The power of fiber lasers has been increasing, and high-power laser systems have been developed by combining the beams of low-power lasers. Coherent beam combining (CBC) and spectral beam combining (SBC) methods are widely used [1]. In the CBC method, the phase of each laser beam must be adjusted coherently for phase matching, by applying a feedback signal to the seed lasers. Thus CBC systems have complicated structures requiring many components. SBC is a simpler method, since a diffraction grating can be used to combine a few laser beams incoherently with slightly different wavelengths, which is also known as wavelength beam combining (WBC) [2-5].

The diffraction grating is one of the key components of an SBC system. Due to ease of fabrication, metals and semiconductors are commonly used to make reflection-type diffraction gratings. Metal gratings such as gold, silver, and aluminum have high reflectance over a broad range of wavelengths, but their laser-induced damage threshold (LIDT) is low, due to the absorption loss of light in the metal. Absorption-free multilayer dielectric (MLD) mirrors are widely used instead of metal reflectors, for their high LIDT and high diffraction efficiency, as shown in Fig. 1. A phase diffraction grating is placed on top of an MLD mirror, and a matching layer is inserted between them. The grating’s parameters are its period p, duty cycle f, depth h, and matching-layer thickness t.

Perry et al. were the first to demonstrate an MLD diffraction grating using ZnS and ThF₄ for chirped-pulse compression [6]. Frank and Collischon proposed a method using an MgF₂ etch-stop layer for perfect etching of an SiO₂ top grating [7]. Neauport et al. proposed a trapezoid-shaped MLD grating, and achieved 96% diffraction efficiency for a –1^st-order TE wave at 1053 nm [8]. Martz et al. demonstrated a large MLD grating with more than 97% diffraction efficiency across the clear aperture area [9]. Li et al. proposed a two-layer trapezoidal grating for a polarization-independent high efficiency MLD grating at the wavelength of a Ti:sapphire laser [10].

The purpose of this study is to design and fabricate a high-diffraction-efficiency MLD grating for spectral beam combination for the wavelengths of a Yb-doped fiber laser. Large angular dispersion is also required to combine many wavelengths in the 1040~1075 nm range from the fiber lasers. In this study, high diffraction efficiency was designed at the –1^st-order TE wave near the Littrow condition, and compared to the experimental value. To this end in design, the diffraction modes were analyzed by varying the incidence angle and grating line density at a given wavelength, and a modal method was used for the duty cycle and grating depth. The diffraction efficiency was calculated using the finite-difference time-domain (FDTD) method [11, 12]. Two grating designs with different duty cycles were fabricated on top of MLD reflectors, using photolithography and reactive-ion etching. The cross sections were observed using a scanning electron microscope (SEM), the diffraction efficiency was measured, and the laser-induced damage threshold (LIDT) was obtained. The analysis and results in this study could be helpful for various applications, such as unpolarized MLD diffraction gratings with high laser-induced damage, MLD chirped-pulse amplifier gratings, and nanophotonic MLD grating devices.

Spectral beam combination of low-power laser beams using a diffraction grating is a simple way of incoherently increasing the power of a laser system. In an SBC system, all the laser beams must be diffracted at a specific diffraction order, then combined to form a high-power laser beam. The combined beam needs to be diffraction limited, as well as having high radiance and high beam quality in the far field. In other words, the diffraction grating for an SBC system should have high diffraction efficiency and high beam quality. Furthermore, if many laser beams over a wide angle of incidence are combined, the angular dispersion should be large. We follow basic principles to design the initial gratings and multilayer dielectric mirrors separately, then refine the parameters of the MLD grating system (grating + matching layer + multilayer mirror) using a matching layer to obtain high diffraction efficiency.

The diffraction-grating equations in reflection (R) and transmission (T) are

where p is the period of the grating, n_i and n_s are the refractive indices of the incident and transmitted media respectively, θ_m is the diffraction angle, θ_i is the angle of incidence, m is the diffraction order, and λ is the wavelength of incident light [13, 14]. It is well known that very high diffraction efficiency at the m^th order can be obtained from a Littrow grating, which diffracts an incident beam backward toward the source, i.e. θ_−m = −θ_i [14]. The diffraction efficiency of the –1^st order becomes 100% if the Littrow grating for an SBC system diffracts only at the m = –1^st order (i.e. Eq. (1) in R mode becomes sinθ_d = ), and if zeroth-order specular reflection is suppressed completely.

The figure of merit for the quality of a Gaussian laser beam is M², and the combined beam at the Littrow grating can be expressed by

where ω₀ is the beam-waist radius of the incident beam, and ∆λ is the bandwidth for a laser beam of wavelength λ [3]. High beam quality (M² ≈ 1) for an SBC beam can be obtained at the Littrow grating if the beam width (ω₀), diffraction angle (θ₋₁), or laser bandwidth (∆λ) is small, or if the grating period (p) is large.

Hehl et al. used the effective index of a diffraction grating to set the range of the grating density, and the incidence angle at which each diffraction mode can exist [15]. Based on their method, Fig. 2 shows the range of diffraction modes as a function of the incidence angle and grating density at a wavelength of 1055 nm, with n₀ = 1.0 and n_s = 1.46. The –1^st orders in T and R radiate below the lines of and respectively. The +1^st and –2^nd orders in T are evanescent above the lines of and , respectively. Therefore, the area in red surrounded by the R_–1, T₊₁, and T_–2 lines is for only –1^st-order diffraction in R and T. The Littrow condition at which the –1^st order is diffracted back into the incident direction is shown as a long-dashed line .

Similarly, other specific orders in different colors can be chosen. For example, the blue area is only for the –1^st orders in R and T and the +1^st order in T mode. Figure 2 is very useful for designing a grating of any specific orders in R and T.

The angular dispersion of a diffraction grating is given by , and the incidence angle at the Littrow condition of θ_i = −θ₋₁ can be determined by [16]

The period can be determined from the Littrow condition,

If the angular dispersion of diffraction is , the incidence angle from Eq. (3) is θ_i ≈ 62°, which is located near the Littrow line in the red area of Fig. 2. The grating period p then becomes 597 nm, according to Eq. (4). This design is shown as a dot, inside the area of the –1^st order in R only and near the Littrow line, in Fig. 2. The period of the fabricated gratings was 575 nm, which is sufficient to achieve the final goal of the SBC system.

The duty cycle (f) and depth (h) of a grating are also important parameters to determine. Clausnitzer et al. used a simple modal method for estimating the grating efficiency, and showed that the results agree well with those of a rigorous calculation [17]. The dispersion equation of a 1-dimensional periodic diffraction grating with a ridge of thickness d_r and a groove of thickness d_g is:

where is the Bloch wave vector in the x direction, p = d_r + d_g is the period of the grating, is the duty cycle, and are respectively the propagation wave vectors in a ridge and groove in the x direction, n_e is the effective index of the grating as a waveguide in the z-direction, and Γ depends on the polarization: for a TE wave, and for a TM wave.

An effective index of a propagating mode for transmission in the direction inside the grating can be determined graphically or numerically from Eq. (5), which is a function of , i.e., F(). At the Littrow condition of Eq. (4), the Bloch wave vector is and the left-hand side of Eq. (5) is cosK_x,inp = –1. Effective indices of two guided modes for each TE and TM wave are presented as a function of the duty cycle in Fig. 3, in which p = 575 nm, θ_i = 62°, and λ = 1055 nm.

The difference in effective indices between n_e0 and n_e1 for a TE wave is around 0.5 in f = 0.3~0.6, which is much larger than for a TM wave. Two guided modes of n_e0 and n_e1 are reflected at a high reflective mirror. If the guided modes interfere constructively to couple completely with only the –1^st order diffraction, the diffraction efficiency of the grating at the –1^st order for a TE wave is , where h is the optical phase thickness. A diffraction efficiency of η₋₁ = 100% can be obtained if the height of the grating is

The diffraction grating depth was obtained from Eq. (6) as h = 538~643 nm, using the effective refractive indices f = 0.3~0.6 in Fig. 3.

In the near-infrared wavelength region, HfO₂ and SiO₂ are widely used as high (n = 1.89) and low (n = 1.45) refractive index materials in an MLD mirror, for high LIDT [18, 19]. A 20-layer quarter-wave dielectric reflector was designed and fabricated by electron-beam evaporation. Figure 4 shows the reflectance of both the designed and deposited multilayer dielectric mirrors, at an incidence angle of 62° [20]. The deposited mirror’s reflectance for s-polarized light is almost 100% around 1055 nm, which matches well with the design.

It was found that the diffraction efficiency for a diffraction grating on top of an MLD mirror system (grating + MLD mirror) was low, due to destructive leaky modes, so a matching layer was inserted between the grating and MLD reflector to obtain high diffraction efficiency, as shown in Fig. 1. In the case of a (grating + matching layer + MLD mirror) system, the design parameters of duty cycle, matching layer thickness, and grating depth obtained using the basic principles above should be optimized further, using an FDTD simulation. The simulations were performed in a duty cycle range of f = 0.3~0.7, with matching layer thicknesses of t_m = 210~650 nm, and grating depths of h = 210~650 nm.

Figure 5 shows the diffraction efficiency (η_–1) of the –1^st-order beam as a function of the grating depth (h) and matching layer (t_m) at duty cycles of f = 0.3, 0.4, 0.5, and 0.6. In the area of high η_–1 (in red), at a given duty cycle the grating depth tends to decrease as the matching layer thickness increases, which may ease fabrication of the grating. As the duty cycle increases, the area of high η_–1 decreases and becomes a thin line, where the matching layer thickness is inversely proportional to the grating thickness. Figure 6 shows η_–1 as a function of the grating depth and duty cycle, at matching layer thicknesses of t_m = 310, 410, 510, and 610 nm. The area of high η_–1 increases and shifts to small duty cycle and grating thickness, as the matching layer thickness increases to 510 nm. However, the area decreases at 610 nm and shifts toward a smaller duty cycle and grating thickness.

Based on the FDTD results and for easy fabrication, we set the matching layer thickness as t_m = 430 nm and the grating depth as h = 430 nm at duty cycles of f = 0.35 and 0.5. Figures 7(a) and 7(b) show the calculated diffraction efficiency as a function of wavelength and incidence angle. A duty cycle of f = 0.35 exhibits η₋₁ = 94.5% at λ = 1035 nm and θ_i = 62°, while a duty cycle of the f = 0.5 reveals η₋₁ = 98.1% at λ = 1060 nm and θ_i = 62°. Figure 7(b) shows η₋₁ as a function of incidence angle, at λ = 1050 nm and 1064 nm and f = 0.35.

Two types of diffraction gratings were fabricated using photolithography and reactive-ion etching. The gratings had the following characteristics: period p = 575 nm, grating depth h = 430 nm, and matching layer thickness t = 430 nm, with different duty cycles of f = 0.35 and 0.5. Two types of Cr photomasks (10 mm²) were fabricated, and a stitching process was used to pattern the binary grating on an MLD mirror coated on Si substrate (50 × 150 mm) using a 1:4 KrF scanner (ASML Co. Ltd.). Grating structures were fabricated by reactive-ion etching (EXELAN HPT, LAM Co. Ltd.) with a gas mixture of C₄F₈, O₂, and Ar, with 200 W of rf power.

Figure 8 shows SEM images of the fabricated MLD diffraction gratings. The low-magnification SEM images in Figs. 8(a) and 8(c) show the grating (SiO₂), matching layer (SiO₂), and high index layer (HfO₂). The high-magnification images in Figs. 8(b) and 8(d) clearly show the shapes of the diffraction grating. A rectangular MLD grating was formed for the grating with a duty cycle of 0.5, as shown in Fig. 8(d), while a slightly trapezoidal shape was produced for the grating with a duty cycle of 0.35, as shown in Fig. 8(b).

The performance of the fabricated MLD gratings was measured using in-house equipment, including a 20-mW DFB laser (QLD1061-5330, QD Laser) with wavelengths of 1050 nm, 1052 nm, 1061 nm, and 1064 nm, and a thermal infrared power detector (CLD 1015, Thorlab). Measured diffraction efficiency at four wavelengths is shown in Fig. 7(a), along with the simulations. The maximum efficiency for the duty cycle 0.35 MLD grating was 95.7% at 1052 nm, and that for the duty cycle 0.5 was 99.1% at the same wavelength. It is noted that the measured diffraction efficiencies at four wavelengths for both MLD gratings are quite close to the simulated curves. Figure 7(b) shows the diffraction efficiency as a function of incidence angle, for duty cycle 0.35. The measured maximum efficiency at 1050 nm was 93.4% at an incidence angle of 66°, while the maximum efficiency at 1064 nm was 96.2% at 68°. It is noted that the measured diffraction efficiency at 1064 nm is quite close to the simulated curve, while that at 1050 nm shows a slight difference between the two. The discrepancy in diffraction efficiency between simulation and measurement might have come from alignment error in the measurement system, or instability of the detector or light source.

The laser-induced damage threshold of the fabricated MLD gratings was measured using a cw laser (1 kW output power, IMPAC IN5, Lumasense Inc.) with a beam diameter of 5.85 mm at the MLD grating. The surface of the MLD grating was irradiated by the laser beam and observed by a CCD camera. Temperature variation of the surface was measured by a pyrometer (IMPAC IN5, Lumasense Inc.). As shown in Fig. 9, the surface temperature gradually increased with increasing irradiation time, and the temperature change was larger when the power of the laser was higher. The maximum temperature for the duty cycle 0.35 MLD grating increased up to 45°C during 55 seconds of laser irradiation time, while the temperature for duty cycle 0.5 was up to 55°C. No visual damage was found in the CCD camera, and, furthermore, no trace of laser damage was observed upon optical-microscope inspection at the maximum laser power irradiation of 3.76 kW/cm². It seems that the LDIT of the fabricated MLD grating was greater than 3.76 kW/cm², which was the maximum, due to the limit of the laser’s power and the focal length of the focusing lens.

The electric field intensity distribution of the diffraction grating was investigated, to identify the diffraction efficiency and the LIDT of the MLD gratings. Figure 10(a) shows the intensity distribution of the grating with f = 0.5 at θ_i = 62° with high diffraction efficiency. The –1^st-order diffracted beam with well-aligned wavefronts propagates backward compared to the incident wave’s direction, which indicates that the grating modes are constructively interfering within the grating, and are coupled to the –1^st-order diffraction beam. A strong intensity distribution is not present at the edge or interface of the diffraction grating, and exists outside of the grating structure, which implies that the LIDT could be high.

Figure 10(b) shows the electric-field intensity distribution of the grating with f = 0.5 at θ_i = 30° with low –1^st diffraction efficiency. The diffracted intensity is very low in the incident medium, and the wavefronts are not observed, which indicates low diffraction efficiency. There is high intensity in the ridge of the grating, which could result in low LIDT. This figure agrees well with the result from Neauport et al., in that the presence of high intensity within the grating reduces the LIDT of the MLD grating [8].

This study analyzed the design and fabrication of high-diffraction-efficiency MLD diffraction gratings for spectral beam combining of Yb-doped fiber laser wavelengths. We reported basic design steps and a modal analysis for a near-Littrow grating with high diffraction efficiency. We found a range of grating densities at a wavelength of 1055 nm and incidence angles that allow only the 0^th and –1^st orders of diffraction in the reflection. Two effective indices of the grating modes were calculated as a function of the duty cycle, from the dispersion equation of the Littrow grating. The maximum-interference condition coupled with –1^st-order diffraction was used to determine the range of duty cycle and grating depth. Finally, an FDTD simulation was used to obtain optimized design parameters for the grating and the matching layer, for high diffraction efficiency.

Two MLD gratings with the same grating parameters and matching layer thickness were fabricated, at different duty cycles of 0.35 and 0.5. The SEM images clearly showed the cross sections of the grating and MLD reflector. The diffraction efficiency and LIDT of each fabricated MLD diffraction grating were measured, and the diffraction efficiency was compared to the designed value. The analysis and results in this study could be helpful for the design and fabrication of MLD diffraction gratings for polarization control and high laser-induced damage, MLD chirped-pulse amplifier gratings, and nanophotonic MLD grating devices.