Efek Sagnac: Perbedaan antara revisi
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'''Efek Sagnac''' ({{lang-en|Sagnac effect}}, juga disebut "Interferensi Sagnac"), adalah suatu gejala yang dijumpai dalam [[interferometri]] yang ditimbulkan oleh [[rotasi]]. Dinamai menurut penemunya, seorang ahli Fisika dari
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A [[gimbal]] mounted mechanical [[gyroscope]] remains pointing in the same direction after spinning up, and thus can be used as a rotational reference for an [[inertial navigation system]]. With the development of so-called [[laser gyroscope]]s and [[fiber optic gyroscope]]s based on the Sagnac effect, the bulky [[Inertial navigation system#Gimballed gyrostabilized platforms|mechanical gyroscope]] is replaced by one having no moving parts in many modern inertial navigation systems.
The principles behind the two devices are different, however. A conventional gyroscope relies on the principle of [[Conservation of angular momentum#Conservation of angular momentum|conservation of angular momentum]] whereas the sensitivity of the ring interferometer to rotation arises from the invariance of the [[speed of light]] for all [[inertial frame of reference|inertial frames of reference]].
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== Pemerian dan operasi ==
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Biasanya digunakan 3 kaca atau lebih sehingga berkas cahaya anti propagasi mengikuti suatu jalur tertutup seperti sebuah segitiga atau bujur sangkar. (Gambar 1) Sebagai alternatif, [[serat optik]] dapat digunakan untuk mengarahkan cahaya melalui jalur tertutup. (Gambar 2) Jika platform dimana interferometer cincin itu dipasang berputar, maka tepi-tepi interferensi akan berpindah dari posisinya dibandingkan jika platform itu tidak berputar. Besarnya perpindahan ini sebanding dengan kecepatan angular platform yang berputar itu. Sumbu rotasi tidak harus berada di dalam area yang ter lingkup.
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The Sagnac effect in a circular loop can be understood as follows. When the loop is rotating, the point of entry/exit moves during the transit time of the light. The backwards-propagating beam covers less distance than the forwards-propagating beam and arrives earlier.(Fig. 3) This creates a shift in the interference pattern. The shift of the interference fringes is thereby proportional to the platform's angular velocity.
The rotation thus measured is an [[absolute rotation]], that is, the platform's rotation with respect to an [[inertial reference frame]].
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== Sejarah ==
{{See also|Sejarah relativitas khusus#Eksperimen Fizeau dan Sagnac}}
Usulan awal pembuatan suatu interferometer cincin raksasa untuk mengukur [[Rotasi Bumi|rotasi bumi]] dikemukakan oleh [[Oliver Lodge]] pada tahun 1897, dan kemudian oleh [[Albert Abraham Michelson]] pada tahun 1904. Mereka berharap bahwa Interferometer semacam itu memungkinkan penentuan satu dari dua ide berlawanan, yaitu (1) aether stasioner (tidak bergerak), atau (2) aether yang bergerak di permukaan bumi (sedangkan bumi tidak berputar). Jika aether bergerak maka hasilnya negatif, sedangkan jika aether stasioner hasilnya positif. Ternyata hasilnya negatif.<ref>{{Cite journal| author=Anderson, R., Bilger, H.R., Stedman, G.E.| year=1994| title=Sagnac effect: A century of Earth-rotated interferometers| journal=Am. J. Phys.|volume=62|issue=11|pages=975–985|doi=10.1119/1.17656|bibcode = 1994AmJPh..62..975A }}</ref><ref>{{Cite journal|author=Lodge, Oliver| year=1897| title=[[s:Experiments on the Absence of Mechanical Connexion between Ether and Matter|Experiments on the Absence of Mechanical Connexion between Ether and Matter]]| journal=Phil. Trans. Roy. Soc.| volume=189| pages=149–166}}</ref><ref>{{Cite journal|author=Michelson, A.A.| year=1904| title=[[s:Relative Motion of Earth and Aether|Relative Motion of Earth and Aether]]| journal=Philosophical Magazine| volume=8| issue=48| pages=716–719}}</ref> [[Max von Laue]] pada tahun 1911 meneruskan pekerjaan Michelson, dan juga menyertakan [[relativitas khusus]] dalam perhitungannya. Ia meramalkan bahwa hasil positif ( dalam order pertama v/c) akan membuktikan baik relativitas khusus dan aether stasioner, karena menurut teori-teori ini kecepatan cahaya tetap sama tanpa tergantung dari kecepatan sumbernya, sehingga waktu propagasi untuk pancaran anti propagasi tidak sama jika dilihat dari [[kerangka acuan inersial]]. Kenyataan hasil yang negatif menyanggah teori-teori itu, sebaliknya membuktikan model pergerakan aether pada bumi yang tidak berputar.<ref name=pauli>{{cite book|last=Pauli|first=Wolfgang|title=Theory of Relativity|publisher=Dover|location=New York|year=1981|isbn=0-486-64152-X}}</ref><ref>{{Cite journal| author=Laue, Max von| year=1911| title=[[s:On an Experiment on the Optics of Moving Bodies|On an Experiment on the Optics of Moving Bodies]]| journal=Münchener Sitzungsberichte| pages=405–412}}</ref> Laue membatasi penelitiannya pada kerangka-kerangka inersial. [[Paul Langevin]] (1921/35) dan yang lain menjelaskan efek ini jika dilihat dari kerangka acuan yang mengalami rotasi (bal dalam relativitas khusus maupun umum, lihat [[Born coordinates]]).<ref>{{cite book|author=Guido Rizzi, Matteo Luca Ruggiero|title=Relativity in Rotating Frames|editor=G. Rizzi and M.L. Ruggiero|chapter=The relativistic Sagnac Effect: two derivations|publisher=Kluwer Academic Publishers|location=Dordrecht|year=1981|isbn=0-486-64152-X|arxiv=gr-qc/0305084}}</ref><ref>L.D. Landau, E.M. Lifshitz, (1962). "The Classical Theory of Fields". 2nd edition, Pergamon Press, pp. 296 - 297.</ref>
Pada praktiknya, eksperimen pertama menggunakan interferometri untuk mengamati korelasi kecepatan angular dan pergeseran fase dilakukan oleh ilmuwan
|author=Sagnac, Georges
|year=1913
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|journal=Comptes Rendus
|volume=157
|pages=1410–1413}}</ref> Sagnac percaya bahwa hasilnya akan membuktikan adanya aether yang stasioner. Kenyataannya, adalah pergeseran fase ini menunjukkan perbedaan kecepatan cahaya yang tidak sejalan dengan relativitas khusus, sehingga efek ini digunakan untuk mengkoreksi perhitungan relativitas khusus. Dua tahun sebelumnya, sebagaimana disebutkan sebelumnya, Max von Laue sudah menunjukkan efek ini konsisten dalam kaitannya dengan relativitas khusus.<ref name=pauli /> Eksperimen yang dilakukan pada tahun 1911 oleh [[Franz Harress]], bertujuan mengukur gerakan aether atau "Fresnel drag" dari cahaya yang berpropagasi melalui gelas bergerak, pada tahun 1920 dikenali oleh Laue sebagai suatu bentuk
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In 1926, an ambitious ring interferometry experiment was set up by [[Albert Abraham Michelson|Albert Michelson]] and [[Henry Gale (astrophysicist)|Henry Gale]]. The aim was to find out whether the rotation of the Earth has an effect on the propagation of light in the vicinity of the Earth. The [[Michelson–Gale–Pearson experiment]] was a very large ring interferometer, (a perimeter of 1.9 kilometer), large enough to detect the angular velocity of the Earth. The outcome of the experiment was that the angular velocity of the Earth as measured by astronomy was confirmed to within measuring accuracy. The ring interferometer of the Michelson-Gale experiment was not calibrated by comparison with an outside reference (which was not possible, because the setup was fixed to the Earth). From its design it could be deduced where the central interference fringe ought to be if there would be zero shift. The measured shift was 230 parts in 1000, with an accuracy of 5 parts in 1000. The predicted shift was 237 parts in 1000.<ref>Albert Abraham Michelson, Henry G. Gale: ''[http://adsabs.harvard.edu/abs/1925ApJ....61..140M The Effect of the Earth's Rotation on the Velocity of Light]'', in: ''The Astrophysical Journal'' 61 (1925), S.
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== Teori ==
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Pergeseran tepi-tepi nterferensi dalam suatu interferometer cincin dapat dilihat sebagai konsekuensi dari perbedaan ''jarak'' yang ditempuh oleh cahaya karena perputaran cincin light. (Gambar 3)<ref name=BrownSagnac>{{cite web|last=Brown|first=Kevin|title=The Sagnac Effect |publisher=MathPages |url=http://mathpages.com/rr/s2-07/2-07.htm |accessdate=15 February 2013}}</ref> Derivatisasi paling sederhana dari suatu cincin melingkar yang berputar pada suatu kecepatan angular <math> \omega </math>, tetapi hasilnya umum untuk geometri melingkar pada bentuk-bentuk lain. Jika suatu sumber cahaya memancar ke dua arah dari satu titik pada cincin berputar, cahaya yang ke arah sama dengan arah rotasi perlu menempuh jarak lebih dari satu kali [[keliling lingkaran]] sebelum akhirnya mencapai sumber cahaya dari belakang. Waktu <math> t_1 </math> Yang dibutuhkan untuk mengejar sumber cahaya itu mempunyai persamaan:
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Penghilangan <math> \Delta L </math> Dari kedua persamaan itu akan menghasilkan:
: <math> t_1 = \frac {2 \pi R }{c - R \omega}.
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Demikian pula, cahaya yang berjalan dengan arah berlawanan dari arah rotasi akan menempuh jarak kurang dari satu kali keliling lingkaran sebelum mencapai sumber cahaya dari sisi depan. Jadi waktu yang ditempuh cahaya dari arah ini untuk mencapai sumber bergerak adalah:
: <math> t_2 = \frac {2 \pi R }{c + R \omega}. </math>▼
Perbedaan kedua waktu:
Untuk <math> R \omega = v \ll c </math>, dapat disederhanakan menjadi
: <math>\Delta t \approx \frac {4 \pi R^2 \omega} {c^2} = \frac {4 A \omega} { c^2}, </math>
[[Berkas:Sagnac-Interferometer.png|jmpl|Gambar 4. Rumus area Sagnac berlaku pada bentuk melingkar apapun.]]
Meskipun derivasi sederhana ini untuk cincin melingkar, hasilnya secara umum berlaku pada semua bentuk apapun yang melingkar dengan luas area ''A''.(Gambar 4)
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We imagine a screen for viewing fringes placed at the light source (or we use a beamsplitter to send light from the source point to the screen). Given a steady light source, interference fringes will form on the screen with a fringe displacement proportional to the time differences required for the two counter-rotating beams to traverse the circuit. The phase shift is <math>\Delta \phi=\frac { 2 \pi c \Delta t }{\lambda} </math>, which causes fringes to shift in proportion to <math>A</math> and <math>\omega</math> .
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When light propagates in fibre optic cable, the setup is effectively a combination of a Sagnac experiment and the [[Fizeau experiment]]. In glass the speed of light is slower than in vacuum, and the optical cable is the moving medium. In that case the relativistic velocity addition rule applies. Pre-relativistic theories of light propagation cannot account for the Fizeau effect. (By 1900 [[Hendrik Lorentz|Lorentz]] could account for the Fizeau effect, but by that time his theory had evolved to a form where in effect it was mathematically equivalent to special relativity.)
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[[File:Generalized Sagnac effect.gif|thumb|351px|Figure 5. Conceptually, a conventional fibre optic gyro (FOG), shown on the left, can be divided into two semicircular sections with extended fibre connecting the end sections as shown on the right, creating a fibre optic conveyor (FOC).]]
The Sagnac effect has stimulated a century long debate on its meaning and interpretation,<ref name=Stedman1997>{{cite journal |last=Stedman |first=G. E. |title=Ring-laser tests of fundamental physics and geophysics|journal=Rep. Prog. Phys. |year=1997 |volume=60 |pages=
=== Other generalizations ===
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It is also possible to construct a ring interferometer that is self-contained, based on a completely different arrangement. This is called a [[ring laser]] or [[ring laser gyroscope]]. The light is generated and sustained by incorporating laser excitation in the path of the light.
To understand what happens in a ring laser cavity, it is helpful to discuss the physics of the laser process in a laser setup with continuous generation of light. As the laser excitation is started, the molecules inside the cavity emit photons, but since the molecules have a thermal velocity, the light inside the laser cavity is at first a range of frequencies, corresponding to the statistical distribution of velocities. The process of [[stimulated emission]] makes one frequency quickly outcompete other frequencies, and after that the light is very close to monochromatic.
[[File:Ring laser interferometry shift.png|frame|left|Figure 7. Schematic representation of the frequency shift when a ring laser interferometer is rotating. Both the counterpropagating light and the co-propagating light go through 12 cycles of their frequency.]]
For the sake of simplicity, assume that all emitted photons are emitted in a direction parallel to the ring. Fig. 7 illustrates the effect of the ring laser's rotation. In a linear laser, an integer multiple of the wavelength fits the length of the laser cavity. This means that in traveling back and forth the laser light goes through an integer number of ''cycles'' of its frequency. In the case of a ring laser the same applies: the number of cycles of the laser light's frequency is the same in both directions. This quality of the same number of cycles in both directions is preserved when the ring laser setup is rotating. The image illustrates that there is wavelength shift (hence a frequency shift) in such a way that the number of cycles is the same in both directions of propagation.
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==== Zero point calibration ====
[[File:Sagnac effect256x128.gif|frame|right|Figure 8. The red and blue dots represent counter-propagating photons, the grey dots represent molecules in the laser cavity.]]
In passive ring interferometers, the fringe displacement is proportional to the first derivative of angular position; careful calibration is required to determine the fringe displacement that corresponds to zero angular velocity of the ring interferometer setup. On the other hand, ring laser interferometers do not require calibration to determine the output that corresponds to zero angular velocity. Ring laser interferometers are self-calibrating. The beat frequency will be zero if and only if the ring laser setup is non-rotating with respect to inertial space.
Fig. 8 illustrates the physical property that makes the ring laser interferometer self-calibrating. The grey dots represent molecules in the laser cavity that act as resonators. Along every section of the ring cavity, the speed of light is the same in both directions. When the ring laser device is rotating, then it rotates with respect to that background. In other words: invariance of the speed of light provides the reference for the self-calibrating property of the ring laser interferometer.
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===Zero-area Sagnac interferometer and gravitational wave detection===
The Sagnac topology was actually first described by Michelson in 1886,<ref name=hariharan1975>{{cite doi|10.1364/AO.14.2319_1|noedit}}</ref> who employed an even-reflection variant of this interferometer in a repetition of the [[Fizeau experiment]].<ref name=mich>{{Cite journal|author=Michelson, A. A. and Morley, E.W.|title=[[s:Influence of Motion of the Medium on the Velocity of Light|Influence of Motion of the Medium on the Velocity of Light]] |journal=Am. J. Science |volume=31|year=1886|pages=377–386}}</ref> Michelson noted the extreme stability of the fringes produced by this form of interferometer: White-light fringes were observed immediately upon alignment of the mirrors. In dual-path interferometers, white-light fringes are difficult to obtain since the two path lengths must be matched to within a couple of [[micrometers]] (the [[coherence length]] of the white light). However, being a [[common path interferometer]], the Sagnac configuration inherently matches the two path lengths. Likewise Michelson observed that the fringe pattern would remain stable even while holding a lighted match below the optical path; in most interferometers the fringes would shift wildly due to the [[refractive index]] fluctuations from the warm air above the match. Sagnac interferometers are almost completely insensitive to displacements of the mirrors or beam-splitter.<ref name=Hariharan2003>{{cite book|last=Hariharan|first=P.|title=Optical Interferometry, Second Edition|url=https://archive.org/details/opticalinterfero00hari_855|year=2003|publisher=Academic Press|isbn=0-12-311630-9|pages=[https://archive.org/details/opticalinterfero00hari_855/page/n44 28
[[File:Zero-Area Sagnac Interferometer.svg|thumb|225px|Figure 9. Zero-area Sagnac interferometer]]
The fringe shift in a Sagnac interferometer due to rotation has a magnitude proportional to the enclosed area of the light path, and this area must be specified in relation to the axis of rotation. Thus the sign of the area of a loop is reversed when the loop is wound in the opposite direction (clockwise or anti-clockwise). A light path that includes loops in both directions, therefore, has a net area given by the difference between the areas of the clockwise and anti-clockwise loops. The special case of two equal but opposite loops is called a ''Zero-area'' Sagnac interferometer. The result is an interferometer that exhibits the stability of the Sagnac topology while being insensitive to rotation.<ref name=Sun1996/>
The [[LIGO|Laser Interferometer Gravitational-Wave Observatory]] (LIGO) consisted of two 4-km [[Fabry-Pérot interferometer|Michelson-Fabry-Pérot interferometers]], and operated at a power level of about 100 watts of laser power at the beam splitter. A currently ongoing upgrade to Advanced LIGO will require several kilowatts of laser power, and scientists will need to contend with thermal distortion, frequency variation of the lasers, mirror displacement and thermally induced [[birefringence]].<ref name=Sun1996/>
A variety of competing optical systems are being explored for third generation enhancements beyond Advanced LIGO.<ref name=punturo2010>{{cite doi|10.1088/0264-9381/27/8/084007|noedit}}</ref> One of these competing proposals is based on the zero-area Sagnac design. With a light path consisting of two loops of the same area, but in opposite directions, an effective area of zero is obtained thus canceling the Sagnac effect in its usual sense. Although insensitive to low frequency mirror drift, laser frequency variation, reflectivity imbalance between the arms, and thermally induced birefringence, this configuration is nevertheless sensitive to passing [[gravitational wave]]s at frequencies of astronomical interest.<ref name=Sun1996>{{cite journal |last=Sun| first=K-X. |coauthors=Fejer, M.M.; Gustafson, E.; Byer R.L. |title=Sagnac Interferometer for Gravitational-Wave Detection |journal=Physical Review Letters |year=1996 |volume=76 |issue=17 |pages=
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== Lihat pula ==
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== Pranala luar ==
* Mathpages: [http://www.mathpages.com/rr/s2-07/2-07.htm The Sagnac Effect]
* [http://www.physics.berkeley.edu/research/packard/related/Gyros/LaserRingGyro/Steadman/StedmanReview1997.pdf
* [http://relativity.livingreviews.org/open?pubNo=lrr-2003-1&page=node1.html The Sagnac Effect and its Application for GPS] {{Webarchive|url=https://web.archive.org/web/20060330121448/http://relativity.livingreviews.org/open?pubNo=lrr-2003-1&page=node1.html |date=2006-03-30 }} GPS-related article by Neil Ashby
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