Pupilaperture

That's a good approach. With that NA, it should work for any launch conditions. For favorable launch conditions, it can work even with a lower lens NA.

Particularly, if it is a single-mode waveguide, the optimum coupling tells us that there you have best matching to the guided mode of the waveguide. Then you will have a similar mode profile at the output of the waveguide. The divergence in air should then be roughly the same as that of the laser beam. This is not exact, however, since the shape of the waveguide mode may somewhat differ from that of the laser beam.

A smaller NA can reduce the divergence angle (set a limit to it), but may make it more difficult to get enough light into the fiber. Alternatively, you try to inject light with smaller divergence, while also avoiding tight bending.

No, that factor results from the assumption that the beam radius is chosen to be only half the NA in order to avoid substantial beam clipping and aberrations.

Questo è evidentemente un vantaggio enorme per chi adora fotografare esemplari di fauna ai quali, per mille motivi, non è possibile avvicinarsi, in quanto l’utilizzo di ottiche con lunghezze focali più corte consente di ridurre i costi e gli ingombri.

There is a weak dependence of numerical aperture on the optical wavelength due to the wavelength dependence of the focal length, which also causes chromatic aberrations.

Why do we define the numerical aperture of a fiber in this way? Is there any reason that we call it numerical aperture? Does it have a certain relation with the numerical aperture of a lens?

Does the numerical aperture of the fiber need to match the numerical aperture of a collimator and objective lens? Does the mismatch of numerical aperture result in higher divergence of the output beam?

How does the NA change as one moves out of the nominal operating wavelength range? I have got a telecom fibre for 1300–1600 nm (NA = 0.14) and launch visible light into it.

Numerical Aperturecalculator

Light propagation in most optical fibers, and particularly in single-mode fibers, cannot be properly described based on a purely geometrical picture (with geometrical optics) because the wave nature of light is very important; diffraction becomes strong for tightly confined light. Therefore, there is no close relation between properties of fiber modes and the numerical aperture. Only, high-NA fibers tend to have modes with larger divergence of the light exiting the fiber. However, that beam divergence also depends on the core diameter. As an example, Figure 3 shows how the mode radius and mode divergence of a fiber depend on the core radius for fixed value of the numerical aperture. The mode divergence stays well below the numerical aperture.

A somewhat smaller spot size may be possible with correspondingly larger input beam radius, if the performance is not spoiled by aberrations. In case of doubt, one should ask the manufacturer what maximum input beam radius is appropriate for a certain lens.

Let's assume that we have a diode laser with fiber output, which has a certain NA and core diameter. How to determine its BPP or M2?

Dall’altro lato, però, l’esperienza insegna che le ottiche hanno una qualità che è la migliore al centro e che più o meno velocemente degrada quando ci si sposta verso i bordi. I sensori APS-C, come abbiamo detto, catturano la parte centrale dell’immagine restitituita dalla lente e pertanto ne usano la parte migliore.

Numerical aperture

In your discussion on the NA of a lens above you provide the equation <$w_\textrm{lens} = D / 4 = NA \cdot f / 2$>. Why is there a 1/2 factor in the NA definition? Does this mean NA is normally full angle for lenses?

For the maximum incidence angle, it is demanded that the light can get through the whole system and not only through an entrance aperture.

numericalaperture中文

One might expect to obtain a tighter focus after the lens if the input light is already converging. However, the convergence angle of the light after the lens is limited by the NA of the lens. Trying to operate a lens in that way would mean that you violate its specifications, and the result would probably be substantial beam distortions, which may well prevent you from getting a tighter focus.

A parere di chi scrive i sensori APS-C, che indubbiamente sono visti un po’ da tutti come i “fratelli minori” dei blasonati full-frame, hanno molto da dire in futuro. Gli unici svantaggi che presentano sono il ridotto angolo di campo e il maggiore rumore nelle fotografie ad alti ISO, mentre i vantaggi in termini di costo e ingombro sono ben evidenti. Per quanto riguarda gli svantaggi, però, notiamo che le cose sono in evoluzione. Sempre di più sono a disposizione ottiche dedicate che consentono di raggiungere angoli di campo comunque elevati (chi vi parla ha da poco acquistato un Sigma 8-16mm, equivalente circa al comune grandangolo 12-24) o, comunque, di ridurre l’ingombro e il peso degli obiettivi. Il rumore sul sensore è un fattore su cui l’avanzamento tecnologico può incidere parecchio e già lo sta facendo. Una delle differenze da valutare tra modelli vecchi e nuovi presentati dalle case madri, prima ancora degli abusatissimi megapixel, è la riduzione del rumore raggiunta alle alte sensibilità, che di fatto consente di salvare molti scatti in più fatti in condizioni di scarsa illuminazione.

The relation between the numerical aperture and the beam divergence angle of an output beam emerging from a fiber end is generally not trivial:

Tuttavia l’utilizzo del formato 135 ha avuto talmente tanto successo da essere diventato uno standard, e quindi anche nel mondo digitale sono stati creati sensori grandi 36×24 mm, che dati i costi, però, sono sempre stati relegati alle macchine fotografiche professionali, che hanno un prezzo decisamente meno abbordabile rispetto a tutte le altre fasce di mercato e che risultano più ingombranti e pesanti. Tali macchine sono appunto le cosiddette Full Frame.

E quali altri formati esistono? La fotografia digitale ha consentito di introdurre sensori fotografici nei dispositivi più disparati, dalle macchine reflex ai cellulari passando per le centinaia di modelli di compatte. Per questo motivo non esiste solo il sensore full frame, ma sono presenti sul mercato moltissimi formati, che vanno dal formato APS-C (il più usato sulle reflex, appunto) ai piccolissimi sensori da un quarto di pollice.

Fiber NA

Che cosa vogliono dire questi nomi? Beh innanzitutto bisogna dire che da sempre la fotografia ha fatto uso di un variegato insieme di supporti impressionabili su cui catturare le immagini, sia in funzione dei costi che dell’uso che si voleva fare delle fotografie stesse.

In Figure 4 one can see that the angular intensity distribution somewhat extends beyond the value corresponding to the numerical aperture. This demonstrates that the angular limit from the purely geometrical consideration is not a strict limit for waves.

The numerical aperture of an optical system is defined as the product of the refractive index of the beam from which the light input is received and the sine of the maximum ray angle against the axis, for which light can be transmitted through the system based on purely geometric considerations (ray optics):

If an aspherical lens with high NA (> 0.55) is used as focusing optics, how is the beam divergence angle defined after beam focus? Would it be possible to determine the angle directly via the NA?

The comment that higher NA decreases optical losses seems misleading as for a multimode fiber higher NA leads to optical path increase inside the core material.

The requirement of total internal reflection would seem to set a strict limit for the angular distributions of fiber modes. However, some modes are found to exceed that limit significantly. We investigate that in detail for single-mode, few-mode and multimode fibers.

I see, the idea is that light may do more of a zig-zag path, which is longer than a straight path through the fiber. However, that argument is questionable; for example, consider that light in any guided fiber mode does not perform a zig-zag path; it has wavefronts perpendicular to the fiber axis and propagates strictly in that direction. Only for light rays (which are anyway a problematic concept for fibers), you can imagine an increased path length, and that would be a quite weak effect. Anyway, other aspects as explained in the article are definitely more important.

Dopo tanti anni di fotografia dall’analogico al digitale dalla camera oscura al PC con fotoshop ecc.ecc. leggere articoli come questo, che normalmente dai per scontato, ti accorgi di scoprire sempre un qualche cosa che per motivi diversi avevi dimenticato o messo in archivio. Ma sopratutto servono anche ai neofiti perchè mi accorgo sempre più che dai libretti di istruzioni si leggono le attenzioni che devi usare, o meglio che non devi fare, prima di scattare una foto piuttosto che un utille spiegazione di come utilizzare al meglio le varie tecnologie della fotocamera. Un grazie a tutti i collaboratori del progetto.

How to control the divergence angle from a multimode optical fiber, by changing light launched condition or selecting fibers with different NA.

Could you comment on the effect of the clear aperture of the lens (provided by manufacturers), and the impact of spherical aberrations for w = D/4 vs. D/3 (99.9% vs. 99% transmitted of a Gaussian beam)?

If you don't use that technology, however, it is usually better to have a single-mode fiber. Therefore, the numerical aperture should not be too large.

It is often not recommended to operate a lens or its full area, since there could be substantial spherical aberrations. The numerical aperture, however, is a completely geometrical measure, which is not considering such aspects.

In the case of a step-index fiber, one can define the numerical aperture based on the input ray with the maximum angle for which total internal reflection is possible at the core–cladding interface:

I sensori più piccoli pertanto hanno sempre un fattore di “taglio” (detto crop factor) che è relativo al formato 135 (se lo standard fosse un altro, magari proprio il sensore APS-C, sarebbe il Full Frame ad avere un fattore di “aggiunta”, quindi tutto è relativo) e che per i sensori Canon è di 1,6x mentre per quelli Nikon-Sony-Pentax è di 1,5x. Questo “taglio” è proprio dovuto al fatto che l’angolo di campo catturabile sul sensore in realtà è appunto 1,6 o 1,5 volte più piccolo rispetto a quello che si ottiene su un 135.

In photography, it is not common to specify the numerical aperture of an objective because such objectives are not thought to be used with a fixed working distance. Instead, one often specifies the aperture size with the so-called f-number, which is the focal length divided by the diameter of the entrance pupil. Usually, such an objective allows the adjustment of the f-number in a certain range.

According to my knowledge, the numerical aperture of a photonic crystal fiber is not even clearly defined. Some people take it to be the sine of the half divergence angled of a mode, but I don't consider that as appropriate, particularly because the results for a simple step-index fiber do not agree. In science, we should not use conflicting definitions of the same term.

In the example case above, the numerical aperture of the lens is determined by its diameter and its focal length. Note, however, that a lens may not be designed for collimating light, but for example for imaging objects in a larger distance. In that case, one will consider rays coming from that object distance, and the obtained numerical aperture will be correspondingly smaller – sometimes even much smaller. This shows that the numerical aperture depends on the location of some object plane determined by the designer according to the intended use.

Essendo la fotografia essenzialmente una proiezione della realtà su una superficie piana (il sensore appunto) fatta con l’utilizzo di un obiettivo che ha una determinata lunghezza focale, è evidentemente diversa l’immagine che si ottiene con due sensori di area differente, in quanto sul sensore più piccolo si perderà una certa porzione d’immagine ai lati (considerando appunto l’immagine come rettangolo).

Let us assume that I have a certain waveguide, where we know that the optimal coupling between laser and the waveguide can be reached when the beam waist at the focal point has a diameter of 38.4 μm. Can we somehow predict the divergence of the output ray at the exit of the waveguide?

F-stops

Some lenses are used for focusing collimated laser beams to small spots. The numerical aperture of such a lens depends on its aperture and focal length, just as for the collimation lens discussed above. The beam radius <$w_\textrm{lens}$> at the lens must be small enough to avoid truncation or excessive spherical aberrations. Typically, it will be of the order of half the aperture radius of the lens (or perhaps slight larger), and in that case (<$w_\textrm{lens} = D / 4 = {\rm NA} \cdot f / 2$>, with the beam divergence angle being only half the NA) the achievable beam radius in the focus is

At a first glance, you may think it is not possible, since the refractive index contrast stays the same – but it can actually change into different ways:

Uno dei criteri di scelta da valutare quando si decide di acquistare una macchina fotografica reflex digitale è la dimensione del sensore, che solitamente può essere di tipo APS-C (Advanced Photo System type-C) o Full Frame, entrambi mutuati dal mondo della pellicola.

The critical angle for total internal reflection is <$\arcsin(1 / n_\rm{YAG})$>, but note that this is measured against the surface normal. The angle against the rod axis is <$\pi / 2 - \arcsin(1 / n_\rm{YAG})$>, and the sine of that gives you the NA.

Da un altro punto di vista, che riguarda però sempre lo stesso fenomeno, l’utilizzo di un sensore più piccolo ma con una maggiore densità di elementi sensibili (pixel) consente di ottenere un’immagine più dettagliata di quel frammento di immagine, consentendo così di parlare, a volte impropriamente, di focale equivalente, in quanto quello che si ottiene a parità di risoluzione, è un’immagine più “ingrandita”, o, per essere più precisi, più ravvicinata.

The output is a beam, and that cannot have a numerical aperture, but only a beam divergence. So your question should be whether the beam divergence is determined by the NA of the fiber.

In principle yes, if you apply the technique of mode division multiplexing: an increased numerical aperture gives you more modes and therefore in principle a potential for higher data rates.

As an rule of thumb, the half-angle beam divergence in radians should not exceed the NA of the fiber, regardless of the core diameter. Then you should be able to get most of the light launched, assuming that is also all hits the fiber core at the interface.

I sensori Full Frame, come abbiamo visto, solitamente hanno una concentrazione di pixel inferiore rispetto agli APS-C e questo consente ai primi di avere un vantaggio sui secondi per quanto riguarda il rumore che si manifesta nelle fotografie quando scattate ad alte sensibilità. Infatti, una minore densità dei componenti elettronici consente di ridurre le interferenze che questi percepiscono, e quindi permettono ai fotografi di scattare ad alti ISO con disturbi inferiori.

Using the term numerical aperture for laser beams is actually discouraged. I assume, however, that you mean the divergence angle of a beam which is convergent on the way to the lens.

Exail (formerly iXblue) offers a wide range of specialty optical fibers for lasers and amplifiers. We master erbium, erbium/ytterbium, ytterbium, thulium, holmium, thulium/holmium, neodymium, dysprosium, and phosphorous gain media. PM version are available, and Large Mode Area (LMA) or Very Large Mode Area (VLMA) versions as well. Depending of the requirement, single clad fibers are available for core pumping, double clad fibers for clad pumping. Triple clad and all glass structures are also available.

Our large mode area photonic crystal fibers are designed for diffraction-limited high-power delivery. The large mode area prevents nonlinear effects and material damage. With standard fibers, you trade large mode areas for single-mode operation. With our large mode area fibers, you get single-mode operation in a wide range of wavelengths. Also available in a polarization-maintaining version.

In the case of a multimode fiber, the problem is that the beam quality will depend on the unknown power distribution over the fiber modes. The article on multimode fibers contains a formula with which we estimate <$M^2$>.

The answer to that question is no – it generally the beam divergence also depends on the launch conditions, unless you have a single-mode fiber, where the output beam divergence is determined only by the fiber properties, but not specifically by the NA.

If a beam from a laser diode gets launched into a fiber with a NA (which fits to the fiber), will the output have the same NA?

If I have a light beam entering an optical fiber at a slight angle to the optic axis, is all of this beam collected by the SM fiber (ignoring the 4% reflection)? The light path is still well within the numerical aperture of the fiber, but is nevertheless some of the light lost to the coating because the light is not absolutely on axis?

Questi due effetti hanno a che fare col concetto di angolo di campo, ossia la porzione di realtà circondante l’obiettivo che viene effettivamente catturata dal sensore e che si misura in gradi. Come vedremo più avanti, gli obiettivi con focale più corta tendono a catturare angoli di campo più vasti (ad esempio sono adatti alle foto panoramiche) e si chiamano pertanto “grandangoli”, mentre quelli con focale più lunga riprendono un angolo di campo più stretto e pertanto sono detti “teleobiettivi” in quanto isolano una porzione più piccola dell’immagine dando l’idea di essere più vicini al soggetto.

数值孔径

Note that the NA is independent of the refractive index of the medium around the fiber. For an input medium with higher refractive index, for example, the maximum input angle will be smaller, but the numerical aperture remains unchanged.

Indeed, some of the light will then be lost, i.e., not get into the guided mode. You can fully launch into the fundamental mode only if you have the perfect amplitude profile, including flat phase fronts perpendicular to the core axis. Particularly for single-mode fibers, the numerical aperture is not providing an accurate criterion.

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The numerical aperture of such a fiber is simply not defined. At least, I am not aware of a reasonable way of defining it.

Tutti gli obiettivi in commercio sono contraddistinti da una lunghezza focale o da un intervallo di lunghezze focali (per gli obiettivi zoom) espresse in mm. Ad esempio posso utilizzare un grandangolo da 16mm o un teleobiettivo da 200 mm. Queste dimensioni sono, in base allo standard in uso, relative al formato 135, ossia sono effettivamente ottiche da 16 mm e da 200mm solo se usate su sensori da 36×24 mm.

The equation given above holds only for straight fibers. For bent fibers, some modified equations have been suggested, delivering a reduced NA value, called an effective numerical aperture of the bent fiber. Proper references for such equations are missing at the moment.

You cannot calculate the NA for that case. It is only defined for a step index fiber, meaning the core and cladding index are constant. But you may of course take the average values over some range to get an approximation.

Is there an equation relating the numerical aperture and far-field intensity distribution for a single-mode fiber, like figure 4, or does it need to be modelled in detail for each case?

Per questo motivo esistono in commercio obiettivi grandangolari specializzati per i sensori APS-C, che hanno cioé una serie di caratteristiche ottiche che consentono di accorciare notevolmente la lunghezza focale per ottenere, nonostante il crop factor, un angolo di campo elevato.

The numerical aperture (NA) of an optical system (e.g. an imaging system) is a measure for its angular acceptance for incoming light. It is defined based on geometrical considerations and is thus a theoretical parameter which is calculated from the optical design. It cannot be directly measured, except in limiting cases with rather large apertures and negligible diffraction effects.

The extreme rays are limited by the size of the lens, or in some cases somewhat less if there is a non-transparent facet.

Se però proiettiamo un’immagine e ne catturiamo una porzione più piccola su un sensore con una maggior densità di pixel rispetto ad un Full Frame, riusciamo di fatto a fare quello che la stessa Full Frame potrebbe fare (cioé ottenere lo stesso angolo di campo e lo stesso dettaglio) solo con una focale più lunga. Quanta lunghezza focale abbiamo guadagnato, dunque, con l’utilizzo di un sensore più piccolo? Esattamente il rapporto di taglio, ossia il crop factor! Quindi un 200mm su sensore APS-C Canon ha un angolo di campo equivalente a quello che si ottiene con un’ottica da 200×1.6=320mm su Full Frame.

Would it be possible to relate the mode diameter of a single mode photonic crystal fiber to its numerical aperture? In other terms, can we use the divergence angle of a Gaussian beam focused to be the same size of the fiber mode to infer the numerical aperture of the fiber?

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How is the output beam divergence influenced when you have two fibers of different NAs coupled to one another? Is the beam divergence limited by the smallest NA in a fiber coupled system?

f-stop是什么

Is there any reason an extrusion process for a plastic optical fiber would expect to change index of refraction of either core or cladding materials? It seems that if core and cladding IORs are both known, that calculating/predicting NA for a plastic multi-mode fiber should be highly consistent. When measuring finished samples, however, it seems that the numerical aperture fluctuates about 20%. What would be the reasons for fluctuations in measured NA? Could it be that the test system isn’t gauged properly, or have you seen in your experience that NA values will vary even though the theoretical value based on IORs should be consistent?

Tuttavia il concetto di lunghezza focale equivalente è corretto solo se ci si limita a considerare l’angolo di campo. L’immagine che l’obiettivo proietta sul sensore è a monte di quest’ultimo e pertanto, ad esempio, la profondità di campo che si ottiene con un 200mm è comunque superiore a quella di un 320mm, e questa differenza si ripercuote identica su qualsiasi sensore si voglia considerare.

If I want to transmit both 1050 nm and 1550 nm through the same fiber, how do NA, MFD and collimation change for the two wavelengths?

However, your question is probably how the divergence of the light emerging from the fiber output depends on the divergence of the launched input beam. That divergence is limited by the fiber's NA, but can also depend on the launch conditions if it is a multimode fiber. Tentatively, you get a lower divergence out if you launch a low-divergence input beam, but this is not always strictly so. For example, higher-order fiber modes, which lead to larger divergence, may be obtained if you launch a low-divergence input beam at some anger against the fiber axis, or if mode mixing arises e.g. from bending of the fiber.

Per quanto riguarda il sensore APS-C ne esistono due versioni ossia quella Canon da 22,2×14,8 mm o quella usata da Nikon, Sony e Pentax da 23,6×15,7 mm.

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In many cases, the light input comes from air, where the refractive index is close to 1. The numerical aperture is then necessarily smaller than 1, but for some microscope objectives it is at least not much lower, for example 0.9. Other microscope objectives for particularly high image resolution are designed for the use of some immersion oil between the object and the entrance aperture. Due to its higher refractive index (often somewhat above 1.5), the numerical aperture can then be significantly larger than 1 (for example, 1.3).

You can just take the NA of one fiber (assuming that all fibers are having the same NA). The angular limitations of the bundle are the same as those for each fiber.

Quando nacquero le macchine fotografiche digitali per il grande pubblico, negli anni ’90, subito si dovette fare i conti con gli ingenti costi dei sensori digitali che, in quanto apparati microelettronici, seguono una legge in base alla quale più sono piccoli e meno costano (per tutta una serie di motivi che non discuteremo qui). Inoltre un sensore piccolo occupa meno posto, consente l’utilizzo di ottiche più compatte e quindi consente una riduzione dell’ingombro della macchina fotografica, del suo peso e del suo costo. Per quanto riguarda in particolare le macchine reflex, che utilizzano elementi aggiuntivi quali specchi e prismi, l’utilizzo di sensori più piccoli consente di ridurre le dimensioni di tutti questi componenti aggiuntivi con evidenti vantaggi pratici ed economici.

For efficient launching, the NA of the collimator should be at least as large as that of the fiber. A larger value won't hurt. A too small value leads to imperfect collimation, including an increased beam divergence.

E’ assai penalizzato chi invece vuole fare scatti con focali corte, magari con grandangoli molto spinti, in quanto nella fotografia andrà a perdere proprio i bordi dell’immagine, che in questo tipo di fotografia accentuano l’impressione di essere “in mezzo alla scena”.

If you had an end face, you could couple in light even with large incidence angles. However, you probably mean ring resonators, where you do not have an end face to couple in. The coupling is then usually done via evanescent waves, and that may be hard because the evanescent field decays so fast.

If I need to collimate the beam from a multimode fiber, should I use an aspheric lens with a NA matched that of the MM fiber?

For shorter-wavelength light, the refractive indices of core and cladding will generally increase, and the NA will presumably also increase somewhat. For example, for germanosilicate fibers that would be the case.

For a single-mode fiber, the NA is typically of the order of 0.1, but can vary roughly between 0.05 and 0.4. (Higher values lead to smaller effective mode areas, smaller bend losses but to tentatively higher propagation losses in the straight form due to scattering.) Multimode fibers typically have a higher numerical aperture of e.g. 0.3. Very high values are possible for photonic crystal fibers.

I suppose you mean the NA of an optical system. The answer: theoretically yes, practically no, it probably can't be that high.

How to calculate the NA of a step index profile fiber if the core and cladding refractive index is not flat along radial direction?

Assuming a Gaussian laser beam with e.g. an initial NA of 0.1 passes through a lens with e.g. NA = 0.7, what is the resulting NA after the lens to describe the waist radius?

The same kind of considerations apply to microscope objectives. Such an objective is designed for operation with a certain working distance, and depending on the type of microscope with which it is supposed to be used, it may be designed for producing an image at a finite distance or at infinity. In any case, the opening angle on which the numerical aperture definition is based is taken from the center of the intended object plane. It is usually limited by the optical aperture on the object side, i.e., at the light entrance.

I am not sure about the origin of the wording. “Numerical” may just relate to “quantitative”, and “aperture” is a kind of limiting device – in this context, limiting not concerning spatial position, but concerning propagation angles. These aspects also apply to the numerical aperture of a lens.

Per quanto riguarda il mondo delle pellicole, il formato più comune e che sicuramente ciascuno di noi ha usato almeno una volta è il cosiddetto 35 mm o “135”, introdotto da Kodak nel 19341 e che poi ha avuto successo anche nel mondo del cinema. In questo caso il segmento di pellicola impressionabile è alto 24 mm ed è lungo 36 mm.

The NA is a property of the lens, while the beam divergence depends on other factors such as the beam radius before the lens. So you can generally not do that calculation. At most, you can calculate the maximum beam divergence angle with is possible without excessive aberrations.

Normally, that should not be the case. It would require that the refractive index contrast between core and cladding changes, and that is unusual. It may happen that the core diameter somewhat varies, but that does not influence the numerical aperture.

What is the equation that relates the divergence of the laser beam to the fiber core (105 μm) and the numerical aperture of the optical fiber?

Although an optical fiber or other kind of waveguide can be seen as a special kind of optical system, there are some special aspects of the term numerical aperture in such cases.

The clear aperture defines the area to which the light should be restricted. That does not directly translate into a limit for Gaussian beams, which do not have a clear boundary. One will usually limit the Gaussian beam radius to be significantly below that aperture radius – e.g. 2/3 of it.

If it is a single-mode fiber, the <$M^2$> value will be close to 1, somewhat dependent on the mode shape, which can be calculated from the index profile.

The numerical aperture (NA) of the fiber is the sine of that maximum angle of an incident ray with respect to the fiber axis. It can be calculated from the refractive index difference between core and cladding, more precisely with the following relation:

buongiorno Paolo sono possessore di una nikon d5500 pertanto sensore aps-c. che obiettivo grandangolare mi consiglieresti per interni o paesaggi urbani con budget di 500-600 euro ? grazie

There exist microresonators based on silicon nitride as the core (n 2.0) and silica as the cladding (n 1.5). This leads to a NA around 1.32. What does it mean? No light could be sent in/out from/to air?

Presumably, you wonder whether the NA determines the beam divergence in free space. The answer is no for single-mode fibers. See also our case study on the numerical aperture.

La scelta del formato, sia nel mondo della pellicola che dei sensori digitali, non è neutra e ha sempre impatti positivi e negativi sulla fotografia che vogliamo scattare e su altri fattori molto importanti.

Enter input values with units, where appropriate. After you have modified some inputs, click the “calc” button to recalculate the output.

For fibers or other waveguides not having a step-index profile, the concept of the numerical aperture becomes questionable. The maximum input ray angle then generally depends on the position of the input surface. Some authors calculate the numerical aperture of a graded-index fiber based on the maximum refractive index difference between core and cladding, using the equation derived for step-index fibers. However, some common formula in fiber optics involving the NA can then not be applied.

There is only a weak dependence of numerical aperture on the optical wavelength due to chromatic dispersion. For example, the NA of a telecom fiber for the 1.5-μm region is not significantly different from that for the 1.3-μm region.

where <$D$> is the aperture diameter, <$f$> the focal length and <$\lambda$> the optical wavelength. Note that the calculation is based on the paraxial approximation and therefore not accurate for cases with very high NA.

Occasionally, the literature contains statements on the numerical aperture of a laser beam. This use of the term is actually discouraged because the numerical aperture should be considered to be based on ray optics, which cannot be applied here. Still, it can be relevant to understand what is meant with such a statement. Here, the numerical aperture is taken to be the tangent of the half-angle beam divergence. Within the paraxial approximation, the tangent can be omitted, and the result is <$\lambda / (\pi w_0)$> where <$w_0$> is the beam waist radius.

For a homogeneous fiber without a core region, the surrounding medium (e.g. air) is effectively the cladding, and the NA is then typically rather high. In that case, of course, the refractive medium of the surrounding medium matters.

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