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Optics

Optical Systems Finesse&ResolutionofaConfocal Cavity
PPLN Devices λ .The FSR and the FWHM of a representa-tive line shape is shown in Figures 4 & 5. Afinesse (F For a Fabry-Perot cavity, the finesse is ameasure of the interferometers ability toresolve closely spaced spectral features. Theminimum resolvable frequency incrementof an interferometer is based on the TaylorCriteria which stipulates that for two close- ly spaced lines of equal intensity to beresolved, the sum of the two individuallines at the midway point
Spherical Singlets Multi-element Lenses t ) of 294 is measured using a DFBlaser, which has a linewidth that cannot beconsidered infinitely small in comparisonto the resolution of the cavity. Therefore,the true finesse is about 320, assuming a2MHz laser line width.A measured finesse has a number of con-tributing factors: the mirror reflectivityfinesse F
Cylindrical Lenses Aspheric Lenses can at most
Mirrors be equal to the intensity of one of the original lines (see Figure 3). The total finesse of an interferometer isdefined as the ratio of the FSR to
Windows & Diffusers Prisms Gratings r , the mirror surface quality finesseF
q , and the finesse due to the illuminationconditions (beam alignment and diameter)of the mirrors F
Diffractive Optics Polarization Optics i . The total finesse of a sys-tem can be written as follows:1/F
Beamsplitters 2 2 2 1/2 t =[(1/F
R ) +(1/F
q ) +(1/F
i ) ] Eq 4.The effective mirror reflectivity finesseis given by:F
Filters & Attenuators Gas Cells 1/2 R = Ï€ R /(1-R) Eq 5Where R is the Mirror Reflectivity.While the literature is ambiguous on the defi-nition for the reflectivity finesse, Eq 5 is pre- sented as an “effective” finesse that is definedby Eq. 3 when the other contributing factors are negligible. For the SA200 series, the reflectivity finesse dominates when operating with proper illumination as defined by Johnson, J.R. “A High Resolution Scanning Confocal Interferometer” Appl. Opt. 7,1061- 1072, 1968.The values predicted by Eq. 5 agree towithin a few percent of our measured val-ues. Many authors use a formula that pre-dicts a reflectivity finesse that is less by afactor of 2. But, per Johnson, Appl. Opt. 1968, “the apparent loss in finesse ... isfully restored when the full output of aproperly illuminated cavity is observed.”Therefore, the finesse given by Eq. 5 isrealized.Using Eq. 5, the reflective coatings used inthe SA200 series interferometers have beendesigned so that the minimum reflectivity finesse is better than 1.5 times the mini-mum specified finesse across their entireoperating wavelength range for each model(see the table on the product page). Thisfixes the first term of Eq. 4. Figure 3
When two equal Gaussian lineshapes just meetthe Taylor criteria for being resolvable, they are separated by their common FWHM (D) as shown in the plot. ∆ where ∆ is the FWHM of the impulse responsefunction for the system. As can be seen inFigure 3, two lines separated by Figure 4
FSR of a 1550nm, DFB laser (PRO8000series, page 404). Using model SA200-14A, 1.5GHz interferometer, this plot isused to calibrate the time-base of the oscilloscope; knowing the FSR of the interferometer is 1.5Ghz, the calibration factor is found by setting: 1.5GHz =20ms (75MHz/ms), the distance betweenthe two peaks. ∆ , are justresolvable according to the Taylor criteria.Therefore,
Peaks ∆
T= 20ms 2V/div 2.5ms/div ∆ is also used as a measure ofthe resolution of the system.The equation for the total finesse is given by:F
t = FSR/ ∆ Eq 3.FSR is the free spectral range that is calcu-lated from Eq. 1.Note, during the manufacturing of theSA200 series interferometers, F Figure 5
This plot shows a close-up of the actual signalof the laser which results from the convolutionof the laser line width and finesse of the cavity; with the oscilloscope timebase calibrated from Figure 4, at 75 MHz/ms, we determine theFWHM for the interferometer to be 0.068 msx 75 MHz/ms for a FWHM of 5.1 MHz. This puts a minimum value of 294 for the finesse. ∆
T= 68µs t is used toadjust the cavity length to the confocalcondition by maximizing its value. Thismethod provides a very precise means for setting the required length of the cavity tobetter than
2V/div 50µs/div FWHM Sales: 973-579-7227
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