Origins of low transmission loss and birefringence

The comparison between the SEM images and optical images clearly shows the correlation between the emergence of nanoplanes and the transmission drop, which suggests that the randomly distributed nanopores is responsible for the reduced light scattering. Moreover, the oblate shape of nanopores should be responsible for the induced birefringence. To confirm this, we simulated the transmittance and birefringence of the randomly distributed nanopore structures in silica glass (Fig. 4a).

Fig. 4: Simulation of optical properties of the low-loss birefringent modification. a Model for calculation of the birefringence. Oblate nanopores are distributed in silica glass. k indicates the light propagation direction for evaluation of the birefringence. b Plot of the birefringence (n yy − n xx ) against the volume fraction of nanopores with different aspect ratios (d y /d x ). c Optical transmission spectra of silica glass with nanopores of different diameters simulated based on Rayleigh scattering. The volume fraction of nanopores for the simulation is f = 0.005, and the thickness of the volume in which nanopores are formed is 400 μm, which is the same as that of the birefringent structure in Fig. 1c Full size image

The birefringence (n yy − n xx ) originating from oblate nanopores inside silica glass was simulated as a function of the aspect ratio of the nanopores (d y /d x ) and the volume fraction of nanopores (f) in silica glass (Fig. 4a, b) by the Maxwell–Garnett model with anisotropic scattering particles (Section 5 of Supplementary)40. The birefringence is proportional to the volume fraction of nanpores and the slope increases with the aspect ratio of the nanopores. The birefringence (n yy − n xx ) is always positive for d y /d x > 1, meaning that the slow axis is parallel to the long axis of the nanopores, which is consistent with the relation between the slow axis and the elongation of the nanopores in the SEM images (Fig. 2a, b). To explain the observed birefringence of 5 × 10−4 at N p = 150 (Fig. 2a), the volume fraction of nanopores should be ~0.5% (f = 0.005) for mean aspect ratio d y /d x = 2, which was estimated from the SEM image.

The optical transmittance was simulated by Rayleigh scattering41 and the Beer–Lambert law42 (Section 5 of Supplementary) with the nanopore volume fraction of 0.5% estimated above. When the diameter of the nanopores is larger than 40 nm, the transmission drops in the visible region (Fig. 4c). The transmission loss in the visible region significantly decreases with decreasing diameter from 40 to 10 nm. By comparing the measured (blue solid line in Fig. 1e) and simulated spectra, the diameters of nanopores for the low-loss modification could be estimated as between 20 and 30 nm. The average diameter of nanopores from the SEM image (Fig. 2a, N p < 200) is ~30 nm, which shows a good agreement with the estimation.

Elucidation of the origin of the transmission loss and birefringence is crucial for the creation of practical birefringence in glass. Until now, the formation of periodic nanostructures or the alignment of lamellar structures has been believed to be necessary to generate birefringence by laser direct writing. However, the SEM observations and birefringence and transmittance simulations proved that spatially separated nanopores with anisotropic shape are sufficient to produce high enough birefringence with ultralow loss. Although both the birefringence and transmittance can be predicted by classical theories, this is the first demonstration of a new silica structure, which is very different from conventional nanoporous silica where pores aggregate43 or connect to each other44, and of space-selective control of the nanopore anisotropy with a focused polarized light beam.

Mechanism of formation of anisotropic nanopores

The mechanism of polarization-controlled oblate nanopore formation should involve at least two processes: (1) formation of randomly distributed nanopores and (2) elongation of nanopores perpendicular to the polarization of the light beam. The formation of nanopores suggests the generation of oxygen molecules inside silica by laser irradiation, whose relation to defects formation has been investigated in a number of studies35,45,46,47,48. The fact that the low-loss birefringent modification (type X) cannot be observed with short pulse duration (t p < 220 fs) (Fig. 3c) indicates that the formation of nanopores requires a time duration above a critical value. One possible reason is the interaction between the light pulse and transient defect pairs [E′ centre and NBOHC] or self-trapped triplet excitons (STE). Saeta et al. observed the generation of the transient defect pairs within ~250 fs after photoexcitation in silica glass45.

$$\equiv {\mathrm{Si}} - {\mathrm{O}} - {\mathrm{Si}} \equiv \mathop { \to}\limits^{250\;{\mathrm{fs}}} \equiv {\mathrm{Si}} \cdot + \cdot {\mathrm{O}} - {\mathrm{Si}} \equiv$$ (1)

where ≡ Si· is the E′ centre and ≡ Si–O· is the NBOHC. When the pulse duration is longer than 250 fs, the photoexcitation of the NBOHC could occur due to multiphoton absorption or impact ionization by hot electrons (~18 eV, double of the band gap of silica glass, 9 eV) produced by the avalanche mechanism, resulting in the dissociation of oxygen atom:

$$\equiv {\mathrm{Si}} \cdot + \cdot {\mathrm{O}} - {\mathrm{Si}} \equiv \mathop { \to }\limits^{{\mathrm{h}}

u\;{\mathrm{or}}\;{\mathrm{e}}^- } \equiv {\mathrm{Si}}{ \cdot ^+ }{\mathrm{Si}} \equiv +\, {\mathrm{O}}^0 + {\mathrm{e}}^-$$ (2)

where ≡ Si·+Si ≡ is the E δ ′ centre, O0 is an interstitial oxygen atom and e− is an electron. The dissociation of oxygen atoms from the silica structure is essential to generate oxygen molecules, which could facilitate nanopore formation in silica glass. For the laser pulse shorter than 250 fs, the probability of reaction (2) is reduced, resulting in the absence of nanopores for t p < 220 fs. In contrast, at longer pulse durations, more oxygen atoms could be generated from reaction (2) by photoexcitation of the transient defect pairs. In addition, the contribution of avalanche ionization increases with increasing pulse duration, suggesting that the dissociation of the Si–O bond might be driven by high-energy electrons generated by avalanche ionization. The mechanism based on reaction (2) is supported by the absorption and photoluminescence spectra of modifications of different types (Section 6 of Supplementary), in which only the NBOHC is detected in the optically isotropic modification (type I), while both the oxygen-deficiency centers (ODCs) and NBOHC are detected in the birefringent modifications (type X and type II).

We measured the transmission of laser pulses during laser writing and found that 10–15% of the laser pulse energy was absorbed via photoexcitation. If all the absorbed light energy is used for heating the lattice of the glass, then the estimated temperature just after the photoexcitation is 1600–2100 K, which is high enough for cavitation in silica melt. On the other hand, the thermal quenching must be fast enough to avoid coalescence of nanopores. The viscosity of silica melt below the estimated temperature, 2100 K, is as high as 105 Pa s, at which the diffusion coefficient of an oxygen molecule (diameter of 0.35 nm) is ~D = 9.2 × 10−17 m2/s according to the Stokes–Einstein equation42. At this diffusion coefficient, the expected diffusion length in t = 1 μs is (D × t)1/2 = 10 pm, which means no movement without any external force or no coalescence of nanopores by diffusion when the thermal quenching occurs within several microseconds.

For longer pulse durations, the transition from the low-loss to high-loss modification occurs with a smaller number of pulses (Fig. 3c and Section 1 of Supplementary). One of the effects of the longer pulse duration is an excess temperature increase due to the increased contribution of avalanche ionization36,49. Irradiation with a longer pulse could prevent the generation of spatially separated nanopores due to the higher temperature which facilitates the generation, growth and coalescence of nanopores.

Another essential process, elongation of nanopores in the direction perpendicular to the polarization, can be explained by the near-field enhancement around nanopores during laser irradiation27,34. The local electromagnetic field around a nanopore in a dielectric medium is enhanced perpendicular to the polarization. The enhanced field could induce more local ionization and generate an anisotropic stress distribution around the nanopore, which could cause its elongation in the direction perpendicular to the polarization (Section 7 of Supplementary, Fig. S6).

Applications of low-loss birefringent modification

The low-loss birefringent modification provides a variety of birefringent optical elements, such as GPOEs, vector beam convertors, and true zero-order waveplates. The fabricated GP prism or polarization grating has a birefringence distribution with a constant slow axis gradient along the horizontal direction (Fig. 5a). This allows continuous phase shifts without phase resets, in contrast to conventional optical elements, such as blazed gratings and Fresnel lenses, wherein the phase profiles are recorded as optical path variation in the refractive index and thickness. Moreover, the direction of light propagation can be switched by changing the handedness of the circular polarization of incident light (Fig. 5a). The demonstrated diffraction efficiency was higher than 99% at 457 nm, which agrees with that calculated for the measured retardance of 220 nm. A GP lens with a parabolic shape of the slow axis distribution was also fabricated (Fig. 5b). The focusing and defocusing of the GP lens can be switched by changing the handedness of the circular polarization. A 488 nm laser beam was focused to the diffraction-limited spot size of 112 μm, close to the theoretical value of 114 μm. An F-number as small as 50 was demonstrated, which is limited by the phase gradient of ~0.1 π rad/μm. Interestingly, the same highly transparent GP lens in glass could act as an all-in-one concave–convex lens for the correction of short- and long-sightedness.

Fig. 5: Geometric phase (GP) optical elements and vector beam converter imprinted with the low-loss birefringent modification. a Birefringence image of a GP prism with a slow axis gradient of 0.01 πrad μm−1 (upper), and light intensity patterns of 457 nm CW laser beams with different circular polarizations diffracted by the GP prism (lower). b Birefringence image of a GP lens, and intensity patterns of 488 nm CW laser beams with different circular polarizations focused and defocused by the GP lens. The focal lengths are ±208 mm for the wavelength of 488 nm. c Ten-millimetre vector beam converter without (left) and with (middle) a polarizer under linearly polarized white light illumination. The slow axis distribution in the central part of the converter is shown on the right. d Intensity pattern of a 343 nm laser beam after the converter without a polarizer (left). Intensity patterns of the radial (middle) and azimuthal (right) vector beams produced by the converter after a polarizer Full size image

Another important application is a polarization vector beam converter (Fig. 5c). In the converter, the retardance was chosen to as half of the target wavelength (343 nm) and the slow axis was linearly varied from 0° to 180° with respect to the azimuth (Fig. 5c right). The imprinted beam converter was highly transparent (Fig. 5c left), while it could be clearly observed under cross-polarizers (Fig. 5c middle). A high-quality 343 nm dounut-shaped beam with radial and azimuthal polarization was generated (Fig. 5d). Transmittance through the beam converter as high as 91% was measured without any evidence of damage for the 343 nm laser beam with an average power of 1.2 W, beam width of 4 mm, pulse duration of 190 fs and repetition rate of 1 MHz.

In summary, we observed ultrafast laser-induced modification in silica glass with the evidence of anisotropic nanopore formation representing a new type of nanoporous material. The modification enabled fabrication of ultralow-loss birefringent optical elements including geometrical phase elements, vector beam converters and zero-order retarders, which can be used for high power lasers and UV light sources. The high transmittance from the UV to near-infrared, high damage threshold and thermal resistance of the fabricated optical elements in silica glass overcome the limitations of GP and polarization shaping using other materials including liquid crystals and meta-surfaces. The space-selective birefringent modification with high transparency also enables high density multiplex data storage in silica glass50.