Naidoo, D., Ait-Ameur, K., Brunel, M. & Forbes, A. Intra-cavity generation of superpositions of Laguerre-Gaussian beams. Appl. Phys. B 106, 683–690 (2012).

Describelaser modes

The focal length of a lens deter­mines its mag­ni­fy­ing pow­er, which is the appar­ent size of your sub­ject as pro­ject­ed onto the focal plane where your image sen­sor resides. A longer focal length cor­re­sponds to greater mag­ni­fy­ing pow­er and a larg­er ren­di­tion of your sub­ject, and vice ver­sa.

2019522 — Concave vs. Convex · Concave describes shapes that curve inward, like an hourglass. · Convex describes shapes that curve outward, like a ...

Our laser cavity, as shown in Fig. 1, consists of a conventional folded resonator configuration with an Nd:YAG laser crystal as the gain medium (see Methods section). What is unconventional is the use of a phase-only reflective SLM as the back optical element of the cavity. The SLM is used to display computer-generated holograms, sometimes called digital holograms, encoded as pixelated grey-scale images. The SLM is calibrated such that a full phase cycle from 0 through 2π is represented graphically by grey-scale colours ranging from white through black, in 256 levels (8-bit encoding). For example, a linear ramp in colour from white to black would represent a linear ramp in phase from 0 to 2π, otherwise known as a diffraction grating. In a similar way, virtually any desired phase may be encoded using the SLM. One can consider the colour change on the SLM as equivalent to the depth change in a standard diffractive optical element, and herein lies the advantage: it is easy to change colours in images but rather time consuming to refabricate depth changes in diffractive optical elements. As the device acts as our back mirror and displays a digital hologram to change the phase of the reflected light, we will refer to it as a digitally addressed holographic mirror (or holographic mirror for short). The key properties required of the SLM for this application are high resolution, high efficiency, high reflectivity at the desired polarization, small phase–amplitude crosstalk, reasonable damage threshold and a large phase shift at the laser wavelength.

Laser modeswikipedia

Dudley, A., Vasilyeu, R., Belyi, V., Khilo, N., Ropot, P. & Forbes, A. Controlling the evolution of nondiffracting speckle by complex amplitude modulation on a phase-only spatial light modulator. Opt. Commun. 285, 5–12 (2012).

We also point out that all of the techniques we used in designing the holograms for mode selection are standard and well known, that is, no new tools are needed to implement the digital laser approach. We have illustrated this point by creating modes traditionally generated by phase-only diffractive optical elements (for example, Airy beam), amplitude-only filters (for example, Hermite–Gaussian beams) and combinations of the two (high-order Laguerre–Gaussian beams). Importantly, all the modes that we have shown here required only a change to a picture—no new optics and no additional alignment of the laser cavity. It is the simplicity of our approach that makes it so powerful: we offer a direct and easy means to mode control, suitable with standard tools, without any special optics and only a commercial SLM, which we can assume many researchers are familiar with and have access to. This makes our approach accessible to all.

Thus, although our SLM is calibrated for a phase-only response from 0 (black) to 2π (white), appropriate holograms can result in amplitude variations from 0 to 1. An example of a high-loss annular ring is shown in Fig. 3c, with the zoomed-in checkerboard shown in Fig. 3b.

There are two types of wide-angle lens­es, rec­ti­lin­ear and fish­eye (some­times termed curvi­lin­ear). The vast major­i­ty of wide-angle lens—and oth­er focal lengths, too—are rec­ti­lin­ear. These types of lens­es are designed to ren­der the straight ele­ments found in a scene as straight lines on the pro­ject­ed image. Despite this, wide-angle rec­ti­lin­ear lens­es cause ren­dered objects to pro­gres­sive­ly stretch and enlarge as they approach the edges of the frame. In pho­tog­ra­phy, all fish­eye lens­es are ultra wide-angle lens­es that pro­duce images fea­tur­ing strong con­vex cur­va­ture. Fish­eye lens­es ren­der the straight ele­ments of a scene with a strong cur­va­ture about the cen­tre of the frame (the lens axis). The effect is sim­i­lar to look­ing through a door’s peep­hole, or the con­vex safe­ty mir­rors com­mon­ly placed at the blind cor­ners of indoor park­ing lots and hos­pi­tal cor­ri­dors. Only straight lines that inter­sect with the lens axis will be ren­dered as straight in images cap­tured by fish­eye lens­es.

In this article, we'll tell you everything you ever wanted to know about compressed air and then some. Here are the top 10 compressed air questions we've ...

In conclusion, we have demonstrated a novel digital laser that allows arbitrary intra-cavity laser beam shaping to be executed on the fly. This differs substantially from other intra-cavity laser beam-shaping approaches as only a grey-scale image needs change for the laser mode to be selected. We have shown that the digital laser can replicate conventional stable resonator cavities as well as ‘custom’ laser resonators to produce more exotic laser modes. The digital laser is at present limited in the power that it can output, but this may be overcome with careful engineering of bespoke liquid crystals. Just as SLMs external to the laser cavity have proved an excellent means for testing high-power beam-shaping elements before fabrication, and have in the process opened up many avenues for low-average-power applications of structured light (for example, holographic optical tweezers), the digital laser may well become an robust, easy-to-implement, test bed for intra-cavity beam-shaping ideas. Moreover, as the digital laser is rewritable it allows for dynamic intra-cavity beam shaping, as we have shown by ‘playing a video’ inside a laser for the first time. Applications of this would range from controlling thermal lensing and aberrations in real-time to real-time mode control and switching. Customized laser modes are now only a picture away.

In gen­er­al, a short focal length—or short focus, or “wide-angle”—lens is one whose angle of view is 65° or greater. Recall from above that angle of view is deter­mined by both focal length and image sen­sor size, which means that what qual­i­fies as “short” is pred­i­cat­ed upon a camera’s image sen­sor for­mat. There­fore, on full-frame cam­eras, the thresh­old for wide-angle lens­es is 35 mm or less, and on APS‑C cam­eras, it’s 23 mm or less. Lens­es with an angle of view of 85° or greater are called “ultra wide-angle,” which is about 24 mm or less on full-frame and 16mm or less on APS‑C cam­eras.

Jul 22, 2024 — Diffraction gratings separate incident light into different wavelengths by passing it through a narrow slit, which causes the light wave to ...

(a) Schematic of the complex plane showing two phase-only values, A and B, lies on the unit circle (unit amplitude). The average of these is vector C, representing amplitude modulation as it is not on the unit circle. (b) Example of a checkerboard pattern of the two phase values A and B. (c) Zoomed out image of b showing the complete annular ring created with this checkerboard pattern to result in zero transmission in the annular ring.

Cherezova, T. Y., Kaptsov, L. N. & Kudryashov, A. V. Cw industrial rod YAG:Nd3+ laser with an intracavity active bimorph mirror. Appl. Opt. 35, 2554–2561 (1996).

The selection of the Hermite–Gaussian and Laguerre–Gaussian modes (Fig. 4) exploited complex amplitude modulation to implement amplitude modulation on the phase-only SLM24,25,26. In other words, the SLM can be used to create customized apertures, for example, the fine wires (loss-lines) used in the past for Hermite–Gaussian mode selection2,3. The digital hologram for the creation of the radial Laguerre–Gaussian beam (p=1, l=0) comprised a high-loss annular aperture, together with a phase-only radius of curvature. In this case, the checkerboard consisted of the two phase values, 0 and π, for a resultant of zero amplitude inside an annular ring. This low-loss ring was positioned at the zero of the first radial Laguerre–Gaussian function to select the pure LG10 mode shown in Fig. 4. The radius of curvature was used to select and control the mode size, following equation (1). Many techniques exist for the design of intra-cavity diffractive optics5,6,7,8,9,10 for particular mode selection, all of which may readily be applied to the digital laser. We illustrate this in Fig. 4 where an Airy beam27 and flat-top beam7 are created by phase-only digital holograms.

S.N. and L.B. performed the experiments under the guidance of I.L. and A.F.; A.F. wrote the manuscript; all authors contributed to analysis of the data and editing of the final manuscript.

As a proof-of-principle experiment, we programmed the holographic mirror to mimic a conventional concave mirror with a radius of curvature, R, chosen to ensure that the resonator formed a stable plano-concave cavity (Fig. 2a). This requires a digital hologram of a lens to be programmed to the SLM, with focal length f=R, so that the hologram mimics the curvature of the mirror. The waist size (at the flat OC) of the Gaussian mode that oscillates in such a cavity may be described analytically as2:

Two Laguerre–Gaussian modes of opposite but equal azimuthal index, and of azimuthal order |l|=25, are combined coherently in the digital laser to produce this high-order superposition.

Sub­ject size is direct­ly pro­por­tion­al to the focal length of the lens. For exam­ple, if you pho­to­graph a soc­cer play­er kick­ing a ball, then switch to a lens that is twice the focal length of the first, the ren­dered size of every ele­ment in your image, from the per­son to the ball, will be dou­bled in size along the lin­ear dimen­sions.

In pho­tog­ra­phy, the term macro refers to extreme close-ups. Macro lens­es are nor­mal to long-focus lens­es capa­ble of focus­ing on extreme­ly close sub­jects, there­by ren­der­ing large repro­duc­tions. The mag­ni­fi­ca­tion ratio or mag­ni­fi­ca­tion fac­tor is the size of the sub­ject pro­ject­ed onto the image sen­sor in com­par­i­son to its actu­al size. A macro lens’ mag­ni­fi­ca­tion ratio is cal­cu­lat­ed at its clos­est focus­ing dis­tance. A true macro lens is capa­ble of achiev­ing a mag­ni­fi­ca­tion ratio of 1:1 or high­er. Lens­es with mag­ni­fi­ca­tion ratios from 2:1 to 10:1 are called super macro. Ratios over 10:1 cross over into the field of microscopy. When shop­ping for a macro lens, keep in mind that in the con­text of kit lens­es and point-and-shoot cam­eras, some man­u­fac­tur­ers use the macro moniker as mar­ket­ing short­hand for “close-up pho­tog­ra­phy.” These prod­ucts do not achieve 1:1 mag­ni­fi­ca­tion ratios. When in doubt, check the tech­ni­cal spec­i­fi­ca­tions.

The higher losses of the SLM do manifest themselves as a higher threshold for lasing, as noted in Fig. 2d. The losses are due to the overall diffraction efficiency of the device as well as the losses due to the fill factor. These two factors can reduce the apparent reflectivity of the SLM mirror by 15–20%.

Alltest Instruments, Inc. is a leading provider of used and refurbished benchtop test and measurement equipment at competitive prices.

How to cite this article: Ngcobo, S. et al. A digital laser for on-demand laser modes. Nat. Commun. 4:2289 doi: 10.1038/ncomms3289 (2013).

Ngcobo, S., Litvin, I., Burger, L. et al. A digital laser for on-demand laser modes. Nat Commun 4, 2289 (2013). https://doi.org/10.1038/ncomms3289

All the beam shapes shown here were possible because the holograms fell well within the resolution of the SLM. At 800 × 600 pixels of pitch 20 μm, the resolution is significantly higher than that of an adaptive mirror but substantially lower than that of a typical diffractive optical element. As the number of pixels decreases for each phase ramp of 0–2π, so does the diffraction efficiency, as well as the functionality of the hologram (for example, Moiré patterns will degrade the resulting beam). Nevertheless, for a wide range of typical beam shapes, the standard devices more than suffice; moreover, SLM resolution has tended to increase of late.

Bourderionnet, J., Brignon, A., Huignard, J.-P., Delboulbe, A. & Loiseaux, B. Spatial mode control of a diode-pumped Nd:YAG laser by an intracavity liquid-crystal light valve. Opt. Lett. 26, 1958–1960 (2001).

It’s impor­tant to rec­og­nize that the con­ve­nience and flex­i­bil­i­ty of zoom lens­es can inspire lazy pho­tog­ra­phy. The ease of chang­ing the angle of view encour­ages pho­tog­ra­phers to set­tle on com­po­si­tions that are good-enough, instead of seek­ing out bet­ter per­spec­tives and gain­ing a deep­er under­stand­ing of their sub­jects. What­ev­er lens you have, be it zoom or prime, it’s vital for the devel­op­ment of good pho­tog­ra­phy to con­sid­er your sub­ject from sev­er­al per­spec­tives by walk­ing towards, step­ping away, and cir­cling around them.

Leger, J. R., Chen, D. & Wang, Z. Diffractive optical element for mode shaping of a Nd:YAG laser. Opt. Lett. 19, 108–110 (1994).

A prime or fixed focal length lens has a set focal length that can­not be changed. There are sev­er­al crit­i­cal dif­fer­ences between prime and zoom lens­es that you should know. Prime lens­es are gen­er­al­ly small­er, faster, and have bet­ter opti­cal char­ac­ter­is­tics than zoom lens­es. Despite this, pho­tog­ra­phers fre­quent­ly opt to shoot with zoom lens­es because of their con­ve­nience: a sin­gle lens can replace sev­er­al of the most pop­u­lar focal length prime lens­es. This is espe­cial­ly impor­tant when you’d pre­fer to pack light, such as dur­ing a trip or a hike.

Arrizon, V., Ruiz, U., Carrada, R. & Gonzalez, L. A. Pixelated phase computer holograms for the accurate encoding of scalar complex fields. J. Opt. Soc. Am. A 24, 3500–3507 (2007).

Lubeigt, W., Valentine, G., Girkin, J., Bente, E. & Burns, D. Active transverse mode control and optimization of an all-solid-state laser using an intracavity adaptive-optic mirror. Opt. Express 10, 550–555 (2002).

As you have learned in the sec­tion on aper­tures and f‑numbers, “an increase in focal length decreas­es the inten­si­ty of light reach­ing the image sen­sor.” This rela­tion­ship is most obvi­ous in zoom lens­es. A “vari­able” aper­ture zoom lens is a lens whose max­i­mum aper­ture becomes small­er with increased focal length. These types of zoom lens­es are sim­ple to spot because they list a max­i­mum aper­ture range instead of a sin­gle num­ber. The range spec­i­fies the max­i­mum aper­ture for the short­est and longest focal lengths of the zoom range. Vari­able aper­ture lens­es are the most com­mon type of zoom lens. A con­stant aper­ture or “fixed” aper­ture zoom lens is one whose max­i­mum aper­ture remains con­stant across the entire zoom range. Fixed aper­ture lens­es are typ­i­cal­ly more mas­sive and more expen­sive than their vari­able aper­ture coun­ter­parts. They are also more straight­for­ward to work with when prac­tic­ing man­u­al expo­sure at the max­i­mum aper­ture since no com­pen­sa­tion for lost light is required dur­ing zoom­ing.

By complex amplitude modulation, a customized set of high-loss regions create a Hermite–Gaussian beam (n=3, m=0) and a superposition of Laguerre–Gaussian beams (p=0, l=±4) as the laser output. By phase-only modulation, a flat-top beam and Airy beam are created as the stable modes of the cavity. Combining amplitude and phase effects allows for the selection of a Laguerre–Gaussian beam (p=1, l=0) of a chosen size.

Laser modespdf

Dainty, J. C., Koryabin, A. V. & Kudryashov, A. V. Low-order adaptive deformable mirror. Appl. Opt. 37, 4663–4668 (1998).

Lens­es with an angle of view of 35° or nar­row­er are con­sid­ered long-focus lens­es. This trans­lates to a focal length of about 70 mm and greater on full-frame cam­eras, and about 45 mm and longer on APS‑C cam­eras. It’s com­mon for pho­tog­ra­phers to (incor­rect­ly) refer to long-focus lens­es as “tele­pho­to” lens­es. A true tele­pho­to lens is one whose indi­cat­ed focal length is longer than the phys­i­cal length of its body. Due to this ubiq­ui­tous mis­use of the word, there exists a fur­ther clas­si­fi­ca­tion of long-focus lens­es whose angle of view is 10° or nar­row­er called “super tele­pho­to” lens­es (equal to or greater than 250 mm on full-frame cam­eras and 165 mm on APS‑C cam­eras). For­tu­nate­ly, super tele­pho­to lens­es are more often than not actu­al tele­pho­to designs. A great exam­ple is the Canon EF 800 mm f/5.6L IS USM Lens, which is only 461 mm long.

A zoom lens allows pho­tog­ra­phers to vary its effec­tive focal length through a spec­i­fied range, which alters the angle of view and mag­ni­fi­ca­tion of the image. Zoom lens­es are described by stat­ing their focal length range from the short­est to longest, such as 24–70 mm and 70–200 mm. The focal length range of a zoom lens direct­ly cor­re­lates to its zoom ratio, which is derived by divid­ing the longest focal length by the short­est. Both of the lens­es above have a zoom ratio of approx­i­mate­ly 2.9x, or 2.9:1. The zoom ratio also describes the amount of sub­ject mag­ni­fi­ca­tion a sin­gle lens can achieve across its avail­able focal length range.

Leger, J. R., Chen, D. & Dai, K. High modal discrimination in a Nd:YAG laser resonator with internal phase gratings. Opt. Lett. 19, 1976–1978 (1994).

Pare, C., Gagnon, L. & Belanger, P. A. Aspherical laser resonators: an analogy with quantum mechanics. Phys. Rev. A 46, 4150–4160 (1992).

Finally, we note that the switching from one mode to another required nothing more than a change to the grey-scale image making up the digital hologram—no realignment and no additional optical elements were necessary. Traditionally, to create the spectrum of modes shown in Fig. 4 would require several laser resonator set-ups, each with a custom (expensive) optic. We exploit the versatility of the digital laser by operating the laser in ‘video’ mode: the fundamental mode of the laser was changed in real-time (at video fresh rates) by dynamically changing the digital hologram. The results are shown in Supplementary Movies 1 and 2, the first time this has ever been done in a laser and represent a shift in thinking about laser resonators.

The rela­tion­ship between the angle of view and a lens’s focal length is rough­ly inverse­ly pro­por­tion­al from 50mm and up on a full-frame cam­era. How­ev­er, as the focal length grows increas­ing­ly short­er than 50mm, that rough pro­por­tion­al­i­ty breaks down, and the rate of change in the angle of view slows. For exam­ple, the change in angle of view from 100mm to 50mm is more pro­nounced than the change from 28mm to 14mm.

Longitudinal mode

It’s impor­tant to under­stand that the degree to which the focal length mag­ni­fies an object does not depend on your cam­era or the size of its image sen­sor. Assum­ing a fixed sub­ject and sub­ject dis­tance, every lens of the same focal length will project an image of your sub­ject at the same scale. For exam­ple, if a 35 mm lens casts a 1.2 cm image of a per­son, that image will remain 1.2 cm high regard­less of your camera’s sen­sor for­mat. How­ev­er, on a Micro Four Thirds for­mat cam­era, the image of that per­son will fill the height of the frame, where­as it will occu­py half the height of a full-frame image sen­sor, and about one-third the height of a medi­um for­mat image sen­sor. As you progress from a small­er sen­sor to a larg­er one, the 1.2 cm high pro­jec­tion of the per­son remains unchanged, but it occu­pies a small­er part of the total frame. There­fore, although the absolute size of the image will stay con­stant across vary­ing image sen­sor for­mats, its size in pro­por­tion to each image sen­sor for­mat will be dif­fer­ent.

(a) Schematic of the stable plano-concave resonator with a waist plane at the flat OC. (b) Measured intensity profiles for two curvature cases (R=400 and 500 mm), comparing the digital laser output (SLM) with that of physical mirrors (Mirror). (c) The change in measured beam size with digitally imposed curvature matches the theoretical curve. (d) The threshold of the digital laser is higher than that of the conventional laser owing to the additional losses from the SLM shown here for the R=400 mm case. The black lines are fits to the data and error bars are s.d..

Mode-lockedlaser

Here we overcome the aforementioned limitations through the use of intra-cavity digital holograms, implemented on a phase-only reflective SLM, to form a rewritable holographic mirror in place of the standard laser cavity mirror, the digital laser. This allows an on-demand mode selection with high resolution and with a very wide dynamic range of phase values. This approach simplifies significantly the task of intra-cavity beam shaping, reduces the time to test concepts and only supposes the ability to create appropriate grey-scale images. To put this another way, creating custom modes is reduced to that of creating pictures of what you want, and the tools to do this are very well established (see, for example, the vast literature on shaping light with digital holograms). The advantage of our approach over that of others is that the abovementioned capability comes at minimal complexity: one only requires a commercial SLM and an otherwise standard laser cavity. Moreover, all the known tools for intra-cavity mode selection may be implemented in the digital laser. We demonstrate that the digital laser can mimic a conventional stable cavity and verify on-demand mode selection by dynamically changing the mirror hologram to output a variety of laser modes in real-time. We accomplish this feat by ‘playing a video’ inside a laser cavity, requiring a shift in our thinking of mode control in laser resonators.

Dec 10, 2015 — 0.8 mV is the resolution of the ADC, over its entire range. That is, the ADC can detect changes by 0.8 mV. This difference corresponds to ...

A true zoom lens, known as a par­fo­cal lens, main­tains a set focus dis­tance across its entire focal length range. In the days before dig­i­tal photography—before elec­tron­ic aut­o­fo­cus, even—it was com­mon prac­tice to focus a zoom lens at its longest focal length before tak­ing the pic­ture at the desired (if dif­fer­ent) focal length. This tech­nique is no longer pos­si­ble because con­tem­po­rary vari­able focal length lens­es designed for pho­tog­ra­phy are almost exclu­sive­ly var­i­fo­cal lens­es, which do not main­tain set focus across their zoom range. In prac­tice, most pho­tog­ra­phers do not know the dif­fer­ence because the aut­o­fo­cus algo­rithms in their cam­eras com­pen­sate for the slight vari­a­tions.

Arrizón, V. Optimum on-axis computer-generated hologram encoded into low-resolution phase-modulation devices. Opt. Lett 28, 2521–2523 (2003).

TE mode

Lubeigt, W. et al. Control of solid-state lasers using an intra-cavity MEMS micromirror. Opt. Express 19, 2456–2465 (2011).

Due to their abil­i­ty to mag­ni­fy dis­tance objects, long-focus lens­es present pho­tog­ra­phers with many uses. They are almost uni­ver­sal­ly laud­ed for por­trai­ture because their nar­row angle of view allows for a high­er mag­ni­fi­ca­tion of the sub­ject from con­ven­tion­al­ly more pleas­ing per­spec­tives. As a rule of thumb, a desir­able focal length for a por­trait lens starts at twice the nor­mal focal length for the cam­era sys­tem (about 85 mm for full-frame and 56 mm for APS‑C).

Bélanger, P. A., Lachance, R. L. & Pare, C. Super-Gaussian output from a CO2 laser by using a graded-phase mirror resonator. Opt. Lett. 17, 739–741 (1992).

Caley, A. J., Thomson, M. J., Liu, J., Waddie, A. J. & Taghizadeh, M. R. Diffractive optical elements for high gain lasers with arbitrary output beam profiles. Opt. Express 15, 10699–10704 (2007).

Several SLMs were used in the testing of the digital laser, and finally a Hamamatsu (LCOS-SLM X110468E) series device was selected for the digital laser. Previous tests with other SLMs failed mainly because of the phase–amplitude coupling that becomes pronounced during intra-cavity operation. The gain medium was a 1% doped Nd:YAG crystal rod with dimension of 30 mm (length) by 4 mm (diameter). The crystal was end-pumped with a 75-W Jenoptik (JOLD 75 CPXF 2P W) multimode fibre-coupled laser diode operating at 808 nm. The OC (flat curvature) had a reflectivity of 60%, whereas the SLM had a measured reflectivity of 91% at the desired polarization (vertical) and 93% at the undesired polarization (horizontal). To force the cavity to lase on the vertical polarization, an intra-cavity Brewster plate was used. On this polarization, calibration tests on the SLM reveal typical efficiencies of ~86% into the first order and ~1% into the zeroth order. In the intra-cavity configuration, this large difference results in suppression of the zeroth order because of the significantly higher round trip losses, and thus the SLM could be operated at normal incidence and without a grating. The SLM efficiency had a s.d. of ~0.4% across all grey levels, that is, minimal amplitude effects during phase modulation. The nominal length of the cavity was ~390 mm but was determined to have an effective length of 373 mm to compensate for the small thermal lensing due to pump absorption in the crystal as well as the refractive index of the crystal. The effective length was used in all calculations for the mode sizes. The resonator output was 1:1 imaged onto a Spiricon CCD camera for intensity measurements, and could also be directed to a second SLM for modal decomposition studies. For far-field tests, the first lens of the telescope was removed.

where L is the effective length of the resonator and λ is the laser wavelength. Before testing the digital laser, two physical concave mirrors were used (separately) in the same set-up in place of the SLM, and the Gaussian beam size was recorded at the output. The results for these two cases, R=400 and 500 mm, are shown in Fig. 2b and plotted in Fig. 2c together with the theoretical curve, following equation (1). The same test curvature examples were programmed digitally and are shown alongside the physical mirror measurements in Fig. 2b. From a mode selection perspective, the laser performs identically in the two configurations. Next, as the digital hologram’s programmed curvature was changed (Fig. 2c) the measured output Gaussian beam size changed in accordance with equation (1). This confirms that the digital laser behaves as a standard stable cavity and it is clear from the results that the SLM mimics the stable cavity with high fidelity. In addition to confirming the desired behaviour of the digital laser, this experiment also brings to the fore another practical advantage: whereas with physical mirrors it is commonplace to have a limited and discrete selection on hand, with the digital approach virtually any mirror curvature can be created, on demand, by simply changing the grey-scale image representing the digital hologram, and is limited only by the resolution of the SLM used.

The con­stant angle of view of a prime lens forces this type of experimentation—“zooming with your feet”—because the oth­er options are either bad pic­tures or no pic­tures. Fur­ther­more, restrict­ing your­self to a sin­gle focal length for an extend­ed peri­od of time acquaints you to its angle of view and allows you to visu­al­ize a com­po­si­tion before rais­ing the cam­era to your face.

A “nor­mal” lens is defined as one whose focal length is equal to the approx­i­mate diag­o­nal length of a camera’s image sen­sor. In prac­tice, such lens­es tend to fall into a range of slight­ly longer focal lengths that are claimed to pos­sess an angle of view com­pa­ra­ble to that of the human eye’s cone of visu­al atten­tion, which is about 55°.

If you’re into math—and who isn’t?—the gen­er­al for­mu­la for cal­cu­lat­ing the angle of view when you know the focal length and the sen­sor size is:

Customizing the output beam shape from a laser invariably involves specialized optical elements in the form of apertures, diffractive optics and free-form mirrors. Such optics require considerable design and fabrication effort and suffer from the further disadvantage of being immutably connected to the selection of a particular spatial mode. Here we overcome these limitations with the first digital laser comprising an electrically addressed reflective phase-only spatial light modulator as an intra-cavity digitally addressed holographic mirror. The phase and amplitude of the holographic mirror may be controlled simply by writing a computer-generated hologram in the form of a grey-scale image to the device, for on-demand laser modes. We show that we can digitally control the laser modes with ease, and demonstrate real-time switching between spatial modes in an otherwise standard solid-state laser resonator. Our work opens new possibilities for the customizing of laser modes at source.

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To illustrate this technique’s applicability for intra-cavity mode control with the digital laser, we consider the generation of high-order modes and their superpositions in the laser cavity using complex amplitude modulation. In Fig. 5, we illustrate higher-order modes from the Laguerre–Gaussian basis, and in Fig. 6 we show a very high superposition state of the Laguerre–Gaussian modes with azimuthal indices of l=25 and −25, creating a petal-like structure with 50 lobes. This is the highest pure azimuthal combination created in a laser that we are aware of. It is clear from these examples that a myriad of modes may be created within the laser cavity using our approach.

For instance, on full-frame cam­eras, whose image sen­sors mea­sure 36×24 mm, the diag­o­nal length is approx­i­mate­ly 43 mm, and yet, the 50 mm lens is con­ven­tion­al­ly con­sid­ered nor­mal. On APS‑C cam­eras (24 × 16 mm), whose diag­o­nal spans about 28 mm, a 35 mm focal length is regard­ed as nor­mal pri­mar­i­ly because its angle of view is sim­i­lar to the 50 mm lens on the full-frame for­mat. There­fore, nor­mal focal lengths will dif­fer as a func­tion of the camera’s image sen­sor size. In fact, as you con­tin­ue read­ing, keep in mind that descrip­tive terms such as “ultra-wide,” “short,” “long,” et cetera, implic­it­ly refer to the angle of view of a lens.

The angle of view describes the breadth, or how much, of a scene is cap­tured by the lens and pro­ject­ed onto your camera’s image sen­sor. It’s expressed in degrees of arc and mea­sured diag­o­nal­ly along the image sen­sor. Thus, the angle of view of any lens of a giv­en focal length will change depend­ing on the size of the cam­er­a’s image sen­sor. For exam­ple, a 50 mm lens has a wide angle of view on a medi­um for­mat cam­era, a nor­mal angle of view on a full-frame cam­era, a nar­row­er angle of view on an APS‑C cam­era, and a nar­row angle of view on a Micro Four-Thirds cam­era.

Wide-angle lens­es rep­re­sent the only prac­ti­cal method of cap­tur­ing a scene whose essen­tial ele­ments would oth­er­wise fall out­side the angle of view of a nor­mal lens. Con­ven­tion­al sub­jects of ultra wide-angle lens­es include archi­tec­ture (espe­cial­ly inte­ri­ors), land­scapes, seascapes, cityscapes, astropho­tog­ra­phy, and the entire domain of under­wa­ter pho­tog­ra­phy. Wide-angle lens­es are often used for pho­to­jour­nal­ism, street pho­tog­ra­phy, auto­mo­tive, some sports, and niche por­trai­ture.

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Beyond por­trai­ture, long-focus lens­es are use­ful for iso­lat­ing sub­jects in busy and crowd­ed envi­ron­ments. Pho­to­jour­nal­ists, wed­ding, and sports pho­tog­ra­phers exploit this abil­i­ty reg­u­lar­ly. Due to their mag­ni­fy­ing pow­er, super tele­pho­to lens­es are a main­stay for wildlife and nature pho­tog­ra­phers. Last­ly, long-focus lens­es are fre­quent­ly used by land­scape pho­tog­ra­phers to cap­ture dis­tant vis­tas or to iso­late a fea­ture from its sur­round­ings.

The laser was optically pumped by a high-power laser diode that was coupled into the cavity through a mirror coated for high transmission at the diode wavelength (808 nm) and high reflectance at the lasing wavelength (1064, nm). This folding mirror forms an L-shaped cavity so that the high-power diode beam does not interact with the SLM, thus avoiding damage. An important feature of the cavity is the intra-cavity Brewster window to force the laser to oscillate in the desired polarization for the SLM (vertical in our set-up). The light is passed out of the cavity through the output coupler (OC).

For any giv­en cam­era sys­tem, nor­mal lens­es are gen­er­al­ly the “fastest” avail­able. Adjec­tives such as “fast” and “slow” always describe lens speed, which refers to a lens’ max­i­mum aper­ture open­ing. For instance, a lens with a ƒ/2 or larg­er aper­ture is gen­er­al­ly con­sid­ered fast; a lens with a ƒ/5.6 or small­er aper­ture is deemed to be slow. How is speed rel­e­vant to aper­ture? Recall the reci­procity law: larg­er aper­tures per­mit more light into the cam­era, there­by allow­ing you to use faster shut­ter speeds, and vice ver­sa.

Raman spectroscopy. Raman spectroscopy is a technique of probing matter that requires little to no sample preparation. In a Raman spectrometer, a monochromatic ...

The output mode from the digital laser (6x real-time speed) created by dynamically changing the pattern on the spatial light modulator. (AVI 11937 kb)

Next, we employ the digital laser to select the well-known Hermite–Gaussian, Laguerre–Gaussian, super-Gaussian (flat-top) and Airy beams. The digital laser may be used to implement amplitude-only, phase-only or amplitude and phase modulation by simply altering the digital hologram (grey-scale picture) written to the device. The SLM is a phase-only device, yet many of the desired holograms require both amplitude and phase change to the field. To achieve this, we make use of the well-known method of complex amplitude modulation24,25,26, because this is suitable for implementation on SLMs. There are several means by which to implement this (see Arrizon et al.25,26 and references therein), and for the benefit of the reader we briefly outline one approach used in the creation of our modes. Consider for example a desired field u(x,y)=u0 exp(iφ), with u0 the real amplitude and φ the phase of the desired beam. To encode the amplitude term, we introduce high spatial frequency modulation in the form of a checkerboard pattern with alternating phases between two values. The two phases are chosen so that their average value is equal to the desired complex value. For example, if the two phase values are given by A=exp(iφ+iα) and B=exp(iφ–iα), then the desired amplitude u0 may be expressed as u0=cos α. This checkerboard may be varied spatially to create arbitrary amplitude modulation as a function of position. A graphical interpretation of the process is shown in Fig. 3a, where the modulation between two phase-only values (A and B) gives an average return of C, which is no longer on the unit circle in the complex plane, that is, amplitude modulation of the input field. The checkerboard corresponding to this is shown in Fig. 3b. This can be understood from basic diffraction theory: some of the incoming light is diffracted by the checkerboard grating into higher diffraction orders, so that the resulting light in the desired order is now less than before. In this sense the desired light has been amplitude modulated, although the pattern on the SLM is phase-only.

In pho­tog­ra­phy, the most essen­tial char­ac­ter­is­tic of a lens is its focal length, which is a mea­sure­ment that describes how much of the scene in front of you can be cap­tured by the cam­era. Tech­ni­cal­ly, the focal length is the dis­tance between the sec­ondary prin­ci­pal point (com­mon­ly and incor­rect­ly called the opti­cal cen­tre) and the rear focal point, where sub­jects at infin­i­ty come into focus. The focal length of a lens deter­mines two inter­re­lat­ed char­ac­ter­is­tics: mag­ni­fi­ca­tion and angle of view.

(a) Schematic of the digital laser concept showing the SLM, Brewster window (BW), high reflectivity (HR) mirror at an angle of 45°, Nd:YAG gain medium pumped by an external laser diode (LD) source and the output coupler (OC). (b) Photograph of the experimental set-up.

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Laser beam-shaping tools1 have matured over the past few decades to allow external (to the laser cavity) reshaping of a laser beam to a desired transverse profile, and may be implemented by a variety of methods, for example, by diffractive optical elements, free-form optics or more recently by digital holograms written to a spatial light modulator (SLM). However, there are advantages to rather shaping the light inside the laser cavity (intra-cavity laser beam shaping) and this has been a subject of interest for a number of years2,3,4, with several design techniques available5,6,7,8,9,10, some of which have successfully been implemented, for example, using phase-only11,12,13,14, amplitude-only15,16 and phase–amplitude combination17 optical elements for spatial mode selection. All of these techniques require custom optics and in some cases (for example, Bourderionnet. et al.17) additional external beam-shaping optics, a wavefront sensor and an optimization routine to iterate towards the desired phase profile. There have also been attempts at dynamic intra-cavity beam control with deformable mirrors18,19,20,21,22,23, but such elements have very limited stroke, are limited in the phase profiles that can be accommodated18,19, and thus have found little application in laser mode shaping. Rather, such mirrors have been instrumental in high-power applications such as correcting mode distortions (for example, because of thermal load) or in maximizing energy extraction and optimization of laser brightness20,21,22,23. To date, no technique has been demonstrated for on-demand selection of arbitrary laser modes in real-time.

Lubeigt, W., Griffith, M., Laycock, L. & Burns, D. Reduction of the time-to-full-brightness in solid-state lasers using intra-cavity adaptive optics. Opt. Express 17, 12057–12069 (2009).

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Piehler, S., Weichelt, B., Voss, A., Ahmed, M. A. & Graf, T. Power scaling of fundamental-mode thin-disk lasers using intracavity deformable mirrors. Opt. Lett. 37, 5033–5035 (2011).

by G Sluder · 2013 · Cited by 30 — All objectives are designed to be used with the specimen at a defined distance from the front lens element of the objective (the working distance) so that the ...

We note from our results that two conditions must be simultaneously satisfied for the digital laser to function: the gain of the laser must be sufficiently high to overcome the losses, but the intra-cavity circulating intensity must not exceed the damage threshold of the SLM. We manage this by virtue of a high-power pump source and an L-shaped cavity, but there are several other valid approaches (for example, increasing the doping concentration of the crystal). When these conditions are balanced, the digital laser functions as designed.