1. Introduction

High power scaling combining good beam quality (i.e. in single-mode operation) and light intensity is quite desirable in the field of laser development [1]. Single mode fibers or waveguides can be used as mode filters selecting the fundamental mode, which ensures a significantly improved beam quality (M² factor close to unity). Unfortunately the conventional single mode waveguide usually delivers restricted power because of the relatively small mode size. The typical light confinement in waveguides with reduced dimensions is prone to excite nonlinear effect or even to cause materials damage. Thus it is potentially useful to design optical[REMOVED HYPERLINK FIELD] single-mode (SM) waveguiding concepts with large effective mode areas (LMA) which can be advantageous for high efficiency power delivery or compact high power oscillating laser devices. In addition large mode fields are also interesting for larger-wavelength transport in the mid-infrared regions where several applications in the field of sensing and imaging for astrophotonics and medical applications [2–4].

Several efforts were made to achieve LMA SM waveguides. A straightforward approach involves decreasing the refractive index difference between the core and the cladding, while properly increasing the core size at the limit where the normalized frequency still remains below 2.405 (for circular symmetric cross section waveguide with step profiled index distribution). Extrapolation of this design includes depressed-cladding waveguides. However, this approach weakens the spatial modal confinement so that arising losses become sensitive to material inhomogeneity or waveguide bending. To achieve relatively robust single-mode guidance with LMA, several developments were presented based on more complex optical strategies such as chirally coupled core (CCC) waveguide [5,6] or leakage channel waveguide [7–9]. Both structures utilize the strong asymmetric loss between the fundamental mode and higher-order mode during wave propagation along the refined structure (i.e. high-order mode experience very large loss while fundamental mode can be hardly affected). Another feasible way is determined by the use of all solid photonic crystal-like structure. The core of this waveguide consists of bundles of several evanescently coupled sub-cores which support the transport of in-phase-propagating supermode with LMA [10–13]. This design is well adapted for ultrafast photoinscription techniques, particularly in MIR domains [14]. A hexagon arranged 37-core structure written in longitudinal laser scan was discussed in [15]. Longitudinal writing requires nevertheless power/phase tailoring during laser inscription to compensate wave front distortion caused by the air-dielectric interface. Transverse geometries with slit-shaped profiles or multi-scan strategies were equally used, where the cross section becomes comparable to the writing confocal distance, therefore limited to few microns for reasonable processing times. Larger sections with flexible 3D design become thus desirable and periodic index structures carry an interesting potential. The embedded expanded-core waveguide (ECW), which consists of a one dimensional layered array of narrow index planes with waveguiding properties can indeed operate at single-mode with LMA and with stronger mode confinement compared to conventional designs of single core over a wide range of index-contrast conditions.

In this respect ultrafast laser tools have demonstrated their capability in rapid prototyping and microstructure fabrication. In 3D structuring, ultrafast laser induced refractive index modification inside a transparent dielectric is already an efficient method for optical waveguides fabrication [16–20]. In this technique both the physical response of the material and the optical geometry are important. In several materials, under specific conditions (within the photo-inscription window), laser generated positive index changes, denoted as type I, can occur. This is for example the case of fused silica but other materials are also showing these characteristics. In terms of optical writing, transverse irradiation greatly facilitates the flexibility in waveguide production, albeit profile asymmetry, which allows one to write waveguides or photonic circuits with arbitrary shapes (straight or curved) of any length in 3D integrated optics. The typical transverse asymmetries when no shaping techniques are employed can in specific conditions be of advantage. When typically low NA focusing and ultrashort pulses are employed in transversal writing configuration below the catastrophic self-focusing threshold, elongated waveguide section with aspect ratio up to 30 could be obtained. In this work a set of type I slab waveguides are closely arranged in a layered array to construct the ECW in order to efficiently confine the input radiation in LMA patterns. The mode distributions can be affected by factors such as the separation of the guiding layers, the number of layers and the magnitude of the refractive index change. This expanded-core structure can reduce the fabrication time for LMA guides and improve the uniformity of the waveguide along the propagation length as being less sensitive to wavefront distortions during fabrication.

In this paper, firstly the ultrafast laser-assisted fabrication of expanded-core structures is reported in fused silica. We discuss here the fabrication conditions and performances of the ECW optical design, and its practical applications for LMA. The guiding characteristics of ECW in different parameter configurations are discussed in detail. The loss and polarization effects of the single mode ECW are investigated. We make a further step to fabricate a Y-branching splitter which conserves fairly well the single mode and LMA feature after beam splitting. We equally extend and demonstrate the ECW in MIR chalcogenide Gallium Lanthanum Sulfide GLS glasses.

2. Experimental setup

The schematic of the ECW writing setup is shown in Fig. 1. A regeneratively amplified Ti:Sapphire ultrafast laser system (Spitfire, Spectra Physics) is employed as the irradiation source for ECW fabrication in fused silica. The system delivering 300mW average power emits train of pulses at a repetition rate of 1 kHz with a center wavelength of 800nm and nominal pulse duration of 120fs. To obtain a moderate dose of photon accumulation, the pulse energy is adjusted by a half wave plate, in combination with a thin film polarizer (TFP). The amplified pulse is linearly polarized in the horizontal direction (Y direction) after the TFP. An electromechanical shutter is used to control the exposure time during photo-inscription. A 10 × Mitutoyo microscope objective with numerical aperture of NA = 0.28 (working distance 33.5 mm) is chosen to focus the pulsed laser inside the bulk sample. A polished sample of fused silica (Corning 7980-5F), with a size of 15.0 × 25.0 × 5.0 mm³ is mounted on the XYZ precision motion stages (Physik Instrumente) that allow translation parallel or perpendicular to the laser propagation axis (X direction). The waveguide was written in transverse geometries along the direction of Z axis as shown by the arrow indicated in Fig. 1. Both the shutter and the 3D translation stage are controlled by a computer. An Olympus BX51 positive phase contrast microscope (PCM) is used to inspect the interaction region in real time in top-view geometry. 980nm optical source is used to characterize the guiding properties. A second laser source of higher repetition rate (100 kHz) and NA = 0.42 20 × Mitutoyo focusing objectives were used for laser structuring in chalcogenide glass in a similar positioning and imaging setup. 10.0 × 20.0 × 2.0 mm³ gallium lanthanum sulfide samples (Southampton ChG) are used. Electro-mechanical shutters were employed for controlling the irradiation dose. Guiding properties were tested at 800nm.

 

Fig. 1 Schematic of the experimental setup used for ECW fabrication in fused silica: HWP half wave-plate, TFP thin film polarizer, ES electromechanic shutter. Both the shutter and the 3D translation stage are automatically controlled by a computer.

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3. Results and discussion

We first discuss below the structuring results in fused silica and the impact of geometry and irradiation conditions. Secondly, an example in GLS is outlined.

3.1 Guiding characteristics of ECW

Under 10 × microscope objective focusing, the cross section of the type I single slab waveguide indicates sizes of about 2µm width and 60µm length. The experiment was arranged as follows. Three groups of ECW structure arrangements (i.e. 13 traces with 4µm separation, 9 traces with 5µm separation and 8 traces with 6µm separation) were designed in order to inspect the influence on the guided mode. In each group we have chosen four scan velocities (i.e. 80µm/s, 120µm/s, 160µm/s and 200µm/s) to allow for variable index contrast and identify single mode supporting parameters. All of the ECW structures have a same length of 10mm and were written approximately 300µm below the surface (measured from surface to the midpoint of the elongated modification zone). The pulse energy is fixed to 3.6µJ throughout this paper.

To examine the performance of waveguiding at the same time with the trace morphology, we superpose via a 45° beam splitter, incoherent white light illumination for imaging and collimated 980nm diode laser (fiber coupled output with elliptical polarization) for injection. These are simultaneously projected onto one end face of the waveguide using an aspheric lens with focal length f = 18mm. Another facet of the waveguide is imaged to a charge coupled device (CCD) by a 5 × microscope objective. Thus, the structure of the ECW and the location of near-field mode distribution of the 980nm injected laser radiation can be conveniently distinguished at the same time.

The first ECW processed under 80µm/s scan velocity is consisting of 13 single trace with 4µm separation. Figure 2(a) shows the white-light transmission illumination microscopy of the laser generated structures. The whole cross section of ECW was composed of an array of alternating type I single traces becoming bright under white light illumination due to partial guiding. The guiding properties of the waveguide structure are evaluated under 980nm illumination. The near field images of this ECW output indicate a behavior which is generally multimode at 980nm. The excited mode depends on the injection position. The various mode characteristics are similar to those of higher normalized frequency single core waveguides or fibers that contain higher-orders. Typical modes observed in the experiment are presented on the top row of Fig. 2. For example, Fig. 2(b) shows the distinctive pattern distribution which represents the LP₂₁ mode. Figures 2(c) and 2(d) depict the two spatial modes of LP₁₁ in the orthogonal direction, and Fig. 2(e) exhibits the Gaussian profiled LP₀₁ mode. The bottom row of Fig. 2 presents the simulation result of power flow distribution corresponding to the experimental conditions, calculated by the finite element method (FEM) with calculation details given as follows. The cladding index is defined as the optical constant of the substrate fused silica material in the simulation regardless of the material absorption (i.e. $n_{clad}$ = 1.45). Since the fs laser induced refractive index change in fused silica usually in the range of 10⁻⁴, the increase of the index in the guiding layer core is set as 2.2 × 10⁻⁴. 13 slices of rectangle cores sized as 60 × 2µm² are separated at 4µm distance according to the experimental conditions. It can be inferred from the mode distribution that the experiment results are in good agreement with the simulations.

 

Fig. 2 The excited near-field modes of an expanded-core waveguide in fused silica consisting of 13 type I waveguides with 4µm separation. The top row indicates experimental results and guiding characteristics upon 980nm injected laser light. (a) optical transmission microscopy image of the ECW end face structure. The photoinscribing laser pulses are coming from the top. (b)~(e) Over exposed near field mode images depicting LP₂₁,LP₁₁ and LP₀₁ mode of 980nm laser radiation supported by the ECW. The mode image is superposed on white LED illumination emphasizing the processed structure. The bottom row show corresponding FEM simulation results of the supported mode of ECW. The structure is written by 3.6µJ, 150fs, 1kHz laser scan pulses at the speed of 80µm/s. The length of the waveguide is 10mm.

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Next we sweep three different photoinscription and geometry parameters by decreasing the number of guiding layers from 13 to 8, enlarging the separation offsets from 4µm to 6µm and reducing the induced $\Delta n$ (by means of increasing the scanning velocity from 80µm/s to 160µm/s) in the ECW structure. Finally the single-mode operation ECW is obtained in a stable manner as shown in Fig. 3(a). To verify the stability of the operation we change the injecting spatial position of the laser source. No other higher mode is excited, confirming the solely fundamental mode supported operation. Despite the discrete 8 sub-cores structure, the electric field generally distributes uniformly on the entire cross section of the waveguide (Fig. 3(c)) due to the relatively strong evanescent field coupling between the single guiding layers and the dynamic balance of mode propagation along the waveguide. As demonstrated in Figs. 3(d) and 3(e), the mode field possesses a good Gaussian profile in both horizontal and vertical direction. The mode field diameter (MFD) at 1/e² is measured to be 29.43µm in X direction and 34.81µm in Y direction, denoted as$D_x$and$D_y$. Estimate simply as$A_{eff}=\pi D_x{D}_y/4$, a total effective mode area as large as 804.61µm² is achieved. We specify that the processed ECWs with parameters in between the cases shown here (i.e. the entire speed range of 9 traces structure) generally give mode of LP₀₁ and LP₁₁ or superposed hybrid mode but still did not support single mode only operation.

 

Fig. 3 Single mode supported ECW consisting of 8 Type I traces with 6µm separation in fused silica. (a) optical white-light transmission microscopy image of the ECW end face, (b) over exposed near field mode image for 980nm laser radiation injected in the center of structure with and (c) without white LED illumination, (d) Gaussian fitted mode field intensity distribution in X direction and (e) in Y direction. The structure is written by 3.6uJ, 150fs, 1kHz laser pulses at the speed of 160 µm/s. The whole length of the waveguide is 10mm.

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3.2 Conditions for single mode operation

It can be concluded from the experimental result above that the single mode ECW can be obtained under conditions of smaller layer numbers and lower index change of the guiding single layers. The fact becomes apparent when considering the equivalent index method in which the ECW structure is replaced by one equivalent core layer with index of $n_{eq}$. Here for the sake of simplification, we only take TE mode (with polarization of guided light parallel to the plane of the thin guiding layer) into consideration in the whole analyzes as following. Under the Root-Mean-Square (RMS) approximation [21–23], the equivalent index of the core in ECW can be expressed as

The general theory of electromagnetic field propagation in one-dimensional periodical optical media has been presented by Yeh et al. [24]. Imposing the continuity of $E$ and $\partial E/\partial x$ at each layer interface, a 2 × 2 matrix is introduced as a translation operator to relate the field of the adjacent unit cells. Employing the concept of Bloch waves, the field at a distance equivalent to the lattice constant has a phase factor of$e^{-iK\Lambda }$, where K is the Bloch wave number and $\Lambda$ is the period of the 1D lattice. Thus $e^{-iK\Lambda }$ can be considered as the eigenvalue of the translation matrix, and subsequently the Bloch wave number can be derived as

Here A and D are the diagonal elements of the translation matrix which can be considered as functions of the propagation constant $\beta$ at any given frequency$\omega$. Note that only the region where $\left|\left(A+D\right)/2\right|<1$ corresponds to an allowed band of Bloch waves, otherwise the region becomes a forbidden band for wave propagation.

For a structure of N cells of alternating high and low index layers bounded by low index substrates, and by setting the amplitude of the inward radiating waves to be zero at two boundaries of the waveguide array, the mode dispersion relation can be obtained for the guided mode using the matrix method, denoted as in [24]

It has been demonstrated in appendix A of [25] that there are exactly N roots for the above equation (thus N propagation constants $\beta$ for the guided mode) in each complete allowed band, i.e. $m\pi <K\Lambda <\left(m+1\right)\pi$. The normalized thickness of a single guiding layer T is defined to be $T=\frac{2\pi }{\lambda }t\sqrt{{{\displaystyle n}}_{core}^2-{{\displaystyle n}}_{clad}^2}$ where $t$ is the actual thickness of the single guiding layer and $n_{core}$ is the index of it. When T is smaller than $\pi$ (this condition can be easily satisfied in our case because of the weak-guiding features of the fs laser inscribed individual traces in fused silica), ECW structure only leaves one allowed band with N possible guided mode states in the region of the first Brillouin zone (m = 0) . To decrease the number of guided modes, the occupied range of $K\Lambda$ should be suppressed. The condition for single mode operation of ECW has been derived by Ramadan relying on the above mentioned considerations for sets of parameters normalization and analysis [26]. There are two conditions that should be simultaneously satisfied to achieve the single mode operation.

Condition I is virtually the necessary condition for single mode operation. It is based on the fact that if the expanded core is single mode, then when the interlayer gradually shrinks to zero, the coupling between guiding layers becomes stronger and they still support a single mode. So the normalized thickness of ECW should be less than$\pi$.

 

Fig. 4 Condition I for the single-mode operation for various wavelengths and index contrasts. The actual N number must not exceed the marked lines. The guiding wavelengths are shown in the chart. The thickness of the guiding layers is set to be 2μm.

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Condition II is the sufficient condition for single mode operation based on the method mentioned above allowing to suppress the range of$K\Lambda$, for$0<K\Lambda <\pi /N$, or its use in equivalent form.

Figure 4 depicts the allowed maximum number of layers N versus the index change in the frame of condition I. The curves for three different wavelengths (800nm, 980nm and 1550nm) are plotted in the diagram. The thickness of each single guiding layer is set at 2µm. The N number is rounded down to the nearest integer according to the relation (4). The index change ranges from zero to 10⁻³. As wavelength increases or the index change decreases, the higher N number appears appropriated to sustain a single mode operation. One can also note that, when the index change $\Delta n$ is fixed around 2 × 10⁻⁴, the N number is located approximately between 9 and 10 for the 980nm wavelength (the point is indicated by the arrow) corresponding to the experimental condition (note that the presumed index change values are validated by far-field measurements of the ECW mode). For the first ECW we fabricated (shown in Fig. 2), there are 13 guiding layers that apparently exceed the allowed number. This means that the corresponding ECW should give preferentially multimode operation, as demonstrated. While considering the 8 guiding layers ECW described in Fig. 3, the index change is lower due to an increased scan velocity. The critical N ought to be even larger than 10, so that single mode operation can possibly be supported. The experiment result verifies the correctness of this analysis.

Three degrees of freedom are available to design optimal ECWs by ultrafast laser processing: the positive index change induced for the each guiding layer; the number of guiding layers; the separation between each guiding layer. Figure 5 investigates the impact of these three variables on the mode operation using the dispersion relation function (3). Note that X axis is the normalized propagation constant ${\beta }_n$ defining as

 

Fig. 5 Dispersion relation with implication of condition II versus (a) index change of guiding layers $\Delta n$ with N = 13, s = 2µm, (b) number of guiding layers N with $\Delta n$ = 0.0001, S = 2µm, (c) thickness of interlayer s with $\Delta n$ = 0.0001, N = 8. X axis is the normalized propagation constant ${\beta }_n$ defined in the text.

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3.3 Loss, estimate and potential polarization effects

The dominant propagation losses in the case of an ECW should mainly originate in the scattering loss due to material inhomogeneities in the waveguide, interface roughness and light confinement degree. In the present case we can anticipate nevertheless a lower loss here compared to typical single mode guiding individual type I trace previously reported in fused silica (around 0.5dB/cm or higher [27,28]) as the ECW has a stronger light confinement. From another perspective, scattering loss is mainly generated from the laser modified region, however the interlayers of the ECW partially preserve the low attenuation feature of the bulk material.

To estimate the attenuation of the single mode ECW we followed both scattering measurements and cut-back techniques. Free space light of 980nm is coupled on ECW input face using an aspheric lens with focal length of f = 18mm. The generated foci has a similar dimension as the supported mode (approximately 30µm), maximizing thus the coupling efficiency. The weak scattered light along the ECW is monitored and following observations can be made.

3.4 Y-branching structure of ECW

Utilizing the single mode parameters obtained for the ECW previously, we make a further attempt to fabricate a Y-branching structure in fused silica using the ECW concept. The structure is accomplished by firstly sketching a single ‘Y’ trace and then replicating this single ‘Y’ seven times with a 6μm displacement. The 3D schematic of ECW splitter is given in Fig. 6(a). Figure 6(b) shows the profile of the Y-branching structure under phase contrast microscopy. The PCM features appearing dark in the laser irradiated region correspond to zones indicating a positive change of the refractive index. The whole structure can be divided into three parts. The entrance of the structure in the left part is a section of straight single mode ECW with the length of 3mm. In the middle part the ECW split gradually with 120μm separation spanning a 5mm horizontal distance. The eight traces cross each other at the beginning and separate totally as the horizontal axes increases. We emphasize that the image is composed by stitching 34 images together. The oscillating brightness of the background is due to an inhomogeneous illumination of the single microscope image. In order to have a bird’s eye view of the whole arrangement, we scale down the image in width by a factor of 20. The exit port of the structure is composed of two parallel ECWs with 3mm length and 120μm separation. Figures 6(c) and 6(d) shows the exit end face image of the splitter and the corresponding near field intensity distribution image at 980nm wavelength. It is clear that the ECW splitter conserves fairly well the single mode and LMA feature after beam splitting.

 

Fig. 6 Single mode supported ECW was designed to construct a Y-branching structure functioning as a beam splitter. (a) 3D schematic of the ECW splitter. (b) Top view of the PCM image of the Y-branching structure. The image is composed by stitching together 34 images, each scaled down in width by a factor of 20. (c) End view of the optical transmission microscopy image. (d) Near field mode image with 980nm laser radiation.

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3.5 Extrapolation of ECW concept to MIR materials

The potential of ECW demonstrated above for fused silica has a particular interest for mid-infrared materials. We have therefore investigated the applicability of the ECW concept in chalcogenide Gallium Lanthanium Sulfide glass, particularly due to its intrinsic transparence properties in the MIR down to 10µm. The GLS chalcogenide glass shows a reasonable processing window for type I structures generation, making the ECW concept feasible. The structure was written with 40mW, 3ps 800 nm laser pulses at 100 kHz repetition rate, a ps pulse being required to keep the nonlinear distortions low while still preserving the type I positive index fabrication conditions. The resulting structure is indicated in Fig. 7 and shows LMA (~850µm²) single mode guiding at 800 nm. Thus the ECW concept becomes appealing for a range of materials and designs.

 

Fig. 7 10 × 5µm ECW in GLS. (a) White-light image of the structure. (b) Single mode at 800 nm.

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4. Conclusion

Expanded-core structures based on type I layered waveguides are fabricated by ultrafast laser direct writing technique inside optical glasses, primarily fused silica. The guiding characteristics of expanded-core waveguides (ECW) are designed and experimentally investigated as a function of the structure geometry. The conditions for single and multimode guiding with large mode area are emphasized. When the structure is designed to be consisting of 8 guiding layers with 6µm separation and specific index change, ECW exhibits single-mode with mode field area of ~805µm². The condition of single mode operation is also discussed using the dispersion relation of wave guiding in periodical dielectric structures. The parametric study indicates that the decrease in the index change$\Delta n$, number N and thickness S leads to single mode operation. The ECW structure show intrinsic low-loss propagation. A Y-branching splitter was equally designed and fabricated in fused silica, preserving the modal operation. A further example of ECW LMA guiding is given in chalcogenide GLS glass. In conclusion, fs laser inscribed ECW provides to be a flexible way of writing large mode area waveguides. By extrapolation, various materials at near and mid-infrared infrared region which have specific advantages for energy and wavelength transport can share the benefit of ECW concept.