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Intracavity spatial mode conversion by holographic phase masks

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Abstract

Past beam-shaping techniques, developed to transform a Gaussian beam into other waveforms, rely on a wide selection of available tools ranging from physical apertures, diffractive optical elements, phase masks, free-form optics to spatial light modulators. However, these devices – whether active or passive – do not address the underlying monochromatic nature of their embedded phase profiles, while being hampered by the complex, high-cost manufacturing process and a restrictive laser-induced damage threshold. Recently, a new type of passive phase devices for beam transformation – referred to as holographic phase masks (HPMs), was developed to address these critical shortcomings. In this work, we demonstrated the first integration of HPMs into a laser cavity for the generation of arbitrary spatial modes. Our approach allowed for different phase patterns to be embedded into the outputs of a laser system, while preserving the spatial structure of its intracavity beams. The optical system further possessed a unique ability to simultaneously emit distinct spatial modes into separate beampaths, owning to the multiplexing capability of HPMs. We also confirmed the achromatic nature of these HPMs in a wavelength-tunable cavity, contrary to other known passive or active beam-shaping tools. The achromatism of HPMs, coupled to their ability to withstand up to kW level of average power, makes possible future developments in high-power broadband sources, capable of generating light beams with arbitrary phase distribution covering any desirable spectral regions from near ultraviolet to near infrared.

© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement

1. Introduction

The growing adoption of lasers in manufacturing, medicine, and science has resulted in the demand for coherent sources producing optical beams with specialized waveforms, each possesses a set of distinct spatial properties. They include – but not limited to – diffraction-free beams (e.g., Airy [1], Bessel [2], or 1D light sheet [3]) capable of propagating unchanged over long distances, ideal for applications in telecommunication and sensing; or twisted vortex beams (e.g., Laguerre-Gaussian with or without orbital angular momentum [4]) featuring an intensity singularity on their spatial distributions, uniquely suited for trapping of minute particles, laser micro-machining, or biomedical imaging. In practice, due to the geometry of laser sources and their pumping schemes, the spatial profile of most coherent optical beams follows a Gaussian distribution. Such a beam is referred to as the Gaussian beam.

Various beam-shaping techniques were developed to transform a Gaussian beam into other waveforms, which can be accomplished via either amplitude or phase modulation, or a combination of both [5]. These methods rely on a wide selection of available tools ranging from physical apertures, diffractive optical elements, phase masks, free-form optics (e.g., digital micro-mirror devices) to spatial light modulators (SLMs). However, these beam-shaping tools – whether active or passive – do not address the underlying monochromatic nature of their embedded phase profiles, while being hampered by the complex, high-cost manufacturing process and a restrictive laser-induced damage threshold. Recently, a new type of passive phase devices for beam transformation, hereinafter referred to as holographic phase masks (HPMs), was developed to address these critical shortcomings [6,7].

The HPM element is produced by embedding the desired phase information onto a transmissive volume Bragg grating (TBG), and holographically recorded into a thick medium of photo-thermo-refractive (PTR) glass [8]. Current PTR-glass technology allows up to 1000 ppm of refractive-index change that could not be bleached by laser radiation, while possesses minimal absorption and scattering from 300 (near ultraviolet, NUV) to 2000 nm (near infrared, NIR) [9]. These specific properties of PTR glass enable the fabrication of HPMs with near-unity diffraction efficiency, and an extended degree of tolerance to high average- or peak-power laser beams, mechanical shocks, and elevated temperatures. These HPMs can reconstruct the encoded phase profiles over a broad range of wavelengths that meet the Bragg condition of the TBG. Only the diffracted beam incurs the embedded phase distribution, while uncoupled light in the transmitted beam observes minimal to no phase modulation. By designing the TBG with a broad acceptance bandwidth, a complete phase reconstruction can be achieved for all operating frequencies fallen within the allowed spectrum [7,10].

The unique attributes of HPMs encoded in PTR glass further position these elements for applications that require prolonged exposure to elevated laser radiation, such as an optical cavity. In the present work, we shall demonstrate the usage of holographic phase masks as intracavity mode-converting output-couplers in a continuous wave, wavelength-tunable linear cavity. Although the approach to partial mode conversion via intracavity output coupling is not a new concept in itself, the utilization of HPMs for the same purpose presents a novel alternative to other beam-shaping tools employed in prior works [1113]. Furthermore, the achromatic nature of these HPMs makes possible the emission of non-Gaussian, complex transverse modes over an extended spectral range. Such work can be further adapted to broadband, pulsed optical sources, or monochromatic, spectrally tunable lasers spanning any desirable spectral regions from NUV to NIR.

2. Experimental results

2.1 Construction of an HPM

The HPM is a TBG in which a phase profile of interest is inscribed [6]. The holographic-recording setup for a typical HPM follows a standard Mach-Zehnder interferometer, as illustrated in Fig. 1. A volume of PTR glass is exposed to the standing-wave pattern produced by interfering the signal and reference UV beams of the interferometer. Once the TBG’s Bragg period is determined, the half-angle separation $\theta _\textrm {rec}$ between two interfering beams is adjusted to produce a periodic pattern with matching modulation period. Upon further thermal development, a permanent change in local refractive-index is induced, forming the volume Bragg grating [14]. To construct an HPM, either a master phase-plate or SLM, encoding the desired phase distribution, is inserted into one of the interferometric arms (Fig. 1(I)) [15]. The phase element’s spatial profile incurred by the signal beam is transferred to the photosensitive recording medium, superimposing onto the plane phase-front of a periodic pattern originated from the interference between the signal and reference beams (Fig. 1(II)).

 figure: Fig. 1.

Fig. 1. Interferometric setup for the holographic construction of an HPM. The red dot-dashed lines denote different positions at which the following transverse phase profiles are quantified: I. the master phase-plate’s phase distribution, and II. standing-wave interference pattern produced by the signal and reference beams. NBS: non-polarizing beamsplitter, M: flat mirror, PM: phase-only mask, and PTR: photo-thermo-refractive glass sample.

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2.2 HPMs as diffractive optical elements

Using the interferometric setup presented in Fig. 1, HPMs with any desirable phase distributions can be constructed. For demonstration purposes, a TBG carrying the phase information of a 1st-order optical vortex ($l$ = +$1$) was fabricated and tested, wherein the spin structure of a diffracted vortex can help reveal the complex operation of an HPM. Another Mach-Zehnder interferometer, outlined in Fig. 2, was built to analyze the recorded HPM’s phase profile. Here, each diffracted beam of the HPM was allowed to interfere with a diverging reference Gaussian beam in the far field, yielding either a clockwise or anti-clockwise, single-null spiral. Each optical vortex is identified by a number, the topological charge $l$, which corresponds to the number of twists the electric field performs in one wavelength [4]. When co-propagating along another beam with a spherical wavefront, the positive-charge vortex, $l$ = +$1$, results in a clockwise-spiral interference pattern. This pattern reverses its spin for the negative-charge vortex, $l$ = -$1$.

 figure: Fig. 2.

Fig. 2. A Mach-Zehnder interferometer used to test the recorded HPMs. EX: beam expander, NBS: non-polarizing beamsplitter, M: flat mirror, HPM: holographic phase mask, BD: beam dump, L: convex lens, FL: Fourier lens, and CCD: digital camera.

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High-efficiency volume Bragg gratings couple most of the incident radiation into a single diffracted order. Depending on the mutual orientation between the grating and its input beam, there exist two orders of diffraction that can be independently accessed [16]. Illustrations of these orders for an incident beam launched to the grating’s front facet are shown in Fig. 3(a) and 3(b). Here, Fig. 3(a) a negative-order diffracted beam along the forward propagation axis (+$z$) is observed when its wavevector kd is rotated counter-clockwise relative to the grating vector K, yielding a negative angle of diffraction (-$\theta _\textrm {diff}$). On the other hand, Fig. 3(b) a positive-order diffracted beam along the forward propagation axis is realized when its wavevector kd is rotated clockwise with respect to the grating vector K, resulting in a positive angle of diffraction (+$\theta _\textrm {diff}$). The same pair of diffraction orders is expected for the input beam entering the opposing grating-facet. As an example, a positive-order diffracted beam along the backward propagation axis (-$z$), defined by the positive angle of diffraction (+$\theta _\textrm {diff}$), is illustrated in Fig. 3(c).

 figure: Fig. 3.

Fig. 3. HPM’s orders of diffraction: a. forward, negative order; b. forward, positive order; and c. backward, positive order. K – grating vector; kinc, kt, kd – wavevectors of the incident, transmitted, and diffracted beams; $\theta _\textrm {inc}$, $\theta _\textrm {diff}$ – Bragg angles of the incident and diffracted beams; and $\pm$z – forward and backward propagation directions.

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To understand the working principles of a holographic phase mask inscribed in a TBG, the vortex HPM was inserted into the interferometer presented in Fig. 2 for further analysis. Spiral phase structures of the positive- and negative-charge vortices are plotted in Fig. 4(a). Note that only phase information of the 1st-order, positive-charge vortex, as highlighted by the red frame in Fig. 4(a), was encoded into the HPM. Far-field interference profiles corresponding to each generated vortex are simulated in Fig. 4(b) for reference purposes. First, the interferometer’s signal beam is allowed to enter one of the two grating-facets. Angular tuning of the HPM in the plane of diffraction allows either the negative or positive diffraction order ($m$) of the underlying grating to be realized (Fig. 3(a) and 3(b) respectively). Each diffracted signal beam, upon recombination with the diverging reference, produces an interference pattern, whose intensity profile is presented in the first two-column of Fig. 4(c). The positive-order diffracted beam incurs the phase distribution of a positive-charge vortex, characterized by the clockwise, single-null spiral observed in the interference pattern. Switching to the other order of diffraction results in the optical vortex with opposite charge. The experiment, repeated with the signal beam launched to the opposing grating-facet (Fig. 3(c)), yields similar outcomes, as demonstrated by the far-field interference profiles shown in the last two-column of Fig. 4(c).

 figure: Fig. 4.

Fig. 4. Generation of 1st-order optical vortices by an HPM, whose inscribed phase structure is highlighted in the red frame. a. Theoretical phase distributions with a continuous phase transition from 0 to 2$\pi$, corresponding to the negative-charge (top), and positive-charge (bottom) vortices. b. Theoretical interference profiles in the far field between each vortex of opposing charges and a diverging Gaussian beam. c. Experimental interference profiles, obtained when the HPM is under either forward or backward illumination, for the negative ($m$ = -$1$) and positive ($m$ = +$1$) orders of diffraction.

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As presented in Fig. 4, diffracted beams of opposite orders ($m$ = -$1$ and +$1$) are phase-conjugated to each other, evident from the two interference patterns with counter-rotating spins. More precisely, the negative-order diffracted beam incurs a mirrored copy of the original phase distribution encoded in the HPM, correlating to a negative-charge, 1st-order optical vortex. Similar results are observed for other cases, in which the grating was illuminated from the back facet. Hence, the following statement can be inferred: an HPM pertains two mirrored copies of its phase information, which can be accessed depending upon the selected order of diffraction, irrespective of the readout grating-facet. These features of HPMs are important for further understanding of their behaviors in the presence of two counter-propagating beams inside a laser resonator.

2.3 HPMs as intracavity mode-converting output-couplers

HPMs encoded in PTR glass are uniquely suited for applications that demand extended exposure to elevated laser radiation, such as an optical cavity. To illustrate the concept, a linear resonator was constructed following the schematic in Fig. 5(a), using the HPM element as an intracavity mode-converting output-coupler. In this setup, the gain medium is optically pumped by a fiber-coupled, continuous wave, 981-nm laser diode, producing up to 40 W of average power. A pair of aspheric lenses, arranged in a 4$f$ configuration, is used to image the diode output into a spot size of approximately 250 µm at the gain element. A dichroic mirror, optimized for the transmission of the pump beam at 0-degree incident angle, is placed between the pump optics and the gain volume, functioning as an end-mirror in the cavity. The birefringent, single crystal Yb3+:KYW (ytterbium-doped potassium yttrium tungstate) with 2 at.% dopant concentration was chosen as the active gain medium. The fluorescence spectrum of such material possesses a broad bandwidth [17], providing spectral tunability for the proposed optical system. The selected crystal is cut along its Np axis to a thickness of 3 mm. A spherical lens ($f$ = $100$ mm) was inserted approximately one focal-length away from the gain element’s end-facet, followed by a high-reflecting mirror positioned the same distance apart. This geometry results in an unfolded confocal cavity, emitting close to a single transverse-mode Gaussian beam. Note that although the gain medium is birefringent, HPMs, nonetheless, are polarization insensitive.

 figure: Fig. 5.

Fig. 5. HPM as the intracavity mode-converting output-coupler. a. Layout of the laser cavity. DM: dichroic mirror, CX: gain crystal, f: lens, HPM: holographic phase mask, M: flat mirror, and $\pm$z: forward and backward propagation axis. b. Schematic diagram for the transformation of intracavity beams at the HPM along the forward and backward propagation axis. K – grating vector; kinc, kt, kd – wavevectors of the incident, transmitted, and diffracted beams; and $\theta _\textrm {inc}$, $\theta _\textrm {diff}$ – Bragg angles of the incident and diffracted beams.

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By design, the HPM is intended as an output-coupling device, whose coupling strength can be adjusted via the diffraction efficiency of the underlying TBG to maximize for the system’s output power. As a proof of concept, an HPM element with 10% diffraction efficiency was recorded and placed into the cavity outlined in Fig. 5(a). The device was then angularly tuned to the Bragg angle, at which two concurrent diffracted outputs could be observed. Detailed descriptions of the interaction between the HPM and two intracavity counter-propagating beams are depicted in Fig. 5(b). Here, a fraction of the intracavity radiation propagating along the denoted positive +$z$ axis is diffracted by the HPM, yielding the first output beam that emerges from the element’s back facet. This diffracted output beam kd(+) shall incur the HPM’s embedded phase structure. The transmitted component kt, unperturbed by the HPM, continues downstream towards the high-reflecting end-mirror, where it is returned for a second pass through the diffractive element. Simultaneously, a second diffracted beam, originating from the intracavity radiation traveling along the negative -$z$ axis, is observed on the HPM’s opposing facet. Consequently, there are two diffracted outputs for each cavity roundtrip, resulting in a total output-coupling ratio of 19% for an HPM with 10% diffraction efficiency. In addition, HPMs fabricated in this work were not anti-reflection coated, incurring parasitic losses of up to 4% per pass due to Fresnel reflections at the two opposing facets of each element. As a result, the average power collected at each diffracted output was limited to 200 mW at 5 W of absorbed pump power. These output beams incur identical phase information encoded by the HPM, leading to the same spatial mode in the far field. On the contrary, since the intracavity beams transmitted through the HPM experience no phase perturbation, the intracavity mode remains unaltered. Note that the phase information incurred by each output beam can be transformed into a mirrored copy by selecting the opposing order of diffraction, via the HPM’s angular tuning illustrated in Fig. 3(a) and 3(b). In the case of a vortex HPM, mirrored vortices produced by such laser shall possess a topological charge with opposite sign, evident from the experimental results demonstrated in Fig. 4.

To compare the intracavity and output modes produced by the proposed laser, the optical cavity depicted in Fig. 5(a) was incorporated into a Mach-Zehnder interferometer, following the schematic in Fig. 6. In the modified cavity, the high-reflecting end-mirror is replaced by a partial-reflecting one, which allows a fraction of intracavity radiation to leak out forming an additional output beam. This transmitted beam, which carries the intracavity spatial mode, constitutes the interferometer’s reference arm. On the other hand, one of the diffracted outputs enabled by the HPM would serve as the signal beam to be further analyzed. The reference and signal beams are expanded and subsequently recombined by a non-polarizing beamsplitter, completing the interferometer. A Fourier lens ($f$ = $250$ mm), placed at one of the beamsplitter’s output ports, produces at focus the far-field interference pattern, whose intensity profile is captured by a digital camera. To improve the quality of acquired data, a pinhole could be inserted into each beam expander for spatial-mode filtering.

 figure: Fig. 6.

Fig. 6. Incorporation of the laser cavity in Fig. 5 into a Mach-Zehnder interferometer, for comparison between spatial modes of the diffracted output and intracavity beams. DM: dichroic mirror, CX: gain crystal, HPM: holographic phase mask, PM: partial-reflecting mirror, EX: beam expander, NBS: non-polarizing beamsplitter, M: flat mirror, BD: beam dump, FL: Fourier lens, and CCD: digital camera. I. HPM’s phase structure. II. Far-field spatial distribution of the diffracted beam. III. Intensity profiles bisecting the top and bottom lobes of the far-field interference pattern (inset) produced by combining the signal and reference beams.

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A binary HPM, vertically sectioned into two regions with $0$ and $\pi$ phase shifts (Fig. 6(I)), was fabricated and placed into the cavity. The recorded far-field spatial distribution of a diffracted output beam, shown in Fig. 6(II), corresponds to the TEM01 mode. The diffracted beam, which forms the interferometer’s signal arm, is allowed to interfere with the reference beam transmitted through the cavity’s partial-reflecting end-mirror. Detailed structures of the far-field interference pattern produced by the signal and reference beams are presented in Fig. 6(III). The interference profile, displayed in the inset, features two vertically separated spatial lobes, correlating to those of the generated TEM01 mode. Intensity lineouts bisecting the top and bottom lobes are plotted as the red and green curves respectively. The presence of interference fringes on both intensity data reveals a coherent relationship between the diffracted output and intracavity beams. As highlighted by the dot-dashed vertical line, interference peaks in one plot correspond to troughs in the other, further indicating a $\pi$ phase-shift between two spatial lobes of the diffracted beam. The experimental data, thus, provides the evidence that matches the output beam’s phase distribution to that of the binary HPM.

To demonstrate the practicality of our approach, HPMs with more complex phase patterns – presented in column a to d of Fig. 7 – were selected and sorted according to I. the spatial variations of their phase structures: (1) those with radial symmetry, such as the phase profiles of 2nd- and 4th-order optical vortices; and (2) those with a radial component, namely the phase distributions of an axicon and an Airy beam. These elements were recorded and used as an output-coupling device in the linear cavity described in Fig. 5(a). II. Far-field spatial structures of an output beam diffracted by the HPMs were simulated and used as reference to III. the corresponding measured profiles. Unlike the binary phase-shifted HPMs featuring along their spatial structures one to multiple $\pi$ discontinuities, these elements are characterized by a continuous phase incursion from $0$ to $2\pi$, adding a new layer of complexity to the embedded phase information. Nonetheless, the flexibility of holographic technique allows such phase information to be inscribed into HPMs in a single-step process. The integrity of these complex phase structures is mainly dependent on that of the master phase-masks used for holographic recording. These masks, designed for the UV recording wavelength, are typically produced via optical lithography, wherein a specific master phase-mask is required for each desired phase pattern. Recently, a new approach to HPM recording was developed, in which these masks were replaced by an SLM for an all-optical, digital-holography recording setup [15]. Such dynamic device enables on-demand switching between different phase patterns, further simplifying the HPM’s writing procedure.

 figure: Fig. 7.

Fig. 7. Rows: I. Encoded phase structure of each HPM inserted into the laser cavity in Fig. 5. II. Theoretical far-field spatial distributions of the encoded phase structures. III. Experimental far-field spatial distributions of an output beam diffracted by the HPMs. Columns: Phase information of a. the 2nd-order optical vortex, b. the 4th-order optical vortex, c. the axicon with an apex angle of 179 degrees, and d. the Airy beam.

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In practice, individual HPMs featured in Fig. 7 were mounted on an X-Y stage, allowing their spatial structures to be centered on the transverse profile of intracavity beams. For HPMs with radially symmetric phase patterns such as those shown in column a and b of Fig. 7, the optical quality of generated spatial modes is dependent on the lateral position at which intracavity beams intersect the elements. Far-field spatial modes of the output beam diffracted by the vortex HPMs are in good agreement with their corresponding simulated profiles. On the other hand, HPMs with radially dependent phase structures, similar to those presented in column c and d of Fig. 7, place a further requirement on the intracavity beamsize at the elements. Figure 7(c.) A Bessel beam carrying the phase structure of an axicon, obtained at one diffracted output of the HPM, is allowed to incident onto a Fourier lens, resulting in the far-field structure of a ‘perfect’ vortex that matches its respective theoretical profile [18]. On the contrary, Fig. 7(d.) the far-field pattern of an Airy beam, measured at one of the HPM’s diffracted outputs, features only the main intensity-lobe while lacking the decaying tails – spatial characteristics unique to an Airy profile as observed in the simulated data. Note that the intracavity beamsize was kept constant in both cases of Fig. 7(c) and 7(d). In the case of the Airy HPM, the outcome implies a mismatch in size between the intracavity beam-diameter at the element and its phase structure. As a result, the dimensions of any embedded phase structures lacking the radial symmetry should be designed to match the intracavity beamsize at which the HPM shall be used.

HPMs are passive devices – that is, the phase profile encoded in each element is permanently fixed, in contrast to active electro-optical devices such as SLMs. A form of digital lasers, utilizing an SLM to enable all-optical, on-demand switching of intracavity spatial modes, was recently developed [19,20]. Unlike SLMs, each recorded HPM presented in Fig. 7 contains only the phase information of a single waveform that cannot be modified. However, the unique ability to embed multiple phase patterns into the same volume of PTR glass has been previously demonstrated [6]. While these HPMs are physically overlapped in space, their operations are optically independent, owning to the distinct Bragg condition each element possesses; that is, the HPM’s angles of incidence and diffraction are determined by the period and orientation of the underlying TBG. For instance, the multiplexing of several HPMs into a single device, each having a unique Bragg angle, enables the switching capability between different phase patterns through angular tuning, as illustrated in Fig. 8(a). Alternatively, the simultaneous generation of multiple diffracted beams, each carries a distinct phase structure, can be achieved by fabricating a multiplexed device whose embedded HPMs share the same angle of incidence (Fig. 8(b)).

 figure: Fig. 8.

Fig. 8. Alternative operating schemes of a multiplexed HPM. a. Each embedded HPM possesses a distinct set of incident and diffraction angles. b. Individual HPMs in the multiplexed device share a common angle of incidence, while diffract into separate beampaths. $I_i$: incident beams, $T_i$: transmitted beams, and $D_i$: diffracted beams.

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Two TBGs, designed for a common incident angle but allowed for diffraction into distinct paths, were embedded into the same volume of PTR glass to form a multiplexed HPM. These TBGs were further inscribed with the phase profiles of a two- and four-quadrant, $\pi$ phase-shifted masks. The multiplexed device, intended as an intracavity output-coupler, was placed into the laser system outlined in Fig. 9(a). Two forward-diffracted outputs, originating from the intracavity beam propagating along the +$z$ axis, were simultaneously produced into different directions, as denoted by the red and blue arrows. Both diffracted beams, each incurs a unique phase distribution, yield the desired TEM01 and TEM11 spatial modes in the far field (Fig. 9(b)). Similar results were obtained for the backward-diffracted output beams, generated from the intracavity radiation traveling along the -$z$ axis. Contrary to other known passive or active beam-shaping devices, such a multiplexed HPM provides the host cavity a unique capability for the simultaneous emission of distinct spatial modes into separate paths. Furthermore, the application of HPMs recorded in PTR glass for the spatial-mode conversion of kW-level laser beams has been demonstrated in our recent work [15], far exceeding the laser-induced damage threshold of a typical SLM.

 figure: Fig. 9.

Fig. 9. Simultaneous generation of different spatial modes by a multiplexed HPM used as an intracavity output-coupler. a. Optical scheme of the multichannel laser. DM: dichroic mirror, CX: gain crystal, f: lens, MHPM: multiplexed holographic phase mask, M: flat mirror, and $\pm$z: forward and backward propagation axis. b. Phase structures of individual HPMs in the multiplexed device and their corresponding far-field spatial distributions.

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TBGs recorded in PTR glass have been shown to possess a spectral bandwidth up to several tens of nanometers [16]. The spectroscopic properties of an HPM are similar to those of the host TBG [6,15]. To illustrate this concept, an HPM encoding the phase structure of a 2nd-order optical vortex was placed into a laser cavity, following the configuration in Fig. 10(a). A custom diffractive element, containing two adjacent reflective Bragg gratings fabricated into the same volume of PTR glass, was utilized as a high reflecting, spectrally selective end-mirror for the cavity. These gratings were designed for the Bragg wavelengths at 1033.6 and 1038.6 nm with near-unity diffraction efficiency. Emission wavelengths of the cavity, along with the HPM’s simulated diffraction spectrum, are presented in Fig. 10(b). The HPM’s spectrum features a maximum diffraction efficiency of 10% at 1035 nm, exhibiting a spectral width around 6 nm (FWHM). The cavity’s emission wavelengths, denoted by the red and blue curves, are independently obtained by the lateral displacement of the two-section Bragg mirror. Note that both generated wavelengths are within the spectral selectivity of the HPM.

 figure: Fig. 10.

Fig. 10. HPM as the intracavity mode-converting output-coupler in a wavelength-tunable laser. a. Optical layout of the laser. DM: dichroic mirror, CX: gain crystal, f: lens, HPM: holographic phase mask and its phase profile, and MRBG: multiwavelength RBG. b. Measured emission wavelengths (red and blue curves) and their corresponding far-field spatial structures, along with the HPM’s simulated diffraction spectrum (dotted orange plot).

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The HPM, once angularly set to the respective Bragg angle, requires no further inputs during operation. Far-field spatial distributions of the transformed cavity mode at both spectral lines, projected by the Fourier lens onto a digital camera, are shown in Fig. 10(b). According to the captured data, the intended 2nd-order optical vortex was obtained for each diffracted beam output-coupled from the cavity, independent of the operating wavelength. Such capability is unique to HPMs – contrary to the monochromatic behavior of conventional beam-shaping tools, in which access to the encoded phase information is inherently restricted to the designed wavelength [5]. The host TBG of an HPM, thus, sets the spectral width to which spatial mode conversion can be attained, allowing the HPM to afford an extended degree of achromatism. In practice, a transversely chirped volume Bragg grating, whose period varies along the direction orthogonal to the intracavity beam-axis, is recommended to provide a continuous spectral tunability for the proposed optical system [21].

3. Conclusion

A holographic phase mask (HPM) recorded in photo-thermo-refractive (PTR) glass provides a unique and robust solution to encode the phase information of any desirable spatial distributions into a laser beam. We have demonstrated, in this paper, the first work on the integration of HPMs into a laser cavity for the generation of complex spatial modes. This approach allows for different phase patterns to be embedded into the outputs of a laser system, while preserving the spatial structure of its intracavity beams. The proposed optical system further possesses a unique ability to simultaneously emit distinct spatial modes into separate beampaths, owning to the multiplexing capability of HPMs in PTR glass. Contrary to other known passive or active beam-shaping tools, the achromatic nature of these HPMs – with up to several tens of nanometers in achievable bandwidth, coupled to their ability to withstand up to kW level of average power, makes possible future developments in high-power broadband sources, capable of generating light beams with arbitrary phase distribution covering any desirable spectral regions from near ultraviolet to near infrared.

Funding

IPG Photonics Inc.

Acknowledgments

The authors would like to thank Dr. Aleksandr Mingareev and Dr. Pavel Shirshnev for the development of high-quality PTR glass samples used in this work.

Disclosures

The authors declare no conflicts of interest.

Data Availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

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Data Availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

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Figures (10)

Fig. 1.
Fig. 1. Interferometric setup for the holographic construction of an HPM. The red dot-dashed lines denote different positions at which the following transverse phase profiles are quantified: I. the master phase-plate’s phase distribution, and II. standing-wave interference pattern produced by the signal and reference beams. NBS: non-polarizing beamsplitter, M: flat mirror, PM: phase-only mask, and PTR: photo-thermo-refractive glass sample.
Fig. 2.
Fig. 2. A Mach-Zehnder interferometer used to test the recorded HPMs. EX: beam expander, NBS: non-polarizing beamsplitter, M: flat mirror, HPM: holographic phase mask, BD: beam dump, L: convex lens, FL: Fourier lens, and CCD: digital camera.
Fig. 3.
Fig. 3. HPM’s orders of diffraction: a. forward, negative order; b. forward, positive order; and c. backward, positive order. K – grating vector; kinc, kt, kd – wavevectors of the incident, transmitted, and diffracted beams; $\theta _\textrm {inc}$, $\theta _\textrm {diff}$ – Bragg angles of the incident and diffracted beams; and $\pm$z – forward and backward propagation directions.
Fig. 4.
Fig. 4. Generation of 1st-order optical vortices by an HPM, whose inscribed phase structure is highlighted in the red frame. a. Theoretical phase distributions with a continuous phase transition from 0 to 2$\pi$, corresponding to the negative-charge (top), and positive-charge (bottom) vortices. b. Theoretical interference profiles in the far field between each vortex of opposing charges and a diverging Gaussian beam. c. Experimental interference profiles, obtained when the HPM is under either forward or backward illumination, for the negative ($m$ = -$1$) and positive ($m$ = +$1$) orders of diffraction.
Fig. 5.
Fig. 5. HPM as the intracavity mode-converting output-coupler. a. Layout of the laser cavity. DM: dichroic mirror, CX: gain crystal, f: lens, HPM: holographic phase mask, M: flat mirror, and $\pm$z: forward and backward propagation axis. b. Schematic diagram for the transformation of intracavity beams at the HPM along the forward and backward propagation axis. K – grating vector; kinc, kt, kd – wavevectors of the incident, transmitted, and diffracted beams; and $\theta _\textrm {inc}$, $\theta _\textrm {diff}$ – Bragg angles of the incident and diffracted beams.
Fig. 6.
Fig. 6. Incorporation of the laser cavity in Fig. 5 into a Mach-Zehnder interferometer, for comparison between spatial modes of the diffracted output and intracavity beams. DM: dichroic mirror, CX: gain crystal, HPM: holographic phase mask, PM: partial-reflecting mirror, EX: beam expander, NBS: non-polarizing beamsplitter, M: flat mirror, BD: beam dump, FL: Fourier lens, and CCD: digital camera. I. HPM’s phase structure. II. Far-field spatial distribution of the diffracted beam. III. Intensity profiles bisecting the top and bottom lobes of the far-field interference pattern (inset) produced by combining the signal and reference beams.
Fig. 7.
Fig. 7. Rows: I. Encoded phase structure of each HPM inserted into the laser cavity in Fig. 5. II. Theoretical far-field spatial distributions of the encoded phase structures. III. Experimental far-field spatial distributions of an output beam diffracted by the HPMs. Columns: Phase information of a. the 2nd-order optical vortex, b. the 4th-order optical vortex, c. the axicon with an apex angle of 179 degrees, and d. the Airy beam.
Fig. 8.
Fig. 8. Alternative operating schemes of a multiplexed HPM. a. Each embedded HPM possesses a distinct set of incident and diffraction angles. b. Individual HPMs in the multiplexed device share a common angle of incidence, while diffract into separate beampaths. $I_i$: incident beams, $T_i$: transmitted beams, and $D_i$: diffracted beams.
Fig. 9.
Fig. 9. Simultaneous generation of different spatial modes by a multiplexed HPM used as an intracavity output-coupler. a. Optical scheme of the multichannel laser. DM: dichroic mirror, CX: gain crystal, f: lens, MHPM: multiplexed holographic phase mask, M: flat mirror, and $\pm$z: forward and backward propagation axis. b. Phase structures of individual HPMs in the multiplexed device and their corresponding far-field spatial distributions.
Fig. 10.
Fig. 10. HPM as the intracavity mode-converting output-coupler in a wavelength-tunable laser. a. Optical layout of the laser. DM: dichroic mirror, CX: gain crystal, f: lens, HPM: holographic phase mask and its phase profile, and MRBG: multiwavelength RBG. b. Measured emission wavelengths (red and blue curves) and their corresponding far-field spatial structures, along with the HPM’s simulated diffraction spectrum (dotted orange plot).
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