A chiral microchip laser using anisotropic grating mirrors for single mode emission

3.1 General considerations

Anisotropic Bragg mirrors at normal incidence require the introduction of form anisotropy; this can be realized with nanostructured optical thin films by using two classes of techniques. The first one is a bottom–up approach wherein artificial anisotropic effective materials are made by glancing angle deposition to produce anisotropic mirrors for laser resonators. These are nanoporous structures, whose morphology is such that the in-plane effective indices have values differing by Δn ≈ 0.1 [31]. Such a concept was demonstrated in ref. [32] with the goal to achieve a twisted-mode laser for eliminating multimode emission.

An alternative approach consists in using nanofabrication techniques for inscribing a one-dimensional periodic grating on top of a multilayer Bragg mirror to create adequate anisotropic optical responses of TE and TM polarization states at normal incidence. The optical response of different polarization states depends on the property of the layers (i.e., refractive index and thickness) and the dimension of the grating (i.e., grating depth, period and fill factor) and this offers the possibility to control both the reflected amplitude of the TE and TM polarizations, i.e., diattenuation, and their phase shift, i.e., diretardance. It is this approach that was followed in this work.

We designed a pair of anisotropic grating mirrors such that a π phase shift and differential amplitudes exist between reflected TE and TM polarization states at the operating wavelength, λ = 1030 nm, of a Yb⁺³-doped YAG laser. When a standing wave resonator is formed with two such mirrors, adjusting the relative orientation, α, of the two mirrors’ principal axes also enables one to adjust the contrast of the intra-cavity standing wave by changing the proximity of the polarization states of the two counter-propagating waves, as explained in Section 2.

The design of the chiral laser resonator is shown in Figure 2. We consider a laser-diode, end-pumped Yb³⁺-doped Y₃Al₅O₁₂ (YAG) microchip laser equipped with anisotropic mirrors having both diattenuation and diretardance. The ideal characteristics of such mirrors are as follows. The pump mirror is highly transparent (HT) at the pump wavelength (λ_p = 935 nm). In addition, the pump mirror is highly reflecting (HR) around the emission wavelength, λ_l = 1030 nm, for both TE and TM polarizations and the phase shift between reflected TE and TM polarizations is π. The output mirror also produces a phase shift of π at λ_l in reflection, and also diattenuation, with design values R T E ≡ r T E 2 = 97 % and R T M ≡ r T M 2 = 54 % . The latter numerical values are chosen to obtain an EP at the twisting angle α₀ ≈ 5°, which is large enough for easily controlling the transition from region I to region II in an actual experiment.

Figure 2:

Sketch of the chiral microchip laser equipped with anisotropic mirrors, with their specifications.

3.2 The determination of the grating parameters

The fundamental idea of the anisotropic mirror produced with a diffraction grating lies in the use of grating-mediated waveguide resonances, which couple light from the grating into the uppermost layers of the multilayer system, which is then coupled back to reflected or transmitted diffraction orders of the grating. This coupling can lead to a significant enhancement or suppression of the base reflection characteristics of the underlying multilayer [33]. In this work, the strong dependence of such waveguide coupling on the polarization of the incoming light is used [34]. This mechanism is often applied to select one polarization in reflection and/or transmission to achieve polarization selective devices, e.g., for intracavity polarization selection [35, 36]. Here, the polarization-dependent complex reflection amplitude is the desired property, wherein the introduction of a π phase shift between TE and TM polarizations is necessary. As is shown in [33], analytical models can predict the coupling coefficients between grating and waveguide modes, showing that they depend strongly on the polarization, in both amplitude and phase. It is therefore justified to look for a grating mirror configuration that fulfills the specifications outlined in Section 3.1.

The grating mirror design is based on the Fourier modal method, which is a method very well adapted to the scope of the problem, i.e., only stationary solutions to Maxwell equations are required and the inhomogeneous region has periodic boundary conditions in the lateral directions. It allows one to rigorously model the complete system of multilayer mirror and grating at the same time and it is also fast and accurate. For this paper, the software MCGrating [37] was used, since it is highly optimized and allows fast numerical parameter sweeps and optimizations. Details about the optimization procedure can be found in the Supplementary Materials. The best solutions for the pump and output mirrors found with this approach for the laser wavelength of λ_l = 1030 nm are shown in Figure 3. The spectral behavior of the reflectance and the TE/TM phase difference around the laser wavelength are shown in Figures 4 and 5 for the pump and output mirrors. The transmittance around the pump wavelength for the pump mirror is also shown in Figure 4(c).

Figure 3:

Optimized grating mirror design for (a) the pump and (b) output mirrors.

Figure 4:

Calculated optical properties of the pump mirror. (a) Reflectance as a function of the incident light wavelength, with dashed line and annotation at the laser wavelength of 1030 nm. (b) TE and TM phase shift deviation from π around the laser oscillation wavelength. (c) Transmittance as a function of the incident light wavelength, with dashed line and annotation at the pump wavelength of 935 nm.

Figure 5:

Calculated optical properties of the output mirror. (a) Reflectance as a function of the incident light wavelength, with dashed line and annotation at the laser wavelength of 1030 nm, and (b) TE and TM phase shift deviation from π of the output mirror.

4.1 Fabrication of the anisotropic mirrors

The anisotropic mirrors consist of a Bragg multilayer with alternating TiO₂ and SiO₂ layers and a grating made of TiO₂ on top, as shown in Figure 3. The multilayer coatings were prepared with thin film deposition techniques, while the TiO₂ grating was fabricated by Electron-beam lithography and inductively coupled plasma reactive-ion etching (ICP-RIE), where a 50-nm-thick chromium (Cr) layer was used as an etching mask and a thin layer of Al₂O₃ served as an etch-stop layer for TiO₂ etching. The different steps are outlined in Figure 6 and described in more detail in the Supplementary Materials. To achieve the required phase shift of π with as small an error as possible, ten grating patterns with slightly different linewidths but with the same period were prepared on one substrate. A scanning electron micrograph (SEM) cross-section of an output coupler is shown in Figure 7. Other SEM images are shown in the Supplementary Materials.

Figure 6:

Schematic of the fabrication process. (a) Thin film deposition; (b) E-beam lithography; (c) ICP-RIE Cr etching and (d) ICP-RIE TiO₂ etching and Cr removal.

Figure 7:

Scanning electron micrograph cross-section image of a representative output mirror.

4.2 The ellipsometric characterization of the mirrors

The calculation of polarization eigenstates and eigenvalues requires the estimation of the parameters R T E ≡ r T E 2 , R T M ≡ r T M 2 and Δ for each mirror, cf. Eqs. S7 and S8 of Supplementary Materials. The general phase factor exp i φ T E of each mirror is neither accessible nor important for that calculation. This can be done by using ellipsometry. A special ellipsometric setup, described in the Supplementary Materials, was designed to measure these optical properties at normal incidence and at the emission wavelength of the laser, λ _l = 1030 nm.

The measurement results are gathered for all pump mirrors in Table S1, and those of the output mirrors are shown in Tables S2 and S3 for reflection and transmission respectively in the Supplementary Materials. From Table S1, it appears that all the pump mirrors have high R_TE and R_TM reflectance values of similar magnitude at λ_l = 1030 nm, ranging from 92% to 97%, as desired. For both mirrors, measured differences in phase shift between different gratings can be traced to the different fill factors of the gratings, as can be seen in Figure 8(a) and (b) by the monotonous trend of the Δ values as a function of the fill factor. Also shown in dashed lines are the phase shift values predicted by numerical simulations. Pump mirror H has the phase shift (Δ = 178.4°) closest to the targeted 180° value. The transmission of the pump mirror at the pump wavelength of λ = 935 nm is about 91%. For the output mirror, from Table S2, the results vary greatly from one grating to another. Grating C is the one displaying the phase shift value (Δ = 188.8°) closest to the targeted 180° value. It also displays R_TE and R_TM reflectance of 89% and 48%, not too far from the specifications. Hence, most laser experiments were carried out with pump mirror H and output mirror C forming a standing wave resonator.

Figure 8:

TE and TM phase shift of the (a) pump mirror and (b) output coupler in reflection as a function of the fill factor. The dashed lines are the corresponding simulation results and the thin dotted lines in red are a guide for the eye.

5.1 Polarization eigenvalues and eigenstates, and other laser characteristics

The elements of the Jones matrix of each mirror were obtained from ellipsometric measurements, except for an unimportant (and inaccessible) general phase factor, cf. Section 4.2. From the knowledge of the Jones matrices of the two mirrors, M₁ and M₂, and their relative orientation, α, the Jones matrix of a round trip of the passive resonator, J_RT, was obtained. The magnitude of the two eigenvalues, ω₁ and ω₂, of J_RT determines the round-trip losses of the two modes, while their different phase values determine their frequency difference.

The mode with the lowest losses, i.e., with the largest magnitude of the eigenvalue, max ω i , determines the threshold of laser emission, which is the minimum pump power required to achieve laser oscillation, P_th, proportional to (cf. Supplementary Materials, Eqs. S14–S17):

where N is the Yb³⁺ doping concentration, σ_as is the effective absorption cross-section at the lasing wavelength, d is the thickness of the active material, and A is the distributed roundtrip loss. The first term on the right-hand side of Eq. (1) is known, the second term is assumed negligible, and the third term is the main contribution arising from the α-dependent eigenvalues calculated from J_RT. Experimental values of P_th as a function of α are shown in Figure 9(a), together with the theoretical values calculated from Eq. (1) with only one adjustable scaling factor. Experimentally measured values of P_th follow the theoretical predictions well. As can be seen in Figure 9(a), the two modes have very different losses around α = 0° and 90°; hence, we expect that only one polarization eigenstate oscillates for α values in those neighborhoods. On the other hand, round-trip losses are very similar between α = 30° and 60°, as well as between α = 120° and 150°; dual polarization oscillation is thus expected for these α values.

Figure 9:

Measured and calculated threshold pump power values, P_th. (a) Measured (circles) and calculated (dotted and solid curves for modes 1 and 2 respectively) P_th values of each polarization eigenmode as a function of twist angle α. (b) Similarly measured P_th values showing the threshold for dual polarization emission.

If the pump power is increased well above P_th, it is possible to detect the threshold of dual polarization emission. This happens when the round-trip losses of the weaker mode are not too large compared to those of the main mode. Dual polarization emission can then be easily observed by using an elliptical polarizer, made of a quarter waveplate and a linear polarizer. A proper adjustment of the orientation angle of each element will block a specific mode and partially transmits the other. Threshold of dual polarization emission is shown for modes 1 and 2 in Figure 9(b). As expected, dual polarization oscillation is well suppressed near α = 0° and 90° even at pump power values that exceed the threshold value by several times. As α departs from 0°, a second threshold eventually appears, first at very high pump power, and then decreases to reach values similar to the first threshold for α values around 45°; at that point, dual polarization emission takes place as soon as the threshold of oscillation is reached. It is noteworthy that the second threshold shown in Figure 9(b) is significantly higher than what Figure 9(a) suggests. This is due to the saturation of the gain medium during laser operation, which restraints the growth of the excited population, N₂, as the pump power is increased. It was shown that, in the presence of gain saturation of a homogeneous active material, the gain of the competing modes does increase with pump power above threshold due to spatial hole burning [38], although much slower than below threshold.

The polarization state of the two modes was then determined by measuring the angular positions of the quarter waveplate and the polarizer that achieve extinction in turn determine the orientation and eccentricity of the ellipse of polarization. The latter can be mapped on (x, y, z) coordinates of the Poincaré sphere, cf. Supplementary Materials. The calculated coordinates of the two polarization eigenstates inside the resonator for the wave travelling towards the output mirror are shown in Figure 10(a). The measured coordinates of the two eigenstates outside the resonator are shown in Figure 10(b). The knowledge of the Jones matrix of the output mirror in transmission, accessible from the data of Table S3, enables one to compare experimental with calculated values. Experimental polarization states agree well with those calculated from the experimentally measured Jones matrices, Figure 10(b). One can also see that the polarization state of the output beam, Figure 10(b), rapidly changes from nearly right circular at α ≈ −2.5° to the circular state of opposite chirality at α ≈ 2.5°, passing through horizontal polarization near α = 0°; a similar phenomenon takes place near α = 90°. Having a laser mode of well-defined chirality is a direct consequence of the resonator itself being chiral for α ≠ 0° and α ≠ 90°: taking a mirror image of the resonator is equivalent to changing α into −α; as a result, the beam’s chirality, both inside and outside the resonator, is also reversed and the (x, y, z) Poincaré coordinates are transformed into (x, −y, −z) when replacing α by −α, as shown in Supplementary Materials, Figure S13.

Figure 10:

Poincaré coordinates of the polarization eigenstates. (a) Calculated coordinates (x, y, z) on the Poincaré sphere of the two polarization eigenstates inside the resonator. (b) Measured and calculated coordinates (x, y, z) of the two polarization eigenstates outside the resonator.

The output power as a function of absorbed pump power is shown in Figure 11(a) for several α values. The threshold of oscillation and the optical slope efficiency vary with the α value. As the latter is increased from 0°, the power leaking from the output mirror is increased, so the threshold increases, while the slope efficiency increases. Threshold pump power ranges between 40 and 70 mW while the slope efficiency with respect to the absorbed pump power ranges between 50% and 76%: it is highest in the region where multimode emission is best suppressed as shown in Section 5.2.

Figure 11:

Measured slope efficiencies, degree of polarization and beam quality of the chiral laser. (a) Measured output power as a function of absorbed pump power for several α values.  For each α value, the slope efficiency is shown in the figure. (b) Measured degree of polarization as a function of α. (c) M² measurements and beam profile obtained for α = 12^o.

The degree of polarization, p, for various α values is shown in Figure 11(b). This was done by measuring the polarization extinction ratio, η, of the output beam. The parameters p and η are related by the equation: p = η − 1 / η + 1 . We found p to be higher than 0.99, for most α values except near α = 0°, where it is still higher than 0.9. We note that the change of p value strongly correlates with the rapid change of the polarization state inside the resonator, from rectilinear to circular between α = 0° to 10°_, cf. Figure 10(a). This high degree of polarization value close to 1 validates our approach using a Jones matrix formalism.

The quality of the output beam was also measured for several α values; in all cases and for any pumping power, the M² value was found to be very close to unity. An example of beam diameter measured as a function propagation distance for α = 12° is shown, together with a Gaussian beam profile, in Figure 11(c). This is the result of the good mode matching of the pump beam with the fundamental gaussian mode of our resonator. This rules out the existence of multiple transverse modes in laser operation.

5.2 The emission spectra

As shown in Figure 1(a), adjusting α makes it possible to control the contrast of the standing wave of the laser mode. At α angles different from 0° or 90°, the contrast is significantly reduced, and one would expect good suppression of multiple longitudinal mode emission arising from spatial hole burning in this region. The spectral separation between consecutive longitudinal modes of our laser is in the order 64 GHz, i.e., smaller than the resolution available with our spectrometers. Hence, we used a Fabry–Perot étalon (FPE) to separate the spectral components of the emitted beam. The free spectral range and finesse of the étalon, respectively FSR_FE = 200 GHz and F = 25, are large enough to easily identify consecutive modes of our laser without overlapping interference orders. Details of the experimental setup are shown in the Supplementary Materials, Figure S12.

Emission spectra are shown in Figure 12 for α values ranging from 0° to 42°, Figure 12(a), and from 48° to 90° in Figure 12(b). The emission spectrum of a similar laser using isotropic mirrors is shown for comparison at the bottom of each figure. For all the shown traces, the laser operated at twice the laser oscillation threshold. For each α value, ten different traces are shown, showing the reproducibility of the measured emission spectra. For the anisotropic resonator, the emission spectrum was found to change significantly as the twist angle α between the two mirrors was changed. For α = 0°, the grating lines of the two mirrors were aligned and this forced laser oscillation to take place in the linear TE polarization state, which has lower losses than TM-polarized light. However, multimode operation was found because the counterpropagating waves produced maximum interferential contrast resulting in spatial hole burning, like in a standard resonator. At α = 12°, the spectrum became bimodal and at α = 24°, the second mode almost disappears. At α = 42°, the spectrum became multimode again. At α = 48° and α = 66°, the measured spectra were single mode although, at the former angle α = 48°, the polarization state was found to occasionally hop from one polarization eigenstate to the other. The emission spectrum then became increasingly multimode as the α value approaches 90°. For a conventional resonator, the emission spectrum was found to contain several peaks inside one free spectral range of the FP étalon, cf. the bottom traces of Figure 12(a) and (b).

Figure 12:

Emission spectra for ten CCD images for a standard resonator for various α values of the grating mirrors (a) from α = 0 to α = 42° (b) from α = 48° to α = 90°. The emission spectra for an identical laser using isotropic mirrors are shown at the bottom. The spectral lines repeat at every free spectral range of the Fabry–Perot, FSR_FP. The spectra are vertically shifted for clarity.

The evolution of emission spectra as a function of the pump power is shown in Figure 13 for the case of (a) α = 42°, (b) α = 66°, (c) α = 90° and (d) a resonator of similar geometry with conventional isotropic mirrors. The current intensity in the pump laser diode was increased from 1.2 to 3 times the threshold value. The emission remained mostly single mode for α = 66°, while for α = 42°, the emission became mainly bimodal from a pumping intensity equal to twice the threshold value. For the anisotropic resonator with α = 90°, the number of modes increased from 3 to 5, while for an isotropic resonator, the number of frequencies increased from 5 to 6 for the same pumping range. The highly multimode operation observed near α = 0° and α = 90° and the improvement of the single mode character between these two values were consistent with the quasi cancellation of axial hole burning phenomenon away from α = 0° and α = 90°, as seen in Figure 1(a), curve B. Also, the coexistence of polarization states, which is more frequently seen around 42° and 48° than at α values closer to α = 0° and α = 90°, was consistent with the discrimination predicted by calculations shown in Figure 9(a) and confirmed by the measurements of the second threshold in Figure 9(b).

Figure 13:

Evolution of the emission spectrum as a function of the pumping intensity for anisotropic resonators (a) α = 42°, (b) α = 66° and (c) α = 90°, and (d) for a resonator with isotropic mirrors for a pumping intensity I ranging from 1.2, 1.5, 2 and 3 times the threshold current intensity, Ith, in the diode laser.