Kovacs-like memory effect mediated fiber Bragg grating: resembling a silica quipu

Abstract

In antiquity, civilizations employed stone carvings and knotted quipu cords for information preservation. Modern telecommunications rely on optical fibers - silica glass strands engineered for light transmission - yet their capacity as archival media remains untapped. This study explores a novel fiber Bragg grating (FBG) configuration exhibiting thermally programmable memory effects for optical data storage. Capitalizing on temperature-dependent spectral characteristics, we demonstrate finite spectral tuning through controlled thermal annealing, achieving irreversible spectral modifications via a light-induced stress mechanism analogous to the Kovacs memory effect in glassy materials. The engineered dual-dip FBG architecture enables multiplexed wavelength encoding, functioning simultaneously as a thermal history recorder and laser-writable data medium - mirroring the information knots of ancient quipu devices. This optical quipu concept pioneers one-dimensional photonic memory technology, opening new avenues for optical fiber applications in the information age.

This work introduces a dual-dip fiber Bragg grating (FBG) with thermally programmable memory. Leveraging light-induced stress and thermal annealing, it enables irreversible spectral tuning—mimicking the Kovacs effect. The FBG serves as a laser-writable, multiplexed optical data storage medium and thermal history recorder.

Introduction

Information storage and dissemination is one of the most precious treasures for the development of human civilization and has accompanied mankind all along the journey. Shape is the most intuitionistic and straightforward message for memorizing and transmitting. Ancient Inca civilization utilized an assemblage of knotted fiber cords as the information storage media, dubbed as quipu. The encoding strategy using colors and layout of the fibers, and the knotting fashion and spatial distribution of the knots on the fibers makes the quipu a facile and elaborate shape-based memory system of information¹, which intrigues great attention of extensive fields from Mathematica, information technology to engineering^{2, 3–4}.

At present, the shape-based memory functionality is routinely realized by plastic or amorphous materials, which have the capability of altering their shape through an external stimulus. For instance, the thermally induced shape-memory effect in such materials can be activated through heating, offering benefits across a range of industries including medicine, textiles, manufacturing, and architecture^{5, 6, 7, 8–9}. Glass, as a typical thermosetting substance with an out-of-equilibrium nature, can retain memory of its experience, giving rise to unexpectedly intricate pathways of equilibration^{10, 11–12}. Normally, a single annealing process applied on glass would result in a monotonic transition from a higher energy state to a lower one^13,14. By contrast, a double annealing process (a higher temperature followd by a low temperature) would elicit a non-monotonic relaxation of energy state in glass, represened by the anomalously increasing enthalpy and volume at the beginning of the second annealing before finally decreasing as equilibrium is reached. This phenomenon was termed as Kovacs memory effect, which could acount for the rejuvenation and high temperature resistance of glass¹⁵. Furthermore, a strain-driven Kovacs-like memory effect was has recently been reported, characterized by non-monotonic stress relaxation phenomena during a two-step (high-to-low) strains stimulation, which enriched the modulation approach of memory effect of glass substances¹⁶.

Glass-based optical fibers are conceptualized as a novel high-technology fiber for the transmission of light-based messages, having interwoven the global telecommunication network and triggered a new informational revolution^17,18. As a superior and commercially viable passive integrated fiber-optic device, fiber Bragg grating (FBG) with a permanent UV modulation structure holds a trememdous promise to function as bit-recording nodes -optical fiber quipu due to its advantages of minimal channel occupancy and multiplexing capabilities^{19, 20, 21–22}. Early studies have indicated that the process of UV inscription of fiber gratings is accompanied by changes in stress and refractive index^23,24, which typically involve the core-network compression and relaxation²⁵, and, more importantly, the spectral signal of FBG is dictated by the periodic modulation, providing a direct means to observe the changes under stimulatioin in the glass material. It is intriguing to explore the occurrence of UV-strain driven Kovacs-like memory effect in FBG and its potential application in data recording.

In this work, we present the exploration of a unique type of fiber Bragg grating called Kovacs-like memory effect fiber Bragg grating (KM-FBG) that possesses the feature of high-temperature spectral shaping and memory. Analogs to the tailoring of the shape of materials, the inherent double-dip spectrum of KM-FBG, including a Type I-like dip (single UV-strain stimulation) and a type-IIa dip (double UV-strain stimulation), can also be shaped by the heating stimulus through the different responsivity of the two dips in terms of the applied temperature, presenting a spectral melting effect. Furthermore, the melt spectrum can retain its shape as the KM-FBG is cooled down, conferring the temperature-induced memory functionality. The principle of the spectral melting effect of KM-FBG is revealed by elucidating the role of the negative index change component formed in the FBG inscription process, which shares similar mechanism to the latter low-strain stimulation driven Kovacs-like memory effect¹⁶. We subsequently demonstrated that active spectral shaping using laser irradiation can make ‘knots’ on optical fiber to form optical quipu by cascading KM-FBGs with the wavelength-multiplexing method. Taking advantage of the exceptional heat resistance and anti-interference, the KM-FBG can log the peak temperature event during a period without the need of establishing a sensing network. Furthermore, the fast response to annealing stimulation endow KM-FBG with the capability of laser-activated data encoding. The optical quipu, utilized as the one-dimensional digital memorizers, can open up a new degree of freedom of light encoding, which would benefit from the reservoir of the astronomical yields of optical fibers (more than four billion kilometers of optical fibers have been manufactured so far, which is almost enough to link the Earth to Neptune)^26,27. The exploration of KM-FBG may not only provide new solutions and insights for the annealing relaxation studies of glass materials, but also propel the optical fiber from a sole information transmitter and sensor extending to data storage media.

Results

Type I and Type IIa fiber Bragg gratings represent the quintessential styles within the domain of fiber optic technology. These Bragg gratings can be distinguished based on the different evolutionary phases. As depicted in Fig. 1a, Type I grating predominantly undergoes a phase of positive refractive index modulation. In contrast, Type IIa grating is characterized by a negative refractive index modulation, which occurs after the saturation of Type I growth. Accordingly, Type I grating manifests a steady rise in the internal strain imposed within the optical fiber throughout the inscription process, while Type IIa grating is associated with an initial increase of internal strain, followed by a subsequent decline, as shown in Fig. 1b. The standard FBG (typically type-I and IIa), as is shown in Fig. 1c, was generated by the uniform modulation. A Bragg resonance derives from the modulation turns around the transmitting light of the phase-matched wavelength, presenting a single dip in the transmission spectrum and the corresponding peak in the reflection. Conventionally, the Bragg resonance moves to a longer wavelength as the ambient temperature increases and is restored as the heat is removed. The spectral profile of the Bragg resonance remains unaltered throughout the heat-and-cool annealing cycle. In contrast, the KM-FBG exhibits a unique dual-resonance spectrum, comprising both Type I-like (left) and Type IIa (right) dips, as depicted in Fig. 1d. Previous studies have demonstrated stress-independent temperature sensing by constructing Type I and IIA signals using two separate gratings^28,29. In contrast, the inscription method reported in this paper formed two reflection signals through a single grating inscription process. The two dips are given rise by the two modulation structures interleaved in the fiber core, which are mediated by the Talbot-type pattern of the incident laser beam, in which the higher orders of diffraction light of the phase mask participation^{30, 31–32} (see Supplementary Fig. S1). Unlike the π-phase-shifted gratings produced by the odd harmonics^{33, 34–35}, the KM-FBG is observed only in the negative modulation phase. Intriguingly, the KM-FBG shows an extraordinary phenomenon when exerting an annealing cycle. In the course of heating, the dual dips both migrate towards longer wavelengths but converge within the spectral realm. Notably, the KM-FBG retains its newly acquired spectral configuration at elevated temperatures and maintains this form upon cooling.

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Fig. 1

Diagram and exploration of fiber Bragg grating with temperature-induced spectral memory.

a Diagram of evolutional manners of Type I and Type IIa fiber Bragg grating. b Schematic of fiber grating internal strain loading with different grating types. c Working principle of standard FBG. d Working principle of the memory effect FBG (KM-FBG). e Spectral evolution of a sample KM-FBG regarding the annealing cycle. The spectral profile of the two resonances demonstrated a phenomenon referred to as spectral melting throughout the heating process. This melted spectral pattern preserved its configuration following cooldown, akin to a two-flavored ice cream blending in a warm environment and re-solidifying upon return to the freezer.

Figure 1e presented an example of KM-FBG which was subjected to an annealing cycle. Initially, the KM-FBG has a maximum grating strength of 15.5 dB and a wavelength gap between the dual dips (Δλ) of 0.32 nm, respectively. Upon the application of heat to the KM-FBG, a redshift was observed in both dips, with the type-I-like dip (positioned on the left) exhibiting a more pronounced sensitivity compared to the type-IIa dip (situated on the right). This differential response led to a narrowing of Δλ to 0.29 nm upon reaching 250 °C. As the KM-FBG was subjected to further temperature elevation to 450 °C, the type-I-like dip caught up with the type-IIa counterpart, resulting in a fusion of the two. This dip merging gave rise to a heightened attenuation band characterized by an asymmetric blade-shaped transmission spectrum. The symmetrical evolution of the merged dip could be observed in the following temperature rising process, inferring that the two dip components continued their evolutionary pace. Eventually, the grating exhibited a symmetrical shape at 600 °C. By cooling the KM-FBG, the merged dip no longer recurred to the initial dual-wavelength spectrum but maintained the spectral shape as same as 600 °C. In addition, the dip wavelength of the annealed KM-FBG was significantly shorter than the initial dip wavelength at 25 °C, where the room temperature fluctuation was less than 1 °C. In other words, the spectral gap of the two dips would memorize the heating temperature experienced, which could be dubbed as a spectral melting effect. The effect was akin to a melt-two-tastes ice cream, in which the two ice cream balls blended in the hot environment and frozen as it was chilled again.

The KM-FBG was explored in the small core fibers(commercial photosensitive Er-doped fiber, M5 from Fibercore Ltd.), whose core diameters are smaller than half of Talbot length of incident ultraviolet (UV) laser passing through the phase mask^36,37. The detailed spectral evolution of KM-FBG is elaborated in Supplementary Fig. S2. The two dips of KM-FBG are generated in single inscription process at the early stage of Type IIa dip formation, and then remerge as the grating is further inscribed. For the most part, the KM-FBG exhibits a single peak, and the separation of the two grating signals is only observed in the early stage of Type IIa. Furthermore, the external strain applied on the fiber can accelerate the inscription process of KM-FBG grating. This is because the applied stress affects the photosensitivity of the thin-core fiber, thereby accelerating the formation of type IIa gratings^38,39

The Kovacs memory effect¹⁵ and strain-driven memory effect¹⁶ of glass both undergo two-step stimulation in the annealing process but are dictated by annealing temperature and stress loading, respectively, which are shown in top and upper-middle schematics of Fig. 2a. The glass material can remember the first step simulation and resist change in the second, enabling the non-monotonic evolution. The UV inscription of FBG also introduces a photo-induced stress into glass^25,40, indicating a similar strain-driven Kovacs-like memory effect theoretically.

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Fig. 2

Kovacs-like memory effect produced in FBGs.

a Schematic mechanism of Kovacs memory effect (top), strain-driven Kovacs-like memory effect (upper middle), UV induced Kovacs-like memory effect which related to Type IIa FBG (lower middle), and UV and external strain mixed Kovacs-like memory effect (bottom). b Bragg wavelength change of varous types of FBGs undergoing the same 350 °C annealing process. c Relative reflectivity changes of the FBGs undergoing the annealing process. KM-FBG, Type I and strain preloaded KM-FBG were annealed at 350 °C, and two IIa FBGs were annealed at about 300 °C and 700 °C, respectively.

High-temperature annealing has the potential to efface the fiber Bragg grating structure due to the relaxation of photo-induced stress. To avert this erasure, it is imperative that the FBG undergoes an initial phase of high UV intensity modulation, which is then followed by a decrement in the modulation level. This procedural sequence is in concert with the inscription technique utilized for Type IIa gratings, as illustrated in the lower middle segment of Fig. 2a. The lower panel of Fig. 2a reveals the another type of a Kovacs-like memory effect that harnesses the overlay of the UV exposure (internal stress) and applied external stress.

In contrast to Type I FBG, which exhibits a degradation in dip strength accompanied by a corresponding blueshift in wavelength (Δλ_Blue) during high-temperature annealing, Type IIa FBG manifests the resilience to thermal-induced recession by unleashing the second phase of UV-induced internal stress. Research⁴¹ has also point out that Type I gratings are consistently present as a component within Type IIa gratings, and their extent is affected by the inscription duration. The thermal stability of Type IIa gratings is associated with the decay of the Type I component. Regardless, the final results indicate a more pronounced Δλ_Blue while concurrently preserving the stability of the dip strength. Figure 2b presents the comparison of wavelength evolution for four distinct types of FBGs following a uniform annealing procedure of 350 °C. The Type I FBG exhibited the smallest Δλ_Blue of 0.16 nm post-annealing, attributable to the negligible photo-induced internal stress. In contrast, the other three FBGs, all incorporating Type IIa characteristics, demonstrated more substantial Δλ_Blue values. The Type IIa FBG registered the highest Δλ_Blue of 0.38 nm. The KM-FBGs, with and without pre-stress, exhibited Δλ_Blue values of 0.37 nm and 0.34 nm, respectively. Notably, during the annealing process, the two distinct dips of the KM-FBGs coalesced into a single signal at elevated temperatures. In other words, upon cooling, the Type IIa dip (refer to Supplementary Fig. S2e, f) exhibited a larger Δλ_Blue compared to the Type I-like dip.

Figure 2c showcases the intensity change of Bragg reflections of the different types of gratings throughout the annealing process. Each FBG exhibited a single reflection signal after annealing. In contrast to type I FBG following the monotonic decreasing of reflectivity, the other three types of FBGs showed a Kovacs-like rise before decreasing. Type IIa FBG features its Kovacs-like rise characteristic under about 300 °C annealing and the effect is more prominent under 700 °C annealing. A similar effect was also discernible for the KM-FBG subjected to annealing at 350 °C, despite that the increase in reflectivity was less pronounced compared to that of the Type IIa FBG. This discrepancy can be attributed to the reduced strain relaxation induced by the UV irradiation during the second phase of modulation, in alignment with Tong’s findings¹⁶. The application of additional external strain enabled the KM-FBG to achieve the necessary level of strain relaxation post-modulation, thereby manifesting a comparably significant Kovacs-like intensity increase akin to the Type IIa FBG. This outcome further corroborates the mechanism of FBG formation, emphasizing the role of UV-induced strain within the silica fiber matrix.

We subsequently embarked on a quantitative investigation into the phenomenon of spectral melting exhibited by the KM-FBG sample subjected to annealing at diverse temperatures, utilizing this as a case study. Notably, we incorporated an additional Type I FBG on the same fiber as a cascade to facilitate a more comprehensive comparison. The KM-FBG and Type I FBG exhibited Bragg wavelengths of 1544.5 nm and 1546.5 nm, respectively, as depicted in Fig. 3a. The annealing sequence was performed using a stepwise temperature increase, culminating at a maximum temperature of 600 °C. The spectral evolution of both FBG types throughout the annealing process is illustrated in Fig. 3b, with comprehensive data provided in Fig. 3c.

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Fig. 3

Investigation of the underlying mechanism of the temperature memorized effect.

a Schematic of a cascade consisting of a KM-FBG and a Type I FBG, which were annealed with a maximum temperature of 600 °C. b Spectral evolution of the cascaded grating logged from each step of the heating processes. c Temperature sensitivity of the three dip signals with the range of room temperature to 600 °C extracted from the spectral variation. Type I-like dip and Type IIa dip represented KM-FBG’s two dips, and Type I dip represented the normal Type I FBG’s dip, respectively. d Comparison of the Raman spectra from the blank fiber without (w/o) grating, raw KM-FBG, and annealed KM-FBG. The peak at 495 cm⁻¹ associated with fourfold rings and 606 cm⁻¹ associated with three fold rings.

As the temperature rose, the Bragg resonances for both grating types redshifted to longer wavelengths. The Δλ of the KM-FBG progressively diminished from an initial 0.4 nm, eventually becoming indiscernible above approximately 400 °C. The overall reflectivity of KM-FBG had no significant decay throughout the annealing process. For the Type I FBG, in tandem with the redshift of the Bragg resonance, the reflectivity of the grating experienced thermal degradation due to the direct erasure of the first phase of refractive index modulation at elevated temperatures. The reflectivity of the grating plummeted from an initial 18.41 dB to a mere 5.63 dB by the end of the process. The decline in reflectivity signifies the dissipation of the refractive index modulation within the grating, affecting not only the contrast of the index fringes but also the average index change^21,42. Nonetheless, the magnitude of the blueshift, which corresponds to the reduction in the average index change, for the Type I FBG (0.44 nm) was less pronounced than that observed for the KM-FBG (0.76 nm for Type I-like dip and 1.16 nm for Type IIa dip). This was the case even though the KM-FBG managed to preserve its reflectivity to a significant extent. This abnormal phenomenon observed in the comparative test endowed us with a telltale for unveiling the mechanism of the discovered spectral melting and temperature memory effects.

From Fig. 3c, it can be clearly observed that the temperature response of Type IIa dip (12 pm/°C) is lower than that of Type I-like dip (12.9 pm/°C) and Type I FBG (13.7 pm/°C). As mentioned above, Type IIa FBG with the second phase of negative index modulation (UV induced strain relaxation)^38,43 can resist the thermal decay due to the Kovacs like memory effect. The effect of various modulations on the spectrum in KM-FBG is given by the following equations:

1

$\mathrm{\Delta }{\lambda }_N=\mathrm{\Delta }{\lambda }_{\eta }-\mathrm{\Delta }{\lambda }_D$

2

$\mathrm{\Delta }{\lambda }_D=0\left(T\le T_D\right)$

3

$\mathrm{\Delta }{\lambda }_D=2\left(\frac{d\overline{\mathrm{\Delta }n}}{dT}\right)\left(T-T_D\right){\mathrm{\Lambda }}_g\left(T>T_D\right)$

4

$\mathrm{\Delta }{\lambda }_x=\mathrm{\Delta }{\lambda }_{\eta }-{\alpha }_x\mathrm{\Delta }{\lambda }_{Neg}$where ${\mathrm{\Delta }\lambda }_N$ and ${\mathrm{\Delta }\lambda }_x$ mean the overall wavelength shifts of the Type I FBG and KM-FBG, respectively, and x indicates either of the dual dip signals (x = I means type-I-like signal, x = IIa means the type-IIa signal). ${\mathrm{\Delta }\lambda }_{\eta }$ represents the thermo-optic effect induced wavelength shift. And ${\mathrm{\Delta }\lambda }_D$ means the thermal decay mediated wavelength blueshift, which depends on the loss of the average index change ($\overline{\mathrm{\Delta }n}$). T and T_D refer to the heating temperature and decay temperature of the FBG (normally 250 ~ 300 °C for Type I FBG). ${\Lambda }_g$ represents the grating period and ${\mathrm{\Delta }\lambda }_{Neg}$ means the negative index change induced blueshift of the Bragg wavelength and α indicates the amount of negative index change component involved. The equations indicate that thermal decay induces a detectable damping on the positive wavelength shift attributed to the thermo-optic phenomenon.

Although a damping effect is similarly observed for the type-I-like dip during the entire annealing process, the distinct origin is indicative of negative index modulation, which can be speculated by the minimal thermal decay observed. Consequently, the pursuit of the Type IIa dip by the type-I-like dip in the real of spectral wavelength as the temperature increases is also ascribed to this damping effect, where the type-I-like dip has less amount of negative index change component, i.e. the smaller $\alpha$. And it can be speculated that the difference of damping between the two dips, which can be described by the factor of $\left({\alpha }_I-{\alpha }_{IIa}\right)\mathrm{\Delta }{\lambda }_{Neg}$, would leave the footprint as the annealing process is finished, thus enabling the memory effect of the spectrum tailored by the high temperature annealing.

This hypothesis could be verified by delving into the fundamental mechanisms governing the photosensitivity of optical fibers. The photon induced refractive index increase of fiber core involves the inelastic compaction of microscopic core network structure, in which the transformation of network structure from high-order ring to low-order ring takes place^23,44,45. For the Type I FBG, the annealing-induced decay of the grating is consistent with a regime characterized by the removal of densification via thermal excitation, as evidenced by the concurrent blueshift of the Bragg wavelength and the reduction in grating strength. The Type IIa grating, by contrast, has already experienced a strength-decreasing phase during UV exposure, whereas the average index change remains increasing. This elucidates that the core network structure is still compressed in this phase as the incident region of the fiber core reaches the limit of compaction. Once the grating modulation is overwhelmed by the overall compaction-that is, the highest refractive index change, the refractive index is subsequently subjected to a downward phase, where the dilation of the core network structure takes over^25,43,46. The negative index change of the incident region endows the grating with the strength increase accompanied by the blueshift of Bragg wavelength.

Raman spectral analysis is a powerful tools to uncover internally structural change of silica⁴⁷.The dilation of core network structure correlates with an increase in the prevalence of lower-order rings, such as fourfold and threefold symmetries, as evidenced by Raman spectroscopic analysis⁴⁸. We tested the three types of fiber samples, the unmodified blank fiber, the raw KM-FBG, and the KM-FBGs post-annealing at 600 °C. As is shown in Fig. 3d, the peak at 495 cm⁻¹ (associated with fourfold rings) remains relatively stable across the three samples. In contrast, the peak at 606 cm⁻¹ (corresponding to threefold rings) exhibits a marked increase from the blank fiber through the raw KM-FBG to the annealed KM-FBG. The enhancement of threefold ring structures within the KM-FBG corroborates the Raman spectral analysis of the Type-IIa grating, wherein the predominant structural expansion drives the grating formation. The marked intensification of the 606 cm⁻¹ peak following annealing underscores a substantial increase in threefold ring structures, which persistently contribute to the structural expansion and, consequently, the negative index shift at elevated temperatures. The reason why the spectrum of KM-FBG cannot return to its original state after annealing is the small rings (e.g., 3- and 4-membered) are not regenerated upon cooling^{47,49, 50–51}, expressing an irreversible spectral melting phenomena, namely, the temperature memory effect.

In the subsequent study, we examined the spectral melting characteristics of a KM-FBG subjected to various annealing temperature cycles. A KM-FBG sample was fabricated with an initial dip separation (Δλ₀) of 0.44 nm. The increased Δλ₀ facilitated an enhancement in the spectral merging threshold temperature, permitting a distinguishable Δλ up to 500 °C. The entire annealing process encompassed a sequence of successive stages, extending up to 600 °C, with each stage targeting a specific temperature increment of 100 °C. During each cycle, the fiber Bragg grating was heated to the designated temperature and sustained there for a duration of 1 h before being allowed to cool back to room temperature (25 °C). The spectral evolution of the KM-FBG was monitored in each annealing cycle, as is shown in Fig. 4a. By analyzing the spectral data, the dip separation post-annealing (Δλ_P) was meticulously recorded and juxtaposed with the dip separation at the target annealing temperature (Δλ_T) for each cycle, as depicted in the right panel of Fig. 4a. As the annealing cycle advanced, both Δλ_P and Δλ_T exhibited a decreasing trend with the elevation of temperature. The recorded Δλ_P values were 0.44 nm, 0.42 nm, 0.38 nm, 0.35 nm, and 0.29 nm, ultimately becoming indiscernible at the 600 °C mark. The discrepancy between Δλ_P and Δλ_T was less than 0.01 nm. In more straightforward terms, the wavelength discrepancy between the two resonant dips (Δλ) can be utilized to gauge the influence of ambient temperature on the KM-FBG. Figure 4b demonstrates the stability of the KM-FBG following multiple rapid annealing cycles (5 min each) at a constant annealing temperature of 400 °C. The Δλ₀ was roughly 0.43 nm, while the Δλ_P was 0.41 nm. As illustrated in Fig. 4c, the discrepancy between Δλ_Ps after different cycles was less than 0.01 nm. This suggests that the KM-FBG is capable of preserving the memorized signal, influenced by the peak temperature encountered, across multiple cycles, irrespective of the cycle count, until the maximum temperature is increased further.

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Fig. 4

Characteristics of the temperature memorized of KM-FBG.

a Spectral evolution of the KM-FBG and comparison of the dip separation of the dual dips (Δλ) in and after heating regarding several annealing processes with the step-increasing maximum temperatures from 200 to 600 °C. ‘H’ and ‘C’ represent the heating and cooling, respectively. b Spectra of KM-FBG recorded from the pre-annealing and three cycles of annealing with the same temperature of 400 °C. c Wavelength gaps of the KM-FBG corresponding to the different annealing cycles of 400 °C. d Spectra of KM-FBG recorded from the phases of a strain loading and releasing cycle applied to the KM-FBG. e The Δλ of the KM-FBG corresponding to the phases in the strain loading and releasing cycle.

We have taken into account additional factors that could potentially influence the spectral characteristics, including the refractive index (RI), polarization, and axial strain. Given that the diameter of the cladding for the fiber utilized in this study is identical to that of conventional fibers, and the Bragg grating structure is precisely inscribed within the fiber core, the ambient refractive index is unlikely to have a significant impact on the KM-FBG spectrum. Furthermore, the dual-dip KM-FBG exhibits insensitivity to polarization, as evidenced by Supplementary Fig. S3, which leads to a minimal response of the KM-FBG to lateral pressure. Supplementary Fig. 4d illustrates the gradual application and subsequent release of stress on the KM-FBG. The spectral shape remains consistent when an equivalent magnitude of strain is applied. As strain intensity increases, the spectrum of the KM-FBG displays a stepwise separation, as depicted in Fig. 4e. Contrary to the spectral fusion induced by high temperatures, the Δλ transformation induced by strain reverts to its original state once the strain is removed, indicating that the KM-FBG does not retain a memory of the maximum strain experienced. It is concluded that the spectral shape of the KM-FBG, characterized by Δλ, is significantly more stable than the single wavelength encoding method. This stability is attributed to a spectral shape protection mechanism, which confers the ability to counteract ambient perturbations, thereby reducing cross-sensitivity issues.

We present two practical applications that harness the unique memory effect of the KM-FBG. These applications encompass a high-temperature indicator and a data memory module inspired by the ancient quipu knotting system. At first, we developed a series of KM-FBGs with diverse Δλ₀s to quantify the alterations following annealing at a range of temperatures. The results are illustrated in Fig. 5a as a two-dimensional heat map. Notably, Due to the influence of the actual UV modulation on the dual-peak spacing of the KM-FBG, the KM-FBG with a smaller Δλ₀ would see its dual dips coalesce at elevated temperatures, rendering the wavelength gap information unreadable. Enhancing the grating’s thermal response at low temperatures (e.g., <200 °C) might necessitate altering the optical fiber’s constituent materials. However, this improvement could result in an indiscernible dual-peak spectrum at even lower temperatures, necessitating a trade-off for practical applications. As an alternative approach, we utilized the variation in the 5 dB bandwidth of the grating spectrum as an indicator to correlate with the annealed temperature. The past annealing temperature can be reconstructed by interpreting the data on the horizontal axis, which is determined by the initial bandwidth and the subsequent change in bandwidth.

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Fig. 5

Demonstration of the application of KM-FBG as the temperature indicator and one-dimensional data storage bit.

a The two-dimensional heat map of the bandwidth change of the KM-FBGs in terms of the initial bandwidth and the annealed temperature. Note: The 5-dB bandwidth information was used. b Real product of custom-made heating plates with different patterns. c Layout of KM-FBG arrays on the heating plates with different operative heating temperatures. d Heat map of the historically operated temperature derived from the bandwidth changes of KM-FBG array. e Recorded temperature value versus the applied temperatures of the heating plates. Statistical distinctions among the groups at several typical time ends. Statistical analysis is performed by one-way ANOVA followed by Tukey’s post hoc test. ns no significance, *P < 0.05; **P < 0.01; ***P < 0.001; ****P < 0.0001. f Photograph of quipu (photographed by the author in the exhibition of Guangdong museum). g Schematic of laser mediated quipu encoded in optical fiber. The optical quipu involved the cascaded array of KM-FBGs to enable the digital data bits using wavelength multiplexing. Inset: The initial (dual dips) and annealed (single dip) spectra of KM-FBG were regarded as digital codes 0 and 1, respectively, resembling the one knot and double knots quipus (note: these codes are not the real meaning of quipu knots). h Spectral evolution of two KM-FBGs with distinct initial wavelength gap in terms of the tuning of laser power (% meant the percentage count of the maximum laser power of 50 W). i Laser induced data encoding in the cascaded array consisted of seven KM-FBGs with different center wavelengths. The encoded binary data strings represented ‘J’, ‘N’, and ‘U’ by following the ASC II code.

We utilized custom-made heating plates with the patterns that were devised as the abbreviation of Jinan University (JNU), as is shown in Fig. 5b. We fabricated another batch of KM-FBGs and laid them out as the temperature indicator arrays on the surface of the pattern, as illustrated in Fig. 5c. The substrates labeled ‘J’, ‘N’, and ‘U’ were subjected to thermal treatment at 300 °C, 400 °C, and 500 °C, respectively, and maintained at these temperatures for a duration of ten minutes. Subsequent to cooling the substrates to ambient temperature, the KM-FBG sensor arrays were carefully removed and evaluated using a fiber-optic interrogation setup. Through the documentation of the initial bandwidths and subsequent changes post-annealing, a heating map was constructed, illustrating the historical peak temperatures encountered by each KM-FBG, as depicted in Fig. 5d. The substrate designated as ‘U’ revealed an overall elevation in temperature records compared to the other substrates. Conversely, a nuanced discrepancy was noted between the substrates labeled ‘J’ and ‘N’. Figure 5e presents a comparison of the historical temperatures recorded by the KM-FBGs against the applied temperatures on the respective substrates. The recorded temperatures typically underestimate the applied temperatures, a phenomenon attributed to the open design of the patterns and the non-uniform heating across the surface of the substrate. Testing under conditions of external thermal insulation should yield more accurate results. The decrease in bandwidth of the KM-FBG exhibits an exponential correlation with the annealing temperature experienced. The decrement in bandwidth at lower annealing temperatures is insufficient for precise interrogation, resulting in elevated error margins in the recorded historical temperatures. Nonetheless, the temperature read-outs become more reliable at higher applied temperatures, where a pronounced distinction is evident compared to the lower temperature ranges. This study demonstrates the potential of KM-FBG as a cost-effective and spatial temperature sensor without the need of sensing system construction.

Building upon the tailoring of dual dips via the rapid annealing process, we can repurpose the KM-FBG as a node within a data memory module, analogous to the quipu depicted in Fig. 5f, which was previously used by the Incas civilization for storing and transmitting codified information⁴. As a facile design, the quipu utilizes multicolored spatial arrays of knotted fiber cords to construct a model of logical-numerical recording³. The configuration of the knots of quipu with double- and single-loop can be analog to the double- and single-dip spectrum of the raw and post-annealed KM-FBGs, as is shown in the inset of Fig. 5g. We can assign the spectral signatures of the raw (characterized by dual dips) and annealed (characterized by a single dip) states of the KM-FBG as digital bits, with ‘0’representing the former and ‘1’ the latter (it should be noted that these binary codes do not correspond to the actual significance of the knots in a real quipu). A cascade of KM-FBGs, each with distinct wavelengths, can be conceptualized as a one-dimensional data storage medium. This medium can be spatially modulated by a heating source, such as a flame generator or a laser, to encode information. In this experiment, we used the carbon dioxide (CO₂) laser as the heat source recorder, as is shown in Fig. 5f. The CO₂ laser can be programmed to implement suitable thermal actuation to the KM-FBG knot with high spatiotemporal controllability about the optical fiber. The laser annealing temperature conducted on the KM-FBG could be managed through tuning the laser power as well as the relative distance between the KM-FBG and laser focal plane(see Supplementary Fig. S4). The position of fiber at the laser focal plane would be subjected to the largest amount of heat compared with non-focal planes. The larger the distance set between the KM-FBG and the focal plane would result in the lower annealing temperature. In order to provide a sufficient annealing temperature while maintaining the strength of the KM-FBG after annealing, the distance was adjusted to ~1.5 cm. Figure 5h shows the spectral evolution of the KM-FBGs under laser annealing. For an KM-FBG with a Δλ₀ of 0.47 nm, 20% of the maximum laser power (50 W) imparted the grating with a change of Δλ to 0.03 nm. As the laser power was raised to 40%, a melted single dip was formed. Further increasing the laser power to 60% may deteriorate the grating structure manifested by the decay of dip. A similar trend can be observed for another KM-FBG with a smaller Δλ₀ of 0.43 nm. This time, 36% of the lasing max power could sufficiently melt the two dips. As a result, 40% of the lasing max power was set as the coding power and the coding duration could be confined to less than 0.6 seconds for each KM-FBG. The detailed experiment results of the optimization of the laser annealing can be found in Supplementary Fig. S4.

To demonstrate the concept of the one-dimensional fiber-optic data memory, like silica quipu, we prepared three tandem arrays of KM-FBGs using the wavelength multiplexing method. Each array comprised seven KM-FBGs, each possessing a unique center wavelength of reflection. The wavelengths were mapped to the spatial positions of the KM-FBGs, with KM-FBG1 corresponding to the shortest wavelength and KM-FBG7 to the longest. Laser-annealing was applied to KM-FBG1, KM-FBG4, and KM-FBG6 of the initial array to encode a character sequence. The spectral contrast before and after laser-annealing is depicted in Fig. 5i. All the annealed KM-FBGs exhibited a single dip, signifying that the spectral melting was effectively induced by the rapid laser heating process. The annealed single-peak KM-FBGs are recorded as 1, while the non-annealed double-peak KM-FBGs are recorded as 0. A maximum temperature of ~600 °C can ensure both the distinction and stability. Consequently, the binary data string was interpreted as 1001010, which corresponds to the letter ‘J’ in ASCII code. Similarly, the letters ‘N’ and ‘U’ were encoded and preserved in the second and third arrays by annealing the respective data bits of the KM-FBGs (1001110 for ‘N’ and 1010101 for ‘U’). This proof-of-concept demonstration illustrates the potential of the KM-FBG array as an optical quipu for data encoding and storage purposes.

In summary, we introduce a novel technology that enables information logging and transmission through the utilization of the KM-FBG. This fiber optic device exhibits a high-temperature memory effect, which is analogous to temperature-induced shape-memory materials, thanks to its spectral resilience in response to thermal actuation. The UV-induced Kovacs-like memory effect is pivotal in this mechanism. We have furnished fresh insights and empirical evidence to investigate disorder materials glassy materials, with a particular focus on the Kovacs-like memory phenomenon. The two resonant dips of the KM-FBG undergo a spectral melting transformation upon exposure to thermal modulation, and this spectral configuration is preserved even after cooling, thereby endowing the grating with a temperature-induced memory. Raman spectral analysis indicates a pronounced alteration in the triple ring structure, affirming the significance of the negative refractive index change component (constituting the second phase of the grating inscription process) within the temperature-induced memory mechanism. Boasting exceptional stability due to its spectral profile protection mechanism, the KM-FBG is capable of recording and memorizing the highest temperature event it has encountered through an irreversible change in its spectral profile. This historical temperature data can be decoded by analyzing the dip separations. This characteristic positions the device ideally within application scenarios that require single-use temperature logging, thereby obviating the need for costly and intricate sensing networks. Such applications are particularly relevant in fields like oil exploration, aerospace, and geology, where the deployment of single-use temperature loggers offers a practical and efficient solution. Moreover, the spectrum of the KM-FBG can be precisely tailored through fast laser annealing, facilitating the realization of data encoding. The spectrum itself can be conceptualized as an optical knot, paving the way for the creation of an optical quipu. Leveraging the robust wavelength-multiplexing capabilities of KM-FBGs, the arrangement of a grating cascade functions akin to a digital thread, capable of recording information such as ASCII codes.

Although the current recording method is one-time and does not including for erasing and rewriting tests, for inexpensive fiber materials, directly replacing the fiber may be more cost-effective than erasing and rewriting. The current methodology is constrained by a limited storage capacity due to the confines of the accessible spectral range, but this innovation presents a groundbreaking strategy for encoding and recording with silicon-based materials, particularly the optical fibers. This fiber data recorder, due to its compatibility with the backbone communication network, possesses advantages such as long-distance communication and transmission that other storage materials do not have. In addition, it can withstand relatively high temperatures, can be supported by astronomical amounts of fiber production, and has a unique ability to resist electromagnetic interference. Future research endeavors will be directed at enhancing the versatility of the KM-FBG by fabricating negative-index-change-induced dual dip gratings within various commercial optical fiber types^33,38 and by boosting the efficiency of the grating inscription process. This work still has room for further research to understand the potential competitive mechanisms inside the grating and the influence of doping^41,52. Additionally, the development of space-division multiplexing technology, as well as the advancement of complex spectral shape demodulation technologies, such as artificial intelligence-assisted data processing, will significantly enhance the capabilities of data storage and retrieval. This work not only provides new solutions for directly deciphering the annealing related equilibrium of glass materials, but also open up an enticing light encoding technique by introducing a new degree-of-freedom to utilize, which can take full advantage of vast optical fiber productivity, and extend the utilization of optical fibers to the low-cost data storage media. Given that the UV laser with phase mask is a mature and commercialized FBG inscription technology, we anticipate that the practical application of this innovative device is within close reach.

Methods

Instrumentation and materials

A 193 nm excimer laser (Compex 110, Coherent, Inc.) and a series of phase masks with the pitch of from 1067 to 1085 nm were used to inscribe FBGs and KM-FBGs with designed resonant wavelengths. Approximately 150 mJ/cm² per pulse of ultraviolet (UV) energy density was obtained through a cylindrical lens, which compressed the vertical dimension of the laser beam. The repetition of the laser was 50 Hz. The CO₂ laser was purchased from SYNRAD with a home-made lasing-manipulation system (SYNRAD 48, Mukilteo, WA, USA). A broadband LED source (GoLigtht Ltd, Shenzhen, China) was utilized to launch a continuous spectrum light ranging from 1250 to 1650 nm into the optical fiber. An optical spectrum analyzer (OSA, AQ6370D, YOKOGAWA, Tokyo, Japan) was used for monitoring the output spectrum of the microfiber. A Raman Spectrometer(DXR3, Thermo Fisher Scientific Waltham, MA USA) uses an excitation wavelength of 785 nm was employed to characterize the structure change of the optical fiber. A tube furnace (SK2-1-12,Y-feng,Shanghai) was used to actuate heat on the fiber Bragg gratings. The commercial single-mode telecom silica fiber (8/125 μm) with numerical aperture (N.A.) of 0.14 (SMF-28, Corning, NY, USA) was used to fabricate normal FBG and a commercial photosensitive Er-doped fiber (M5) with cladding diameter of 125 μm and core diameter of 3 μm with an N.A. of 0.24 was employed to make KM-FBG.

Optical system

The optical system was made up of a broadband light source with bandwidth from 1250 to 1650 nm, FBG/KM-FBG and an optical spectrum analyzer. They are connected sequentially via standard fiber optic connectors. A polarizer, and a polarization controller was additionally introduced into the optical path for optical polarization-related purposes (corresponding to Supplementary Fig. S3). An optical fiber circulator is also employed for collecting the grating reflection spectrum signals, with the ports of the circulator sequentially connected to the light source, KM-FBG, and optical spectrum analyzer.

Heating system

The optical fiber was bent and secured to a stainless steel ruler using high-temperature-resistant tape, after which the grating-inscribed section was inserted into a heated tubular furnace(SK2-1-12,Y-feng,Shanghai). The tail of the fiber could be connected to an external optical system for data collection. The grating was then subjected to several hours of continuous high-temperature heating or a stepwise temperature increase. The plates (refer to Fig. 5), which had the same size of 20 cm $\times$20 cm (length × width), could be heated by an independent temperature controller.

Fabrication of KM-FBG

A 193 nm excimer laser (Compex 110, Coherent, Inc.) and phase masks with the pitch of from 1067 to 1085 nm were used to inscribe KM-FBGs. We use the fix-point exposure method to inscribe KM- FBG, in which the exposed length of the fiber is kept still. A strain of 200 με is pre-loaded onto the fiber to accelerate the inscription. The grating was inscribed on M5 fibers, and by controlling the inscription time, the grating was brought to the early stage of the IIa stage, causing the originally merged grating signals to separate into two. The grating spectrum evolves with the growth of the cumulative fluence caused by UV laser, See Supplementary Fig. S2. KM-FBG cascades (Fig.  5) with distinct wavelengths were achieved through the use of phase masks with varying pitches, allowing for precise engineering of the sensor characteristics. The KM-FBGs within the array were designed to operate across a wavelength spectrum from 1545 nm to 1570 nm, and were spaced 10 cm apart to prevent spectral and spatial interference during the laser-induced coding process.

Laser mediated quipu encoded in optical fiber

The CO₂ laser with an output wavelength of 10.6 μm (SYNRAD 48, Mukilteo, WA, USA) was used as the heat source recorder. The scanning speed of the laser was set to 500 mm/s, the frequency to 1 kHz, and the laser power to 40% of 50 W. The grating was placed 1.5 cm away from the focal plane. The spot pattern consisted of 200 vertical lines, each 1 cm in length, with an interval of 0.01 cm, and the laser modulation time was 0.6 s for each KM-FBG.

Statistical analysis

Separated experiments were conducted more than three times. The statistic is presented as mean ± standard errors of the mean (SEM). All statistic data was processed by GraphPad Prism 7.0 software (GraphPad Software, La Jolla, CA). Differences among the three groups were evaluated using one-way ANOVA followed by Tukey’s post hoc test. *P < 0.05 was considered a significant difference. (**P < 0.01; ***P < 0.001).

Acknowledgements

This work is supported by National Natural Science Foundation of China (62335010) Y.R., the Local Innovative and Research Teams Project of Guangdong Pearl River Talents Program (2019BT02X105) B.G., Guangdong Special Support Plan(2023TQ07A263), Guangzhou Science and technology planning project(SL2024A04J00585) Y.R., and “Big Master” Project of Jinan University (YDXS2404) Y.R.

Author contributions

Y.R. and B.G. Conceptualized the study, supervised experimental design and data interpretation, and coordinated manuscript revisions. Q.Y. Performed core experiments, analyzed primary data, drafted the initial manuscript and coordinated manuscript revisions. Z.X. Collaborated on the experimental design and data collection. X.Y. Collaborated with the preparation of the sensors and data analysis. J.L. Conducted statistical validation, and generated figures. H.W. Conducted literature research and optimized experimental protocols. Y.Z. Fabricated the cascaded sensors and collaborated on data collection. F.F. Provided theoretical guidance for the article and revised the discussion section. All the authors reviewed and commented on the manuscript.

Peer review

Peer review information

Nature Communications thanks Oleg V. Butov, and Zhenggang Lian for their contribution to the peer review of this work. A peer review file is available.

Data availability

The Main data generated in this study are provided in the Source Data file.  are provided with this paper.

Competing interests

The authors declare no competing interests.

Supplementary information

The online version contains supplementary material available at https://doi.org/10.1038/s41467-025-61538-y.

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

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