity transmission required by future opticalnetworks.OBJECTS OF THE INVENTION

[0011] To highlight the advantages and technical contributions achieved over the existingstate of the art, few objects of the present disclosure are set forth. These objects are notintended to limit the scope of the disclosure but to facilitate a better understanding of itssalient features and improvements.

[0012] It is an object of the present disclosure to provide a method and a system forbroadband amplification using few mode fibers capable of delivering a flat gain in abroadband range of operation.

[0013] It is another object of the present disclosure to minimize mode-dependent andwavelength-dependent gain variations in few mode fiber amplifiers.

[0014] It is yet another object of the present disclosure to provide a method and a systemfor broadband amplification in few mode fibers capable of delivering flat gain in abroadband range of operation that is scalable.

[0015] It is yet another object of the present disclosure to provide a mechanism that reducessystem complexity while achieving high-capacity optical communication.

[0016] It is yet another object of the present disclosure to provide a system that is lesssensitive to fabrication precision, and provides consistent gain performance.

[0017] These and other objects and advantages of the present subject matter will be apparentto a person skilled in the art after consideration of the following detailed description takinginto consideration accompanying drawings in which preferred embodiments of the presentsubject matter are illustrated.SUMMARY OF THE INVENTION

[0018] This section is provided to introduce certain aspects of the present disclosure in asimplified form that are further described below in the detailed description. This summaryis not intended to identify the key features or the scope of the claimed subject matter.

[0019] In an aspect of the present disclosure, a method for generating a gain-equalizedamplified broadband signal using few mode fibers (FMFs) is disclosed. The methodcomprises amplifying, by a first amplification (FA) unit, an input signal to generate a firstamplified signal. The FA unit comprises a few-mode fiber, and the input signal is a multimode broadband optical signal. The method further comprises receiving, by a spatial spectral filtering (SSF) unit from the FA unit, the first amplified signal. The method furthercomprises determining, by the SSF unit, a transmission coefficient matrix associated with atarget gain value, said matrix corresponding to one or more wavelengths and one or moremodes associated with the first amplified signal, for selective attenuation of the firstamplified signal. Further, the method comprises selectively attenuating, by the SSF unit,power intensity of the first amplified signal, based on the transmission coefficient matrix,to generate a second signal. The method further comprises amplifying, by a secondamplification (SA) unit, the second signal, based on a gain guiding mechanism applied inthe SA unit on the second signal, to generate a second amplified signal as a gain-equalizedoutput signal if the second amplified signal corresponds to the target gain value obtainedacross the one or more wavelengths and the one or more modes associated with the firstsignal.

[0020] In an embodiment, the method further comprises in case of second amplified signalnot corresponding to the target gain value. The method further comprises updating thetransmission coefficient matrix based on the target gain value vide an Adam optimizationscheme. Further, the method comprises communicating the updated transmission matrix tothe SSF unit to re-generate the second signal for communication to the second amplificationunit.

[0021] In an embodiment, the updating the transmission coefficient matrix comprisesupdating the transmission coefficient matrix vide an Adam optimization scheme, based onexponential moving averages of the gradient and squared gradient defined by first andsecond moments.

[0022] In an embodiment, the moments are bias-corrected by a power term and combinedto iteratively compute at least one adaptive coefficient.

[0023] In an embodiment, coefficients whose performance metric lies within a predefinednarrow tolerance band are held constant to prevent unnecessary perturbation, andcoefficients in different spectral channels are updated with a distinct step size.

[0024] In an embodiment, the selective attenuation comprises computing, by the FA unit, aset of mode fields. The method further comprises determining, by the FA unit, a set ofoverlap integrals based on the computed mode fields. The method further comprisesdetermining, by the SSF unit, one or more high-amplification modes based on the overlapintegrals for selective attenuation. The high amplification modes are modes among the oneor more modes, that have higher modal overlap with doped core region of the FA unit ascompared to other modes.

[0025] In an embodiment, the selective attenuation further comprises reducing, by the SSFunit, respective powers of the one or more high-amplification modes.

[0026] In an embodiment, the method further comprises pumping, by one or more pumpsources, the input signal and the second signal during amplification.

[0027] In an embodiment, a gain variation in one or more modes of the output signal is in arange of -0.4 decibel (dB) to +0.4 dB.

[0028] In another aspect of the present disclosure, a system for generating a gain-equalizedamplified broadband signal using few mode fibers (FMFs) is disclosed. The systemcomprises a first amplification (FA) unit. The FA unit is configured to amplify an inputsignal to generate a first amplified signal. The FA unit comprises a few-mode fiber, and theinput signal is a multi-mode broadband optical signal. The system further comprises aspatial-spectral filtering (SSF) unit. The SSF unit is configured to receive, from the FA unit,the first amplified signal. Further, the SSF unit is configured to determine a transmissioncoefficient matrix associated with a target gain value, for selective attenuation of the firstamplified signal. The transmission coefficient matrix corresponds to one or morewavelengths and one or more modes associated with the first amplified signal. Further, theSSF unit is configured to selectively attenuate power intensity of the first amplified signal,based on the transmission coefficient matrix, to generate a second signal. Further, the systemcomprises a second amplification (SA) unit. The SA unit is configured to amplify the secondsignal, based on a gain guiding mechanism applied in the SA unit on the second signal, togenerate a second amplified signal as a gain-equalized output signal if the second amplifiedsignal corresponds to the target gain value obtained across the one or more wavelengths andthe one or more modes associated with the first signal.BRIEF DESCRIPTION OF DRAWINGS

[0029] The accompanying drawings, which are incorporated herein, and constitute a part ofthis disclosure, illustrate exemplary embodiments of the disclosed methods and systemswherein like reference numerals designate corresponding parts in various figures. It is to beexpressly understood, however, that the drawings are for the purpose of illustration anddescription only and are not intended as a definition of the limits of the invention.Accordingly, the following description simply illustrates certain selected embodiments thatare consistent with the subject matter as disclosed, wherein:

[0030] Figure 1 illustrates a schematic diagram of a system for gain-equalized broadbandamplification in few mode fibers, according to embodiments of the present disclosure;

[0031] Figure 2 illustrates an exemplary architecture diagram of the system for gain equalized broadband amplification in few mode fibers, according to embodiments of thepresent disclosure;

[0032] Figure 3 shows exemplary supported modes of a few-mode fiber at pump sourcewavelengths and signal wavelengths;

[0033] Figure 4 illustrates a schematic simulation workflow of a signal in a few mode fiberamplifier;

[0034] Figure 5 illustrates a simulation workflow of a signal through the system for gain equalized broadband amplification in few mode fibers, according to embodiments of thepresent disclosure;

[0035] Figure 6 shows characteristics of evolution of the forward-propagating signal modesin the first amplification unit of the system for gain-equalized broadband amplification infew mode fibers, according to embodiments of the present disclosure;

[0036] Figure 7(a) shows characteristics of evolution of the forward-propagating signalmodes in the second amplification unit of the system for gain-equalized broadbandamplification in few mode fibers, according to embodiments of the present disclosure;

[0037] Figure 7(b) shows an input signal power of various modes coupled to the secondamplification unit of the system for gain-equalized broadband amplification in few modefibers, according to embodiments of the present disclosure;

[0038] Figure 8(a) shows amplified spontaneous emission (ASE) characteristics of forward propagating signal modes in the first amplification unit of the system for gain-equalizedbroadband amplification in few mode fibers, according to embodiments of the presentdisclosure;

[0039] Figure 8(b) shows ASE characteristics of backward-propagating signal modes in thefirst amplification unit of the system for gain-equalized broadband amplification in fewmode fibers, according to embodiments of the present disclosure;

[0040] Figure 8(c) shows ASE characteristics of forward-propagating signal modes in thesecond amplification unit of the system for gain-equalized broadband amplification in fewmode fibers, according to embodiments of the present disclosure;

[0041] Figure 8(d) shows ASE characteristics of backward-propagating signal modes in thesecond amplification unit of the system for gain-equalized broadband amplification in fewmode fibers, according to embodiments of the present disclosure;

[0042] Figure 9 shows a comparison of gain between the first amplification unit and thesecond amplification unit of the system for gain-equalized broadband amplification in fewmode fibers, according to embodiments of the present disclosure; and

[0043] Figure 10 illustrates a method for gain-equalized broadband amplification in fewmode fibers, according to embodiments of the present disclosure.DETAILED DESCRIPTION

[0044] A detailed description of various exemplary embodiments of the disclosure isdescribed herein. The present disclosure, as well as the methods of operation and functionsof the related elements of the system and the combination of parts, will become moreapparent upon consideration of the following description and the appended claims withreference to the accompanying drawings, all of which form a part of this specification. Itshould be noted that the embodiments are described herein in such details as to communicatethe disclosure. However, the amount of details provided herein is not intended to limit theanticipated variations of embodiments. On the contrary, the intention is to cover allmodifications, equivalents, and alternatives falling within the spirit and scope of the presentdisclosure.

[0045] In the following description, for the purposes of explanation, various specific detailsare set forth in order to provide a thorough understanding of embodiments of the presentdisclosure. It will be apparent, however, that embodiments of the present disclosure may bepracticed without these specific details. Several features described hereafter can each beused independently of one another or with any combination of other features. An individualfeature may not address all of the problems discussed above or might address only some ofthe problems discussed above. Some of the problems discussed above might not be fullyaddressed by any of the features described herein.

[0046] The ensuing description provides exemplary embodiments only and is not intendedto limit the scope, applicability, or configuration of the disclosure. Rather, the ensuingdescription of the exemplary embodiments will provide those skilled in the art with anenabling description for implementing an exemplary embodiment. It should be understoodthat various changes may be made in the function and arrangement of elements withoutdeparting from the spirit and scope of the disclosure as set forth.

[0047] Also, it is noted that individual embodiments may be described as a process that isdepicted as a flowchart, a flow diagram, a data flow diagram, a structure diagram, or a blockdiagram. Although a flowchart may describe the operations (or actions) as a sequentialprocess, many of the operations (or actions) can be performed in parallel or concurrently. Inaddition, the order of the operations may be rearranged. A process is terminated when itsoperations are completed but could have additional operations not included in a figure. Aprocess may correspond to a method, a function, a procedure, a subroutine, etc.

[0048] The word "exemplary" and / or "demonstrative" is used herein to mean serving as anexample, instance, or illustration. For the avoidance of doubt, the subject matter disclosedherein is not limited by such examples. In addition, any aspect or design described hereinas "exemplary" and / or "demonstrative" is not necessarily to be construed as preferred oradvantageous over other aspects or designs, nor is it meant to preclude equivalent exemplarystructures and techniques known to those of ordinary skill in the art. Furthermore, to theextent that the terms "includes," "has," "contains," and other similar words are used in eitherthe detailed description or the claims, such terms are intended to be inclusive in a mannersimilar to the term "comprising" as an open transition word without precluding anyadditional or other elements.

[0049] Reference throughout this specification to "one embodiment" or "an embodiment"or "an instance" or "one instance" or "an implementation" means that a particular feature,structure, or characteristic described in connection with the embodiment is included in atleast one embodiment of the present disclosure. Thus, the appearances of the phrases "inone embodiment" or "in an embodiment" or "in an implementation" in various placesthroughout this specification are not necessarily all referring to the same embodiment.Furthermore, the particular features, structures, or characteristics may be combined in anysuitable manner in one or more embodiments.

[0050] The terminology used herein is for the purpose of describing particular embodimentsonly and is not intended to be limiting of the disclosure. As used herein, the singular forms"a", "an", and "the" are intended to include the plural forms as well, unless the contextindicates otherwise. It will be further understood that the terms "comprises" and / or"comprising," when used in this specification, specify the presence of stated features,integers, steps, operations, elements, and / or components, but do not preclude the presenceor addition of one or more other features, integers, steps, operations, elements, components,and / or groups thereof. As used herein, the term "and / or" includes any and all combinationsof one or more of the associated listed items.

[0051] Figure 1 illustrates a schematic diagram of a system (100) for gain-equalizedbroadband amplification in few mode fibers, according to embodiments of the presentdisclosure. As shown in Figure 1, the system includes a first amplification unit (102), aspatial-spectral filtering unit (104), a second amplification unit (106), and a processing unit(108). In an embodiment, the processing unit (108) is a separate unit (108) operablyconnected to the spatial-spectral filtering unit (104). In another embodiment, the processingunit (108) is integrated with or located within the spatial-spectral filtering unit (104) forperforming processing tasks for the spatial-spectral filtering unit (104).

[0052] The input signal may be a multi-mode broadband optical signal. For amplifying theinput signal, the FA unit (102) includes a few-mode fiber. The few-mode fiber may be anoptical fiber doped with rare-earth elements such as, but not limited to, erbium (Er),ytterbium (Yb), neodymium (Nd), thulium (Tm), and holmium (Ho), or any combinationthereof. The FA unit (102) amplifies the input signal to generate a first amplified signal.

[0053] Figure 2 illustrates an exemplary architecture diagram (200) of the system (100) forgain-equalized broadband amplification in few mode fibers. As shown in Figure 2, thesystem (100) includes FA unit (102). The input signal (shown as Psignal in Figure 2) is fed tothe FA unit (102). The FA unit (102) and the SA unit (106) both are bidirectionally pumpedusing pump sources 202A, 202B, 202C, and 202D. Here, the term "pump" refers to a high power optical pump light that is injected into the fiber to provide the energy needed foroptical gain. The FA unit (102) is pumped by the pump sources (202A) and (202B), and theSA unit (106) is pumped by the pump sources (202C) and (202D). Notably, the pumpsources (both in forward and backward direction) are used to pump all the signals as theyare injected simultaneously in the fiber. Also, the pump power utilized by the signal dependson various factors including the degree of overlap between the pump and signal mode.Accordingly, in an embodiment, the disclosure encompasses pumping, by one or more pumpsources, the input signal and the second signal during amplification. In an embodiment, thenumber of pump sources used depends upon the total gain that is required / desired at theoutput of the SA unit (106). In an embodiment, the pumping used in system (100) isbidirectional pumping using two pump sources. The pump sources (also referred to as"pump") are used for phase masking in the input signal. The modes are combined by themode combiner (204) to pass the signal through the few-mode fiber, such as the TDF (206).Further, the first amplified signal is generated by the FA unit (102). Accordingly, in anembodiment, the disclosure encompasses amplifying, by the FA unit (102), an input signalto generate a first amplified signal, wherein the FA unit (102) comprises a few-mode fiber,and the input signal is a multi-mode broadband optical signal. The first amplified signal ispassed through the SSF unit (104) where selective attenuation is performed. Thus, in anembodiment, the disclosure encompasses receiving, by the SSF unit (104) from the FA unit(102), the first amplified signal. The SSF unit (104) after selectively attenuating the firstamplified signal generated the second signal for feeding to the SA unit (106). Accordingly,in an embodiment, the disclosure encompasses selectively attenuating, by the SSF unit(104), power intensity of the first amplified signal, based on the transmission coefficientmatrix, to generate a second signal. The SA unit (106) amplifies the second signal togenerate the second amplified signal at the output. The second amplified signal is the gain equalized amplified broadband version of the multimode broadband input signal. Thus, inan embodiment, the disclosure encompasses amplifying, by the SA unit (106), the secondsignal, based on a gain guiding mechanism applied in the SA unit (106) on the second signal,to generate a second amplified signal as a gain-equalized output signal if the secondamplified signal corresponds to the target gain value obtained across the one or morewavelengths and the one or more modes associated with the first signal.

[0054] In an embodiment, the FA unit (102) as well as the second amplifier (SA) unit (106)employs a step-index thulium-doped multimode fiber (TDF). Under the weakly guidingapproximation, the fiber (i.e., TDF) supports several linearly polarized (LP) modes at bothpump and signal wavelengths. The LP modes are computed numerically using the Besselfunction-based field solutions to the scalar wave equation. The transverse electric fielddistribution E(r,Phi)of a mode with azimuthal index l is expressed in cylindrical coordinatesas given in equation (1) below.PhiEquation... (1)where Jland Kl are the Bessel and modified Bessel functions, respectively. The modalparameters are defined as given in equation (2) below.Equation... (2)with the normalized frequency parameter V and normalized propagation constant b given by:u = V(root)(1 - b), and w = V(root)b . Here, k0is the free-space wavenumber, and n1andn2denote the core and cladding refractive indices, respectively.

[0055] The physical and optical parameters are summarized in Table 1 below.Table 1:

[0056] The amplification process in the fiber (i.e., TDF) is governed by populationdynamics between the lower (N1) and upper (N2) manifolds of Tm3+ions. A two-levelatomic model describes the steady-state population densities of the lower and upper energylevels. The model accounts for pump absorption, stimulated emission at the signalwavelength, and amplified spontaneous emission (ASE). At each position along the fiber,the population densities of the lower and upper levels can be obtained by solving the steadystate rate equations. Assuming steady-state operation, the population densities satisfy therate equations given as equations (3) and (4) below.Equation... (3)Equation... (4)where:N0(x, y)is the total ion concentration, Gammais the excited-state lifetime, Ps,i,kand PASE, i, kare the optical powers of the i th signal mode and amplified spontaneous emission (ASE) at the k th wavelength, Pp,j is the pump power in mode j, (lamda) es,k, (lamda) as,k, (lamda) ep, and (lamda)a pare the emission and absorption cross-sections for the signal and pump, (Psi)s,i,k(x, y)and (Psi)p,j(x, y)are the normalized intensity distributions of the signal and pump modes, respectively, h is Planck's constant, and vs , v pare the optical frequencies of the signal and pump waves.The equations include contributions from all spatially guided pump and signal modes, eachweighted by its normalized intensity distribution within the fiber cross-section. The spatialvariation of N2(x, y, z) defines the population inversion map, which directly governs thelocal gain experienced by each mode.

[0057] Once the inversion distribution is known, the longitudinal evolution of the pump,signal, and ASE powers along the fiber axis is described by a set of coupled differentialequations. These equations account for local gain and absorption, mode coupling, andbidirectional pump propagation. For the signal and ASE in mode i and the pump in mode j,the propagation equations are given as equations (5), (6), and (7) below.Equation... (5)Equation... (6)Equation... (7)where Delta v denotes the ASE bandwidth per spectral component, and ds, iq, dp, jq represent themodal coupling coefficients between signal and pump modes, respectively. The signal andASE powers are amplified according to the spatial overlap with the inverted region, whilethe pump power decreases through absorption by the active ions. The model includesforward and backward pump propagation, enabling bidirectional pumping.

[0058] Mode coupling effects arising from imperfections or bending in the fiber wereincorporated using coupling coefficients that depend on the overlap between modal fieldsand the refractive index perturbation. The coupling coefficients are expressed as given inequations (8), (9), and (10) below.Equation... (8)Equation... (9)Equation...(10)where w is the angular frequency, 0is the permittivity of free space, and ne(x, y)is theperturbed refractive index distribution given by equation (11) below.Equation... (11)where Rx and Ry are the bending radii along orthogonal directions. This couplingredistributes optical power among spatial modes, influencing modal gain dynamics and theoverall amplifier performance.

[0059] The complete model is solved numerically by discretizing the fiber cross-section anditeratively updating the power and population values along the fiber length. Both forwardand backward propagation are computed alternately using the set of boundary conditionsfor the launched pump, signal, and ASE powers as given in the equations (12), (13), (14),(15), and (16) below.Equation... (12)Equation... (13)Equation... (14)Equation... (15)Equation... (16)where R is the reflectivity at the fiber ends and L is the fiber length. Each forward-backwardpass constitutes one iteration, and the process was repeated until the relative change inpower values between successive iterations satisfied a predefined convergence criterion.

[0060] The predefined convergence criterion is calculated as mentioned below in steps S1,S2, S3, and S4 given below.

[0061] S1: Let iteration (roundtrip) index be t. Indices: s = 1, Equation... ,Ns(signal wavelengths),m = 1, Equation... , Nm(modes), z = 1, Equation... , Nz(step-size along the length L of the fiber amplifier).Calculate point-wise absolute error as per equations (17), (18), and (19) below.Equation... (17)Equation... (18)Equation... (19)

[0062] S2: Calculate root mean square value along the fiber (over length z of the fiber)according to equations (20), (21), and (22) below.Equation... (20)Equation... (21)Equation... (22)

[0063] S3: Calculate error values from the RMS values according to equations (23), (24),and (25) below.Equation... (23)Equation... (24)Equation... (25)

[0064] S4: Check convergence. If the error value is less than a pre-set tolerance (Gamma) , thenthe convergence criterion is met. This checking of convergence is described in equation (26)below.Equation... (26)

[0065] Figure 3 shows exemplary supported modes (300) of a few-mode fiber at pumpsource wavelengths and signal wavelengths. In an exemplary embodiment, the supportedlinearly polarised (LP) modes of the FA unit (102) and the SA unit (106) at the pump andsignal wavelengths are illustrated in Figure 3. The computed mode fields are subsequentlyused to evaluate the overlap integrals for the pump and signal interactions with the dopedregion.

[0066] Figure 4 illustrates a schematic simulation workflow (400) of a signal in a few modefiber amplifier. Thus, the workflow of a signal in FA unit (102) and the SA unit (106) issame as shown in the Figure 4. As shown in Figure 4, at 402, the forward boundaryconditions are known for launching the signal. Thus, at z=0, the signal is launched accordingto the boundary conditions given above in equations (12), (14), and (16). Further, the signalpropagates in the forward direction. At 404, the forward propagation of the signal iscalculated according to the equations (3), (4), (5), (6), and (7). At 406, it is checked whetherthe convergence criterion is met or not. If the convergence criterion is met, then the outputobtained after 406 is the desired output and process stops at 408. In case the convergencecriterion is not met, then, the signal continues for backward propagation. Thus, at 410, thesignal is launched for backward propagation with boundary conditions as given above inequations (13) and (15). Further, the signal propagates in the backward direction. At 412,the backward propagation of the signal is calculated according to the equations (3), (4), (5),(6), and (7). Further, the signal is again launched for forward propagation and the cyclecontinues until convergence occurs.

[0067] Figure 5 illustrates a simulation workflow (500) of a signal through the system (100)for gain-equalized broadband amplification in few mode fibers. As shown in Figure 5, at502, the first amplified signal shown as Ps,m,(Lamda)(1)(L) is generated by the FA unit (102). The FAunit (102) primarily establishes the modal energy distribution. The first amplified signalPs,m,(Lamda)(1)(L) is fed to the SSF unit (104). The SSF unit (104) applies both spatial and spectralconditioning to the first amplified signal Ps,m,(Lamda)(1)(L) before injection of the first amplifiedsignal Ps,m,(Lamda)(1)(L) into the SA unit (106). The SSF unit (104) guides the first amplified signalPs,m,(Lamda)(1)(L) by the mechanism of selective attenuation. In selective attenuation, the SSF unit(104) suppresses the strongly amplified channels (or modes and wavelengths) in the firstamplified signal Ps,m,(Lamda)(1)(L) and the preserves of weaker amplified modes. This induces anadaptive redistribution of gain in the subsequent amplifier stage, that is, in the SA unit (106).The present step 502 corresponds collectively to steps 402 till 412 of Fig. 4. Mathematically,if Ps,m,(Lamda)(1)represents the first amplified signal at mode m and wavelength (Lamda) after the firstamplification stage, i.e., at the output of the FA unit (102), the attenuated signal entering theSA unit (106) is expressed as given in equation (27) below.Ps,m,(Lamda)Equation... (27)where tm,(Lamda) denotes the transmission coefficient matrix determined numerically to flattenboth spatial and spectral gain responses. This attenuation profile is obtained through anumerical optimization process aimed at minimizing the gain variance across all channels,defined as given in equation (28) below.Equation... (28)where Gm,(2)(Lamda)is the total gain at the output of the SA unit (106) and G- is the target gain value.In an embodiment, the target gain value is set by the user. For example, the user may set thetarget gain value of 50 dB at the output of the SA unit (106). Then the output generated afterthe SA unit (106) will have a flat gain of 50 dB with a slight variation. In an embodiment,the flat gain encompasses a variation of ±0.4 dB across approximately 100 nm bandwidth.The optimized transmission coefficient tm,(Lamda) effectively attenuates stronger channels whileallowing weaker ones to retain more power for subsequent amplification. Accordingly, theSSF unit (104) generates second signal as the output at 504.

[0068] Accordingly, in an embodiment, the selective attenuation encompasses computing,by the FA unit (102), a set of mode fields. Further, in this embodiment, the selectiveattenuation further encompasses determining, by the FA unit (102), a set of overlap integralsbased on the computed mode fields. Further, in this embodiment, the selective attenuationfurther encompasses determining, by the SSF unit (104), one or more high-amplificationmodes based on the overlap integrals for selective attenuation, wherein the highamplification modes are modes among the one or more modes, that have higher modaloverlap with doped core region of the FA unit (102) as compared to other modes. In anotherembodiment, the selective attenuation further encompasses reducing, by the SSF unit (104),respective powers of the one or more high-amplification modes.

[0069] The second signal is fed to the SA unit (106) for further amplification. The gain guiding effect manifests in the SA unit (106), where the input power distribution is spectrally and spatially shaped by the filtering performed by the SSF unit (104). This gain-guiding effect arises when the spectral-spatial filtering in the SSF unit (104) shapes Ps,m,(Lamda) (2) (0) such that the weakly amplified channels (m & (Lamda)) exploit the available pump power and inversion more efficiently before saturation occurs in the stronger channels. The attenuated strong channels enter the SA unit (106) at lower powers, resulting in reduced saturation of the available inversion. Consequently, weaker spatial or spectral channels, now with relatively higher inversion access, experience enhanced amplification. This dynamic redistribution of gain among the supported modes ensures that the available pump energy is guided preferentially toward the under-amplified channels, naturally driving the system toward intrinsic gain uniformity.

[0070] Notably, the filtering scheme in a single-mode fiber (SMF) is fundamentallydifferent from that in a few-mode or multi-mode (FMF / MMF). In a single-mode fiber(SMF) scheme only one spatial mode exists. The single-mode fiber system only needs tohandle wavelength channels, not mode-wavelength combinations. Filtering is thereforeone-dimensional, typically expressed as t(Lamda). On the contrary, in the few-mode or multi-modecase, each wavelength channel contains multiple spatial modes. When the signal passesthrough the first amplifier stage (which uses a few-mode fiber), intermodal coupling occurs.Because of this modal mixing, the output of the first amplifier contains different powerlevels for every combination of mode and wavelength. Therefore, the filtering step mustoperate on a two-dimensional grid of channels - spatial modes (m) and wavelengths ((Lamda)). Tocapture this, in an embodiment of the present disclosure, the attenuation / filteringcoefficients are arranged in the transmission coefficient matrix tm,(Lamda). In an embodiment, thetransmission coefficient matrix tm,(Lamda)is a 3×2 matrix (i.e., 3 modes × 2 wavelengths). Eachelement of the transmission coefficient matrix tm,(Lamda) represents the attenuation factor appliedto a specific mode-wavelength pair, ensuring proper power coupling to the secondamplification stage, that is, the SA unit (106).

[0071] In an embodiment, the output generated by the SA unit (106) at 506, i.e., the secondamplified signal, is further analysed at 508. The present step 506 corresponds collectivelyto steps 402 till 412 of Fig. 4. At 508, the analysis incudes checking whether the secondamplified signal has reached the target gain value or not. In a case where the secondamplified signal has reached the target gain value, then the second amplified signal is thegain-equalised amplified broadband signal as shown in 510. Thus, in an embodiment, thedisclosure encompasses amplifying, by the SA unit (106), the second signal, based on a gainguiding mechanism applied in the SA unit (106) on the second signal, to generate a secondamplified signal as a gain-equalized output signal if the second amplified signal correspondsto the target gain value obtained across the one or more wavelengths and the one or moremodes associated with the first signal. Also, in an embodiment, a gain variation in one ormore modes of the output signal is in a range of -0.4 decibel (dB) to +0.4 dB. In anothercase where the second amplified signal has not reached the target gain value, the secondamplified signal is fed back to the SSF unit (104) to update the transmission coefficientmatrix tm,(Lamda) as shown in 512. Thus, in an embodiment, the disclosure, in case of secondamplified signal not corresponding to the target gain value, encompasses updating thetransmission coefficient matrix based on the target gain value vide an Adam optimizationscheme. The disclosure, in this embodiment, further encompasses communicating theupdated transmission matrix to the SSF unit (104) to re-generate the second signal forcommunication to the second amplification unit (106),

[0072] In an embodiment, the transmission coefficient matrix tm,(Lamda) is updated using anAdam optimisation scheme. For updating the transmission coefficient matrix tm,(Lamda) using theAdam optimisation scheme, the SSF unit (104) includes an Adam optimizer to adapt thecoefficients. In an embodiment, the Adam optimization scheme is implemented by theprocessing unit (108). For each coefficient the Adam optimizer maintains exponentialmoving averages of the gradient and squared gradient (first and second moments). Thesemoments are bias-corrected by a power term and combined to compute an adaptive, per coefficient step: the coefficient is incremented by the bias-corrected first moment dividedby the square root of the bias-corrected second moment plus a small stability constant.Coefficients whose performance metric lies within a predefined narrow tolerance band areheld constant to prevent unnecessary perturbation, and coefficients in different spectralchannels are updated with a distinct step size. The procedure iterates until the gain-flattening(or gain-equalised) target gain value is achieved at the SA unit (106). The optimizationbegins by computing the per-coefficient error DeltaJ(sf, nf), and each coefficient of the two-dimensional filter function tm,(Lamda) (sf, nf) is then iteratively updated to minimize this error.Each coefficient is initially assigned a random decimal value uniformly sampled between 0and 1. In an embodiment, the Adam optimisation scheme is implemented according to theequations (29), (30), (31), (32), (33), and (34) below.Equation... (29)Equation... (30)Equation... (31)Equation... (32)Equation... (33)Equation... (34)n the equations (29-34), alpha denotes the optimization step size (or the learning rate) thatcontrols how aggressively each filter coefficient is adjusted during every iteration. Theparameter Beta1 represents the decay rate for the first-moment estimate (momentum term); atypical value of 0.9 assigns higher weight to the most recent gradient information while stillretaining a short history of past gradients. The parameter Beta2 is the decay rate for the second moment estimate (squared gradients), commonly set to 0.999 to maintain a long-term, stableestimate of variance across iterations. Finally, element of is a small constant (usually 10-8) added tothe denominator of the update rule to prevent division by zero and ensure numerical stabilityduring the processing for the Adam optimization scheme. Accordingly, in an embodiment,the disclosure encompasses updating the transmission coefficient matrix vide an Adamoptimization scheme, based on exponential moving averages of the gradient and squaredgradient defined by first and second moments. Further, in an embodiment, the moments arebias-corrected by a power term and combined to iteratively compute at least one adaptivecoefficient. Notably, the power term refers to the iteration number used as an exponent inthe bias-correction step of the Adam optimization scheme. Since this iteration index is raisedto the power of Beta during the moment calculations, it is described as a "power term". In afurther embodiment, the coefficients whose performance metric lies within a predefinednarrow tolerance band are held constant to prevent unnecessary perturbation, andcoefficients in different spectral channels are updated with a distinct step size.EXAMPLE

[0073] In an example, the FA unit (102) consists of a 10 m-long thulium-doped fiber (TDF) supporting four pump modes and three signal modes-LP01, LP11e , and LP110. The distribution of launched pump powers among these modes is listed in Table 2 below.Table 2:Further, a bidirectional pumping scheme is implemented, where the forward pump ispredominantly launched into the LP11 family, while the backward pump power is distributedbetween LP11 and LP02 modes to enhance spatial coverage of the inversion region. Forcomputational efficiency, only one polarization component of each degenerate LP mode isincluded in the simulation, since the x- and y-polarized counterparts share identicalpropagation constants and overlap integrals. This simplification effectively reduces thenumber of spatial signal channels to three without loss of generality, while preserving theessential modal interaction physics. Inclusion of both polarization components wouldsimply redistribute the available gain equally between them, leaving the overall modal gaindynamics unchanged. Two representative wavelengths, 1840 nm ((Lamda)1) and 1940 nm ((Lamda)2),separated by 100 nm, are considered to assess the amplifier's broadband performance. Eachspatial-spectral signal channel is assigned an identical input power of -17.7 dBm, ensuringa uniform excitation condition across all modes and wavelengths.

[0074] Figure 6 shows characteristics (600) of evolution of the forward-propagating signalmodes in the FA unit (102) of the system (100). The characteristics of evolution of theforward-propagating signal modes in the FA unit (102) as shown in Figure 6, reveal a mode dependent gain behaviour. The LP01 mode exhibits the highest amplification, primarily dueto its stronger confinement and superior overlap with the centrally doped region of the fiber.The LP11 modes, in contrast, exhibit weaker gain due to their larger mode field radii andreduced overlap with the doped core. This spatial mismatch limits their access to theavailable inversion, causing slower power growth along the fiber.

[0075] In addition to spatial variation, a strong wavelength-dependent gain imbalance isalso observed. The emission cross-section of Tm3+ decreases gradually with increasingwavelength beyond 1.9 µm, leading to reduced amplification efficiency at 1940 nmcompared to 1840 nm. As a result, all modes exhibit a declining gain trend toward longerwavelengths, with the LP01 mode maintaining overall dominance across the spectral range.The observed gain imbalance highlights the challenge of achieving simultaneous modal andspectral gain uniformity in a multimode amplifier. To address this, a gain-guidingmechanism is implemented through combined spatial and spectral filtering, thecharacteristics of which are elucidated through the analysis of the output of the SA unit(106).

[0076] Further, in the second stage configuration, the spectrally and spatially filtered outputfrom the first stage is injected into a 6-meter-long Tm-doped fiber (TDF). The pumpconfiguration and modal power distribution employed in this stage are summarized in Table3 below.Table 3:The input signal power ratios of the modes coupled to the SA unit (106) are determinedthrough numerical optimization using the Adam optimization scheme, targeting a flat gainof approximately 50 dB. The optimization process adjusts the initial power ratios tominimize gain differences between the spatial channels. This step ensures that weakermodes are preferentially amplified, thereby compensating for inherent mode-dependent gaindisparities. Figure 7(a) shows characteristics of evolution of the forward-propagating signalmodes in the SA unit (106) of the system (100), and Figure 7(b) shows an input signal powerof various modes coupled to the SA unit (106) of the system (100). The power evolutionalong the fiber, shown in Figure 7(a), shows the convergence of modal powers, signifyingan active redistribution of gain among the modes. All three signal modes reach nearly equaloutput power of about 0.8 W, validating the effectiveness of the proposed gain-guidingmechanism in achieving intrinsic modal equalization.

[0077] Figure 8(a) shows amplified spontaneous emission (ASE) characteristics of forwardpropagating signal modes in the FA unit (102) of the system (100), Figure 8(b) shows ASEcharacteristics of backward-propagating signal modes in the FA unit (102) of the system(100), Figure 8(c) shows ASE characteristics of forward-propagating signal modes in theSA unit (106) of the system (100), and Figure 8(d) shows ASE characteristics of backwardpropagating signal modes in the SA unit (106) of the system (100). The Figures 8(a-d) showthat the forward ASE component increased progressively, while the backward ASEdiminished and remained at a much lower level. The higher forward ASE is primarily dueto residual ASE carried over from the FA unit (102), but its contribution remained minorcompared to the second amplified signal, indicating that the amplifier operated well belowsaturation.

[0078] Figure 9 shows a comparison (900) of gain between the FA unit (102) and the SAunit (106) of the system (100). In Figure 9, the "Stage 1" refers to the amplification by theFA unit (102), and "Stage 2" refers to the amplification by the SA unit (106). Also, the targetgain value was set to 50 dB. Figure 9 shows that the gain variation of the second amplifiedsignal is within ±0.4 dB across the wavelength range of 1840-1940 nm, nearly 100 nmbandwidth. This confirms that the gain-guiding mechanism, in conjunction with optimizedmodal attenuation and pump distribution, successfully suppresses both wavelength dependent and mode-dependent gain fluctuations.

[0079] Figure 10 illustrates a method (1000) for gain-equalized broadband amplification infew mode fibers. As shown in Figure 10, at 1002, the method (1000) includes amplifying,by the FA unit (102), an input signal to generate a first amplified signal, wherein the FA unit(102) comprises a few-mode fiber, and the input signal is a multi-mode broadband opticalsignal. The input signal is amplified by the FA unit (102) as disclosed above in the presentdisclosure. The present step 1002 corresponds to step 502 of Fig. 5. Further, at 1004, themethod (1000) includes receiving, by the SSF unit (104) from the FA unit (102), the firstamplified signal. The present step 1004 corresponds to step 504 of Fig. 5. Further, at 1006,the method (1000) includes determining, by the SSF unit (104), a transmission coefficientmatrix associated with a target gain value, said matrix corresponding to one or morewavelengths and one or more modes associated with the first amplified signal, for selectiveattenuation of the first amplified signal. The determination of the transmission coefficientmatrix for selective attenuation of the first amplified signal is explained above in the presentdisclosure and the same is not repeated here for the sake of brevity. The present step 1006corresponds to step 506 of Fig. 5. At 1008, the method (1000) includes selectivelyattenuating, by the SSF unit (104), power intensity of the first amplified signal, based on thetransmission coefficient matrix, to generate a second signal. The details related to selectiveattenuation of the power intensity of the first amplified signal are explained above in thepresent disclosure and the same are not repeated here for the sake of brevity. The presentstep 1008 corresponds to step 508 of Fig. 5. At 1010, the method (1000) includesamplifying, by SA unit (106), the second signal, based on a gain guiding mechanism appliedin the SA unit (106) on the second signal, to generate a second amplified signal as a gain equalized output signal if the second amplified signal corresponds to the target gain valueobtained across the one or more wavelengths and the one or more modes associated withthe first signal. The present step 1010 corresponds to step 510 of Fig. 5. The details relatedto amplification of the second signal to generate the second amplified signal are explainedabove in the present disclosure and the same are not repeated here for the sake of brevity.

[0080] In view of the above, the present disclosure provides a method and a system forbroadband amplification using few mode fibers capable of delivering a flat gain in abroadband range of operation. Due to selective attenuation performed by the SSF unit, adesired coupling power was calculated and coupled in the second signal that was input tothe SA unit, thereby minimizing mode-dependent and wavelength-dependent gain variationsin the output of the SA unit. Further, since the system involves the few-mode fibers capableof amplifying the signals inherently, by selective attenuation performed by the SSF unit,makes the system highly scalable and also reduces system complexity while achieving high capacity optical communication. Also, since gain-equalisation depends on selectiveattenuation instead of using the known gain-equalisers, the system is less sensitive tofabrication precision. Further, the system offers significant potential across various photonicdomains due to its ability to deliver flat, broadband, and mode-equalized gain through amulti-pass configuration. Additionally, the disclosed system can be employed in mode division-multiplexed (MDM) systems to simultaneously amplify multiple spatial modeswith minimal mode-dependent gain variation. This ensures uniform amplification acrosschannels, enabling higher data throughput and improved spectral efficiency in next generation optical networks. The flat and mode-balanced gain characteristics make thesystem suitable for high-power multimode laser architectures, where gain redistributionsuppresses nonlinear distortions and modal instabilities. This leads to enhanced beamquality and power scalability, which are critical in industrial and defence laser applications.Furthermore, the broadband amplification provided by the system and method can improvesignal strength and sensitivity in distributed fiber sensing and multimode imaging systems.Its ability to manage modal gain also ensures stable and repeatable measurements.

[0081] While the foregoing describes various embodiments of the disclosure, other andfurther embodiments of the invention may be devised without departing from the basicscope thereof. The scope of the disclosure is determined by the claims that follow. Thedisclosure is not limited to the described embodiments, versions, or examples, which areincluded to enable a person having ordinary skill in the art to make and use the disclosurewhen combined with information and knowledge available to the person having ordinaryskill in the art.

Claims

1. A method for generating a gain-equalised amplified broadband signal using few mode fibers (FMFs), comprising: amplifying (1002), by a first amplification (FA) unit (102), an input signal to generate a first amplified signal, wherein the FA unit (102) comprises a few-mode fiber, and the input signal is a multi-mode broadband optical signal; receiving (1004), by a spatial-spectral filtering (SSF) unit (104) from the FA unit (102), the first amplified signal; determining (1006), by the SSF unit (104), a transmission coefficient matrix associated with a target gain value, said matrix corresponding to one or more wavelengths and one or more modes associated with the first amplified signal, for selective attenuation of the first amplified signal; selectively attenuating (1008), by the SSF unit (104), power intensity of the first amplified signal, based on the transmission coefficient matrix, to generate a second signal; and amplifying (1010), by a second amplification (SA) unit (106), the second signal, based on a gain guiding mechanism applied in the SA unit (106) on the second signal, to generate a second amplified signal as a gain-equalized output signal if the second amplified signal corresponds to the target gain value obtained across the one or more wavelengths and the one or more modes associated with the first signal.

2. The method as claimed in claim 1, further comprises in case of second amplified signal not corresponding to the target gain value, updating the transmission coefficient matrix based on the target gain value vide an Adam optimization scheme; and communicating the updated transmission matrix to the SSF unit (104) to regenerate the second signal for communication to the second amplification unit (106).

3. The method as claimed in claim 2, wherein updating the transmission coefficient matrix comprises: updating the transmission coefficient matrix vide an Adam optimization scheme, based on exponential moving averages of the gradient and squared gradient defined by first and second moments.

4. The method as claimed in claim 3, wherein the moments are bias-corrected by a power term and combined to iteratively compute at least one adaptive coefficient.

5. The method as claimed in claim 4, wherein coefficients whose performance metric lies within a predefined narrow tolerance band are held constant to prevent unnecessary perturbation, and coefficients in different spectral channels are updated with a distinct step size.

6. The method as claimed in claim 1, wherein the selective attenuation comprises: computing, by the FA unit (102), a set of mode fields; determining, by the FA unit (102), a set of overlap integrals based on the computed mode fields; and determining, by the SSF unit (104), one or more high-amplification modes based on the overlap integrals for selective attenuation, wherein the high amplification modes are modes among the one or more modes, that have higher modal overlap with doped core region of the FA unit (102) as compared to other modes.

7. The method as claimed in claim 4, wherein the selective attenuation further comprises: reducing, by the SSF unit (104), respective powers of the one or more high amplification modes.

8. The method as claimed in claim 1, the method further comprising: pumping, by one or more pump sources, the input signal and the second signal during amplification.

9. The method as claimed in claim 1, wherein a gain variation in one or more modes of the output signal is in a range of -0.4 decibel (dB) to +0.4 dB.

10. A system for generating a gain-equalized amplified broadband signal using few mode fibers (FMFs), comprising: a first amplification (FA) unit (102) configured to amplify an input signal to generate a first amplified signal, wherein the FA unit (102) comprises a few-mode fiber, and the input signal is a multi-mode broadband optical signal; a spatial-spectral filtering (SSF) unit (104) configured to: receive, from the FA unit (102), the first amplified signal; determine a transmission coefficient matrix associated with a target gain value, said matrix corresponding to one or more wavelengths and one or more modes associated with the first amplified signal, for selective attenuation of the first amplified signal; and selectively attenuate power intensity of the first amplified signal, based on the transmission coefficient matrix, to generate a second signal; and a second amplification (SA) unit (106) configured to amplify the second signal, based on a gain guiding mechanism applied in the SA unit (106) on the second signal, to generate a second amplified signal as a gain-equalized output signal if the second amplified signal corresponds to the target gain value obtained across the one or more wavelengths and the one or more modes associated with the first signal.