Generation of high-power spatially structured beams using vertical external cavity surface emitting lasers

Michal L. Lukowski; Jason T. Meyer; Chris Hessenius; Ewan M. Wright; Mahmoud Fallahi

doi:10.1364/OE.25.025504

1. Introduction

Over the past couple of decades Vertical External Cavity Semiconductor Lasers (VECSELs) have been developed to provide high output powers over a wide range of fundamental lasing wavelengths (670 nm – 2.4 µm) as a result of semiconductor heterostructure bandgap engineering [1–3]. In particular, the well-developed VECSEL heterostructures based on GaAs/InGaAs semiconductors are ideal for generating high power continuous wave (cw) outputs in the 900 nm to 1200 nm range [4]. The free-space external cavity of VECSELs combined with optical pumping allows for excellent mode quality in a compact and flexible device [5]. The access to the high intracavity circulating power also allows for efficient second harmonic generation (SHG) providing tunability via the second-harmonic in addition to the fundamental, and single frequency operation can be obtained if intracavity etalons or birefringent filters are used [6,7].

So far VECSEL technology has been exclusively aimed at producing high power and wavelength tunable beams with a Gaussian transverse profile. On the other hand, higher-order modes other than the Gaussian are currently of great fundamental and technological interest, including Hermite-Gaussian [8], Laguerre-Gaussian [9], and Bessel-Gauss beams [10] to mention a few. Some previous works have considered laser systems for generating these higher-order modes [11–15], including Laguerre-Gaussian modes from a microlaser [13], optically pumped solid state lasers [14,15], and spatially structured vertical cavity surface emitting lasers with mode shaping with integrated optical elements [16–18]. These important works do not, however, offer the potential for combined high power and tunability, and are not necessarily well adapted to intracavity SHG as VECSELs are. In the context of nonlinear optics, the generation of light with controllable spatial patterns using single-pass sum frequency generation (SFG) in a quasi-phase matched crystal [19], as well as sum frequency and second harmonic generation with laser beams carrying orbital angular momentum [20, 21] have been explored. This opens up the door to generating spatially structured light using wave mixing.

Our goal in this paper is to initiate the experimental and theoretical study of the generation of high-power spatially structured beams in VECSELs, both at the fundamental wavelength and for the beams generated via intracavity SHG. As a first step in Section 2 we show that a mode-control element (MCE) inserted into a linear cavity VECSEL can be used to control oscillation of the cavity field on a selected higher Hermite-Gaussian beam for the fundamental field. Thus, in this paper we focus attention on HG-like modes. In the next stage in Section 3 we consider intracavity SHG using a lithium triborate (LBO) crystal in a V-cavity geometry, and with a variety of HG modes for the fundamental as selected by the MCE. Here we show that the spatial structure of the generated light may be controlled using both phase-matching in the LBO crystal and changing the spatial position of the crystal with respect to a flat cavity mirror. We remark that the spatial structure of the generated light is HG-like in that it has the intensity structure of those modes, but not necessarily the phase structure. Having said this for most if not all applications of HG modes, such as atom trapping [22–24] and manipulation of biological cells [25], rely on the intensity structure alone. This highlights the utility of VECSEL technology as a source of structured light for such applications.

2. Hermite-Gaussian modes at the fundamental wavelength

In this Section, we describe the properties and operation of a linear cavity VECSEL as illustrated in Fig. 1. In particular, we demonstrate that this system may be made to operate on higher-order HG modes at the fundamental wavelength and we characterize the mode properties.

Fig. 1 Schematic of the VECSEL setup for fundamental operation.

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2.1 VECSEL gain medium and fabrication

In the experiments reported here, metal oxide chemical vapor deposition (MOCVD) is used to grow a VECSEL heterostructure designed to emit at ~1070 nm. The active region consists of 12 compressively strained 8 nm thick InGaAs quantum wells (QW) with GaAs pump absorbing barriers and a layer of GaAsP between each QW for strain compensation. On top of the multi-quantum wells (MQWs) are 25 pairs of alternating AlGaAs/AlAs layers grown to serve as a high reflectivity (~99.9%) distributed Bragg reflector (DBR) at the emission wavelength. The specific thickness and composition of the heterostructure layers were designed to achieve resonant periodic gain (RPG) such that each QW is positioned at the antinodes of the laser cavity standing wave. Thermal management is crucial for the efficient operation of a VECSEL. This is accomplished by solder bonding a VECSEL chip to a chemical vapor deposition (CVD) diamond. Once bonded, selective chemical wet etching is used to remove the GaAs substrate. The surface of the chip was antireflection (AR) coated at the pump wavelength of 808 nm and the device was mounted and clamped to a water-cooled copper heat sink for temperature control purposes.

2.2 Experimental results

A standard linear laser cavity configuration was used in the first part of the experiment, as shown in Fig. 1. The VECSEL chip together with a 30 cm radius of curvature (RoC) mirror formed a roughly 25 cm long resonant cavity. The curved mirror with appropriate coatings served as a 97% reflective output coupler. The fiber-coupled 808 nm diode pump was refocused onto the surface of the VECSEL chip to a spot with diameter of ~400 µm, which was slightly larger than the ~380 µm fundamental transverse mode size defined by the cavity length and the mirror RoC. The copper heat sink was maintained at a temperature of 15°C. Additionally, for the purpose of the experiment a mode-control element was placed in proximity of the output coupler, which allowed for operation on higher-order modes as opposed to the Gaussian mode. For the MCE, we used fused silica transparent substrate that we selectively patterned to provide minimum loss for any targeted HG mode compared to all the other modes. Thus, when insterted in the laser cavity, the highest gain occurred for targeted HG mode.

During the experiment, the MCE was adjusted to achieve different Hermite-Gaussian mode intensity profiles, which output powers and beam profiles were measured. In order to characterize the transverse beam structure, a DataRay BeamMap2 scanning slit beam profiler was used. To obtain an image of the lasing mode, the beam was refocused into the profiler sensor and was tens of microns in diameter. In Fig. 2, the fundamental mode as well as other recorded beam shapes are shown. The (a) HG₀₀, (b) HG₀₁, (c) HG₁₀ and (d) HG₁₁ transverse intensity profiles can be clearly recognized going from left to right.

Fig. 2 Intensity profiles of the (a) fundamental Gaussian mode along with the (b) HG₀₁, (c) HG₁₀ and (d) HG₁₁ transverse modes.

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Figure 3(a) presents the output power characteristics for the fundamental Gaussian lasing as well as for HG₀₁, HG₁₀ and HG₁₁ transverse mode operation. The Gaussian mode resulted in the highest output power exceeding 4 W. The HG₀₁ mode maximum power was ~3.8 W, whereas the HG₁₀ and HG₁₁ modes both reached a peak output power of ~2.5 W. To understand this, we first recognize that the MCE introduced a small amount of loss. Furthermore, since higher-order modes have larger effective areas the pumped gain area, optimized for the Gaussian mode, provided less gain to the higher-order modes. Thus, it is natural that the output power decreases for higher-order modes in our experiment. Moreover, the HG₁₀ mode experienced less gain than the HG₀₁ mode by virtue of the fact that the pump beam is incident at an angle leading to an elliptically shaped gain profile. This gain profile asymmetry is responsible for the lower output powers for the HG₁₀ and HG₁₁ modes in Fig. 3(a). Since the pump spot area remained fixed for all modes, the HG₁₁ mode resulted in smaller output power compared to the other modes. Higher efficiency can be achieved by optimized the pump spot size with the modes. Figure 3(b) illustrates the fact that the output wavelength was maintained in all cases and was equal to ~1063 nm. The measured output powers and wavelength were stable within the 1 Å resolution limits of our optical spectrum analyzer (OSA) and the resolution of the power meter.

Fig. 3 (a) Output power characteristics for beams with various HG transverse profiles; (b) the lasing wavelength maintained for all the cases.

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3. Spatially structured beams via intracavity second harmonic generation

3.1 Second-harmonic generation in a V-cavity VECSEL

For the second part of the experiment, a common V-folded laser cavity configuration was used in the experiment, as shown in Fig. 4. This cavity type, compared to linear geometry, is advantageous in the case of nonlinear conversion because it allows easy control of the transverse mode size in both the gain medium and the nonlinear crystal [6]. The spherical concave mirror with radius of curvature equal to 10 cm served as a folding mirror, while the VECSEL chip and the flat end mirror enclosed the resonant cavity. Both mirrors were high reflectivity coated for ~1070 nm, thus ensuring high fundamental lasing circulating power, while the flat mirror was also HR coated for ~535 nm. This allowed all of the green light to be extracted through the folding mirror that had a low reflectivity (<10%) coating at 535 nm. Similarly, as in the linear cavity, the distances between the VECSEL chip and the mirrors were chosen to ensure fundamental Gaussian operation while mode matching to the optical pump spot size and maintaining the appropriate focusing into the nonlinear crystal. The same optical pumping arrangement with a pump spot of ~400 µm in diameter on the chip surface was utilized. The distance from the chip to the curved mirror was ~21 cm and the distance from the curved to the flat mirror was ~6 cm. Based on these cavity dimensions, the calculated fundamental mode diameter was equal to ~100 µm at the flat mirror and ~380 µm at the chip surface. The same MCE as before was next inserted into the cavity to control which Hermite-Gaussian mode the fundamental beam operated on. For the purpose of second harmonic generation, a LBO crystal with dimensions of 3 × 3 × 15 mm³ and both facets antireflection coated for both ~1075 nm and ~537 nm was used. It was cut for type I angular phase-matching condition with angles $θ = 90 °$ and $ϕ = 11 °$ [26]. The LBO crystal was inserted into the shorter arm of the laser resonator a variable distance d away from the flat mirror. In addition, a 3 mm thick birefringent filter was employed for wavelength stabilization and for maintaining a narrow linewidth.

Fig. 4 The schematic of the green VECSEL setup for second harmonic generation.

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3.2 Theoretical model and simulations

Our simulations were performed in the undepleted pump beam approximation. Following the notation of [26], propagation of the second-harmonic field in the LBO crystal is described by the paraxial wave equation

\pm (\frac{\partial A_{2}}{\partial z} + δ \frac{\partial A_{2}}{\partial x}) = \frac{1}{2 k_{2}} \nabla_{T}^{2} A_{2} + \frac{i ω_{2}^{2} d_{e f f}}{k_{2} c^{2}} A_{1}^{2} e^{i Δ k z}

where

A_{1, 2}

are the slowly varying envelopes of the fundamental and second-harmonic fields that are propagating dominantly along the z-axis, the

\pm

signs correspond to propagation in the forward and backward directions in the LBO crystal, we have included diffraction via the transverse Laplacian term, and also walk-off with angle

δ

along the x-axis. Here

d_{e f f} ≃ 1 p m / V

is the effective nonlinear coefficient, and

Δ k

is the wavevector mismatch. The fundamental field obeys a similar equation with no walk-off (we maintain

θ = 90 °

) or nonlinearity, and the subscript 2 replaced by 1. In writing Eq. (1) we have assumed that the second-harmonic field is polarized along the x-axis, so that is the direction of the walk-off.

In the experiment and our simulations there are two control parameters, namely the distance $d$ between the flat mirror and the LBO crystal, see Fig. 4 and the wavevector mismatch. $Δ k$ Based on the estimated fundamental spot size $w_{0} = 50 μ m$ at the flat mirror and the mode selected for the fundamental by the MCE, for the HG mode with mode indices $(n, m)$ the fundamental field at the flat mirror is set as

A_{1} (x, y) = A_{0} H_{n} (\frac{x}{\sqrt{2} w_{0}}) H_{m} (\frac{y}{\sqrt{2} w_{0}}) e^{- (x^{2} + y^{2}) / w_{0}^{2}}

where

A_{0}

controls the fundamental power. Then given the distance

d

, the fundamental field was determined at the input facet to the LBO crystal using linear propagation, along with the corresponding spot size

w_{i n}

at the input facet. The fundamental and second-harmonic fields are then propagated over the length

L

of the crystal using the Beam Propagation Method [27], from the input facet to the facet nearest the flat mirror. Both the fundamental and second harmonic fields are next propagated free-space style using standard Fourier optics over the distance

2 d

back to the crystal, including the phase difference arising from the dispersion of air [28]. Finally, the fundamental and second-harmonic are propagated in the reverse direction through the LBO crystal to determine the profile of the output second-harmonic.

We have performed extensive simulations based on the above model. In what follows we shall neglect walk-off and comment on this in the experimental section. Before presenting the simulation results we discuss some general expectations. The second-harmonic polarization is in general driven by the square of the fundamental field $P_{2} \propto A_{1}^{2}$ . Now if the fundamental field is taken as a one-dimensional Hermite-Gaussian for illustration, then the polarization for the second-harmonic will vary as

P_{2} (x) \propto H_{m}^{2} (\frac{x}{\sqrt{2} w_{0}}) e^{- 2 x^{2} / w_{0}^{2}} \propto \sum_{k = - \infty}^{\infty} a_{k} H_{k} (\frac{x}{w_{0}}) e^{- 2 x^{2} / w_{0}^{2}}

That is, the second-harmonic field will be driven by a polarization that is a superposition of Hermite-Gaussian beams with amplitudes

a_{k}

and based on the spot size

w_{0} / \sqrt{2}

, so depending on phase-matching the output second-harmonic can cover a variety of spatial structures. Two general points arise: Due to the complexity of our geometry, in particular the free-space section of length

d

, it is not trivial to generalize the phase-matching analysis of Kleinmann and Boyd [29] to our case for HG modes. Second, in the absence of walk-off the sum over

k

in Eq. (3) will only be non-zero for even values of

k

since

P_{2}

must be an even function of

x

. Strictly speaking this means that only even order HG modes of the second-harmonic light can strictly be generated by our approach, and odd order HG modes with the characteristic odd parity of their phase profiles cannot arise. Nonetheless we shall see that the nonlinear interaction can yield spatial intensity profiles quite close to odd order HG modes, and we use the term HG-like modes to distinguish this case. Such modes remain of relevance since many applications, such as optical trapping, rely on the intensity profile of the HG modes and are not dependent on the associated phase.

Turning now to our simulations, Fig. 5 shows results as a function of the scaled phase-mismatch $σ = Δ k w_{0}^{2}$ [28] for a fundamental HG₀₁ beam, so $(n, m) = (0, 1)$ , and $d = 0$ , meaning the LBO mirror is up against the flat mirror. The scaled phase-mismatch can be tuned by slightly varying the angle of the crystal. Figure 5(a) shows the generated second-harmonic power relative to the fundamental power, and (b) shows the calculated second-harmonic output intensity profile ${| A_{2} (0, y) |}^{2}$ as a function of the scaled coordinate $y / w_{i n}$ , $w_{i n}$ being the fundamental spot size at the input facet: The second-harmonic profile remains largely Gaussian along the x-axis in this example. In Fig. 5(b) the peak intensity is normalized to unity in each case so that the profiles for different $σ$ can be compared. What is clear is that as the phase-mismatch is varied the spatial structure of the generated second-harmonic changes drastically along the y-axis, from HG₀₂ at $σ = 0$ to Gaussian-like at. $σ = - 2$ To give a qualitative measure of the mode content in Fig. 5(c) we plot the effective mode index $m_{e f f}$ : This is obtained by calculating the numerical value of the beam quality $M^{2}$ [30] evaluated along the y-axis for the second-harmonic field, and using the relation $m_{e f f} = (M^{2} - 1) / 2$ , which is exact for HG modes [31]. We see therefore that phase-matching can be used as a parameter to control the spatial structure of the generated second-harmonic. We also note from Fig. 5, that the peak second harmonic power need not coincide with where integer values of $m_{e f f}$ arise. So, there is a tradeoff between trying to maximize power and realizing a given spatial field structure.

Fig. 5 Simulation results as a function of the scaled phase-mismatch for a fundamental ^HG₀₂beam: (a) second-harmonic power relative to the fundamental power, (b) second-harmonic intensity profile and (c) the effective mode index.

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Figure 6 shows the same as Fig. 5 except for $σ = 0$ and as a function of $d$ , and Fig. 6(b) demonstrates that $d$ can be used to control the spatial profile. For example, around $d = 25 μ m$ we find $m_{e f f} ≃ 2$ . Figure 6(a) suggests low conversion at that point but we find that this can be countered by varying the phase-matching parameter $σ$ : In this example, peak power is obtained for $σ = - 1$ . This coincides with what is done experimentally, that is, for a given value of $d$ the crystal angle can be adjusted to strike a balance between power and the spatial structure of the generated second-harmonic.

Fig. 6 Simulation results as a function of $d$ for a fundamental $H G_{01}$ beam: (a) second-harmonic power relative to the fundamental power, (b) second-harmonic intensity profile and (c) the effective mode index.

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We have found from our simulations that for a HG_0m fundamental beam the second harmonic effective mode index $m_{e f f}$ can range between zero and $2 m$ as the phase-matching is changed, leading to a rich variety of spatial mode structures. This can be extended to the case of a HG_nm fundamental beam with the caveat that the effective mode index evaluated along each direction can vary from zero to $2 n$ , and zero to $2 m$ . We shall present examples of two-dimensional beam profiles when comparing to the experimental results in the next section.

3.3 Experimental results

In this section, we present examples of the measured spatially structured second harmonic beams and their properties. The spatially structured beams were generated by utilizing the 1070 nm higher-order HG modes excited in the V-cavity using the MCE. As a reference, initially the Gaussian mode SHG output was measured for a Gaussian fundamental. Next, the MCE was again introduced into the cavity to create a circulating HG₀₁ fundamental mode, which was then converted in the LBO crystal into green output. The spatial structure of the green beam depended on the fine-tuning of the phase-matching angle as well as the position of the crystal away from the flat end mirror (beam waist position) as predicted by the simulations in the previous section. Figure 7 shows the measured green beams for a) $d = 25 m m$ yielding a HG₀₁-like beam, and b) $d = 0 m m$ yielding a HG₀₂ beam. As remarked earlier, although Fig. 7(a) shows an intensity profile like a HG₀₁ beam, it cannot have the associated phase profile, and for this reason we use the terminology HG₀₁-like beam. This terminology has relevance as many applications, such as optical trapping, rely on the intensity profile of the HG modes and are not dependent on the associated phase. Similarly, Fig. 7 also shows the measured profiles for a HG₁₁ fundamental for c) $d = 25 m m$ yielding a HG₁₁-like beam, and b) $d = 0 m m$ yielding a HG₂₂ beam. These results demonstrate that the VECSEL with intracavity nonlinear conversion is able to generate a rich variety of spatially structured second harmonic beams.

Fig. 7 Captured images of SHG green structured beams with HG₀₁-like, HG₀₂, HG₁₁-like and HG₂₂ intensity profiles.

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The green output power was also characterized for each of the structured beams and the results are compared in Fig. 8(a). The green output for the HG₀₀ fundamental mode had the highest power of ~3.1 W. For the structured beams, the second harmonic power decreases for the same reasons as in the linear cavity case, in addition to there being a lower nonlinear conversion efficiency. The HG₀₁-like and HG₀₂ modes reached maximum power at ~1 W and ~2.6 W, respectively, while the HG₁₁-like and HG₂₂ modes highest powers were ~0.21 W and ~0.6 W, respectively. The significant power drop between these two pairs of outputs is a result of the LBO crystal placement in the laser cavity. While for HG₀₂ and HG₂₂ beams, the crystal was placed near the flat mirror, for the HG₀₁-like and HG₁₁-like beams the crystal was placed 25 mm away from the flat mirror. In the latter case, the nonlinear conversion occurred for a highly expanded beam, $w_{i n} ≫ w_{0}$ , leading to lowered output powers. Finally, Fig. 8(b) presents the spectrum for the green light that peaks around ~530 nm and has linewidth of ~0.1 nm, which was maintained throughout the measurements. Again, the measured output powers and wavelength were stable as indicated previously.

Fig. 8 (a) Output power characteristics for green structured beams with various HG and HG-like transverse profiles; (b) the lasing wavelength maintained of green beams.

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Next, we compare the results of the spatially structured beams from of our numerical simulations with the experimental measurements. Figure 9 shows the simulations results corresponding to Fig. 7 with parameters for plots (a, c) $d = 25 m m$ and $σ = - 1$ , and for plots (b, d) $d = 0 m m$ and $σ = 0$ . Here we see good qualitative agreement between theory and experiment. Finally, we address the issue of walk-off. It is clear from the experimental results in Fig. 7 that there are spatially asymmetries in the measured spatially structured beam profiles, and these most certainly arise from walk-off in the system. For the phase-matched case the walk-off angle for LBO is quoted as $0.4 °$ for $ϕ = 11 °$ and $θ = 90 °$ . If this value is included in our code we cannot reproduce the agreement in Fig. 9, but rather we find that a walk-off angle $< 0.2 °$ is needed to reproduce the experimental simulations with only mild asymmetries. We interpret this to mean that under the conditions of the experiment, with the focused HG beams and with the free-space section of length $d$ , the actual phase matching condition is quite removed from $ϕ = 11 °$ , and this can yield smaller walk-off than the conventional phase-matching condition. In a sense, the fact that we can see HG-like modes with only mild asymmetries is a diagnostic of the reduced value of the walk-off angle.

Fig. 9 The simulation results corresponding to Fig. 7. (a) HG₀₁-like, (b) HG₀₂, (c) HG₁₁-like and (d) HG₂₂.

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4. Conclusions

In conclusion, we have shown that VECSELs can generate high power spatially structured light at the fundamental wavelength using a mode-control element whereby Hermite-Gaussian modes can be selected. Using this in conjunction with intracavity SHG we have demonstrated that the spatial structure of the second-harmonic light can be manipulated using phase-matching along with the spatial position of the nonlinear crystal. The experimental results were shown to be in acceptable agreement with our simulations. What these results show is that VECSEL technology is a promising candidate for the generation of high-power and tunable spatially structured light beyond the usual Gaussian mode, and it could serve as a source for the myriad of applications [22–25]. In future work, we shall go beyond this proof-of-principle demonstration and build the concept of VECSELs as a viable source for structured light. In addition, these HG modes can be utilized to generate various LG modes by using an astigmatic mode converter [32], broadening their application. Finally, by the means of intracavity etalon and birefringent filter single frequency and broad wavelength tuning is achievable with watt-level output power.

Funding

ECCS Division of National Science Foundation (NSF) and State of Arizona Technology and Research Initiative Funding (TRIF).

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Generation of high-power spatially structured beams using vertical external cavity surface emitting lasers

Abstract

1. Introduction

2. Hermite-Gaussian modes at the fundamental wavelength

2.1 VECSEL gain medium and fabrication

2.2 Experimental results

3. Spatially structured beams via intracavity second harmonic generation

3.1 Second-harmonic generation in a V-cavity VECSEL

3.2 Theoretical model and simulations

3.3 Experimental results

4. Conclusions

Funding

References and links

Cited By

Figures (9)

Equations (3)

Optics Express