Joshua Yablon Ye Wang Shih Tseng Dr. Selim Shahriar

Transcription

1 Joshua Yablon Ye Wang Shih Tseng Dr. Selim Shahriar

2 Sensitivity Enhancement of Metrological Devices Vibrometry/Accelerometry Gyroscopy Gravitational Wave Detection Applications Inertial Navigation Defense Systems Enhancement of LIGO

3 Empty Cavity: Cavity with medium of index n: L o = mλ L 2 o c o m m m n n

4 L o o m m m n 2 c n n(ω) n n(ω) n o /ω If the quantity nω is constant, then we have White Light Cavity (WLC) condition ω o ω Demonstration of a Tunable-Bandwidth White Light Interferometer using Anomalous Dispersion in Atomic Vapor, G.S. Pati, M. Messal, K. Salit, and M.S. Shahriar, Phys. Rev. Lett. 99, (September 28, 2007).

5 S l o n(ω) S EC is empty cavity sensitivity S WLC is white light cavity sensitivity S WLC =ξ*s EC. ξ is equal to 1/n g, where n ( n) g Group velocity is superluminal as long as n g <1. If (nω) is constant, then n g vanishes, and group velocity (as well as cavity sensitivity) becomes infinite. In practice, n g can never truly vanish due to higher-order nonlinearities in the dispersion. ω o ω

6 Cavity linewidth is enhanced by the same order of magnitude as the enhancement factor when the dispersive element is present. Minimum measurable value is inversely related to cavity linewidth. Device sensitivity will therefore not be enhanced solely with a dispersive element. This constraint can be circumvented by inserting the dispersion into an active cavity instead of a passive interferometer. "Ultrahigh enhancement in absolute and relative rotation sensing using fast and slow light", M.S. Shahriar, G.S. Pati, R. Tripathi, V. Gopal, M. Messall and K. Salit, Physical Review A 75 (5): Art. No MAY 2007 Demonstration of displacement measurement sensitivity proportional to inverse group index of intra-cavity medium in a ring resonator, G.S. Pati, M. Salit, K. Salit, and M.S. Shahriar, Optics Communications, 281 (19), p , (2008). Superluminal ring laser for hypersensitive sensing, H.N. Yum, M. Salit, J. Yablon, K. Salit, Y. Wang, and M.S. Shahirar, Optics Express, Vol. 18, Issue 17, pp (2010) Model for beat noise in a fast-light enhanced ring laser gyroscope, M. Salit, J.H. Shapiro, and M.S. Shahriar, (preprint at )

7 Gain Dip Unsaturated Gain frequency cavity loss unsaturated gain Traditional Kramers-Kronig relations are not applicable inside a medium which is lasing, since gain is forced to equal loss in steady state, over entire lasing bandwidth. Single-Mode Laser Equations: Saturated Gain under Lasing frequency cavity loss saturated gain (sensitivity enhancement) Optics Express, Vol. 18, Issue 17, pp (2010)

8 Unsaturated Gain frequency cavity loss unsaturated gain Modified Kramers-Kronig Relations Plug into: R (enhancement factor compared to an empty cavity) reaches a maximum of ~1.8x10 5

9 IOP PUBLISHING Kramers-Kronig relations for a probe MUST and DO exist inside a medium which is lasing. JOURNAL OF OPTICS J. Opt. 12 (2010) (6pp) doi: / /12/10/ Pump probe model for the Kramers Kronig relations in a laser J. Opt. 12 (2010) H N Yum and M S Shahriar H N Yum 1 and M S Shahriar 1,2 (a) 1 Department of Electrical Engineering and Computer Science, Northwestern University, Evanston, IL 60208, USA 2 Department of Physics and Astronomy, Northwestern University, Evanston, IL 60208, USA n probe Journal of Optics 12 (2010) Received 24 March 2010, accepted for publication 7 July 2010 Published 24 September 2010 Online at stacks.iop.org/jopt/12/ J. Opt. 12 (2010) H N Yum and Abstract (n-n 0 )/2p GHz In this paper, we study theoretically a pump probe H N model Yum and for the MKramers Kronig S Shahriar (KK) relations during laser operation. A solution of laser equations reveals that the dispersion profile r op =0, D=0 r op =0, D=2p s -1 Figure 2. Schematic of a laser cavity in the presence of a probe of a saturated laser gain (b) medium is non-analytical at the boundary which between is introduced thetolasing observeand the gain theand dispersion of the non-lasing spectral region. Such a non-analyticity cannot be explained medium. B.S.; in terms beam splitter. of theνprobe; KKprobe frequency, νlaser; lasing relations. In order to interpret this situation, it is important to consider frequency. carefully the physical basis of the KK relations. We conclude that the KK relation is expected to apply only to an independent probe applied to the medium, which n probe is under excitation by the pump producing the gain as well as the lasing mode. The absorption/gain and dispersion profiles are then analytical, and satisfy the KK relations. Specifically, these are variants of the so-called Mollow Ezekiel d spectra of probe absorption/gain and dispersion in the presence of a pump, with the exception (a) (c) D that in this case the medium is inverted. (n-n B.S. 0 )/2p B.S. GHz b Gain Medium Keywords: Kramers Kronig relations, laser cavity, dispersion, Mollow Ezekiel spectrum (n 2 -w ba )/2p 100MHz (n 2 -w ba )/2p 100MHz (Some figures in this article are in colour only in the electronic n laser version) (c) r r op = 2G, D=2p s -1 op =2G, D= 0 W 2 Dispersion in a laser cavity is an important issue in high precision laser interferometric measurements such as rotation sensing, vibrometry and gravitational wave detection [1]. For these applications, the sensitivity of the cavity is defined as the ratio of the amount of a resonance frequency shift to a (n-n particular change in length of the cavity, 0 )/2p GHz and is enhanced by tailoring dispersion Figure 1. Illustration [1, 2]. Recently, of effective gain, wedispersion have shown and intensity [1] that by using a gain profiles for awith ring laser a dip under at the steady center, state operation it is indeed (a) χ, (b) possible χ, to realize a(c) so-called 2. superluminal laser with the property that the group velocity becomes much larger than the free space e 2. Schematic of a laser cavity in the presence of a probe is introduced to observe the gain and dispersion of the m. B.S.; beam splitter. ν probe ; probe frequency, ν laser ; lasing r op B.S. Gain Medium n 1 n 2 This non-analyticity is present even for a simpler system where the unsaturated gain profile is simply Lorentzian, without a dip. Therefore, such a behavior is a generic property of a single mode laser. Of course, a since the underlying equations are causal, the non-analytic behavior of the effective Figure 3. Two level atom incoherently pumped for population inversion gain and via optical dispersion pumping atmust the ratealso of rop, be andcausal. illuminated by Thus, a one might strong expect pumpthe ν1 (the KK lasing relations field) and ato weak apply, probe ν2. since these relations are dictated by requiring simply that the response of a system be causal. In this paper, we explain why the KK relations do benot similar hold. to what Specifically, has been studied we point extensively out, in asthe explained context below, that B.S. n laser (b) (n 2 -w ba )/2p 100MHz of probe gain produced by a driven two Figure level atom 4. Imaginary [15 20]. (solid lines) and real (dashed lines) parts of the susceptibility of a probe frequency ν. For resonant pump: (d) (n 2 -w ba )/2p 100MHz

10 Beat Detector O.C. Gain Dip Bi-directional lasing Rotation creates frequency shift between the two counter-propagating beams, due to cavity round-trip interference conditions Frequency difference between the two beams is enhanced due to superluminal lasing Frequency difference is equal to the beat-note frequency, from which we can deduce angular velocity experienced by the gyroscope.

11 Top Laser: Unidirectional ring laser with anomalous dispersion (optical diode not shown in diagram) Zero Area (Insensitive to Rotation) Magnitude of diaphragm vibration is proportional to a x. The lasing frequency shifts with changes in cavity length. This frequency shift is enhanced by the negative dispersion. Bottom Laser: Same as top laser, but deformable diaphragm is replaced with a fixed mirror. The frequency of this laser is insensitive to a x. This signal is used as a reference. Beat frequency is equal to the frequency shift in the top laser, which is enhanced due to anomalous dispersion. From this frequency shift, we can deduce the acceleration.

12 Optics Express 17, (2009). Raman Depletion In Rubidium Vapor (FWHM 1 MHz) Negative Dispersion

13 e resonant frequency shift with respect to the length variation decreases ft in an empty ous dispersion ncy shift is l to 1/n g times ift in the empty mine the actual tive cavity, we sh the explicit on the lasing s end, we first ady state ( ) for. Since E and, the tion yields the ld E in steady er cavity as a frequency. Fig. 5. Energy levels for (a) 795-nm Rb laser to produce broadband gain, (b) Raman

14 - iode umped lkali aser Gain Medium: Vacuum-sealed cell with ARcoated windows; contains Natural Rubidium (72% 85 Rb, 28% 87 Rb mixture), combined with various pressures of 4 He buffer gas D2 line is optically pumped with diode laser Collisions with buffer gas atoms create a rapid transition from the 5 2 P 3/2 to the 5 2 P 1/2 states, creating a population inversion between the 5 2 P 1/2 and 5 2 S 1/2 states D2 line λ pump =780 nm 5 2 P 3/2 5 2 P 1/2 D1 line λ laser =795 nm 5 2 S 1/2

15 Using Rb as a gain medium complements our Raman depletion scheme for the dip Narrow gain bandwidth (FWHM ~ 10GHz 0.02nm) will make single-mode operation easier High unsaturated gain value enables deeper dip in the center of the gain profile more lasing dispersion 1> Hamiltonian with Decay Rates: 1> 2> 3> 4> probe 3> 5P 1/2 (F=2,3) pump 4> 5P 3/2 (F=1,2,3,4) 2> 3> 4> 31 probe ( =795 nm) 1> 5S 1/2 (F=2) 2 pump 2 probe H pump ( =780 nm) 2> 5S 1/2 (F=3)

16 Pump Power = 800 mw, Γ 43 = 500 GHz Pump Power = 800 mw, Γ 43 = 190 GHz (FWHM 120 GHz) (FWHM 50 GHz) Pump Power = 800 mw, Γ 43 = 45 GHz Pump Power = 800 mw, Γ 43 = 8 GHz (FWHM 30 GHz)

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18 Gain Measurement: Probe has same frequency and waist size as lasing mode Probe input power = 1.3 μw (far below saturation) Delta = 0 is defined as frequency between F=3 (5P 1/2 ) and F=3 (5S 1/2 ) Lasing occurs at Delta = 0 Photodetector Probe Out Pump Out Rb/He Pump In ( =780 nm) Single-Pass Probe Gain vs. Pump Power Gain Pump ( =780 nm) Probe In ( =795 nm) H.R Rb/He P.B.S. O.C. DPAL output ( =795 nm) Gain (Pump=1220 mw) Gain (Pump=1070 mw) Gain (Pump=835 mw) Gain (Pump=605 mw) Delta (GHz)

19 Ring DPAL Setup: Gain cell is optically pumped with two counter-propagating beams (pump powers are 1.00 W and 1.20 W) Pump wavelength = 780 nm Optical isolator prevents mode competition. Rb/He DPAL Output P u m p P u m p

20 DPAL: Ring DPAL without isolator produces 40 mw of power, but there exists severe competition between cw and ccw modes. With isolator inside, DPAL produces 30 mw of power with no competition between directions. Next step: Measure DPAL output linewidth, verify that DPAL (with isolator) is stably single-mode, and that output frequency is tunable Mode Competition: DPAL response to gently tapping cavity mirrors shows severity of mode competition between clockwise and counterclockwise directions.

21 Cavity Mirror Cavity Mirror Output Coupler Pump In Rb/He Cell Pump In To Helium Tank Rb Oven To Vacuum Pump

22 Short-Term: than one. Hence, the resonant frequency shift with respect to the length variation decre compared to the shift in an empty cavity. For anomalous dispersion (n g <1), the frequency shift is amplified to be equal to 1/n g times the amount of the shift in the empty cavity. Verify that ring DPAL is stable and single-mode Make DPAL output frequency tunable (using an internal etalon or PZT on a cavity mirror) Mid-Term: In order to determine the actual value of R for an active cavity, we need first to establish the explicit dependence of on the lasing frequency,. To this end, we first Add Raman depletion into cavity to create negative dispersion lasing Long-Term: solve Eq. (3.b) in steady state ( ) so that for. Since is a function of E and, the solution to the equation yields the saturated electric field E in steady state inside the laser cavity as a function of the lasing frequency. Implement this negative-dispersion laser to into various metrological devices to enhance sensitivity Fig. 5. Energy levels for (a) 795-nm Rb laser to produce broadband gain, (b) Ram depletion to induce narrowband absorption dip. (c) Schematics of the experimenta up to realize a superluminal laser: PBS, polarizing beam splitter; BS, beam splitte AOM, acousto-optic modulator. Note that the superluminal laser is the same as th Raman pump. The scheme shown is for 85 Rb atoms. The broadband gain is produc by side-pumping with a diode laser array. Let us consider the case in which the cavity contains a medium with a narrow absorption as well as a medium with a broad gain. This configuration creates a gain profile with a dip in the center.

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