Schematic Representation of a Confocal Fabry Perot Interferometer

Features

• Analyze Spectra of CW Lasers
• Free Spectral Range of 1.5 and 10 GHz
• Finesse of at Least 150
• Controller Available

Thorlabs' Scanning Fabry-Perot (FP) Interferometers are spectrum analyzers that are frequently used to examine the fine structure of the spectral characteristics of CW lasers. These interferometers offer a high-finesse of at least 150, and free spectral ranges (FSRs) of either 1.5 or 10 GHz.

The confocal FP cavity acts as a very narrow bandpass filter. The transmission frequency of the cavity is tuned by adjusting the length of the cavity using piezoelectric transducers. The transmitted light intensity is measured using a photodiode, amplified by the transimpedence amplifier in the SA201 controller (or equivalent amplifier) and then displayed / recorded by an oscilloscope or data acquisition card.

Alignment
The confocal design of the FP Interferometer cavity is relatively insensitive to the alignment of the input beam. As a result, the optical axis of the FP Interferometer can be aligned with sufficient accuracy to the input beam by mounting the interferometer on a standard kinematic mirror mount (see the Alignment Guide tab for more details).

Operation
The SA201 controller generates a sawtooth or triangle wave voltage required to repetitively scan the length of the FP cavity in order to sweep through one FSR of the interferometer. The SA201 controller also houses a transimpedance amplifier that can be used to amplify the output of the photodiode detector in the FP Interferometer; this detector measures the intensity of the light transmitted through the confocal FP cavity. The controller also provides a trigger signal to the oscilloscope, which allows the oscilloscope to easily trigger at the beginning or the middle of the scan. The time axis of the oscilloscope can be precisely by calibrated measuring the time elapsed between the same spectral feature by separated one FSR.

Theoretical Mirror Reflectivity and Mirror Finesse

The Excel file contains the data used to make the plot above. Please remember that the actual reflectivity of the mirror will vary slightly from coating run to coating run within the specified region and can vary significantly from coating run to coating run outside of the specified region. The total cavity finesse depends on additional factors. Please see the online tutorial for more information.

Specified Regions

-3B Series: 350 - 535 nm
-5B Series: 535 - 820 nm
-8B Series: 820 - 1275 nm
-12B Series: 1275 - 2000 nm
-18B Series: 1800 - 2500 nm

SA200/SA210 Series Scanning Fabry-Perot Interferometers

Scanning Fabry-Perot Interferometers

The core of Thorlabs' scanning Fabry-Perot interferometers is an optical cavity formed by two, nearly identical, spherical mirrors separated by their common radius of curvature as shown in Figure 1. This configuration is known as a mode-degenerate, confocal cavity design, which is generally referred to as a confocal Fabry-Perot. The cavity is mode degenerate because the frequency of certain axial and transverse cavity modes are the same (degenerate). This degeneracy greatly simplifies the alignment of the instrument by eliminating the need to carefully mode match the input to the cavity. The confocal design offers several benefits over flat-plate interferometers such as easier alignment since the confocal interferometer is fairly insensitive to angular alignment. Additionally, the confocal design offers a unique property that at constant finesse as resolving power increases, so does the etendue (etendue is defined as the radiation from a source within a solid angle, Ω, subtended by an aperture with area A). By contrast, in a flat-plate interferometer as resolving power increases (at constant finesse) the etendue decreases; meaning that an increase in light intensity decreases resolution and vice-versa.

The inner concave surface of each mirror has a highly reflective coating, while the outer convex surface has a broadband antireflection coating. The curvature on the outer surface, which matches that of the inner surface, eliminates lensing effects. In a confocal system, the mirror spacing matches the curvature of radius (r) as depicted in Figure 1. To illustrate the operation of this confocal cavity, it is useful to follow a ray as it enters the cavity off-axis and travels one round trip through the cavity. As seen in Figure 2, the beam enters the cavity at a height H. A portion of the ray follows the path numbered 1, 2, 3, and 4; it is then reflected onto path 1 again. The dotted lines exterior to the cavity in Figure 2 represent the portion of the ray that is transmitted through the cavity mirrors when the cavity is resonant with the input (i.e., when the round trip distance equals mλ, where m is an integer, and λ is the wavelength of the input radiation). The approximate optical path length (L) of one round trip through the cavity can be expressed as

when 0<H<<r.

Resonance and Free Spectral Range (FSR)

In order to achieve a maximum in resonance from a Fabry-Perot cavity, the complete round-trip phase delay must be a multiple of 2π. For a plano-plano Fabry-Perot cavity with a round trip distance of 2r, this condition is satisfied when the frequency is mc/2r, were m is any integer, c is the speed of light in air, and r is the mirror separation. Therefore, the separation, or Free Spectral Range (FSR) between two transmission peaks is c/2r.

For a confocal Fabry-Perot cavity, we must take into account that the modes of the cavity are Gaussian. By taking into account the phase shift of a Gaussian mode in the confocal cavity, it can be shown [1] that resonance frequencies of the transverse modes either overlap or fall exactly halfway between the longitudinal mode resonances. Therefore, the FSR for a confocal cavity the free spectral range is c/4nd.

Total Corrected Round Trip Distance

Because the actual optical path length of the confocal Fabry-Perot cavity is dependent on H, the resonance condition will vary across the input beam. This variation across the input aperture is a critical practical consideration when using a confocal Fabry-Perot Interferometer.

In order to develop an equation that relates the resolution of the interferometer to H, the geometrical optical path length with a correction for spherical aberration must be considered. Doing so with the approximation that 0 < H << r, yields an optical path length of

As the input beam diameter increases, the second term in Eq. (2) becomes significant in comparison to λ.

Finesse and Resolution of a Confocal Cavity

For a Fabry-Perot cavity, the finesse is a measure of the interferometer's ability to resolve closely spaced spectral features. The minimum resolvable frequency increment of an interferometer is based on the Rayleigh Criterion, which stipulates that for two closely spaced lines of equal intensity to be resolved, the sum of the two individual lines at the midway point can at most be equal to the intensity of one of the original lines (see Figure 3).

The total finesse of an interferometer is defined as the ratio of the FSR to the FWHM of the resonant peak, where Δ is the FWHM. As can be seen in Figure 3, two lines separated by Δ are just resolvable according to the Rayleigh criterion. Therefore, Δ quantifies the resolution of the system.

The equation for the total finesse is given by

Note that during the manufacturing of the SA200 series interferometers, F_t is maximized in order to adjust the cavity length to the confocal condition by maximizing its value. This method provides a very precise means for setting the required length of the cavity to better than λ.

The FSR and the FWHM of a representative lineshape are shown in Figures 4 and 5, respectively. An F_t of 294 is measured using a DFB laser with a linewidth that cannot be considered infinitely small in comparison to the resolution of the cavity. Therefore, the true F_t is about 320, assuming a 2 MHz laser linewidth.

A measured finesse has a number of contributing factors: the mirror reflectivity finesse F_R, the mirror surface quality finesse F_q, and the finesse due to the illumination conditions (beam alignment and diameter) of the mirrors F_i. Therefore, the total inverse of the finesse of a system can be written as

where, for mirrors with a reflectivity close to 1, the effective mirror reflectivity finesse is given by

Here, R is the mirror reflectivity.

While the definition for the reflectivity finesse is ambiguous, Eq. (5) is presented as an effective finesse that is defined by Eq. (3) when the other contributing factors are negligible. For the SA200 series, the reflectivity finesse dominates when operating with proper illumination [2].

Using Eq. (5), the reflective coatings in the SA200 series of interferometers have been designed so that the minimum F_R is better than 1.5 times the minimum specified finesse across their entire operating wavelength range for each model (see the table on the product page). This fixes the first term of Eq. (4).

The second term in Eq. (4) involves F_q, which accounts for mirror irregularities that cause a symmetric broadening of the lineshape. The effect of these irregularities is a random position-dependent path length difference that blurs the lineshape. The manufacturing process that is used to produce the cavity mirrors ensures that the contribution from F_q is negligible in comparison to our specified total finesse for each model.

The final term in Eq. (4), which deals with the illumination finesse F_i, will reduce the resolution as the beam diameter is increased or as the input beam is offset. When the finesse is limited by the F_i term, the measured lineshape will appear asymmetric. The asymmetry is due to the path length difference between an on-axis beam and an off-axis beam, resulting in different mirror spacings to satisfy the maximum transmission criteria. The approximate decrease in path length for a beam at a distance H off axis is given by the second term in Eq. (2).

To quantify the effects of the variable path length on F_i, consider an ideal monochromatic input, a delta function in wavelength with unit amplitude, entering the Fabry-Perot cavity coaxial to the optic axis and having a beam radius a. The light entering the interferometer at H = +e, where e is infinitesimally small but not zero, will negligibly contribute to a deviation in the transmitted spectrum. Light entering the cavity at H = +a will cause a shift in the transmitted output spectrum, since the optical path length of the cavity will be less by an approximate distance of a⁴/4r³. Assuming the input beam has a uniform intensity distribution, the transmitted spectrum will appear uniform in intensity and broader due to the shifts in the optical path length. As a result, the wavelength input delta function will produce an output peak with a FWHM of H⁴/4r³.

Assuming that only F_i contributes significantly to the total finesse, then Eq. (3) can be used to calculate F_i for the idealized input beam:

Substituting λ/4 for the FSR, and (H⁴/4r³) for FWHM, yields

The λ/4 substitution for the FSR is understood by considering that the cavity expands by λ/4 to change from one longitudinal mode to the next. For an input beam with a real spectral distribution, the effect of the shift will be a continuous series of shifted lineshapes.

It should be noted that the shift is always in one direction, leading to a broadened or assymmetric lineshape due to the over-sized or misaligned beam.

Now, using Eq. (4), the total finesse, which includes significant contributions from both F_R and F_i can be found (Note: F_q is still considered to have a negligible effect on F_t):

Replacing F_i and F_R yields:

Eq. (8) is used to provide an estimate (albeit an overestimate) of effects of beam diameter effects on the total finesse of a Fabry-Perot Interferometer. Several assumptions lead to the overestimation of finesse. One is that the diameter of the beam is the same as the diameter of the mirror, in practice the diameter of the beam is typically significantly smaller than that of the mirror (this also helps to reduce spherical aberration) [2]. Another assumption is that the light is focused down to an infinitesimally small waist size, even for monochromatic light the minimum waist size is limited by diffraction, and in multimode applications the waist size can be quite large at the focus. Figure 6 provides a plot of Eq. 8 for the two cavity designs offered (r = 50 mm and r = 7.5 mm). The traces in the plot were made with the assumption that the reflectivity finesse is equal to 300, which is the typical value obtained for mirrors used in the SA200 series interferometers.

Spectral Resolving Power and Etendue

The spectral resolving power of an interferometer is a metric to quantify the spectral resolution of an interferometer, and is an extention of the Rayleigh criterion. The spectral resolving power, SR, is defined as:

In Equation (9), v is the frequency of light and λ is its wavelength. It can be shown that for a confocal Fabry-Perot interferometer, the SR is given by:

In Equation (10), F is the finesse of the interferometer, r is the radius of curvature of the mirrors, and λ is the wavelength. However, to achieve this maximum instrumental profile while the interferometer is in scanning mode, the aperture of the detector would need to be infinitesimally small; as the aperture is opened wide enough, the spectral resolving power begins to decrease. The spectral resolving power must be balanced with the etendue of the interferometer. The etendue (U) is the metric for the net light-gathering power of the interferometer. When the light source is a laser beam, the etendue provides a measure of the alignment tolerance between the interferometer and the laser beam. The etendue is defined as the product of the maximum allowed solid angle divergance (Ω) and the maximum allowed aperture area (A). For the confocal system the etendue is given by:

In Equation (11), F is the finesse of the interferometer, λ is the wavelength, and d is the mirror spacing. For proper use of the interferometer the spectral resolving power and etendue need to be balanced such that enough light is allowed to enter the system without significantly reducing the resolution of the interferometer. The accepted compromise for this balance is to increase the mirror aperture until the the spectral resolving power is decreased by 70% (0.7*SR) [3]. Under this condition the "ideal" etendue becomes π²λr/F, where r is the mirror's radius.

[1] Yariv, A., 1991, Optical Electronics 4th Edition, Holt, Rinehart & Winston, Philadelphia, 736 p.
[2] J. Johnson, "A High Resolution Scanning Confocal Interferometer," Applied Optics, vol. 7, no. 6, pp. 1061 - 1072, 1968.
[3] M. Hercher, "The Spherical Mirror Fabry-Perot Interferometer," Applied Optics, vol. 7, no. 5, pp. 951 - 966, 1968.

General Instructions

The SA200 and SA210 series of Scanning Fabry-Perot Interferometers have confocal FP cavities. Since the transverse modes of a confocal cavity are degenerate, the cavity is fairly insensitive to the alignment of the input beam. As seen in the ray trace to the right, even an off axis input beam that is not parallel to the optical axis of the FP cavity will make one round trip through the cavity with an approximate path length of 4r-H⁴/r³ where r is the radius of curvature of the mirrors and H is the distance that the input beam is from the optical axis when the beam enters the cavity. As long as the second term in the path length expression is much less than the wavelength of the light, then the off axis input beam will be degenerate with the on axis input beam. The second term in the path length expression also limits the diameter of the input beam. In practice, the cavity can be aligned by mounting the confocal FP interferometer in a standard kinematic mirror mount (KS2 for SA200 and KS1 for SA210) which is then placed in a free space beam after a fold mirror. While the cavity is being scanned, iteratively adjust the position of the mirror and FP interferometer until the cavity is aligned with the input beam. After the cavity is aligned to the beam, a lens should be placed in the beam so that a beam waist with the specified diameter is formed in the center of the cavity.

SA200 Series
The diameter of the collimated free space beam before the lens should be ~4 mm and a 250 mm focal length lens should be positioned ~220 mm in front of the flange on the interferometer. This will create the 600 µm diameter beam waist at the center of the confocal cavity.

SA210 Series
The diameter of the collimated free space beam before the lens should be ~1 mm and a 100 mm focal length lens should be positioned ~75 mm in front of the flange on the interferometer. This will create the 150 µm diameter beam waist at the center of the confocal cavity.

For examples of how to integrate an SA200 or SA210 series interferometer into Thorlabs' cage system, see below.

Example Setup that Facilitates the Coupling of a Free Space Beam into an SA210 Series Fabry-Perot Interferometer Using Cage System Components

Below is an explanation of the parts used at each numbered stage, a description of how the system was aligned, and a table of the products used in the setup pictured above.

Stage 1: A BE02M-A is used to reduce a beam of light to the required collimated beam diameter of 1 mm, as specified in the manual (the magnification factor of the beam expander/reducer is application specific). The beam expander/reducer is held in the 30 mm cage system using a CP06 cage plate. Notes: The beam expander/reducer should be adjusted so that it outputs a collimated beam prior to inserting it into the cage system. Alternatively, the mirror can be removed from the first KCB1 mount to allow a sufficiently long beam path to ensure that the output of the beam expander/reducer is collimated.

Stage 2: A BB1-E02 is held in a KCB1 kinematic cage mount. This is the first of two steering mirrors used to control the propagation direction of the beam of light being coupled into the SA200 series Fabry-Perot Interferometer. The KCB1 is supported by a TR series post and PH4E pedestal post holder.

Stage 3: A BB1-E02 is held in a KCB1 kinematic cage mount. This is the second of two steering mirrors. The KCB1 is supported by a TR series post and PH4E pedestal post holder.

Stage4: A CT1 30 mm cage translation stage is used to hold the mounted AC254-100-A-ML achromatic lens. The center of the lens should be positioned approximately 250 mm from the front plate of the KC1 mount with the z-axis micrometer set in the middle of its adjustment range. The CT1 can be replaced by the combination of a CP02 cage plate and an SM1V05 adjustable length lens tube.

Stage 5: A KC1 is a 30 mm kinematic cage mount that is being used to mount the SA210 series Fabry-Perot interferometer. The KC1 is being supported by a TR series post and an PH4E pedestal post holder.

Alignment Guide:

For a complete alignment procedure, please see the operations manual.

After the beam expander was adjusted so that it produced a collimated 1 mm diameter beam of light when inserted into the free space laser beam used for testing this setup, the entire cage system was assembled as shown in the picture. The assembly was then situated on the optical table and adjusted so that the free space beam, which was already propagating parallel to the table, passed through the center of the CPA1 alignment guide when it was placed before and after the stage 1 components. At this point the pedestal post holders were locked down to the optical table using the CF175 clamps. The CPA1 alignment guide was then positioned immediately before stage 3 and the stage 2 kinematic mirror was used to steer the beam to the alignment mark. The CPA1 was then positioned immediately before the stage 5 components and the stage 3 kinematic mirror was used to steer the beam to the alignment mark. Turn on the Fabry-Perot controller box and start scanning the length of the cavity since light will only be transmitted when the cavity length is resonant with the wavelength of the light beam. At this point it might be necessary to remove the detector from the back of the Fabry-Perot cavity in order coarsely align the cavity, however this was an unnecessary step when this setup was tested. Iteratively adjust the adjustment knobs on the mounts in stages 3, 4, and 5 until the Fabry-Perot cavity is correctly aligned.  

^a The correct choice for a beam expander/reducer is dependent on the properties of the beam of light that needs to be coupled into the Fabry-Perot cavity. The beam after the beam expander/reducer should be collimated and approximately 4 mm in diameter. Be sure to choose a beam expander with the correct AR coating.
^b In addition to the visible (400-700 nm) achromatic lens listed in the table Thorlabs also sells achromatic lenses suitable for the 650-1050 nm and 1050-1620 nm spectral ranges. However, these lenses are not mounted and as a result an SM1L03 should be purchased to mount an unmounted achromatic lens.
^c In addition to the visible (400-750 nm) spectral range broadband dielectric mirror in the table Thorlabs sells Broadband Dielectric Mirrors suitable for the 750-1100 nm and 1280-1600 nm spectral ranges. Alternatively, a protected metallic mirror made from silver or aluminum could also be used.
^d Optional 30 mm cage system alignment guide. This guide precisely locates the optical axis of a 30 mm cage system. This greatly simplifies the alignment of the Fabry-Perot Interferometer the setup pictured above is used.

Example Setup that Facilitates the Coupling of a Fiber Coupled Source into an SA210 Series Fabry-Perot Interferometer Using Cage System Components

When using a fiber coupled light source, stages 1 and 2 of the free space setup shown at the top of the page can be replaced with a cage mounted fiber collimation system. The diameter of the beam output from the fiber collimator needs to be approximately 1 mm (not larger) in diameter. One possible fiber collimation solution would be to use a CFC-5 series adjustable collimator. The collimator could be incorporated into the 30 mm cage system using an AD9.5F adapter and a CP06 cage plate.

Example Setup that Facilitates the Coupling of a Free Space Beam into an SA200 Series Fabry-Perot Interferometer Using Cage System Components

Below is an explanation of the parts used at each numbered stage, a description of how the system was aligned, and a table of the products used in the setup pictured above.

Stage 1: A BE02M-A is used to reduce a beam of light to the required collimated beam diameter of 4 mm, as specified in the manual (the magnification factor of the beam expander/reducer is application specific). The beam expander/reducer is held in the 30 mm cage system using a CP06 cage plate. Notes: The beam expander/reducer should be adjusted so that it outputs a collimated beam prior to inserting it into the cage system. Alternatively, the mirror can be removed from the first KCB1 mount to allow a sufficiently long beam path to ensure that the output of the beam expander/reducer is collimated.

Stage 2: A BB1-E02 is held in a KCB1 kinematic cage mount. This is the first of two steering mirrors used to control the propagation direction of the beam of light being coupled into the SA200 series Fabry-Perot Interferometer. The KCB1 is supported by a TR series post and PH4E pedestal post holder.

Stage 3: A BB1-E02 is held in a KCB1 kinematic cage mount. This is the second of two steering mirrors. The KCB1 is supported by a TR series post and PH4E pedestal post holder.

Stage4: A CP02 holds the SM1V10 adjustable length lens tube in which the AC254-250-A-ML achromatic lens is mounted. The center of the lens was positioned approximately 22 cm from the front plate of the KC2 mount with half of the threads on the adjustable length lens tube threaded into the CP02 cage plate. An LCP02 is used to convert the cage system from the 30 mm format to the 60 mm format.

Stage 5: A KC2 is a 60 mm kinematic cage mount that is being used to mount the SA200 series Fabry-Perot interferometer. The KC2 is being supported by a TR series post and an PH4E pedestal post holder.

Alignment Guide:

For a complete alignment procedure, please see the operations manual.

After the beam expander was adjusted so that it produced a collimated 4 mm diameter beam of light when inserted into the free space laser beam used for testing this setup, the entire cage system was assembled as shown in the picture. The assembly was then situated on the optical table and adjusted so that the free space beam, which was already propagating parallel to the table, passed through the center of the CPA1 alignment guide when it was placed before and after the stage 1 components. At this point the pedestal post holders were locked down to the optical table using the CF175 clamps. The CPA1 alignment guide was then positioned immediately before stage 3 and the stage 2 kinematic mirror was used to steer the beam to the alignment mark. The CPA1 was then removed and the LCPA1 was positioned immediately before the stage 5 components and the stage 3 kinematic mirror was used to steer the beam to the alignment mark. Turn on the Fabry-Perot controller box and start scanning the length of the cavity since light will only be transmitted when the cavity length is resonant with the wavelength of the light beam. At this point it might be necessary to remove the detector from the back of the Fabry-Perot cavity in order coarsely align the cavity, however this was an unnecessary step when this setup was tested. Iteratively adjust the adjustment knobs on the mounts in stages 3, 4, and 5 until the Fabry-Perot cavity is correctly aligned.  

^a The correct choice for a beam expander/reducer is dependent on the properties of the beam of light that needs to be coupled into the Fabry-Perot cavity. The beam after the beam expander/reducer should be collimated and approximately 4 mm in diameter. Be sure to choose a beam expander with the correct AR coating.
^b In addition to the visible (400-700 nm) achromatic lens listed in the table Thorlabs also sells achromatic lenses suitable for the 650-1050 nm and 1050-1620 nm spectral ranges. However, these lenses are not mounted and as a result an SM1L03 should be purchased to mount an unmounted achromatic lens.
^c In addition to the visible (400-750 nm) spectral range broadband dielectric mirror in the table Thorlabs sells Broadband Dielectric Mirrors suitable for the 750-1100 nm and 1280-1600 nm spectral ranges. Alternatively, a protected metallic mirror made from silver or aluminum could also be used.
^d Optional 30 mm cage system alignment guide. This guide precisely locates the optical axis of a 30 mm cage system. This greatly simplifies the alignment of the Fabry-Perot Interferometer the setup pictured above is used.
^e Optional 60 mm cage system alignment guide. This guide precisely locates the optical axis of a 60 mm cage system. This greatly simplifies the alignment of the Fabry-Perot Interferometer when the setup pictured above is used.