High efficiency quasi-three level thin film laser enabled on a sinusoidal grating substrate

Wenda Cui; Hongyan Wang; Kai Han; Weihong Hua; Xiaojun Xu

doi:10.1364/OE.25.004097

1. Introduction

In the field of higher-power solid state laser (HPSSL) study, it is priority to make the surface-to-volume ratio of gain medium higher so that heat dissipation will be fast enough for the HPSSL to obtain a perfect thermal property and beam quality [1, 2]. However, lots of blocks will arise when the cross section or thickness is compressed. In the Yb:YAG thin disc laser, the pump radiation should be sufficiently absorbed to get higher optical efficiency, so quite high Yb³⁺ concentration is necessary [3]. However, the higher concentration of the Yb ions the faster the excitation energy migrates between them [4], whereupon the concentrations are generally optimized as about 10 at%. Regarding that a thinner gain disc is better for heat dissipation in the thin disc laser, it’s hard to realize a high single-pass absorption in Yb-doped disc. Although multi-pass architecture is designed to increase the absorption by N-fold (N is the passing times of pump beam) [5, 6], it is hard to build a compact system since the optical assembling and material processing like cutting and welding can be great engineering blocks. Nanostructure is used in the optical materials to achieve many practical applications such as optical modulators, photo detectors and solar cells [7–9]. Since light field can be significantly localized by nanostructures, optical materials with characteristics such as enhanced absorption and emission rate that are not available in nature can be achieved by nanostructure materials [10–12]. Total absorption in narrow spectral bands in metallic periodic structures has been reported [13], but the surface plasma could cause considerable energy loss. However, it is possible to improve absorption by structuring the surface of the dielectric substrate as a pyramidal or sinusoidal profile [14, 15], and strong resonance effects originating from the guide-mode resonance (GMR) could occur inside the layer that deposited on the substrate. GMR structures have been studied extensively and previous results demonstrate that GMR structures can enhance the absorption and emission significantly [16, 17]. A compact system could be realized by nanostructure design in this paper, namely the pump beam could be sufficiently absorbed in one pass and simultaneously highly reflected by the gain medium.

2. Design and simulation of the sinusoid grating Yb-doped thin film

We theoretically investigated the Yb-doped thin film on a 1D grating structure and a sufficiently absorption was achieved in the wavelength range (900-980 nm) by appropriate design. Figure 1(a) shows the schematic of a laser oscillator based on sinusoidal grating Yb³⁺ doped film. Surface of the substrate is sculptured and a Yb³⁺ doped film is deposited on it. P presents the pump source; S1 is the collimating lens; M1 and M2 are the laser cavity mirrors; H is the heat sink. The grating thickness is presented as $h_{g}$ and $θ$ indicates the incident angle of laser beam. A homogeneous layer of gain film is on the top of grating substrate whose thickness $h_{s} = 500 n m$ . $Λ$ is the period and $Λ / N$ means that there are N sinusoidal cycles in one grating period. The incident area refractive index $n_{a i r} = 1$ , $n_{r}$ is the sinusoidal fluctuation’s refractive index.

Fig. 1 Schematic of a sinusoidal grating gain film laser oscillator (a) laser structure (b) gain film structure

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The gain medium’s dispersive relationship calculated by Kramers–Kronig integral [18, 19] is depicted in Fig. 2.

Fig. 2 Dispersive curve of Yb-doped material

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For $Λ = 400 n m$ Rayleigh anomaly occurs at $λ_{s} = n_{s} Λ$ below which higher diffraction orders appear [20]. Since the diffraction efficiency is lower for higher orders, the grating period $Λ < λ_{s} / n_{s}$ is required. For waves that above $λ_{s}$ , the GMR phenomena may occur in which an efficient interaction between the incident light and the gain film can be achieved. In that way, a TM light can be totally absorbed with proper grating parameters [16]. If resonant mode coincides with pump wavelength, the enhanced local field in waveguide layer will increase the absorption of associated laser wavelength and at the same time the leaky-mode resonance leads to high reflection efficiency. Provided the incident angle, grating period or grating depth change, the resonant peaks would shift so it’s possible to locate the reflection peaks at the excitation and emission wavelength simultaneously. We simulated the device using rigorous coupled wave analysis (RCWA) and series of parameters were denoted as $Λ = 400 n m$ , $n_{s} = 1.5$ , $n_{r} = 2.5$ , $N = 3$ , $h_{g} = 750 n m$ , $θ = 40^{\circ}$ and $50^{\circ}$ in Fig. 3.

Fig. 3 Reflectivity spectrum for TM polarization

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Figure 3 shows that for incident angle $θ = 40^{\circ}$ the reflectivity almost reaches 100% at several wavelength locations, namely guided-mode resonance happens near $λ = 830 n m$ , $894 n m$ , $952 n m$ and $1036 n m$ . At the wavelength $λ = 952 n m$ the local light field is enhanced and the excitation would be enhanced efficiently. The absorbance is defined as

A = 1 - (\sum_{i} R_{i} + \sum_{i} T_{i})

_{$R_{i}$} and $T_{i}$ are the efficiencies of the i-th reflected and transmitted diffraction orders. If we change the parameters like grating period and incident angle, the resonance would shift with them. In the laser application of Fig. 1, reflectivity at the absorption peak $λ = 942 n m$ of Yb-doped material should be high and the corresponding absorption would be enhanced either. Figure 4 shows the spectral reflectivity and absorption at different wavelength with the grating period $Λ = 380 n m$ and $θ = 48^{\circ}$ . There are two high reflectivity peaks at $λ =942 n m$ and $1022 n m$ in the figure and the reflectivity of $λ = 942 n m$ is above 90%.

Fig. 4 Reflectivity and absorption versus wavelength with $θ {=48}^{\circ}$

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Compared with the absorption efficiency of the gain film on a planar substrate, the absorption enhancement factor $F$ on the grating substrate is defined as:

F = \frac{A (λ)}{N_{i o n} σ_{p} (λ) d}

The denominator $N_{i o n} σ_{p} (λ) d$ indicates the absorption of a gain layer without grating structures and $d$ is the layer thickness. The reflectivity and absorption enhancement map is shown in Figs. 5(a) and 5(b). There are three high reflectivity and absorption arms in Fig. 5 and the maximum F value is about 100, which means for $λ = 940 n m$ , there are series of incident angles at which the absorption could be enhanced. It is obvious that the high reflectivity and enhanced absorption are corresponding to each other. Figure 5(b) shows that the absorption efficiency is extremely low below $Λ = 0.25 μ m$ , so the grating period is better being larger than $0.25 μ m$ . Besides the pump light, the emission light should also be highly reflected at the same time. However, in Fig. 4 the reflectivity of $1030 n m$ is much lower when incident angle $θ = 48^{\circ}$ , instead, the high reflectivity point of emission is at about $1020 n m$ .

Fig. 5 Reflectivity and absorption as a function of grating period and incident angle (a) reflectivity maps (b) absorption enhanced factor

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Since the grating depth and incident angle could also affect the reflectivity efficiently, it is possible to change the resonance location to Yb³⁺ icons’ excitation and emission wavelength. Assuming the incident angle $θ = 35^{\circ}$ in the calculation, the resonance reflection spectra with different grating depth and wavelength is presented at Fig. 6(a). As the grating thickness increases, the grating film could support more resonance modes [20, 21] and the resonance-free range in wavelength also changes with different grating depth, so it’s very likely that a set of appropriate parameters could lead to the excitation and emission light resonating simultaneously.

Fig. 6 Reflectivity as a function of (a) grating depth and wavelength (b) incident angle and wavelength

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Since $λ = 940 n m$ and $1030 n m$ are chosen, free spectral range between resonance wavelength should be $Δ λ = 90 n m$ . Referring to Fig. 6(a), the grating depth is set as about $0.45 μ m$ . In Fig. 6(b) multimode-resonance occurs at different incident angles and it shows that high reflectivity and enhanced absorption at emission and excitation wavelength can be achieved simultaneously by choosing the appropriate incident angle $θ = 20^{\circ}$ . Reflectivity and absorption versus wavelength with $θ =2 0^{\circ}$ is presented in Fig. 7.

Fig. 7 Reflectivity and absorption versus wavelength with $Λ =0 .45 μ m$ , $θ = 20^{\circ}$ , $h_{g} = 0.74 μ m$

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The absorption is enhanced at $λ = 936 n m$ and $1028 n m$ in Fig. 7, but the reflectivity peaks locate at $λ = 936 n m$ and $1030 n m$ , so the enhanced wavelength will shift a little [22].

Figure 8(a) and 8(b) present the amplitude distribution of magnetic field at the pump and emission wavelength $λ = 936 n m$ and $λ = 1030 n m$ . One can see that the magnetic field is quite weak in the substrate and the light field is quite high in the air area, which means the pump and emission beam are both highly reflected. Meanwhile, the magnetic field is extremely localized in part of the grating high index material as well as the gain medium between grating ridges which covers the grating substrate. As is known that strong light field confinement could enhance the interaction between light and gain medium, the absorption of resonance wavelength would be enhanced significantly. In laser oscillator, the optical efficiency depends highly on the pump absorption and the laser reflectivity of the grating gain film. With an effectively enhanced absorption of pump power, a high efficient laser can be expected.

Fig. 8 $| H_{y} |$ distribution in the GMR structure (a) $λ = 936 n m$ (b) $λ = 1030 n m$

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3. Laser properties

A simple model of the laser oscillator is set up assuming the gain film is pumped homogeneously and the pump light is polarized (TM mode). Referring to the thin disc laser model [23], rate equations of a quasi-three-level system are as follows:

\frac{d n_{2}}{d t} = \frac{E_{p} λ_{p}}{h c} \frac{η_{a b s}}{N_{i o n} d} - \frac{n_{2}}{τ} - M_{r} \frac{E_{c a v} λ_{l}}{h c} [n_{2} σ_{e} (λ_{l}) - n_{1} σ_{a} (λ_{l})]

\frac{d E_{c a v}}{d t} = M_{r} E_{c a v} N_{i o n} [n_{2} σ_{e} (λ_{l}) - n_{1} σ_{a} (λ_{l})] \frac{c d}{2 l} - E_{r e s} \frac{c}{2 l} [- \ln (1 - T) - \ln (1 - L)]

_{$N_{i o n}$} is the bulk density of laser ions; $n_{2}$ is the fraction of laser ions in the upper manifold; $E_{p}$ is pump energy density and $η_{a b s}$ is the absorption efficiency. $E_{c a v}$ is the laser energy density in the cavity and $M_{r}$ is the number of laser radiation passing through the gain layer per resonator round trip. $σ_{a} (λ_{l})$ and $σ_{e} (λ_{l})$ are absorption and emission cross sections at laser wavelength, $τ$ is the lifetime of upper manifold and $l$ is the cavity length. $T$ is the transmission of the output coupler at laser wavelength; $L$ is the integrated losses per round trip, which presents the reflectivity at 1030 nm. Since the gain film is so thin that the excited ions distribution is considered uniform along perpendicular direction. The absorption efficiency $η_{a b s}$ is defined as:

η_{a b s} = 1 - \exp (σ_{a} (λ_{p}) d Δ n N_{i o n})

Here

Δ n

is the integrated inversion fraction coupled by the pump Stark levels [24].

Δ n = 1 - (1 + \frac{1}{f (λ_{p})}) n_{2}

With the steady-state condition

n_{2}

is given by Eq. (4):

n_{2} = \frac{f (λ_{l})}{1 + f (λ_{l})} + \frac{[- \ln (1 - T) - \ln (1 - L)]}{N_{i o n} \times d \times M r \times σ_{e} (λ_{l})} \frac{1}{1 + f (λ_{l})}

Optical efficiency of the laser is given by

η_{o p t} = η_{a b s} T \frac{λ_{p}}{λ_{l}} (1 - \frac{E_{t h}}{E_{p}}) / [- \ln (1 - T) - \ln (1 - L)]

The factor

f (λ)

relates the absorption and emission cross section which is defined as

f (λ) = σ_{a} (λ) / σ_{e} (λ)

.

E_{t h}

denotes the threshold pump density which is given by

E_{t h} = \frac{h c}{λ_{p} η_{a b s}} \frac{d N_{i o n} n_{2}}{τ}

Considering Eqs. (3)-(9), Laser icons’ bulk density $N_{i o n}$ and the thickness $d$ could be replaced by one factor $N_{0} = N i o n \times d$ for simplification. Parameters used in this model are shown in Table 1.

Table 1. Parameters used in the simulation.

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Figure 9 shows the optical efficiency and threshold power density curves with increasing enhancement factor, in which different symbols present the icon area density $N_{0}$ ranging from $2.0 \times 10^{19} / c m^{2}$ to $4.7 \times 10^{19} / c m^{2}$ .

Fig. 9 Optical efficiency and threshold power density versus enhancement factor.

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As presented in Fig. 9, the optical efficiency will increase dramatically as the absorption cross section is enhanced. For a typical laser without GMR structures, the enhancement factor F is equal to 1 and the threshold density is about 8000 W/cm². Since we set the pump power density as 5000 W/cm² in this model, there would not be laser output at all. In terms of the calculation above, F could achieve about 100 with the designed GMR structure and the threshold density could be lower than 1000 W/cm². The optical efficiency achieves almost 70% when the enhancement factor is above 40 in Fig. 9 and with higher $N_{0}$ , the optical efficiency would achieve the highest value more quickly. The enhancement factor should be larger than 1.4 so that enough laser icons could be excited to the upper manifold. Referring to Eq. (2) and Fig. 7, the designed enhancement factor is about 28.9 while the highest optical efficiency is about 65% and the corresponding threshold density is about 803.5 W/cm².

4. Conclusions

In conclusion, a Yb-doped film on the sinusoidal grating substrate with high reflectivity and enhanced absorption is designed. Based on this grating gain film, a high efficiency laser is realized. The pump and emission beam are reflected at the same time on the grating gain film. By choosing the appropriate parameters reflectivity at 936 nm and 1030 nm is above 90% and the pump absorption enhancement factor is about 28.9. Optical efficiency can be improved dramatically and in the meantime threshold is lowered exponentially as the enhancement factor increases. Furthermore, the electromagnetic field and mode volume are adjusted either in the grating film so an efficient enhancement of emission could be expected and the effects of the emission enhancement on lasing behavior needs further study next.

References and links

1. A. Giesen and J. Speiser, “Fifteen years of work on thin-disk lasers: results and scaling laws,” IEEE J. Sel. Top. Quantum Electron. 13(3), 598–609 (2007). [CrossRef]

2. D. J. Richardson, J. Nilsson, and W. A. Clarkson, “High power fiber lasers: current status and future perspectives [ Invited ],” J. Opt. Soc. Am. B 27(11), 63–89 (2010). [CrossRef]

3. M. Javadi-Dashcasan, F. Hajiesmaeilbaigi, H. Razzaghi, M. Mahdizadeh, and M. Moghadam, “Optimizing the Yb: YAG thin disc laser design parameters,” Opt. Commun. 281(18), 4753–4757 (2008). [CrossRef]

4. K. Petermann, D. Fagundes-Peters, J. Johannsen, M. Mond, V. Peters, J. J. Romero, S. Kutovoi, J. Speiser, and A. Giesen, “Highly Yb-doped oxides for thin-disc lasers,” J. Cryst. Growth 275(1-2), 135–140 (2005). [CrossRef]

5. A. Giesen, A. Voss, K. Wittig, and U. Brauch, “The thin-disc laser: a scalable concept for efficient diode-pumped solid-state lasers with high beam quality,” in Conference on Lasers and Electro-Optics Europe (IEEE, 1994), pp. 79. [CrossRef]

6. S. Erhard, A. Giesen, M. Karszewski, T. Rupp, C. Stewen, I. Johannsen, and K. Contag, “Novel pump design of Yb: YAG thin disc laser for operation at room temperature with improved efficiency,” in Advanced Solid State Lasers, Vol. 26 of OSA Trends in Optics and Photonics (Optical Society of America, 1999), paper MC3.

7. O. Limon, A. Rudnitsky, Z. Zalevsky, M. Nathan, L. Businaro, D. Cojoc, and A. Gerardino, “All-optical nano modulator on a silicon chip,” Opt. Express 15(14), 9029–9039 (2007). [CrossRef] [PubMed]

8. A. Karar, C. L. Tan, K. Alameh, Y. T. Lee, and F. Karouta, “Metal nano-grating optimization for higher responsivity plasmonic-based GaAs metal-semiconductor-metal photodetector,” J. Lightwave Technol. 31(7), 1088–1092 (2013). [CrossRef]

9. L. Zeng, P. Bermel, Y. Yi, B. A. Alamariu, K. A. Broderick, J. Liu, C. Hong, X. Duan, J. Joannopoulos, C. Kimerling, L. Zeng, P. Bermel, Y. Yi, B. A. Alamariu, K. A. Broderick, J. Liu, and C. Hong, “Demonstration of enhanced absorption in thin film Si solar cells with textured photonic crystal back reflector,” Appl. Phys. Lett. 93(22), 221105 (2008). [CrossRef]

10. P. Lodahl, A. Floris Van Driel, I. S. Nikolaev, A. Irman, K. Overgaag, D. Vanmaekelbergh, and W. L. Vos, “Controlling the dynamics of spontaneous emission from quantum dots by photonic crystals,” Nature 430(7000), 654–657 (2004). [CrossRef] [PubMed]

11. D. Lu, J. J. Kan, E. E. Fullerton, and Z. Liu, “Enhancing spontaneous emission rates of molecules using nanopatterned multilayer hyperbolic metamaterials,” Nat. Nanotechnol. 9(1), 48–53 (2014). [CrossRef] [PubMed]

12. Y. Liu, S. H. Sun, J. Xu, L. Zhao, H. C. Sun, J. Li, W. W. Mu, L. Xu, and K. J. Chen, “Broadband antireflection and absorption enhancement by forming nano-patterned Si structures for solar cells,” Opt. Express 19(S5Suppl 5), A1051–A1056 (2011). [CrossRef] [PubMed]

13. T. V. Teperik, F. J. Garcia de Abajo, A. G. Borisov, M. Abdelsalam, P. N. Bartlett, Y. Sugawara, and J. J. Baumberg, “Omnidirectional absorption in nanostructured metal surfaces,” Nat. Photonics 2(5), 299–301 (2008). [CrossRef]

14. C. Li, L. Xia, H. Gao, R. Shi, C. Sun, H. Shi, and C. Du, “Broadband absorption enhancement in a-Si:H thin-film solar cells sandwiched by pyramidal nanostructured arrays,” Opt. Express 20(S5Suppl 5), A589–A596 (2012). [CrossRef] [PubMed]

15. E. Popov, D. Maystre, R. C. McPhedran, M. Nevière, M. C. Hutley, and G. H. Derrick, “Total absorption of unpolarized light by crossed gratings,” Opt. Express 16(9), 6146–6155 (2008). [CrossRef] [PubMed]

16. W. Wu and R. Magnusson, “Total absorption of TM polarized light in a 100 nm spectral band in a nanopatterned thin a-Si film,” Opt. Lett. 37(11), 2103–2105 (2012). [CrossRef] [PubMed]

17. J. H. Lin, C. Y. Tseng, C. T. Lee, H. C. Kan, and C. C. Hsu, “Guided-mode resonance enhanced excitation and extraction of two-photon photoluminescence in a resonant waveguide grating,” Opt. Express 21(20), 24318–24325 (2013). [CrossRef] [PubMed]

18. G. Andermann, A. Caron, and D. A. Dows, “Kramers-Kronig dispersion analysis of infrared reflectance bands,” J. Opt. Soc. Am. 55(10), 1210–1216 (1965). [CrossRef]

19. R. K. Ahrenkiel, “Modified Kramers–Kronig analysis of optical spectra,” J. Opt. Soc. Am. 61(12), 1651–1655 (1971). [CrossRef]

20. S. S. Wang and R. Magnusson, “Theory and applications of guided-mode resonance filters,” Appl. Opt. 32(14), 2606–2613 (1993). [CrossRef] [PubMed]

21. Z. S. Liu and R. Magnusson, “Concept of multiorder multimode resonant optical filters,” IEEE Photonics Technol. Lett. 14(8), 1091–1093 (2002). [CrossRef]

22. X. Sheng, S. G. Johnson, J. Michel, and L. C. Kimerling, “Optimization-based design of surface textures for thin-film Si solar cells,” Opt. Express 19(S4Suppl 4), A841–A850 (2011). [CrossRef] [PubMed]

23. K. Contag, M. Karszewski, C. Stewen, A. Giesen, and H. Hugel, “Theoretical modelling and experimental investigations of the diode-pumped thin-disk Yb: YAG laser,” Quantum Electron. 29(8), 697–703 (1999). [CrossRef]

24. R. J. Beach, “CW theory of quasi-three level end-pumped laser oscillators,” Opt. Commun. 123(1-3), 385–393 (1996). [CrossRef]

Incident angle	20°
Grating period	450nm
Grating thickness	740nm
Homogeneous gain thickness	500nm
Output coupler reflectivity	0.75
Pump reflectivity	0.95
Cavity transmission	0.99
Pump density	5000W/cm2

High efficiency quasi-three level thin film laser enabled on a sinusoidal grating substrate

Abstract

1. Introduction

2. Design and simulation of the sinusoid grating Yb-doped thin film

3. Laser properties

4. Conclusions

References and links

Cited By

Figures (9)

Tables (1)

Equations (9)

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