Femtosecond-Laser Direct Writing of Double-Line and Tubular Depressed-Cladding Waveguides in Ultra-Low-Expansion Glass

Abstract

Addressing the stability requirements of photonic integrated devices operating over wide temperature ranges, this work achieves controlled fabrication of femtosecond-laser direct-written Type II double-line waveguides and Type III depressed-cladding tubular waveguides within ultra-low-expansion LAS glass-ceramics. The light-guiding mechanisms were elucidated through finite element modeling. The influences of laser writing parameters and waveguide geometric structures on guiding performance were systematically investigated. Experimental results demonstrate that the double-line waveguides exhibit optimal single-mode guiding performance at 30 μm spacing and 120 mW writing power. For the tubular depressed-cladding waveguides, both single-mode and multi-mode fields are attainable across a broad processing parameter window. Large-mode-area characteristics manifested in the 50 μm core waveguide, exhibiting an edge-shifted intensity profile for higher-order modes that generated a hollow beam, enabling applications in atom guidance and particle trapping.

1. Introduction

The rapid advancement of photonic integrated circuits (PICs) in fields such as optical communications, quantum computing, and integrated optics necessitates highly stable and low-loss optical signal transmission through their core component, optical waveguides, within complex operational environments [1,2]. While traditional waveguide materials like silicate glasses or crystals offer excellent optical properties, their relatively high coefficient of thermal expansion (CTE) renders them susceptible to deformation under temperature fluctuations, leading to waveguide performance degradation. Consequently, transparent glass-ceramics, exhibiting an ultralow CTE (<1 × 10⁻⁷ K⁻¹), high mechanical strength, and chemical stability, have emerged as promising substrate materials for photonic devices operating over wide temperature ranges. Notably, lithium aluminosilicate (Li₂O-Al₂O₃-SiO₂, LAS) glass-ceramics achieve near-zero thermal expansion characteristics via controlled crystallization. This process precipitates β-quartz or β-eucryptite solid solution phases [3], whose negative thermal expansion effectively counterbalances the positive expansion of the residual glass matrix. This unique composite structure simultaneously delivers high mechanical performance [4] and excellent optical transmittance (>80%) [5]. Although such materials are already widely employed in high-precision astronomical telescope mirrors [6], laser gyroscope resonators [7], and aerospace optical platforms [8], their potential within integrated photonics remains largely untapped.

Depending on the mechanism of laser-induced refractive index modification, optical waveguides are primarily categorized into three types, the waveguide configuration is schematically illustrated in Figure 1: Type I waveguides are formed directly by a positive refractive index change within the laser-written region, creating a guiding core. This type offers advantages including low propagation loss and high integration density. Crucially, the scanning path inherently defines the waveguide geometry, enabling the flexible fabrication of complex three-dimensional structures such as waveguide arrays and wavelength-division multiplexers [9,10]. Type II waveguides employ a double-line geometry, utilizing low-refractive-index damage tracks on both sides to confine the core and enhance its refractive index, forming a symmetric guiding channel [11]; the birefringence induced by this confinement effect facilitates effective separation of TE and TM modes [12].Type III waveguides (depressed-cladding waveguides) function by reducing the refractive index in the cladding region surrounding an unwritten core. Due to the absence of direct laser-writing defects within the core itself, Type III waveguides typically exhibit lower propagation losses compared to their Type I counterparts [13].

Facing the challenge that traditional waveguide preparation methods, such as ion exchange [14] and chemical etching [15], struggle to meet the requirements for low cost, high efficiency, and high integration density, femtosecond-laser direct writing (FsLDW) stands out as an efficient and flexible tool for complex waveguide fabrication. This is due to its submicron spatial resolution, three-dimensional processing flexibility, and material versatility. The core mechanism involves the extremely high peak power of femtosecond-laser pulses (on the order of 10⁻¹⁵ s) focused inside transparent materials via a high numerical aperture objective lens. This induces nonlinear absorption through multiphoton ionization and avalanche ionization [16], leading to structural phase transitions or stress field reconfiguration. Consequently, permanent refractive index modulation is achieved. Compared to traditional ion exchange or chemical etching processes, FsLDW offers distinct advantages [17]: (1) maskless and chemical-free direct writing of three-dimensional waveguide networks within the material bulk; (2) minimal thermal diffusion effects due to ultrashort pulses, reducing the accumulation of microcracks or residual stress; and (3) applicability to diverse media including crystals, glasses, and heterogeneous glass-ceramics. Currently, femtosecond laser-induced modified structures have enabled significant applications in integrated optics [18,19,20,21], optical communications [22,23,24,25], optical sensing [26,27,28,29], and Photonic crystals [30,31]. Consequently, femtosecond laser processing has emerged as a prevailing technique for modern high-precision micro/nano-fabrication due to its submicron fabrication precision and material versatility [32]. This capability provides a technical foundation and feasibility basis for fabricating the double-line and depressed-cladding waveguide structures proposed in this work.

Our prior work fabricated waveguides in PTR glass and analyzed their guiding modes and performance [33]. Given that LAS glass-ceramics exhibit lower coefficient of thermal expansion (CTE) and broader operating temperature range than PTR glass, inherently addressing waveguide stability requirements under elevated temperatures, we have extended this research to waveguide fabrication in LAS glass-ceramics. Waveguide fabrication in LAS glass ceramics was previously reported in 2021 [34]. That study revealed negative refractive index modulation induced by lasers in LAS glass-ceramics and investigated laser parameter effects on modulation magnitude. Depressed-cladding waveguides were fabricated using a lateral writing scheme, with subsequent performance analysis establishing fabrication feasibility. However, Type II waveguide research and mode control were not addressed. This work focuses on fabricating waveguides within ultra-low-expansion LAS glass-ceramics using femtosecond-laser direct writing. First, the temperature and stress distribution in the glass under laser irradiation was simulated using the finite element method to elucidate the physical mechanism of light guidance in the waveguides. Subsequently, Type II and Type III waveguide structures were successfully fabricated in the ultra-low-expansion glass-ceramics via lateral and longitudinal writing configurations. The waveguiding characteristics under varying writing power conditions were investigated, including their impact on the near-field mode profile. Furthermore, the influence of different laser repetition rates on waveguide performance was analyzed at identical power levels, and the guiding properties of the waveguides were characterized. The waveguides hold promise for various applications, including optical interconnection with glass-based integrated circuits, as well as utilization in waveguide polarizers and high-power lasers.

2. Materials and Methods

2.1. Simulation

First, a finite element model simulating the interaction between femtosecond lasers and LAS glass-ceramics was established using COMSOL Multiphysics 6.2. Parameters used in the simulation included the following: a single-pulse energy of 1.2 µJ, a laser central wavelength of 1030 nm, a pulse duration of 300 fs, a Gaussian spatial and temporal beam profile, and the built-in Schott Zerodur^® (Schott AG, Mainz, Germany) glass-ceramic material properties, the glass material parameters are listed in

Table 1. Physical constants of Zerodur^® glass-ceramic.

Property	Parameters
Thermal conductivity @20 °C [W/(m · K)]	1.483
Specific heat @20 °C [J/(g · K)]	0.75
Young’s modulus @20 °C [GPa]	90
Poisson’s ratio	0.245
Density [g/cm3]	2.53
Refractive index	1.543
Thermal diffusivity @20 °C [10−6 m2/s]	0.786
Thermal expansion coefficient α0/50 °C [10−8/K]	0 ± 2

. The relevant parameters are presented in the following table. To simplify calculations, a two-dimensional model with symmetric configuration was adopted. Infinite element domains were applied at boundaries to eliminate finite-size effects. When ultrafast lasers focus inside materials, self-focusing and defocusing cause beam filamentation along the propagation direction. Therefore, the laser spatial distribution inside the material was approximated as a two-dimensional elliptical profile. The major and minor axes of this ellipse were derived [35] from the lens numerical aperture by

$${\omega }_x={\displaystyle \frac{0.32\lambda }{NA}},$$

(1)

$${\omega }_y={\displaystyle \frac{0.532\lambda }{\left[\begin{array}{c}{n}_i-\sqrt{n_i^2-N{A}^2}\end{array}\right]}},$$

(2)

where λ denotes the laser wavelength, NA the numerical aperture of the focusing lens, and n_i the material refractive index. Additionally, 50% of absorbed laser energy was assumed to convert into heat, with no thermal diffusion considered during photon–electron coupling.

The distributions of the temperature field and stress field within the material 2 ps after femtosecond laser focusing were calculated, as shown in Figure 2. When the femtosecond laser beam is focused inside LAS glass-ceramics, it induces nonlinear absorption, leading to plasma generation within the material. From Figure 2a, it can be observed that, depending on the size of the laser interaction zone, pulse energy, and the thermophysical properties of the glass-ceramic, the temperature at the laser focus rises to a maximum of 3400 K. Simultaneously, the temperature within an approximate volume of Ø1.2 µm × 10 µm surrounding the focus also exceeds 2500 K. This high temperature causes a nanocrystal vitrification inside the glass-ceramic; for instance, β-eucryptite crystals begin to melt within the range of 1350–1450 °C [36]. The destruction of the crystal structure during this crystal-to-glass phase transition results in diminishing refractive index in the laser-modified region.

Furthermore, the high temperature gradient induced displacement within the material, generating stress. In the focal center region, the volumetric strain caused by thermal expansion was constrained by the surrounding material, producing compressive stress with a maximum value of −14.2 MPa (the negative sign indicates pressure). Tensile stress peaking at 0.274 MPa developed in the vicinity of the laser interaction zone. Concurrently, in the focal region, the rapid expansion of the plasma induced two dynamic processes: (1) under the constraint of the surrounding material, the pressure gradient from rapid expansion formed a shock wave and (2) highly charged ions that had lost electrons underwent further compression against the surrounding material by the Coulomb explosion process dominated by interionic Coulomb repulsion. These processes collectively led to a decrease in material density within the focal region, while the material in the vicinity of the focus was densified due to compression [37,38,39,40], resulting in an increase in the refractive index. Consequently, the combined effect of these two factors formed the physical mechanism for light guidance in Type II waveguides within LAS glass-ceramics.

2.2. Experimental Setup

Zerodur^® glass-ceramic produced by SCHOTT AG (Mainz, Germany) was used in the experiments. Prior to waveguide writing, the glass was machined into dimensions of 20 mm × 9 mm × 2.5 mm, and all six sides were polished to high optical quality. Figure 3 shows a schematic of the femtosecond-laser waveguide writing. A femtosecond laser system (YSL, FemtoYL, Wuhan, China) operating at a wavelength of 1030 nm was used. The pulse widths spanned 300 fs to 5 ps, while repetition rates ranged from 25 kHz to 5 MHz. The laser beam was focused 150 μm below the surface of the Zerodur^® glass-ceramic using a 20× objective lens (NA = 0.4). The incident energy was precisely controlled from 0 to 40 μJ via a λ/2 wave plate and a polarizer. Double-line waveguides and depressed-cladding waveguides were fabricated inside the glass-ceramic using transverse and longitudinal writing configurations, respectively. The sample was mounted on a 3D precision air-bearing translation stage. The scanning speed of sample with respect to the laser was fixed at 200 μm/s, and the processing area was monitored with a top-mounted CCD camera.

After waveguide fabrication, the glass sample was ultrasonically cleaned in industrial ethanol. The waveguide morphology was observed using a positive phase-contrast microscope (PCM, BX51, Olympus, Tokyo, Japan). Then the waveguides were illuminated via an aspheric lens with a focal length of 18 mm using a fiber laser of 683 nm. The output from the opposite end was imaged onto a CCD camera through a 20× microscope objective, and the near-field mode was captured using the end-face coupling system.

3. Results and Discussion

3.1. Double-Line Waveguide

Figure 4a shows the end-face images of waveguides with different spacings (20, 25, 30, and 35 µm), and Figure 4b–e display the corresponding near-field mode patterns under 683 nm injection. To characterize the guiding properties of femtosecond-laser direct-written double-line waveguides, structures were fabricated in glass at 100 kHz repetition rate with varied writing powers (60, 80, 120, and 160 mW). Near-field mode analysis revealed that waveguides exhibited single-mode transmission when the double-line spacing was within 30 µm (region left of the yellow dashed line in the figures). At a writing power of 60 mW, due to low laser energy, the small refractive index modulation in both the tracks and inside the tracks resulted in poor guiding performance. Guiding performance gradually improved as writing power increased (80 and 120 mW). However, for 60–160 mW writing powers and 20–25 µm double-line spacings (region within the red dashed box), the excited guided modes showed a slightly elliptical distribution, with the long axis aligned parallel to the laser propagation direction. This can be attributed to increased refractive index at the ends of the tracks, elongating the light confinement region vertically. Significant scattering loss occurred under this mode, hindering efficient coupling. When the spacing was increased to 30 µm, the near-field mode distribution became uniform and symmetric, indicating good guiding performance. Further increasing the spacing to 35 µm led to multi-mode guiding. However, at 160 mW writing power, the increased refractive index modulation in the Zerodur^® glass-ceramic caused the waveguide with 30 µm spacing to support higher-order modes. Comparing these results demonstrated that the double-line waveguide with 30 µm spacing and 120 mW writing power achieved optimal single-mode guiding with good mode uniformity, as shown in Figure 4(d3). The total waveguide loss, including coupling loss and propagation loss, was determined by measuring the 683 nm laser power injected into and output from both ends of the double-line waveguide. The total waveguide loss is calculated via the following:

$$\phi =-\left(10/L\right)\lg \left(P_1/P_2\right),$$

(3)

where L denotes length, and P₁ and P₂ represent the input and output power. For the waveguide with 30 µm spacing and 120 mW writing power, the total loss was 2.30 ± 0.02 dB/cm.

Additionally, laser repetition rate effects on double-line waveguide guiding performance were investigated under fixed writing power. Figure 5 presents the test results for double-line waveguides fabricated at 120 mW writing power and 30 μm spacing, including positive phase-contrast microscopy (PCM), optical white-light transmission, and near-field mode images. In the positive PCM images, the bright white regions indicate areas of relatively decreased refractive index. As shown in Figure 5a, when the femtosecond laser is focused inside Zerodur^® glass-ceramic, the refractive index in the laser-modified track decreases. This can be correlated with the crystal-to-glass phase transition process, as analyzed previously. The results revealed that as the laser repetition rate increased, the guiding mode of the waveguides shifted from multi-mode to single-mode, while weakening guiding performance (Figure 5c). This is attributed to the diminished single-pulse energy at elevated repetition rates under constant average writing power. Consequently, the refractive index modulation in the tracks diminished and the stress intensity in the surrounding area decreased, leading to degraded waveguide guiding performance.

To study the guided-mode characteristics of the double-line waveguide fabricated at a writing power of 120 mW and a spacing of 35 μm, 683 nm laser light was injected through the end-face, and the corresponding near-field mode images were captured. The results demonstrated that the excited guided modes depended on the laser injection position. This phenomenon arises because waveguide modes are governed by phase-matching conditions

$$2(k_0{n}_{0}d\cos \theta -\delta )=m\cdot 2\pi ,$$

(4)

where k₀ is the wave vector, n₀ the core refractive index, d the waveguide diameter, θ the laser incidence angle, δ material-dependent phase lag, and m the mode order. It demonstrates that variations in laser incidence angle directly alter guided-wave mode distributions. Figure 6a shows the observed diverse mode distributions, whose patterns correspond to the TEM₀₀, TEM₁₁, and TEM₂₁ modes, respectively. Furthermore, the power flow distribution within the waveguide was numerically simulated using the finite element method (FEM), with the results presented in Figure 6b. The simulation parameters were strictly based on the experimental conditions: a double-line spacing of 35 μm, a line thickness of 2 μm, and a substrate refractive index of 1.542 for Zerodur^® glass-ceramic. Based on the single-mode near-field pattern, finite-difference numerical methods were employed to calculate refractive index changes by [41]

$$\Delta n(x,y)={\displaystyle \frac{{\lambda }^2}{16{\pi }^2{n}_{0}I(x,y)}}[{\nabla }^{2}I(x,y)-{\displaystyle \frac{1}{2I(x,y)}}{(\nabla I(x,y))}^2],$$

(5)

where n₀ is the substrate refractive index and λ is the measurement wavelength, yielding a 0.005 reduction in the laser-modified region and a 0.008 increase in the guiding zone. Comparing the mode distribution features shown in Figure 6a,b confirmed a high degree of agreement between the simulation and experimental results. These experimental findings indicate that the double-line waveguide transmission mode can be effectively controlled by modulating the waveguide spacing and writing pulse energy. Such control enables the waveguide to support higher-order mode transmission adaptable for specific applications.

3.2. Depressed-Cladding Tubular Waveguide

Depressed-cladding tubular waveguides were fabricated using a longitudinal parallel writing scheme. Their structural characteristic features a chain of laser-written cylindrical tracks with negative refractive index changes surrounding a core of defined diameter. The optical confinement capability depended significantly on the number of cladding tracks; increasing the track count facilitated the formation of smoother and more rounded cladding walls, effectively suppressing optical leakage. In the experiments, waveguides with 30 μm, 40 μm, and 50 μm core diameters were fabricated with corresponding cladding track counts of 20, 25, and 32, respectively; their cross-sectional structures are shown in Figure 7a. Figure 7b–e show the near-field mode distributions of tubular cladding waveguides with 30 μm, 40 μm, and 50 μm core diameters, fabricated at 60 mW, 80 mW, 120 mW, and 160 mW writing powers, measured via end-face coupling under 683 nm illumination. Analysis revealed the following: (1) the waveguide’s spatial confinement of the optical field enhanced progressively with increasing writing power (i.e., increasing negative refractive index contrast of the cladding); (2) for the 30 μm core diameter waveguide, good single-mode transmission characteristics were observed across the tested writing power range; and (3) waveguides with 40 μm core diameters and above supported higher-order modes, with the 50 μm core diameter in particular exhibiting complex hybrid-mode field distributions formed by mode superposition. Furthermore, the tubular cladding waveguide with a 50 μm core maintained large-mode-area (LMA) guiding characteristics over a wide writing power range (60–160 mW). This enables applications in high-efficiency power delivery within integrated optical circuits and in the construction of compact high-power oscillating laser devices.

To analyze the optical characteristics of the depressed-cladding tubular waveguide with a 50 μm core diameter, the near-field mode of the cladding waveguide was first simulated using the FEM. Figure 8a shows the observed near-field mode image under 683 nm laser injection, while Figure 8b presents the corresponding FEM simulation result. The mode distribution demonstrated good agreement between simulation and experiment. Secondly, stress distribution at the tubular waveguide end-face was observed using cross-polarized microscopy, as shown in Figure 8c. Birefringent regions were detected within and around the cladding ring, resulting from localized volume expansion during femtosecond laser processing. This generated a residual stress field around the modified region, causing stress-induced birefringence [42]. Additionally, the mode field diameter at 1/e² intensity was measured for the 50 μm core tubular cladding waveguide. Figure 8d indicates a mode diameter of 46.023 μm. These observations confirmed the tubular structure as an effective depressed-cladding waveguide with strong optical confinement. The 50 μm core waveguide exhibited large-mode-area (LMA) guiding properties, this characteristic reduces power density through expanded mode field dimensions, thereby effectively mitigating inherent nonlinear effects and thermal damage in solid materials under high-power operation, demonstrating potential for efficient high-power delivery in optical waveguide design. Furthermore, differences between Figure 8(a1,a2) were analyzed. Figure 8(a1) demonstrates waveguide mode confinement at the core center, whereas Figure 8(a2) exhibits mode distribution shifted toward the cladding periphery. This phenomenon originates from Zerodur^® glass-ceramic properties: compressive stress near the cladding elevates the refractive index, while minimal stress-induced modification occurs in the central region due to the large waveguide radius. Consequently, a refractive index contrast (Δn > 0) develops between the cladding ring and core. This caused the peak intensity of some guided modes to shift away from the center of the near-field mode, manifesting as an edge-shifted intensity profile toward the waveguide periphery. This unique intensity distribution generates hollow beams that can confine cold atoms within their central dark region. Such confinement prevents direct interaction with high-intensity light fields, while positioning atoms in the beam’s minimum intensity zone substantially reduces photon absorption. Consequently, the probability of atomic scattering decreases, enabling efficient low-temperature non-contact atomic guidance, showing promising potential for developing micro-nano devices in applications such as particle trapping and cold atom guidance [43,44].

4. Conclusions

This study fabricated Type II double-line waveguides and Type III depressed-cladding tubular waveguides within ultra-low-expansion LAS glass-ceramics using femtosecond laser direct writing. Their light-guiding mechanism originates from the synergistic effect of laser-induced crystal-to-glass phase transition and stress field reconfiguration. Experiments demonstrated that double-line waveguides achieved optimal guiding performance at 30 μm spacing and 120 mW writing power. Under constant average writing power, increasing the repetition rate reduced single-pulse energy, leading to diminished refractive index modulation and consequently degraded guiding performance. Good agreement was observed between simulation and experimental results for the fabricated waveguides. Tubular waveguides exhibited favorable optical confinement and waveguiding characteristics. Single-mode guiding was observed at a waveguide diameter of 30 μm. Multi-mode fields were obtained by controlling the waveguide diameter. Cross-polarized microscopy observations further revealed the contribution of cladding stress-induced birefringence to light guidance. It is particularly noteworthy that an edge-shifted intensity profile of higher-order modes was observed in the 50 μm core waveguide, generating hollow beams and providing alternative options for the design of micro-nano photonic devices. Precise control over single-mode transmission, multi-mode coupling, and special beam generation was achieved by adjusting laser writing parameters and waveguide dimensions. Future research will explore beam-shaping effects on stress distributions, utilizing cylindrical lenses coupled with circular apertures to generate uniform filamented damage tracks [45] for enhanced waveguiding performance. To address length limitations in longitudinal depressed-cladding tubular waveguide fabrication imposed by Gaussian beam diffraction, zero-order Bessel beams produced via axicon shaping will be implemented [46], improving processing length and efficiency. Concurrently, applications in micro/nano-photonic devices, including waveguide beam splitters [47,48], polarizers, and high-power lasers, will be investigated.