Round-trip gain

Optical oscillators, commonly referred to as lasers, are optical feedback systems in which two fundamental conditions must be satisfied for stable oscillation at the lasing wavelength the round-trip gain must be unity, and the round-trip phase must be an integer multiple of 2ti radians. Consequently there are two fundamental elements in any optical fiber laser, i.e., a source of optical in, and an optical feedback path either or both may be in fiber. For the purposes of this article optical fiber lasers will be defined as lasers in which the optical gain element is an optical fiber amplifier. Extra elements may be added to facilitate coupling of optical energy in and out of the laser cavity, or to control the temporal and spectral characteristics of the laser. 

The wave is amplified if the gain overcomes the losses per round trip that is,... 

Between 1898 and 1910, Taylor devoted most of her spare time to research work in organic and physical chemistry at University College, Bristol, producing a range of papers in those fields. On weekends, she would often cycle to and from the Bristol chemistry laboratories, an 80-mile round trip.109 She signed the 1904 petition for admission of women to the Chemical Society and the 1909 letter to Chemical News (see Chap. 2). In addition, she was one of the first batch of women to gain admittance to the Chemical Society. 

Figure 6.10 Frequency response of a SAW delay line, showing both the magnitude (solid curve, left ordinate) and phase (dotted curve, right ordinate) of the transmitted signal as a function of excitation frequency. The upper horizontal line represents a gain of 2S dB from a hypothetical amplifier used in constructing an oscillator loop the lower horizontal line represents zero phase shift (or any integral multiple of 2ir). The three points indicated on the frequency curve by filled circles indicate the frequencies at which the two conditions necessary for loop oscillation are satisfied less insertion loss than the gain of the amplifier, and a round-trip phase shift of zero.

Here V is the amplification for one traversal and Fa for a round trip of the photons in the cavity with mirror-loss coefficients Ri, R2 and transmission loss T. The optical gain V on the other hand is described by Eq. (2) as F=exp a AN l. With Eqs. (2) and (17) the threshold inversion density AN0 is obtained. 

If the modulator is placed inside the laser resonator with the mirror separation d and the mode frequencies = vo m cjld (m = 0,1,2,...), the sidebands coincide with resonator mode frequencies if the modulation frequency / equals the mode separation Av = cjld. The sidebands can then reach the oscillation threshold and participate in the laser oscillation. Since they pass the intracavity modulator they are also modulated and new sidebands y = vq i 2/ are generated. This continues until all modes inside the gain profile participate in the laser oscillation. There is, however, an important difference from normal multimode operation the modes do not oscillate independently, but are phase-coupled by the modulator. At a certain time the amplitudes of all modes have their maximum at the location of the modulator and this situation is repeated after each cavity round-trip time T = 2d c (Fig. 6.8c). We will discuss this in more detail The modulator has the time-dependent transmission... 

The optimum gain for the dye-laser pulses is achieved if they arrive in the active medium (dye jet) at the time of maximum inversion AN(t) (Fig. 6.15). If the optical cavity length d2 of the dye laser is properly matched to the length d of the pump laser resonator, the round-trip times of the pulses in both lasers become equal and the arrival times of the two pulses in the amplifying dye jet are synchro-... 

Control loop tuning was another important aspect that needed to be addressed to make the system widely applicable without requiring extensive testing or expertise on the part of the user, in particular, the dynamic characteristics of the process as seen by the measurement system depend upon the number of cycles between measurements, which is determined by the round trip time of the TCS. This depends upon the number of measurements made within a round trip, and therefore on the number of cavities and sections, which is both job and machine dependent To address this issue, an analytical method was developed and implemented to compute controller gains explicitly accounting for the actual TCS round trip time. 

To achieve a sustained oscillation in a laser, amplification in the gain medium must at least balance out with the optical loss during each round-trip of the cavity. Therefore, when the pump rate increases beyond a threshold value, an intense coherent laser beam is generated whose power rises linearly with the excess pump rate. At low pumping rates, the excitations in the gain medium are radiated in all directions as spontaneous emission. 

In a VCSEL, the effective single-pass gain is approximately 1% since the thickness of the gain layer is thin in the direction of the lasing emission As a lesulf in order for VCSELs to have a threshold current comparable to that of edge emitters, the mirror reflectivity needs to be 99% to assme that the round-trip losses do not exceed the gain. 

The loop gain of a laser is defined as the ratio of the intensity of the light wave at any point in the resonator, after and before completing a full round trip (loop) in the resonator. The factors to be considered in determining the loop gain are shown schematically in Figure 3.4. 

For example, contemplate a laser cavity system with the following characteristics reflectivity of the HR mirror 7 i = 0.998 reflectivity of the output coupler R = 0.958 round-trip loss (excluding mirror loss) Lrt = 0.08 amplifier gain Ga = 1.05. Using these values in Equation (3.2) one obtains Gl = 1.045 this is a typical value encountered for CW gas lasers near laser threshold (see Section 3.4). 

---