Scatter and isolation

Backscattered light is a significant concern for an OPO installed at the dark port of a GW detector. Imperfect isolation from the interferometer’s output Faraday isolator (OFI) leads to a small fraction of carrier power undergoing a round trip along the squeezing injection path and returning to the interferometer at its most sensitive point. Any motion of the squeezing source relative to the interferometer modulates the phase of the returning light. Fields of these parasitic interferometers contain frequency components of the squeezer motion who’s sidebands interfere with and compete the gravitational wave signal. The backscatter noise contribution is neatly expressed as a ratio of Relative Intensity Noise of the scattered light (RINsc) relative to the quantum noise (RINqn). For small OPO motion

zsc, compared to the carrier wavelength , this is expressed as [145]

RINsc RINqn (f) = 4⇡ zsc(f) r ⌘P DPsc hc , (6.4)

where ⌘P D is the quantum efficiency of the detection photodiode, and, h and c are the

Planck constant and speed of light. The backscattered power, Psc, is the total power

that reaches the output photodetector after propagating the full round trip including any isolating elements. Psc may be expressed in terms of the incident carrier power originating

from the detectorPincand the isolation a↵orded by the round trip losses⌘loss(e.g. Faraday

isolators) and the reflection coefficient of the OPO ROPO:

Psc=PincROPO⌘loss. (6.5)

Therefore the relative intensity noise scales directly proportional to the motion and as the square root of scatter power: this means that reductions in RINsc from seismic isolation

of OPO motion o↵ers twice the e↵ective reduction in RINsc compared to equivalent rel-

ative reductions in optical power in decibels (dB) terms. In order to provide sufficient clearance below shot-noise and with enough margin to also ensure clearance from related non-stationary up-converted e↵ects from scatter3, a rule of thumb requirement is to allow for a factor of ten clearance for scatter RIN below quantum noise [146]

RINsc RINqn (f) 10 s/20 10 = ⇢ 1/20 (case 6dB SQZ) 1/32 (case 10 dB SQZ) (6.6)

where s is the dB level of noise reduction made available by squeezing.

Estimates of the optical and motional isolation requirements for a squeezed light source are informed by the expected displacement noise from various OPO mounting options. Characteristic displacement noise spectra typically increase with reducing frequency, with the lowest frequency components defining the upper bound for contributions to RINsc.

As the Advanced LIGO detection band extends down 10 Hz, we reference calculations relative to length noise characterised at this point. Power incident from the interferometer is assumed to be 100 mW with a detection PD efficiency of 99% [146]. For an OPO mounted directly on an optics table in air, similar to squeezer injection preparation optics for the LIGO-H1 test, motion is expected to be on the order of 10 9m/pHz

3_{These arise from non-linear couplings within the instrument that up-convert low frequency noise into}

at 10 Hz [162, 163]. To reach a RIN a factor 10 below quantum noise level for the 6 dB e↵ective squeezing case this would require optical power reduction of 1/1014.5 _or

145 dB of optical isolation (149 dB isolation for the 10 dB squeezing case): this is a demanding requirement. On the other hand, mounting the OPO on the seismically isolation platforms within the Advanced LIGO vacuum envelope provides a degree of motional isolation, reducing the displacement noise to order 10 11_m/p_{Hz at 10 Hz}

[163]. Thus a mounting within this seismically isolated environment would reduce the optical isolation requirements to 105 dB for 6 dB squeezing (109 dB for the case of 10 dB e↵ective squeezing). A step further would be to also suspend the OPO assembly from a 1 Hz pendulum, thereby reducing motion at 10 Hz by about another decade bringing the isolation requirements to 85 dB for 6 dB squeezing or (89 dB isolation for 10 dB squeezing).

In principle the optical isolation requirements could be met by cascaded Faraday isolators. However, each stage of this kind of isolation is lossy and degrades the e↵ective squeezing. This is undesirable. Instead significant isolation may be provided by building the OPO cavity in a travelling wave design which o↵ers an estimated 50 dB (ROPO = 10 5)

of intrinsic isolation [86]. The promptly reflected spurious light from the OPO front coupler is spatially separated by its angle of incidence and dumped. By entering in the counter-propagating mode, the fraction of spurious light entering the cavity is significantly impeded from being parametrically amplified in the presence of the pump light4. Linear cavity OPOs by contrast are over-coupled cavities where a significant portion of promptly reflected light is reflected at normal incidence, directly back into the squeezing mode. The remainder enters the cavity, co-propagating with the pump, to be potentially amplified by the non-linear parametric process. All the spurious light incident on the OPO expected to return (ROPO 1, with intra-cavity amplifying e↵ects). A disadvantage of bow-tie

travelling wave cavities is that the increased number of necessary optical elements increases the intra-cavity round trip loss. However, significant developments in the engineering of double resonant type designs in the last decade have led to optimisation of pump and fundamental resonant enhancements that deliver satisfactory escape efficiencies (_⇠0.98) at reasonable input pump threshold power levels (see _§6.4 and similar previous work carried out in [26, 27, 101]). The trade o↵ of a very small reduction in OPO escape efficiency for 50 dB of intrinsic backscatter isolation is a good one, removing the need for an additional Faraday isolator (with up to 20 dB to spare) that may have a loss of up to 3% on each pass. This is why we have selected and built a bow-tie type OPO.

Limiting the number of squeezing path isolators to one for reasons of loss (in addition to the interferometer’s output Faraday isolator), two scenarios are viable [146]. With 30 dB of isolation from the interferometer’s output isolator mounting the OPO on the LIGO isolated stage within vacuum requires an additional squeezed path isolator (of 30 dB isolation) to reach the order of RIN reduction needed for 1/20 (6 dB squeezing) requirement. Alternatively, if the OPO were mounted on an additional 1 Hz pendulum mount, reductions in relative motion would make removal of this squeezing path isolator possible. In both cases, a bow-tie OPO is necessary and in vacuum mounting essential to meet the basic isolation requirements demanded of a Advanced LIGO squeezing injection sub-system. In vacuum operation for an OPO vacuum squeezed source will be essential

4_{Some forward scattering may occur as a result of defects in cavity optics, however this is a second}

for squeezed light upgrades for Advanced LIGO and beyond.

In summary, the following requirements are expected to be met by building a vacuum compatible doubly resonant bow-tie travelling-wave OPO with a monolithic glass cavity construction:

• A rigid glass cavity with inherently low length noise will be an inherently low phase noise source for quadrature squeezed states with a estimated RMS phase noise of 0.1 mrad or less based on existing specifications for the LIGO OMC. By having an inherently low noise source, a portion of the coherent control lock point errors are avoided, reducing the expected contribution to the injection phase noise budget;

• The vacuum compatibility of such a devices allows for mounting on isolation stages within the LIGO vacuum envelope, lowering mechanical couplings that might drive cavity length noise and reducing relative motion of the squeezing injection sub- system, lowering the scatter relative intensity noise by at least a factor 100;

• The inherent optical scatter isolation a↵orded by a travelling wave bow-tie type cavity is expected to provide on the order of 50 dB intrinsic isolation lowing the scatter induced relative intensity noise by an order of 25 dB;

• combining these characteristics and the fact that doubly resonant OPOs o↵er high es- cape efficiency by design, despite increase optical surfaces, means that fewer Faraday type optical isolators are required, making a scatter light isolated squeezed source path and low degradation of state from lossy mitigating isolation optics.